Mesoscopic theory

Pokrovskii, V. N. The Mesoscopic Theory of the Slow Relaxation of Linear Macromolecules. Vol. 154, pp. 143-219. 

Therefore, we tried to develop the adequate mathematical formalism of the fluctuation-controlled chemical kinetics based on a concept of active particles. Simultaneously, the mesoscopic theory of concentration field fluctuations was developed by a number of investigators (see Chapter 2) having more qualitative character. Undoubtedly, these two approaches - microscopic and mesoscopic - overlap, since a lot of fundamental results like asymptotic... 

Of special interest in the recent years was the kinetics of defect radiation-induced aggregation in a form of colloids-, in alkali halides MeX irradiated at high temperatures and high doses bubbles filled with X2 gas and metal particles with several nanometers in size were observed [58] more than once. Several theoretical formalisms were developed for describing this phenomenon, which could be classified as three general categories (i) macroscopic theory [59-62], which is based on the rate equations for macroscopic defect concentrations (ii) mesoscopic theory [63-65] operating with space-dependent local concentrations of point defects, and lastly (iii) discussed in Section 7.1 microscopic theory based on the hierarchy of equations for many-particle densities (in principle, it is infinite and contains complete information about all kinds of spatial correlation within different clusters of defects). 

Abstract The discussion of relaxation and diffusion of macromolecules in very concentrated solutions and melts of polymers showed that the basic equations of macromolecular dynamics reflect the linear behaviour of a macromolecule among the other macromolecules, so that one can proceed further. Considering the non-linear effects of viscoelasticity, one have to take into account the local anisotropy of mobility of every particle of the chains, introduced in the basic dynamic equations of a macromolecule in Chapter 3, and induced anisotropy of the surrounding, which will be introduced in this chapter. In the spirit of mesoscopic theory we assume that the anisotropy is connected with the averaged orientation of segments of macromolecules, so that the equation of dynamics of the macromolecule retains its form. Eventually, the non-linear relaxation equations for two sets of internal variables are formulated. The first set of variables describes the form of the macromolecular coil - the conformational variables, the second one describes the internal stresses connected mainly with the orientation of segments. 

Inspired by a mesoscopic theory for mixtures of immiscible liquids (Doi and Ohta 1991 see also Section 9.3.3), Larson and Doi (1991) have derived mesoscopic equations for polydomain nematics by multiplying the Leslie-Ericksen equation (10-13) by the director... 

Hongladarom and Burghardt (1994) measured the components of this tensor for a 13.5% solution of PBDG using polarimetry and found that, in accord with the mesoscopic theory, the birefringence is indeed independent of shear rate in Region II. The experimental birefringence tensor was found to be... 

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