Main chain motions rates

Carbon-13 rotating-frame relaxation rate measurements are used to elucidate the mechanism of gas transport in glassy polymers. The nmr relaxation measurements show that antiplasticization-plasticization of a glassy polymer by a low molecular weight additive effects the cooperative main-chain motions of the polymer. The correlation of the diffusion coefficients of gases with the main-chain motions in the polymer-additive blends shows that the diffusion of gases in polymers is controlled by the cooperative motions, thus providing experimental verification of the molecular theory of diffusion. Carbon-13 nmr relaxation... 

From this molecular theory, we see that the diffusion coefficient depends on the frequency of cooperative main-chain motions of the polymer, v, which cause chain separations equal to or greater than the penetrant diameter. Pace and Datyner were able to estimate v by adopting an Arrhenius rate expression in which the pre-exponential factor, A, is a function of both AE and T. The diffusion coefficient is given by,... 

Higher pressures of CO2 cause correspondingly larger increases in . At 800 torr an increase of 19% to 183 sec-1 is observed. Based on standard relaxation rate theory (29), increased relaxation rates are indicative of a shift in the average cooperative main-chain motions to higher frequencies. Conversely, this means that even small amounts of CO2 increase the cooperative motions of the polymer chains. 

In conclusion, the average rotating-frame relaxation rate of the methylene- and methine-carbons correlate with the apparent diffusion coefficients for H2 and CO in PVC when the main-chain molecular motions of the polymer are altered by an additive. (Fig. 2). These results provide experimental evidence that main-chain cooperative motions control the diffusion of gases through polymers. In Section IIB we will show that perturbation of polymeric cooperative motions is not restricted to classical plasticizing additives. 

The results presented in Table II show that even small amounts of gas affect the cooperative main-chain molecular motions of glassy polymers. Evidence that the presence of gases in polymer cause structural and dynamic changes can be seen in the depression of the Tg (42, 43, 44), and in the increased viscoelatic relaxation rates (43, 44) of... 

According to this model, the temperature dependence of molecular motions for adsorbed and non-adsorbed chain units in filled PDMS containing hydrophilic Aerosil is shown in Fig. 9 [9]. The lowest temperature motion is a C3 rotation of the CH3 groups around the Si-C bond (line 1 in Fig. 9). The rate of the a-relaxation (points 2 in Fig. 9) in filled PDMS is close to that for unfilled sample (line 2 in Fig. 9). It has been proposed that independence of the mean average frequency of a-relaxation process on the filler content in filled PDMS is due to defects in the chain packing in the proximity of primarily filler particles [7]. Furthermore, the chain adsorption does not restrict significantly the local chain motion, which is due to high flexibility of the siloxane main chain as well as due to fast adsorption-desorption processes at temperatures well above Tg. 

Two broad generalisations may be drawn from these studies and applied to local motions in polymers. The first is that, in the absence of unusual steric restrictions, the atoms of a side-chain will increase in both their extent and rate of motion as the number of bonds from the main-chain increases. This will result in a lengthening of T, and in most (but not all) cases an increase of NOE, for both carbons and comparable protons, e.g. in a methylene chain. However, the underlying motions will usually not have the extent anticipated for free rotation at each bond. This generalisation will hold true for both the solution state and the bulk polymer above Tg, where the local motions are similar. 

The other key factor is that when a compatible chemical is present, it plasticizes the polymer and allows more main-chain segmental motion. So, there can be a large (orders of magnitude) increase in diffusion coefficient as the chemical diffuses into the polymer. If the chemical is sufficiently compatible to disrupt the crystalline (essentially impenetrable) domains, then the increase in rate of diffusion can be dramatic. 

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