arXiv subjects

P. D. Gujrati

Publications and source records attributed to P. D. Gujrati.

57 records · Page 4Linked to original sources

arXiv2003

Reliably Estimating Bare Chi from Compressible Blends in the Grand Canonical Ensemble

The bare chi characterizing polymer blends plays a significant role in their macroscopic description. Therefore, its experimental determination, especially from small-angle-neutron-scattering experiments on isotopic blends, is of prime importance in thermodynamic investigations. Experimentally extracted quantity, commonly known as the effective chi is affected by thermodynamics, in particular by polymer connectivity, and density and composition fluctuations. The present work is primarily concerned with studying four possible effective chi's, one of which is closely related to the conventionally defined effective chi, to see which one plays the role of a reliable estimator of the bare chi. We show that the conventionally extracted effective chi is not a good measure of the bare chi in most blends. A related quantity that does not contain any density fluctuations, and one which can be easily extracted, is a good estimator of the bare chi in all blends except weakly interacting asymmetric blends (see text for definition). The density fluctuation contribution is given by (Delta v^bar)**2/2TK_T, where Delta v^bar is the difference of the partial monomer volumes and K_T is the compressibility. Our effective chi's are theory-independent. From our calculations and by explicitly treating experimental data, we show that the effective chi's, as defined here, have weak composition dependence and do not diverge in the composition wings. We elucidate the impact of compressibility and interactions on the behavior of the effective chi's and their relationship with the bare chi.

cond-mat.soft↗

arXiv2003

Theory of Crystallization under Equilibrium Polymerization in a Solution and the Investigation of its Melting Properties

We generalize a recently investigated lattice model of semiflexible polymers formed under equilibrium polymerization in a solution and conduct a comprehensive investigation of its melting properties. The model is characterized by six energies, three of which are for the interaction between the middle-group, the end-group and the solvent, and the remaining three represent energies for a gauche bond, a hairpin turn and a pair of neighboring parallel bonds. A polymer has two end-groups and at least one chemical bond. Two activities control the end-group and the middle-group densities, respectively, and give rise to polydisperse chains whose number is not fixed. We study the melting properties with various model parameters under conditions of fixed pressure, and compare our results with experimental data on fixed length and polydisperse polymers, whenever available. We investigate the effect of monomer interactions, nature of end-groups, chain rigidity, solvent quality, degree of polymerization, etc on the melting properties such as the melting temperature, latent heat, and energy and entropy of fusion. Our theory is thermodynamically consistent in the entire parameter space and improves upon the classical theories; hence our results should prove useful.

cond-mat↗

arXiv2003

General Theory of Statistical Fluctuations with Applications to Metastable states, Nernst Points, and Compressible Multi-component Mixtures

The general fluctuation theory is reviewed with special attention to the role played by different ensembles, and is extended to incorporate stationary metastable states obtained in the long time limit. The fluctuation in a quantity depends on the nature of the ensemble and contains at most n different fluctuation contributions, where is the number of fluctuating extensive quantities in the ensemble. We prove four general theorems and a corollary for statistical fluctuations valid for any thermodynamic system. We also demonstrate by two examples that the results of the theory remain valid regardless of the magnitude of the fluctuations. To avoid certain physical paradoxes, it is postulated that stationary metastable states like the ideal glass cannot exist in Nature. We also prove a generalized Nernst theorem valid at Nernst points at which certain susceptibility like the heat capacity vanishes. The theorem is no longer restricted to absolute temperature. We calculate statistical fluctuations in the number of monomers and other physical quantities of interest in a compressible mixture. We demonstrate that the density and composition fluctuations are in general not statistically independent, which is contrary to some recent claims. The standard isothermal compressibility at constant monomer numbers does not represent the density fluctuation in all ensembles. We show that the density fluctuation at constant composition is a meaningless concept, except at absolute zero. We prove a relation between the weighted monomer number fluctuation and the volume fluctuation in a multi-component system, which is an extension of a well-known similar relation for a single component system.

cond-mat.stat-mech↗