2040
Langmuir 1991, 7, 2040-2047
Measurement of Mass and Thickness of Adsorbed Films on Colloidal Particles by Sedimentation Field-Flow Fractionation Ronald Beckett Water Studies Centre, Department of Chemistry, Monash University, Caulfield East, Victoria 3145, Australia
John Ho, Yong Jiang, and J. Calvin Giddings' Field-Flow Fractionation Research Center, Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 Received January 2,1991. I n Final Form: April 12, 1991 A sensitivemethod has been developed for measuring the mass and mean thickness of an adsorbed layer on colloidal particles using sedimentation field-flow fractionation (SdFFF). The two types of particles used in these experiments were 0.198-pm polystyrene latex spheres and neutrally buoyant (in water) latex beads (0.369 pm) composed of a vinyl toluene-tert-butylstyrene copolymer. The adsorption of a thin film of material on the particles results in a change in their effective mass that can be mathematically related to a corresponding change in the measured retention time. This shift in retention is significantproviding the mass of the coating is greater than a few 10-16 g. From the observed change in retention, the mass and the thickness of the film can be calculated. The mass and thickness of adsorbed films of human y-globulin, ovalbumin, ribonucleic acid (RNA),cortisone,and barbital were determined. The mean thickness of the surface films, with values ranging from -0.1 to 20 A, was found to vary with the concentration of the coating materials in the suspension. The experimental data were used to plot adsorption isotherms. Furthermore, the two adsorbed proteins led to partial aggregation of the beads to form dimers, trimers, etc., as evidenced by additional peaks in the fractograma. The presence of dimers and trimers in these peaks was confirmed by electron microscopy.
Introduction The adsorption of polymers, proteins, and other organic materials on particles is important in numerous industrial and clinical applications. Examples include numerous latex agglutination immunoassay tests,' the performance of biomedical implants,2 microbial a d h e ~ i o nand , ~ wastewater treatment.' Recent studies have demonstrated that natural organic coatings on soils, sediments, and aquatic suspended particulate material mediates many of their properties such as adsorption behavior, surface charge, and colloid ~ t a b i l i t y In . ~ addition, ~~ the literature contains numerous reports of research on the adsorption of metals and other pollutants onto various solid substances.6 The importance of this in determining the fate and effect of environmental pollutants has attracted particular attention.' Several techniques are available for measuring the average thickness of an adsorbed layer. These include photon correlation spectroscopy or PCS? ultracentrifugationSJ0 ellipsometry,ll small-angle neutron scattering,12 and the hydrodynamic flow method.13 However, all of * Corresponding author. (1) Bangs,L. B. Uniform Latex Particles; Seradyn, Inc.: Indianapolis, IN, 1984. (2) Absolom, D. R.;Neumenn, A. W. J.Biomed. Mater. Res. 1987,21, 161. (3) Marshall, K. C. Adu. Colloid Interface Sci. 1986, 25, 59. (4) Beckett, R.,Ed. Surface and ColloidChemistry in Natural Waters and Water Treatment; Plenum: London, 1990. (5) Beckett, R.; Le,N. P. Colloids Surf. 1990,44, 35. (6) Harding, I.; Healy, T. W. Prog. Water Technol. 1979, 11, 265. (7) Hart, B. T.,Ed.The Role of Particulate Matter in the Transport and Fate of Pollutants; Water Studies Centre, Chisholm Institute of Technology: Melbourne, 1988, pp 200. (8)Killmann, E.; Maier, H.; Kaniut, P.; Gutling, N. Colloids Surf. 1985, 15, 261. (9) Fontana, B.J.; Thomas, J. R.J. Chem. Phys. 1961,65,480. (10) Cohen, Y.;Metzner, A. B. Macromolecules 1982, 15, 1425.
