Molecular modelling polymer motion

From the NMR data of the polymers and low-molecular models, it was inferred that the central C—H carbons in the aliphatic chain in polymer A undergo motions which do not involve the OCH2 carbons to a great extent. At ambiet temperatures, the chemical shift anisotropy of the 0(CH2)4 carbons of polymer A are partially averaged by molecular motion and move between lattice positions at a rate which is fast compared to the methylene chemical shift interaction. 

The topic of molecular motion is an active one in experimental and theoretical polymer physics, and we may expect that in time the simple reptation model will be superseded by more sophisticated models. However, in the form presented here, reptation is likely to remain important as a semi-quantitative model of polymer motion, showing as it does the essential similarity of phenomena which have their origin in the flow of polymer molecules. 

Following the above conclusion it is clear that the rather bizarre spectra of these polymers derive from the special features of 1,2-enchainment. Examination of molecular models reveals that runs of 1,2-enchained segments are considerably more restricted in their degrees of motional freedom than are runs of 1,4- enchained segments. The restriction arises partly from the absence of a "crankshaft" mode with 1,2-enchainment and partly from the steric interference of substituents on adjacent phenylene rings. 

Polymethacrylates and polyacrylates have extensively been studied from the viewpoint of relaxations occurring in the glassy state. Though a vast amount of information has been collected to date, even a qualitative interpretation of the relaxation phenomena on a molecular level often remains questionable. This situation exists despite some favorable circumstances, i.e. polymethacrylates are amorphous polymers with comparatively simple molecular motions and it is possible to alter systematically their constitution and prepare various model polymers. 

Section IA summarizes the molecular model of diffusion of Pace and Datyner (1 2) which proposes that the diffusion of gases in a polymeric matrix is determined by the cooperative main-chain motions of the polymer. In Section IB we report carbon-13 nmr relaxation measurement which show that the diffusion of gases in poly(vinyl chloride) (PVC) - tricresyl phosphate (TCP) systems is controlled by the cooperative motions of the polymer chains. The correlation of the phenomenological diffusion coefficients with the cooperative main-chain motions of the polymer provides an experimental verification for the molecular diffusion model. 

We have tried to give a quick glimpse of the interrelationships among some commonly used constitutive equations for polymer melts and solutions. None predicts quantitatively the entire spectrum of the rheological behavior of these materials. Some are better than others, becoming more powerful by utilizing more detailed and realistic molecular models. These, however, are more complex to use in connection with the equation of motion. Table 3.1 summarizes the predictive abilities of some of the foregoing, as well as other constitutive equations. 

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

The Rouse model is the simplest molecular model of polymer dynamics. The chain is mapped onto a system of beads connected by springs. There are no hydrodynamic interactions between beads. The surrounding medium only affects the motion of the chain through the friction coefficient of the beads. In polymer melts, hydrodynamic interactions are screened by the presence of other chains. Unentangled chains in a polymer melt relax by Rouse motion, with monomer friction coefficient C- The friction coefficient of the whole chain is NQ, making tha diffusion coefficient inversely proportional to chain length ... 

To determine the usefulness and limits of the TICT chromophore as a fluorescence probe, we have to study the basic photophysies of the chromophore in polymers. The objective of this study is to examine the rotational motion of the amino group in polymer bonded 4-(N,N-dlmethylamino)benzoate (DMaB) chromophore in polymer solutions. The effects of polymer concentration, temperature and pressure on the TICT phenomenon of DMAB in the PMMA side chain were compared with those of a small molecular model compound, ethyl N,N-dimethylamino-benzoate, in solution. Our concern is to have an inside look into how polymeric environment influences the TICT phenomenon. 

Several detailed analyses of the diffusion process in both rubbery polymers and in hindered glasses are offered in Chapter 2 (28). Approximate molecular interpretations have been offered for the parameters in these models (25). Nevertheless, more work is needed to verify any molecular scale connection between such parameters and the structures and motions of the polymer backbone. Spectroscopy and molecular modeling of the differences in segmental motions in a systematically varied family of polymers, e.g, the polyesters, or polyamides, can offer insight in some cases. Unfortunately, the exact segmental motions involved in the diffusive process are only partially understood, so one must be cautious about drawing conclusions based on such studies unless they are supported by actual complementary transport data. Hopefully the structure-property results presented in this book will further stimulate thinking to improve the connection between spectroscopically sensed motions, and diffusion to complement the correlations based on specific free volume in Chapters 5 S 7 (50,51). ... 

The various models developed to describe the diffusion of small gas molecules in polymers generally fall into two categories (1) molecular models analyze specific penetrant and chain motions together with the pertinent intermolecular forces, and, (2) "free-volume" models attempt to elucidate the relationship between the diffusion coefficient and the free volume of the system, without consideration of a microscopic description. 

Remembering that the viscosity of a generalized Maxwell model is just the sum of the viscosities of the individual Maxwell elements will help shed light on the 2.4 factor in equation (3-92). We have already noted that all of the viscosity of a high-molecular-weight polymer derives from long-range translational motion of the polymer, that is, from motions with zp > zc or where the friction factor ps is operative. Thus we may write... 

In order to achieve a coherent discussion of these results it is instructive to consider them against the background of a molecular model of polymer motion, and to do this we have chosen the cooperative model of Adam and Gibbs 17). We shall consider in turn the measured values of activation energy, the effects of cross-linking, and finally multiple... 

The physical effects of introducing constraints into a molecular model have been discussed by several authors. > This chapter is concerned mainly with the methods of constraint dynamics. In addition to descriptions of bond-stretch and angle-bend constraints, dihedral (or torsional) constraints are explicitly considered. Torsional modes generally have frequencies comparable to those of other modes, and the weak coupling condition is not satisfied in this case. Hence the constraint approximation is not justified for torsion. This fact is particularly important because torsional motions play a major role in conformation interconversion in small molecules as well as polymers, and constraining them can seriously alter the dynamics of the original, unconstrained system. 

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