M ulti layer Ioni c Transducers

by

B arbar J.A kl e

Thesi ssubm itted to theFacul ty ofthe

V irgi nia Polytechni c Insti tute and StateUni versi ty

in parti alf ulfil lm entofthe requi rem entsf or the degreeof

M aster O fSci ence

in

M echanicalEngi neeri ng

Donald J.Leo,Chai rDanielInm an

W illiam Saunders

Apri l2003

Blacksburg,V i rgi nia

Keywords: Ioni cPolym er,M ul ti layer,Sensor- actuator,M i cro A i rVehi cl e.

Copyri ghtby BarbarJ.Akl e 2003

M ulti layer Ioni c Transducers

BarbarJ.Akl e,M S

V irgi nia Polytechni c Insti tute and StateUni versi ty,2003

Advisor:Donal d J.Leo

A bstract

A transducerconsi sti ngofm ul ti plelayersofi oni cpol ym erm ateri ali sdevel oped

for appl icati ons i n sensi ng,actuati on,and control . The transducer consi sts of two

to f our i ndi vi dual l ayers each approxi m atel y 200 m icrons thi ck. The transducers

are connected i n paral lel to m i nim ize the el ectri c fiel d requi rem ents f or actuati on.

The tradeoff i n deflecti on and f orce can be control led by control ling them echani cal

constrai ntat the i nterf ace.Packagi ng the transducer i n an outercoati ng producesa

hard constrai ntbetween l ayersand reducesthedeflecti on with a f orce that i ncreases

linearl y with thenum berofl ayers.Thi sconfigurati on al so i ncreasesthebandwi dth of

the transducer.Rem ovi ng the outerpackagi ng producesan actuator thatm ai ntai ns

the deflecti on ofa si ngl e layer but has an i ncreased f orce output. Thi s i s obtai ned

by al lowing the l ayers to sl ide rel ati ve to one another duri ng bendi ng. A Fi nite

Elem entAnal ysi s(FEA)m ethod capabl eofm odel ing thestructureofthem ul ti layer

transducers i s devel opped. It i s used to m odelthe i nterf aci alf ri cti on i n m ulti layer

transducers.

Experi m ents on transducers wi th one to three l ayers are perf orm ed and the

resul ts are com pared to Newbury’ s equi val ent ci rcui t m odel , whi ch was m odified

to accomm odate the m ul ti layer pol ym ers. The m odi ficati on wasperf orm ed on f our

di fferent boundary condi ti ons,two el ectri calthe seri es and the paral lelconnecti on,

and two m echani calthe zero i nterf aci alf ri cti on and the zero sl ip on the i nterf ace.

Resul tsdem onstratethatthel argestobstacl etoobtai ninggood perf orm ancei s

watertransportbetween the i ndi vi duall ayers.W atercrossoverproducesa nearshort

ci rcui t el ectri calcondi ti on and produces f eedthrough between actuati on layers and

sensi ng l ayers.El ectri calf eedthrough due to watercrossoverel im inatestheabi lity to

producea transducerthathascom bi ned sensi ng and actuati on properti es.El im inat-

ing water crossover through good i nsul ati on enabl es the devel opm ent ofa sm al l(5

mm x 30 mm )transducer thathassensi ng and actuati on bandwi dth on the orderof

100 Hz.

Due to the m echani calsi m ilari ti es of i oni c transducers to bi ologi calm uscl es

and thei r l arge flappi ng di spl acem ent capabi liti eswe are studyi ng the possi bi lity of

thei rusei n flappi ngM icroA i rVehi cl e(M AV)appl icati on,asengi nes,control lersand

sensors. The FEA m odel ing techni que capabl e isused to desi gn two i oni c pol ym ers

actuated flappi ng wings.

iii

To m y father,

Jawad Akl e,

m y m other,

Nazira Akl e,

and m y si sterand brothers,

Angele,Eti enne,and Si m on

A cknow l edgm ents

First Iwoul d l ike to thank m y advi sor,D r.Donal d J.Leo,f orhi shel p and pati ence

throughoutm y graduatestudi es.H i sgui danceand com pl etesupportm adem ywork-

ing and l earni ng experi ence,a very speci alone. A l so,Iwant to extend m y thanks

to D r.Dani elInm an and Dr.W i lliam Saundersf or thei rsupportand enthusi asm as

m embersofm y advi sory comm i ttee.

In addi ti on,Iwantto thankm ycol leaguesi n theCenterf orIntel ligentM ateri al

System sand Structures(CIM SS).Thegood hum orofeverybodym adei tan enj oyabl e

experi ence. A l so m y great thanks to m y research partnersM athi ew Bennet,K evi n

Fari nhol t,John Frankl in,and CurtCothera.Thei rgeneroushel p and f ri endshi p was

inval uabl e in assi sti ng m y research. Iappreci ate the support ofthe U. S.Arm y Re-

search Laboratory and theU . S.Arm y Research O ffi ce undercontract/grantnum ber

DAAD19-02-1-0275 M acrom ol ecul arA rchi tecture f orPerf orm ance (M AP)M URI.

Final ly, I woul d l ike to expressm y deep grati tude to the support I recei ved

from my fri ends at Em i lio’s and m y greatest appreci ati on to the l ove and support

provi ded bym y parentsand m y brothersand si sterduri ngm y yearsatV i rgi nia Tech.

B arbar J.A kle

v

C ontents

A bstract i i

A cknow l edgm ents v

Li st ofTabl es x

Li st ofFi gures xi

C hapter 1 Introducti on 1

1.1 Probl em Statem ent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Li teratureRevi ew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Electro- Acti vePol ym ers(EAP) . . . . . . . . . . . . . . . . . 4

1.2.2 H istori calBackground ofIoni c pol ym ers . . . . . . . . . . . . 4

1.2.3 M anufacturi ng ofIoni c pol ym ers . . . . . . . . . . . . . . . . 4

1.2.4 Actuati on M echani sm . . . . . . . . . . . . . . . . . . . . . . 6

1.2.5 Interesti ng properti esofIoni c pol ym ers . . . . . . . . . . . . . 8

1.3 Ini ti alM oti vati on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3.1 Potenti alappl icati ons. . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Overvi ew ofThesi s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4.1 Research Obj ecti ves . . . . . . . . . . . . . . . . . . . . . . . 10

1.4.2 Contri buti on . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4.3 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

C hapter 2 Experi m entalSetup 15

vi

2.1 Introducti on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Experi m entsOutput . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 TypesofExperi m ents . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Electri calIm pedance . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.2 M echani calIm pedance . . . . . . . . . . . . . . . . . . . . . . 17

2.3.3 SensorSensi ti vi ty . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.4 Blocked Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.5 Freedi spl acem ent . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Equipm entDescri pti on . . . . . . . . . . . . . . . . . . . . . . . . . . 21

C hapter 3 C haracteri zati on of Ioni c Pol ym er Stacks 24

3.1 Introducti on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Stacki ng techni ques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.1 Seri esstacki ng . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.2 Paral lelstacki ng . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.3 Com pari son . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 SensorStacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.1 Com pari son ofSeri esand Paral lelM ul ti layerSensors . . . . . 29

3.3.2 Am plifierVari ati on . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4 ActuatorStacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4.1 Com pari ng Seri esand Paral lelStacksasActuators . . . . . . 36

3.4.2 Interf aci alFri cti on and M echani calProperti es . . . . . . . . . 39

3.5 TheFi ni teEl em entAnal ysi sm ethod . . . . . . . . . . . . . . . . . . 43

3.5.1 Veri ficati on oftheFEA m ethod . . . . . . . . . . . . . . . . . 45

3.5.2 FEA sim ulati onsf or the paral lelstacks . . . . . . . . . . . . . 46

3.5.3 Analysi softhe i nterf aci alf ri cti on . . . . . . . . . . . . . . . . 48

3.6 Summ ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

C hapter 4 C om bi ned Sensor-A ctuator Stacks 51

4.1 Introducti on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2 Combined Sensorvs.Sel f-sensi ng Actuator . . . . . . . . . . . . . . . 51

vi i

4.3 A lternati ve configurati ons . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4 Fabri cati on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4.1 Electri calconnecti ons. . . . . . . . . . . . . . . . . . . . . . . 53

4.4.2 M echani calproperti esand theFEA m ethod . . . . . . . . . . 56

4.5 Characteri zati on ofthe combi ned stacks . . . . . . . . . . . . . . . . 56

4.6 Feed- through . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.6.1 Insul ati on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.6.2 Characteri zati on off eed- through . . . . . . . . . . . . . . . . . 62

4.7 Summ ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

C hapter 5 M odel ing m ulti layer stacks 63

5.1 Introducti on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2 M odelOvervi ew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.3 Descri bing and M odi fyi ng theEl ectrom echani calTerm sf orM ul ti layer

Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3.1 TheElectri calTerm s . . . . . . . . . . . . . . . . . . . . . . . 65

5.3.2 TheM echani calTerm s . . . . . . . . . . . . . . . . . . . . . . 66

5.3.3 TheElectrom echani calTerm . . . . . . . . . . . . . . . . . . . 68

5.4 M odified Input- OutputRel ati onshi psf orM ul ti layerTransducers. . . 70

5.4.1 Im pedances . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.4.2 ActuatorEquati ons . . . . . . . . . . . . . . . . . . . . . . . . 71

5.4.3 SensorEquati ons . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.5 Com pari son ofM odelwi th Experi m entalResul ts . . . . . . . . . . . 74

5.6 Summ ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

C hapter 6 M i cro A i r Vehi cl e 77

6.1 Introducti on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.2 Appl icati on:M AV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.2.1 Design Param eters . . . . . . . . . . . . . . . . . . . . . . . . 78

6.2.2 W ing Desi gns . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.2.3 Com pari son to requi rem ents . . . . . . . . . . . . . . . . . . . 79

vi ii

6.3 Summ ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C hapter 7 Sum m ary and C oncl usi ons 81

7.1 Introducti on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.2 Thesi sSumm ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.3 Contri buti onsto theFi eld . . . . . . . . . . . . . . . . . . . . . . . . 83

7.4 Concl usi on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.5 Futurework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

B ibl iography 87

V ita 89

ix

List ofTabl es

1.1 Changeson the cathodeand theanodeoff ouractuati on m echani sm s(Bar-

Cohen,2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1 M ateri alproperty com pari son between i oni c pol ym ersand pi ezo PSI- 5A4E

ceram i c (Newbury (2002)and Pi ezo System s(2003)) . . . . . . . . . . . 52

x

List ofFi gures

1.1 (a)A schem ati c drawi ng showi ng the hysteresesofpol ym ersduri ng opera-

ti on and (b),the rel axati on. . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Schem ati c ofan Ioni c Polym er. . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Schem ati c drawi ng showi ng the experi m entalsetup f or the bl ocked f orce test. 17

2.2 Schem ati c drawi ng showi ng the experi m entalsetup f or the bl ocked f orce test. 18

2.3 Schem ati c drawi ng showi ng the experi m entalsetup f or the bl ocked f orce test. 19

2.4 Schem ati c drawi ng showi ng the experi m entalsetup f or the bl ocked f orce test. 20

2.5 Fixture 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6 A picture showi ng the new fixturewi th detai lson the parts. . . . . . . . . 23

3.1 A CAD drawing showi ng the di fferentpartsofa seri esstack. . . . . . . . 25

3.2 Schem ati c representati on ofthe el ectri c connecti on fora seri esstack. . . . 26

3.3 A CAD drawing showi ng the di fferentpartsofa paral lelstack. . . . . . . 27

3.4 Fabri cati on a 3 l ayersparal lelstack. . . . . . . . . . . . . . . . . . . . . 28

3.5 Schem ati c representati on ofthe el ectri c connecti on fora paral lelstack. . . 29

3.6 The transf er f uncti on ofparal lelstackswi th 1,2,3,and 4 l ayers. . . . . . 31

3.7 The transf er f uncti on ofseri es stackswi th 3 and 4 l ayerspl otted wi th two

di fferentsi ngl e layerspol ym ers. . . . . . . . . . . . . . . . . . . . . . . 32

3.8 Transf er f uncti on ofthe sam e pol ym er but wi th a di fferent val ue ofR 1 in

the am pl ifierci rcui t . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.9 Transf er f uncti on ofthe sam e pol ym er but wi th a di fferent val ue ofR 2 in

the am pl ifierci rcui t . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

xi

3.10 Transf er f uncti on ofthe sam epol ym erbutw i th di fferentam pl ifierci rcui ts 35

3.11 TheBlocked f orce step response ofthe di fferentl y l ayered paral lelstacks . 37

3.12 TheBlocked f orce transf er f uncti on ofthe di fferentl y l ayered paral lelstacks 38

3.13 The bl ocked f orce transf er f uncti on ofseri esm ulti layered actuators . . . . 39

3.14 A canti levered beam wi th an appl ied pressurew. . . . . . . . . . . . . . 40

3.15 Step response f orunpackaged paral lelstacks . . . . . . . . . . . . . . . . 41

3.16 Frequency response f uncti on forunpackaged stacksparal lelstacks . . . . . 42

3.17 Step response f orpackaged paral lelstacks . . . . . . . . . . . . . . . . . 42

3.18 Naturalf requency vari ati on ofpackaged stacks . . . . . . . . . . . . . . 43

3.19 The free di spl acem ent f requency response f orpackaged stacks . . . . . . . 44

3.20 The 2D planarm odeloutput f or the f ree di spl acem entstep i nput . . . . . 45

3.21 The 2D planarm odeloutput f or the bl ocked f orce step i nput . . . . . . . 46

3.22 The 2D planarm odeloutput f or the bl ocked f orce step i nput . . . . . . . 47

3.23 The experi m entaland FEA outputs f orpackaged and unpackaged f ree di s-

placem entstep outputasa f uncti on ofnum berofpol ym ers. . . . . . . . . 48

3.24 The experi m entaland FEA outputs f or packaged and unpackaged bl ocked

force step outputasa f uncti on ofnum berofpol ym ers. . . . . . . . . . . 49

4.1 A 3D CAD drawing representi ng the com bi ned stack. . . . . . . . . . . . 54

4.2 Schem ati c drawi ng showi ng the el ectri c connecti onsofthe com bi ned stack 55

4.3 Two FRF functi on for the sam e stack,one sensed wi th a pol ym er sensor

and the otherw i th l aservi brom eter. . . . . . . . . . . . . . . . . . . . . 57

4.4 The experi m entaland m odeltransf er f uncti onsofthe actuator. . . . . . . 58

4.5 The experi m entaland m odeltransf er f uncti onsofthe sensor. . . . . . . . 59

4.6 TheFRF ofdi fferentcom bi ned stacks,onewi th f eed through and theother

w ithout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.7 Schem ati c drawi ng showi ng the f eed through between the sensor and the

actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1 The geom erti c param etersofthe stack. . . . . . . . . . . . . . . . . . . 65

5.2 Electri cali m pedancem odelpredi cti on versusexperi m entaldata . . . . . . 73

xi i

5.3 Sensi ti vi ty m odelpredi cti on versusexperi m entaldata . . . . . . . . . . . 73

5.4 Blocked f orcem odelpredi cti on versusexperi m entaldata . . . . . . . . . 73

5.5 M echanicali m pedancem odelpredi cti on versusexperi m entaldata . . . . . 74

6.1 The deflecti on col orm ap outputofthe FEA anal ysi softhe firstw i ng desi gn. 79

xi ii

C hapter 1

Introducti on

M ulti layered stacksofi oni ctransducershavebeen devel oped and characteri zed i n the

CenterofIntel ligentM ateri alsand Sm artStructures(CIM SS)Lab atV i rgi nia Tech.

They were configured as sensors,actuators,and combi ned sensor- actuators stacks.

They were connected i n seri es,and i n paral lel .The f ol lowing chaptersare rel ated to

the expl orati on ofthe stacki ng process,characteri zi ng i t,m odel ing i t,and studyi ng

itspossi ble appl icati ons.

1.1 P robl em Statem ent

Ioni c Polym ers are sof t transducers whi ch bel ong to the f am ily of El ectro- Acti ve

Polym ers(EAP).Theyhaveseverali nteresti ngm echani calproperti es,especi al ly thei r

large di spl acem ent,l arge sensi ti vi ty to m oti on,and l ow operati on vol tage. On the

otherhand,i oni c pol ym ers f ace severaldi sadvantages,especi al ly i n the sm al lf orces

they can generate.

In addi ti on to sm al lf orce output, i oni c pol ym ers exhi bit ‘ perm anent strai n’

effectsand rel axati on thati sdetri m entalto thei ruseasel ectrom echani calactuators.

Figure 1. 1 (a) i s an i llustrati on ofthe perm anent strai n effect. Thi s effect occurs

when thepol ym eri sexci ted wi th a step vol tageand then theel ectrodesarepl aced at

ground.The resul ti ng m oti on ofthem ateri alproducesa non- zero perm anentstrai n

that i sattri buted to perm anentcharge redi stri buti on withi n thepol ym er(Newbury,

1

Figure 1. 1: (a)A schem ati c draw i ng show i ng the hysteresesofpol ym ersduri ngoperati on and (b), the rel axati on.

2002). In addi ti on to perm anent strai n,severalresearchers have noted that certai n

ioni c pol ym er transducers exhi bi t a rel axati on phenom enon when subj ected to step

changes i n the vol tage (see Fi gure 1. 1). Thi s rel axati on phenom enon reduces the

quasi -stati c actuati on authori ty ofthe actuator.

Stacki ng techni quesweredevel oped i n orderto i ncrease thegenerated f orceof

ioni c pol ym eractuators. Ini ti al ly we started stacki ng the si ngl e-layer i oni c pol ym ers

electri cal ly i n seri es,whi ch i ssi m ply l ayi ng thestri psofpol ym erson top ofeach other

and appl y the el ectri c potenti alacross the whol e stack. Seri es stacki ng sol ved onl y

part of the probl em . It provi ded hi gher saturati on vol tage,but kept the f orce per

overal lvol tage approxi m atel y the sam e as the si ngle layer pol ym er. Theref ore the

seri esstack di d notperf orm better than the si ngle layerpol ym er i fwe com pl y with

the el ectrol ysi sstartvol tage. In orderto i ncrease the vol tageper l ayer,and i ncrease

the overal lgenerated f orce wi thout i ncreasi ng the vol tage per stack,we devel oped

paral lelstacks. Paral lelstacks are si ngl e layers i oni c pol ym ers overl aid on top of

each otherm echani cal ly,and connected i n paral lelel ectri cal ly. The resul t i sa stack

that generates l arger f orces wi thout exceedi ng the el ectrol ysi s l im it vol tage. Thi s

techni queworked properl y and encouraged usi nto f urther i nvesti gati ons.

