Elimination of Electroosmotic Flow in Analytical Particle

17 Elimination of Electroosmotic Flow in Analytical Particle Electrophoresis F. J. NORDT, R. J. KNOX, and G. V. F. SEAMAN

Downloaded by MONASH UNIV on June 7, 2013 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0031.ch017

Department of Neurology, University of Oregon Health Sciences Center, Portland, Oreg. 97201

I n t e r e s t i n surface coatings which w i l l markedly reduce or e l i m i n a t e the z e t a p o t e n t i a l a t a chamber w a l l stems from the p r a c t i c a l i s s u e of e l i m i n a t i n g e l e c t r o o s m o t i c f l o w during e l e c t r o p h o r e s i s . I n a closed c y l i n d r i c a l g l a s s e l e c t r o p h o r e s i s chamber c o n t a i n i n g an e l e c t r o l y t e the negative charge a t the g l a s s w a l l r e s u l t s i n an i n c r e a s e i n c o n c e n t r a t i o n of c a t i o n s c l o s e t o t h i s s u r f a c e . A p p l i c a t i o n of an e x t e r n a l e l e c t r i c a l f i e l d r e s u l t s i n movement of f l u i d near the w a l l (electroosmosis) toward the cathode and a concurrent f o r c e d r e t u r n flow through the center of the tube. I t can be shown from hydrodynamics that there i s a c y l i n d r i c a l envelope ( s t a t i o n a r y l e v e l ) i n the chamber where no net f l o w of f l u i d occurs during e l e c t r o p h o r e s i s . F i g u r e 1 i l l u s t r a t e s the general f e a t u r e s of laminar e l e c t r o o s m o t i c f l u i d f l o w f o r a c l o s e d c y l i n d r i c a l tube i n c l u d i n g the p a r a b o l i c f l u i d f l o w p r o f i l e , regions of e l e c t r o o s m o t i c f l o w , r e t u r n f l u i d flow and l o c a t i o n of the s t a t i o n a r y l e v e l . In a n a l y t i c a l p a r t i c l e e l e c t r o p h o r e s i s true e l e c t r o p h o r e t i c v e l o c i t i e s of p a r t i c l e s may be measured a t the s t a t i o n a r y l e v e l w h i l e v e l o c i t i e s determined elsewhere i n the chamber w i l l be comprised of c o n t r i b u t i o n s from both e l e c t r o p h o r e s i s and e l e c t r o osmosis. I n p r e p a r a t i v e a p p l i c a t i o n s of e l e c t r o p h o r e s i s the boundary of a concentrated suspension (sample) becomes p a r a b o l o i d a l i n contour as a r e s u l t of electroosmosis of the suspending medium i n the chamber. The non-planar sample d i s t r i b u t i o n introduces d i f f i c u l t i e s i n separating or r e s o l v i n g p a r t i c l e populations which d i f f e r i n e l e c t r o p h o r e t i c m o b i l i t y . I n analyt i c a l p a r t i c l e e l e c t r o p h o r e s i s the presence of e l e c t r o o s m o t i c f l o w r e q u i r e s that measurements be c a r r i e d out a t the s t a t i o n a r y l e v e l . Since t h i s l e v e l i s i n f i n i t e l y t h i n e l e c t r o o s m o t i c f l o w w i l l always c o n t r i b u t e t o experimental e r r o r . The w a l l charge i n e l e c t r o p h o r e s i s chambers a r i s e s from e i t h e r the i o n i z a t i o n of surface charge groups or as a consequence of r e d i s t r i b u t i o n of ions from the suspending medium (adsorption or d e s o r p t i o n ) . The w a l l charge may be reduced o r e l i m i n a t e d by: a) use of adherent or adhesive f i l m s ( 1 ) . 225

In Hydrogels for Medical and Related Applications; Andrade, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1976.


