химический каталог




Компьютерное материаловедение полимеров

Автор А.А.Аскадский, В.И.Кондращенко

ies by almost three orders of magnitude; a high predictive capability of Expression (250) should be noted.

Gradient materials are obtained by directed regulation of chemical composition of a network within the same sample with corresponding smooth variation of

508

Summary

modulus of elasticity from values typical for rubbers to values typical for plastics, without any boundaries.

It is shown taking polyisocyanurates as an example that to determine the properties of such unconventional materials one should take into consideration the process of microphase separation caused by a substantially different surface energy of organosilicon chains (21 dyne/cm) and isocyanurate cross-linked points (35 dynes/ cm) The presence of microphase separation process is confirmed by appearance of two distinct maxima in the curve of the polymer mechanical loss factor versus temperature (Fig. 80).

Chapter XI

Description of Relaxation Processes in Polymers

Recently some variants of memory functions in the corresponding Bollzmann -Udterra equations have been proposed for description of processes of stress relaxation and creep in polymers (112). The analysis of the existing memory functions shows that they express the course of relaxation processes with a sufficient accuracy provided appropriate parameters have been selected, but the physical meaning of those parameters is not always clear. In this respect more appropriate approach to obtaining relaxation memory functions seems to be based on consideration of thermodynamic functions and their variation m the course of relaxation process 17]. Such an approach is based on presenting the process of strain relaxation as a result of interaction and diffusion of kinetic units - relaxers, which may be various atomic groups, repeating units, particular elements of free (empty) volume, i.e. mictocavities, stress concentrators, etc. In this respect a polymeric material can be treated as consisting of relaxers and non-relaxers. Interaction between relaxers and non-relaxers and their mutual diffusion leads to production Df entropy S in the system which increases during stress relaxation due to transition of relaxers into non-relaxers and their intermixing caused by mutual diffusion. Memory functions were obtained issuing from the assumption that the driving force of relaxation process is production of system entropy, which grows during stress relaxation and reaches its maximum value Smax.

Relaxers transform into non-relaxers because of their interaction and diffusion. Tlie description of process of interaction between relaxers is based on я kinetic equation of the n-tli order (268). By integration and subsequent transformations of this equation a memory function Т^т) is obtained caused by an irreversible transition of relaxers into non-relaxers due to interaction between relaxers. If a reversibility of such a transition is assumed, when a non-relaxing material can produce relaxers in the course of the process, then the kinetic equation (268) takes the form (286), and a corresponding memory function У3(т) is described by Equation (290)

509

Summary

Under diffusion mechanism of relaxation a random roaming of relaxers is considered whereas the percentage of non-relaxers is described by relation (278). Substituting relation (278) for (267) and having made necessary transformations we can find Expression (289) for determination of a corresponding memory function T^T). By substitution of the memory functions obtained into Boltzmann equation (276) we obtain relations (293)-(295) which describe the stress relaxation in the polymer for time / Numerical values of integrals in these expressions are specified in Tables 38^10. An experimental test for obtained memory functions conducted on polymethylmetacrylate, polyoxadiazole, polybenzoxazole and other polymers showed the efficiency of calculation procedure and a high prediction capability of the equations obtained.

The discussed approach to description of relaxation phenomena in polymers may be applied to such processes as sorption and swelling because they lake place not only by filling pores in a polymer body but also cause a conformational rearrangement of macromolecules, thus, are accompanied by relaxation processes. A relative amount of sorbed matter Л'/(/)Л-/(а>) is determined from Equation (316) obtained by solution of the diffusion equation (306) in which, in turn, the velocity of particle diffusing in a polymer body 9 is determined according to (310) or (311) depending on the type of the relaxation mechanism Equation (310) corresponds to the interactive mechanism, whereas Equation (311) is used to describe diffusion of kinetic units. In the final form a relative amount of sorbed matter is described by Equation (326) if the sorption process is determined predominanUy by interaction of polymer relaxers, whereas sorption process limited by diffusion of relaxers is desenbed by Equation (327). The acceptability of Equations (

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