Faraday Discuss. Chem. SOC., 1987, 83, 297-307 Brownian Motion of a Hydrosol Particle in a Colloidal Force Field Dennis C. Prieve and Foo Luo Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. Frederick Lanni Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. Total-internal-reflection microscopy (TIRM) was used to monitor Brownian fluctuations in separation between a 10 pm polystyrene sphere and a glass plate when the two bodies are separated by a fraction of a micrometre of aqueous solution. Preliminary results clearly show evidence of double-layer repulsion which is weakened by increasing the ionic strength. Potential- energy profiles were obtained with a resolution of 2.5 nm.Although this falls short of the atomic resolution obtained with the crossed-mica cylinder technique for measuring colloidal forces, TIRM allows one of the interacting bodies to have colloidal dimensions. Besides measurement of colloidal and hydrodynamic forces, other applications include the study of hindered diffusion of the particle near a flat boundary and reversible adsorption of a single particle onto a plane surface. Van der Waals and double-layer forces play an important role in the aggregation of colloidal particles” and their adsorption onto For example, the van der Waals attraction between like particles accounts for the inherent instability of dispersions of lyophobic particles; their ultimate fate is to aggregate. Double-layer repulsion between bodies of like charge can delay the inevitable by retarding the rate of aggregation or adsorption.Moreover, the depth of the potential-energy well into which particles adsorb determines the equilibrium constant for adsorption. Several techniques have been developed to probe colloidal forces directly.*-” The most widely used technique is that of Israelachvili and ad am^.^'^ Cleaving mica sheets along crystal planes, they obtain surfaces which are smooth at the atomic scale. Gluing the mica on polished glass cylinders, which are placed at right angles and then pushed together with a known force, they measure the equilibrium separation by interferometry as a function of the force. With this technique, they can determine separation distances down to contact with an accuracy of *0.2nm.Israelachvili and Adams’ found that the double-layer repulsion measured in dilute KN03 solutions (< 10 mol m-’) decayed exponentially with separation distance as expec- ted. The decay lengths determined from these measurements were found to be within 4% of the Debye length calculated from the solution composition. At much higher salt concentrations (ca. 1000 mol m-’), adsorption of hydrated cations again gave rise to a strong repulsion through hydration forces.12 This same technique has 1 7 been applied to the study of solvation (oscillatory) forces in non-polar liquids,’” the hydrophobic interaction of mica surfaces bearing a monolayer of CTAB,I4 and the steric interaction of surfaces bearing adsorbed polymer chains.” developed a technique to determine the interac- tion between a single colloidal sphere and a flat plate separated by a glycerol-water Recently, Prieve and 297298 Brownian Motion of a Hydrosol Particle solution.They obtained the potential-energy profile from the equilibrium distribution of separation distances using Boltzmann’s equation. The instantaneous separation distance was deduced from the measured translation speed of the sphere in linear shear flow along the wall. When pure glycerol was used in place of the glycerol-water solution, they also observed a flowrate-dependent hydrodynamic repulsion. On the basis of the creeping flow equations, whose solution was used to deduce the instantaneous separation distance, no hydrodynamic force is expected to arise between the sphere and the plate in linear shear flow.’* Moreover, inertial forces, which are neglected in the equations for creeping flow, should be less important in the more viscous fluid where hydrodynamic repulsion was observed.Prieve and Bike’9 suggest that a repulsive force, which they call ‘electro- kinetic lift’, can arise from the streaming potential developed as a result of sliding motion between the sphere and the plate. Whatever the cause of the flowrate-dependent force, the failure of the creeping flow equations to predict it casts doubt on predictions by the same equations of the relation between the measured speed of the sphere and its distance from the wall. Another technique, which is independent of the hydrodynamics, is needed to measure the separation distance.In this paper we use total-internal-reflection microscopy (TIRM) to measure the instantaneous distance separating a sphere and a plate when the sphere undergoes Brownian motion. The intensity of light scattered by the sphere in an evanescent wave is measured and translated into separation distance. Scattering also results from surface defects. Indeed, TIRM is a term introduced by Temple,” whose used the technique to inspect optical surfaces for damage. As such, TIRM is similar to surface-contact microscopy,2’ which has been used to study the movements of fibrocytes,22 and to total-internal-reflection fluorescence, which has been successfully used to size free viruses,23 to measure the chemisorption of fluorescent molecules on a liquid/solid interfa~e’~ and to observe the organization of cells growing on glass substrate^.