Stacki ng ofi oni cpol ym ersnotonl y sol ved theprobl em ofsm al lf orcesbutal so

proved to resol ve theprobl em ofthecom pl ex non- uni form behavi or.Non- uni form i ty

2

in ioni cpol ym erscoul d bedefined ashysteresi s,rel axati on,and theperm anentstrai n

previ ousl y defined. It has been proven that those non- uni form behavi ors coul d be

sol ved usi ng feedback control(K othera,2002). In orderto accom pl ish f eedback con-

trol ,a sensor pol ym erwas i nserted i nsi de a stack ofseveralactuators. Thi s sensor

pol ym erwas i nsul ated,and connected to a sensi ng ci rcui tso i t f ed back them oti on.

Thisform ed thecombi ned sensor- actuatorstack.Resul tsdem onstratethatthel argest

obstacl etoobtai ninggood perf orm ancei swatertransportbetween thei ndi vi duall ay-

ers.W atercrossoverproducesa nearshort ci rcui tel ectri calcondi ti on and produces

feedthrough between actuati on layersand sensi ng l ayers.El ectri calf eedthrough due

to watercrossoverel im inates the abi lity to produce a transducer thathascombi ned

sensi ng and actuati on properti es. El im inati ng water crossover through good i nsul a-

ti on enabl es the devel opm ent ofa sm al ltransducer that has sensi ng and actuati on

capabi liti es. M oreover,f ordesi gn purposesa si m ulati on toolwasessenti alto m odel

al lthose stacki ng processes, theref ore Fi nite El em ent Anal ysi s (FEA)m ethod was

used and val idated by com pari ng i ts output to the experi m entalresul ts. The FEA

m ethod was abl e to m odelcom pl ex actuator geom etri es,but the anal ysi swas onl y

val id to the l ow frequency response. The l im itati onsofthe FEA m ethod m oti vated

us to adaptNewbury constui ti vem odelto handl e them ul ti layerstacks. Newbury’ s

m odel(Newbury,2002) i s capababl e ofm odel ing si m ple canti lever geom etry trans-

ducers,as sensors and actuators f or any type ofresponse. Fi nal ly al lthe tool s and

resul tswere used to set f orth f ora desi gn ofan Ioni cPolym erflappi ng M AV.

1.2 Li terature R evi ew

In thi s secti on,a bri efbackground i nform ati on on Ioni c Polym ers i s provi ded. The

revi ew hasstarted wi th thedefini ti on oftheEl ectro- Acti vePol ym ers.Nexta chrono-

logi calhi stori calbackground i sprovi ded and f ol lowed by abri efovervi ew on them an-

ufacturi ng techni queand theoperati onm echani sm .Fi nal ly,thei nteresti ngproperti es

and thepotenti alappl icati onsofi oni c pol ym ersare expl ored.

3

1.2.1 E lectro-A cti ve Pol ym ers (EA P )

Electroacti ve pol ym ers bel ong to the f am ily of acti ve m ateri als. Acti ve m ateri als

are defined asm ateri als that adapt to a change i n the physi calenvi ronm ent,such

as el ectri cal , therm al ,m agneti c,chem i cal ,pH ,or l ight envi ronm ent. They can be

used i n the f orm ofsensors,actuators,acti ve dam pers,and energy generators. (Leo

coursenotes,2001)EAP reactsto thechangei n theel ectri caldom ai n,l ikethewi del y

used and wel lknown el ectroacti ve m ateri als such as pi ezoel ectri c ceram i cs. Recent

devel opm ents i n the El ectroacti ve Pol ym ers (EAP) have l ead to i ncreasi ng interest

in them ,dueto thereflexi bi lity whi ch m akesthem si m ilarto bi ologi calm uscl es. (Bar-

Cohen et al .,1999) They are al so defined i n four categori es,gel s, i oni c pol ym ers,

conducti ng pol ym ers,and el ectrostri cti ve pol ym ers. In thi s thesi s the i nterest i s i n

ioni c pol ym ers.

1.2.2 H istori calB ackground of Ioni c pol ym ers

Polym er-m etalcom posi teswere devel oped asearl y as1930’ saspreci pitati on ofcol -

loidalSi lver on prepared substrates (Bar- Cohen,2001). In the earl y 1990’ s when

Sadeghi pour et al . were tryi ng to use i oni c pol ym ers as pressure transducers,they

found that they coul d act as vi brati on sensors. Ioni c pol ym ers were devel oped as

”sol id pol ym er el ectrol yte f uelcel lm embranes” (Bar- Cohen,2001). Later i n 1992

whileSadeghi pourand coworkersweregetti ng cl ose to di scoverthei ractuati on capa-

bi liti es,Oguro’ s group i n Japan descri bed the bendi ng ofthe i oni c pol ym ers under

the appl icati on ofa potenti alacross i ts thi ckness. Si nce than,severalgroups i n the

USA and acrosstheworl d areworki ngon i m provi ng them anuf acturi ngprocess,char-

acteri zi ng and m odel ing theperf orm ance,and searchi ng forappl icati onsf orthi snew

intel ligentm ateri al .

1.2.3 M anufacturi ng of Ioni c pol ym ers

Presented here i s the generalm ethod by whi ch i oni c pol ym ers are m anuf actured,

although severalvari ati ons i n thei rm anuf acturi ng have been reported (Bar- Cohen,

4

Figure 1. 2: Schem ati c ofan Ioni c Pol ym er.

2001).Asshown i n Figure 1. 2 ioni cpol ym ersconsi stofan Ioni cpol ym erm embrane

sandwi ched between two m etaloverl ayers.

Them ateri alsused i n m anufacturi ng ioni cpol ym ersarea strong aci d,am etal

sal t,a reduci ng chem icalsol uti on,and perfluori nated i onom erm embrane.A l though

they are not necessari ly the best m ateri al to be used i n ioni c pol ym ers,DuPont’ s

NafionTMproved to havethebestperf orm ancei n thecomm erci ali oni cpol ym ers.The

m anufacturi ng process i s usual ly com posed ofthree m ai n steps. A f ter cl eani ng the

pol ym erwi th a strong aci d such asH N O 3,a cl ean sheet ofpol yperfluoroethyl ene-

sul fonatem embrane (Nafion TM) i s soaked i n a m etalsal t sol uti on (P t(N H 3)C l 2) to

popul atei twi th a reduci blem etal(Bar- Cohen,2001).Duri ng thi sstep them etalsal t

willexchangehydrogen i on in thepol ym erbackbone.Than thi ssam ple issubm erged

in a chem icalreductantsuch asLi thi um Borohydri de(Li B H4),whi ch can’ tpenetrate

thei oni cpol ym er,thusthereducti on willoccuraccordi ng toequati ons(1. 1)and (1. 2)

onl y at the surf aceofthe pol ym er.

Li B H4 + 4[P t(N H 3)4]2+ + 8OH− −→ 4P t0(s)+ 16N H 3(g)+ Li BO2(sd)+ 6H 2O

(1. 1)

5

and

LiB H4 + 4H2O −→ 4H2(g)+ Li OH (Li + + OH− )+ B (OH ) 3(sd) (1. 2)

Equati on (1. 2)provi desthehydroxyli onsneeded i n equati on (1. 1),theref ore9

m olesofLi BH4arerequi red to reduce4m ol es[P t(N H 3)4]2+ .Noti cei n equati on (1. 1)

that the productsare pl ati num m etalswhich f orm the dendri ti c el ectrode. The am -

m onia gaswi llevaporate and theLi thi um Boroxi dewillpreci pitate.Asf orequati on

(1. 2),thehydrogen gaswi llevaporate theB (OH ) 3 preci pitate,thehydroxyli on will

reactaccordi ng to equati on (1. 1),whi le the Li thi um ion willchai n with thepol ym er

insi de the cl usters.

Currentl y several researchers are worki ng on opti m izi ng thi s process. The

surf aceconducti vi ty i sessenti ali n chargi ng them embrane(Bar- Cohen,2001).In the

CIM SS lab,M attBennett hasbeen worki ng on thi s probl em ,and f urther tryi ng to

incorporate i nexpensi vem etal ssuch ascopperi nto theconducti ng overl ayer.Fi nal ly

a thi rd m anuf acturi ng step m i ght be requi red to exchange the cati on with another

one (e. g. repl ace the Na+ wi th Li + ),whi ch willeffect the perf orm ance ofthe i oni c

pol ym eras i twi llbedescri bed l ater.

1.2.4 A ctuati on M echani sm

To date the physi calm echani sm sthatproduce actuati on are sti lluncertai n.Several

researchersaresuggesti ng di fferentactuati on m odels.The realactuati on m echani sm

coul d be one ofthose m odel s,or a combi nati on ofthem . A l lofthose m odel s con-

si der the pol ym er’ s i oni c m embrane as hydrophi lic cl usters i nsi de the hydrophobi c

fluorocarbon pol ym erbackbone.

The m ain assum pti on i s that ani ons i n the cl usters are attached to the fluo-

rocarbon backbone (Bar- Cohen,2001),whi le the f ree cati ons wi llm ove wi thi n the

water m edi um under the appl icati on of an el ectri c fiel d, causi ng them to m i grate

towards the cathode. Thi s redi stri buti on willcause som e changes i n the properti es

ofthe pol ym erm embraneat the anodeand cathode si des.Tabl e 1.1 del ineate those

changes.

6

Anode CathodeDecrease i n the effecti ve sti ffness Increase i n the effecti ve sti ffnessofthem embrane ofthem embraneGenerati on ofa repul si veel ectrostati c An increase i n the attracti ve f orces,force between the fixed ani onswhi ch holding the fixed ani onscl oserto eachincrease the cl ustersi ze i ncreasi ng othersdecreasi ng theentropy, and i ncreasi ngtheentropy,and rel ax thepre stretched theel asti c energy ofthe pol ym er.pol ym erchai nsdecreasi ng theel asti c energy.W ater i nsi de the cl usters,whi ch i sa On theCathode si de thi sdecrease i n thedielectri cm ateri al ,tendsto reori ent effecti veperm i tti vi ty ofthe cl usters,underthe appl icati on ofel ectri c fiel d; increase theel ectrostati c force betweendecreasi ng theeffecti ve perm i tti vi ty of the cati onsand theani ons.the cl usters,reduci ng theel ectrostati crepul si ve f orce between the fixed ani ons.Duri ng thei rm igrati on,the cati onswi ll This i ncrease i n water i nsi de the cl usterscarry som ewaterwi th them ,decreasi ng on theCathode si de,i ncrease the vol um ethe vol um eofthe cl usters ofthe cl usters.Decrease i n the osm oti c pressure i nsi de Increase i n the osm oti c pressure i nsi dethe cl usters the cl usters

Tabl e 1.1: C hangeson the cathode and the anode off our actuati on m echani sm s(B ar-C ohen,2001)

7

1.2.5 Interesti ng properti es of Ioni c pol ym ers

Ioni cPolym ersaresof tactuatorsthatperf orm largebendi ng and flappi ng deflecti ons

when a sm allvol tage i sappl ied acrossthei r thi ckness.Thedi spl acem entcapabi liti es

are i n the orderof2% -5% (com pared to 0. 1% -0.3% for the el ectroacti ve ceram i cs)

(Shahi npooretal .,1998).M oreoverthosem ateri alsaresof t,flexi ble,and m echani cal

parts f ree whi ch m akes them hi ghl y dexterous and robust. Fi nal ly i oni c pol ym ers

are abl e to operate i n harsh cryogeni c condi ti ons (sui tabl e for space appl icati ons,

where they operate on tem peratures are as l ow as -130c and pressure of f ew Tor-

res. )(Shahi npooretal .,1998). They are al so characteri zed by l ow actuati on vol tage

(el ectri c potenti al) i n the order of1 5V for the 0. 184 mm thickness pol ym ers. (Akl e

and Leo,2003)(sui tabl e lessthan 1. 23V in orderto avoi d electrol ysi s.) On theother

hand i oni c pol ym ers have a num ber ofdi sadvantages to overcom e. A m aj or prob-

lem developersf acesm ostofthe ti m ewhen dealing with i oni c pol ym ers i s that they

need to be hydrated al lthe ti m e to operate properl y (thi s m ight be an advantage

in case ofunderwater appl icati ons,or bi om edicalappl icati on in which they wi llbe

im plem ented i nsi de thehydrated hum i d hum an body. ) Furtherm ore,i oni cpol ym ers

rel axe af ter they bend due to a step response,and i t i s bel ieved that thi s i s due to

the back di ffusi on ofwater (Bar- Cohen,2001). Thi s property m akes i tm ore l ike a

vel oci ty actuator,rather than a posi ti on actuator,and the sam e appl ieswhen they

areused assensors(Thesensi ngsi gnalbehavesl ikean i m pulse,when astep deflecti on

is appl ied to the pol ym er. ) Fi nal ly they are non- linear i n there behavi or,and ti m e

vari ant,whi ch m akescharacteri zati on and controldi ffi cul t.

1.3 Ini ti alM oti vati on

The initi alf ocusofthe thesi swas to study the f easi bi lity ofusi ng ioni c pol ym ersas

flappi ng m echani sm s for flappi ng fli ght based M i cro A i r Vehi cl es (M AV).Fl appi ng

fli ghti sa very com pl ex aerodynam i cprobl em which i ssti llunderresearch.Theref ore

we deci ded to rel y on l iterature f or obtai ning som e rough numbers Ioni c Polym ers

has to m eet i n order to fly theM AV.A f ter an el aborate l iterature survey,a revi ew

8

paper f or W eiShyy et al . (1999) “Fl appi ng and flexi ble wings f or Bi ologi caland

m icro ai r vehi cl es” i n the Progress i n Aerospace Sci ences provi ded us wi th those

num bers. Com pari ng the aerodynam i c requi rem entswi th the experi m entaldata on

Ioni c Polym ers,we real ized that si ngle layer i oni c pol ym ersare f ar f rom bei ng abl e

to fly an M AV.Them aj ordi ffi cul ty wasthesm al lf orce Ioni cPolym erscan generate,

thusthe f ocuswenton i ncreasi ng i t.Atfirstweexpl ored thepossi bi lity ofi ncreasi ng

the actuati on vol tage.Thi sattem ptwent i n vei n af ter the i oni c pol ym ers reached a

saturati on vol tage and thi s i ncrease i n vol tage al so i nduced the el ectrol ysi sofwater

insi de the pol ym ers. Thus the opti on of i ncreasi ng the vol tage was el im inated f or

water based i oni c pol ym ers. Fi nal ly we were l eft wi th the opti on ofstacki ng ioni c

pol ym ers,whi ch proved effecti ve. Furtherm ore,m uti layer i oni c pol ym ers proved to

sol ve severalprobl em s rel ated to i oni c pol ym ers and thei r appl icati ons. Theref ore,

we changed the ai m ofthi s thesi s toward characteri zi ng and i m provi ng the stacki ng

ofi oni c pol ym ers.

1.3.1 Potenti alappl icati ons

A llthe i nteresti ng properti esm enti oned i n the previ oussecti on gi ves i oni c pol ym ers

a number ofpotenti alappl icati ons. Those appl icati ons can range f rom usi ng them

as sensors or as actuators. They coul d be used i n water subm erged appl icati ons,

or i n other envi ronm ents ei ther as packaged pol ym ers or i oni c l iquid sol vent based

pol ym ers (Bennett and Leo,2003). Ioni c pol ym ersare usual ly m ade in the f orm of

thi n plates (50 184 m i crom eter) enabl ing them to be use i n M EM S (M icro El ectro-

M echanicalSystem ).They m i ghtbe used assensors to createm i cro- accel erom eters,

or as actuators to create m i cro swi mm ing robots. Another i nteresti ng property of

ioni cpol ym ersi sthatthey arenottoxi c forhum an si nce they arem adeofNafion TM ,

nobl e m etal s (Pl ati num ,and Gol d for the coati ng),and LiorNa i ons. Thi sm akes

itpossi ble for them to be i m plem ented i nsi de the body.Appl icati on can range f rom

heal th m oni tori ng aspressure and pul se sensors,or as acti ve vei ns as actuators. A

currentappl icati on underresearch by ourgroup,i susi ng those transducersto detect

acousti c si gnal s generated by the turbul ance i nduced by a stenosi s (artery cl osure).

9

Detecti ng and characteri zi ng thi s turbul ance enabl es us to m easure the severi ty of

the cl osure. The end product of thi s research i s a non- invasi ve i oni c transducer

devi ce capabl e ofdetecti ng earl y stenosi s.AsactuatorsM attBennett i n ourteam i s

tryi ng to createan adapti vem irorf orouterspaceappl icati ons.Thepol ym erswi llbe

plated wi th a reflecti vem ateri al ,and thepotenti alappl ied acrossthetransducerswi ll

deform the shape ofthem i ror i ncreasi ng ordecreasi ng the convexi ty. Furtherm ore,

ioni c pol ym erm echani calproperti es are qui te si m ilar to the hum an muscl e,whi ch

rai se there potenti alofrepl aci ng Hum an muscle.Shahi npooretal .(1998).

Thei r hi gh dexteri ty m akes them perf ect f or roboti cs appl icati ons, they can

be used to bui ld end- effectors asdexterousas the hum an hand or as sof tm al leabl e

end-effectors

M oreover thi s thesi s has f ocused on two potenti alappl icati ons f or the i oni c

pol ym ers. Due to thei rm echani calsi m ilari ti es to bi ologi calm uscl esand thei r l arge

flappi ng di spl acem ent capabi liti es we were i nterested i n studyi ng the possi bi lity of

thei r use i n flappi ng M icro A i r Vehi cl e (M AV) appl icati on,as engi nes, control lers

and sensors.Asf or the combi ned sensors- actuatorsstack,wegaveattenti on to thei r

appl icati on assof t,l arge di spl acem entm i croposi ti oner.

1.4 O vervi ew ofT hesi s

1.4.1 R esearch O bj ecti ves

Theobj ecti ve ofthi s thesi s i s to bui ld and characteri zem ulti layer i oni c transducers.

Ioni cactuatorsgeneratesm al lf orceson theorderof0. 5m N fora 22mm *5mm *0.2mm

beam .Theoperati on ofthose transducersdependson them obi lity ofi onsi nsi de the

pol ym er cl usters. A sol vent i s requi red f or i ons to m ove,and those sol vents have a

certai n el ectri calstabi litywi ndow.Forwaterthi sstabi litywi ndow isaround 1. 2V ;the

vol tageatwhi ch waterstartsto decay i nto hydrogen and oxygen gases(el ectrol ysi s).

