химический каталог




Компьютерное материаловедение полимеров

Автор А.А.Аскадский, В.И.Кондращенко

classes of organic polymers. The results of calculation fit well with experimental values of e (Table 34a). In some cases, especially for polymers being in the rubbery state at room temperature, the accuracy of e calculation increases the share of the molar packing coefficient dependence upon temperature k(T). For copolymers the value of e is calculated according to Expression (223") or (223"").

For organic liquids the value of the molecular packing coefficient varies in a wide range (0.45 to 0.705) which makes calculation of density and molar volume necessary to define e of the liquid too difficult. At the same time calculation shows that this factor is not critical for accurate prediction of ? of organic solvents. It has been shown that the value of molar refraction correction AR for the same polar group contained in polymers and in low-molecular liquids must be different. It is true not only for comparison of behaviour of organic liquids and polymers but also for comparison of the liquids themselves belonging to the same class. Thus, the contribution into the value of AR from an OH-group is not identical in the row of alcohols, it depends upon the chemical structure of an alcohol. In Table 34b for eleven classes of liquids the relations between AR and Van-der-Waals volume of organic solvent molecules are given The applicationof these relations led to calculate values of the dielectric constant for organic solvents. As we sec, a sufficiently good agreement is observed between calculated and experimental values of e for organic liquids, which was not attained before (Table 34a).

Chapter X

Equilibrium Rubbery Modulus for Polymer Networks

To evaluate the equilibrium rubbery modulus E„ and the molecular mass of linear chains between cross-linked points Mc in the case of elastomer networks with sufficiently rare cross-links the equation of lhe classic rubber elasticity theory has been used (224). The application of this equation to high cross-linked polymers causes a substantial divergence between experimental and calculaled values of and Mc. Expression (223) for modulus of elasticity of amorphous polymers as ob Summary 507

tained in paper [103] may be used to some degree of approximation only for wide cross-linked polymers. The explanation lies in the fact that for wide cross-links Van-der-Waals volume of cross-linked points is immeasurably less than Van-der-Waals volume of linear fragments between them and, therefore, it may be neglected at evaluation of compressibility of a cross-linked system. That cannot be done in the case of high cross-linked networks because the total Van-der-Waals volume of cross-linked points is roughly equal to the total Van-der-Waals volume of linear fragments and may even exceed it.

Regarding a polymer network, on the one hand, as a system consisting of two subsystems - elastic and rotational-isomeric ones, and on the other hand, by presenting a polymer network as a mixture of linear fragments and cross-linked points (238) we obtain Expression (250) for calculation of the equilibrium rubbery modulus for the polymer networks Ec depending on their chemical structure Transformation of (250) leads to Expression (259) for determination of the molecular mass Klc of polymer networks. Using (250) the modulus of rubber elasticity Ec has been calculated for a model network on the basis of polydimethylsiloxane, its value increasing with increasing distance between the cross-linked points and reaching Ec = 148 MPa at n = 1; in this case glass transition temperature remains lower than room temperature (Table 36).

Calculation schemes for evaluation of glass transition temperature Tg and the equilibrium rubbery modulus E„ were used to create polymer materials with unconventional properties - materials with their modulus of elasticity varying in a very wide range for particular samples remaining constant for a single sample, and gradient materials whose moduli of elasticity can vary in a very wide range along the length of the same sample without any noticeable boundaries A theoretical basis for obtaining such a polymer is Expression (256) which states that the value of ?oo reaches its highest limits during transition to high cross-linked networks with bulky cross-linked points when и = 1 and p > 1. To maintain a low glass transition temperature Tg and to somewhat regulate the value of ?<ю in a wide range, the linearfragments between cross-linked points have to be very flexible. As representatives of such structures containing rigid bulky cross-linked points connected by flexible chains -R- polyisocyanurates were synthesized, lheir chemical structure being shown on page 251. In this case isocyanuric cycle serves as a cross-linked point, short organosilicion chains being linear fragments. Calculations according to (250) showed (Table 37) that for such a polymer at glass transition temperature under room temperature depending on the length of linear fragments n the rubbery modulus var

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