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Supplemental Information The supplementary information for ‘Mechanoelectrochemistry of PPy(DBS) from Correlated Characterization of Electrochemical Response and Extensional Strain’ is organized to provide detailed instructions for the following- Substrate fabrication Sample fabrication and preparation Glass electrode fabrication for shear force imaging Shear force imaging for extensional actuation Extensional actuation of PPy(DBS) samples from shear force imaging Substrate Fabrication Silicon wafers with 300nm thick silicon nitride layer and gold pads were fabricated in OSU Nanotech West cleanroom following the procedure discussed in Northcutt and Sundaresan 9 and diced into rectangular units. Each unit has two gold pads measuring 5mm 5mm connected by a 500μ m wide gold line. One of the pads is used for electropolymerization of polypyrrole and other as a connector pad for electrical access. An acrylic piece is fabricated with a laser-cutting machine from a stock sheet (McMaster-Carr) and attached to the wafer using epoxy as shown in Figure 9. The acrylic piece serves as the aqueous chamber above the pad dur- ing electropolymerization, electrochemical and mechanoelectro- chemical characterization. The prepared wafer unit is attached to a 3D printed delrin apparatus with spring loaded connector for electrical access. The delrin apparatus with the wafer is attached to the HEKA ElproScan3 stage with standard set screws and lev- eled to the stage. The CE and RE were connected to a Pt wire and Ag/AgCl wire and suspended in the solution, and the WE was pinned to the Au pad using a small spring. Sample Preparation Electropolymerization: The objective of this article requires deposition of PPy(DBS) of various thickness. This is achieved by potentiostatic electropolymerization of PPy(DBS) to predeter- mined charge densities (0.1 - 0.8 mC/cm -2 ). PPy(DBS) samples were grown on the gold pads by potentiostatic electropolymeriza- tion to a targeted total accumulated charge. The charge accumu- lated over time during electropolymerization is calculated from chronoamerpometry and data for planar PPy(DBS) samples for densities between 0.1-0.8 C.cm -2 is shown in Figure 9. For an example charge density (such as 0.1 C.cm -2 ), the num- ber of redox sites can be calculated following Equation 1 as shown below: N r = Q p (h p - h c )F = 0.025(C) 7.2 96485(C/mol) = 3.6 10 -8 mol (7) SEM Imaging A comprehensive SEM graphic for the surface features of planar and vesicle-templated samples is given as Figure 10 to demon- strate the presence of nanoscale surface features over a mesoscale range. Images were taken in OSU NanoSystems Laboratory with a FEI Helios Nanolab 600 FIB/SEM with a distance of 4.1 mm between the SEM probe and the samples. The magnification was kept constant between all samples, with a 30 μ m scale bar being provided on the bottom right of the image. It can be seen that there is an increased number of morphological features in sam- ples with charge density greater than 0.4 C.cm -2 , with a loss of features occurring at 0.8 C.cm - 2. The images shown in the main article show the samples’ cross-section at a 52 o angle for thickness measurement. 0 50 100 150 200 250 300 350 400 Time (sec) 0 25 50 75 100 125 150 175 200 Charge (mC) Charge accumulation vs time - Polymer growth 0.1 C/cm 2 0.2 C/cm 2 0.4 C/cm 2 0.6 C/cm 2 0.8 C/cm 2 Working electrode Reference/ Working electrode Accumulated Charge (mC) 25 50 100 150 200 Charge Density (C.cm -2 ) 0.1 0.2 0.4 0.6 0.8 Mass (μg) 77 158 308 461 615 Fig. 9 (top left) Delrin apparatus with nitrided silicon wafer shown on the SECM xy-stage; (top right) Charge data gathered during the fabrication of planar PPy(DBS) membranes; (bottom) Table of fabrication of specifications for PPy(DBS) membranes Fabrication of Nanoelectrodes The materials used for nanoelectrode fabrication were quartz cap- illaries (I.D.: .5 mm, O.D.: 1 mm, L: 10 cm, Sutter Instrument, USA), borosilicate capillaries (I.D.: 1.16 mm, O.D.: 2 mm, L: 20 cm, Sutter Instrument, USA), platinum wire (d: 25 μ m, Purity: 99.9%, Hard, Goodfellow, England), silver ink (Stan Rubinstein Assoc., USA), standard copper wire (d: .25 mm), and D-sub con- nector pins (d: 1mm, RadioShack, USA). The different steps re- quired for the fabrication of the electrode using a Sutter P-2000 puller is shown in Figure 11(a). The various steps in the fabrica- tion are: (i) threading Pt-wire, (ii) sealing glass capillary around Pt-wire, (iii) parting step, (iv) finishing step and (v) polishing. As obtained 1 mm quartz capillaries from Sutter were threaded with the 25 μ m platinum wire and placed into a Sutter P-2000 micro- pipette puller (Sutter Instrument, USA). The capillaries were con- nected to a vacuum pump at each end through silicon tubing and 10 | 1–14 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2015
Transcript
Page 1: ElectronicSupplementaryMaterial(ESI ... · A comprehensive SEM graphic for the surface features of planar and vesicle-templated samples is given as Figure 10 to demon-strate the presence

