8.1

CHAPTER 8SEPARATION BY EXTERNAL FIELDS (Sc METHODS)

:ELECTROPHORESIS AND SEDIMENTATION

8.1 TYPES AND USES OF FIELDS

Field : defined asexternal force acting through space causing the relativedisplacement of components w.r.t. surroundingselectrical - electrophoresis, isoelectric focusing,..sedimentation - isopycnic sedimentation,

rate zonal sedimentation, disc centrifuge....temperature - thermophoresis

Sc technique -------- zonal procedure

ZONAL SEPARATION - not by differential transport ratesby the fact that comp. seek diff. st.-st. position

zones are left distributed along the separation path.

8.2

8.2 TRANSPORT AND THEORETICAL PLATES

general transport eq:

for Sc separation: W = U + v U

thus:

further:

since:

substitution ofW = U and DT = θ D gives:

dtdc = - U dx

dc + θ Ddx2d2c

8.3

Plate heightwe have:

from Chapt. 3:

thus:

H = W2DT = U

2θD

H =- dµext / dx

2θRT

note: a) H is independent of f.b) . Thus H F-1.F = −dµext / dx ∝

8.4

Number of theoretical plates

since N = X/H:

however:

thus:

−(dµext / dx)X = −∆µext

Peak capacitysince: nc ~ 0.25 N1/2

we get:

8.5

8.3 ELECTROPHORESIS: CAPILLARY, GEL,AND OTHER FORMS

electrophoresis - general characteristics:a) Sc method driven by E fieldb) applicable to charged speciesc) strong heat generationd) convection prone -

migration velocity U −1f

dµext

dxSeparation media - anticonvective

a) capillary tubeb) gel (also gives sepn effect)c) granular mediad) fibrous media (e.g., paper)

other anticonvective strategiesa) rotating tubeb) zero gravityc) 40C

8.6

Capillary electrophoresis (CE) or CZEthin tube - convection can be suppressed

high surface/volume gives high f, heat dissipation1981 Jorgenson & Lukacs : CZE

variants of CEa) MCE - for neutral moleculesb) gel CE - electrophoretic prop. + sieving

8.7

Gel electrophoresis (GE)other media : starch granules

membranespaper

----- cellulose acetate ------- PAGEagarose gel

purpose: vary f, give size dependent high degree of crosslinking - sieving effect

selective tool

U = -f1

dxdµE

variantsgels in capillariesgels in thin stripsgel gradientspulsed field GEpolymer solutions for gelsmain usesproteins (SDS), DNA

8.8

Other electrophoretic techniques- ion mobility spectroscopy (gaseous electrophoresis)- isotachophoresis (nonlinear-displacement)- isoelectric focusing (sections 8.10 and 8.11)- 2D electrophoresis - discrete zones- 2D electrophoresis - continuous (preparative)

8.9

8.4 SEPARATION POWER IN ELECTROPHORESIS

electrostatic force:

we have:

thus:

since: V = EX

we get N from Eq. 8.6

−∆µ ext = FX

for an ideal process (q=1) at T=290K, N = 20zV

nc becomesnc ≅ 4

1 N

8.10

given:

assume: T = 290 K, q = 1, F= 96,500 coulombs/mol,R = 8.314 J/mol-deg

N becomes:

thus for: V=102-5x104V, z = 1-10we get: N = 2000-10,000,000

nc becomes:

again for: V=102-5x104V, z = 1-10

we obtain: nc = 10-800

8.11

8.5 ELECTROPHORESIS: ADDITIONAL CONSIDERATIONS

separation power V (voltage)ex) 30,000 V along 60 cm capillary

500V/cm end up with HEAT problem !

heat - decompose sampleconvection, evaporation of volatile sample

heated center cause viscosity reductionhigh velocity band broadening

consider Joul heat.H =

L2κV2

Heat Must Be Removed !reduce heat ?

8.12

Heat Must Be Removed !reduce heat ?

