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Anal. Chem. 1990, 62, 2668-2672
proteins. That is, changes in the carbohydrate content/ structure may result in a more or less sensitive dose response with each of the homogeneous lectin-based assays (i.e., change in the ED,, value for given glycoprotein). Such an approach is currently under study with the development of additional assays (e.g., sialic acid) and the specific application of this methodology for detecting changes in carbohydrate structure within recombinant glycoprotein therapeutic products.
ACKNOWLEDGMENT We gratefully acknowledge I. J. Goldstein from the Biochemistry Department a t the University of Michigan Medical School for his helpful preliminary discussions regarding this work. We also wish to thank Hanae Kaku from the same department for assisting us in determining the degree of saccharide substitution within the enzyme-saccharide conjugates used in these studies. LITERATURE CITED Monroe, D. Anal. Chem. 1984, 56,920A-931A. Voller, A., Bidwell, D. E., Collins, W. P., Eds. Alternative Immunoassay; John Wlley & Sons: New York, 1985; pp 77-86. Maggio, E. T., Ed. Enzyme-Immunoassay; CRC Press: Boca Raton, FL, 1980. Ollerich, M. J . Clin. Chem. Clin. Biochem. 1980, 18, 197-206. Tsalta, C. D.; Rosario, S. A.; Cha, G. S.; Bachas, L. G.; Meyerhoff, M. E. Mikrochim. Acta 1989, I , 65-73. Rubenstein, K. E.; Schnekler, R. S.; Ullman, E. F. Biochem. Biophys. Res. Commun. 1972, 47. 846-851. Bachas, L. G.; Meyerhoff, M. E. Anal. Chem. 1988, 58, 956-961. Tsalta, C. D.; Bachas, L. G.: Daunert, S.;Meyerhoff, M. E. Biotechnology 1987, 5 (2). 148-151. Cha, G. S.;Meyerhoff, M. E. Anal. Chim. Acta 1988, 208, 31-41. Tsaka, C. D.; Meyerbff. M. E. Anal. Chem. 1987, 59, 837-841. Daunert, S. S.; Bachas, L. G.; Meyerhoff, M. E. Anal. Chim. Acta 1988, 60,43-62.
(12) Daunert, S. S.; Bachas, L. G.; Ashcom, G. S.; Meyerhoff, M. E. Anal. Chem. 1900, 62, 314-318. (13) Provost, Y.; Frinotti, R. J. J . h u m . Clin. 1984, 3, 197-213. (14) So,L. L.; Goldstein, 1. J. J. BM. Chem. 1967, 242(7), 1617-1622. (15) Goldstein, I.J.; Hollerman, G. E.; Smith, E. E. Biochemistry 1985, 4 , (5), 876-883. (16) Goldstein, I.J., Ed. The Lectins, Properties, functions, and Applications in Biolcgy and Medicine; Academic Press: New York, 1986. (17) Bubney, J. T. Mol. Cell. Biochem. 1978, 27,43-63. (18) Ebisu, S.; Iyer, R. N.; Goldstein, I.J. Carbohydf. Res. 1978, 67, 129-131. (19) Iyer, R. N.; Goldstein, I.J. Immunochemistry 1973, 70, 313-332. (20) Schultz, J. S.; Mansouri, S.; Goldstein, 1. J. Diabetes Care 1982, 5, 245-253. (21) Schaal, V. D.; Ineke, A. M.; Logman, T. J. J.; Diaz, C. L. Anal. Biochem. 