Paral lelm ul ti layerstacksare devel oped to m i nim ized the el ectri c fiel d requi rem ents

foractuati on,and therf ore i ncreasi ng thef orceperuni tvol tage.Them echani calcon-

10

strai nt at the i nterf ace i sproven to provi de a tradeoff between deflecti on and f orce.

Characteri zi ng thi si nterf aci alf ri cti on provi desdesi gnersa control lableparam eterf or

thei r appl icati on. In order to m odelthe i nterf aci alf ri cti on in m ulti layer transduc-

ers,a Fi nite El em entAnal ysi s (FEA)m ethod capabl e ofm odel ing thei rm echani cal

structure i sdevel oped.

M oreover,com bi nedm ulti layerstacksaredevel oped f orusei n feedbackcontrol .

They are f abri cated asan i oni c sensorem bedded i nsi de a multi layer i oni c actuator.

The combined m ulti layer transducers offers a com pact sensor- actuator that wi llbe

used i n preci si on appl icati ons.

Another obj ecti ve was to devel ope a m odel ing toolcapabl e of representi ng

m ulti layerpol ym ersas transducers. Newbury’ sequi val ent ci rcui tm odeli sm odified

to accomm odate the m ul ti layer pol ym ers. The m odi ficati on i s perf orm ed on f our

di fferentboundary condi ti ons,two el ectri cal :seri esand paral lelconnecti on;and two

m echanical :zero i nterf aci alf ri cti on and zero sl ip on the i nterf ace.

1.4.2 C ontri buti on

Them ain contri buti on ofthi s research i s the devel opm entand characteri zati on ofa

stacki ngprocessf ori oni cpol ym erm ateri als.In orderto characteri zethestacki ng,we

m easured thef reedi spl acem ent,bl ocked f orce,transf erf uncti on,resonancepeaks,and

thesensi ti vi ty f ordi fferentstacki ng techni quesand di fferentnum berofstacks.Duri ng

thecharacteri zati on processwereal ized thatthef reedi spl acem entcoul d becontrol led

by control ling the i nterf aci alsl ip between the i oni cpol ym erl ayers. Ifthere i sno sl ip

the stack wi llbehave as i f i t was one com pl ete bl ock,thus the naturalf requenci es

willi ncrease,whi le the f reedi spl acem entwi llbe reduced.On thecontrary i fthere i s

no fri cti on between the f aces,both thenaturalf requenci esand the f reedi spl acem ent

willbepreserved.Asf orthebl ocked f orce,i t i ncreased wi th thenumberofl ayersf or

the paral lelstacki ng,whi le i t rem ai ned approxi m atel y the sam e f or seri es stacki ng.

In sensi ng,i twas f ound that those pol ym ersactsascharge generatorsand si ncewe

were m easuri ng the short ci rcui t current am pl ifiers,we f ound that paral lelstacki ng

increases the sensi ti vi ty proporti onal to the num ber of stacks,whi le in the seri es

11

stacki ng i trem ai ned constant.Asf orthecom bi ned sensor- actuatorstack,them aj or

probl em was to el im inate the f eed- through. Feedthrough i s defined as the porti on

ofthe actuati ng si gnalofthe adj acent i oni c pol ym er that i s di rectl y fed through to

the output si gnalofthe sensor. The f eed- through wasm ai nly due the hum i dity i n

the gaps between stacks whi ch created a short- ci rcui t between the sensor and the

actuator(s).

Newbury’ s equi val ent ci rcui t representati on of i oni c pol ym ers was m odi fied

to accomm odate the m ul ti layer pol ym ers. The m odi ficati on wasperf orm ed on f our

di fferentboundary condi ti ons,two el ectri cal(seri esand theparal lelconnecti on)and

twom echani cal(zero i nterf aci alf ri cti on and zero sl ip on thei nterf ace).Thi sm odified

m odelhastheabi lity to m odelcanti leverm ul ti layeri oni c transducersassensorsand

actuators. It provi desa transf er f uncti on that coul d be used i n control ,and system

leveldesi gn ofi oni c transducerdevi ces.

By usi ng theFEA m ethod and stacki ng techni quewewereabl e to desi gn two

di fferentM AV wi ngs. The first wi ng was desi gn to be f ul ly m ade ofi oni c pol ym er

sheets. It was desi gned as a sem i ci rcul ar wi ng to m ake the best use of the area

covered (keepi ng the si ze oftheM AV assm al las possi ble). W hi le the second wi ng

wasdevel oped and wascom posed oftwodi fferentm ateri als:thepassi vel ightm ateri al

that f orm s thewi ng surf ace,and a stack of10 i oni c pol ym ersheetsof7 x 5 cm si ze

thatperf orm ed asm uscl esto actuate thewi ng.

Final ly thi swhole research coul d evol ve i nto a proj ect ofl arger scope to de-

vel op m icro- layered i oni c pol ym ersstacks,thatcoul d perf orm much better than the

si ngle ioni c pol ym erssheets.These stackswi llprovi de hi gher f orces,whi le thei r f ree

displ acem entand resonancecoul d becontrol led by them anuf acturi ng process,m ore-

overwem i ghtbe abl e to i ntegrate som e sensor l ayers f or f eedback control ,whi ch i n

turn wi llbeabl e to reduceorel im inate thesl ow rel axati on and hi gh overshootwhi ch

characteri ze i oni c pol ym ers.

12

1.4.3 A pproach

Chapter2 provi desan overvi ew forthefivedi fferentcharacteri zati on testsweperf orm

in order to characteri ze i oni c transducers. The output ofthose tests are descri bed,

and a descri pti on ofthe two testsetupswi th al lthere parts i spresented.

C hapter3 i s devoted f or the characteri zati on of Ioni c pol ym er stacks. At

firstan expl anati on oftheparal leland seri esstacki ng techni quesi spresented,and a

com pari son between them i sal so provi ded.Than both seri esand paral lelstacksare

characteri zed as sensor stacks and actuator stacks i n two di fferent secti ons. Char-

acteri zed was the f ree di spl acem entand bl ocked f orce,f ora step response,and asa

transf erf uncti on.Fi nal ly aFEA m ethod wasprovi ded,veri fied,and used to si m ulate

the behavi orofthe stacks.

C hapter4 i ntroduces the combi ned sensors- actuators,expl ores i ts potenti al

appl icati onsand i m portance.Thi schapterwi lldi scussthem anuf acturi ng techni ques,

which f ocuseson theel ectri calconnecti onsand i nsul ati ons. Ital so el aborateson the

si gnalf eed- through probl em .Fi nal ly i twi llexpl ore theLapl acedom ain m odelwhi ch

coul d beused i n controlappl icati ons.

C hapter5m odi fiesNewbury’ sm odeltoaccomm odatethem ul ti layerpol ym ers.

Them odificati on wasperf orm ed on f ourdi fferentboundary condi ti ons,two el ectri cal

theseri esand theparal lelconnecti on,and twom echani calthezero i nterf aci alf ri cti on

and the zero sl ip on the i nterf ace. Fi nal ly experi m entalresul tson transducerswi th

one to f our l ayers are perf orm ed and the resul ts are com pared to the new m odi fied

equi val entci rcui tm odel .

C hapter6 i s devoted to the finaldesi gn oftheM i cro A i rVehi cl e (M AV).It

illustrates the requi rem entsprovi ded by the revi ew paperprevi ousl y ci ted. Further-

m ore two Fi nite El em entdesi gnswi llbe dem onstrated and expl ained.And final ly a

summ ary with concl usi onsand proposi ti onsf orf uturework arepresented i n the l ast

secti on.

Atl ast,C hapter7 provi ded a bri efovervi ew ofthe thesi s. Ital so provi ded our

contri buti on to thefiel d,wi th concl usi onsbei ng drawn.And final ly,f uturework was

13

proposed.

14

C hapter 2

Experi m entalSetup

2.1 Introducti on

In thi s chapter a descri pti on of the i oni c pol ym er testi ng experi m ents wi th thei r

fixtures and ci rcui ts i s presented. Fi ve experi m ents are usual ly perf orm ed i n order

to f ul ly characteri ze the transducer. The experi m ents are the el ectri cali m pedance,

m echanicali m pedance,sensorsensi ti vi ty,bl ocked f orce,and f ree di spl acem ent tests.

Each experi m enti srun usi ng a step i nputora random i nput.Thefive testsarefirst

descri bed,wi th detai ls on the ci rcui try and equi pm entused. In the l ast secti on the

outputofthe experi m entsareel aborated.

2.2 Experi m ents O utput

Each experi m enti srun wi th two typesofi nputs,a step ora random i nput.Thestep

input i s used to determ i ne the l ow frequency response (DC) ofthe transducer. As

fortherandom i nput,i ti susual ly awhi tenoi sewith an evenl y di stri buted f requency

spectrum appl ied to thepol ym er.Thi stesti snotanal yzed i n theti m edom ain;rather

iti stransf orm ed to thef requency dom ai n usi ng theFouri ertransf orm ati on.Theout-

putofthi stesti sa FrequencyResponseFuncti on (FRF),whi ch i sthem agni tudeand

phaseoftheoutputasa f uncti on off requency.Thedurati on ofthe testi sa f uncti on

ofthreevari ables;i ti si nversel y proporti onalto thesam pl ing rate,proporti onalto the

15

num berofdata poi ntsperf ram e,and proporti onalto thenumberofaveragestaken.

The sam pling rate F s determ i nes the f requency range ofthe FRF.Ideal ly the range

oftheFRF extendsto Fs2 ,butdue to the i ncorporati on ofanti -al iasi ng fil tersaround

28% ofthi srangeareel im inated.Thenum berofpoi ntsperf ram eN p determ i nesthe

resol uti on oftheFRF whi ch i sequalto FsNp

.Severalf ram esofdata are gathered and

the resul ti ng FRFs are averaged to obtai n the finalFRF.The FRFs ofeach f ram e

are com pared together and a coherence f uncti on i s com puted. W hen the FRFsare

identi calthecoherence i sone,and i fthey are total ly di ssi m ilarthecoherence i szero.

Ideal ly for a causalsystem the coherence shoul d be one,but noi se and som e other

sam pling effects rui ns i t by i ntroduci ng random data to the output or i nput ofthe

system orboth.A l ow coherencem eansa sm al lsi gnalto noi se rati o.Fi nal ly a win-

dow functi on i susual ly m ulti pl ied by each f ram e forbef oreprocessi ng.In thi sthesi s

thepopul arHanni ng window wasused throughout.The rol eoftheHanni ng window

isto reducethel eakagedueto sam pl ing,reducetheeffectoftheuncorrel ated content

in the begi nning and theend ofthe f ram edue to phaseshi ft.

2.3 Types ofExperi m ents

The five di fferent experi m ents are expl ained i n thi s secti on. Both i m pedance tests

are conventi onalto any m ateri al ,whi le the el ectrom echani cal ly coupl ed experi m ents

are custom i zed f or i oni c pol ym ers.

2.3.1 E lectri calIm pedance

Electri cali m pedance i sdefined asel ectri calresi sti vi ty and capaci tance ofthe trans-

ducer.Theref oretheoutputofthi sexperi m enti sa tranf erf uncti on fortheresi stance

and capaci tanceofthe i oni c transducer.

Theexperi m entstartswi th appl yi ng a known vol tageacrossthe i oni cpol ym er

whilem easuri ng the open ci rcui tcurrent.The currentm easuri ng ci rcui t i sshown i n

Figure2. 1.Theel ectri cali m pedance i stheknown vol tage(V)appl ied di vi ded by the

16

Figure 2. 1: Schem ati c draw i ng show i ng the experi m entalsetup f or the bl ockedforce test.

currentsensed (I).

ZE =V

I(2. 1)

Theresi sti vi ty i stherealpartofthei m pedance,whi lethecapaci tancei sthei m aginary

part.

2.3.2 M echani calIm pedance

Ioni c pol ym ersare consi dered vi scoel asti cm ateri als thatarem odel ed usi ng two m e-

chani cali m pedance term s. The first term i s the stati c m odulus,whi le the second i s

a frequency dependent term .Newbury and Leo (2002)have used theGHM m ethod

to si m ulate the f requency dependent term .

A schem ati c ofthe setup used i n thi s experi m ent i s shown Fi gure 2. 2. The

shakerappl iesam echani caldef orm ati on while the l inearpotenti om eterm easuresthe

displ acem ent(D )and the l oad cel lm easuresf orce (F).Them echani cali m pedance i s

ZM =F

D(2. 2)

The testi ng configurati on used i n thi sfixture i sval id forl ow-frequency m easurem ent.

Thiswasshown by John Frankl in in theCIM SS,butthi sconfigurati on i shandf ulf or

the next test.

17

Figure 2. 2: Schem ati c draw i ng show i ng the experi m entalsetup f or the bl ockedforce test.

18

Figure 2. 3: Schem ati c draw i ng show i ng the experi m entalsetup f or the bl ockedforce test.

2.3.3 Sensor Sensi ti vi ty

Thesetup shown i n Figure 2. 2 isal so used to determ i ne thesensorsensi ti vi ty ofthe

ioni c transducers. The shaker i s appl yi ng the m echani caldef orm ati on,but i nstead

ofm easuri ng the l oad at the ti p a short ci rcui t current sensor i sm easuri ng current

form ed dueto theappl ied strai n.Thesensorsensi ti vi ty ofi oni cpol ym ersi sm easured

eitherasachargeoracurrent(S).A vol tagesensorprovi desl esssensi ti vi ty si ncethose

transducersare hi ghl y capaci ti ve (Newbury,2002).The sensi ti vi ty i sm easured as

Sensi ti vi ty =S

D(2. 3)

2.3.4 B locked Force

In thi s experi m ent the pol ym er i s connected to a power suppl y,and i t i s actuated

with a known appl ied vol tage (V) on the el ectrodes. On the other si de,a l oad cel l

is bl ocki ng the m oti on ofthe pol ym er and m easuri ng the f orce generated (F).The

setup i sshown i n Figure 2. 3.The bl ocked f orce i s them axi m um force thi spol ym er

19

Figure 2. 4: Schem ati c draw i ng show i ng the experi m entalsetup f or the bl ockedforce test.

can generate and com puted asf ol lows:

Blocked f orce=F

V(2. 4)

2.3.5 Free di spl acem ent

Thefreedi spl acem entexperi m enti sanotheractuati on experi m ent,buti tdi ffersf rom

thebl ocked f orce testby them echani calboundary condi ti on.

Theexperi m entalsetup i sshown i n Figure 2. 4.A known vol tage(V)i sappl ied

to the pol ym er,whi le a laservi brom eterm easures the transducers ti p di spl acem ent

(D )wi thoutaddi ng any obstacl e to the f reem oti on.The f reedi spl acem ent i s:

Freedi spl acem ent=D

V(2. 5)

20

Figure 2. 5: F ixture 1.

2.4 Equi pm ent D escri pti on

In thefiveprevi ousl y descri bed experi m entsi oni cpol ym erswerecl am ped atoneend

with two gol d electrodes. A l lthe experi m ents are conducted i n ai r,and dei oni zed

waterwasbrushed on pol ym erapproxi m atel y once a m i nute. Thi s i nsured that the

hydrati on leveli skeptwi thi n an acceptabl e range.W hen noti n use,the transducers

were stored i n dei oni zed water.

Two testfixtureswere used the experi m ents i n thi s thesi s. Fi xture 1 wasac-

qui red f rom previ ous researchers i n the CIM SS l ab Newbury (2002) and shown i n

Figure 2. 5. It i s com posed oftwo separate apparatus to perf orm al lthe five tests.

Thesensi ng and m odul ustestwasperf orm ed on thefixturewi th theAPS Dynam i cs

APS 113 long stroke shaker,whi ch provi des l arge di spl acem ent up to 50 Hz. The

displ acem ent i sm easured wi th a Novotechni k T25 Li nearpotenti om eterand an ap-

21

propri ate ci rcui t condi ti oning ci rcui t. The si gnalam pl ifiers used f or characteri zi ng

the perf orm ance ofthe stacks i s a current am pl ifier of10 5 V /am p sensi ti vi ty,wi th

the schem ati cs shown i n Figure 2. 2. M anuf acture’ s speci ficati ons of the l inear po-

tenti om eter i ndi cate a repeatabi lity of0. 002mm and a lineari ty of0. 06mm . For the

m odulus test a Transducer Techni quesGSO-10 10 gram l oad cel lwasm ounted on

the shaker arm ature and used to m easure the f orce due to the def orm ati on of the

pol ym er.Thi s l oad cel lwasused wi th a TM O-1 si gnalcondi ti oning ci rcui t. Itspre-

ci si on,repeatabi lity and l ineari ty were 0. 02m N.TheGSO-10 load cel lwasal so used

to m easure the bl ocked f orce on the actuati on apparatus. The actuati on apparatus

isshown i n Figure 2. 5 and i scom posed ofthe l oad cel lon a vari abl e cursorso that

it i seasy to change the boundary condi ti on f rom bl ocked f orce to f ree di spl acem ent.

For the f ree di spl acem enta Pol ytecOFV- 303 l aservi brom eterhead wi th OFV-3001

control lerand OVD-20 dem odulatorwasused.Theresol uti on ofthi ssetup was5µm .

The laser vi brom eterwasused f or f requency response,and sm al ldi spl acem ent step

responsesdue to i tshi gh resol uti on.But i n casea l arge ti p di spl acem enti sexpected

a RedLake i m aging M oti on Scope PCI2000 S hi gh f requency di gi talvi deo cam era

wasused to m easure the def orm ati on. Thi scam era coul d capture vi deo with a rate

up to 2000Hz.Im ageExpressM oti onTrace i m ageanalysi ssof twarewasused to track

the transducer’ sti p,and generatea ti p di spl acem entpl otasa f uncti on ofti m e.The

resol uti on ofthe trace sof tware depends on the i m age quality and the f ocall ength

used. Itcoul d locate a poi ntwi thi n a resol uti on ofa tenth ofa pi xel .A pi xeli n our

experi m entscorrespondsto approxi m atel y 0.1mm .

Thesecond fixturewasrecentl ybui ltbym embersoftheCIM SS l ab.Iti sshown

in Figure 2. 6with al lthecom ponents.Thel oad cel land thel inearpotenti om eterare

thesam eonesused i n theol d fixture.Thi sfixturei sbui ltto autom atef ourofthefive

experi m ents:bl ocked f orce,el ectri cali m pedance,m echani cali m pedance,and sensi ng

sensi ti vi ty. Those five experi m ents are suffi ci ent to f ul ly characteri ze the pol ym er.

