Amorphous polymers dynamics

K. Binder. Monte Carlo and molecular dynamics simulations of amorphous polymers. In J. Bicerano, ed. Computational Modeling of Polymers. New York Marcel Dekker, 1992, pp. 221-295. 

In summary, it is clear that water absorbs into amorphous polymers to a significant extent. Interaction of water molecules with available sorption sites likely occurs via hydrogen bonding such that the mobility of the sorbed water is reduced and the thermodynamic state of this water is significantly altered relative to bulk water. Yet accessibility of the water to all potential sorption sites appears to be dependent on the previous history and physical-chemical properties of the solid. In this regard, the water-solid interaction in amorphous polymer systems is a dynamic relationship depending quite strongly on water activity and temperature. 

As we discussed in the section on the structural properties of amorphous polymers, the relative size of the bond length and the Lennard-Jones scale is very different when comparing coarse-grained models with real polymers or chemically realistic models, which leads to observable differences in the packing. Furthermore, the dynamics in real polymer melts is, to a large extent, determined by the presence of dihedral angle barriers that inhibit free rotation. We will examine the consequences of these differences for the glass transition in the next section. 

D. Axelson For the polyethylenes, at least, there is a major effect of morphology on linewidth. This is going to make more difficult a detailed description of the dynamics of the low frequency motion relative to a completely amorphous polymer. 

Figure 12. Typical dynamic behavior of uncrosslinked amorphous polymers. The material is a copolymer of styrene-butadiene 25)...

The sensitivity of the three relaxation times to the molecular dynamics and structure will be discussed in a subsequent section. The general temperature dependence of Tj, T1 and T2 for a typical linear amorphous polymer with one side group attached to a backbone is shown in Fig. 4. 

The approach developed in this paper, combining on the one side experimental techniques (dynamic mechanical analysis, dielectric relaxation, solid-state 1H, 2H and 13C NMR on nuclei at natural abundance or through specific labelling), and on the other side atomistic modelling, allows one to reach quite a detailed description of the motions involved in the solid-state transitions of amorphous polymers. Bisphenol A polycarbonate, poly(methyl methacrylate) and its maleimide and glutarimide copolymers give perfect illustrations of the level of detail that can be achieved. 

In another paper in this issue [1], the molecular motions involved in secondary transitions of many amorphous polymers of quite different chemical structures have been analysed in detail by using a large set of experimental techniques (dynamic mechanical measurements, dielectric relaxation, H, 2H and 13C solid state NMR), as well as atomistic modelling. 

The sorption coefficient (K) in Equation (2.84) is the term linking the concentration of a component in the fluid phase with its concentration in the membrane polymer phase. Because sorption is an equilibrium term, conventional thermodynamics can be used to calculate solubilities of gases in polymers to within a factor of two or three. However, diffusion coefficients (D) are kinetic terms that reflect the effect of the surrounding environment on the molecular motion of permeating components. Calculation of diffusion coefficients in liquids and gases is possible, but calculation of diffusion coefficients in polymers is much more difficult. In the long term, the best hope for accurate predictions of diffusion in polymers is the molecular dynamics calculations described in an earlier section. However, this technique is still under development and is currently limited to calculations of the diffusion of small gas molecules in amorphous polymers the... 

As a general comment about the dynamic mechanical relaxational behavior of this polymer, the results are consistent with dielectric data [210] and with the fact that no glass transition phenomenon is observed, at least in the range of temperature studied. This is striking in an amorphous polymer. It is likely that the residual part of the molecule mechanically active above the temperature of the ft relaxation is only a small one, and this is the reason for the low loss observed in the a zone. 

T. Inoue, H. Hayashihara, H. Okamoto, and K. Osaki, Birefringence of amorphous polymers. I. Dynamic measurements on polystyrene, Macromolecules, 24, 5670 (1991) T. Inoue, H. Okamoto, and K. Osaki, Birefringence of amorphous polymers, I. Dynamic measurement and relaxation measurement, J. Polym. Sci. Part B. Polym. Phys., 30,409 (1992). 

T. Inoue, H. Okamoto, and K. Osaki, Birefringence of amorphous polymers. I. Dynamic measurements of polystyrene, Macromolecules, 24, 5670 (1991). 

Inoue T, Okamoto H, Osaki K (1991) Birefringence of amorphous polymers. 1 Dynamic measurements on polystyrene. Macromolecules 24 5670—5675 Isayev AI (1973) Generalised characterisation of relaxation properties and high elasticity of polymer systems. J Polym Sci A-2 116 2123—2133 Ito Y, Shishido S (1972) Critical molecular weight for onset of non-Newtonian flow and upper Newtonian viscosity of polydimethylsiloxane. J Polym Sci Polym Phys Ed 10 2239— 2248... 

Paul W, Smith GD (2004) Structure and dynamics of amorphous polymers computer simulations compared to experiment and theory. Rep Prog Phys 67 1117-1185 Peterlin A (1967) Frequency dependence of intrinsic viscosity of macromolecules with finite internal viscosity. J Polym Sci A - 2 5(1) 179-193 Peterlin A (1972) Origin of internal viscosity in linear macromolecules. Polym Lett 10 101— 105... 

As is well known todays MD simulations are better suited to describe at a true atomistic level the host matrix and the dynamics of the penetrants. However, most of the MD performed so far are dealing with purely amorphous polymers and with very simple penetrants. In the packaging practice however most of the polymers are partly crystalline and the penetrants are often complex organic molecules. 

In general, most polymers lose their ductile properties below the glass transition temperatures (Tg), the point at which the movements of polymer chain segments become extremely restricted. In amorphous polymers, the characteristics of the low temperature relaxations are directly related to the chemical structure and the dynamics of polymer chains. There are several possible types... 

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