Study of molecular phenomena in the nucleation of crystallisation by computer simulation and application to polymer crystallisation theory

Abstract

The classical nucleation theory, as set up by Volmer and based on the ideas of Gibbs, considers the nucleus both as an equilibrium configuration and as being in equilibrium with the parent phase. The existence of real equilibrium is doubtful, however, since a nucleus is not large as compared with the fluctuations that establish a thermodynamic equilibrium between phases. Moreover, the size of the nucleus, as calculated according to classical theory, is in some cases below molecular dimensions.Monte Carlo simulation of nucleation and crystal growth according to a model similar to that used by Volmer shows that the initiation of a stable crystal proceeds via a multitude of possible paths of growth involving all types of non-equilibrium configurations rather than via a nucleus of equilibrium shape. A well-defined nucleus does not appear to exist and, therefore, the “work of formation of nucleus” as used for the calculation of nucleation frequency or rate of crystal growth is a misleading concept. The latter two quantities viz, nucleation frequency and crystal growth, can be determined more justifiably form the parameters governing the attachment of molecules to and their separation from the growing crystal. This object is achieved e.g. through the Monte Carlo simulation by means of a computer. All this has important consequences for a number of theories where the equations of nucleation frequency and rate of crystal growth are based on a activation-free energy of nucleation (work of formation of a nucleus), the latter being calculated on the basis of a model nucleus. The implications for some current polymer crystallisation theories are discussed. The crystallisation of polymers is supposed to proceed via attachment of segments of one or a few repeating units rather than by steps of a whole “fold length” at once. Chain folding as a prerequisite for crystallisation must be rejected; it may be the result of crystallisation.Unfortunately, one cannot decide from data on crystallisation kinetics alone which theory is right or wrong, since it is the derived interfacial free-energy parameters that are actually the adjustable parameters of either theory.