^^ Total-internal-reflection Microscopy When a ray of light strikes a planar interface from the more optically dense medium at an angle of incidence greater than some critical angle, f?,, total internal reflection results.Although all light energy is ultimately reflected back into the more dense medium, there is an optical disturbance in the less dense medium which takes the form of an evanescent wave. Unlike the incident beam, whose electric field magnitude is stationary across surfaces of constant phase (plane wavefronts), the evanescent wave decays exponentially with distance from the interface. The intensity of the evanescent wave, which is proportional to the square of the electric field magnitude, also decays exponentially with the distance h from the interface:26 L ( h ) = U O ) exp (-PW p = (4~/A,)(sin’ 6,-sin’ 1 9 , ~ ) ” ~ where ( 1 ) sin 6, = n2/ n , where A , is the wavelength of light in the more dense medium, n is index of refraction, 0 is an angle measured from the normal to the interface, and where the subscripts 1 or 2 refer to the medium on the incident side or opposite side of the interface, respectively. Note that the decay length for the exponential ( p ’> can be comparable to the wavelength of the incident light.D.C. Prieve, F. Luo and F. Lanni 299 If a third medium (having refractive index n,> n2) is brought through medium 2 near to the interface and if 8, is less than the critical angle for media 1 and 3, the evanescent wave in medium 2 gives rise to a plane wave in medium 3.Since light energy will now be transmitted across both interfaces, this situation is called ‘frustrated’ total internal reflection. When medium 3 is a colloidal particle, we can think of this transmitted light energy as scattering of the evanescent wave by the particle. Chew et ~ 1 . ~ ’ extended their theoretical analysis of Lorenz-Mie scattering of plane waves by a dielectric sphere to elastic scattering of evanescent waves. Assuming that back-scattering of the evanescent wave and reflection of the scattered wave at the interface causes no significant perturbation of the field at the location of the particle, this extension takes the form of an analytic continuation of their earlier result onto the complex plane of wavenumbers.Results are reported for the incident wave polarized both parallel to the plane of incidence and perpendicular to it. F0.r either type of polarization, the scattered electric field has the following asymptotic for1 1 in the far-field limit ( r + a): where k is the magnitude of the wavevector in medium 2 and Bl,ml are expressions containing vector spherical harmonics. Note that the intensity of the scattered light, which is proportional to the product of Esc and its complex conjugate, has the same dependence on the sphere-plate separation distance as the intensity of the unscattered evanescent wave. In particular, where Ixc( h, a) is the integral of the scattering intensity over some cone of solid angle corresponding to the numerical aperture of the microscope objective.Thus the scattering intensity is exponentially sensitive to the separation distance with a decay length p-’ comparable to the wavelength and adjustable uia the angle of incidence. Measurement of Interaction Energy Consider a single sphere which has settled through a less dense fluid and resides near the flat bottom of the container. If both the sphere and the flat plate forming the bottom of the container bear surface charges of sufficient magnitude and of like sign, then intimate contact between them is prevented by double-layer repulsion. Under the influence of the opposing forces of gravity and the electrical double layer, the particle will assume an equilibrium position near the plate. Through Brownian motion, the sphere randomly samples different locations around this equilibrium over the course of time.Let the probability of finding the particle at a location between h and h + dh be denoted by p ( h)dh, where h is the shortest distance between the sphere and the plate. Sampled over a sufficiently long interval of time, the probability density p ( h ) will be a Boltzmann distribution: p(h’l = A exp [ - 4 ( h ) / k T ] ( 3 ) where $ ( h ) is the total potential energy of the particle when it is at elevation h, k is Boltzmann’s constant, T is the absolute temperature and A is a normalization constant chosen such that p ( h ) dh = 1. Although the particle’s mobility and diffusion coefficient depend on h, this dependence does not alter the equilibrium distribution given by eqn (3).17 Thus, by observing the distribution of elevations, p ( h ) , assumed by the sphere over a long period of time, the potential energy of the sphere can be deduced as a function of its location relative to the plate.300 Brownian Motion of a Hydrosol Particle Expected Contributions to 4 ( h ) Besides double-layer repulsion and gravity, which were mentioned above, van der Waals attraction between the sphere and the plate also contributes to the interaction when the separation is small enough.For a macroscopic sphere (as opposed to a single atom) at a fixed