1984, 140, 48-55. (22) Dubios, M.; Gills. K. A.: Hamikon, J. K. Anal. Chem. 1958. 28 (3). .. 350-356. (23) Rowley, G. L.; Rubenstein, K. E.; Hurjm. J.; Ullman, E. F. J . Biol. Chem. 1975, 250,3759-3766. (24) Hayes, C. E.; Goldstein, I . J. J. Biol. Chem. 1974, 249 (6), 1904- 1914. (25) Kumar, G. S.; Appukuttan, P. S.;Basu, D. J. Biosci. 1982, 4 , 257-261. (26) Kabakoff, D. S.; Greenwood, H. M.; Alberti, K. G. M. I n Recent Advances in Clinical Blochemistry; Price, C. P., Ed.; Churchill Llvlngstone: London, 1981; Vol. 2. (27) Williams, T. J.; Shafer, J. A.; Goldstein. I.J. J. Biol. Chem. 1978a. 253,8533-8537. (28) Williams, T. J.; Homer, L. D.; Shafer, J. A.; Goldstein, I. J.; Garegg, P. J.; Hultber, J.; Irersen, T.; Johansson, R. Arch. Biochem. Biophys. 1981, 209,555-554. (29) Brewer, C. F.; Brown, R. D. J. Biochem. 1979, 78, 2555-2562. (30) Biewenga, J.; Hiemstra, P. S.; Steneker, I.; Daha, M. R. Mol. Immuno/. 1989, 26 (3). 275-281. (31) Hagiwara, K.; Cassare, D. C.; Kobayashi, K. J.; Vaerman, P. Mol. I m munol. 1988, 25 (I), 69-83.
RECEIVED for review July 5 , 1990. Accepted September 17, 1990. This work was supported by a grant from the National Science Foundation (NSF No. 8813952).
Influence of Particle-Wall and Particle-Particle Interactions on Retention Behavior in Sedimentation Field-Flow Fractionation Yasushige Mori,* Kazuyoshi Kimura,’ and Masataka Tanigaki Department of Chemical Engineering, Kyoto University, Kyoto 606, Japan I n sedmentatiar flekctlow fradlonatbn (SdFFF) experiments carrled out with carrier solutions of low surfactant concentratlons or disWed water, the retentlon ratlo of the sample partlcles increased from the values predlcted by the theory of 0kldk.rgS and his coworkers, in which the sterlc effect has been taken Into conskleration. To explorln thk phenomenon, this paper discusses theoretically the perturbation behavlor In the retention by the partidewall and the partlcle-particle interactk#rs due to electrostatic repulsive and van der Waals’ attractlve forces. The influence of these lnteractkns was-not significant at low sample concentratlons below 0.1 % and at hlgh lonk strengths of the carrier solution above M. However, under low lonlc strength conditions of the carrler solutlon, the concentration profiles in the channel spread wldely, and the estimated retention time decreases from the Glddlngs’ theory. The contrlbutlon of the partlcle-partlcle interaction Increases at hlgh sample concentration. The retention t h e calculated by the theory described in thls paper agreed fair’ well with the experhnental data at varlow Ionic strengths of the eluent.
* To whom correspondence should be addressed. Present address: Sumitomo Electric Industries Co., Osaka, Japan.
