JOURNAL OF COLLOID AND INTERFACE SCIENCE 25, 519-525 (1967)

A Double-Tube Flat Microelectrophoresis Cell

J. D. HAMILTON AND T. J. STEVENS

Division of Building Research, Commonwealth Scientific and Industrial Research Organization, Melbourne, Australia

Received May 8, 1967

ABSTRACT

Details are given for the construction and operation of a double-tube microelec- trophoresis cell with capillaries of rectangular cross section. The theory of the cell design is discussed and experimental results are presented to compare the perform- ance of the new cell with that of its single-tube counterpart.

INTRODUCTION

Capillary-type mieroelectrophoresis cells are broadly classifiable according to the number and shape of their tube components. Single-tube units with cylindrical bores have been widely used by colloid scientists (1-8). The theory underlying the operation of such cells has been discussed by Abramson (9) and Smith and Lisse (10). Although simplest in design and construction, they are the least satisfactory from the point of view both of accuracy and of ease of use. Refraction by the curved capillary wails usually causes images of the migrating particles to be highly distorted and difficult to observe without accurately collimated, narrow-beam, high- intensity lighting. Even under the best condi- tions only materials which scatter light strongly can be examined with any degree of precision. Focusing along the bore diameter in the cylindrical capillary becomes progres- sively more difficult as the depth of observa- tion is increased, and consequently great care must be exercised in restricting and position- ing the illuminating beam or focus of the microscope objective to ensure that particle velocity measurements are made at exactly ealculated levels in the tube (11-13). Ac- curacy in depth setting is especially critical for observations at the stationary liquid levels (9(a)), situated at points of maximum velocity gradient in the parabolic flow pat- tern.

The double-tube cylindrical cell of Smith and Lisse (10) also has unsatisfactory optical characteristics. I-Iowever, it is potentially more accurate than the single-tube device by virtue of the fact that the level of zero electroosmotic flow, at which the readings are made, is located at the axis of the ob- servation tube where the velocity gradient is minimum, and thus where slight focusing errors do not seriously affect the precision of the eleetrophoretic velocity determina- tions.

The design of the single flat tube cell used by Abramson (14, 15) offers the alternative advantage of good optics. Precise focusing is attainable in these cells, and this largely offsets the difficulties of measuring particle velocities in regions of high flow gradient. The absence of optical distortion also con- tributes to the improvement of dark-field conditions in the cell--an important con- sideration if materials with low light-scatter- ing power are to be examined.

The twin-tube flat eleetrophoresis cell described here offers all the important ad- vantages of the earlier designs. Thus the flat capillary system has been utilized to provide maximum clarity for observation in all regions of the cell, linear depth/focus relationships, and highest precision in focus- ing. The double-tube arrangement also adds to the precision of the instrument by provid e ing a half-depth observation level.

519

520 HAMILTON AND STEVENS

DESCRIPTION OF THE CELL

The structural details of the new cell are given in Fig. 1. The main central unit con- sists of a heavy stainless steel tube frame, with two flanged Pyrex chambers cemented into the ends. These are the inner halves of the suspension reservoirs. Two precision bore rectangular capillary tubes (also Pyrex) of appropriate I dimensions link these reservoir units via slots cut at their inner extremities. The capillaries extend well into the chambers and are sealed in place with white silicone rubber. The tubes are coplanar, with their lower surfaces parallel to and lust clearing the surface of the microscope stage, which fits into a large recess in the underside of the tube frame. A smaller opening in the upper side of the mount allows passage of the microscope objective during observation of the contents of the capillary tubes.

The outer halves of the reservoirs have grotmd flanges which mate with those on the central unit (the completed joints are held intact by means of large spring clips). The detachable units each carry a platinum disc electrode coated with platinum black? The electrode plates are coupled to terminals on the outer surfaces of the chambers and are sealed in place with silicone rubber. The electrode chambers are also fitted with small stoppered funnels and air vent tubes to facilitate filling and displacing air from the cell. Stopcocks seal off these parts from the main system when the cell is in operation. The capacity of the complete cell is approxi- mately 100 ml.

OPERATION OF THE CELL

The Leitz microscope used in conjunction with the new cell is fitted with a 20X long working distance (6.2 ram.) dry objective and a 25X graduated eyepiece. One hundred divisions of the scale are equal to 400 ~ for the 500X magnification used. Dark-field illumination for the observation tube, pro-

1 See discussion in the section Theory of the Cell Design.

2 The simple plate electrode system is unsatis- factory when ceil currents are high (greater than about 300 ~a. (at 200 v.)). For testing the more conductive suspensions, alternative end chambers with nonpolarizing Cu-CuSO4 electrodes are used.

duced by a Leitz D.0.80 substage condenser, can be regulated by means of an iris dia- phragm incorporated in the objective lens. The standard fine-adjustment knob of the microscope has been replaced by a large calibrated dial, by means of which the focus- ing level can be set with an accuracy of 4-1 ~. A system of stops and brackets holds the cell on the microscope stage and ac- curately locates the observation tube relative to the optical system, but allows easy re- moval of the whole unit for cleaning and other necessary maintenance.

