Chain dynamics, theory

The static properties of an isolated chain constitute a good starting point to study polymer dynamics many of the features of the chain in a quiescent fluid could be extrapolated to the kinetics theories of molecular coil deformation. As a matter of fact, it has been pointed out that the equations of chain statistics and chain dynamics are intimately related through the simplest notions of graph theory [16]. 

Finally, there is a large body of experimental and theoretical contributions from investigators who are mainly interested in the dynamic and conformational properties of chain molecules. The basic idea is that the cyclisation probability of a chain is related to the mean separation of the chain ends (Morawetz, 1975). Up to date comprehensive review articles are available on the subject (Semiyen, 1976 Winnik, 1977, 1981a Imanishi, 1979). Rates and equilibria of the chemical reactions occurring between functional groups attached to the ends or to the interior of a flexible chain molecule are believed to provide a convenient testing ground for theories of chain conformations and chain dynamics in solution. 

This author is perfectly aware that he could add very little to the work done by these workers if an attempt was made to focus on intramolecular catalysis phenomena or on the relevance to cyclisation of available models of chain conformation and chain dynamics instead, the aim will be the presentation of a general treatment of the subject, namely, one that includes the cyclisation of very short chains as well as that of very long chains of, say, 100 atoms or more. With a subject as vast as this, an encyclopaedic review would be a hopeless task. Therefore, the subject will be treated in a systematic and critical way, with more concentration on reaction series with regular and wide variations in structure, rather than on scattered examples. The aim will be to show that the field of intramolecular reactions is a mature area in which the merging of concepts from both physical organic chemistry and polymer chemistry leads to a unified treatment of cyclisation rates and equilibria in terms of a few simple generalisations and theories. 

As pointed out above, the RPA theory predicts that the dynamics of the respective homopolymers should be observed at high Q in the Rouse regime. While the experiment shows that the predicted Q dependencies are reproduced well by the data, the absolute values for the observed relaxation rates disagree with the predictions (see Table 6.2). In particular the observed Rouse factors for PE are considerably smaller than predicted, (Wf )expt=2xl0 s" compared to Wf pa=3.8x 10 A s at T=473 K. At low Q values, the two blocks display the same single chain dynamics. 

It can thus be deduced that the "dilution effect" of short chains is a dynamical process which does not act at short times. On the contrary, at longer times, as reptation theory postulates, the topological constraints which govern the chain dynamics appear looser as the concentration of short chains is increased. Indeed, even in an environment of equivalent local chain characteristics, as... 

Several interesting theoretical papers have appeared dealing with molecular dynamics and excimer formation in polymer systems. Frank and coworkers have developed a model to describe the transport of electronic excitation energy in polymer chains. The theory applies to an isolated chain with a small concentration of randomly placed chromophores, and a three-dimensional transport model was used to solve the problem which is based on a diagrammatic expansion of the transport Green function. (The Green function is related to time-dependent and photostationary depolarization and to transient and steady-state trap fluorescence.) The analysis is shown to be... 

Dynamical Theories. These involve a full treatment of multiple scattering by a layer method. The scattering within a single atom is determined first, then the scattering within one atomic layer and finally the scattering between layers. The technique has been extended by considering first single atom-chains, which are then... 

This paper presents summaries of unique new static and dynamic theories for backbone liquid crystalline polymers (LCPs), side-chain LCPs, and combined LCPs [including the first super-strong (SS) LCPs] in multiple smectic-A (SA) LC phases, the nematic (N) phase, and the isotropic (I) liquid phase. These theories are used to predict and explain new results ... 

The theories in this paper are first-principles statistical mechanics theories used to calculate static thermodynamic and molecular ordering properties (including solubilities of LCPs in various kinds of solvents) and dynamic properties (diffusion from Brownian motion). The diffusion of the LCP molecules constitutes a lower limit for the speed of processing of the LCPs. The static theory is used to calculate the packing of the bulky relatively rigid side chains of SS LCPs these calculations indicate that head-to-tail polymerization of the monomers of these SS LCPs will be very strongly favored. The intermolecular energies and forces calculated from the static theory are used in the dynamic theory. 

For some of the first theoretically designed candidate SS LCPs, new results are now presented for (1) enhanced solubilities of the molecules (compared with backbone LCPs) in nonpolymeric LC solvents calculated using the static theory, (2) diffusion (i.e., lower limit of processability) of the molecules calculated using the dynamic theory, and (3) head-to-tail polymerization of the monomers predicted from the packing of the bulky relatively rigid side chains of the molecules as calculated using the static theory. Melt processability of some SS LCPs is also discussed. 

We conclude this section by drawing attention to various theories considering the dynamics of block copolymer melts rheology of these systems has been considered [340-342], single chain dynamics and selfdiffusion [343, 344], nu-cleation of the ordered phase [61], ordering kinetics [345,346], and dynamics of concentration fluctuations [347]. These topics are not under consideration here, just as other extensions of the theory random copolymer melts [348, 349], multiblock copolymer melts [350] etc. 

Only recently has the theory of chain dynamics been extended by Peterlin (J [) and by Fixman (12) to encompass the known non-Newtonian intrinsic viscosity ofTlexible polymers. This theory, which is an extension of the Rouse-Zimm bead-and-spring model but which includes excluded volume effects, is much more complex than that for undeformable ellipsoids, and approximations are needed to make the problem tractable. Nevertheless, this theory agrees remarkably well (J2) with observations on polystyrene, which is surely a flexible chain. In particular, the theory predicts quite well the characteristic shear stress at which the intrinsic viscosity of polystyrene begins to drop from its low-shear Newtonian plateau. 

In the last chapter we discussed the relation between stress and strain (or instead rate-of-strain) in one dimension by treating the viscoelastic quantities as scalars. When the applied strain or rate-of-strain is large, the nonlinear response of the polymeric liquid involves more than one dimension. In addition, a rheological process always involves a three-dimensional deformation. In this chapter, we discuss how to express stress and strain in three-dimensional space. This is not only important in the study of polymer rheological properties in terms of continuum mechanics " but is also essential in the polymer viscoelastic theories and simulations studied in the later chapters, into which the chain dynamic models are incorporated. 

Doi has proposed a theory, which will be discussed in detail in Chapter 12, describing A) as the relaxation of tension on the primitive chain. The theory predicts that the t, A) process is not observable in the linear region, which has been found to be in agreement with experiment. However, corresponding to the dynamics of A), there is a process... 

---