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In this paper, the average bond conformations of polypropylene chains in the second-order interaction approximation, and of isotactic polypropyleneoxide chains in the third-order interaction approximation are investigated. We calculate the a priori probabilities using numerical value calculation method. The average bond conformations may be used as a tool to assess the energies of various rotational isomeric stages, especially for chains that have poorly defined rotational isomers.

The mean-square radius of gyration of polymer chains with side-groups was formulated using the method of matrix algebra with the rotational isomeric state approximation. If the effect of the side-groups is neglected, the expression reduces to that reported by Flory. The molecular weight dependence of the root-mean-square radius of gyration for isotactic polypropylene was obtained as S 2 1 2 =0.34M 1 2 p] in fair agreement with experimental data from small-angle neutron scattering, reported by Ballard et al.

We introduce the parameter of probability of movement and study the dynamics of polymer chains by using the improved body-centred cubic lattice model. The model can approach to simulate the dynamics of real polymer chains. We find that the relaxation times obey the relation TR(P) ∼ (N - 1)2.05/P0.75 in the absence of excluded volume and the relation TR(P) ∼ (N - 1)2.33/P0.95 in the presence of excluded volume, also the relation Tk(P) ∼ Tk(1)/Pβk (β1 = β2 = 0.77, β3 = 0.90) in the absence of excluded volume. Comparisons with theoretical predictions are made.

A theoretical treatment of the unperturbed mean-square radius of gyration for the monosubstituted polymer chains is presented. The characteristic ratio and the temperature coefficient for an atactic polystyrene chain are evaluated to be 1.89 and − 1.3 × 10−3 deg−1 by the derived formulas, respectively, which agree well with the experimental data.

The ratio 〈 S2p 〉0/〈 R2p 〉0 for the random-flight chain is independent of n and is only dependent on p. The ratio 〈 S2p 〉/〈 R2p 〉 for the self-avoiding chain has not been studied so far. We compute the ratio 〈 S2p 〉/〈 R2p 〉 for the self-avoiding chain by using Monte Carlo simulation on a tetrahedral lattice model considering the hindrances of bond angle and potential barrier, and find the ratio 〈 S2p 〉/〈 R2p 〉 for the self-avoiding chain is also independent of n (when n → ∞) and only dependent on p. The ratio 〈 S2p 〉/〈 R2p 〉 for the self-avoiding chain may be written 〈S 2p 〉/〈R 2p =c/a p The ratio 〈 S2p 〉/〈 R2p 〉 for the self-avoiding chain is greater than the ratio 〈 S2p 〉0/〈 R2p 〉0 for the random-flight chain (except for p = 1).

The relation between conformational states and orientations of the diamond lattice chain is developed on the basis of the rotational-isomeric state model of polymer chains. Diamond lattice chains were generated by a restricted walk on a body-centred cubic lattice. Calculations of the partition function as a function of temperature were made for short polymethylene chains up to N = 16 bonds, with and without the presence of conformational states g ± g ∓ . The configurational entropy was derived from the partition function using the canonical ensemble approach. It was found possible to extrapolate the value determined for the configurational entropy per bond to determine the value for infinite chains, there being a linear relation between configurational entropy and N .

This paper uses Monte Carlo simulation on a diamond lattice model to calculate the dimension of a polymer chain confined in a sphere while considering the hindrances of bond angle and potential barrier. The results agree with those of Wu Da c hen g and Qian Renyuan et al. Further, an empirical formula relating to h2/ho2 is obtained. This formula can also be derived according to equiprobability hypothesis.