finite distance from a plate, the van der Waals force between the sphere and plate is proportional to a, whereas gravity is proportional to a3, where a is the radius of the sphere.28 Thus for a large sphere, gravity will dominate the van der Waals attraction, except at very small separations.For simplicity in this preliminary study, we will neglect van der Waals interactions. As it turns out, the most probable location of the 10 p m sphere used in the present work is of the order of 30-60nm from the plate. Since this separation distance is also several times larger than the Debye length, we can estimate the double-layer potential energy between a spherical particle and a flat plate using the linear superposition and Derjaguin approximations: B=16&a __ tanh ( - e i u l ) tanh (*) 4kT 4kT for a 1 : 1 electrolyte, where 1/ K is the Debye length, and iu2 are the Stern potentials of the particle and the plate, e is the dielectric constant, e is the protonic charge, and a is the sphere's radius.This approximation for the double-layer interaction is expected to be valid when Ka >> ~h >> 1. The gravitational contribution is G = ( 4 / 3 ) r a 3 ( A p ) g where Ap is the difference in density between the particle and the fluid and g is the gravitational acceleration. Adding eqn ( 4 ) and ( 5 ) yields the total potential energy: This function has a single minimum at a separation distance, h l , which is given by ~ h , =In ( K B I G ) . (7) This expression can be used to eliminate B from eqn (6). After rearranging, eqn (6) becomes: where x = K ( h - h , ) is the displacement from the most probable separation distance normalized with respect to the Debye length. As a sample calculation, consider the case in which a = 5 pm, 1/ K = 3 nm, $, = G2 = 50 mV, and Ap = 0.05 g Eqn (7) yields ~ h , = 12.Owing to the logarithm in eqn (7) this result is not very sensitive to changes in the assumed values of the parameters. Thus the technique is expected to probe double-layer interactions at separations for which the degree of overlap of opposing double layers is slight and where eqn (4) should be applicable.D. C. Prieve, F. Luo and F. Lanni 301 Experimental Sample Preparation Solutions containing polystyrene latex microspheres were prepared by diluting a 10% stock dispersion (Duke Scientific, Palo Alto, CA) in which the particle diameter was 10.04~0.06 pm. In addition to NaCl in various concentrations, 5 mol dm3 of SDS was included to inhibit sticking of particles to the glass plate.Clean microscope slides were rinsed sequentially with dichlorodimethylsilane, methanol and distilled water, then allowed to dry in air. Using a mixture containing equal amounts of Vaseline, lanolin and paraffin, a circle of wax was formed on upper surface of the microscope slide, which was large enough to contain 2 cm3 of the solution. Using immersion oil, the bottom side of the microscope slide was optically coupled to a prism 25 x 36 x 25 mm. Apparatus A 2 mW helium-neon laser ( A o = 632.8 nm) serves as the light source for the scattering. After reflection from a mirror mounted on a rotating stage, the laser beam passes through one side of the cubic prism ( n , = 1.5222), is internally reflected off the top surface of the microscope slide and passes out the other side of the prism.The angle of incidence at the microscope slide ( Oi = 70.94" for the data reported here) is controlled by rotating the mirror while the polarization is perpendicular to the plane of incidence (s-polarized). The entire apparatus is mounted on an optical bench with vibration isolation supports. A 40x water-immersion objective is submerged in the aqueous solution ( n2 = 1.3330) contained in the well on the microscope slide and then focused on particles near the bottom. A Zeiss Universal microscope equipped with a Zeiss photometer 01 was used to measure the intensity of scattering from a single sphere. Light incident upon the photomultiplier tube first passes through a 0.5 transmission filter to reduce the signal and a changeable aperture stop to reduce the background noise.Besides the eyepieces mounted below the image-plane aperture, the microscope was equipped with a single ocular mounted above the aperture to permit centering the particle in the aperture. After conversion of current to frequency, the output of the photometer was fed to a digital correlator (Malvern, type K7023) operating in the probability density mode. In 3ms intervals over 5 or lOmin, the correlator averages the frequency, which is proportional to the current from the photomultiplier tube, and increments the count by one in the appropriate bin of a digital storage device containing a total of 100 bins. In this way, a histogram of the sampled photocurrent is accumulated. Procedure During scattering measurements, the room was darkened.Ca. 2 cm' of solution contain- ing the particles was placed on the microscope slide. Ca. 10min was allowed for the particles to settle to the bottom. The field of view was adjusted until a single sphere appeared which was then centred under the aperture using the ocular. At higher salt concentrations, some of the particles were motionless and apparently stuck to the glass plate. Such particles were not examined