Cooperative main-chain motions

Gas Transport and Cooperative Main-Chain Motions in Glassy Polymers... 

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... 

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. 

Section IIA summarizes the physical assumptions and the resulting mathematical descriptions of the "concentration-dependent (5) and "dual-mode" ( 13) sorption and transport models which describe the behavior of "non-ideal" penetrant-polymer systems, systems which exhibit nonlinear, pressure-dependent sorption and transport. In Section IIB we elucidate the mechanism of the "non-ideal" diffusion in glassy polymers by correlating the phenomenological diffusion coefficient of CO2 in PVC with the cooperative main-chain motions of the polymer in the presence of the penetrant. We report carbon-13 relaxation measurements which demonstrate that CO2 alters the cooperative main-chain motions of PVC. These changes correlate with changes in the diffusion coefficient of CO2 in the polymer, thus providing experimental evidence that the diffusion coefficient is concentration dependent. 

I. DIFFUSION AND COOPERATIVE MAIN-CHAIN MOTIONS A. Diffusion Theory... 

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,... 

In Section IB we showed that carbon-13 rotating-frame relaxation measurements can be used to measure cooperative main-chain motions in polymers (28). We report here the effect of CO2 on the main-chain motions of PVC. 

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 Section IB we presented experimental evidence that diffusion coefficients correlate with PVC main-chain polymer motions. This relationship has also been justified theoretically (12). In the previous section we demonstrated that the presence of CO2 effects the cooperative main-chain motions of the polymer. The increase in with increasing gas concentration means that the real diffusion coefficient [D in eq. (11)] must also increase with concentration. The nmr results reflect the real diffusion coefficients, since the gas concentration is uniform throughout the polymer sample under the static gas pressures and equilibrium conditions of the nmr measurements. Unfortunately, the real diffusion coefficient, the diffusion coefficient in the absence of a concentration gradient, cannot be determined from classical sorption and transport data without the aid of a transport model. Without prejustice to any particular model, we can only use the relative change in the real diffusion coefficient to indicate the relative change in the apparent diffusion coefficient. 

We have shown in the preceding chapter (7) that the presence of gas increases the cooperative main-chain motions of glassy polymers (9). The diffusion model of Pace and Datyner (13)... 

In the case of plasticized poly(butyral-co-vinyl alcohol) [73], use of dipolar rotational spin-echo CNMR in conjunction with C) determinations, has shown that the frequencies but not the amplitudes of cooperative main-chain motions of the polymer in the hard regions, corresponding to solid polymer associated with partially immobilized plasticizer, are influenced by interactions with the soft regions attributed to liquid plasticizer containing mobile polymer. From this result, a schematic representation of the partitioning of the polymer and plasticizer in terms of a two-phase domain model has been proposed. 

The a transition involves long segments of the polymer chain where the movement causes other chain segments to move out of the way. These cooperative main-chain motions are increasingly prevalent at the Tg and can be used to define the Tg of a material. 

The double-peak structure has not been reported so far for the side-chain relaxation of copoly(amino acid)s. In case of the conventional random copolymer, a single relaxa-tionowing to a cooperative main-chain motion[31] and respective relaxations owing to non-cooperative local motions of each monomer unit[32] are observed. Our results indicate that there is the cooperativity in side-chain motion of the copoly(amino acid) in the a-helical form though not so large as the main-chain motion of the conventional random copolymer. ... 

Glassy state In amorphous plastics, below the Tg, cooperative molecular chain motions are frozen , so that only limited local motions are possible. Material behaves mainly elastically since stress causes only limited bond angle deformations and stretching. Thus, it is hard, rigid, and often brittle. 

The investigations of PMMA at two temperatures (- 40 and 60 °C) by multidimensional solid-state 13C and 2H NMR (Sect. 8.1.4) have led to quite a precise description of the ester group motions and the associated main-chain motions. However, it has not been possible to get information on the origin of the observed distribution of activation energies, nor on the extent of cooperativity along the main chain required by the 7r-flip of the asymmetric ester group. 

We have been interested in the nature of cooperative motions in polymers for some time and have used carbon-13 nuclear magnetic resonance for examining main-chain motions in solids (22-27). Carbon-13 nmr with cross-polarization and magic-angle... 

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... 

It is interesting to point out the change in the relative heights of the and a peaks between PMMA and CMIM20 (Fig. 129). In the latter polymer, only a small part of the dielectric relaxation happens through the j3 motional processes. The cooperative motions involved in the a transition are required for achieving an important relaxation, whereas it is the opposite for PMMA. Such a behaviour is consistent with the hindrance of main-chain cooperativity by the rigid CMI units. 

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