Компьютерное материаловедение полимеров
As we can see, the relation between molecular packing index/t and temperature according to Equations (192)-(195) being taken into consideration increases the accuracy of и calculation for polymers with low glass transition temperature values (second values of «c„fcin Column 4, Table 28).
Another important property of polymers in the glassy state is stress-optical coefficient Ca used in optical polarization method of studying strain state of materials and products. Sometimes strain-optical coefficient Q is used Those coefficients are connected by the relation (201).
Empirical and semiempirical approaches to numerical evaluation of stress-optical coefficient C„ based on chemical structure of a polymer repeating unit are discussed.
Under the empirical approach in relation (202) Uie influence of chemical structure parameters of a polymer repeating unit is taken into consideration using the values of increments C, obtained by calibration and characterizing the contribution of each atom and each type of intermolecular interaction into a polymer stress-optical coefficient (Table 29). Table 30 where the calculated and experimental values of С„ coefficient are given shows that this value is widely varied depending upon the polymer chemical structure. According to Equation (202), the contribution of separate atomic groups into the value of С„ coefficient has been evaluated.
The results of calculation are given on page 238. As we can see, the largest negative anisotropy of polarizability is inherent in С = 0 polar group. A similar equation for copolymers has the form (202').
At the same time an advantage of relation (215) obtained on the basis of semiempirical approach is in determining a connection between stress-optical coefficient and modulus of elasticity, refraction index and glass transition temperature of polymers. This relationship allows to calculate nol only Ccvalue, but, for instance, the modulus of elasticity E of a glassy polymer from its chemical structure with an acceptable degree of accuracy (see Table 32).
The relations obtained allowed to analyze the contribution of particular atoms and polar groups into the values of the C„ coefficient and modulus of elasticity E and to obtain for the dynamic photoelasticity method a polymer possessing an extremely high modulus of elasticity at glass transition temperature lower than room temperature. A polymer of that kind based on a carbofunctional organosiliconpoly-isocyanurate network has short chains between cross-linked points as distinct from the polymers traditionally used in the dynamic photoelasticity method. Traditional I polymers have practically identical values of dynamic modulus of elasticity under
different static values of modulus of elasticity, which precludes their application to solution of dynamic problems using the dynamic photoelasticity method (Table 33).
; Chapter IX
Dielectric Constant of Polymers and Organic Solvents
\ The calculation of dielectric constant e for polymers on the basis of their cliem^ ical structure is an important task from the point of view of the directed synthesis of polymers with the preset dielectric constant. On the other hand, it is necessary to know the values of E for the polymerand organic solvent in orderto predict solubility of the polymer in the solvent.
Expression (222') for calculation of dielectric constant of a substance from its chemical structure has been obtained on the basis of the Glausius-Mossotti formula (221).
There are some peculiarities in application of Expression (222') for calculation of the value of dielectric constant of non-polar, polar dielectrics and organic liquids. For glassy amorphous polymers, the molecular packing coefficient at room temperature is evaluated to be 0,681, while at the polymer glass transition temperature it is 0,667. For nonpolar dielectrics, i.e. polymers with polar groups absent in their chemical structures (polyethylene, polybuladiene, polvtetrafluorethylene, etc.), molar polarization P actually coincides with molar refraction Я of a polymer repeating unit. In this case, as well as for evaluation of molar refraction, the value of molar polarizability P is additive consisting of polarizabilities of atoms and of polar506 Summary
izability increments connected with various types of chemical bonds and other peculiarities of molecular structures.
For polar dielectrics the value of polarization P is larger than the value of refraction Л of a polymer repeating unit due to orientation of constant dipoles emerging from the presence of polar groups like -OH, -CO-, -COO-, -CI, -NHCO-, NHCOO-, -CN, etc. Using the linear regression analysis and Expression (223), as well as refraction and dielectric constants of a large number of polar polymers, molar refraction corrections AR have been obtained for the most frequent polar groups in polymers (Table 34). These data were used to calculate dielectric constants for a large number of various
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