SYNOPSISThe free volume of poly( trimethylsilyl propyne) (PTMSP), a glassy polymer distinguished by extremely high gas permeability and diffusion coefficients, was determined by means of two probe techniques-the positron annihilation method and the electrochromism method. Lifetime analysis of positron annihilation spectra revealed an additional long-lived component that is not typical for most of previously studied polymers. A model that has been developed earlier predicts that this lifetime corresponds to the larger size of free-volume elements having an intrinsic radius of about 6 A. Therefore, PTMSP should be similar to porous inorganic sorbents. A comparison with the literary data for zeolites and silica gel confirms this. According to the electrochromism method, the temperature dependence of the size of free-volume elements for PTMSP is much weaker than that for regular glassy polymers like polystyrene. It was concluded that the great free volume in glassy PTMSP is associated with very loose packing of the chains. 0 1993 John Wiley & Sons, Inc. INTRODUCTIONPoly( 1-trimethylsilyl-1-propyne) (PTMSP) synthesis, which has been described by Masuda et al., has drawn great attentionThe gas permeability coefficients ( P ) of PTMSP are at least 1-2 orders of magnitude higher than those of the most permeable synthetic polymers, rubbery or glassy. Additionally, it has been shown that this polymer is characterized by high diffusion coefficients ( D ) , solubility coefficients (S) , and great Langmuir hole saturation constant Ch. This parameter of sorption isotherms is usually considered as a rough measure of the excess free volume in glassy polymers. Interestingly, for this polymer, anomalously low densities have been r e p~r t e d ,~ which for some samples are as low as 0.7 g/cc.It was only natural to explain all these peculiarities as the manifestation of the greater free volume * To whom correspondence should be addressed. of PTMSP. Indeed, it has been assumed that the larger free volume associated with such structural features of glassy PTMSP as the rigid main chain and the bulky Si ( CH3)3 side-chain group is responsible for the observed unusual properties of this p01ymer.~-~ Recently, so-called probe methods have been extensively used to estimate the free volume or characteristic size of its elements in glassy polyrner~.~-~ This work presents the results of the study of PTMSP by means of the positron annihilation method and the electrochromism method. For comparison, two other polymers were studied. The first, poly( vinyl trimethylsilane) (PVTMS) is a vinylictype polymer having the same side-chain group as has PTMSP attached directly to main chain. Transport and thermodynamic properties of PTMSP and PVTMS have been compared earlier.3~'0 The other polymer, polystyrene, was considered as a "typical" glassy polymer whose transport and other physicochemical properties have been extensively studied, including the investigations by means of positron annihilation and electrochromism methods.

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We study, in detail, the s t r u m of the stochastic layer of a resonantly kicked oscillator. For the resonantly kicked case the stochastic layer has a crystalline or quasicrystalline structure depending on the parameter wg? = 2Rn/m, where r is thc kicking period, 2rrfwg the natural period of the oscillator and n and m are integers. For this resonant case we obtain the underlying orbit structure and the exact mechanism responsible for the diffusion in phase space is established. The diffusion of orbits in the stochastic layer is eiamined and a general universal form for the diffusion coefficient obiained.,

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