these techniques suffer from certain limitations, and discrepancies have been found in the results obtained from various studies.12 For example, none of the methods that directly measure particle diameter and obtain film thickness by subtraction (e.g., PCS,neutron scattering, and hydrodynamic flow) are very sensitive to layer thicknesses less than a few percent of the particle diameter. In this paper we develop an alternative approach for measuring the mass and thickness of adsorbed layers using sedimentation field-flow fractionation (SdFFF). This method is relatively simple in operation and highly sensitive to small amounts of adsorbed material. The theory and versatility of field-flow fractionation (FFF) for particle and polymer fractionation and characterization are well documented in the 1iterature.l4JsFFF is an elution method analogous to liquid chromatography that can be used to fractionate a broad range of samples from molecules as small as lo00 Da up to particles 100 pm and larger in diameter. FFF consists of various subtechniques responsive to different particle properties and applicable to different parts of the overall size range. SdFFF was used in this study as the most appropriate FFF subtechnique because the measured elution volume of the sample is directly related to the effective mass of (11) Takahashi,A,; Kawaguchi, M.; Hayashi, K.; Kato, T. In Polymer Adsorption and Dispersion Stability; Goddard, E. D., Vincent, B., Eds.; ACS Symposium Series 240; American Chemical Society: Washington, DC, 1984; p 39. (12) Cosgrove, T.;Vincent, B.; Crowley, T. L.; Cohen Stuart, M. A. In Polymer Adsorptionand Dispersion Stability; Goddard, E. D., Vincent, B., Eds.; ACS Symposium Series 240; American Chemical Society: Washington, DC, 1984; p 147. (13) Kniewske, R.;Kulicke, W. M. Macromol. Chem. Phys. 1983,184, 2173. (14) Giddings, J. C. Chem. Eng. News 1988, 66, 34. (15) Janca, J. Field-Flow Fractionation; Chromatographic Science Series; Marcel Dekker: New York, 1988 Vol. 39, p 336.
0743-7463/91/2407-2040$02.50/0 0 1991 American Chemical Society
Langmuir, Vol. 7, No. 10, 1991 2041
Measurement of Thickness of Films by SdFFF
its constituent particles (includingany adsorbed material) by well-established equatioml6 In SdFFF, the sample particles are carried by a laminar flow stream through an unpacked ribbonlike channel coiled within a centrifuge rotor (see Figure 1 ) . The flow axis is perpendicular to the direction of sedimentation. Particles of different effective masses (thus normally of different sizes or densities) sediment differentially against the outer wall of the channel, forming equilibrium clouds of differing average thickness. Separation of particulate materials is subsequently brought about by the flow-induced transport of sample components at different velocities according to the mean positions of the sample clouds within the laminar flowstream of carrier fluid. Thus the more massive particles, whose clouds are driven closer to the accumulation wall, are displaced by the slower moving fluid laminae near the wall. These particles will be retained longer than their less massive counterparts according to this mechanism. The level of retention and fractionation can be controlled by the applied sedimentation force on the particles. Because of the simplicity of the system, the elution time of each homogeneous fraction is related, by rather direct theory, to particle mass and thus size and density. Accordingly, it has been demonstrated that spherical colloidal materials can be accurately characterized with respect to particle diameter and density using this method.17J8 In this study, a heterogeneous particulate system consisting of adsorbed materials on uniform colloidal particles is examined. For the case of polystyrene latex beads, which have a density of 1.050 g/cm3,17the surface coating (if denser than the aqueous carrier) results in an increase in the measured retention time compared with that observed for the uncoated beads. Neutrally buoyant latex particles (vinyltoluene/tert-butylstyrene), with a density very close to 1 g/cm3, were also employed in this study. The neutrally buoyant particles are not retained under the experimental conditions utilized; however, the additional mass adsorbed on the particles results in noticeable retention. In both cases the measured retention can be used to calculate the mass of the adsorbed coating with an exceptional sensitivity down to levels of a few attograms (10-’8 g), which is sufficiently small to detect much less than a monolayer coverage on the particle surface. We will demonstrate below how the SdFFF method is capable of generating adsorption isotherms utilizing this ability to directly measure the increase of mass of the particles due to the adsorbed molecules. A modified SdFFF theory is developed to calculate the thickness of the coating materials on the colloid particles.