1. lowering -- choose electrolyte low ionic conductance2. cooling3. thin capillary (heat dissipation) - reduce convection

cooling process ?needs heat flow from the heated center

to the cooled boundarytemp. gradientheated center : low viscosity

high velocity zone broadening

Thin capilary 30 kV 106 N

8.13

electrophoretic mobility

separation z and fTo calculate µ

need to know accurate z

what is z ?z : effeictive charge

= specie's charge - double layer chargedouble layer thickness = h-1

µ = EU

∝

h-1 = (8πe2IεkT )1/2

zionz = 1 + h a

1 =h-1 + a

h-1

=ionzz

8.14

by looking at

want retardation of sample !needs small z small h-1 large I large c

for colloids a >> h-1

h-1 = (8πe2IεkT )1/2

large a

impossible for colloid separation

z ∝ afor colloids, µ =

8.15

8.6 SEDIMENTATION (Sc Tech.)general characteristics

driven by gravitational or centrifugal accelerationapplicable to particles of finite ∆ρseparation (δX) from δm, δρ, δf

gravitationapplicable d > 1µmnatural separationslaboratory separations

centrifugation (or ultracentrifugation)applicable to macromolecules and colloidsconvection prone (multiplied by G)ρ gradients required

8.16

8.6 SEDIMENTATION (cont.)

disc centrifuge- separation space between two discs- density gradient needed- optical detection- multicomponent separation

8.17

8.7 SEPARATION POWER IN SEDIMENTATION

net sedimentation force: force buoyant force

thus:

mass x accelerationbuoyancy factor

substitute:where:

GVGVF sss ρ−ρ=

sv ρ= /1

=⎟⎠⎞

⎜⎝⎛

∂∂

=pTm

Vv,

partial specific volume

8.18

given:

for gravity: G = constant,

for centrifugation: , thus:

note: ρ variation omitted

F becomes: (8.23)

F = M ( 1 - υ ρ ) G

FXext =µ∆−

rG 2ω= ∫=µ∆−2

1

r

r

ext Fdx

8.19

since:

we get:

substitute: ,

we obtain:

N = 2θRT- ∆µext

v = 1 / ρs rrrrrrrr ∆=−+=− 212122

12

2 ))((

8.20

examplesgiven:

working parameters: gravities ~∆ρ ~ 10 cm/s2, T = 300 K, θ = 1,

52 10~rω 108cm / s2

ω2r∆r ~ 109cm2 / s2

(1− ρ / ρs ) ~ 0.5

we get:for M ~ 105 (some proteins), N ~ 103

for M ~ 107 (some viruses), N ~ 105

for M ~ 1012(bacterial cells), N ~ 1010 (never achieved)

8.21

8.8 THERMAL DIFFUSION

thermal diffusion: DT: solute driven by the action of temp. gradient

rather than by conc. gradient (or chemical potential)

DT alone ?

flux by thermal diffusion

J = Tα c D

dxdT

8.22

since U = J/c

since H = 2qD/U

for ex.given as

when θ=1, ∆T/T = 1/3 (∆T ~ 100oC)Nmax ≅ 6

α

given as

N = 50, nc ~ 2 peaks

nc ≅ 41 N

8.23

thermal diffusionfails to act on molecules

However with flow - F(+)cd

Thermal FFF (Ch.9)Clausius-Dickels thermogravitational col.

8.24

8.9 OPTIMIZATION IN STATIC FIELD (Sc) SYSTEMS

maximize Rs & nc

requires maximum N

electrophoresis

sedimentation

Rs = W∆W

16N nc ≅ 4

1 N

8.25

N: efficiency of separationN/t : time-based rate of efficiency = separation speed

from eq.8.5

tN =

2θRTf(dµext / dx)2

increase sep. speed decrease friction(note N is independent of f)

for electrophoresis

8.26

8.10 STEADY-STATE VARIANTS OF Sc METHODS: ISOELECTRIC FOCUSING ANDISOPYCNIC SEDIMENTATION

isoelectric focusinggeneral requirement:

primary gradient + secondary gradient

8.27

Righetti: ampholyte bonded to a gel matrix 0.003pH units

8.28

8.10 STEADY-STATE VARIANTS OF Sc METHODSHow to make stable pH gradients?

Righetti : ampholytes bonded to a gel matrix-- gives 0.003 pH units

see Fig 8.8 (p136)

Improvementby combination of IEF followed by GE

isopycnic sedimentation1st gradient -- sedimentation field2nd gradient - density gradient

separation is based on density differences