Supplemental InformationThe supplementary information for ‘Mechanoelectrochemistry ofPPy(DBS) from Correlated Characterization of ElectrochemicalResponse and Extensional Strain’ is organized to provide detailedinstructions for the following-

• Substrate fabrication

• Sample fabrication and preparation

• Glass electrode fabrication for shear force imaging

• Shear force imaging for extensional actuation

• Extensional actuation of PPy(DBS) samples from shear forceimaging

Substrate FabricationSilicon wafers with ⇡300nm thick silicon nitride layer and goldpads were fabricated in OSU Nanotech West cleanroom followingthe procedure discussed in Northcutt and Sundaresan9 and dicedinto rectangular units. Each unit has two gold pads measuring5mm ⇥ 5mm connected by a 500µm wide gold line. One of thepads is used for electropolymerization of polypyrrole and other asa connector pad for electrical access. An acrylic piece is fabricatedwith a laser-cutting machine from a stock sheet (McMaster-Carr)and attached to the wafer using epoxy as shown in Figure 9. Theacrylic piece serves as the aqueous chamber above the pad dur-ing electropolymerization, electrochemical and mechanoelectro-chemical characterization. The prepared wafer unit is attached toa 3D printed delrin apparatus with spring loaded connector forelectrical access. The delrin apparatus with the wafer is attachedto the HEKA ElproScan3 stage with standard set screws and lev-eled to the stage. The CE and RE were connected to a Pt wire andAg/AgCl wire and suspended in the solution, and the WE waspinned to the Au pad using a small spring.

Sample PreparationElectropolymerization: The objective of this article requiresdeposition of PPy(DBS) of various thickness. This is achievedby potentiostatic electropolymerization of PPy(DBS) to predeter-mined charge densities (0.1 - 0.8 mC/cm�2). PPy(DBS) sampleswere grown on the gold pads by potentiostatic electropolymeriza-tion to a targeted total accumulated charge. The charge accumu-lated over time during electropolymerization is calculated fromchronoamerpometry and data for planar PPy(DBS) samples fordensities between 0.1-0.8 C.cm�2 is shown in Figure 9.

For an example charge density (such as 0.1 C.cm�2), the num-ber of redox sites can be calculated following Equation 1 as shownbelow:

N

r

=Q

p

(hp

�h

c

)F=

0.025(C)7.2⇥96485(C/mol)

= 3.6⇥10�8mol (7)

SEM ImagingA comprehensive SEM graphic for the surface features of planarand vesicle-templated samples is given as Figure 10 to demon-strate the presence of nanoscale surface features over a mesoscalerange. Images were taken in OSU NanoSystems Laboratory witha FEI Helios Nanolab 600 FIB/SEM with a distance of 4.1 mmbetween the SEM probe and the samples. The magnification waskept constant between all samples, with a 30 µm scale bar beingprovided on the bottom right of the image. It can be seen thatthere is an increased number of morphological features in sam-ples with charge density greater than 0.4 C.cm�2, with a loss offeatures occurring at 0.8 C.cm�2. The images shown in the mainarticle show the samples’ cross-section at a 52oangle for thicknessmeasurement.