4 t
high-mass
particles
particles
Figure 1. Schematic diagram showing the cross section (edge view) of an SdFFF channel and the separation mechanism for particles of different effective mass as explained in text.
x from the accumulation wall is thereforel9
c = co exp(-x/l) (1) where co is the concentration at the accumulation wall (at x = 0) and 1 is the mean particle distance from the wall. The distance 1 is related to the sedimentation force F exerted on a single particle byI9
1 = kT/II;1
(2)
where k is Boltzmann’s constant and T is the absolute temperature during elution. The mean particle elevation 1is often expressed in terms of the dimensionless retention parameter X X = l / w = kT/II;lw (3) where w is the channel thickness. The sedimentation force exerted on a homogeneous spherical particle of mass m,,density p,, and diameter d is ?r
F = m,C(l - p/p,) = - Gd3 Ap, (4) 6 where p is the carrier density, G is the field strength expressed as acceleration, and Ap, = pp - p. We note that this treatment is applicable when Ap, and hence F are either positive or negative, the positive values indicating that the particles “sink” and thus accumulate at the outer wall of the channel, whereas negative values are obtained when the particles “float” toward the inner wall. When eq 4 is substituted into eq 3, we get the wellknown relationship between X and particle mass n or diameter dz0 A=
kT m,wGI(1 - p / p p ) l
--
6kT ?rwGd31Ap,l
(5)
The retention parameter X is, in turn, related to the retention ratio R by the general retention equation
Theory The mechanism of retention in SdFFF has been described previously.16 In brief, particles in a small sample of a colloidal suspension injected into the channel are forced to accumulate at one of the channel outer walls by the applied centrifugal force. In the majority of cases, where the particles are more dense than the carrier fluid, accumulation will occur at the outer wall as depicted in Figure 1. When sedimentation equilibrium has been established, the concentration profile across the channel is exponential; the concentration c of particles at distance
where t o is the void time and t , is the retention time (Le., the time required to elute a given retained sample component). Equation 6 can be closely (within -5%) approximated by16
R = 6X(1- 2h) R = 6X when R
(16) Giddings, J. C.; Karaiskakis,G.; Caldwell, K. D.;Myers,M.N. J.
Colloid Interface Sci. 1983, 92, 66. (17) Giddinas. J. C.: Karaiskakis. G.: Caldwell, K. D.SeD. Sci. Technol. 1981, 16, 607. (18) Nagy, D . J. Anal. Chem. 1989,61, 1934.
(7)
provided R < 0.7 or
< 0.15.
(19) Giddings, J. C.; Yang,F. J. F.;Myers, M. N. Anal. Chem. 1974,
46, 1917.
(20)Giddings, J. C.; Karaiskakis, G.; Caldwell, K. D. Sep. Sci. Technol. 1981, 16, 607.
Beckett et al.
2042 Langmuir, Vol. 7, No. 10,1991
-
Transformation of eq 11 gives
7 particle
P Figure 2. Nature and dimensions of idealized particle and adsorbed coating considered in this paper. The particle is neutrally buoyant when pD = p; under these circumstances only the adsorbed coating is subject to a sedimentation force, measurable by SdFFF.
Thus the use of one of the equations (6-8) in combination with eq 5 enablesthe mass or diameter of a colloidal particle to be calculated in terms of measured retention provided the densities of the carrier and particles are known. For the case in which the particle has an adsorbed film or coating of mass m , and average density p,, the net force acting on the particle and its coating in the centrifuge is obtained as an extension of eq 4
F = mp(AP,/P,)G + mc(APc/Pc)G
(9)
where Ap, (which may also be either positive or negative) is the density difference between the coating material and the carrier solution. For spherical particles with a thin outer coating of mean thickness h (see Figure 2), the sedimentation force will be
F = Ed3 App G + r d 2 h Ap, G = d2rG(% 6
6
+ hAp,)
(10) Equation 10 has been simplified by writing the shell volume as rd2h rather than by using the rigorous form r ( d 2 h + 3dh2 + 4h3+ 4h3/3). The former is a good approximation when h > h or ( d / 6 ) p p>> hp,. Unfortunately, for thin coatings this will generally be the case.