further. About once per minute, the collection of scattering intensity was suspended briefly to recentre the particle in the aperture. If the particle drifted outside the aperture (even partially}, the results accumulated to that moment were discarded and the run was restarted after recentring the particle. To eliminate variations among washed slides, one microscope slide was used for all the measurements.After results at one salt concentration were obtained, the solution was removed from the well using a pipette. The well was then flushed several times3 02 Brownian Motion of a Hydrosol Particle using the next solution (higher concentration) before refilling. The total residence time in the well of any one solution was kept below 30 min to avoid any significant increase in salt concentration due to evaporation. Data Analysis Background photocurrent was generally much less than the current due to scatter from a microsphere. Also, because the photon count rate was generally much faster than the inverse relaxation time of the Brownian motion, the photocurrent was treated as an analogue variable and scaled down by current-to-frequency conversion to average over shot noise. The histograms of scattering intensity were therefore used directly to obtain the histogram of particle-plate separation distance.Scattering intensities can be translated into separation distances using eqn (2). We can eliminate the pre-exponential factor by dividing through by the most probable intensity. Solving for the separation yields: where Isc( h,, a) is the most probable scattering intensity and h2 is the separation distance corresponding to the most probable scattering intensity. In the limit of an infinite number of observations, the shape of the histogram of intensities, N ( I ) , corresponds to the shape of the probability density function for scattering intensity, P( I ) . To convert this into the probability density function for separation distance, we note that the probability, p ( h ) dh, of finding a particle at a separation distance between h and h + dh is the same as the probability, P(I)dI, of observing a scattering intensity between I and I + d I : where I = Isc(h, a).Since dp/dh = 0 does not imply d P / d l = 0, the most probable separation distance, 11, , is generally not equal to the separation distance, h,, correspond- ing to the most probable scattering intensity. Given p ( h ) , the potential profile can be deduced from Boltzmann’s eqn (3). The normalization constant, A, can be eliminated by dividing through by p at some convenient location, say p ( h , ) . The ratio, p ( h ) / p ( h , ) , can then be evaluated by applying eqn (2) and (10): p ( h ) = P ( I ) d l / d h (10) Approximating the ratio of probability densities for scattering as the ratio of the number of observations, the local potential energy can be estimated from: where N ( I ) is the number of observations of scattering intensity in the interval ( I , I + A I ) and N [ I ( h , ) ] is the maximum o f N ( I ) .Results and Discussion Effect of Ionic Strength Fig. 1 shows the histograms of scattering intensities separately obtained for each of five solutions having different ionic strengths. Although the histograms overlap to some extent, the average intensity clearly increases with ionic strength. Since the refractive index of the solution changes very little (from 1.3330 to 1.3340) over this range of salt concentration, such a large increase in scattering clearly indicates a decrease in sphere- plate separation with ionic strength.D.C. Prieve, F. Luo and F. Lanni Oe20 r 303 0.1 s 6 z g 0.10 W 0.05 0.00 scattering intensity (arb. units) i Fig. 1. Five histograms of scattering intensities for a 10 p m polystyrene sphere in five solutions differing in ionic strength (see table 1). The increase in scattering intensity with ionic strength occurs as a result of Debye screening. Table 1. Properties of solutions specific ionic debye calcd" obsd solution [ NaCl] conductance refractive strength length h, I J h J no. /molm-3 /mS index /molm-3 /nm /nm (arb. units) 1 0 0.350 1.3330 4.89 4.35 44-56 21 2 5 0.850 1.3330 8.82 3.24 34-43 51 3 20 2.29 1.3332 21.3 2.08 23-28 96 5 100 10.7 1.3340 103 0.95 11-14 4 50 5 9 0 1.3333 54.6 1.30 15-18 a h, is calculated from eqn (7) using assumed values of q!! ranging from 25 mV to a.A decrease in separation distance with increasing ionic strength is expected through Debye screening of the double-layer repulsion between the sphere and the plate. A weakening of double-layer repulsion means that the sphere must approach the plate more closely before double-layer repulsion will have the same magnitude as gravity. Although ionic strength can also affect van der Waals attraction, Lifshitz theory predicts a weakening of attraction through ionic screening of the low-frequency contribu- t i ~ n . ~ ~ This would result in an increase in separation distance and a decrease in scattering intensity, which is contrary to our observations. Similarly, adding salt will reduce the gravitational attraction by increasing the density of the fluid.Since only double-layer forces can produce the trend observed in scattering intensity with ionic strength, we conclude that double-layer repulsion