Stephen L. Brenner’s research while affiliated with National Institutes of Health and other places

We assess modifications of the capacitance and interaction of planar double layers due to image forces. These forces come from the polarization induced at the salt solution/electrode interface by the ions in the aqueous phase. For both metallic and low dielectric electrodes, image forces have a small (<10%) effect both on the charge density necessary to maintain a given surface potential and on the pressure acting between a pair of electrodes immersed in a salt solution.

Photon correlation spectroscopy has been used to probe standing displacement waves set up in cuvettes exposed to mechanical vibrations. The dependence of mode frequencies on cuvette dimensions agrees with predictions of a simple theoretical model. Time behavior of the oscillating portion of the measured photon autocorreation functions is found to be independent of Q (the Bragg wave vector), also in accord with theory. Values of longitudinal sound speed are obtained and corresponding values of elastic moduli are determined. Agarose and polyacrylamide gels of differing concentration have been investigated, establishing that materials whose elastic moduli fall within the range 102105 dyn/cm2 can be studied by this technique. Elastic moduli of agarose are found to vary with weight percentage of polymer ρ according to E ∼ ρm, where m ≃ 4.1. Corroborative measurements have been made with instrumentation designed to analyze the frequency distribution of scattered light.

We analyze a scheme, originally suggested by Smoluchowski, by which a diffusion coefficientD can be estimated by measuring the number of particles occupying a fixed region of a surface at various times. An expression is derived relating the variance of the estimated valueD to several experimental parameters. This expression is evaluated numerically to determine how statistical uncertainty depends on adjustable variables. Particular attention is given to experiments involving locomotion of migrating leukocytes.

A theory of laser inelastic light scattering from soft polymer gels is developed. The scattering process probes density fluctuations in the gel, which here are assumed to result from standing displacement waves. The gel is modeled as a continuum and allowable displacement waves are found by solving the elasticrty equations subject to boundary conditions appropriate to an open oblong cuvette. Only a subset of the resulting frequencies is sampled by the light scattering experiment. The derived photon correlation function can be expressed as a product of an oscillatory time-dependent part, which is independent of scattering angle, and an angle-dependent form factor i.e. I(Q,t) = f(Q) cos ωt. The observable frequencies {ω} are proportional to the longitudinal sound velocity in the gel multiplied by a geometrical factor which depends on the sample dimensions.

A possible explanation is presented for the unexpected decrease in corneal swelling pressure with increasing temperature. It is shown that the form used in previous studies for the Donnan osmotic pressure is valid only in certain limiting cases. When the predominant force is a repulsion between fixed electrostatic charges, there are regimes of charge separation for which the temperature coefficient of the swelling pressure is negative. The simple model used here to illustrate the effect gives the observed swelling pressure and its temperature coefficient only for unexpectedly high values of the fixed charge density. It does make a qualitative prediction for experimental test to decide whether a more refined model is worthwhile.

We examine the role of electrostatic repulsion and van der Waals' attraction in determining interviral spacings in 'equilibrium' gels of tobacco mosaic virus. The observed spacings are inconsistent with a force-balance model. Experimental probes of the role of forces are suggested.

A recent calculation by Brenner, McQuarrie, and Olivares on the effect of attractive forces on the order-disorder phase transition in a gas of long hard rods is extended to include a more realistic attractive interaction potential. Rather than use the conventional square-well potential, we modify the attractive part of the potential such that the attractive interaction energy is proportional to area of overlap of the attractive regions. This is meant to reflect the fact that the more two rods are in register, the stronger is their attraction. The effects of well depth and well width on the thermodynamic parameters characterizing the phase transition are re-examined. This modified model yields significantly different results than the previous one for several of the transition parameters.

The screened Coulomb interaction between polyelectrolyte cylinders immersed in an ionic bath is examined. The electrostatic force and torque acting between a pair of unlike rods is formulated for all separations in which the electrostatic potential on some dividing surface between rods can be written as a linear superposition of isolated cylinder potentials. (The surface potential on the rods themselves may be much higher than that permitted by a superposition approximation.) The mutual energy in the case of skewed rods is found to be exponential in separation and proportional to 1/sin theta where theta is the twist angle of one rod relative to the other. Rods with similar charge repel each other with a torque acting to make the rods perpendicular while rods of opposite charge attract with the parallel arrangement preferred.

A variational principle associated with the free energy is used to determine an accurate yet simple analytical form for the electrostatic potential surrounding a spherical colloid particle. Although the proposed function contains only one variational parameter, fixed by optimization of the free energy, it is of comparable accuracy to exact numerical solutions even in regions of relatively large particle size and high surface potentials. Furthermore, the potential approaches the Debye-Hückel limiting case for dilute electrolyte solutions or very small surface potentials. It is anticipated that this solution will be useful in investigations of colloid stability and micelle-micelle interactions.

The effect of attractive forces on the order‐disorder phase transition in a gas of long hard rods is examined. The model system is that proposed by Zwanzig and consists of a gas of rectangular parallelepipeds which can orient only in the direction of three perpendicular coordinate axes. We extend Zwanzig's model by including a rectangular parallelpiped of attractive potential which surrounds the hard core in a symmetrical manner. A study is made of the effects of well depth and well width on the parameters characterizing the first‐order phase transition from an isotropic gas in which the long axes of the rods point in random directions to an anisotropic (ordered) gas. It is observed that even a shallow well (e.g., with a depth of 0.1 kT) can yield significant changes in the transition parameters. The results of this study may have implications in the study of nematic ordering in liquid crystalline systems.