where the plus (+) sign applies when the particles are driven ("sink") to the outer wall, a condition specified by (d/6)ApP+ hAp, > 0, and the minus (-) sign is used when they "float" to the inner wall, (d/6)ApP+ hAp, < 0. We note that for surface films with an open (e.g., strongly hydrated) structure, the effective Apc will be lower and the h correspondingly larger than for a compact surface film. Alternately the mass of adsorbed material, based on eqs 9 and 3, is given by
where the same sign convention applies as for eq 13. Equation 13 can be used to calculate h from a single retention measurement provided d , Ap,, and Apc are known. Again the accuracy of the estimate of h obtained by using eq 13 will be reduced if the two terms on the left-hand side are large compared to the value of h. This will occur if the effective mass of the uncoated particle is much greater than the effective mass of the coating. Suitableconditions can be found by decreasing the ratio lAp,l/lAp,l. This ratio becomes zero when Ap, = 0, which applies when the particles are neutrally buoyant in the carrier medium. Under these conditions eq 13 reduces to
h=
kT XGw r d 21 ApJ
The corresponding mass of the adsorbedfilm m,is obtained from eq 14
m, =
kT X G 4 APcl/&I
(16)
Since meaningful retention (relative to that of the void peak) can be measured for X values as large as 0.2, masses as small as a few multiples of 10-18 g (a few attograms), corresponding to mean layer thicknesses of less than 0.1 A, can be distinguished under practical conditions. Plots of minimum detectable coating thickness (at X = 0.2 and w = 254 pm) versus G (in gravities) are shown in Figure 3 for various values of d2Apc. For example, in the case of y-globulin with a density of 1.36 g/mL adsorbed to neutrally buoyant particles in a dilute aqueous solution, use of the d2Ap, = 0.1 line would be appropriate for 0.53 pm diameter beads whereas the d2Ap, = 1 line would be used for 1.7 pm sized particles. We note that average layer thicknesses of less than a few angstroms imply less than monolayer coverage. The fact that average layer thicknesses as low as 0.01 A or less can be discerned illustrates the high sensitivity of the FFF technique for measuring the amounts of material adsorbed from solution. Subangstrom thicknesses clearly represent sparsely covered surfaces. Also given in Figure 3 is a plot of the minimum detectable effectivecoating mass (i.e., actual coating mass minus mass of carrier fluid displaced by coating material) versus G . While Figure 3 is ostensibly plotted for neutrally buoyant particles coated with adsorbate, the same results are approximatelyapplicable to slightly denser (or less dense) particles. A high sensitivity to small adsorbate deposits will still be realized for particles that are already retained
Langmuir, Vol. 7, No. 10, 1991 2043
Measurement of Thickness of Films by SdFFF I
PS latex + y-globulin
1
FFFmctionotion S 101
FFF System I Ilkis sludyl
lo4
I
0
G
(gravities)
5
IO
15
20
25
TIME (mid
Figure 4. Comparison of fractograms (from system I) of un-
Figure 3. Minimum detectable effective coating mass (dashed line, right-hand ordinate) and coating thickness (solid lines for different values of d*Ap,, left-hand ordinate) plotted against field strength (in gravities). In these calculations it is assumed that X must be 0.2 or less in order to adequately resolve the sample peak from the void peak.
coated polystyrene latex and the same latex beads treated with 1and 5 mg/mL of human y-globulin, respectively. The shift of the peaks to the right with exposure to increasing amwnts of protein is due to the increasing mass of the microspheres caused by protein adsorption. Run conditions were field strength 390 g (1500 rpm), stop-flow time 5 min, flowrate 0.73 mL/min.
moderately (e.g., tr = 1.5 to 5t0) before the surface layer is adsorbed.
flow period of 12 min was used for relaxation, after which the run proceeded under various specified conditions. Barbital and cortisone (used to coat the VT/BS latex) were dissolved in a minimum amount of methanol and diluted to the desired concentration with water. Yeast type IX RNA and ovalbumin were dissolved in water. An aliquot of 0.5 mL of each solution was added to 2.0 mL of the diluted (0.1% (w/w)) VT/ BS latex suspension. The suspension was allowed to stand at ambient temperature for about half an hour before analysis. FFF Conditions. For system I (used for the y-globulin coating experiment) the mixture was diluted further before injection. This was usually done by adding 150 pL of the Tris buffer to an aliquot of 5 pL of the mixture. A sample volume of 5 pL of this diluted solution was injected. The external field used was 390 g, which corresponds to a 1500rpm rotation rate of the centrifuge. The flowrate was held at -0.73 mL/min. The carrier for the FFF system was the same Tris buffer solution (pH 9.0) described above. The sample was detected. at 254 nm. For system I1 (used for barbital, cortisone, RNA, and ovalbumin), 20 pL of the dilute suspension prepared as described above was injected onto the channel and the centrifuge set at 9000 rpm (8628g). The temperature for all experiments was maintained at 25 "C and the carrier fluid was deionized water. After 20 min for relaxation, the carrier flow was started at 1.5 mL/min. Sample elution was recorded by using the system's UV detector at a wavelength of 254 nm.