HYDROGELS FOR MEDICAL AND RELATED APPLICATIONS

Figure 1. Electroosmotic fluid flow in a closed cylindrical tube, (a) A longitudinal crossectional view of the fluid velocity profile and fluid streamlines for a tube with radius, R (fluid velocity is plotted in terms of V , the fluid flow at the tube wall), (b) A transverse crossection where maximum electroosmotic fluid flow is shown by dense shading, and the unshaded area shows the region of the stationary level where fluid flow tends to zero, (c) Fluid flow parabola which is a plot of fluid velocity vs. distance from the tube wall. s



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b) covalent bonding m a t e r i a l s ( 2 ) . c) p h y s i c a l adsorption of substances ( 3 ) . E l e c t r o p h o r e t i c t e s t i n g of the s t a b i l i t y and completeness of d i f f e r e n t surface treatments or coatings may be c a r r i e d out i n v a r i o u s ways: i ) A f t e r coating the i n s i d e of the e l e c t r o p h o r e s i s chamber the electroosmotic f l o w i s c a l c u l a t e d from experimental measurements of the e l e c t r o p h o r e t i c v e l o c i t i e s of stand ard p a r t i c l e s a t v a r i o u s d i s t a n c e s from the tube w a l l , i i ) The e l e c t r o p h o r e t i c m o b i l i t i e s of coated or modified p a r t i c l e s made from the same m a t e r i a l s as the e l e c t r o p h o r e s i s chamber are measured by standard a n a l y t i c a l electrophoresis. i i i ) The zeta p o t e n t i a l of coated tubes may be a l s o determined from e l e c t r o o s m o t i c flow or streaming p o t e n t i a l measure ments. The f i r s t approach i s the more d e s i r a b l e t e s t of any coating procedure but f o r screening purposes the second t e s t approach w i l l s i g n i f i c a n t l y reduce the time needed f o r the i n i t i a l survey or t e s t i n g of coatings or m o d i f i c a t i o n procedures. Theoretical The e l e c t r o p h o r e t i c m o b i l i t y , u, i s defined as the e l e c t r o p h o r e t i c v e l o c i t y , v, of a p a r t i c l e per u n i t f i e l d s t r e n g t h , χ: ν

/.\

The r e l a t i o n s h i p between e l e c t r o p h o r e t i c m o b i l i t y , u, and zeta p o t e n t i a l , ζ, f o r nonconducting p a r t i c l e s whose r a d i u s of curvature, a, i s l a r g e i n comparison to the e f f e c t i v e thickness of the e l e c t r i c a l double l a y e r , l/κ, i s u s u a l l y described a c c u r a t e l y f o r Ka > 300 by the Helmholtz-Smoluchowski equation (4):

where ε and η are the d i e l e c t r i c constant and v i s c o s i t y , respec t i v e l y , w i t h i n the e l e c t r i c a l double l a y e r which are assumed t o be the same as the bulk v a l u e s of the suspending medium. E x p e r i mental measurements of ν r e s u l t i n an observed e l e c t r o p h o r e t i c v e l o c i t y , v , which i s subject t o e r r o r as i s the experimentally derived e l e c t r o p h o r e t i c m o b i l i t y , u . A p p l i c a t i o n of an e l e c t r i c f i e l d t o a suspension of charged p a r t i c l e s contained i n a closed c y l i n d r i c a l chamber w i t h a charged w a l l r e s u l t s i n e l e c t r o p h o r e s i s of the p a r t i c l e s and electroosmotic flow of the suspending medium. The observed v e l o c i t y , v , of a p a r t i c l e i n the tube i s thus the sum of i t s e l e c t r o p h o r e t i c v e l o c i t y , v , and the v e l o c i t y of the suspending e

e

Q

e


228

HYDROGELS FOR

MEDICAL AND RELATED APPLICATIONS

medium, v : w

v

=

o

v

e

+

v

w

I t has been shown by Bangham et a l . (5) that the observed v e l o c i t y of the p a r t i c l e i s r e l a t e d to i t s d i s t a n c e , r , from the a x i s of the tube by the expression: v

