No abstract

Calculations of the conformational preferences of isolated single chains of poly(2,6-dimethylphenylene oxide) (PPO) and bisphenol-A polycarbonate (PC) predict that the rings of both chains are nearly free rotors at room temperature. However, experimental dipolar rotational spin-echo 13C NMR shows that in the glass, the rings of PPO execute only small-amplitude motions while those of PC undergo primarily 180°r ing flips (a hindered rotation) superimposed on some wiggles. Geometrical considerations of the dense packing of chains in the glass suggest that the rings of adjacent chains block rotational freedom. We propose that the mobility of the PC main chain results in lattice distortions which allow ring flips not permitted by the stiffer PPO main chain.

Monte Carlo simulations have been performed on a diamond lattice model of semiflexible polymers for a range of flexibilities and a range of chain lengths from 50 to 800 segments. The model includes both repulsive (excluded volume) and attractive segment–segment interactions. It is shown that the polymers group into two classes, ‘‘flexible’’ and ‘‘stiff.’’ The flexible polymers exhibit decreasing chain dimensions as the temperature decreases with a gradual collapse from a loose random coil, high temperature state to a dense random coil, low temperature state. The stiffer polymers, on the other hand, exhibit increasing chain dimensions with decreasing temperature until at a critical temperature there is a sudden collapse to an ordered high density, low temperature state. This difference is due to the relative strength of the segment–segment attractive interactions compared to the energetic preference for a trans conformational state over a gauche state. When the attractive interaction is relatively strong (flexible case) the polymer starts to collapse before rotational degrees of freedom freeze out, leading to a disordered dense state. When the attractive interaction is relatively weak (stiff case) the polymer starts to freeze out rotational degrees of freedom before it finally collapses to a highly ordered dense state.

In order to obtain the mechanism for the infrequent phenyl ring π-flips in glassy polycarbonate, a generalized Langevin dynamics simulation was performed on a reduced model consisting of a flipping ring and its keeper ring. The frequency of π-flips and activation energy for π-flips obtained from the simulation are in agreement with experiment. A phenyl ring π-flip occurs when there is an increase in the separation distance between the ring and its nearest neighbor ring on another chain, accompanied by, and in synchrony with, an increase in its rotational kinetic energy.

On the basis of model calculations, we argue heuristically that the dilatation-transformation method is applicable to all potentials, even those that are not dilatation analytic. In particular, we show that resonances are converted into bound (localized) states on the nonphysical sheet of the complex energy plane under the action of a dilatation transformation.