can be studied with TIRM. Table 1 summarizes the properties of the five solutions used for the data in fig. 1. Ionic strength was estimated from the measured specific conductance using equivalent conductances reported for NaCl and SDS (below the critical micelle concentration). Owing to the presence of 5 mol m-3 of SDS in each solution, the ionic strength generally exceeds the concentration of NaC1. The difference in the two concentrations is expected to decrease with increased ionic strength as a result of micellization (recall3' that the c.m.c.for SDS is reduced from 8.1 mol m-' in de-ionized water to 1.4 mol mP3 in 100 mol m-3 NaCI).304 Brownian Motion of a Hydrosol Particle Also shown in table 1 are values of the most probable separation distance, h , , calculated from eqn (7) and the most frequently observed intensity of scattering. In the absence of complete characterization of the electrical properties of the polystyrene and glass surfaces, a range of h , is reported corresponding to surface potentials between 25 mV and infinity. Owing to the logarithm in eqn (7), the result is not very sensitive to the assumed value. To estimate the sensitivity of the scattering intensity to separation distance, we can compare (for example) the first two solutions in table 1.Assuming the surface potentials are independent on the ionic strength, eqn (7) predicts that the separation distance will decrease by 24% whereas the intensity of scattering more than doubles. Thus TIRM seems to provide a very sensitive measure of separation distance. Using eqn (2), the ratio of scattering intensities can be used to estimate the change in h,. Eqn (1) yields a value for the critical angle of 8, = 61.13" and an evanescent decay length of p-' =93.01 nm. 'Then, eqn (2) predicts that, between the first two solutions in table 1, h, changes by 83 nm, which is considerably larger than the 10-13 nm change expected in h , . Although there is no reason to expect h , to be equal to h2 [see discussion following eqn (lo)], the potential energy profile determined below indicates that the differences in the two is considerably smaller than the discrepancy above. Other explanations of this discrepancy include back-scattering of the evanescent wave, which was neglected in eqn (2), or colloidal forces in addition to those considered in eqn (6).Reversible Adsorption of the Spheres Three of the five histograms in fig. 1 are unimodal and have a shape which agrees, at least qualitatively, with that predicted by eqn (3) and (6). However, the remaining two histograms are either irregular or clearly bimodal. Moreover, at these high ionic strengths, a significant fraction of the spheres appeared to be immobilized in the sense that no lateral Brownian motion could be observed by normal viewing through the microscope.The particular spheres chosen for scattering measurements appeared to be mobile, at least at the outset of the 10 mill interval. At such high ionic strengths, the separation distance might become small enough that van der Waals attraction becomes significant compared to gravity. If so, more than one minimum can be expected in the potential-energy profile. One of these minima, corresponding to a very small separation distance, is probably the energy well into which particles reversibly adsorb to become temporarily immobilized. Assuming this to be the case, any appreciable energy barrier separating the two minima would significantly reduce the rate of diffusion between the minima, thereby increasing the time required for an equilibrium sampling of accessible energy levels.Perhaps 10min of sampling (which, with pauses for re-centring the particle in the aperture and recording of intermedi- ate results, requires 30 min) is not sufficient time to obtain the equilibrium probability density at high ionic strength. In future experiments, we intend to increase the sampling time until the shape of the histogram converges. However, this will require some modification of the apparatus to prevent evaporation. With the present apparatus, evaporation over periods longer than 30min were observed to cause a noticeable decrease in volume of liquid on the slide. For the present, we must be content with the possibility that TIRM might also be capable of studying the reversible adsorption of colloidal particles in a 'secondary' minimum.Potential-energy Profile Each of the histograms in fig. I. can be converted into a potential-energy profile. Using eqn (9), the scattering intensities can be translated into displacements from h,; usingD. C. Prieve, F. Luo and F. Lanni 305 I-. U W a I h 0 0 0 Fig. 2. Potential-energy profile deduced from the histogram of scattering intensity observed in solution 3. The solid curve is the prediction of eqn (8). eqn ( 1 l), the relative frequency of observing an intensity within a particular interval can be translated into potential energy relative to that corresponding to the most probable scattering intensity. Fig. 2 gives the potential-energy profile thus obtained using the histogram for solution 3. For comparison, the theoretical prediction of eqn (8) is shown as the solid curve.The following discussion applies equally well to solutions 1 and 2, except that the