D.J. Mitchell

Surfactant diffusion: New results and interpretations

Abstract Data for surfactant diffusion are reported for sodium dodecyl sulfate at 25°C and tetradecyltrimethylammonium bromide at 25, 90, and 135°C, as measured by Taylor tube dispersion. These data are analyzed in terms of two limiting forms of theory, one appropriate to “slow” reaction rates, the other to “fast” rates. It is shown that the usual extrapolation to the critical micelle concentration to infer intrinsic diffusion constants is not permissible. The data are explicable if transport occurs by a process wherein ionic micelles disassociate, diffuse as monomers, and reassemble into micelles. This is directly contrary to current ideas on diffusion of surfactants.

Ordering in colloidal systems

Abstract The role played by statistical mechanics in the ordering of colloidal systems is examined. This role is made explicit through a study of phase (order-disorder) transitions in 1, 2 and 3 dimensions which exist in the examples provided by clay plate, tobacco mossaic virus and latex sphere suspensions. Essentially the statement is that the extrapolation of DLVO theory which attributes stability to a balance between attractive and repulsive two-body forces is not always a panacea. The ideas of Langmuir and Onsager who dealt with statistical mechanics and repulsive forces and considered that attractive long-range forces are not always important are paramount for some systems and must be built into existing theories.

van der Waals Forces between Two Spheres

The van der Waals free energy of interaction between two spheres is evaluated by an extension of van Kampens method. For close separation the zeroth approximation is the Lifshitz result for the interaction between two planes modified by a geometric factor. In next order of approximation the free energy exhibits distinctively new features due to nonadditivity of molecular forces in condensed media interactions. The formulas coincide with earlier expressions of Langbein at large distance, but disagree at close separation since his results here are valid only for dilute media interactions.

The attractive forces between polar lipid bilayers

Long-range attractive forces between lipid bilayers are not well described by the Lifshitz theory of Van der Waals forces between macroscopic media. It is shown that when correlations between polar headgroups are taken into account, the predicted forces take a qualitatively different form consistent with the measured data.

A general formalism for the calculation of free energies of inhomogeneous dielectric and electrolytic systems

Abstract A general formalism based on quantum statistical mechanics is developed which relates the free energy of an inhomogeneous medium to a Greens function. This Greens function is a response function which we calculate using classical electromagnetic theory. We use the formalism to derive the following results: (1) The Debye expression for the bulk free energy of a classical electron gas. (2) The interaction energy of two dielectrics interacting across a planar slab of electrolyte. The well known Lifshitz-van der Waals free energy emerges from this expression as a limiting case. (3) The surface energy of a uniform medium. (4) The change in surface energy of a dielectric upon dissolving in it a dilute strong electrolyte. This last result is identical to that obtained by Onsager and Samaras in 1934.

Deviations of the van der waals energy for two interacting spheres from the predictions of Hamaker theory

Abstract 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 transitions in aqueous suspensions of spherical colloid particles

Abstract Recent observations of order—disorder phase transitions in low density aqueous suspensions of electrostatically stabilised latex spheres are explained using Gouy—Chapman theory and current theories of first-order phase transitions.

Competitive adsorption from binary mixtures: Adhesive hard sphere model

Abstract A model study is given of the phenomenon of competitive adsorption using the theories of liquid state physics. The adsorbate is modeled as a mixture of hard spheres with a short-range attraction. The composition dependence of the specific surface excess is studied as a function of molecular size ratio and intermolecular potentials.

Electrostatic rigidity of charged membranes in systems without added salt

The thermodynamics of surfactants in solution has largely been understood in the framework of the flexible surface model. We calculate the bending rigidity for a case where this model might be put to a strong test: ionic surfactant systems with no added salt to screen the electrostatics. In so doing, we present a perturbative solution to the Poisson-Boltzmann equation for the case of two undulating sheets with intervening counterions. The predictions to which this leads for the bending modulus are shown (for a particular choice of undulation mode) to be identical to that of the solution for the geometry of concentric cylinders. This indicates that the curvature free energy is independent of the global aggregate geometry, even in systems with counterions only.

The force between two charged dielectric half spaces immersed in an electrolyte

Abstract Using a result based on quantum statistical mechanics we obtain an expression for the total free energy of interaction for two charged dielectric half spaces separated by an electrolytic solution.