The shakerused i n thi s fixture i sa Bruel& K j aer Instrum entsshaker,i t i s capabl e

ofhi gher f requenci es (up to 2- 3KHz) than the previ ous shakers. As f or the si gnal

processi ng,we used two di gitalsi gnalprocesses. The Tektroni x FFT anal yzerwi th

22

Figure 2. 6: A picture show i ng the new fixture w i th detai ls on the parts.

a si gnalgeneratorwasused f or the f requency response f uncti on. A dSpace DS1102

DSP wasused to m easure the step response.

23

C hapter 3

C haracteri zati on of Ioni c Pol ym er

Stacks

3.1 Introducti on

Asdefined i n the i ntroducti on,i oni c pol ym ersare sof t actuators thatperf orm large

bendi ngand flappi ngdeflecti onswhen asm al lvol tagei sappl ied acrossthei rthi ckness.

Thei r m aj or di sadvantage i s the l ow forces they appl y. To overcom e thi s probl em

stacki ng was proposed. In thi s chapter stacki ng i s thoroughl y expl ained. Paral lel

and seri esstacki ng techni quesareexpl ained,and thei ruseassensorsand actuatorsi s

discussed.Actuatorstacki ng i sperf orm ed todeterm i nehow interf aci alf ri cti on affects

the f reedi spl acem entand thenaturalf requenci es.Fi nal ly a Fi niteEl em entAnal ysi s

m ethod wi llbe expl ained,veri fied,and used to anal yze theexperi m entalresul ts.

3.2 Stacki ng techni ques

Asprevi ousl ym enti oned twostacki ng techni queswi llbeexpl ored:seri esand paral lel .

Those techni quesare the sam em echani cal ly butdi ffer i n thei rel ectri calcharacteri s-

ti cs. In the nextparagraphs the seri esand paral lelstacki ng willbe expl ained and a

com pari son wi llbe provi ded.

24

Figure 3. 1: A C A D draw ing show i ng the di fferent parts ofa seri es stack.

3.2.1 Seri es stacki ng

Seri esstacki ng consi stsofoverl ayi ng thei oni cpol ym ersheetson top ofeach othersas

shown i n Figure3. 1 and provi ding the vol tageV total acrossthewhol e stack asshown

in Figure 3. 2. Assum i ng that the pol ym ersare ofthe sam e si ze and sam e el ectri cal

im pedance,

V1 = V2 = = Vn =Vtotal

n. (3. 1)

W hile from the m echani calperspecti ve, the f orce generated by the separate

pol ym ers wi llbe added. As f or the f ree- displ acem ent,and resonance f requency, i t

willdepend upon the i nterf aci alf ri cti on,aswi llbe di scussed l ater.

25

Figure 3. 2: Schem ati c representati on of the el ectri c connecti on f or a seri esstack.

3.2.2 Paral lelstacki ng

Paral lelstacki ng i s si m ilar to seri es stacki ng,wi th the onl y di fference i s that each

pol ym erwi llrecei ve a vol tageequalto the overal lstack vol tage:

Vtotal = V1 = V2 = = Vn− 1 = Vn

Them echani calconnecti onsare shown i n figure 3. 3,whi le the el ectri calconnecti ons

are shown i n Figure 3. 4.The f abri cati on process i s i llustrated i n Figure 3. 5.

Forthepurposeofthi sthesi s,thestackswerel ayered by hand.Theconnecti on

leadsarem adeof3M adhesi vecoppertapesandSaranW rapwasused f orthereported

resul tsas i nsul ati on m ateri al .

3.2.3 C om pari son

Them ain advantagesofseri esstacki ng ascom pared to paral lelstacki ng are them an-

ufacturi ng si m plici ty,rel iabi lity,and the l ow actuati on current.Asm enti oned bef ore

seri esstacki ng i ssi m ply l ayi ng thepol ym ersheetson top ofeach otherand appl yi ng

the potenti alacross the whol e stack,whi le the paral lelstack requi res weavi ng the

leads f rom one f ace to the other and addi ng insul ati on as el aborated i n Figure 3. 5.

This i s a very del icate and tedi ous process,f or exam pl e layeri ng a 3 l ayer stack i s

m ore than 40 m i n ofwork. M oreover out ofeach 2 or 3 stacks onl y one wi llwork

properl y,becausetheotherswi llhavesom ei nternalshort- ci rcui tsthrough thei nsul a-

ti on oracrossthe l eads.Thi sshort- ci rcui t i sal so responsi ble fortheshortdurabi lity

26

Figure 3. 3: A C A D draw ing show i ng the di fferent parts ofa paral lelstack.

ofparal lelstacks. Upon usage the i nsul ati on m ight tear,and the l eadswi llm ake a

short- ci rcui t som ewhere i nsi de the stack,thi ssm allshort- ci rcui twi llpropagate eas-

ily and becam e def ecti ve due to the heat i t rel eases,whi ch i n turn m el ts the pl asti c

insul ati on.Apart f rom them anuf acturi ng di ffi cul ti esand shortdurabi lity probl em s,

paral lelstacks are f ar better i n perf orm ance than seri es stacks. They provi de low

operati ng vol tages,whi ch are the sam e across each pol ym er,avoi ding the necessi ty

ofgoi ng to l arge overal lvol tages seri es stacks requi re; theref ore we can saf ely re-

m ain lowerthan the1. 23V electrol ysi svol tage l im it. In the f ol lowing secti onswewill

expl ore theuseofstacksassensorsand actuators.

3.3 Sensor Stacks

Thefirst tests i nvesti gated theperf orm anceand characteri sti csofseri esand paral lel

stacksassensors. In the first subsecti on a seri esand paral lelm ul ti layer sensorsare

com pared,and i n thenextsubsecti on theam pl ifierwasvari ed and theconceptofl ow

27

Figure 3. 4: Fabri cati on a 3 l ayers paral lelstack.

28

Figure 3. 5: Schem ati c representati on of the el ectri c connecti on f or a paral lelstack.

passfil teri ng i sexpl ained.

3.3.1 C om pari son ofSeri es and Paral lelM ul ti layer Sensors

Thissecti on willexpl ore thesensi ng characteri sti csofseri esand paral lelstacki ng.As

m enti oned bef oreweare usi ng currentam pl ifiers,si nce accordi ng to Newburry i oni c

transducersperf orm betterwhen used wi th a charge am pl ifier. Thi s i s due to thei r

low electri cali m pedance.Theref ore thepol ym ersareseen ascurrentgenerators,and

it i s expected that i n paral lel the current wi lladd,and thus the stack sensi ti vi ty

willi ncrease proporti onalto the num berofl ayers.W hi le in seri es the sam e current

willpass through them al l,and theref ore i t i s expected that sensi ti vi ty wi llrem ai n

constant.A l though Newbury’ sm odel(Newbury,2002)predi cted thatthesensi ti vi ty

increase asa f uncti on ofthi ckness,seri esstacksdi dn’ t show such a behavi ordue to

the use ofcurrent sensi ng am plifier ci rcui t. In case ofa vol tage sensi ng ci rcui twas

used (thi sm ight happen i f the el ectri c im pedance ofthe pol ym er i s changed whi le

tryi ng to enhance i t),i t i sexpected that thi s resul twi llbe reversed. Ioni c pol ym ers

arem odel ed asa com bi nati on ofcapaci tors,and resi stors. Thuswhen added to the

am plifierci rcui t they wi llactasa l ow passfil terofapproxi m ate cutoff f requency

t=1

RC

whereR i stheam pl ifierresi stor,and C i sthepol ym erscapaci ti ve i m pedance.(Note

thatthe i nternalresi storofthepol ym eri svery sm al lcom pared to theam pl ifierresi s-

tance1. 2Ω com pared to 100K Ω ).Addi ng thepol ym ersi n paral lelwi lli ncrease thei r

29

capaci ti ve i m pedance proporti onalto the numberofl ayersand the cutoff f requency

willbereduced.Forthi sreason wetri ed toexpl orenew am pl ifierci rcui tsasdi scussed

in the next secti on. Fi gure 3. 6 shows the sensi ti vi ty ( µAm pm ms

) i ncreases proporti onal

to the number ofparal lell ayers. A l so shown i s the decrease i n the phase shi ft due

to the i ncrease i n the capaci ti ve i m pedanceofthe stack whi ch i sproporti onalto the

num berofl ayers. As f or the l astgraph i n Figure 3. 6 it shows the sl ight i ncrease i n

thecoherence,and thi si sdue to the i ncrease i n thesensi ti vi ty i .e. thesi gnalto noi se

rati o.Asf orthe i rregul ari ty around 9Hzshown i n thefigure,i tm ightbedueto som e

resonance i n the shakerend.

As forseri esstacki ng,Fi gure 3. 7 showsa com pari son ofstackswi th di fferent

num ber of l ayers vari ed from 1 to 4 l ayers. A l so i ncl uded i s the transf er f uncti on

oftwo di fferent si ngle pol ym er stri ps,to em phasi ze the vari ati on between pol ym er

stri ps,and val idate that the sensi ti vi ty of the overal lstack i s the average ofeach

pol ym er l ayer. M oreover the phase shi ft di d not vary m uch,though i t i ncreased a

littl e bi t. Thi s i s expected due to the decrease i n the capaci ti ve i m pedance when

the capaci tors are put i n seri es,and therf ore an i ncrease i n the cutoff f requency of

the l ow pass fil ter. To concl ude, paral lel stacki ng had i ncreased sensi ti vi ti es and

decreased the cutoff f requency.W hi le seri esstacki ng di d not i ncrease the sensi ti vi ty

ascom pared to si nglepol ym ers,buti ncreasesthecutoff f rquency.W ebel ieve thati f

vol tageam pl ifierswere used,thi sresul twoul d havebeen i nverted.

3.3.2 A m plifier Vari ati on

Forthepurposeofi m provi ng theperf orm anceoftheam pl ifierci rcui t,especi al ly af ter

the noti cabl e increase i n phase shi ftduri ng paral lelstacki ng,severalam pl ifierswere

tri ed.Idealsensorswoul d havezerophaseshi fti .e.theywi llbef eedi ngback realti m e

datawi thoutdel ay.Them orephase l ag theworse thesensori s,si nce i ti sdi ffi cul tto

add phase l ead to a system usi ng a control ler.Thusthe targeti sto reducephase l ag

asm uch aspossi ble.Thi scoul d beachi eved by i ncreasi ng thecutoff f requency,whi ch

willl ead to a decrease i n the phase l ag at l ow frequenci es.Though severalam pl ifier

ci rcui tswere tri ed,l ike hi gh im pedance chargeam pl ifiersand vol tageam pl ifier.The

30

Figure 3. 6: T he transf er f uncti on ofparal lelstacks w i th 1,2,3,and 4 l ayers.

31

Figure 3. 7: T he transf er f uncti on of seri es stacks w i th 3 and 4 l ayers pl ottedw ith tw o di fferent si ngl e l ayers pol ym ers.

32

Figure 3. 8: Transf er f uncti on of the sam e pol ym er but w i th a di fferent val ueofR 1 in the am pl ifier ci rcui t

currentam pl ifiersproved to betheonl y successf ulones.Theschem ati cofthecurrent

am plifier i s shown i n the previ ouschapter i n Figure 2. 2. Severalparam eters i n thi s

ci rcui twere vari ed,the firstonewasR 1,and the resul t i sshown i n figure 3. 8. The

resi stanceR 1 isam ajorf actori n thecutoff f requency τ = 1R1C

,and thi scan beeasi ly

veri fied i n figure 3. 8. One coul d see that decreasi ng R1 decreases the phase l ag at

lowerf requency,i ndi cati ng hi ghercutoff f requency.

The resi stance R 2 was also vari ed to determ i ne i ts effect on the f requency

response. Theoreti cal ly, i f the Op- am p was idealthi s shoul dn’ t have any effect on

the response. Butasshown i n figure 3. 9 though the phase shi ft di dn’ t change,the

sensi ti vi ty changed dram ati cal ly and wi thoutany pattern.Thi sweird behavi orcoul d

be rel ated to the non- idealbehavi or of the Op- am p. M oreover,once the am pl ifier

ci rcui ti sturned on,a hugeDC offsetwi lli ni ti ate,butwi llsettl edown to som ewhere

cl ose to zero wi thi n 20 to 30 sec. (i tcoul d be cal ibrated to go to zero af ter those 20

33

Figure 3. 9: Transf er f uncti on of the sam e pol ym er but w i th a di fferent val ueofR 2 in the am pl ifier ci rcui t

to 30 sec).

By goi ng back to figure 3. 8 one can noti ce that upon decreasi ng the resi s-

tor R 1, the sensi ti vi ty of the am pl ifier i s decreasi ng. Theref ore al though thi s was

successf uli n increasi ng thecutoff f requency,theoveral lperf orm anceoftheam pl ifier

wasunsati sfactory. Thus i twasdeci ded to decrease the resi stanceR 1,and than use

a vol tage am pl ifier, that wi llsi m ply com pensate f or the l ost i n sensi ti vi ty wi thout

introduci ng any f urtherphase l ag.Asshown i n figure 3. 10 thi sworked properl y,but

the onl y l im itati on on decreasi ng a l otR 1,and keep on com pensati ng with vol tage

am plifier,i s that the l ateram pl ifier i sam plifyi ng both the si gnalcom i ng outofthe

sensor,and thenoi secom ingoutofthecurrentam pl ifierci rcui t.Thusthecl eanerthe

current am pl ifier ci rcui t i s (usual ly betterOp- am ps,and better ci rcui t connecti on.)

them orewecanm akeuseofthi stechni que,and f urtheri ncreasethecutoff f requency.

As itcan benoti ced i n Figure 3. 10,the 10K Ω currentam pl ifiergai n resi stor

(R 1) wi th 100 ti m es vol tage gai n am plifier f orm ed the best com bi nati on for thi s

techni que,i t was abl e to enhance the phase l ag by approxi m atel y 50 degrees,wi th

34

Figure 3. 10: Transf er f uncti on ofthe sam e pol ym er butw i th di fferent am pl ifierci rcui ts

35

an extended cutoff f requency.Goi ng further i n decreasi ng the currentam pl ifiergai n

resi stor,and i ncreasi ng the vol tage gai n,woul d cause hi gh noi se to si gnalrati o and

also l eadi ng the system to i nstabi lity. Thi s coul d be noti ced by the i ncrease i n the

bum ps on the 60Hz,120HZ,and the 180Hz wi th the decrease i n the current gai n

am plifierand i ncrease i n the vol tagegai n am plifier.

3.4 A ctuator Stacks

Them ain purpose ofthi s research was to i ncrease the f orce ofi oni c pol ym ers. The

stacksused i n thi ssecti on arethesam eastheonesused f orthesensoranal ysi s.There-

forethem anuf acturi ng i si denti caltowhatwasprevi ousl y descri bed.In thef ol lowing

secti onswewilldescri betheactuati on characteri sti csoftheseri esand paral lelstacks,

and the rol e interf aci alf ri cti on pl ays i n determ i ning those characteri sti cs.

3.4.1 C om pari ng Seri es and Paral lelStacks as A ctuators

As previ ousl y di scussed the onl y di fference between the seri es stacks and paral lel

stacks i s the way the vol tage and current are provi ded to each pol ym er. Thus i f

we reduce the anal ysi s to vol tage perpol ym er rather than vol tage per stack (i .e. i f

we apply V to the paral lelstack we shoul d appl y n*V to the seri es stack,where n

is the number ofl ayers),we shoul d obtai n the sam e output. For thi s reason al lof

our resul ts are expressed i n term sofvol tage per stack,thus the di fference between

seri esand paral lelwoul d be em phasi zed. In thi s secti on wewilldi scuss the bl ocked

forceresul ts.Resul tsf orthem easurem entoff reedi spl acem entand resonancewi llbe

presented l atersi nce they are rel ated to the i nter- faci alf ri cti on between thepol ym er

layers.

In thi s secti on we willdi scuss the bl ocked f orce resul ts. Bl ocked f orce step

resul tsare shown i n Figure 3. 11 for22mm x 5mm x 0.2mm polym erswi th di fferent

num bersofl ayers.M easuri ng the bl ocked f orce i n ioni c pol ym eronewoul d read the

m axim um force rather than readi ng the steady state,because the steady state wi ll

go to zero wi th ti m edue to i tsi nherentrel axati on property.Looki ng atFi gure9 one

36

Figure 3. 11: T he B locked f orce step response ofthe di fferentl y l ayered paral lelstacks

can noti ce that the bl ocked f orce has i ncreased f rom 0.37mN for the si ngle layer to

approxi m atel y 1.08m N for the three- layer pol ym er. Consi deri ng thi s resul t one can

deduce that they fit theequati on

Ftotal = NLFlayer (3. 2)

whereF total isthetotaloutputofthestack,F layer isthef orceoutputofa si ngle layer,

and N L isthenumberofl ayers.The realbl ocked f orcewi lldevi ate f rom theval ue i n

the equati on with the i ncrease ofthe numberofl ayers i n the stack,and thi sm ainly

due to two reasons. The first i sdue to the el ectri c l osses i n the el ectri call eads that

connectthepol ym erstogether,note thatthi seffectcan bedecreased i n caseofm ore

accuratel ayeri ng.Thesecond reasonm i ghtbedueto thedam pi ng thatthei nsul ati on

m ateri aland thepol ym ersthem sel vesare i ntroduci ng to theoveral lsystem .

Shown in Figure 3. 12 i s the f requency response f uncti on ofthe bl ocked f orce

37

Figure 3. 12: T he B locked f orce transf er f uncti on of the di fferentl y l ayeredparal lelstacks

for a paral lelstack wi th di fferent num bers of l ayers. It provi desm ore evi dence to

supportequati on 3.2.A note i sthatthey axi si n them agni tudepl oti n thi sfigure i s

presented i n a log scal e,thusthedi stancebetween the f ourf uncti ons i snotequal .

Thebl ocked f orceofseri esstackswerecharacteri zed i n thesam em anner.Si nce

thevol tageperl ayerwi lldecreasewi th theaddi ti on ofm ore l ayers(ref erto equati on

3.1) the f orce per l ayer wi lldecrease proporti onal ly, and theref ore the addi ti on of

layers whi le hol ding the overal l stack vol tage constant wi ll not am pl ify the f orce,

but i twi llrem ai n constant,as shown i n Figure 3. 13. The resul ts shown i n Figures

3.11 through 3. 13 represent the bl ocked f orce boundary condi ti on, whi le the f ree

displ acem entboundarycondi ti onwillbei llustrated i n thenextsecti onwhich di scusses

them aj orparam eter i n free di spl acem ent.

