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The van der Waals attraction between uncharged, spherical polymeric latex particles in both aqueous and non-aqueous dispersion media has been calculated using the quantum field theory approach due to Lifshitz and Ninham and Parsegian. It is shown that for close approach it is possible to define a Hamaker function, analogous to the classical Hamaker constant, that is a function of the ratio (δ) of the minimum distance of surface separation to the particle radius. Computations for polymer latex particles in water showed that the Hamaker function for close approach decreases linearly with δ. However for polymers in hydrocarbons, the Hamaker functions are in fact constant. Both results are also derived analytically. A major obstacle to accurate calculations using this approach is the difficulty of converting the readily available gaseous ionization potentials into values for solids and liquids by providing due allowance for the polarization energy of the dielectric medium.

Spontaneous phase separation phenomenon in a nonaqueous monodisperse latex system is studied to verify the Kirkwood-Alder transition in colloid systems. The nonaqueous system might be suitable for our purpose, because both electrical double layers and van der Waals force effect could be negligible therein. Polymethyl methacrylate latex cross-linked with divinylbenzene was dried and then dispersed in benzene at various concentrations. The phase separation occurs in certain particle concentration ranges, depending upon the degree of the cross-linking. The values of the concentration at which the phase separation starts are in the range of from 0.105 to 0.195 by measured volume fraction; smaller values correspond to lower degrees of cross-linking. Correction of the measured volume fractions for the swelling of the particles gives values very close to 0.5, which are independent of the degree of the cross-linking. This is in good agreement with the value 0.497 predicted by Alder, Hoover, and Young [J. Chem. Phys. 49, 3688 (1968)]. In the phase-separated state the ordered phase which forms a sediment exhibits a beautiful opal-like iridescence (demonstrating the existence of polycrystalline structure), while the disordered state is rather translucent and gives weakly iridescent scattering, which would be attributed to the presence of spatial local order, that is, the liquid-like structure. Experimental evidence seems to support the conclusion that the phase separation which occurs in monodisperse latexes cannot be explained by the DLVO theory but could be attributable to the Kirkwood-Alder transition in a hard sphere system.

Numerical calculations of the energy of the van der Waals interaction between two spheres of polystyrene in water, n -heptane and vacuum are carried out using some recent developments of the Lifshitz theory. The results are compared with the Hamaker theory of the interaction. It is found that the Hamaker theory gives a qualitatively incorrect picture of the dependence of the interaction on separation when the dielectric permittivities of the spheres and the medium are very different. In particular, if the medium be water, the microwave contribution to the interaction energy is not described at all adequately by the Hamaker theory. If the dielectric permittivities are fairly similar, then the Hamaker theory can be made to describe the interaction fairly well, both qualitatively and quantitatively.

Phase separation in aqueous monodisperse latexes of high electrolyte concentration being stabilized with nonionic surfactant is studied, in order to confirm the Kirkwood-Alder transition as its explanation. Concentrated latexes were produced by ultrafiltration and the phase separation was detected by observing the appearance of iridescent sediment at the bottom of the containers. The phase transition starts at volume fraction of 0.39–0.49 and is completed at 0.48–0.55. These values depend upon the electrolyte concentration and the surfactant used; high electrolyte concentration and short polyoxyethylene chains give larger values. For short chain length surfactant, the results are in good agreement with Alder, Hoover and Young's [ J. Chem. Phys. 49 , 3688 (1968)] prediction that the transition starts at about 0.5 and is completed at about 0.55. The effects of the van der Waals force on the phase separation seems to be negligible. Above results, thus, substantiate the computer experiments of Alder, Hoover, and Young on the transition between fluid and solid states in hard sphere systems.

We develop a formalism for calculating van der Waals forces between bodies with inhomogeneous dielectric properties in the nonretarded limit. The result obtained by pairwise summation of forces is given and is shown to yield good agreement with more exact calculations when the variations in dielectric properties are not too great. Finally, we calculate the magnitude of the free energy of interaction for spatial variation of the form ( α + βz ) n where z is the spatial coordinate, α and β can depend on frequency, and n is a constant. By varying n we study the effects of different profile shapes on van der Waals interactions. These effects are found to be substantial in some of the cases studied.

Values of ϵ ( iω ), the dielectric permeability on the imaginary frequency axis, have been obtained in the case of liquid water and employed in the calculation of van der Waals forces. Previous work has employed expressions for ϵ ( iω ) calculated from incomplete spectral data in the uv. In the present work an estimation is obtained of how severe these approximations are in the case of liquid water, where nearly complete spectral data exist, by applying Kramers' formulas. Results are in general agreement with previous calculations which employ a damped harmonic oscillator model. However, for frequencies beyond 10 17 rad/sec, the application of Kramers' formulas indicates that values of ϵ ( iω ) previously obtained are somewhat low. By increasing the effective absorption frequency for liquid water from the first to somewhat less than the fourth ionization potential, values of ϵ ( iω ) according to the two methods are in better agreement for large frequencies. The increased effective frequency gives larger values of the van der Waals forces, but it is concluded that, at the most, a 50% increase in their value can be expected.