0 50 100 150 200 250 300 350 400Time (sec)

0

25

50

75

100

125

150

175

200

Cha

rge

(mC

)

Charge accumulation vs time - Polymer growth

0.1 C/cm2

0.2 C/cm2

0.4 C/cm2

0.6 C/cm2

0.8 C/cm210 μm

WE

RE

CE

Working electrode

Reference/Working electrode

10 μm

WE

RE

CE

Fig. 9 From left to right: The experimental configuration, thePt-nanoelectrode, and a micrograph of the Pt-nanoelectrode tip under20x magnification

Time (sec)0 50 100 150 200 250 300 350 400

Cha

rge

(mC

)

0

25

50

75

100

125

150

175

200

Accumulated Charge (mC) 25 50 100 150 200Charge Density (C.cm�2) 0.1 0.2 0.4 0.6 0.8

Mass (µg) 77 158 308 461 615

Fig. 10 (above) A plot of the chronocoulometric response duringelectropolymerization for planar PPy(DBS) membranes. (below) Table ofspecific mass related to charge density

Supplemental InformationThe supplementary information for ’Mechanoelectrochemistry ofPPy(DBS) from Correlated Characterization of ElectrochemicalResponse and Extensional Strain’ is organized to provide detailedinstructions for the following-

• Substrate fabrication

• Sample fabrication and preparation

• Glass electrode fabrication for shear force imaging

• Shear force imaging for extensional actuation

• Extensional actuation of PPy(DBS) samples from shear forceimaging

Substrate FabricationSilicon wafers with ⇡300nm thick silicon nitride layer and goldpads were fabricated in OSU Nanotech West cleanroom followingthe procedure discussed in Northcutt and Sundaresan9 and dicedinto rectangular units. Each unit has two gold pads measuring5mm ⇥ 5mm connected via a 500µm gold line with one of thepads is used for electropolymerization of polypyrrole and other asa connector pad for electrical access. An acrylic piece is fabricatedfrom a stock sheet (McMaster-Carr) with a laser-cutting machineand attached to the wafer using epoxy. The acrylic piece servesas the aqueous chamber above the pad during electropolymeriza-tion, electrochemical and mechanoelectrochemical characteriza-tion. The prepared wafer unit is attached to a 3D printed del-rin apparatus with spring loaded connector for electrical access.The delrin apparatus with the wafer is attached to the HEKA El-proScan3 stage with standard set screws and leveled to the stage.The CE and RE were connected to a Pt wire and Ag/AgCl wireand suspended in the solution, and the WE was pinned to the Aupad using a small spring.

Sample PreparationElectropolymerization: It is required to deposit PPy(DBS) ofvarious thickness. This is achieved by potentiostatic electropoly-merization of PPy(DBS) to predetermined charge densities (0.1 -0.8 mC/cm�2). PPy(DBS) samples were grown on the gold padsby potentiostatic electropolymerization to a predetermined totalaccumulated charge. The charge accumulated over time dur-ing electropolymerization of planar PPy(DBS) samples for 0.1-0.8C.cm�2 is shown in Figure 10.

SEM ImagingA comprehensive SEM graphic for the surface features of planarand vesicle-templated samples is given as Figure 11 to demon-strate the presence of nanoscale surface features over a mesoscalerange. Images were taken in OSU NanoSystems Laboratory witha FEI Helios Nanolab 600 FIB/SEM with a distance of 4.1 mmbetween the SEM probe and the samples. The magnification waskept constant between all samples, with a 30 µm scale bar beingprovided on the bottom right of the image.