Experimental Section FFF Equipment. Two sedimentation FFF systems were used in this work. System I, closely resembling the Model SlOl Colloid/Particle Fractionator from FFFractionation (Salt Lake City, UT), is based on a horizontal rotation axis with a rotation radius of 15.1 cm. In place of the normal 254 pm thick channel of the SlO1,a 127pm thickchannelwasusedfor thiswork. Thechannel walls were constructed of the Ni-rich alloy Hastelloy C. The tip-to-tip channel length L for System I is 86.5 cm. The void volume VO = 2.67 mL. The system was equipped with a Minipuls 2 pump from Gilson (Madison, WI) and a Model 153 UV detector from Beckman Instruments (Fullerton, CA). System I1 is a DuPont SF3 1000 instrument (DuPont Clinical and Instrument Systems Division, Wilmington, DE), based on a vertical rotation axis. This instrumental system has been described elsewhere.*l The channel for this system has a radius of rotation of 9.53 cm, w = 254 pm, L = 57.5 cm, and VO = 3.61 mL. The outer accumulation wall of the channel is titanium and the inner wall is Delrin. Materials. Water, deionized and purified by Barnstead and Nanopure ion exchange and filtration systems, was used to make all solutions including the carrier liquid for both FFF systems. Polystyrene latex beads of nominal diameter 0.198 pm were obtained from Seradyn Diagnostics (Indianapolis, IN). The 10% original suspension was diluted to 1% in a pH 9.0,lO mM Tris buffer solution. The buffer solution was prepared by making a 10 mM tris[hydroxymethyl]aminomethane(Tris) solution, then adding HN03 until the pH 9.0 value is reached. The "neutrally buoyant" particles were provided in a 10% (w/w) suspension of a vinyltoluidine/ butylstyrene copolymer (VT/BS) latex, 0.369 pm in diameter (also from Seradyn Diagnostics). This suspension was diluted to 0.1% in a 0.1% (w/v) FL-70 detergent solution (Fisher Scientific, Fair Lawn, NJ). All organic and biological coating materials were obtained from Sigma Chemical Company (St. Louis, MO). Preparation of the Coated Particles. The human y-globulin sample (used to coat the polystyrene latex) was dissolved in Tris buffer solution (pH 9.0) to get a 40 mg/mL stock solution. The stock solution was then diluted with the same buffer solution to get the desired concentration. An aliquot of 50pL of each solution was added to 50 pL of 1% polystyrene latex suspension (in pH 9.0 buffer solution). The mixture was then allowed to stand at room temperature (24 f 1 "C) for various specified intervals (usually about 2 h) before injection. Following injection, a stop(21) Kirkland, J. J.; Yau, W.W.Anal. Chem. 1983,55, 2165.
Results and Discussion Adsorption on Polystyrene Latex Beads. Figure 4 compares the fractograms (obtained from system I) of the 0.198-pm polystyrene latex sample without added human y-globulin and prepared with the y-globulin a t two different concentration levels (1 and 5 mg/mL). The measured retention time for the uncoated beads of 14.9 min gives a retention parameter X of 0.0412 (from eq 6), a value that in turn can be used to calculate the particle diameter from eq 5. This calculated diameter, 0.200 pm, is in very good agreement with the value of 0.198 pm given by the supplier (Seradyn). As t h e concentration of y-globulin added to the latex suspension increases, the peak generated by the latex particles is shifted to higher retention times, indicating an increase in effective mass of the beads. We take this increase in mass to be due to the adsorption of y-globulin on the particle surface. An equilibration time of about 2 h was used in these experiments, which appeared adequate since additional time did not result in any further shift in the peak position. From the value of the retention
Beckett et al.