38

Figure 3. 13: T he bl ocked f orce transf er f uncti on of seri es m ulti layered actua-tors

3.4.2 Interf aci alFri cti on and M echani calP roperti es

The term i nter- faci alf ri cti on i s ref erred to as the f ri cti on between the pol ym ers i n

the stack. The substanti al di fference i n free di spl acem ent between packaged and

unpackaged pol ym erstacksm adeusreal izethei m portanceofi nter- faci alf ri cti on.As

descri bed i n the i ntroducti on,i oni cpol ym ersm ovedue to oneorseveralm echani sm s

which occur i nsi de thepol ym er.

Form odel ing purposes,onecan l ook atthebendi ngm echani sm (s)asan i nter-

nalpressureappl ied to thepol ym er.Thi si nternalpressurewi lli ncreaseproporti onal

to thenumberofl ayers,whi le i fconsi dered asonebl ock thestack thi cknesswi llal so

increase proporti onal to the number of l ayers. Theref ore the num ber ofpol ym ers

and the thi cknessboth i ncreaseproporti onalto the num berofl ayersn.The ti p di s-

placem entofa canti leverbeam due to an appl ied pressure i s (Shi gley and M ischke,

39

Figure 3. 14: A canti levered beam w i th an appl ied pressure w .

1989)

y =wl3

8E(bh3

12

) , (3. 3)

wherew i stheappl ied pressure,h i sthethi ckness,E i sthem odul usofel asti ci ty,and

is the l ength as shown i n Figure 3. 14. Theref ore i fboth w and h are proporti onal

to N L , y i s proporti onal to 1N 2

L. Thus wi th the i ncrease i n number of l ayers N L ,

theoreti cal ly the ti p di spl acem entorthe f reedi spl acem entwi lldecreaseproporti onal

to N 2L . W hen the l ayers are wel lattached to each other there i s hi gh interf aci al

fri cti on and they wi llact asa si ngle thi ck beam . In thi s case the f ree di spl acem ent

willbereduced.W hi le i fthei nter- faci alf ri cti on i sl ow,thepol ym ersaresl iding f reel y

on each otherand they wi llrem ai n acti ng assi ngl e pol ym ersbutwi th an i ncreased

force.Thepackaged pol ym erstacksareconsi dered tohavehi gheri nter- faci alf ri cti on;

m oreovertheexternalpackagewi llal so bl ock thei nternalm oti on ofthel ayer,l eadi ng

to m orebeam - like behavi or.

Asfortheunpackaged stackswhi ch weconsi derasl ow interf aci alf ri cti on stack,

weused Saranwrap asthei nsul ati on layer(whi ch i sal so responsi bleforthei nterf aci al

fri cti on in theparal lelstacks),whi ch i sasm oothm ateri alespeci al lywhenwet.Shown

in Figure 3. 15 i sthef reedi spl acem entstep responsef orunpackaged paral lelstacksof

1,2,3 and 4 pol ym er l ayers.Onecan noti ce thatthe vari ati on in free di spl acem ent,

which i sm easured at the peak rem ai ned withi n 10% .

40

Figure 3. 15: Step response f or unpackaged paral lelstacks

If one l ooks f urther i n Figure 3. 15, i t can be noti ced that the rel axati on

speed i s qui et di fferent. Though no defini te pattern coul d be noti ced,one can i nfer

that wi th the i ncrease ofnum ber of l ayers, the rel axati on i s getti ng sl ower. Thi s

is m ainly due to the i ncreased dam pi ng of the passi ve i nsul ati on m ateri aland the

pol ym ers them sel ves. As f or the naturalf requenci es,i t can be seen i n Figure 3. 16

thatthepeaksl ocati on changed onl y 26% ,i ndi cati ng thati n the i dealsi tuati on those

frequenci es woul d rem ai n constant. The first m ode l ies approxi m atel y between 19

and 26 Hz range f oral lthe stacks.

In thecaseofa packaged pol ym er,the i nter- faci alf orcesand thepackagi ng are

m aking the stack actasa uni t bl ock. Fi gure 3. 17 shows the uni t step response f or

thepackaged pol ym ers. Itcan beeasi ly noti ced thatthe f reedi spl acem entdecreased

as a f uncti on of the number of stacks. Fi gure 3. 18 shows the l arge vari ati on of

the naturalf requenci eswhich i ncreaseswi th the numberofl ayers,and reach sortof

saturati on.Thedi spl ayed data are f orthefirstthreenaturalf requenci es.Thosedata

are obtai ned f rom theFRF shown i n Figure 3. 19.

41

Figure 3. 16: Frequency response f uncti on f or unpackaged stacks paral lelstacks

Figure 3. 17: Step response f or packaged paral lelstacks

42

Figure 3. 18: N aturalf requency vari ati on ofpackaged stacks

3.5 T he Fi ni te E l em ent A nal ysi s m ethod

In thi ssecti on a Fi niteEl em entAnal ysi s (FEA)m ethod i sused to num eri cal ly si m -

ulate them echani calbehavi orofi oni c pol ym ers. The FEA anal ysi swillbe used to

expl ore,veri fy,and anal yze the i nterf aci alf ri cti on between l ayer stacks. FEA i s a

num eri calm ethod thatcan beused tom odeland si m ulateany physi calphenom enon

ofknown m athem ati calm odelappl ied to a system . Though we coul d have created

a m ore com pl icated m ul ti -physi cs (el ectro- m echanical )m odel ,i n ourcase the struc-

turalanal ysi s was suffi ci ent. In chapter 5 Newbury’ s m odelwi llbe m odi fied and

presented,thi sm odeli scapabl eofm odel ing theel ectrom echanci alcoupl ing forbeam

geom etri es. A l lthe FEA anal ysi swasdone usi ng the structuraltool box ofANSYS

6.0 sof twarepackage.ThePLANE82 2D i m ensional8- NodeStructuralSol id elem ent

wasused when a 2 di m ensionalanal ysi s i s requi red,whi ch i swhen anal yzi ng the i n-

terf aci alf ri cti on ofstacks.Anotherel em entwasused f orthe“2and ahal fdi m ension”

anal ysi swastheSHELL93el em entIti sshel lel em ent,thatcan beused tom odelthi n

3 dim ensionalobj ects.Asm enti oned i n the previ oussecti on,the pol ym eractuati on

coul d bem odeled asan i nternal ly generated pressure that i s tryi ng to overcom e the

sti ffnessofthem om enti n freedi spl acem entcase,and generati ng the ti p force,i n the

43

Figure 3. 19: T he f ree di spl acem ent f requency response f or packaged stacks

44

Figure 3. 20: T he 2D planar m odeloutput f or the f ree di spl acem ent step i nput

blocked f orce case. In the nextsecti on wewillveri fy thi sconceptby com pari ng the

experi m entalresul tswi th the num eri caldata outputoftheFEA.

3.5.1 Veri ficati on of the FEA m ethod

In orderto veri fy thi sm ethod,wecom pare theexperi m entalresul tsto thenum eri cal

sol uti on. The experi m entalresul tsare the f ree di spl acem ent,the bl ocked f orce,and

the natural f requenci es. W e al so m easure the m echani cal properti es of the i oni c

transducer. The densi ty used i s 3100kg/m 3, the Poi sson’ s rati o is assum ed to be

0.45,and theoveral li oni c pol ym erel asti ci ty i scom puted to beE = 260M pa.Asf or

the di m ensions,wem atch the data wi th si m ulati on for the 22mm * 5mm * 0. 5 mm

pol ym ers.In orderto veri fy theexperi m entalm odel ,weusethe2 di m ensionalpl anar

anal yzesshown i n Figure 3. 20.

The idea was to find the pressure that bends the pol ym er such that the ti p

free di spl acem entwoul d m atch the experi m entalresul t of1. 35 mm under appl yi ng

45

Figure 3. 21: T he 2D planar m odeloutput f or the bl ocked f orce step i nput

1.1V acrossi tsthi ckness.Thepressurewasf ound tobearound 8. 5Pa.Lateram odel

as the one shown i n Figure 3. 21 wasanal yzed wi th the ti p bl ocked,and a pressure

of8. 5 Pa appl ied on i t. The reacti on on the ti p was 0.33 m N,which i s withi n 6%

com pared to the0. 35 m N experi m entalresul t.

The next step i s veri fyi ng the shel l93 el em ent m odel . A m odelof i denti cal

dim ensions and m ateri alproperti es i s created usi ng the shel lel em ent as shown i n

figure 3. 22.Theanal ysi s i sdone to gi ve1. 353 mm freedi spl acem ent,and a bl ocked

forceof0. 346 m N.In thi ssecti on theFEA m ethod i sveri fied.

3.5.2 FEA sim ulati ons f or the paral lelstacks

In thi ssecti on an FEA sim ulati on ofthem ul ti layeri oni ctransducerswi llbedi scussed.

A lso the i nterf aci alf ri cti on in the stackswi llbe si m ulated and num eri calresul ts to

experi m entalwi llbe com pared. To si m ulate the extrem e cases ofno f ri cti on,and

no sl ip,the f ol lowing assum pti on wasm ade: For the no sl ip case (or hi gh fri cti on),

46

Figure 3. 22: T he 2D planar m odeloutput f or the bl ocked f orce step i nput

we can choose f rom two m ethods,the firstwasto “G l ue” thepol ym erstogetherand

appl y pressureon each pol ym er.“G l ue” i sa bui lti n comm and in ANSYS,thatwon’ t

al low m otion upon the gl ued nodes. A second m ethod,i s to i ncrease the thi ckness

of the pol ym ers such that i t i s equalto the stack thi ckness,and appl y the overal l

pressure (n*8. 5Pa)on thestack.Thi sm ethod i seasi ercom pared to thefirstm ethod

which i sm orephysi cal ly representati ve.Both m ethodsgavethesam eresul tsgavethe

sam e resul ts.Asf ortheno f ri cti on m odel,up ti llnow wewereonl y abl e to si m ulate

it f or the 2D m odel s,i n which we can onl y represent uni form ed rectangul ar stacks.

The barri er i n upgradi ng i t to the 3D m odel s,was the contact el em ents, i n which

ANSYS 6.0 onl y support l inearcontactel em ents,whi ch can notbe appl ied to areas

(Areasrepresentthecontactbetween the l ayersi n a 3D m odel,whi lea l ine represent

it i n a 2D m odel.). The m odelconsi sts ofdrawi ng the profil e ofthe 2D pol ym ers,

appl y contact el em entson the l ineswhere the l ayers i ntersect,and appl y the 8. 5Pa

pressure on each l ayer.

47

Figure 3. 23: T he experi m entaland FEA outputs f or packaged and unpackagedfree di spl acem ent step output as a f uncti on ofnum ber ofpol ym ers.

3.5.3 A nal ysi s of the i nterf aci alf ri cti on

Asm enti oned bef ore,the no f ri cti on case coul d onl y bem odeled usi ng the 2D pl ane

82 el em entm odel .M oreover the stackscoul d be i n 2 D ,si nce they are uni form and

rectangul ar. The two extrem e casesofno f ri cti on and no sl ip were si m ulated usi ng

the2D approach f or2 and 3 l ayers.Theresul tsf orthef reedi spl acem entFEA output

and the experi m entalresul ts are shown i n Figure 3. 23. It can be noti ced that the

experi m entalresul tsarei ncl uded withi n theextrem ecasesassi m ulated wi th theFEA

m ethod.

As previ ousl y m enti oned the i dealno sl ip and no f ri cti on cases can never be

reached,thus as expected the experi m entaldata waswi thi n the bounds ofthe nu-

m ericalanal ysi s. As f or the bl ocked f orce, the num eri caldata al so envel oped the

experi m entaldata as i tcan beseen i n Figure 3. 24.

48

Figure 3. 24: T he experi m entaland FEA outputs f or packaged and unpackagedblocked f orce step output as a f uncti on ofnum ber ofpol ym ers.

3.6 Sum m ary

In thi s chapter the stacki ng process was thoroughl y expl ained and characteri zed.

Firsttheseri esand paral lelstacki ng techni queswere i ntroduced and com pared.A l so

em phasized was the si m plici ty and rel iable use ofseri es stacki ng versus the better

perf orm ance of the paral lelstacki ng. A f ter the m anuf acturi ng process, the stacks

were characteri zed as actuators and sensors. As actuators the f orce i s am plified

proporti onalto thenumberofl ayersata constantvol tagef ortheparal lelstacks.The

sensorsensi ti vi ty al so i ncreasesproporti onalto the numberofstacksf or the paral lel

m ulti layer stacks. As f or seri es,the saturati on vol tage wi lli ncrease proporti onalto

the number of l ayers,whi le the f orce wi llrem ai n constant i f the stack vol tage was

not i ncreased. As sensors,seri es stacki ng im prove the sensi ti vi ty ofthe transducer.

Furthercharacteri zati on concl usi onswerem adeconcerni ng thef reedi spl acem ent,and

the resonance f requency, i n paral lelwi th the i nterf aci al f ri cti on between the stack

layers. Itwas shown that i fthe i nterf aci alf ri cti on waszero,the stack wi llact asa

si ngle layer,by conservi ng i tsl arge f reedi spl acem ent,and l ow resonance f requenci es.

49

W hilein casethef ri cti on wassohi gh thatthepol ym erscoul dn’ tm ovewi th respectto

each other,the f reedi spl acem entwi lldecreaseproporti onalto 1N 2

L,whi le thenatural

frequency wi ll i ncrease. Fi nal ly an FEA m ethod was expl ained,veri fied,and used

to num eri cal ly val idate the previ ous concl usi ons. In the FEA m ethod two types of

anal ysi swasexpl ored,oneusi ng thepl anar2D approach,whi ch i ssui tabl etosi m ulate

al ltypes ofprobl em s that coul d be si m ulated i n 2D (e. g. rectangul ar stacks. ) The

second wastheshel l3D m ethod,whi ch coul d beused to si m ulateany pol ym ersheet

shape,wi th the drawback ofbei ng abl e to si m ulate extrem e i nterf aci alf ri cti on cases

onl y.

50

C hapter 4

C om bined Sensor-A ctuator Stacks

4.1 Introducti on

The pri m ary purpose of thi s chapter i s to descri be and characteri ze the combi ned

sensor- actuator stack. Asm enti oned i n the i ntroducti on,i oni c pol ym ers show hys-

teresi sduri ng operati on and rel ax af tera step i nput. Researchersproved that those

probl em scoul d besol ved usi ng feedback control .Furtherm ore f eedback controladds

robustnessto theoperati on ofa system .These resul ts l ead usto thedevel opm entof

thecombi ned sensor- actuatorstackswhi ch havetheactuatorand thef eedback sensor

em bedded in it.In thebegi nningofthechapter,thecombi ned sensoractuatori scom -

pared to the sel f-sensi ng pi ezo actuator (sensuator). Next the f abri cati on techni que

with al li tsdi ffi cul ti eswillbeexpl ained,and a speci alf ocusabouttheel ectri calcon-

necti onsand i nsul ati on willbeprovi ded.The f eed- through i ssue i sexpl ored i n depth

in the l astsecti on.Theprobl em ischaracteri zed and di fferentsourcesare di scussed.

4.2 C om bined Sensor vs. Sel f-sensi ng A ctuator

Thesel f-sensi ng actuatorby defini ti on i sthesi m ultaneoussensor/actuator. In pi ezo-

electri c stacks the sensuator was i ni ti al ly devel oped by Dosch,Inm an,and Garci a.

Self-sensi ng actuatori stheuseofthesam epi ezo stack used asan actuatorand f eed-

back sensor.Theconceptofa sensuatorworksdue to theel ectrom echani calcoupl ing

51

M ateri alProperty Ioni cPolym ers Piezo PSI- 5A4E Ceram icPiezoel ectri c Strai n Coeffi ci entd 33 (m /V ) 1.5 ∗10 − 8 3.9 ∗10 − 10

D ielectri cPerm i ti vi ty η T33 (F/m ) 1∗10 − 2 1.6 ∗10 − 8

Elasti cCom pliance s E33 (m 2/N ) 3.3 ∗10 − 9 1.5 ∗10 − 11

k233 (N m /V 2F ) 6.8 ∗10 − 6 6.3 ∗10 − 1

Tabl e 4.1: M ateri al property com pari son betw een i oni c pol ym ers and pi ezoPSI-5A 4E ceram i c (N ew bury (2002) and P i ezo System s (2003))

ofpi ezoel ectri cm ateri al . For the sensuator to be effecti ve,the sensi ng si gnalshoul d

be in thesam eorderofm agni tudeorl argerthan theactuati on si gnal .The f ol lowing

is the chargeequati on in casea vol tage i sappl ied acrossthe stack:

q(s)

V (s)=

nη33A

t

(k233kp

m s2 + cs+ k+ k p+ (1− k 2

33)

)

(4. 1)

Theterm nη33At isthestressf reecapaci tance, k2

33kp

m s2+ cs+ k+ k pisthechargei nduced

due to m echani calm oti on,and (1− k 233) i s the charge due to the el ectri calexi tati on

(Leo course notes,2001). Theref ore the cri ti calterm f or the sensuator i s the k 233 =

d233

ηT33s

E33,whi ch i sdesi red to beasl argeaspossi ble(so thattheterm (1− k 2

33)i sassm al l

aspossi ble) . The term d 233 is the square ofthe pi ezoel ectri c charge constant,s E

33 is

theshortci rcui tm echani calcom pl iance,whi leηT33 isthestressf reecapaci tanceofthe

m ateri al .

Consideri ngtabl e4.1showsthatthek 233 coeffi ci entf orthepi ezoel ectri cm ateri al

is5 ordersofm agni tude l argerthan the coeffi ci ent f or i oni c pol ym ers.A l though the

piezoel ectri c strai n coeffi ci ent i s two orders ofm agni tude l arger f or i oni c pol ym ers

as com pared to pi ezoceram i cs, the el ectri c and m echani cal i m pedances are m uch

larger i n ioni c pol ym ers than i t i s i n piezoel ectri c m ateri als. The perm i tti vi ty of

ioni c pol ym ers i s si x order l arger than pi ezoceram i cs, and the com pl iance i s two

orders l arger. Theref ore the overal lval ue ofk 233 is very l ow in ioni c pol ym ers,such

that experi m ental ly there i s no sensi ble change between bl ocked and f ree boundary

condi ti ons (Newbury,2002). A concl usi on would be that the sensuator concept i s

practi cal ly im possible for the current i oni c pol ym erm ateri als;thi s i sanother reason

that l ed usto thedevel opm entofthe combi ned stacks.