The sources of power for the cell and microscope lamp are housed in the console unit (Fig. 2). The stabilized direct-current supply to the cell can be set and measured with an accuracy of ±0.5 %. Voltage stabil- ity is better than 0.2 %. The voltage can be varied continuously within the range 0-200 v. by means of a precisely calibrated ten- turn potentiometer, and is registered (with about 1% accuracy) by a voltmeter on the console. Current is indicated on a re±cream- meter, shunted by selectable resistance net- works to give full-scale deflections for flows of 50 t~a., 250 ~a., i ma., 5 ma., and 20 ma. On/off and current-direction controls for the cell are provided by a three-position switch.

Viscosity changes and convection in the suspension, due to fluctuations of tempera- ture, may produce significant errors in elec- trophoretic velocity measurements. In order to maintain temperatures as constant as possible during the performance of experi- ments with the cell, an air-conditioned laboratory was used which gave temperature control within ±0.5°C. over periods of several hours. The exact temperature of the cell is registered by a thermistor-sensor, cemented directly to the observation tube and coupled to a resistance bridge and re- cording meter.

Techniques used in determining elec- trophoretic mobil±ties with the new cell are essentially the same as those used with other types of capillary unit. The microscope is focused precisely at the required level (at half-depth in this case) in the observation tube, and the migration rates of the sus- pended colloidal particles are obtained by timing their progress (by means of a stop-

D O U B L E - T U B E FLAT M I C R O E L E C T R O P H O R E S I S CELL 521

Su,spens!on r e s g r v o l r \

Fla6ge Joints

Air/Cock

/

\ Electrode

OUTER CHAMBER (end views)

/ \ SIDE VIEW ~ / / Oufer Chamber In r Chamber Electrode

Stainless S~eel Body COMPLETE CELL

Terminal Cap Capillary -1"2

,"/ M M /

Capillary 1",

FIa. 1. The double- tube flat mieroeleetrophoresis cell

watch) over known intervals on the eyepiece scale. Cell potentials are chosen to give migration speeds amenable to accurate metering. Voltage gradients through the capillary tubes I and II of the cell (Fig. 1) are taken to be Ep/ll, and Ep/12, where Ep is the potential difference between the plates and 11 and/2 are the respective tube lengths. Since the cross-sectional areas of the reser- voir chambers are very large compared with those of the migration tubes, and the dis- tances from the plates to the ends of the capillaries are short compared with the lengths of the capillaries, no significant error is introduced by equating E~ with E t , the actual potential drop between the ends of the capillaries. Potentiometrie measurements

made between the end chambers at different positions in the chambers (including the capillary tube ends) have not revealed volt- age variations greater than 0.5%. During experiments with the cell the current is frequently reversed to minimize the pos- sibility of electrode polarization.

T H E O R Y OF T H E CELL D E S I G N

The hydrodynamic theory of the capillary electrophoresis cell is based on assumptions that the liquid phase of the specimen sol is incompressible and viscous, and that the flow is nonturbulent. Liquid movement due to electroendoosmosis in a rectangular sec- tion cell is governed by the general laws for laminar streaming in pipes (16) and is thus

522 HAMILTON AND STEVENS

]PIG. 2. The double-tube microelectrophoresis cell mounted on microscope (A), with microscope lamp (B), control console (C), and temperature-recording meter (D).

[.. - b ~ + b

Fro. 3. Diagrammatic representation of a capil- lary tube of rectangular section, showing the scheme of dimensions used in the development of the cell formula.

described by the equation

O2u O'~u P [1] OY ~ Jr Oz ~ t~ '

where u is the flow velocity along any (y, z) steamline in the direction x parallel to the length of the tube (Fig. 3), P is the pressure difference per unit length of the tube, and

is the coefficient of viscosity. Single-Tube Cell. Komagata (17) has

shown that for a single tube system in which the vertical (x, z) and horizontal (x, y) surfaces may have different properties, the

differential equation [1] is satisfied by

P @2 __ z 2) u=uo+~

+ ~ (-- 1)~+1 16Pc 2

~=0 t~Tr3(2n 4- 1) a

4(u~ - ub) + ~Tr( 2n -f- 1)

cosh (2n + 1)~ry cos (2n 4- 1)Trz

[21

2b 2b cosh (2n + 1)Irb

2c

b and c being the half width and half height, respectively, of the tube; and uc and ub, the electroendoosmotic velocities at the xy and xz boundaries. For a closed system

b c

b - - c

or

4bc o + 4Pbc _ 3~ ~ =o

L~(2~ 1) 5 + ~r3(2n + 1) a

X tanh (2n + 1)~b _ O. 2c

[4]