latter show that h2 - h , can be as large as 5 nm. A linear relationship is evident in both the experiments and the predictions of eqn (8). Of course, at large enough separation distances, colloidal forces are expected to be negligible compared to gravity which corresponds to a linear relationship between potential energy and separation distance. The slope of this line is GILT: the net gravitational force which causes the latex sphere to settle to the bottom of the solution. Agreement between the slope of the experimental data in the linear region and that of the solid curve is remarkable in that no adjustable parameters have been used either to compute the solid curve or to interpret the experimental data.Indeed, the two slopes could be made equal if the value assumed for the specific gravity of polystyrene were changed from 1.05 to 1.07. This close agreement tends to confirm the validity of eqn (8), and its predecessor eqn (2), which were used to interpret scattering intensity in terms of separation distance. By the same token, the poor agreement between the experimental points and eqn (8) at small separations, where double-layer repulsion is expected to dominate gravity, suggests that the contributions to eqn (8) from colloidal forces are not correct. One possibility is that van der Waals forces are not negligible. Another possibility is that the expression used to predict double-layer repulsion, which was based on linear superposition and Derjaguin’s approximation, is not valid.Spatial Resolution Note that the tic marks on the abscissa of fig. 2 correspond to a displacement of 0.01 p m or 10 nm. Near the minimum in that potential-energy profile there are four data points in one 10nm interval. This implies that spatial resolution for these experiments is 2.5 nm. This is approximately the resolution of a good scanning electron microscope (SEM). However, unlike the SEM, we have achieved this resolution in an aqueous3 06 Brownian Motion of a Hydrosol Particle environment and, at the same time, we can follow dynamic processes such as the Brownian motion of our spherical particle. This is not the best resolution we can obtain. From eqn (9), a displacement of 2.5 nm corresponds to change in scattering intensity of 2.7%.We believe our photomultiplier can resolve smaller changes in light intensity. Instead, the resolution is determined by the limited number of bins available to accumulate the histogram. We are currefitly refining our data acquisition system so that we can remove this restriction. In any case, the angle of incidence can also be increased to reduce the decay tength p-’ for the evanescent wave [see eqn (1 >] which will reduce the displacement corresponding to a given fractional change in intensity. In short, there are several avenues available to refine the spatial resolution which is already comparable to that of SEM. Some Applications of TIRM Although the results presented here must be considered preliminary, we have demon- strated that TIRM can be used to study double-layer repulsion and possible van der Waals attraction.These preliminary results suggest that eqn (4) might not correctly predict the double-layer interaction although K a and K h are very large. If this discrepancy persists upon closer scrutiny, this observation could be significant, especially in light of Pashley’s’’ experiments which verify eqn (4) with respect to h at low ionic strengths when the 10 pm sphere is replaced by a 1 cm cylinder. Even if this discrepancy proves to be an aberration, we should be able to provide an experimental test of Derjaguin’s approximation for the dependence on particle radius. Another application is the study of hydrodynamic forces exerted on the sphere in linear shear flow along the plate. In fluids having low conductivity, Alexander and Prie~e’~.’’ have observed a repulsive force whose magnitude increases with shear rate.Prieve and Bike” speculate that the force has an electrokinetic origin. Moreover, in the proximity of a wall, the mobility both in the tangential and normal directions will be reduced.31332 TIRM permits the observation of such effects using colloid particles. Finally, TIRM can be used to study steric interactions resulting from adsorbed polymer on either the sphere or the plate. By choosing a solvent system that is isorefractive with respect to’the polymer, the scattering intensity will not be affected by the presence of the polymer. Financial support for part of this work came from the National Science Foundation.We also thank Prof. Gary D. Patterson for the use of the correlator. References 1. E. J. W. Verwey and J. Th. G. Overbeek, Theory of the Stability of Lyoplzobic Colloids (Elsevier, Amsterdam, 1948). 2 H. Reerink and J. Th. G. Overbeek, Discuss. Furaday SOC., 1954, 18, 74. 3 R. H. Ottewill and J. N. Shaw, Discuss. Faruday Soc., 1966, 42, 154. 4 E. Ruckenstein and D. C. Prieve, J. Chem. Soc., Furaday Trans. 2, 1973, 69. 1522. 5 J. A. FitzPatrick and L. A. Spielman, J. Colloid Inferface Sci., 1973, 43, 350. 6 G. E. Clint, J. H. Clint, J. M. Corkill and T. Walker, J. Colloid Interface Sci., 1973, 44, 121. 7 D. C. Prieve and M. M. J. 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Rewiued 8 th Decrmher, 1986