The earlier hypothesis of the presence of a liquid crystalline layer at the interface of a stable emulsion has been experimentally verified by means of visual observation in a microscope. It is shown that the emulsions reach the high level of stability, which characterizes emulsions containing liquid crystals, when the liquid crystals begin to be dispersed as separate aggregates besides their location at the interface. Calculations of the influence on van der Waal's interaction between the emulsified droplets show that the relative size of the Hamaker constant of the liquid crystalline layer is a more important factor for the stability than the thickness of the adsorbed layer.

The kinetics of adsorption from a solution of a cyclic decapeptide, tyrocidine B, onto 5 monolayers of barium salts of fatty acids transferred by the Blodgett-Langmuir method on metallized glass slides are described. The adsorption of tyrocidine begins only after a certain critical temperature is reached, which depends linearly on the number of carbon atoms in the fatty acids. The dependence of the adsorption rate at a given temperature on the square root of time indicates that the reaction is diffusion controlled. The activation for the adsorption process involves 10 fatty acid molecules for each tyrocidine molecule adsorbed. The activation energies found are comparable with those obtained by La Mer for the diffusion of water across monolayers of fatty acids. An attempt to account for the specific attraction between fatty acid layers and tyrocidine molecules on the basis of generalized van der Waals' (or Lifshitz) and electrostatic forces is presented.

It is suggested that the tensile strength of a capillary condensed liquid (τ0) can be calculated from the relative vapor pressure corresponding to the lower closure point of the adsorption hysteresis loop obtained when the substance is adsorbed by a porous solid. The ratios of the tensile strengths to the critical pressures of a series of liquids, when plotted against reduced temperature, T T c , fall between the curves corresponding to the van der Waals and the Berthelot equations of state, and close to that derived from an improved equation of state suggested by Guggenheim.

Extensions have been made to the Vold Approach for calculating the van der Waals attraction between colloid particles with adsorbed layers. Particles of various geometries have been considered. New equations to allow for the retardation effect are presented, and a method for calculating the Hamaker constants of the adsorbed layers suggested. In addition, some consideration has been given to the calculation of the residual long range attraction after overlap of the adsorbed layers, and also to the problem of nonuniform adsorbed layers as occur with polymeric adsorbents.

We have developed an accurate and simple method for calculating van der Waals (vdw) forces in condensed media based on the Lifshitz theory and have generalized that theory to apply to the interaction of two planar parallel lipid slabs in an aqueous medium. Several features of vdw forces in lipid-water systems are qualitatively different from the common assumptions of colloid science: (1) vdw energies are not the sum of ( λ / r 6 ) interactions between small elements of the interacting bodies; (2) electromagnetic fluctuations at ultraviolet frequencies, usually considered exclusively, are relatively unimportant compared to fluctuations at infrared and microwave frequencies; (3) by virtue of the strong microwave contribution, vdw forces in lipid-water mixtures increase with temperature and exhibit only weak “retardation” effects. Available spectral information is sufficient to derive these conclusions with little ambiguity. In particular, the feature of nonadditivity (which makes even the algebraic form of the interaction different from that expected) depends primarily on dielectric constants of component materials in the limit of zero frequency. Lifshitz' approach is conceptually clear. It correctly accounts for all frequencies of interaction, implicitly includes all many-body effects, and all consequences of intermediate substances. There is now good reason to use it in practice to calculate vdw forces for colloids at large separation distances.

This paper describes recent studies of the forces between surfaces for separations of the order of tens to hundreds of angstroms. The first part deals with the direct measurement of forces between molecularly smooth mica sheets and shows that normal van der Waals' forces operate for separations less than 100 A, retarded van der Waals' forces for separations greater than 200 A. The second part describes a direct study of the repulsive forces exerted by charged double layers residing on solid surfaces. By using the contact between a soft optically smooth rubber hemisphere and a flat glass surface repulsive forces of the order of 10 5 dyne/cm −2 have been measured for film thicknesses of about 150 A. The equilibrium film thickness decreases with increasing ion concentration and the results are in broad agreement with measurements by Mysels and others on black soap films.

