Molecular motions in an amorphous polymer

To understand the molecular basis for the glass transition, the various molecular motions occurring in an amorphous polymer mass may be broken into four categories. 

Translational motion of entire molecules that permits flow. 

Motions of a few atoms along the main chain (five or six, or so) or of side groups on the main chains. 

Vibrations of atoms about equilibrium positions, as occurs in crystal lattices, except that the atomic centers are not in a regular arrangement in an amorphous polymer. 

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In the amorphous state, the distribution of polymer chains in the matrix is completely random, with none of the strictures imposed by the ordering encoimtered in the crystallites of partially crystalline polymers. This allows the onset of molecular motion in amorphous polymers to take place at temperatures below the melting point of such crystallites. Consequently, as the molecular motion in an amorphous polymer increases, the sample passes from a glass through a rubberhke state imtil finally it becomes molten. These transitions lead to changes in the physical properties and material application of a polymer, and it is important to examine physical changes wrought in an amorphous polymer as a result of variations in the molecular motion. 

Brown (24,29) proposed a model of homogeneous yielding based on the Mie (Lennard-Jones) interaction potential. According to Brown, there are three types of molecular motions in an amorphous polymer up to shear 5deld strain ... 

The molecular motion of a segment at a chain end is more rapid than that in an inner chain site. The fact is clarified by the selective spin labeling in an amorphous polymer. The molecular weight dependencies of glass-rubber transitions at two kinds of sites, the chain end and inner chain sites give a free volume size of micro Brownian motion. 

One approach that would come to mind for choosing (A ) would be to run a molecular dynamics simulation on the pure polymer, setting (A ) equal to an asymptotic value. However, this approach fails in an amorphous polymer. Over long times, mean-square atom displacements increase linearly with time due to diffusive chain motions, leading to... 

As indicated above, a relaxation is associated with molecular motions in which crytalline entities take part. However, the development of this process apparently requires the presence of an amorphous phase. Actually, as shown in Figure 12.32, the relaxation curves of polymethylenic waxes in which the crystallites are formed by totally extended chains (degree of crystallinity 100%) do not present a relaxation (41,42). Since neither totally crystalline nor totally amorphous polymers display a relaxation, one must conclude that this absorption is caused by molecular motions occurring in the crystalline-amorphous interphase. 

The reaction of an amorphous polymer with a solvent is dependent upon diffusion of the attacking reactant. If the polymer is at a temperature above its Tg there is a constant cooperative segmental motion that favors diffusion from hole to hole in the polymer mass wherein hole formation in a polymer above its Tg is related to the relative mobility of the diffusing molecules. The rate of diffusion is dependent on the temperature, the molecular size, and the extent of the compatibility of the corrosive molecules with those of the polymer (36). 

An important technological property of polymers is the glass transition temperature (Tg), that is the temperature at which an amorphous polymer is transformed, in a reversible way, from a viscous or rubbery condition to a hard and relatively brittle one in the vicinity of Tg, a polymer experiences a sudden increase in the rate of molecular motions and, as a result, undergoes a series of conformational transformations. Another important polymer technological property is the refractive index of polymers, whose high values are usually related to highly conjugated, aromatic type, 7i-electron systems that bear heavy elements such as bromine or iodine. 

The glass transition temperature (T ) of an amorphous polymer Is the temperature at which motion occurS In the major segments of the backbone molecular chain of the polymer. However, the effect of water on the T of a hydrophobic polymer has generally... 

Techniques which are more specific to the various morphological states, especially the amorphous domain, are needed. NMR and ESR are two such molecular probes. By monitoring the mobilities of protons as a function of temperature, Bergmann has defined the onset of molecular motion in various polymers (14). The applicability of NMR as a measure of molecular motion in polymer solids has been the subject of several reviews 15,16,17). ESR monitors the rotational and translational properties of stable radicals, usually nitroxides, and relates their mobilities to polymeric transitions. As stated in several works (18,19), the radical s sensitivity to freedom of motion of the polymer chain is infiuenced by its size, shape, and polarity. The above probes are both high frequency in nature, 10 -10 Hz. Measurement at high frequency has decreased resolving power for the various transitions in contrast to low frequency or static experiments, such a dilatometry with an effective frequency of 10 Hz (20). 

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