INTRODUCTION Field-flow fractionation (FFF) is classified as a one-phase chromatography technique in which an externally adjusted force field is applied to the suspended particles under motion in a channel (1-3). Sedimentation FFF (SdFFF) is one FFF technique that uses a centrifugal force field as the external field. It is suitable for the characterization and the fractionation of colloidal particles in the submicron range. The theoretical basis of SdFFF was originally presented by Giddings and his co-workers (4-6). This “standard” theory by Giddings et al. has advantages because it requires only the densities of particles and the eluent and experimental operation conditions, such as the flow rate, the strength of external field, temperature, and the channel dimensions. The average particle sizes converted by thistheory from the retention times measured by using an aqueous solution with 0.1% Aerosol OT (AOT) surfactant as the eluent were generally found to agree well with the values obtained from the suppliers, quasi-elastic light-scattering spectroscopy (BELS), and/or electron microscopy, although SdFFF tended to give sizes somewhat smaller than other techniques (7-11). Recently, Hoshino et al. reported that the retention behavior depended on the kinds and the concentration of surfactant added in the eluent (12). This fact was explained by the authors to be due to the different states of the interface
0003-2700/90/0362-2668$02.50/00 1990 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 62, NO. 24, DECEMBER 15, 1990
between the solvent stream and the channel wall that adsorbed surfactant. Takeuchi et al. (13,14) showed that the dependence of the eluent condition on the retention behavior is due to a small deviation from the parabolic profile of the flow near the channel wall, from their experimental results, which were performed at almost the same conditions as in ref 12. On the other hand, the authors reported that the sizes calculated from the experimental results by using the "standard" theory were underestimated compared with those by QELS due to the interparticle repulsion, when the eluent with low ionic strength was used (11). Hansen et al. (15, 16) reported the perturbation behavior of the retention time due to the particle-wall interaction, the overloading of the sample, and particle-particle interaction, based on the experimental results using various conditions of the carrier solutions. They calculated the contribution of the electrostatic and van der Waals' forces between the particle and channel wall (I@, but did not treat the particle-particle interaction in the same manner (16). This paper reports the theoretical perturbation in the retention in SdFFF due to the particle-wall interaction, in a manner similar to that in ref 15 but using more detailed expressions for the interaction. Effects of the particleparticle interaction including the influence of the injected-sample concentration are also discussed in a fashion similar to that of the particle-wall interaction. Finally, this calculation is compared with the experimental results. THEORY Transport Equation of t h e Particles in FFF. The motion of particles in the channel of FFF is determined by the combined action of the flow, the applied field, and the Brownian migration. The flux of the particles, J, can be written as a vector sum of the x axis component, J,, in the direction of the induced external field, which is perpendicular to the z axis, the direction of the fluid flow, and the z axis component, J,.
J, = -D(&/&)
+ UC
(1)
J , = -D(&/&)
+ uc
(2)
Here, D is the diffusion coefficient of particles whose diameters are D,. U is derived by use of the viscous resistance force of Stokes' law and the external force, FeXt, from the field
u = Fext/
(QnfiDp)
= ~ ( u ) [ ( x / w-) ( x / w ) ~ I
+ UC = 0
J , = uc
to/tR
(9)
where G is the field strength and Ap is the density difference between particle and eluent. The negative sign in eq 9 means that the sign of the x axis is taken to be in the opposite direction of the field. In this case, the concentration profile, c ( x ) , and the retention ratio, R, were obtained by Hovingh et al. (5). c(x) = c, exp[-x/(Xw)]
R=
t,/tR
= 6X(coth [1/(2X)] - 2x1
(10) (11)
Here, X 7 D / (Uw) and is expressed as follows by use of the Stokes-Einstein relationship for the diffusion coefficient of the particle: h = 6kT/(nDP3ApGw)
(12)
where lz is the Boltzmann constant and T is the absolute temperature. The modified retention ratio is obtained by including the steric effect; that is, particles whose radii are a = Dp/2 are excluded from a layer adjacent to the wall (6).
R = 6(a - a2)+ 6 h ( l - 2a){coth [1/(2X*)] - 2X*\
(13)
where a = D,/(Bw) = a/w
(14)
A* = X/(1- 2a)
(15)
ParticleParticle and Particle-Wall Interactions. The total potential energy of interaction between particle spheres, V,,, or between a particle sphere and a plate wall, V,,, is obtained as the sum of that of the London-van der Waals attraction and of electrostatic repulsion ( 17-19).
v~~= v A , ~+~ v R , ~ ~
(16)
The potential energy due to the London-van der Waals attractive force for particle-particle interaction is
and that for particle-wall interaction is
(5) (6)
"Standard" Retention Theory of FFF. The retention ratio R of particles is defined as the ratio of the elution time for the particles, t ~to,that for a nonretained peak,to,as usual in chromatography.
