Verdier-Stockmayer model

Verdier-Stockmayer model of unentangled chain dynamics... 

Mattice and coworkers performed their simulations of diblock copolymer micellization on a cubic lattice, typically of dimensions 44 x 44 x 44 and with a coordination number of c = 6. As in the case of Larson s model, only one energy parameter, f, is considered for all interactions, namely, the interaction between the tail and the solvophilic (head and solvent) beads. The base structure used for the copolymer is hiQtio. The chains are rearranged using reptation and Verdier-Stockmayer [53] type local motions, both of which are discussed in detail in Sec. III. C. Wijmans and Linse [50] also based their simulations on this model and surfactant structure. 

M. Rubinstein (Eastman Kodak Company) In the des Cloizeaux double reptation model which is similar to the Marrucci Viovy model, it is assumed that a release of constraint chain A imposes on chain B when chain A reptates away completely relaxes the stress in that region for both chains. This would imply that for a homopolymer binary blend of long and short chains would be completely relaxed after each of these K entanglements is released only once. But if an entanglement is released, another one is formed nearby. I believe that to completely relax this section one needs disentanglement events and that the Verdier-Stockmayer flip-bond model or the Rouse model is needed to describe the motion and relaxation of the primitive path due to the constraint release process, as was proposed by Prof, de Gennes, J. Klein, Daoud, G. de Bennes and Graessley and used recently by many other scientists. The fact that double reptation is an oversimplification of the constraint release process has been confirmed by experiments. 

Verdier,P.H., Stockmayer, W.H. Monte Carlo calculations on the dynamics of polymers in dilute solution. J. Chem. Phys. 36, 227-235 (1962). See also Verdier,P.H. Monte Carlo studies of lattice-model polymer chains. 1. Correlation functions in the statistical-bead model. J. Chem. Phys. 45,2118-2121 (1966). 

The MC method was first applied to polymer chain dynamics by Verdier and Stockmayer, using a bead model on a simple cubic lattice. Beads are moved from site to site on the lattice, in a way which satisfies certain criteria e.g. chain connectivity, excluded volume effects), and both the equilibrium average chain dimensions, and (by sampling to obtain the time correlation function) the relaxation behaviour of chains may be studied. One of the results is that excluded volume effects slowed the relaxation times significantly. Deutch and Boots have criticized the original model, attributing this unexpected result to unrealistic... 

Before embarking on a discussion of the results of these studies let us add one historical note. The difficulty with swinging the polymer tails in a conformational transition has been recognized for many years. A means of circumventing was proposed by Schatzki. Verdier and Stockmayer had earlier invoked a similar principle but used it only to produce Rouse modes. We know now that slow Rouse modes are insensitive to the details of the faster time-scale dynamics. The proposed motions are completely local, and involve going from one equilibrium rotational isomeric state to another by moving only a finite, small number of atoms. Mechanisms of this class have come to be known as crankshaft motions (a term applicable in the strictest sense only to the Schatzki proposal). Because of the limited amount of motion and the simplicity of the dynamics these models are easy to understand, analyze, and simulate. This probably contributes to the continued attention devoted to them. The crankshaft idea has helped to focus attention on the necessity to localize the motion associated with conformational transitions, but complete localization is too restrictive. There are theoretical objections that can be raised to the crankshaft mechanism, but the bottom line is that no signs of it are found in our simulations. 

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