DOUBLE-TUBE FLAT MICROELECTROPHORESIS CELL 523

For large values ~ of /c = b/c, the velocity equation for y = 0 reduces to the approxi- mate form

u . = o _ { 1 - 3 ( 1 - ~/c ~) Uc

X [1 - - 16/7r3]c(1 -- u~/u~)]} [51

× (2 - 384/~5]~) -1

I f ub = u~ = U (e.g., as in a glass capillary tube), then and

uv=0 _ 1 3 (1 -- z2/e 2) [6] U 2 - - 384/~5]c '

and zero velocity levels in the median plane occur at

z~=0 = ± c + ~rqc "

Double-Tube Cell. For a closed system consisting of two rectangular tubes (I and I I ) in parallel, the flow equation is

ff~ff~u~dydz bl Cl

Is]

f f? + u ~ dy dz = O. b2 c2

Here bl and b~ are the half widths and c~ and c~ the half heights of tubes I and I I , respectively. With the use of approximations valid only for tubes with large width/height ratios (/~), Eq. [8] may be expanded to give:

4/91b~e~ 3 256P~c~ ~ 4blC~U~ ~ Jr- . . . .

3~ ~

_ 64c~(u~ ~ - - u~ ~) _+_ 4b2c~u~ ~ 7r 3

4P~b2c2 ~ 256p~c~ ~ [9] +

3~ ~r ~

2 64c~ (u~ -- u J ~)

- - ~ O , 7~ 3

in which P1 and Pz are the pressure gradients then n and u~ ~, in tubes I and I I , and u~ I, ub ~, u~,

are the corresponding pairs of eleetroendo- osmotic velocities. Considering two uniform

3 For /~ = 15 the error introduced by the ap- proximation is of the order of 0.2%.

capillaries with identical surface properties we may assume

Uc I = Ub I = g l

and [i0]

uy = uy = U2

Now, since P l

P2 = - - al a2

[11]

U1 U2 ~ - - a t

a2

where a l , a2 are the lengths of tubes I and I I , respectively, Eq. [9] m a y be simplified to

4Plb~cl 3 256P1@ 461el U1 -~-

3 tL ~ ~r 5

4b2c2 Ulal 4P~b2c2al 3 -t- - - [12]

a2 3t~a2

256Plc2al ~ - - O .

/~7~5a2

According to Eq. [2], the velocity of flow at the center (yl = 0, zl = 0) of tube I is:

= U1 + Plc~2/2t~. [13] UO,O

For the case Uo,o

~ff l = --PIcI2/2U, [14]

and from Eq. [12] we m a y derive

--4/91 bl cl 3 4/91 bl cl 3 256 P1 @ + 2u 3u ~ 5

4P~ b2 c12c2 al 4P~ b2 c23a~ + [15]

2ua2 3ua2

256 P1 c2 ~ al - 0 .

~ 5 a 2

Now since

Plal = constant

51 el ~ b~ c~ '~ 64 c~ 4 - - _ _ .-]-

2 a l 3a l 7r5al

52 c12c2 52 c23 + 2a2 3a2

64 c24 ~r5a2

- - 0 .

[161

524 HAMILTON AND STEVENS

If we put cl/c2 = H, al/a2 = L, and bl = b2 , Eq. [16] becomes

H a H 2 1 64 ( H ~ 1 \ = 0, [171

6L 2

k~, k2 being the width/height ratios for tubes I and II, respectively.

For the particular case in which the cell tubes are of equal widths and lengths and kl = 20,

L = I

and Eq. [17] gives

H = 0.730

In the construction of the prototype cell, rectangular capillaries of cross section 0.532 X 10.04 ram. and 0.735 X 10.02 ram. were used as observation (I) and return flow (II) tubes, respectively. For these

H = 0.724,

K1 = 18.86, and

K~ = 13.62.

In order to establish the required zero elec- troendoosmotic flow condition at the center of tube I, the capillary lengths were adjusted according to the value of the ratio L = 1.427, given by Eq. [17] upon substitution of the above data. The specific lengths chosen were 194 ram. (tube I) and 136 mm. (tube H).