R =
Fext= F, = -nD;ApG/6
(4)
In the "standard theory of FFF, the concentration gradient in the x direction is assumed to be at a steady-state or quasi-equilibrium condition. In the z direction, the first term in eq 2 is assumed to be much smaller than the second one. -D(&/dx)
In eq 8, u p ( x ) is replaced by u ( x ) , because small particles can safely be assumed to move with the same velocity as the fluid at the center of the particles. Once the expressions for the external force are known, c(x) can be calculated from eq 5, and R from eq 8. In the "standard theory", the centrifugal force, F,, only is considered as the external force in the case of SdFFF
(3)
and u is the velocity of the laminar flow in the channel whose thickness is w. U(X)
2669
(7)
Since the average velocity of the sample, (up), and that of the eluent, ( u ) , are inversely proportional to t R and to,respectively, the ratio R can also be written as
R = ( u p ) / ( u ) = ( c ( ~ ) ~ , ( x ) ) / [ ~ c ( ~ ) ) ( ~(8)) l
H is the gap distance between two particle surfaces. The effective Hamaker constant A's can be calculated by the fundamental Hamaker constants. Subscripts 1 and 3 refer, respectively, to the particle and the wall material, and subscript 2 represents the medium; that is water in the present case. The expression of electrostatic interaction is known only as approximate equations at the limited value of Ka, where 1 / refers ~ to the Debye-Hukel electrical double-layer thickness. For particle-particle interaction
2670
ANALYTICAL CHEMISTRY, VOL. 62, NO. 24, DECEMBER 15, 1990 KU
>> 1
V,,,, = (32actoa[kT\k,/(Ze,)]2) In [I + exp(-~H)] (20)
+
64~tt,u(kT\k,)~(H a )
1
Z2eO2(H+ 2a) and for particle-wall interaction
vR,pw
KU
--
>> 1
(64att,a\k,\kw[kT/(Ze,)]2) In (1+ exp[-K(x KU
--
v R , ~ ~
1
2 3 Ipm) Figure 1. Local concentration profile of 506-nm particles at various ionic strength solutions. (N = eq 10; S = steric effect included; s o l i lines = particle-wall interaction included.)
0
X
- a ) ] ) (22)
> 1. As the range of KU in the present work is from 0.05 to 30, eqs 21 and 23 are used instead of eqs 20 and 22, when Ka is lower than 10. The particle-wall interaction force, Fpw, can be calculated by differentiating V,, with respect to x .
F~~ = -(av,,/ax)
(26)
The calculation of the particle-particle interaction force, Fpp, is a little more complicated, because V,, is expressed as a function of H. The particle-particle interaction force can be expressed as
F,,
= -(a
v,,/am
ac)(ac / ax
(27)
T o obtain the relationship between c and H, particles were assumed to be located at the center of spheres whose radii are a + H / 2 . The local particle concentration by volume fraction can be expressed by the maximum packing volume ratio, P,, as follows: c = a3pp/vp,
+ [ ( a + ~ / 2 ) 3 / ~-, a3ipL)
(28)
where pp and pL are the densities of particle and eluent, respectively. The value of P, is taken to be 0.74. H is derived from eq 28 as
H = 2a([(pp/c - A p ) P m / p ~ l ” ~- 11
(29)
To include the particle-wall interaction as an extra force, eq 5 has to be integrated by substituting F, + Fpwinto Felt Fppshould further be added to Fext,to account for the particle-particle interaction. In order to calculate the concentration profile by numerical integration, the channel thickness was divided into lo00 points with finer spacings near the wall. The minimum interval corresponds to the space divided equally into 6400 points. The method of backward differentiation formula was used in this numerical integration, because
0
2
1
3
4
(pm) Figure 2. Comparison of local concentration profiles for 506-nm particles with particle-wall interactin (dashed lines) and those with addffional particle-particle interaction (solid lines) at 0.1 % average Concentration. X
Table I. Constants List for Calculation
wall: Teflon
particle: polystyrene ( v ) = 60 cm/min
T = 293 K LU =
125 pm
channel length = 58 cm
centrifugal speed = 2000 rpm diameter of rotor in centrifuge = 20 cm = 9.5 X
AIz3 = 5.6 X & = -80 mV &. = -10 mV €(water)= 78.3
J J
of the high stiffness of the equation for the calculation of the concentration profile.