2044 Langmuir, Vol. 7, No. 10,1991
Table I. Compilation of Mass m,,Thickness b, and Adsorption Density X of Film of y-Globulin (pc = 1.36 g/mL) Adsorbed on Polystyrene Latex Beads for Different Initial Protein Concentrations concn of y-globulin added, mg/mL 0.5 1.o 2.5 5.0 1.5 10 12 16 20
x 0.0380 0.0352 0.0336 0.0289 0.0290 0.0298 0.0289 0.0284 0.0282
mc, 10-18g 82.1 146 187 336 332 304 336 354 362
h, A 4.8 8.5 11.0 19.6 19.4 11.7 19.6 20.1 21.2
-
0
4,
5
I a-
15
IO r
20 f
I
X, mg/m* 0.61 1.19 1.52 2.13 2.10 2.41 2.13 2.81 2.94
parameter h obtained for eachexperiment, we can calculate the mass m, of y-globulin adsorbed (eq 14) and the mean thickness h of the coating material (eq 13). In addition, from the estimated surface area of each spherical bead (1.23 X m2) we can calculate the adsorption density X (expressed as mass adsorbed per unit surface area). These data are summarized in Table I. The adsorption behavior is displayed in Figure 5a in the form of an adsorption isotherm, specificallya graph of the adsorption density (X)versus the equilibrium concentration (c,) of y-globulin left in solution after uptake by the beads. In these experiments the initial and equilibrium concentrations differ only slightly and thus c, is approximately the same as the concentration of y-globulin added. (If necessary, cBgwas obtained by subtracting the calculated mass of y-globulin adsorbed to the particles in 1 mL of suspension from the initial concentration of y-globulin added.) The isotherm resembles that expected from the Langmuir expression
X = 1 + abc, in that a region in which X increases with ceq is followed by a long plateau region having a limiting adsorption density. This similarity of isotherms is confirmed by the straight line plot of c 9 / X versus ceq shown in Figure 5b. The curve shown in Figure 5a is the Langmuir plot using the parameters a and b obtained from linear regression of the graph in Figure 5b. The limitingadsorption density (givenby 1/ b)was found to be 3.06 mg/m2. This is somewhat below the maximum adsorption level of 6.8 mg/m2 found for human y-globulin adsorbing on 0.22-wm polystyrene (also at pH 9) by Oreskes and Singerg2 using conventional solution uptake techniques. However, our experiments were conducted in Tris buffer with ionic strength 0.0008 M, which is much lower than the 0.05 M ionic strength used by Oreskes and Singer. It is possible that charge repulsion effects between the particle surface and protein or between adsorbed protein molecules could be moderated at the higher ionic strength and result in a greater level of adsorption. In another similar study Fair and Jamiesonzs observed a two-level adsorption isotherm for bovine y-globulin onto polystyrene with an initial plateau region at 6.0 mg/m2and a maximum adsorption density at 14.5 mg/m2. However, their experiments were conducted at pH 7.4, which is close to the isoelectric point of the protein (pH 6.8) which would minimize any possible contributions of charge repulsion. We should also note that in the SdFFF experiments, the sample is continually washed with fresh carrier buffer during its elution, giving ample opportunity for desorp(22)Oreskee, I.; Singer, J. J. Zmmunol. 1961,86, 338. (23) Fair, B. D.; Jamieeon, A. M.J.Colloid Interface Sci. 1980,77,525.
4 t
0 0
0
5
IO ceq (mg/mL)
1
15
20
Figure 5. Adsorption isotherm plots: (a)adsorption density X versus the equilibrium concentration of human yglobulin in solution; (b) straightline plot of c q / X versus c The line in Figure 5a is a Langmuir model curve plotted usingxe parameters a and b obtained from the regression line in Figure 5b.
