Motions, main chain

Tant et al. reported a dynamic mechanical transition of around 100 °C (maximum in G") for acid form Nafion having 1140 EW. o Since this transition also appeared for the sulfonyl fluoride precursor, but at a much lower temperature ( 0 °C), they concluded that it involved main chain motions that are restricted by the conversion to the acid form. These motions were further restricted by the conversion to the Na " sulfonate form owing to strong ionic associations between the side chains. In contrast with the work of Kyu and Eisenberg, no transition appeared at 0 °C in addition to that at 100 °C. While the equivalent weights of the samples utilized by Eisenberg and Kyu and Tant et al. were not quite the same, the notable difference in matrix Tg assignment is cause for confusion. 

The Motion of Diluent Molecules Associated with Local Main-Chain Motions... 

With the exception of local main-chain motions, the above-mentioned types of molecular motions have been investigated on a series of hydrophilic polymethacrylates and polyacrylates by means of dynamic mechanical measurements carried out with a torsional pendulum. For this purpose, the constitution of polymethacrylates was systematically altered and correlated with the dynamic mechanical response spectra. It was established for a series of copolymers of poly(2-hydroxyethyl methacrylate) that the temperature of the y relaxation (140 K 1 Hz), assigned to the motion of 2-hydroxyethyl... 

For this purpose, analysis of the methyl group behaviour is appropriate, as mentioned for 2H NMR investigations (Sect. 5.3.2). Indeed, the ring motions about the 1,4 axis do not drag the methyl groups along, whereas main-chain motions do. 

Main-chain motion was analysed through the movements of the BPA unit as a whole. 

In the case where rings flipped, the process was predominantly rocking the BPA group rotated about an axis parallel to the chain backbone (i.e. parallel to the O - 0" axis) and the rms average of the main-chain motion was around 13° (67% of BPA changes were less than 15°). 

Rocking main-chain motions, which occur in bulk BPA-PC when phenyl rings flip and carbonate groups change conformation, with rms averages around 13° and 11°, respectively. 

Low-amplitude (rms 10° at room temperature) main-chain motions are also present, and are mostly driven by conformation changes of carbonate groups. 

Fig. 116 Dynamics of the asymmetric side group in its asymmetric environment, a Initial side group orientation, b Steric clash with the environment if an exact 180° flip without main-chain motion is assumed, c To fit the asymmetric side group into the volume it had occupied before the flip, a twist around the local chain axis is required. This in turn slightly deforms the environment, d A second jump takes the group back close to its original orientation in a, but not exactly, due to the previous change in the environment in c, which is enhanced by rotation of other side groups that make up that environment (from [77])...

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. 

In the temperature range of the a transition, a shift towards higher temperature is associated with the introduction of increasing amounts of CMI it reflects the effect of the rigid maleimide cycles which hinder the main-chain motions, comparative to PMMA. 

Before entering the discussion, it is worth noting that, as mentioned for PMMA, plastic flow implies main-chain motions such as those occurring above the a transition, whatever the considered temperature. Thus, the plastic flow constitutes a reference. 

As plastic flow corresponds to large chain displacements analogous to those occurring without applied stress above Ta, it implies the main-chain motions involved in the a transition, whatever the temperature at which the plastic flow develops. Thus, the plastic flow constitutes, in some way, a reference. 

C. Under such conditions, according to the proposed mechanism, the carbonate conformation changes induced by the yield stress make it easier to develop the main-chain motions involved in the chain displacements required for plastic flow. The increase of nSSA above 50 °C for TMBPA-PC would have the same molecular origin as the one observed between - 80 and - 20 °C for BPA-PC. 

The plastic flow developing beyond yielding requires main-chain motions similar to those are involved in the glass-rubber transition phenomenon (as mentioned in Sect. 2.2.2). For this reason, the plastic flow can be considered as a reference, since the involved motions are always the same, whatever the considered temperature. 

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,... 

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 molecular theory of Pace and Datyner (12) predicts that the frequency of polymer motions important to diffusion of CO and H2 in PVC is in the range of 105-108 Hz. We can expect RiP(C) measurements performed between 104 to 105 Hz to be sensitive to alterations in v by additives. The dependence of on the rotating-frame Larmor frequency observed for the PVC-TCP system (28) means that a general change in main-chain motions (restriction or enhancement) will result in a change (decrease or increase, respectively) in measured at 34 kHz (29). 

When the concentration of additive is low we observe that the Da of both gases decrease and parallel the decrease in (Fig. 2). The addition of low levels of TCP increases the average interchain potential in PVC and results in a decrease in v, and in lower diffusion coefficients. At high concentrations of TCP both and Da increase (Fig. 2). The dilution of the chains by the low molecular weight additive decreases the interchain potential, thereby increasing the frequency of main-chain motions, and increasing the diffusion coefficients. 

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. 

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