We have derived an expression for the van der Waals interaction between two semi-infinite media across a planar region within which there is an exponential variation of the dielectric susceptibility. The result reduces in two known limits to Lifshitz' original result for a constant dielectric across the planar region and to a result for a triple-layer structure derived by Ninham and Parsegian. For this calculation in the nonretarded limit the free energy of interaction is treated as the sum of surface mode electromagnetic oscillators. By means of numerical calculations and analysis, we find that continuous spatial dependence of dielectric properties presents qualitatively new features for the van der Waals forces between large bodies.

It was proposed that negative interfacial tension due to high film pressure is responsible for the formation of micro emulsions. It now appears that the initial, negative interfacial tension γφ in mixed films of soap and long-chain alcohols is the result not so much of a high initial film pressure π G as of a large depression of the interfacial tension (γo/w)a between the water and the oil phase with its adsorbed alcohol monolayer in accordance with the equation γφ  (γo/w)a  π. This depression is brought about by the spontaneous distribution of alcohol between the interface and the oil phase. It is pointed out that this distribution is dependent upon the initial chemical potential of the particular alcohol in the given oil and that it may vary within wide limits. The fraction of the alcohol that remains in the oil phase is available to depress the oil/water interfacial tension while the remainder of it forms a mixed film with emulsifier adsorbed from the water phase. It is submitted that the interaction of coulombic, hydrogen bonding and van der Waals forces among the heads and tails of the tenants of this film develops an initial pressure gradient across the flat interface which generates the initial film pressure π G . Three stages of pressure development are postulated, the maximum pressure corresponding to an intermediate concentration of alcohol. Hypothetical plots of (γo/w)a and π G as ordinates versus concentration of alcohol as abscissa provide a graphical characterization of the process of microemulsification.

In order to test the adequacy of the present theories of the stability of nonaqueous suspensions, rates of flocculation of Graphon suspensions were determined in heptane from the change of optical density with time in the presence and absence of Triton X-35 and dodecylbenzene (DDB). Viscosities of the solutions and the adsorption isotherm for each of the additives on Graphon were also determined. In the DDB system, the reduced stability ratio calculated from the balance of the van der Waals attraction and the entropic repulsion between particles increases rapidly as a function of the DDB concentration. However, the experimental value increases gradually to an apparent limiting value reached at a mole fraction of DDB corresponding to about 3/4 surface coverage as inferred from the adsorption isotherm. Since the viscosity measurements show a positive value for the second virial coefficient, it is possible that the observed enhancement of stability in this system is due to osmotic rather than entropic effects. Triton X-35 neither increased nor decreased the stability of carbon suspensions in heptane. At lower concentrations, assuming the adsorbed molecules to be flat on the surface so there would be no entropic repulsion, calculation showed that the adsorbed film did not make sufficient change in the van der Waals attraction to change the value of the reduced stability ratio, either because the thickness of the film is too small or because its Hamaker constant is too close to that of the solvent itself. Judging from the viscosity data, the second virial coefficient of the solutions is so close to zero at the concentrations used that no osmotic repulsion would be expected.

A technique has been developed for determining the force of adhesion of spherical particles to a flat substrate in which a liquid flow between concentric cylinders is used. Measurements made with this technique show that the adhesive force of submicron carbon-black particles on a substrate of regenerated cellulose (cellophane) is markedly influenced by the pH of the solution. A maximum adhesive force is found at pH = 3.3. It is suggested that at this pH the force of adhesion is determined solely by van der Waals' forces, since it can be interpreted on the basis of the Lifshitz-van der Waals theory for the sphere/flat plate geometry.

The characteristics of mixed films of cholesterol and lecithin with deoxycholic, lithocholic, and cholanic bile acids were studied. Generally, a mutual solution of mixed monolayer components as well as some type of interaction among the different molecules developed. The results are interpreted in terms of superficial lattices. Changes in the characteristics of the mixed films are ascribed to modifications of intermolecular distances and therefore of the effect of van der Waals' forces between chains. Thus, transitions from one type of lattice to another occurred.

According to the rigorous theory of Lifshitz, the old concept of a characteristic Hamaker Constant, used in the classical theory of van der Waals interactions between macroscopic bodies must be replaced by that of a Hamaker Function of the separation distance. This is evident from computations of interactions between slabs of plastics across water. The requisite dielectric polarizabilities of four plastics—polystyrene, polypropylene, polyethylene, and polytetrafluoroethylene—have been modeled using tabulated static dielectric constants, indices of refraction, absorption spectra, and ionization potentials. In the limit of large separations (⪆ 10,000 A), the Hamaker function goes to 3.2 × 10 −14 erg for all four plastics; in the opposite limit, as separations approach zero, H.F. values range from 9 × 10 −14 erg for polystyrene to 3.6 × 10 −14 erg for polytetrafluoroethylene. Furthermore, the Hamaker functions defined as coefficients of force vs those defined as coefficients of energy can differ by 13% for the materials examined here.