RESULTS AND DISCUSSION Effect of van der Waals’ and Electrostatic Interactions on Concentration Profiles. Figure 1 illustrates the concentration profiles obtained from eq 5 considering the particle-wall interaction as an extra force, for polystyrene latex (D,= 506 nm, pp = 1054 kg/m3). The conditions for the calculation are listed in Table I together with Hamaker constants and the surface potentials (15). The profde at high ionic strength of the eluent is approximately similar to that calculated from the “standard” theory including steric effect (line S). But as the ionic strength decreases, the profile spreads widely, and the position of average concentration along the x axis deviates from that of the “standard” theory. The retention time, then, is expected to become shorter. Figure 2 shows the comparison of the concentration profiles when the particle-particle interaction is considered in addition to the particle-wall interaction. At high ionic strength condition, both profiles closely coincide with each other, because of the small Debye length, 1 / ~ compared , with the distance between particle surfaces. In the case of lower ionic strength,
ANALYTICAL CHEMISTRY, VOL. 62, NO. 24, DECEMBER 15, 1990
2671
60
a . DP =SO6 nm
I
$ + 3
I=
I
$
M
f 40
40
20 U
0 0
2
4 X
8
6
10
2
0
4
(pm 1
Flgure 3. Effect of average concentration on local concentration profile (I = lo-’ M, D, = 506 nm): (solid lines) considering all interactions, ( c ) = 5, 2, 1, 0.5,0.2,0.1 % from top to bottom; (dashed lines) with particle-wall interaction only, ( c ) = 0.2, 0.1 % from top to bottom.
the profiles considering both interactions spread more widely than those when only the particle-wall interaction is considered, because particles cannot approach each other due to the high repulsion force. The concentration profile with particle-particle interaction included strongly depends on the average concentration in the x direction or the concentration a t the sample injection. Figure 3 indicates the effect of the average concentration in the x direction on the local concentration profiles at M ionic strength condition. The local concentrations calculated with particle-wall interaction only are proportional to the average concentration. Since the profiles are similar in shape, the retention ratio does not depend on the average Concentration. On the other hand, the profiles differ considerably when particle-particle interaction is included. In the case of high average concentration, particles cannot be accumulated near the wall as at low average concentration, although the maximum concentration becomes large. The retention ratio is expected to depend on the average concentration. Figure 4 shows the effect of the ionic strength on the concentration profile at high average concentration. In the case of Figure 4a for 506-nm particles, the local concentration calculated without particle-particle interaction becomes over 10070,because the centrifugal force collecting particles near the wall is higher compared with Brownian migration and the electrostatic repulsive force between particles and the wall. The calculated lines including particle-particle interaction show a plateau peak due to the repulsive force among the particles, even at high ionic strength conditions. On the other hand, the local concentration profile does not deviate from the “standard” theory with steric effect at high ionic strength in Figure 4b, because of low centrifugal force due to the small particle mass (Dp = 208 nm, pp = 1054 kg/m3). The local concentration begins to show the plateau again as the ionic strength decreases. It also indicates that particle-particle interaction becomes dominant at low ionic strength. Effect of van der Waals’ and Electrostatic Interactions on Retention. For a first-order approximation in the calculation of the retention ratio