chapter 8 separation by external fields (sc …chem.yonsei.ac.kr/~mhmoon/pdf/advanced/ch8.pdf · -...
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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
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