tion of weakly bound protein molecules. However, it is generally found that protein adsorption is not reversible by simply washing the coated particles with solution of the same pH and ionic strength as used during adsorption.23 The adsorption isotherms of more weakly bound species could, if desired, be obtained by adding adsorbate to the carrier solution, thus maintaining the required equilibrium solution concentration in contact with the particles during their elution through the channel. The complete fractograms for polystyrene beads with added human y-globulin displayed additional peaks not present for the uncoated beads. These peaks are labeled as peaks 2, 3, and 4 in Figure 6 and occur at retention times of approximately twice, three, and four times that for the parent polystyrene peak (peak 1). These peaks are preceded by the void peak which contains unretained (low molecular weight) material. These additional peaks (2, 3, and 4) can almost certainly be attributed to latex aggregates, where aggregation is caused by the protein. The aggregation hypothesis is consistent with earlier studies in which aggregated clusters separate into evenly spaced peaks" and is confirmed by SEM studies which show (seeFigure 6) that sample fractions collectad at peaks 1, 2, and 3 contain nearly pure populations of singlet, doublet, and triplet particle clusters, respectively. The particle aggregation in the present case was quite slow. The kinetics of the process could be monitored by rerunning the sample at different times after mixing the latex beads and the y-globulin. The increase in the concentration of aggregates with time is illustrated clearly by the series of fractograms shown in Figure 7. The results are similar to those found in previous experiments at the Utah laboratories where latex aggregation was chemically induced (B. N. Barman and J. C. Giddings, Langmuir, submitted). In principle, it should be possible to calculate the mass of the aggregated particles and hence their coating mass, thickness, and adsorption density as before. However, we (24) Giddinge, J. C.; Bannan, B. N.; Li, H. J. Colloid Interface Sci. 1989, 132, 554.
Measurement of Thickness of Films by SdFFF
Langmuir, Vol. 7, No. 10,1991 2045
SdFFF of 0 . 2 PS ~ Latex
W
(3909 with 106h exposure to lmg/mL Y-globulin)
void
v)
z
peak
B
VT/BS latex + ovalbumin
v)
W
c a h 0
I
I-
o W
L 0 0
IO 20 TIME (mid
30
Figure 8. Fractogram (from system 11) obtained for neutrally
buoyant 0.369 pm VT/BS beads coated with ovalbumin. Run conditions were field strength 8628g,stop-flowtime 20 min, and flowrate 1.5 mL/min.
15
0
30
60
45
TIME (min)
Figure 6. Fractogram (system I) of polystyrene latex beads after
a 106-h exposure to y-globulin a t an initial concentration of 1 mg/mL. The scanning electron micrographs confirm that the successive peaks (numbers 1 through 4) represent isolated populations of singlet, doublet, and triplet clusters of latex particles. Peak 4 is probably a quadruplet peak, although this was not verified by SEM. Experimental conditions are the same as for Figure 4. I
I
I
I
I
I
I
I
I
I
0
IO
20
30
40
50
1
60
TIME (mid
Figure 7. Fractograms of polystyrene latex after different exposuretimes (asshown)to7.5 mg/mL y-globulin. The doublet and triplet peaks (nos. 2 and 3) are observed to enlarge with time, reflecting ongoing aggregation. Conditions are those of Figure 4.
note that this is not quite as simple as it is for spheres due to perturbations in the retention time caused by steric effects associated with the larger size of the aggregated particles. The steric perturbations are small but still significant compared to the shifts in retention time due to the mass of the adsorbed coating which is to be calculated. An approximate form of the FFF retention equation which includes a steric term is25
R = 6X + 67
E
t 18)
where a is the effective radius of the particle and y is the steric correction factor which accounts for the nonideal migration of particles near the wall. The major problem in utilizing such an expression stems from the uncertainty in choosing the appropriate value of a and y for a doublet (or more highly aggregated) particle. A detailed consideration of such steric corrections is beyond the scope of (25) Myers, M. N.;Giddings, J. C. Anal. Chem. 1982,54,2284.
this paper and is in fact the subject of ongoing work. However, preliminary calculations using y = 1 yield adsorption density values for the doublets ( a = 0.2 pm) close to those calculated for the singlet particles ( a = 0.1 pm) at a given solution concentration, as would be expected. Finally, we note that the complications associated with the steric corrections encountered with the doublet particles do not significantly influence the calculation of the amount of coating material adsorbed to the single particles. Since the presence of the coating makes a very small difference in the particle diameter (generally