52

4.3 A lternati ve configurati ons

W ith thei ncreasei n theneed ofaccuratedevi ces,f eedback controlbecam eanecessi ty

in al ltype ofactuators. Theref ore f eedback i s requi red f or the proper use of i oni c

pol ym ers as actuators. Severalresearchers, i ncl uding Curt Cothera i n CIM SS Lab

worked on usi ng the l aservi brom eterasa f eedback sensor(Kothera,2002).Newbury

devel oped a rotati ng m otorthati sactuated by f ouri oni cpol ym ersand the f eedback

wasdonevi aafif th i oni cpol ym erThi sdevi cewasdesi gned f orthepurposeofveri fyi ng

them odelhe proposed f or Ioni c pol ym ers. Them aj ordi fference between ourworks

isthecom pactness.Newbury’ sdevi ce i sm uch largerthan a stack f orthesam epower

and properti es. But the m aj or drawback ofthe combi ned stack i s the f eed- through

probl em which willbe expl ained and characteri zed thoroughl y i n a latersecti on.

4.4 Fabri cati on

Combined stackscan bem anuf actured i n di fferentconfigurati ons.Theconfigurati on

used i n m ostofthi sanal ysi si stheonesensorand twoactuatorsconnected i n paral lel

stack.Thi sconfigurati on can be j usti fied dependi ng on theappl icati on.Forexam pl e

if hi gh forces are requi red m ore actuati ng pol ym ers wi ll be added, whi le i fm ore

accuracy i srequi red,m oresensorsi n paral lelwi llbeadded.Oneaspectofthedesi gn

isthem echani calbehavi oroftheoveral lstack.Thesam eanal ysi sm adein Chapter2

forthei nterf aci alf ri cti on and theFEA m ethodssti llappl y with m i norchangeswhi ch

willbe descri bed i n the nextsecti on.Bef ore goi ng into the anal ysi softhe combi ned

stacks,wewi llfirstexpl ore theway i n which wem ade theel ectri calconnecti ons.

4.4.1 E lectri calconnecti ons

Each stack i sm anufactured separatel y asdescri bed i n theprevi oussecti onsofparal lel

stack m anuf acturi ng. Forboth the sensorsand the actuatorswe are onl y i nterested

in paral lelconnecti ons f or the to combi ned stacks. Seri es stacki ng can never be an

advantagef orpackaged actuatorstacksbecauseseri esstacksrequi rehi ghervol tagesto

53

Figure 4. 1: A 3D C A D draw ing representi ng the com bi ned stack.

operate.H i ghervol tagesi nduceel ectrol ysi sand resul t i n thedryi ng ofthepol ym ers.

W ith regardsto thesensi ngm echani sm ,asl ong asweareusi ng thecurrentam pl ifier

ci rcui t i t i snotadvantageousto stack thepol ym ersi n seri es.(Ref erto chapter3 f or

furtheri nform ati on on thi ssubj ect).A f terbui lding thesensorstack and theactuator

stack,the el ectri c connecti onsare suppl ied independentl y to the two stacks. In our

caseweonl y needed to suppl y connecti onsto thesensor,si nce theactuatorstack has

been suppl ied f rom the l eadson the testfixture supportbase.

Each stack i s then separatel y i nsul ated and l ayered on top ofeach otherm e-

chani cal ly asshown i n Figure 4. 1. In thi sfigure i sshown the configurati on we fabri -

cated f ortheexperi m entalanal ysi s,wherethepowerto theactuatorstack i sprovi ded

vi a the support l eads.

Anotheri m portanti ssueused to i m prove theperf orm ance i stheuseofa com -

m on ground f orthesensorand actuatorel em ents.Thi si saccom pl ished by connecti ng

the si des f aci ng each otherbetween the sensorstack and actuatorstack asshown i n

54

Figure 4. 2: Schem ati c draw i ng show i ng the el ectri c connecti ons of the com -bined stack

the schem ati c i n Figure 4. 2. Thi s i s im portant because we are usi ng a current am -

pl ifier f or the sensor,and the current am pl ifier f orces the sensor to be ground (the

current am pl ifier i s al so known as short ci rcui t m easuri ng techni que). Thus i f the

sensor i s forced to zero,whi le on the othersi de acrossthe i nsul ati on,there i sa hi gh

appl ied vol tage (i n order to actuate the stack a sm al lcurrentwi llbe i nduced. Thi s

current wi lldi sturb the f eedback si gnal ,and contri bute to the noi se,whi ch i s the

feed- through si gnal s. A l though we are usi ng insul ati ng m ateri als which m akes thi s

resi stancevery hi gh,butthi sm ateri ali svery thi n in orderf ori tto preserve the l arge

displ acem ent. Furtherm ore the currentgenerated by the sensor i svery sm al l,i n the

orderµAm ps,thusany noi se i n thecurrentsi gnalwi llbesi gni ficantand coul d resul t

in a lossofsensi ng capabi lity

55

4.4.2 M echani calproperti es and the FEA m ethod

Accordi ng to Newbury (2002), i oni c pol ym ers doesn’ t change there m echani calor

electri cali m pedancesasa f uncti on ofboundary condi ti ons. Theref ore f rom them e-

chani calstructuralperspecti ve there i sno di fferencebetween a sensororan actuator.

Thus combi ned stacks are treated m echani cal ly as seri es and paral lel transducers,

with two sl ightdi fferences. The firstdi fference i s the f act thatnotal lpol ym ersare

actuators,theref ore the l arge di spl acem entofthe si ngl e actuator can never be con-

served i n the combi ned stack because the sensor’ s sti ffnesswi llact asan extra l oad

on the actuators. M oreover i t i s very di ffi cul t to achi eve the zero i nterf aci alf ri cti on

casebecause the stackshave to bepackaged.

AsfortheFEA m ethod,theonl ychangei n theanal ysi swould occuri n appl yi ng

thepressure f orceon theactuatorpol ym ersonl y.Furtherm ore i ti sbesttom odelthe

stacksaszero sl ip between the l ayers.

4.5 C haracteri zati on of the com bi ned stacks

Combined stacksarecharacteri zed experi m ental ly by appl yi ng a potenti alacrossthe

actuatorstack si m ilarto seri esorparal lelm ul ti layerstacks.W hi le thesensori scon-

nected to thecurrentam pl ifierusi ng i tsown el ectrodes.Forcharacteri zati on purposes

the actuator stack i s som eti m es turned off and an externalm echani caldef orm ati on

is appl ied usi ng the shaker. Thi s i s done i n order to obtai n the FRF ofthe sensor

withoutany possi bi lity ofhavi ng feed- through.

Figure 4. 3 showsa com pari son f ora sensorcharacteri zed usi ng the two m eth-

ods. It i sevi dent that there i ssom edi fference i n the response,especi al ly i n the l ow

frequency range.Thi scoul d beassoci ated wi th theway thepol ym eri sm echani cal ly

actuated i n thedi fferentcom bi nati ons. In theshakerthepol ym eri sactuated on the

ti p while in the combi ned stack the actuati ng pol ym er i s appl yi ng the f orce. The

di fference theappl ied loadsf or the two casescoul d account f orthedi fferencesi n the

m easured sensi ng response.

Thecombined stacksaretobeused i n feedback control ,thusi n thi ssecti on the

56

Figure 4. 3: T w o FR F functi on f or the sam e stack,one sensed w i th a pol ym ersensor and the other w i th l aser vi brom eter.

57

Figure 4. 4: T he experi m entaland m odeltransf er f uncti ons of the actuator.

experi m entalFRFs (or transf er f uncti ons) ofthe combi ned stackswi llbe di spl ayed

and fitted wi th a Lapl acedom ain m odel.

A lso theLapl acedom ain transf erf uncti on wascom puted usi ng the “i nvf reqs”

M atl ab comm and,f or both the sensor and the actuator. The transf er f uncti on for

the actuator i s

G (s)=0.001589s 4 + 0.07389s 3 − 1.964∗10 5s2 + 7.753∗10 8s+ 4. 946∗10 13

s4 + 2205s 3 + 1.032∗10 8s2 + 4.313∗10 10s+ 4. 96∗10 14,

and the f requency responsepl otwi th the experi m entaldata i sshown i n Figure4. 4.

Asfor the sensor,the Lapl acedom ain transf er f uncti on i s

H (s)=− 0.53s3 − 327.4s2 − 3.054∗10 5s+ 2. 817∗10 6

s4 + 571.8s3 + 2.346∗10 5s2 + 2.238∗10 7s− 2. 238∗10 5,

and the f requency responsepl ot i sshown i n Figure4. 5.

58

Figure 4. 5: T he experi m entaland m odeltransf er f uncti ons of the sensor.

4.6 Feed-through

Feed- through i sdefinedasthepartofthesensed si gnal(f eedback)di rectl y transm i tted

from the i nput si gnal . If l arge enough, the f eed- through si gnalwi lldom i nate the

feedback si gnal ; i t coul d be as hundreds i fnot thousand ti m es the f eedback si gnal

and i twi lli m m ediatel y saturate the am pl ifierci rcui t.

A com pari son between a cl ean si gnaland a si gnalwi th f eed through i sshown

in Figure4. 6.Ithasdi fferentsources,whi ch can beputi n threem ai n categori es.The

m osti m portanti sthedi rectf eed- through thewater,orwatervaporexi sti ng between

the sensor, and the actuator stacks, the second i s the f eed- through the i nsul ati on

film between thesensorand actuatorstacks.Thosem enti oned f eed- through areboth

resi sti ve i n nature,whi le the thi rd type i s m agneti c, whi ch i s due to the current

flowing i n the actuati ng pol ym er ci rcui try. M agneti c feed- through i s i nsi gni ficant;

theref orewebel ieve thatwater transport i s the pri m ary causeoff eedthrough.

59

Figure 4. 6: T he FR F ofdi fferent com bi ned stacks,one w i th f eed through andthe other w i thout.

60

Figure 4. 7: Schem ati c draw i ng show i ng the f eed through betw een the sensorand the actuator

4.6.1 Insul ati on

Them ain two sourcesoff eed- through are thewaterand the i nsul ati on fil m between

the stacks. To start wi th the easy probl em ofthe i nsul ati on fil m ,asm enti oned i n

secti on 1.4.1,m ost of thi s probl em was solved by f orci ng the actuator l ayer f aci ng

the sensor stack to ground,and appl yi ng the posi ti ve and negati ve vol tages on the

si de. Thi s techni que was abl e to sol ve m ost of the probl em ,and m ade thi s feed-

through i nsi gni ficant.Nonethel esssom esm al lvol tageswi llsti llappearon the ti p of

thepol ym er,si ncetheground i sappl ied on thebaseofthepol ym er,and thepol ym er

surf acehasafini teval ueresi stance.Thusoncecan sti llfind som eposi ti veornegati ve

sm allvol tageson the ti p.Butagai n thosevol tagesarevery sm al l,and the resi stance

val ueofthe i nsul ati on i svery l arge,theref orewedon’ thave to worry aboutthi svery

m uch.

The second source off eed- through i s the water between the stacks as shown

in Figure 4. 7 . As previ ousl y m enti oned i t i s the m ai n source off eed- through,and

the m ost di ffi cul t to dealwi th. For proper operati on, i oni c pol ym ers need to be

wellhydrated,theref ore water shoul d exi sts al laround the stack. W ater i s a good

conductorofel ectri ci ty,even i n the f orm ofm oi sture.Thuswateri nsul ati on between

thestacksi sveryessenti al .M oreoverthepol ym ercom bi ned stacksshoul d bedesi gned

to sustai n higherf requenci es,whi ch m akeseasi erf orwaterto flow around the stack,

especi al ly at the ti p. The pressure bui ld-up at the ti p ofthe stackswas rem arkabl e

61

duri ng the operati on of f requenci es i n the order of50Hz and above. To concl ude

insul ati on between the two stacks i s very essenti al ,especi al ly the i nsul ati on agai nst

hum idity i s a very cri ti cali ssue. As f or the el ectri c i nsul ati on, i t becam e a m i nor

probl em since i t was resol ved by the use ofthe comm on ground techni que. In the

nextsecti on the f eed- through wi llbe characteri zed so that i t can be betterdetected

and resol ved.

4.6.2 C haracteri zati on of f eed-through

The m ain sources of f eed- through are the water f eed- through, and the i nsul ati on

resi stance f eed- through. They are both resi sti ve l oads i n nature,thus the si gnali s

directl y fed through the sensorstack wi thoutany del ay (phase shi ft).Asm enti oned

in secti on 2.3.1 the i oni c pol ym er connected to the current am pl ifier ci rcui t f orm s

a low passRC fil ter. Thi s i swhy i t i s expected to see the f eed- through as a l inear

si gnali m puted to a l ow passfil terasshown i n Figure 4. 6 . The f eed through si gnal

in Figure 4. 6 was obtai ned by creati ng a sm allbreak i n the i nsul ati on between the

stacks,and com puti ng theFRF.

4.7 Sum m ary

In thi schapterthecombi ned stackswerethoroughl yexpl ored and characteri zed.Fi rst

they were com pared to the sensuatorconcept,and there potenti alappl icati onswere

expl ored. Next the f abri cati on techni queswere expl ained,and the combi ned stack

wascharacteri zed.In thefinalsecti on an em phasi son the f eed- through probl em was

highl ighted. A concl usi on ofthi s chapter woul d be to poi nt the i m portance ofthe

combined stacks,and thei rabi lity tom any probl em srel ated to i oni cpol ym ers.Thei r

m ajor drawback i s the f eed- through probl em which requi res extra care duri ng the

fabri cati on process,and need to begi ven attenti on i fthi sprocessi sto beautom ated.

As in the concl usi on ofthe previ ouschapter,the combi ned stacks f abri cati on needs

to bem oved to them i cro l eveli n orderto be very effecti ve and usef ul.

62

C hapter 5

M odeling m ulti layer stacks

5.1 Introducti on

In thi schapterthem odeldevel oped byNewbury and Leo (2002)i sextended so thati t

isabl e tom odelm ul ti layerpol ym erstacks.Fordesi gn and characteri zati on purposes

m ulti layered i oni cpol ym ersarefitted to am athem ati calm odelthati sabl eto predi ct

thei r perf orm ance. Asm enti oned i n Chapter1,there are severalm odel s that coul d

be used f or i oni c pol ym ers. For com pl eteness and practi cal ity purposesNewbury’ s

em piri calm odelwasused.Them ai n advantagesofthi sm odelare thati t i saccurate

and easy to useand i tal so consi dersboth theactuati on and sensi ng characteri sti csof

ioni cpol ym ers.In thefirstsecti on,a bri efovervi ew ofthem odeli spresented.In the

second secti on,them athem ati calm odeli sm odified tofitthem ul ti layerstacks.W hi le

the thi rd secti on,the experi m entalresul tsare used to obtai n them odelparam eters.

Final ly a chaptersumm ary i sprovi ded.

5.2 M odelO vervi ew

Newbury’ s m odel i s devel oped to be used i n m odeling si ngle layer i oni c pol ym ers

with canti leverboundary condi ti on. Bei ng a scal able to the pol ym ergeom etry,thi s

m odelwasm adeeasy to beadj usted to si m ulate them ul ti layerstacks. In thi sm odel

63

ioni c pol ym ers are presented wi th an equi val ent i dealtransf orm er ci rcui t m odelIt

also assum es that the el ectri caland m echani caldom ai nsare l inearl y coupl ed. Thus

the consti tuti ve rel ati onsconsi stoftwo l inearl y i ndependentsymm etri c equati ons,

v

f

=

a11 a12

a12 a22

i

u

(5. 1)

W here v i s the vol tage across the pol ym er thi ckness and f i s the f orce at the ti p.

As for i i s the current across the pol ym er’ s thi ckness,and ˙ u is the vel oci ty at the

ti p. The coeffi ci ents a 11,a 12,and a 22 are f uncti ons ofthe m ateri alparam eters and

bender geom etry. Bef ore expl aining those param eters,i t i s im portant to note that

equati on 5.1 issi m ilar to the pi ezoel ectri c consti tuti ve equati ons,theref ore a si m ilar

approach i sadopted to determ i ne the coeffi ci ents. Thi sapproach consi stsofsetti ng

som eparam etersto zero i n com pute therem ai ning param eters.Obtai ning them odel

param eterswi llbeexpl ained i n a latersecti on,butsetti ng oneparam eterto zero and

consi deri ng the equati on enabl es us to easi ly i denti fy the coeffi ci ent. To start wi th

a11 coeffi ci ent,setti ng u = 0 reducestheupperpartofequati on 5.1 to

v = a11i , (5. 2)

which reducesa 11 to theel ectri cali m pedanceofthem ateri al .Si m ilarl y,setti ng i= 0

reducesthe l owerpartofequati on 5.1 to

f = a 22u. (5. 3)

The term a 12 is theel ectro- m echanicalcoupl ing term whi ch rel atesthedi spl acem ent

to the actuati on vol tage,and the current generated due to the appl ied m echani cal

force or stress. Now reconsi deri ng the i deal transf orm er equi val ent ci rcui t m odel

shown i n Figure ?? and usi ng any basi c ci rcui t anal ysi s techni que willresul t i n the

fol lowing resul ts f or the coeffi ci entsused i n equati on 5.1,

v

f

=

Rdc (N 2Zm 1+ Zp)Rdc+ N 2Zm 1+ Zp

N RdcZm 1

Rdc+ N 2Zm 1+ Zp

N RdcZm 1

Rdc+ N 2Zm 1+ Zp

(Z m 1+ Zm 2)(R dc+ Zp)+ N 2Zm 1Zm 2

Rdc+ N 2Zm 1+ Zp

i

u

(5. 4)

64

Figure 5. 1: T he geom erti c param eters of the stack.

The last step i n them odeldevel opm ent i sdeterm i ning the el ectrom echani cal

term s i n equati on 5.4,whi ch are the sam e vari ables i n Figure ??. Thi s i sdi scussed

in the nextsecti on with them odi ficati on im plem ented to i ncorporate them ul ti layer

ioni c pol ym ers.

5.3 D escri bing and M odi fyi ng the E l ectrom echan-

icalTerm s f or M ul ti layer Stacks

The fol lowing term sare to be devel oped and m odi fied to extend them odelto m ul -

ti layer stacks: the m echani calterm sZ m 1 and Z m 2,the el ectri calterm sR dc and Z p,

and theel ectrom echani calcoupl ing term N .Them odi ficati on willbeestabl ished f or

thedi fferentstacki ng cases.Thefirstvari ablewould be the typeofel ectri calconnec-

ti ons;the opti onsare paral leland seri esconnecti ons. The second vari able would be

the i nterf aci alboundary condi ti on;the first case woul d be no sl ip,whi le the second

would beno f ri cti on.