It can be seen that there is an increased number of morpho-logical features in samples with charge density greater than 0.4C.cm�2, with a loss of features occurring at 0.8 C.cm�2. This is

10 | 1–13

Fig. 9 (top left) Delrin apparatus with nitrided silicon wafer shown on theSECM xy-stage; (top right) Charge data gathered during the fabricationof planar PPy(DBS) membranes; (bottom) Table of fabrication ofspecifications for PPy(DBS) membranes

Fabrication of NanoelectrodesThe materials used for nanoelectrode fabrication were quartz cap-illaries (I.D.: .5 mm, O.D.: 1 mm, L: 10 cm, Sutter Instrument,USA), borosilicate capillaries (I.D.: 1.16 mm, O.D.: 2 mm, L: 20cm, Sutter Instrument, USA), platinum wire (d: 25 µm, Purity:99.9%, Hard, Goodfellow, England), silver ink (Stan RubinsteinAssoc., USA), standard copper wire (d: .25 mm), and D-sub con-nector pins (d: 1mm, RadioShack, USA). The different steps re-quired for the fabrication of the electrode using a Sutter P-2000puller is shown in Figure 11(a). The various steps in the fabrica-tion are: (i) threading Pt-wire, (ii) sealing glass capillary aroundPt-wire, (iii) parting step, (iv) finishing step and (v) polishing. Asobtained 1 mm quartz capillaries from Sutter were threaded withthe 25 µm platinum wire and placed into a Sutter P-2000 micro-pipette puller (Sutter Instrument, USA). The capillaries were con-nected to a vacuum pump at each end through silicon tubing and

10 | 1–14

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.

This journal is © the Owner Societies 2015

Page 2: ElectronicSupplementaryMaterial(ESI ... · A comprehensive SEM graphic for the surface features of planar and vesicle-templated samples is given as Figure 10 to demon-strate the presence

Pla

nar

Vesi

cle

Tem

plat

ed

0.1 C.cm-2 0.2 C.cm-2 0.4 C.cm-2 0.6 C.cm-2 0.8 C.cm-2

Fig. 10 SEM of planar and vesicle-templated PPy(DBS) membranes for varying charge densities

25 µm Pt-wire

Insertion of Pt-wire

Sealing stepSutter P-2000 puller

Parting stepSutter P-2000 puller

Tygon tubing to vacuum pump

vacuumvacuum

Heat Filament Velocity Delay Pull Heat/Cool Cycles

660 5 60 140 0 40/20s 4

785 2 20 128 150 - -

Quartz capillary (Sutter Instruments)1mm OD, 500µm ID, 10 cm

Finishing stepBorosilicate capillary, Electrical contacts and Polishing

Attaching dither & receiver piezos(for shear force imaging)

RG Value: 13

10 μm

Finished Electrode

Voltage(V)-0.1 0 0.1 0.2 0.3 0.4 0.5

Diff

usio

n Li

mite

d C

urre

nt(p

A)

-800

-600

-400

-200

0

200

400

600

800(a) Electrode Fabrication Steps (b) Electrode Characterization - CV

Frequency (KHz)650 660 670 680 690 700

Shea

r For

ce (m

V)

0

100

20010 7 m Above PPy(DBS)Contacting PPy(DBS)

Frequency (KHz)650 660 670 680 690 700

Phas

e (D

egre

es)

-100

0

100

200 10 7 m Above PPy(DBS)Contacting PPy(DBS)

(c) Electrode Characterization – Shear force spectra

Operating frequency for SFimaging

Fig. 11 (a) Schematic to outline the procedure for SECM-SF imaging nanoelectrode fabrication; (b) CV for electrode in 1mM FcMeOH and 100mMNaCl solution; (c) Shear force spectra from the receiver piezo between 600kHz and 700kHz on and 100µm above the sample.