The adsorption of 3-pentanol, chloroform, cyclohexanol, and cyclohexanone at the mercury-0.1 N perchloric acid solution interface has been studied. Interfacial tension measurements were made with a capillary electrometer of greatly improved precision. The use of a fused-quartz precision pressure gauge instead of the usual manometer enabled measurements of interfacial tension to be taken within a few seconds after renewal of the mercury surface. This procedure eliminated any error caused by diffusion of impurities to the interface. In the analysis of the electrocapillary data obtained for each adsorbate it was found that the surface pressure — In activity curves for different potentials could be superimposed by a translation along the ln a axis. Implications of this superimposability are (1) that the interactions between molecules of the adsorbate are independent of the electrical state of the interface and (2) that the surface charge density varies linearly with surface excess (at fixed potential). The Frumkin equation was used to fit the data for each adsorbate, and a standard free energy of adsorption referred to standard states based on infinite dilution both in solution and on the surface was calculated from its parameters. A correlation between these standard free energies of adsorption and polarizabilities of the molecules was established, indicating that van der Waals forces are primarily responsible for the adsorbate-adsorbent interactions.

The hydrodynamic interaction which occurs when particles are close to each other diminishes the coagulation rate of colloidal particles. We have evaluated this effect, improving a previous treatment by Derjaguin and Muller (7). The absolute rate of rapid coagulation has been computed numerically, with the help of the complete Hamaker equation for the van der Waals force. We have found that hydrodynamic interaction diminishes this rate by a factor of about 0.4 to 0.6, depending on the Hamaker constant. This result agrees completely with that of Spielman (8). The ratio W of the rates of rapid and slow coagulation has been calculated analytically with a simplified Hamaker equation and an approximate expression for the double-layer interaction, following, with modifications, the procedure of Reerink and Overbeek (21). The factor W has also been computed by numerical integration with the complete Hamaker equation. In either calculation the effect of hydrodynamic interaction on d(ln W ) /d (ln c e ) (where c e is the concentration of indifferent electrolyte) is found to be small. We conclude, in agreement with Derjaguin and Muller, that the existing discrepancy between theory and experiment with regard to d(ln W )/d (ln c e ) cannot be explained by this hydrodynamic effect.

The analysis made by Vold of the attractive energy between spherical colloid particles having adsorbed layers has been reevaluated. Particular attention has been paid to the case of the double-sheath models. The conditions necessary for optimum reduction in the attraction have been reappraised, and, in addition, the conditions necessary to produce a net increase in the attraction have been determined.

A theoretical equation of state for monolayers of fatty acids on water has been developed for the liquid expanded state. The equation is Π + π∞md 2 4A 2 A 1 - πd 2 4A 2 = kT where Π is the surface pressure, A is the area per molecule, m is the number of carbon atoms in the chain, d is the diameter of the chain, and ϵ is the minimum Lennard-Jones potential energy. This equation is based on a very simple model with the CH2 groups acting as a stack of hard disks. The theoretical term for van der Waals cohesion between CH2 groups is combined with a co-area term developed for two-dimensional hard-disk fluids. The equation of state is tested with experimental data for many saturated fatty acids. In spite of the fact that there are no adjustable parameters, the theoretical equation predicts the experimental variables, A, m, and T to within about 15% at a given value of II. The equation is approximately valid for unsaturated fatty acids if m is replaced by 2.5 m9, where m9 is the number of carbon atoms to the double bond counting from the ninth carbon atom in the chain. Comparison is made with other equations of state reported in the literature.

The study of aqueous dispersions of uniform colloidal spheres (I in this series) was extended to nonaqueous dispersions. These were prepared from aqueous crosslinked polystyrene latexes by two-stage solvent exchange dialysis, with methanol as intermediate solvent. Non-Newtonian relative viscosities ηr were measured in benzyl alcohol and m-cresol at volume fractions φ up to 0.50, for particle diameters from 0.15 to 0.43 μ. A single rheological equation ηr = f(φ, τr) was found to apply to nonaqueous dispersions in both media, and to aqueous dispersions the interparticle coulombic and van der Waals' forces of which are negligible. Here τ r = τa 3 kT is a reduced shear stress, in which r is the actual shear stress, a the particle radius, k Boltzmann's constant, and T the absolute temperature. The experimentally observed functional form of f was well fitted by Krieger and Dougherty's (1) modification of the Williamson equation, using their expression for the dependence on concentration of the high-and low-shear limiting viscosities.

We have used Lifshitz theory to calculate the force of attraction between two parallel mica plates separated by an air gap. Good agreement with the experimental data of Tabor and Winterton is obtained.