COMPARISON WITH THE SINGLE-TUBE CELL

As a means of confirming the theory and reliable operation of the new cell the elec- trophoretic behavior of gelatin-coated Pyrex glass particles in dilute (0.01M) acetic acid was studied (a) in a single-tube flat cell and (b) in the double-tube device, and the results were compared. In each case the walls of the cell were also coated with gelatin de- posited from the test suspension. The con- centration of gelatin in the acid was mini- mazed (approximately 0.02%) to prevent any superfluous build-up which might alter the critical tube-height relationships in the double cell. Velocities of the particles were determined at various depths in the vertical median plane of the single-tube cell and the observation tube (I) of the twin unit. Suffi- cient levels were investigated to define the

4

/ f ' - - . , \ i / " \ \

i / \ \ ,, 7

I I t I 1 0,2 0.4 0.6 0 . 8 1 . 0

RELATIVE DEPTH

FIG. 4. Particle velocity profiles through gela- tin-coated single-tube (-O O-) and double- tube (-e e-) fiat electrophoresis cells, ob- tained with a suspension of gelatin-coated glass particles in 0.01 M acetic acid. VB = electro- phoretic velocity.

parabolic velocity patterns in the capillaries. Twelve readings were made for each deter- mination. Cell potentials of 100-200 v. were used and the particles were timed over an interval of 200 t~. Readings were corrected for minor temperature fluctuations and scaled to render values in t~/sec./volt/cm.

The results of the two series of experiments are plotted in Fig. 4. Relative heights have been used in the horizontal scale of the dia- gram since the absolute heights of the capillaries in the two cells are different. In both systems the particles adjacent to the tube walls remained stationary, indicating that the electroendoosmotic velocity (U) and electrophoretic velocity (V.) were equal and opposite. In the single-tube cell the relationship

vE ~ 2/iv~,5 , [181 where V0% = liquid velocity at half depth in the cell, thus applies (18), and for the particular width/height ratio of the capillary is mere precisely

VE = 0.6360 V ~ 0.5 • [ 1 9 ]

According to the theory of Komagata (17) the liquid in this cell is stationary at the

DOUBLE-TUBE FLAT MICROELECTROPHORESIS CELL 525

0.200 and 0.800 levels. The eleetrophoretic mobility determined at these points was 1.99 ~/see./volt/cm., very close to the value predicted by Eq. [19], i.e., 2.03 t~/sec./volt/ em. Since the measurement at the center of the tube is undoubtedly more reliable than those made in the regions of maximum velocity gradient, it has been used as the basis for comparison with the electrophoretie mobility determination from the double- tube cell. The velocity of particles at the axis of tube I in the new cell was 2.01 w/see./ volt /em.; this differed by only 1% from that obtained with the single-tube arrange- ment. I t would therefore appear tha t the liquid flow at the center of this tube is very close to zero.

ADV..ANTAGES OF THE NEW CELL

Like the single-tube flat cell, the double- tube flat unit offers many practical advan- rages over the cylindrical capillary units. Not least is its superior optical quality which completely eliminates distortion and allows very precise focusing on particles at any level in the observation tube. With the flat cell, good dark-field conditions are also obtained without elaborate lighting systems. Particles tha t scatter light only feebly require the best dark-field conditions, which may be attained only by minimizing the concentration of particles in the suspension or the light path through the suspension (i.e., reducing the cell height). In the single- tube cell excessive reduction of cell height cannot be tolerated because this tends to increase the velocity gradients at the zero electroosmotic levels and thus reduce the reliability of electrophoretic measurements (9(b)). Consequently, in these cells some sacrifice in tube thinness must always be made for the sake of experimental accuracy. On the other hand, capillary thickness in the twin-tube cell is not a critical considera- tion, since readings are made at the center of the cell where the velocity gradient is zero and depth setting errors have little effect on the results. Thus, with this system the height of the observation tube may be reduced considerably to improve dark-field conditions without impairing the accuracy of the determinations. For technical and other reasons there is clearly a limit to this minimization of cell height. Tubes as thin

as 0.3 ram. (× 1 era. width) have been used by the authors. Tubes smaller than this might be useful, but there would probably be little virtue in attempting to reduce the height below about 0.2 ram., since uniformity of bore would become increasingly difficult to attain at these sizes.

Other specific advantages offered by the double flat-tube cell include (a) ease of location of the working (zero flow) level, which is also the level of maximum resultant velocity of the migrating particles, and (b) insensitivity of the results to slight errors in the selection of observation level, which may arise either through mis-setting of the microscope focus or possibly through the use of too large a depth of focus.

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