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Page 3: ElectronicSupplementaryMaterial(ESI ... · A comprehensive SEM graphic for the surface features of planar and vesicle-templated samples is given as Figure 10 to demon-strate the presence

the capillary holders were restrained by an elastomer band andjaw restraints. The first process is several heating cycles to ensurethat the quartz melts around the Pt wire until it is fully bonded ata singular point in the center, creating an hourglass shape. Dur-ing this time, the capillaries were heated with a 40 second on,20 second off duty cycle (Heat: 660 �C) with a large filamentlength (Filament: 5) for 5 cycles (until quartz melted and fusedwith the Pt wire). The seal was verified via microscopy to ensurethat the Pt wire did not snap or otherwise detach at the center.The quartz capillary with a continuous Pt-wire running along theneck formed from the sealing step was then returned to the mi-cropipette puller and held in the jaws of the P-2000 puller bars. Areference point is added to the capillary to return it to the samelocation in the puller. The capillary was then pulled (Heat: 780�C) over a small filament length (Filament: 2). The base of theresultant piece was then electrically connected with silver ink toa copper wire and inserted into a 2 mm borosilicate capillary toreinforce and seal the electrical connections. The tip of the elec-trode was polished using a HEKA microelectrode polisher (MHK1) to expose the Pt core and produce a smooth, even surface.

Nanoelectrode CharacterizationCyclic Voltammetry: The finish and quality of the electrode pre-pared for SECM-SF imaging is characterized by the built-in mi-croscope in HEKA ElProScan ELP3 and cyclic voltammetry in aferrocene methanol (FcMEOH) solution. An example CV for awell conditioned electrode is shown in Figure 11(b). For a cleanplatinum surface on a flat surface there is a diffusion limited re-gion on the oxidation and reduction peaks as shown below 0.1Vand above 0.4V, limited hysteresis, and insignificant signal noise.This diffusion limited current can be calculated using Equation 8,

I

ss

= knFr

t

D[C⇤]b (8)

in which k is a geometric constant (4 for a disc), n is the numberof electrons, F is Faraday’s constant, r

t

is the electroactive area, D

is the diffusion coefficient, C

⇤ is the concentration of electroactivespecies in bulk solution, and b is a function of r

t

. Based on this,the size of the exposed platinum of the Pt-nanoelectrode is calcu-lated empirically. It is important to note that despite having anelectrochemically active surface, the application of the nanoelec-trodes in this article was limited to shear-force imaging and nopotential was applied across the platinum core during any char-acterization of PPy membranes. The FeMEOH solution and plat-inum were used between trials in order to keep a consistent sur-face condition and then electrically disconnected once the elec-trode was placed in the vicinity of the PPy-sample.

Shear Force Imaging: For shear force imaging techniques,piezoelectric plates (HEKA Elektronik Dr. Schulze GmbH) wereconnected to the Pt-nanoelectrode on the quartz capillary, with a1 cm spacing and approximately 90� rotation between them. The

Pt-nanoelectrode was positioned in the x,y plane directly abovethe PPy(DBS) membrane with a joystick, and brought into con-tact with the sample by moving in the -z direction until an abruptchange in the shear force signal was observed. This signal indi-cates contact with the PPy(DBS) membrane. The curve result-ing from measuring deviations in the receiver piezo during mem-brane approach is typically not smooth until calibration. Theshear force signal applied during approach curves for oxidizedand reduced conditions was selected based on shear force spectrascans. An example SF-spectra plot is shown as Figure 11(c). Con-tact was established as the point in the approach curve where adiscontinuous spike in the receiver piezo potential and a 10 µmdistance was chosen as a sufficient distance away from surfacehydrodynamic forces. The 667kHz frequency was selected as thepoint in which the greatest signal deviation between boundaryconditions and conveniently was a resonance of the vibrationalnatural frequency. The shear force spectra was retaken every in-stance the electrode was polished or the piezoelectric plates werereplaced after cleaning to verify the continued response.