5.3.1 T he E lectri calTerm s

The el ectri cali m pedance i sdescri bed by the two term s,R dc and Z p. The first term

Rdc is theDC resi stancedefined i n the f ol lowing equati on

Rdc =ρdct

L tw, (5. 5)

65

whereρ dc istheresi sti vi tyofthepol ym er,whi letheotherparam etersarethegeom etry

ofthe pol ym er as defined i n Figure 5. 1. As f orm odi fyi ng thi s term to account f or

m ulti layerstacks,i t’ sgood to note that them echani calboundary condi ti on doesn’ t

have any si gni ficant effect on the el ectri cal term s (Newbury,2002), thus the onl y

vari able to be consi dered woul d be the type ofel ectri calconnecti ons. The term R dc

is theDC resi stanceofthem ateri al ,and resi storsadd i n seri eswhi le in paral leli t i s

the i nverse ofthe sum ofthe i nverse.Therf ore the resul ti ng equati on forR dc in case

ofN l (Thi si sdefined asN l to avoi d conf usi on with N thenumberofturnsi n thecoi l)

pol ym ersconnected i n seri es i s

Rdc =Nlρdct

L tw. (5. 6)

In case they are connected i n paral lelthe equati on i s

Rdc =ρdct

NlL tw. (5. 7)

AsforZ p theequati on forsi nglelayerpol ym eri sobtai ned f orm Newbury’ sdi ssertati on

to be

Zp =t

sL tw

1∑ n

i= 1ε i

1+ sε i ρi

(5. 8)

where n,ε i ,and ρ i ,are to bedeterm i ned num eri cal ly f rom experi m entaldata.Si nce

thi s i sanother f orm ofel ectri cali m pedance the sam e rul esas i n Rdc case.Theref ore

theequati on for the paral lelel ectri calconnecti onsbecom es:

Zp =1

Nl

t

sL tw

1∑ n

i= 1ε i

1+ sε i ρi

(5. 9)

asf orseri es i t i s :

Zp = Nlt

sL tw

1∑ n

i= 1ε i

1+ sε i ρi

(5. 10)

5.3.2 T he M echani calTerm s

The m echani cal term s consi st of Z m 1 and Z m 2, and the stacki ng param eters that

affects those term s are the m echani calboundary condi ti ons that are a f uncti on of

66

the i nter- faci al f ri cti on. As f or the el ectri cal connecti ons, theoreti cal ly i t has no

si gni ficant effect,but practi cal ly due to the addi ti on ofnon- acti ve i nsul ati on layers

and the el ectri call eads added to the paral lelstack i t woul d change the m echani cal

term s. For the si ngle layer pol ym er,the m echani calsti ffness i s represented by Z m 1

is com puted usi ng Euler- Bernoul libeam m odel . Accordi ng to Newbury (2002) the

Lapl acedom ain representati on i s

Zm 1=1

s

Ywt3

4L 3d

, (5. 11)

where

Y = Y∞

(

1+ αs2 + 2ξω

s2 + 2ξωs+ ω2

)

(5. 12)

and α,ξ,and ˆ ω are the f requency dependentparam eters,com puted f rom theGHM

m odel(Newbury,2002). On the other hand the equati on for Z m 2 which represents

the i nerti a ofthe pol ym er,i scom puted accordi ng to the f ol lowing

Zm 2= s3L 4

free ρmwt

L3dΓ

4(5. 13)

where ρ m is the densi ty ofthe pol ym erand Γ i s the sol uti on ofthe Eul er- Bernoul li

Beam characteri sti cequati on.Forthefirstm odei n acl am ped freeboundarycondi ti on

the val ue i s 1.875. To m odi fy the m echani cal term s to i ncorporate the m ul ti layer

stacks, start wi th the si m plest case of seri es el ectri cal connecti ons wi th zero sl ip

m echanicalboundary condi ti ons. In thi s case the stack wi llbe treated as a si ngle

pol ym erwi th a thi cknessproporti onalto the numberofl ayers

tstack = Nl ∗ t (5. 14)

.and theref ore them echani calterm swi llbewri tten asf ol lows:

Zm 1=N 3

l

s

Ywt3

4L 3d

(5. 15)

and

Zm 2= sN l

3L 4free ρmwt

L3dΓ

4(5. 16)

67

In case ofzero i nterf aci alf ri cti on,the pol ym erswi llactasspri ngsstacked i n

paral lel ,whi ch the overal lval ue i s the addi ti on ofthe si ngl e ones. The m echani cal

term sare descri bed asf ol lows:

Zm 1=Nl

s

Ywt3

4L 3d

(5. 17)

and

Zm 2= sN l

3L 4free ρmwt

L3dΓ

4(5. 18)

As for the el ectri calvari ables,the probl em swould bewith the paral lelstack,

wheresom ei nsul ati on m ateri ali sadded between thepol ym ers,asdi scussed i n Chap-

ter 2. Thi s i nsul ati on i s a non- acti ve l ayer that woul d increase the sti ffness ofthe

stack and coul d bem odeled as the pol ym ers them sel ves.But f orourpurpose,those

sti ffnessare rel ati vel y sm alland coul d be negl ected. Anotherm i nor probl em is the

electri call eadswhi ch hasa fini te thi ckness.Butthose l eadsareusual ly pl aced i n the

cl am ped part of the stack; theref ore thei r effect under such ci rcum stances i s to be

negl ected.

5.3.3 T he E lectrom echani calTerm

The term whi ch represents the el ectrom echani calcoupl ing in the m odel i s N , the

num berofturnsofthe transf orm er.The turnsrati o N isal lowed to bea f uncti on of

frequency. In them odeldefined by Newbury:

N =

(v

f

) i

=3dL 2

d

ηTL twt(5. 19)

In order to obtai n the equati on for both the m ul ti layer stacks,we have to

assum e thateach si ngle layerpol ym erhasa constant

N = Ns =

(v1f 1

) i

=

(v2f 2

) i

= ...=

(vNl

f N l

) i

= constant (5. 20)

68

Asm enti oned bef ore,al lthestacksdi scussed i n thi sthesi sarel ayered m echan-

ical ly i n paral lel ,l eadi ng to aconstantvel oci ty accrossthel ayers.In orderto si m plify

theprobl em N ism ulti pl ied by thesti ffness(fu

) ito transf orm the f orce i nto vel oci ty

N ∗

(f

u

) i

=

(v

f

) i

∗

(f

u

) i

=( v

u

) i

, (5. 21)

Accordi ng to Newbury(fu

) i= Zm 1+ Zm 2,whi ch reducesthenum berofturns

to

N =( v

u

) i 1

Zm 1+ Zm 2, (5. 22)

In order to devel ope N foral lofthe f ourboundary condi ti ons,firstwe start

with the no f ri cti on interf aci alcondi ti on. Accordi ng to equati ons5. 17 and 5. 18,the

term Z m 1+ Zm 2willscal eprorti onaltoN L .Consi deri ng theel ectri calconnecti ons,f or

seri estheoveral lvol tageofthestack i stheaddi ti on ofthesi ngle layersv total = NL v.

W hile in paral lelconnecti on the overal lvol tage ofthe stack equal s the si ngle layer

vol tage v total = v.Substi tuti ng back i nto equati on 5.22 weobtai n the f ol lowing:

No fri cti on:

Seri es:

N =( v

u

) i 1

Zm 1+ Zm 2= Ns (5. 23)

Paral lel :

N =( v

u

) i 1

NL (Z m 1+ Zm 2)=

Ns

NL(5. 24)

Thenosl ip boundary condi ti on i streated onl y forthel ow frequency casewhere

Zm 2<< Zm 1and tobenegl ected.In thi scasetheterm Z m 1+ Zm 2willscal eprorti onal

to N 3L . As f or the el ectri calboundary condi ti on,the anal ysi sused i n the no f ri cti on

case i ssti llval id.Theref oreN wi llbe scal ed accordi ng to the f ol lowing:

No Slip:

69

Seri es:

N =( v

u

) i 1

N 2L (Z m 1+ Zm 2)

=Ns

N 2L

(5. 25)

Paral lel :

N =( v

u

) i 1

N 3L (Z m 1+ Zm 2)

=Ns

N 3L

(5. 26)

5.4 M odified Input-O utputR el ati onshi ps f orM ul -

ti layer Transducers.

Beforeexpl ori ng the resul ts,firsttheessenti algoverni ng equati onswi llbedevel oped

forthe f ourdi fferentboundary condi ti ons.Them odelused i n thi scom pari son i sthe

sim plified m odel ,wheretheterm sN 2Zm 1<< Zp forthebl ocked boundary condi ti on,

and the term N 2 Zm 1Zm 2Zm 1+ Zm 2

< < Zp for the f ree boundary condi ti onsare negl ected.

5.4.1 Im pedances

The el ectri cali m pedancewillbe reduced to vi = RdcZp

Rdc+ Zp,and them odi ficati onscom -

pared to the si ngl e layers:

Seri es:

v

i=

NLRdcNLZp

NLRdc + NLZp= NL

RdcZp

Rdc + Zp(5. 27)

Paral lel :

v

i=

RdcNL

Zp

NL

RdcNL

+ Zp

NL

=1

NL

RdcZp

Rdc + Zp(5. 28)

Accordi ng to Newbury the open- ci rcui t m echani cali m pedance i s reduced to

the f ol lowing fu = Zm 1+ Zm 2.W hile them odi ficati onsf ortheno f ri cti on and no sl ip

interf aci alboundary condi ti on are:

No fri cti on:

f

u= NLZm 1+ NLZm 2= NL (Z m 1+ Zm 2) (5. 29)

70

No Slip:

f

u= N 3

LZm 1+ NLZm 2≈ N 3L (Z m 1+ Zm 2) (5. 30)

Thisapproxi ati on i sm ade consi deri ng low frequency rangewhereZ m 2<< Zm 1.

5.4.2 A ctuator Equati ons

Thesi m plified bl ocked f orce i sdefined as(fv

) u= N Zm 1

Zpand them odi ficati onsf orthe

fourboundary condi ti onsare:

No fri cti on:

Seri es:

f

v=

N NLZm 1

NLZp=

N Zm 1

Zp(5. 31)

Paral lel :

f

v=

NNL

NLZm 1

1NL

Zp= NL

N Zm 1

Zp(5. 32)

No Slip:

Seri es:

f

v=

NN 2

LN 3

LZm 1

NLZp=

N Zm 1

Zp(5. 33)

Paral lel :

f

v=

NN 3

LN 3

LZm 1

1NL

Zp= NL

N Zm 1

Zp(5. 34)

This im pliesthat i n seri esthebl ocked f orcewi llrem ai n constantf orthesam e

appl ied vol tage,whi le in paral leli t wi llscal e proporti onalto the number ofl ayers.

Thesi m plified m odelf orthe f reedi spl acem enti s uv = − N

sZ pand scal eswith thenum ber

ofl ayersN L asf ol lows:

No fri cti on:

71

Seri es:

u

v=

−N

NLsZ p=

1

NL

−N

sZ p(5. 35)

Paral lel :

u

v=

− NNL

1NL

sZ p=

−N

sZ p(5. 36)

No Slip:

Seri es:

u

v=

− NN 2

L

NL sZ p=

1

N 3L

−N

sZ p(5. 37)

Paral lel :

u

v=

− NN 3

LN 3

LZm 1

1NL

sZ p=

1

N 2L

−N

sZ p(5. 38)

Those equati ons shows how the no sl ip boundary condi ti on can reduce the l arge

deflecti on ofthepol ym er,whi le theno f ri cti on and paral lelel ectri calconnecti on was

able to preserve l argedeflecti ons.

5.4.3 Sensor Equati ons

In Newbury’ sm odelthesensorequati onsaresi m plified to iv = − N Zm 1

Z p which i sequal

to the bl ocked f orce − fv butopposi te si gn.Thi sconcept i s the reci proci ty presented

by Newbury,and i t sti llhol ds i n m ulti layered i oni c transducers. The sensi ti vi ty iv

behaves the sam eas the bl ocked f orce i fone f ol lows the sam e anal ysi s i n subsecti on

5.4.2,thus i t i ncreases proporti onalto the number of l ayers wi th paral lelstacki ng,

while rem ai n constant f orseri esstacki ng.A l lthose equati onsare com pared to som e

experi m entalresul ts i n the nextsecti on,and agreem entcoul d benoti ced.

72

Figure 5. 2: E lectri cal i m pedance m odelpredi cti on versus experi m entaldata

Figure 5. 3: Sensi ti vi ty m odelpredi cti on versus experi m entaldata

Figure 5. 4: B locked f orce m odelpredi cti on versus experi m entaldata

73

Figure 5. 5: M echani cal i m pedance m odelpredi cti on versus experi m entaldata

5.5 C om pari son ofM odelw i th Experi m entalR e-

sul ts

Them odelwascom pared and val idated wi th experi m entalresul ts.Thef ourterm sare

the i m pedance,them odul us,theel ectrom echani calcoupl ing term assensor,and the

electrom echani calterm as an actuator. The f our transf er f uncti ons are shown wi th

com pari son to them odelfitti ng in Figures5. 2,5. 3,5. 4,and 5. 5.Forthe i m pedance,

the si ngle layer i s com pared to a 2 l ayer stack i n seri es, where the m odel scal ed

by bei ng m ulti pl ied by 2, and i t i s noti ced that the m odelscal ed accuratel y (see

Figure 5. 2). On the other hand i t was com pared to a 2 l ayer paral lelstack, and

them odelwasscal ed by 1/2. As i t coul d be noti ced f rom Figure 5. 2,thi s ti m e the

m odeldi dn’ t scal e accuratel y (i t was 18% off), and the error i s attri buted to the

resi stance i n the el ectri c connecti ons. As f or the sensi ng them odelf airl y scal ed the

data,whi ch wasagai n com pared to a 2 l ayerseri esstack,and a 2 l ayerparal lelstack

asshown i n Figure 5. 3. The data f or the seri esconfigurati on i ssupposed to overl ap

the si ngle layer but was sl ightl y off,especi al ly at hi gh f requenci es. Thi s i s due to

the l ow-passfil tereffectassoci ated wi th thecurrentsensi ng ci rcui t.Thi sassum pti on

is furtherval idated when l ooki ng at the paral lelstack,whi ch exhi bits f aster rol lover

due to the i ncrease i n capaci tance. The bl ocked f orce was com pared to 2,3,and 4

74

layersparal lelstacks,and them odelvery accuratel y predi cted thei ncreasei n blocked

force asa f uncti on ofthe numberofl ayersas i tcoul d be seen i n Figure 5. 4.Fi nal ly

them odul ussi ngle layerpol ym erwascom pared to 2 l ayerswi th di fferentm echani cal

boundary condi ti ons and shown i n Figure 5. 5. The first boundary condi ti on ofno

fri cti on,whi ch i ssupposed to scal e by a f actorof2,wasacceptabl y accurate.W hi le

the no sl ip boundary condi ti on,whi ch i s supposed to scal e by a f actor of2 3 = 8,

didn’ tfitwel l.Thi sm ightbedue to theaddi ti onalsti ffnessofthedoubl e tapeadded

to achi eve theboundary condi ti on ofnow sl ip.

5.6 Sum m ary

In thi s chapter Newbury’ s m odelwasm odi fied to accom odate the m ul ti layer i oni c

transducers. Fi rst the two port equi val ent transf orm er ci rcui t m odelwas bri efly

introduced. Than the m odelwas m odi fied on f our di fferent boundary condi ti ons,

two el ectri calseri es and paral lel connecti ons, and two m echani calno f ri cti on and

no sl ip interf aci alboundary condi ti on. The paral leland seri es el ectri calconnecti on

affected the two el ectri cali m pedance term s:R D C and Z P ,and thecoupl ing term N .

RD C and Z P both i ncreased proporti onalto thenumberofl ayersi n seri esconnecti on,

and decreased i nversel y proporti onalto the num berofl ayers i n paral lelconnecti on.

The el ectrom echani calterm i sm odified by al lthe f ourboundary condi ti on. The no

fri cti on and seri esN rem ai ned equalto that ofa si ngl e layer,whi le the no f ri cti on

and paral lelN i s di vi ded by the numberofl ayers. The no sl ip boundary condi ti on

was treated f or the l ow frequency range,and scal ed N by di vi ding i t by the square

ofthe numberofl ayers f or the seri esconnecti on,and the the cube ofthe numberof

layers f or the paral lelconnecti on. In the nextsecti on the i nputoutput rel ati onshi ps

forthem ul ti layertransducerswerepresented.Thescal ing in them odelm atched the

anal ysi sprovi ded i n Chapter3 f rom theexperi m entalresutl s.Thebl ocked f orceand

the sensi ti vi ty i ncreased proporti onalto the numberofl ayers i n paral lelconnecti on,

while rem ai ned constant f or seri es. The no f ri cti on boundary condi ti on al so proved

to preserve the l arge deflecti on,whi le the no sl ip boundary condi ti on decreased the

75

free di spl acem ent by the cube ofthe number ofl ayers f or seri es and the square f or

paral lel . In the l ast secti on the m odelwas com pared to experi m ental resul ts. In

the l ow frequency range the m atchi ng was very good but i t deteri orated at hi gher

frequenci esf or the sensi ng testdue to the change i n capaci tanceofthe transducer.

76

C hapter 6

M icro A i r Vehi cl e

6.1 Introducti on

Finiteel em entsi m ulati onson thepackaged and unpackaged stacksi llustrate thatwe

can accuratel y m odelthem echani calresponseofthe transducers.Thi schapterdeal s

with thedesi gn ofaflappi ngm echani sm using ioni cpol ym erm ateri als.Ioni cpol ym ers

aredesi gned to operateand fly aM i croA i rVehi cl e(M AV).In thenextsecti on weare

going to propose two wi ng desi gns.Thosedesi gnsaresi m ulated usi ng theprevi ousl y

illustrated FEA m ethod. In the next subsecti on the m echani calrequi rem ents that

the i oni cpol ym erhastom eeti n orderto fly theM AV,whi ch areobtai ned f rom W ei

Shyy etal .(1999)arei llustrated.Fi nal ly asumm ary ofthi sshortchapteri sprovi ded.

6.2 A ppl icati on: M AV

M icroA i rVehi cl es(M AV)hasseveralappl icati onsi n thearea ofm i litary and ci vi lian

autonom ous survei llance. In m i litary appl icati ons i t coul d be used f or short range

spyi ng or ammuni ti on gui ding functi ons. Due to i ts sm al lsi ze, i t coul d be easi ly

cam ouflaged and hi dden f rom the enem y. Ioni c transducers hel p in thi s aspect be-

cause they tend to bem orenaturall ooki ng. Ioni c pol ym ersflap asbi rdsand do not

requi reany m echani calgeari ng,thusthey areal so qui etduri ng operati on.In ci vi lian

77

appl icati onsM AVscoul d beused i n traffi c survei llance.

