Andrzej R. Altenberger

On the theory of self‐diffusion in a polymer gel

The problem of self‐diffusion in a random medium consisting of a solvent and a fixed set of scattering centers (obstacles) is discussed. A new equation describing diffusion of a Brownian particle in such a system is derived. We find that the self‐diffraction coefficient of the particle depends on the concentration of scattering centers like D/D0=1−A√C0−BC0+⋅⋅⋅, where A and B are positive constants, depending on the size of particle and repulsive range of scatterers, and D0 is the diffusion coefficient in a pure solvent.

Hydrodynamic screening and particle dynamics in porous media, semidilute polymer solutions and polymer gels

The dynamics of particle interactions in porous media are studied using a newly formulated mean field theory. Statistical correlations in the gel network are analyzed in detail and found to have a crucial influence on the results. Self‐diffusion and mutual diffusion coefficients of Brownian particles moving through a gel are determined. Preaveraged hydrodynamic interaction tensors are derived for two mobile Brownian particles a mobile particle and an obstacle.

UNIQUENESS OF THE MICROSCOPIC STRESS TENSOR

Schofield and Henderson have shown that the balance equation for the density of linear momentum does not provide a unique definition for the microscopic stress tensor. It is argued here that additional conditions of symmetry and physical interpretability, which reasonably can be imposed upon this tensor, are sufficient to establish the uniqueness of the familiar Irving–Kirkwood formula.

On the molecular theory of diffusion and heat conduction in multicomponent solutions

A statistical mechanical analysis is presented of diffusion and heat conduction in multicomponent systems. Explicit molecular expressions are derived for the generalized wave vector and frequency dependent Onsager kinetic coefficients and transport coefficients appropriate to various reference frames and specific to several different sets of independent thermodynamic forces. Relationships are established among the coefficients referred to different flow reference frames and to the lab frame coefficients as well. It is shown that the reciprocal relations are fulfilled only for certain very specific sets of independent thermodynamic forces.

Statistical mechanics of rubber elasticity

A new, statistical mechanical theory is proposed for the elasticity of rubber‐like materials. Deficiencies and contradictions of the traditional approach to the problem are pointed out. It is shown that anharmonic interactions are important to the successful modeling of the non‐Gaussian behavior of elastomers.

Functional self-similarity, scaling and a renormalization group calculation of the partition function for a non-ideal chain

The hypothesis of asymptotic self-similarity for nonideal polymer chains is used to derive the functional and differential equations of a new renormalization group. These equations are used to calculate the partition functions of randomly jointed chains with hard-sphere excluded-volume interactions. Theoretical predictions are compared with Monte Carlo calculations based on the same microscopic chain model. The excess partition function converges very slowly to its true asymptotic form δQ(N→∞)∼κN−1. The conventional asymptotic formula, δQ(N→∞)∼κN−1Nγ−1, is found to be applicable for chains of moderate length and for excluded-volume interactions appropriate to the subclass of flexible self-avoiding chains.

A renormalization group calculation of the swelling factor for a non-ideal, randomly jointed polymer chain

A real-space renormalization group method is used to calculate the swelling factor of a three-dimensional, randomly-jointed chain with hard-sphere excluded-volume interactions. This method differs from more conventional procedures patterned on the field theoretic approach pioneered by Gell-Mann and Low and Wilson. It is specifically designed to produce estimates of the swelling factor for finite values of the chain length and for a broad range of [excluded-volume] bare coupling coefficients. In addition to predictions specific to chains of finite length, the theory produces two distinct power-law scaling formulas for the asymptotic, long-chain limit of the swelling factor. One of these is descriptive of an ideal chain and is associated exclusively with very small values of the bare excluded-volume interaction parameter. The other is appropriate to chains with larger values of the interaction parameter and which exhibit significant deviations from ideality. The “critical exponent” associated with this second class of chains is equal to ν=0.5916, a value which agrees quite well with the results of previous investigations. Our renormalization group calculations are based on a pair of functional equations, one for an effective coupling function and another for the swelling factor.

THE ELASTICITY OF IDEAL POLYMER CHAINS

The systems considered here are composed of noninteracting ideal chains, formed from many identical beads, each of which is bound to its two nearest neighbors with an arbitrary potential of interaction. The thermodynamic properties of these systems are examined for several bond potentials. Comparisons then are made between the properties of the model systems and the experimentally observed behaviors of rubbery materials. Connections also are established between the thermodynamic and elastic properties of these model systems and those given by the traditional theories of polymeric elasticity.

A statistical mechanical theory of transport processes in charged particle solutions and electrophoretic fluctuation dynamics

Formally exact, linearized constitutive relations are derived for the charged particle currents of an electrolyte solution acted upon by an electric field. A new analysis of electrophoretic dynamic light scattering experiments is presented and deficiencies of the traditional, phenomenological irreversible thermodynamics of ionic solutions are pointed out.

Comment on ‘‘Remarks on the mutual diffusion of Brownian particles’’

Relations between diffusion coefficients in binary mixtures are explained. Explicit molecular expressions for the transport coefficients in the laboratory frame of reference are given.