with particle-particle interaction, the concentration profiles in the x direction are assumed to be constant, independent of the z direction. With this approximation, R can be calculated by eq 8. Figure 5 shows the relationship between the retention ratio, R, and the injected concentration, ch,, at the same conditions as in Table I. The retention ratio by eq 13 (line S) is larger than that by eq 11 (line N), due to the steric effect, as can be understood from the difference in the concentration profiles in Figure 1. The retention ratio with particlewd interaction is larger than that of “standard” theory. These three calcu-
401
I
I
I
I
8
6
(pm)
X I
I
I
I
I
I
I
I
I
I
I
3 30 +
3
20 U
10
0
10 15 (pm) Flgure 4. Local concentration profiles at 1 % average concentration in various ionic strength eluents: (a) D, = 506 nm, pp = 1054 kg/m3; (b) D, = 208 nm, pp = 1054 kg/m3. (S= standard theory with steric
5
0
X
effect: solid lines = all interactions included.) lk
1
I1111111
I I1111111
I
I111111l
I
I
“”F4
j/ 0.01
0.001
1
I
0.01
I1111111
0.1 (wt.%)
I
I
I1111111
10
1
Cinj
I1111111
I
/-,-1 IIIII
0 .5 Tr
0. 2
0.001
0.1
0.01 Cinj
1
10
( w t . %1
Flgure 5. Effect of injected concentration on retention ratio: (a) D = 506 nm, p = 1054 kg/m3; (b) D, = 208 nm, p, = 1054 kg/mf (N = eq 11; = eq 13; solid lines = considering particle-wall interactin only, dashed lines = considering all interactions (I = lo“, lo3, M from top to bottom).)
6
latedaretention ratios do not depend on the injected concentration. In contrast, the predicted retention ratio including all interactions increases rapidly with the injected concentration above a certain limiting value. This limiting value is small, when the ionic strength of the eluent decreases or the particle mass increases. This is due to the particle-particle
2672
ANALYTICAL CHEMISTRY, VOL. 62,NO. 24, DECEMBER 15. 1990
~
1
about 4 (11). Considering that AOT is a neutral salt, the ionic strength of the 0.1 % AOT solution is higher than lo4 M. The effect of van der Waals’ and electrostatic interactions on the retention behavior is negligible, if 0.1 70 commercial AOT solution is used as the eluent and a small amount of the sample is injected.
0.1
CONCLUSION At low ionic strength in the eluent solution, the retention of SdFFF deviates from the prediction by the “standard” theory, resulting in the underestimation of the particle size. In this case, the retention ratio can better be estimated by the calculation considering particle-particle and particle-wall interactions. For the operational conditions of high injected concentration and of low ionic strength eluent, the particle-particle interaction becomes important, and the prediction of the retention ratio becomes difficult, because R from eq 8 is not constant through the channel due to the change of the concentration profile. When the retention ratio is calculated considering all interactions, the electrostatic property and Hamaker constants of the particles and the channel wall are necessary. From this fact, the solution with a proper ionic strength, such as M, may be recommended as the eluent of SdFFF. In this case, the “standard” theory including steric effect can safely be used for the prediction of the retention ratio, i.e. particle size.
0011 10
I
I
I 1 I I I I I
100
I
I
I
\~
IUIIi
1
1000
l / h
Figure 6. Comparison of observed and calculated retention ratios at 0.1% injected concentration. (Calculated: N = eq 1 1 ; S = eq 13; solid lines = considering particle-wall interaction only, dashed lines = considering all interactions ( I = lo-’, lo-’, lo-‘, M from top to bottom).) (Experimental: distilled water (0); 0.1 % Emulgen 15WP (A); 0.01% SDS 8); sample concentration and volume in the injection port are 0.2 wt % and 2 gL. respectively: D, = 208,294,410,506 nm, and pp = 1054, 1054, 1056, 1054 kg/m3, from left to right.)