6.2.1 D esi gn Param eters

A lthough no aerodynam i cm odeling wasperf orm ed on theflappi ngm echani sm s,pre-

lim inary numberswere obtai ned f rom the revi ew paper by W eiShyy et al .(1999).

The fol lowing were used i n ourstudy:

• Vehi cl eweightl essthan 50 gm (A i rf ram eof6 gm ,propul si on system of36gm ,

and control sof7 gm ).

• W ingspan i s set to a m axi m um of15cm . Thi s l im itati on i s a standard target

foran M AV.

• Thewi ng shape i ssem ici rcul arto m ake them axi m um useofthe area.

• Thewi ng constantl oadi ng i sobtai ned f rom equati on (40)i n W .Shyy,etaland

assum esa crui si ng speed of30- 60Kph and a ci rcul arwi ng ofdi am eter15 cm :

W

S=

m g

S= 27.8N /m 2 (6. 1)

• Thewi ng beat f requency i sset to 10. 4Hz.

6.2.2 W ing D esi gns

Due to i tsabi lity to m odelcom pl ex shapesofm ul ti layer i oni c transducers,the pro-

posed FEA m ethod wasused to desi gn two di fferentM AV wi ngs.Thefirstwi ng was

desi gned to be f ul ly m adeofi oni c pol ym ersheets.

Itwasdesi gned asa sem i ci rcul arwi ng tom akethebestuseofthearea covered

(keepi ng thesi zeoftheM AV assm al laspossi ble)asshown i n Figure 6. 1.Theradi us

was7.5 cm ,and i trequi red 5 stacksofi oni cpol ym ersheets(200m thi ck),to generate

a di spl acem entof12 mm peak to peak ti p di spl acem entunder the appl icati on of28

N /m 2 lifts f orce at a f requency of10. 1 Hz. A second wi ng was devel oped and was

com posed oftwo di fferentm ateri als: the passi ve l ightm ateri althat f orm s the wi ng

78

Figure 6. 1: T he deflecti on col or m ap output of the FEA anal ysi s of the firstw ing desi gn.

surf ace,and a stack of10 i oni c pol ym er sheets of7 x 5 cm si ze that perf orm ed as

muscles to actuate the wi ng. The stack was abl e to deflect 8 mm at the ti p under

theappl icati on of27. 8N /m 2 forceand f requency of20. 4Hz.Fi nal ly a 1. 1V actuati on

issaf e enough to avoi d electrol ysi s,whi ch starts to occurat1. 22 vol ts. Thus i n our

desi gn one can sti lli ncrease the f orce by approxi m atel y 10% .

6.2.3 C om pari son to requi rem ents

The first wi ng desi gn was cl ose enough to the desi gn requi rem ents. The wei ght of

thepol ym erswascom puted to be41. 4 gm .Thepol ym eri sto repl ace thepropul si on

system and thewi ngs,theref ore thi swilll eave l essthan 10grm sf or the control sand

the power source. Thi s i s consi dered to be a di ffi cul t constrai nt to m eet,especi al ly

when consi deri ng thewei ghtofthebattery.Asf ortheotherl oadi ng condi ti ons,they

m atched wel l the requi rem ents. The second wi ng desi gn has a pol ym er wei ght of

32.8gm ofpol ym er. Thi s i s around 9gm s l ess than the first desi gn,but i t i s good

to note that f or thi s desi gn a wing fram e i s requi red. As f or the other param eters

the ti p peak to peak di spl acem ent i s l ower than the first desi gn, but the beati ng

frequency i sm uch hi gher. These two resul tsdem onstrate thatstacki ng the pol ym er

79

has the potenti alto produce a vi able wing desi gn,but these two desi gnshave to be

consi dered f rom the aerodynam i cspoi ntofvi ew before bei ng consi dered acceptabl e.

It i s im portant to note that both desi gns coul d be m ade much m ore effi ci ent i fwe

able to consi deram i cro- layeri ng process,i n which wewould beabl e to exerta hi gher

potenti alperuni t thi cknesswi thoutexceedi ng theel ectrol ysi s l im it.

6.3 Sum m ary

In thi s chapter two wi ng desi gns that operate as flappi ng M AV are presented. No

aerodynam i c com putati on was perf orm ed,rather we rel ied on data f rom W eiShyy

et al . (1999). The fini te el em ent anal ysi s toolprevi ousl y descri bed i n Chapter 3

was used to si m ulate the desi gns. The first wi ng was desi gned to be f ul ly m ade of

ioni c transducersheets.Thi swing i sdesi gned as5 l ayers200µm sem i ci rcul arsheets

connected i n paral lel . Thi s desi gn was abl e to m eet al l the requi rem ents,but i t’ s

weightwascom puted to be41. 4 gm .The second desi gn com posed ofi oni c pol ym ers

asactuators,and a passi ve l ightm ateri althat f orm sthewi ng surf ace.Com pared to

the firstdesi gn thi swing i scapabl e ofl esspeak to peak deflecti on butoperated ata

higher f requency. The wei ght ofthe acti vem ateri ali n thi s desi gn was32. 8 gm . As

a finalconcl usi on ioni c pol ym erswere abl e to actuate theM AV,but they are heavy

and l eftsm al ll oad f or the powerstorageorpowergenerati on and controldevi ces.

80

C hapter 7

Sum m ary and C oncl usi ons

7.1 Introducti on

In thi schaptera bri efsumm ary ofthewhol e thesi si sprovi ded.Thecontri buti onsto

thefiel d areci ted,and m aj orconcl usi onsaredrawn.Fi nal ly i n the l astsecti on som e

futurework i sproposed.

7.2 T hesi s Sum m ary

W e have devel oped and characteri zed m ulti layer i oni c transducersasseri es,paral lel

and combined stacks. In seri esstacki ng,i oni c pol ym ersare si m ply l ayered on top of

each other.Paral lelstacki ng i sratheram orecom pl icated way ofwi ri ng thepol ym ers

so they are el ectri cal ly i n paral lel . On the other hand,paral lelstacks si gni ficantl y

im proved the perf orm ance regardi ng both actuati on and sensi ng. Asactuators,the

electri cpotenti alperuni tthi cknesswasi ncreased proporti onalto thenumberofl ay-

ersi n theparal lelstack,resul ti ng in largertransducti on forces.Paral lelstacki ng al so

enhanced the sensi ti vi ty,whi ch i s a f uncti on ofthe nature ofthe si gnalm easuri ng

ci rcui t. The m echani calboundary condi ti on represented i n the pol ym er i nterf aci al

fri cti on wasal so characteri zed.Increasi ng the i nterf aci alf ri cti on increased theband-

width whi ledecreasi ng thef reedi spl acem entofthepol ym er,and vi ceversa.A Fi nite

Elem ent Anal ysi s (FEA) m ethod was expl ained,veri fied,and used to num eri cal ly

81

val idate theprevi ousconcl usi ons.Itassum ed an appl ied constantpressure l oad gen-

erated by each l ayer.

The combined stackswere presented and they consi st ofan actuati on stack,

layered on top ofan i nsul ated pol ym er and were used f or f eedback controli n ioni c

pol ym ers.Them aj orprobl em in com bined stackswasto el im inate the f eed- through.

Feedthrough i s defined as the porti on of the actuati ng si gnalof the adj acent i oni c

pol ym er that i s di rectl y fed through to the output si gnalof the sensor. The f eed-

through wasm ai nly due the hum i dity i n the gaps between stacks whi ch created a

short- ci rcui tbetween the sensorand theactuator(s).

Newbury’ s equi val ent ci rcui t representati on of i oni c pol ym ers was m odi fied

to accomm odate the m ul ti layer pol ym ers. The m odi ficati on wasperf orm ed on f our

di fferent boundary condi ti ons,two el ectri calthe seri es and the paral lelconnecti on,

and two m echani calthe zero i nterf aci alf ri cti on and the zero sl ip on the i nterf ace.

Thism odified m odelhas the abi lity to m odelcanti leverm ul ti layer i oni c transducers

assensorsand actuators.Itprovi desa transf erf uncti on thatcoul d beused i n control ,

and system l eveldesi gn ofi oni c transducerdevi ces.

By usi ng the proposed FEA m ethod and stacki ng techni que we were abl e to

desi gn two di fferentM i cro A i rVehi cl e (M AV)wings.The firstwi ng wasdesi gned to

beful ly m adeofi oni cpol ym ersheets.Itwasdesi gned asa sem i ci rcul arwi ng tom ake

the bestuse ofthe area covered (keepi ng the si ze oftheM AV assm al laspossi ble).

The second wi ng was devel oped and was com posed of two di fferent m ateri als: the

passi ve l ightm ateri althat f orm s the wi ng surf ace,and a stack of10 i oni c pol ym er

sheetsof7x5cm si zethatperf orm ed asm uscl estoactuatethewi ng.Fi nal ly theFEA

num eri calsi m ulati onsi ndi cated thati oni cpol ym ershavepotenti alsto beconsi dered

forM AV appl icati ons,al though the wei ght ofthe control s and power source woul d

bea di ffi cul tconstrai nt to m eet i n a practi calappl icati on.

82

7.3 C ontri buti ons to the Fi eld

Them ain contri buti on ofthi s research i s the devel opm entand characteri zati on ofa

stacki ng process f or i oni c pol ym erm ateri als. Thi s m ulti layer stacki ng process was

characteri sed f or f our di fferent boundary condi ti ons,and extended to the desi gn of

thecombi ned multi layertransducers.Theboundary condi ti onsare the two el ectri cal

(seri es and paral lelconnecti ons), and the two m echani cal (no sl ip and no f ri cti on

interf aci alcondi ti on). Those boundary condi ti onsprovi ded the desi gnerofpol ym er

transducer base devi ce the flexi bi lity to i ncrease the f orce output,the sensor sensi -

ti vi ty by usi ng paral lelconnecti on. It al so provi ded the abi lity to controlthe f ree

displ acem entand structuralresonancef requency by control ling the i nterf aci alsl ip.If

there i sno sl ip thestack wi llbehaveasi fi twasonecom pl etebl ock,thusthenatural

frequenci eswilli ncrease,whi le the l arge f ree di spl acem entwi llbe reduced. On the

contrary i ftherei sno f ri cti on between thef aces,both thenaturalf requenci esand the

freedi spl acem entwi llbepreserved.Thecombi ned stacksaredesi gned to beused f or

feedback controli n ioni cpol ym ers.Theyprovi ded acom pactdevi cethati ncorporates

a sof t l arge def orm ati on actuator,and a f eedback sensorem bedded i nsi de the stack.

Signalf eed through proved to be them aj ordi ffi cul ty i n com bined stacks.Itcoul d be

reduced by i ncreasi ng water i nsul ati on between theactuatorand sensorstack.

Twom odeling tool swerepresented,thefini teel em entm ethod and Newbury’ s

em piri calm odel .TheFEA m ethod i susef ultom odelthepeak f orceordi spl acem ent

forcom pl exactuatorgeom etri es.Itcoul d beused tom odeland anal yzethei nterf aci al

fri cti on boundary condi ti on.Newbury’ sem piri calm odelwasm odi fied to handl e the

m ulti layer transducers. Thi s m odel i s usef ul i n determ i ning both the sensi ng and

theactuati ng transi entresponsesofa si m ple canti lever i oni c transducerbeam .Both

m odelswere val idated by successf ul ly com pari ng them to experi m entaldata.

Final ly weproved thatthemul ti layeri oni ctransducerscoul d beused todesi gn

a flappi ng m icro ai rvehi cl e.

83

7.4 C oncl usi on

O ther than the tool s and m ethods previ ousl y descri bed two m aj or concl usi ons can

bem ade for the stacki ng techni que.Fi rst i tprovi ded a controlon the f orce and di s-

placem entoutputand sensi ti vty ofthe transducer.Connecti ng the l ayers i n paral lel

reduces the vol tage requi rem ent of the m echani sm and allows us to appl y vol tages

thatdo notexceed the el ectrol ysi s l im it. A l so i tprovi ded an i ncrease i n bandwidth

sui tabl e for the desi red operated f requenci es. Next,el ectri cal f eed- through due to

watertransport i sa key l im itati on when uti lizi ng sensorsand actuatorsf orf eedback

control .Thi scan beel im inated wi th properpackagi ng techni quesand good l ayer- to-

layer i nsul ati on.

7.5 Future w ork

The m ain target of thi s thesi s was to enhance the perf orm ance of i oni c pol ym ers

usi ng stacki ng techni ques. The hand l ayered paral lelstacks hel ped i ncreasi ng the

generated f orce,buti tal so i ncreased thewei ghtortheam ountofpol ym ersused.On

the other hand thi nner l ayers i n the paral lelstack woul d hel p increasi ng the f orce

without i ncreasi ng thewei ght,resul ti ng in higherenergy capaci ty actuator.Thi nner

layers woul d al so decrease the sti ffness of the sensor l ayer i n the combi ned stack,

preservi ng the l arge f reedi spl acem entofactuatorstack i n it.Theref ore theeffi ci ency

ofthe m ul ti layer techni ques proposed i n thi s thesi s are wel li nvested by decreasi ng

the l ayerthi ckness.

Another probl em we faced was the di ffi cul ty off abri cati ng paral leland com -

bined stacks.Hand l ayeri ng ofa 3 l ayerparal lelstack consum esaround 2 hours,and

the resul tm ightbe a usel essstack wi th shortci rcui ts i n the connecti ons. Theref ore

theautom ati on ofthe l ayeri ng process i sa m ust.

A proposed f uture work i s usi ng Electroni c Sel fAssembl y (ESA) techni ques

in order to m ove the l ayeri ng process to them i cro l evel ,and autom ate i t. TheESA

techni que i s com posed ofseveralsteps,them aj oronesare the pl asm a treatm ent i n

84

order to break the bonds on the surf ace, the next i s to add a m onol ayer on thi s

surf ace,than etchi ng i t usi ng ul tra vi olate l ight through a m ask and final ly deposi t

thegol d on top ofthem onol ayer.Furtherm ore i oni cpol ym ersol uti on such asNafion

TMcoul d beused to bui ld acti ve pol ym erm ateri al ,and an i sol ati ve pol ym ersol uti on

coul d beused f orthe i nsul ati on.ESA wi llcontri bute i n etchi ng a certai n pattern on

the surf ace enabl ing the l ayers to be connected i n paral lelf ora paral lelstack. Thi s

shoul d al so hel p in creati ng a m ore robustcom bi ned stack,by m aki ng the i nsul ati on

between the two stacksm ore consi stent.

Anotheri m provem entwhi ch woul d hel p reduci ng thef eed through i n thecom -

bined stack i s the devel opm ent of a current or charge sensor that doesn’ t requi re

groundi ng ei ther si de ofthe sensor. Thi swasbri efly attem pted duri ng the research

for thi s thesi swithoutany success.

Furtherm ore, Newbury’ s m odelm odi ficati on sti ll requi res f urther i nvesti ga-

ti ons. The extrem e m echani calboundary condi ti ons f or the i nterf aci alf ri cti on (no

sl ip or no f ri cti on) are not generalto cover al lpossi bi liti es. The no f ri cti on bound-

ary condi ti on i s vi rtual ly im possible. The sti ffness ofthe i nsul ati on layer was al so

negl ected i n the m odel . Its effect m i ght be l arge i n som e cases,especi al ly i n the

combined stack where i ti svery cri ti calto the f eedthrough probl em ,and theref orewe

need a thi ck i nsul ati on. The l ast i m provem ent i n them odelwoul d be i n accounti ng

for the el ectri c im pedance across the i nsul ati on layer i n the paral lelstack,and the

resi sti vi ty between theconnecti onsofthepol ym ersi n theseri esstack.Theresi sti vi ty

in the seri es stack i s essenti al ly sm allcom pared to resi sti vi ty ofthe i oni c pol ym er,

but i tm ight becom e m ore pronounced i n case the numbers ofl ayers are i ncreased,

and thei r thi cknessdecreased. As f or the paral lelstack,the capaci tance i ntroduced

across the i m pedance i s fairl y l arge and m i ghtbe com parabl e to the one across the

ioni c pol ym er.

Final ly, new non- aqueous based i oni c pol ym ers are bei ng devel oped withi n

ourgroup. M attBennett hassuccessf ul ly used i oni c l iquidsassol vents f or the new

transducers.Ioni cl iquidshavezerovaporpressure,and they al soofferwi derel ectri cal

stabi lity. They are nonvol ati le which reduces the need f or packagi ng,and the wi de

85

electri calstabi lity provi des l arger operati ng vol tages and theref ore provi des l arger

forcesand di spl acem ent. Them aj or l im itati on which i s under current i nvesti gati on

is the sl ow response. W e bel ieve that thi nner l ayers shoul d be abl e to i ncrease the

response rate, si nce i t wi ll be a shorter travel to the i ons across the transducer.

Therf ore m i cro- layered mul tal yer transducer m i ght hel p in increasi ng the response

rate of the i oni c l iquid based transducers. Furtherm ore the el im inati on of water

would bea hel pfulf or the f eedthrough probl em in the combi ned actuators.

86

B ibl iography

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88

V ita

Icom ef rom Zgharta,a town i n north LebanonwhereIl ived unti lIm oved toBei ruti n

1996tof urtherm yeducati on atTheAm eri canUni versi tyofBei rut,whereIgraduated

with di sti ncti on i n 2001. Ihol d a B.S in M echani calEngi neeri ng and i n the summ er

of2000 I di d an i nternshi p at Uni versi dad Carl os III de M adri d,where I desi gned

an industri alCori ol isEffectFl owM eterto beused i n hazardousl iquidsappl icati ons.

In August of2001,Im oved to V i rgi nia Tech to pursue m y M asters Degree. I am

currentl y worki ng in thearea ofm ul ti layeri oni c transducersactuatorswi th D r.Don

Leo at theCenter f or Intel ligentM ateri alSystem sand Structures

Perm anentAddress:300 Durham Hal l

Blacksburg,VA 24061

United StatesofAm eri ca

This thesi swastypesetwi th LATEX 2ε1 by theauthor.

1LATEX 2ε isan extensi on ofL ATEX .LATEX isa col lecti on ofm acrosf orT EX .T EX isa tradem arkofthe Am eri can M athem ati calSoci ety. Them acrosused i n form atti ng thi s thesi swere wri tten byG reg W alker,Departm entofM echani calEngi neeri ng,V i rgi nia Tech.

89