Unperturbed dimensions of chains

These expressions demonstrate that the change of entropy and internal energy on deformation under these conditions is both intra- and intermolecular in origin. Intramolecular (conformational) changes, which are independent of deformation, are characterized by the temperature coefficient of the unperturbed dimensions of chains d In intermolecular changes are characterized by the thermal expansivity a and are strongly dependent on deformation. The difference between the thermodynamic values under P, T = const, and V, T = const, is vefy important at small deformations since at X - 1 2aT/(/,2 + X — 2) tends to infinity. 

This conclusion permits comparison of the thermomechanical and thermoelastic results for various networks. The most reliable data are summarized in Table 2. The temperature coefficients of the unperturbed dimensions of chains d In intermolecular interactions of the configuration of the network chains. 

Temperature dependence of the unperturbed dimensions of chains, d i. i )oldT... 

Carmichael, J. B., Unperturbed Dimensions of Chains with Any Degree of Polymerization Application to Polydimethylsiloxane. J. Polym. Set, Part A Polym. Chem. 1965, 3, 4279-4283. 

Unperturbed Dimensions of Chains with Simple Stereochemical Sequences... 

Kurata, M. and Stockmayer, W. H. Intrinsic Viscosities and Unperturbed Dimensions of Long Chain Molecules. Vol. 3, pp. 196—312. 

Kurata, M., Tsunashima, Y., Iwama, M., and Kamada, K., Viscosity-molecular weight relationships and unperturbed dimensions of linear chain molecules, in Polymer Handbook, 2nd ed., Brandrup, J. and Immergut, E. H., Eds, John Wiley Sons, New York, 1975, iv, 1-60. 

M Kurata, WH Stockmayer. Intrinsic viscosities and unperturbed dimensions of long chain molecules. Fortschr Hochpolym-Forsch 3 196-312, 1963. 

Flory s viscosity theory also furnishes confirmation of the w temperature as that in which a=V.2, and it permits the determination of the unperturbed dimensions of the Polymer chain. Even if a Q solvent is not available, several extrapolation techniques can be used for the estimating the unperturbed dimensions from viscosity data in good solvents. The simplest of these techniques seems to be that of Stockmayer. 

The mean-square dipole moments of POE and POMg are determined from dielectric constant measurements on dilute solutions in benzene. The values obtained are in good agreement with those predicted using the RIS models for these chains. In addition, the unperturbed dimensions of POMg are calculated as a function of molecular weight using the RIS theory. 

Conformational energies as function of rotational angles over two consecutive skeletal bonds for both meso and racemic diads of poly(Af-vinyl-2-pyrrolidone) are computed. The results of these calculations are used to formulate a statistical model that was then employed to calculate the unperturbed dimensions of this polymer. The conformational energies are sensitive to the Coutombic interactions, which are governed by the dielectric constant of the solvent, and to the size of the solvent molecules. Consequently, the calculated values of the polymeric chain dimensions are strongly dependent on the nature of the solvent, as it was experimentally found before. 

RIS theory is used to study the unperturbed dimensions of PMPS chains as a function of their stereochemical structure. The required conformational energies are obtained from semi-empirical, interatomic potential energy functions and from known results on PDMS. 

The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions of the polyesters PDA and PDS are measured. The experimental value of dlln 0) / d Tshows an anomalous dependence on the elongation ratio of the networks at which the thermoelastic measurements are performed. Although the rotational states scheme gives a fairly good account of the polarity of the chains, it fails in reproducing the experimental values of d (In 0) / d T, the causes of this disagreement are discussed. 

RIS theory is used to predict values of the optical-configuration parameter Aa for ethylene - propylene copolymers as a function of chemical composition, chemical sequence distribution, and stereochemical structure of the propylene sequences. The calculations are based on information available for ethylene and propylene homopolymers, and on the model used to interpret the unperturbed dimensions of these copolymers. Values of Aa are generally found to decrease significantly with increase in the fraction of propene units, but to be relatively insensitive to chemical sequence distribution and stereochemical structure. Geometries and conformational energies are the same as those used for the interpretation of the unperturbed dimensions of these chains. The conformational energies used are E(q) = 0, EM 2.09, and E a>) = 0.37 kJ mol-1. 

Reduction of the unperturbed dimensions of the main chain is calculated when ethyl groups are attached to a polyethylene backbone. Values of most of the paramters are taken from the well-known RIS model for unperturbed polyethylene (Abe, A. Jernlgan, R. L. Flory, P, J, J, Am. Chem. Soc. 1966, 88, 631) the bond angle is 112°, gauche states are located at 60° trans 180°l. First- and second-order interactions are weighted by using o 0.43 and m 0.034 (for 300 K). An additional statistical weight, denoted by t, is required at each bond to an atom that constitutes a trifunctional branch point (Flory, P, J, Sundararajan, P. R. DeBolt, L. C. J. Am. Chem. Soc. 1974, 96, 50151. Calculations are performed with t = 0 and t = [Pg.410]

A model of the randomly colling form of polylrll) based on minimum-energy conformers of UpU is described. The blend of conformers is chosen to fit the C—C rotational populations derived in NMR studies of UpU and poly(rU) and to match the experimental unperturbed dimensions of the poly(rU) chain. In addition, estimates of loop closure based on the model are comparable to the sizes of loops most frequently seen In the model oligonucleotides. Approximately 60% of the conformers constituting the model are characterized by stacked, extended C2 -endo ra cmy = tg g+ rotations. 

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