o = v + v [|j£ " H

(iv)

s

e

where v i s the f l u i d v e l o c i t y adjacent t o the tube w a l l and R i s the r a d i u s of the tube. S o l u t i o n of the flow equation ( i v ) shows that at a d i s t a n c e r = 0.707R from the a x i s there i s no net f l o w of f l u i d , i . e . , a s t a t i o n a r y l e v e l . In theory e l e c t r o p h o r e t i c m o b i l i t y measurements which are made at the s t a t i o n a r y l e v e l are not subject to e r r o r as a r e s u l t of f l u i d flow. However, i n p r a c t i c e e r r o r s a r i s e as a r e s u l t o f : a) the f i n i t e s i z e of the p a r t i c l e s which cannot be c o n t a i n ed i n an i n f i n i t e l y t h i n s t a t i o n a r y l e v e l ; b) f o c u s i n g e r r o r s a t the s t a t i o n a r y l e v e l (requirement f o r appropriate o p t i c a l c o r r e c t i o n s to r e c t i f y the e f f e c t s of r e f r a c t i o n and a b e r r a t i o n , depth of focus, and shape and s i z e of f o c a l f i e l d r e l a t i v e t o the r a d i u s of curvature of the s t a t i o n a r y l e v e l ) ; c) heterogeneous d i s t r i b u t i o n of charge on the tube w a l l r e s u l t i n g i n a s h i f t i n l o c a t i o n of the s t a t i o n a r y l e v e l ; d) Brownian motion and sedimentation of the p a r t i c l e ; and e) thermal convection a r i s i n g from J o u l e h e a t i n g . The magnitude of e r r o r s i n the e l e c t r o p h o r e t i c v e l o c i t y as a r e s u l t of f l u i d flow may be estimated from a d i f f e r e n t i a t e d form of equation ( i v ) :


s

dv

0

= *g£

dr

(v)

D i v i s i o n of equation (v) by the f i e l d g r a d i e n t , χ, gives an expression f o r the change i n the experimentally observed e l e c t r o p h o r e t i c m o b i l i t y at s m a l l r a d i a l increments from the s t a t i o n a r y l e v e l i n terms of the e l e c t r o o s m o t i c m o b i l i t y , u : g

Au

4u r . = — f - Ar 2 q

ο n

I f the f r a c t i o n a l e r r o r i n u as 6, then: δ =

, .v (vi)

R

e

due to f l u i d flow i s defined

Au 4u r = Ar u^ R u~

—0

s

9

z


.. (vu)

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From e x p r e s s i o n ( v i i ) one may c a l c u l a t e the maximum v a l u e of u which w i l l produce f r a c t i o n a l e r r o r s of l e s s than δ i n u at d i s t a n c e s up t o Ar from the s t a t i o n a r y l e v e l . s

e


M a t e r i a l s and Methods Corning #7740 b o r o s i l i c a t e p a r t i c l e s were used as a model system f o r screening the e f f e c t i v e n e s s of p o l y s a c c h a r i d e d e r i v a t i v e s as low z e t a p o t e n t i a l s u r f a c e coatings f o r g l a s s . A l l chemicals were reagent grade and the water was d i s t i l l e d t w i c e i n pyrex ware. The p a r t i c l e s were prepared by g r i n d i n g Corning #7740 g l a s s tubing w i t h water i n an aluminum oxide b a l l m i l l f o r 16 hours. P a r t i c l e s of s u i t a b l e s i z e f o r e l e c t r o p h o r e t i c measurements were obtained by repeated sedimentation f o l l o w e d by removal of p a r t i c l e s having a sedimentation r a t e g r e a t e r than 1 mm/3-4 min. P a r t i c l e s thus obtained were

Elimination of Electroosmotic Flow in Analytical Particle

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