interaction, especially electrostatic repulsion predominant at high injected concentrations. However, as the actual average concentration in the x direction decreases rapidly when particles run through the channel, the retention ratio will be smaller than the values indicated in Figure 5 at high injected concentrations. Figure 6 shows the comparison of the observed retention ratios (14) and the calculated ones. The experiments (14) were carried out at the conditions shown in Table I and in the caption of Figure 6. Three different solutions were used as the eluent in the experiment: distilled water, 0.1% Emulgen 150PP nonionic surfactant solution, and 0.01% sodium dodecylbenzenesulfonate (SDS)anionic surfactant solution (14). The order of the ionic strength for these solutions is estimated to be lo4, and lo-‘ M, respectively, although it could not be estimated precisely. 1 / X in Figure 6 corresponds to the particle mass, because all experiments were performed at the same operational conditions. Approximate agreement between the experimental results and the calculations is recognized. The retention ratios including all interactions (the dashed lines in Figure 6) were calculated, assuming that the sample concentration was kept constant a t 0.1%. However, band broadening is certain to rapidly dilute the sample from the injected concentration and weaken the particle-particle interaction. The retention ratio, which would be predicted from a more precise theory including all interactions in detail, therefore, should lie between the dashed lines and the solid lines. From the above discussion, it can be concluded that the agreement between the calculated and the experimental results is satisfactory. The prediction, at least, is better compared with the “standard” theory. When the eluent has M ionic strength and the injected sample concentration is below 0.1 %, both calculated lines in the present study agree with those predicted by eq 13, i.e. the “standard” theory considering the steric effect, as shown in Figures 5 and 6. The pH value of 0.1% commercial AOT anionic surfactant solution (ca. 2 X M) is reported to be
ACKNOWLEDGMENT We thank M. Takeuchi of JEOL Ltd., Japan, for kindly permitting us to quote his experimental results in advance of publication. LITERATURE CITED Caklweii, K. D. Modern Method.s of fartick Size Analysis; Barth. H. G., Ed.; John Wiiey and Sons: New York, 1984; Chapter 7. Janca, J. Field-Flow Fracflonaffon; Marcel Dekker: New York. 1987. Giddings, J. C. Sep. Sci. 1988, 7 , 123-125. Giddings, J. C. J. Chem. fhys. 1988, 4 9 , 81-85. Hovingh, M. E.; Thompson, G. H.; Giddings, J. C. Anal. Chem. 1970, 4 2 , 195-203. Giddings, J. C. Sep. Sci. Techno/. 1978, 73, 241-254. Kirkland. J. J.: Rementer. S. W.: Yau. W. W. Anal. Chem. 1981. 5 3 . 1730-1736. Yau, W. W.; Kirkland. J. J. Anal. Chem. 1984, 56, 1461-1466. Janca, J.; Pribylova, D.; Konak, C.; Sediacek, B. Anal. Sci. 1987, 3 , 297-300 - - . - - -.
Mori, Y.; Merkus, H. G.; Scariett. B. Part. Part. Syst. Charact., unpublished results. Mori, Y.; Merkus, H. G.; Scariett, B. J. Chromatogr. 1990, 575, 27-35. Hoshino, T.; Suzuki, M.; Ysukawa, K.; Takeuchi, M. J. Chromatogr. 1987, 400, 361-369. Takeuchi, M.; Saito, T.; Hoshino, T. Proceeding of Chromatography Internationel Symposium; The Division of Liquid Chromatography of the Japan Society for Analytical Chemistry: Tokyo, Japan, 1989; pp 71 1-714. Takeuchi. M. Personal communication. Hansen, M. E.; Giddings, J. C. Anal. Chem. 1989, 67, 811-819. Hansen, M. E.; Giddings, J. C.; Becketi R. J. Colloid Interface Sci. 1989, 732, 300-312. Kitahara, Y., Watanabe, A., Eds. Kaimen Denki Gensyou; Kyouritu Shuppan: Tokyo, 1972. Verwey, E. J. W.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloid; Elsevier: Amsterdam, 1948. Ross, S.; Morrison, 1. D. Colloidal System and Interfaces; John Wiley & Sons: New York. 1988.
RECEIVED for review June 19, 1990. Accepted September 7, 1990.
