Kinetic of crystallization from the melt and chain folding in polyethylene fractions revisited: theory and experiment

Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1405&context=physastro_pubs

Random and cooperative sequential adsorption

Publisher Summary This chapter discusses the systems coupled to two reservoirs of energy in such a way that there is a steady energy flow through the system. An example is a resistor in steady state, gaining energy from a battery and losing it to the atmosphere. Even for this restricted class there is no equivalent of Gibbs' framework and, typically, distributions cannot be expressed solely in terms of the internal energies of the system. Thus, in addition to the “technical difficulties” associated with computing averages in a many-body system, one must first solve the “more fundamental” problem of finding the stationary distribution. For systems, which are only weakly perturbed so that they remain “close to equilibrium,” much is known at the level of linear response. The chapter focuses on steady states “far from equilibrium” where such schemes break down. Against this backdrop of a vast theoretical terra incognita, a reasonable approach consists in investigating systems which, while retaining the essence of the difficulties of “far from equilibrium” states, are as simple as possible. In this very spirit, Lenz suggested the Ising model in an attempt to understand the nature of ferromagnetic phase transitions. This philosophy provides one of the main motivations behind the introduction of a simple non-equilibrium system, which is referred to as the “standard model.”

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