Narinder K. Ailawadi

Effective pair potentials for liquid Na and liquid K

Recent x‐ray structure data has been used to generate effective pair potentials for liquid sodium and liquid potassium. This is done on the basis of three current theories (Percus‐Yevick, hypernetted chain, and Born‐Green) which relate the effective pair potential to the radial distribution function. Qualitatively, all the three pair potentials have similar features. Contrary to the recent suggestion of Howells and Enderby, the Born‐Green theory seems to be equally applicable to liquid metals.

Diffusion of Impurities in Smectic A Phases

Abstract A simple model, based on a hybrid of solid state and liquid theory, is introduced to obtain the impurity diffusion tensor of spherical molecules at low concentration in ordered systems. The anisotropy ratio of the diffusion coefficients D⊥ (perpendicular to the preferred direction of molecular alignment) and D (parallel to it), for tetramethylsilane (TMS) dissolved in the smectic A liquid crystal of 4-n-butoxybenzylidene-4′-n-octylaniline (BBOA) is calculated at the temperature T = 53[ddot]C. The result D⊥/D∥ = 8.6 agrees rather well with the experimental data of Murphy et al.

Statistical mechanical theory of polymers. II. Thermodynamic functions of a single ring polymer

Statistical thermodynamics of a single ring polymer with an intersegmental interaction is developed. Volume in this system is defined in terms of the mean‐square radius of gyration. The concept of compressed and expanded states of the polymer is developed by introducing a coefficient‐of‐expansion σ. In this way, the volume of the single polymer can be varied and change of free energy with this variation in volume can be studied. Tension is now defined as the infinitesimal change in free energy due to an infinitesimal change of volume, i.e., infinitesimal expansion of the system. The chemical potential is the change in free energy due to charging (or severing of) one of the segments of the polymer chain. Using these definitions and methods analogous to statistical mechanical theory of fluids, explicit expressions are derived for the equation of state as well as other thermodynamic properties in terms of the binary intersegmental correlation function g(2)(R) and the intersegmental interaction u (R). The tec...

Collapse Transition in Polymers

Abstract The collapse transition in a single polymer with modified Lennard Jones intersegmental interaction is considered. After defining the appropriate state variables, the equation of state of the system is derived by straightforward statistical mechanics. From approximate numerical solutions for the radial distribution function g(R), it is possible to reproduce the collapse transition observed experimentally.

Critical scattering in A3B compounds at structural transitions

Abstract A theory of critical scattering in A 3 B compounds having A 15 structure at structural transitions (martensitic phase transitions) is developed. The theory is based on the assumption that the critical scattering is due to density fluctuations. This primary variable is coupled to current density fluctuations considered as secondary variable. Zwanzig-Mori projection operator technique is used to derive equations of motion. The time dependence of thememory function describing the delayed response of the stress tensor due to a change of rate of shear is modeled and is assumed to decay exponentially. This description takes into account elastoviscous effects in solids, and leads, near the transition temperature, to a correct three-pole structure around ω = 0 and includes the central peak and the resonances of the conventional soft phonon mode. The central peak is predicted whenever elastoviscous effects are important. Our theory clarifies the phenomenological expressions for the dynamic structure factor proposed by Shirane and Axe. If order-parameter fluctuations were considered to be responsible for the dynamic structure factor, our results would correspond to theories proposed by Schwabl and Schneider for perovskites. Our paper thus helps clarify and unify the existing theories on critical dynamics at structural transitions in A 3 B compounds and AB O 3 perovskites.