A list of specific experimental steps to perform a mechanoelec-trochemical analysis of faradaic materials is as follows:

• Mount the electrode to z-stage

• Mount the sample to x,y-stage, add electrolytic solution andapply an oxidation signal to the sample (ring electrode)

• Use zz-motors to position electrode tip into solution and x,y-motors to position the electrode tip above the sample

• Use “Tip Down” procedure with current regulation (10%) toapproach the sample until the electrode is in the immediatevicinity

• Use the “2D Scan” with z-piezo motor selected to approachthe sample at a rate of -0.05 µm/sec while simultaneouslymonitoring current and shear force signals

• Upon reaching the “Contact Condition” (characterized by adiscontinuous current response or shear response) manually”Stop” the “2D Scan”

• Perform “Shear Force Spectra” procedure with the electrodemaintained at “Contact” position

• Set origin in ElProScan: Motors window

• Perform the ”Distance Calibration” procedure for with a 2.5µm distance with a 3 nm step size

• Perform the “Shear Force Spectra” procedure with the elec-trode maintained at the “Non-Contact” position

• Overlay the two shear force spectra plots to select an opera-tional frequency

12 | 1–14

Page 4: ElectronicSupplementaryMaterial(ESI ... · A comprehensive SEM graphic for the surface features of planar and vesicle-templated samples is given as Figure 10 to demon-strate the presence

• Perform a CA with the PGF generator to reduce the samplewhile monitoring the current

• After fully reduced, use the “2D Scan” procedure with thez-piezo motor selected to approach sample at a rate of -0.05µm/sec while monitoring shear force - stop at ”Contact”

• Use the “Go Back" option to return the electrode to a positionof 2.5 µm above sample

• Perform a CA with the PGF generator to oxidize the samplewhile monitoring the current

• After fully oxidized, use the “2D Scan” procedure with thez-piezo motor selected to approach sample at a rate of -0.05µm/sec while monitoring shear force - stop at ”Contact”

• Check resultant data to ensure full CA and Approach Curvedata satisfies measurement criteria - repeat as necessary

• Remove the electrode from solution by moving zz-motors inthe positive direction before turning off the software

Comprehensive Approach Curve DataThe complete set of results from SF approach curves for planarand vesicle-templated PPy(DBS) membranes is presented in Fig-

ures 12, 13. The point of contact was an unreliable metric tomeasure the deviation in thickness due to redox processes, asthe modulus of elasticity varies with electrochemical boundaryconditions, as seen in the slope of the shear force spectra. Thisdeviation of Young’s modulus in a soft material causes the shearforce to be insufficiently sensitive to contact, as seen in both pla-nar and vesicle-templated samples. Therefore, the sense lengthof the electrode was used as the detection criteria for the PPy-membrane surfaces. A nanoelectrode sense length is dependenton the diameter of glass electrode tip and was measured as thepoint in which a 5% deviation in the non-contact signal duringapproach. This technique is significantly more accurate as it isunaffected by the material properties of the surface during ap-proach and reliant only on the distance in which the shear forceprofile from the nanoelectrode begins acting on the surface. Itis noted that the 0.8 C.cm�2 samples followed a different behav-ioral trend during approach. This is due to a difference in shearforce spectra behavior as a result of polishing. This change causedthe most sensitive frequency to occur at 672.4 kHz, and producedan approach curve with biphasic behavior. As the sense lengthis independent of frequency, this trend difference does not affectmeasurement accuracy.

1–14 | 13

Page 5: ElectronicSupplementaryMaterial(ESI ... · A comprehensive SEM graphic for the surface features of planar and vesicle-templated samples is given as Figure 10 to demon-strate the presence

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.1 C/cm2

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.2 C/cm2

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.4 C/cm2

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.6 C/cm2

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.8 C/cm2

Oxidized PPy(DBS)Reduced PPy(DBS)

Planar

Oxidized PPy(DBS)

Reduced PPy(DBS)

Z-P

ositi

on

Dither Response

!"!

Fig. 12 Approach curves for planar PPy(DBS) membranes for varying charge densities

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.1 C/cm2

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.2 C/cm2

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.4 C/cm2

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.6 C/cm2

Shear Force Amplitude (mV)50 100 150 200 250

Z-Di

stan

ce (n

m)

-500

0

500

1000

1500

2000Charge Density = 0.8 C/cm2

Oxidized PPy(DBS)Reduced PPy(DBS)

Vesicle Templated

Z-P

ositi

on

Dither Response

!""

Fig. 13 Approach curves for vesicle-templated PPy(DBS) membranes for varying charge densities

14 | 1–14


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