Zhang Linxi

MONTE CARLO SIMULATION OF THE DYNAMICS AND CONFIGURATIONAL DEPENDENT PROPERTIES OF POLYMETHYLENE CHAINS

The dynamics and configurational-dependent properties of polymethylene (PM) chains are studied using the modified bond-fluctuation model and the rotational-isomeric state model. In this article, the tetrahedral lattice model is adopted because it gives a reasonable approximation to the carbon–carbon backbones of PM chain. In our bond-fluctuation model, a Kuhnian bond includes four carbon–carbon bonds. Our statistical mechanics properties of chains are in good agreement with the Flory theory. The relaxation times τ rise with the chain length N by a power law of the form τ (N)−N2 in the absence of excluded volume and τ (N)−N2.17 in the presence of excluded volume, and the diffusion coefficients D behave as D−1/N both in the absence and presence of excluded volume. Our modified bond-fluctuation model can also be used to investigate the glass transition of polymer chains.

Studies of distribution function P(S) of polymer chains.

The distribution function P(S) of the radius of gyration can not be calculated exactly. In this paper, we calculate the distribution function P(S) of the unperturbed linear polymer chains by using Monte Carlo simulation on the simple cubic lattice. Our function P(S) doesn’t agree with the Flory-Fisk function P(S), and comparisons with some theoretical predictions are made.

Effect of branch points on the dynamics of polymer chains

Abstract The dynamics of polymer chains, such as (A) n , (A R ) n and A(A R A) n′ , where R is the side group, are studied using the bond-fluctuation model in order to investigate the effects of branch points on the dynamics of polymer chains. It is found that the relaxation times T R of the end-to-end vector of linear polymer chains are less than those of chains with side groups, especially for the excluded-volume case. The ratio T R T RO (where T RO is the relaxation time of the linear chain) is almost the same for various chain lengths, and the relaxation times T R . of chains with side groups also obey the scaling law T R − ( n − 1) 2 without excluded volume and T R − ( n − 1) 2.5 with excluded volume for d = 2, where d represents a dimension.

Simulation studies of mean-square radius of gyration of polyethylene chains

Abstract The mean-square radius of gyration of polyethylene chains, considering the effect of hydrogen atoms, is investigated by using Monte Carlo simulation and the rotational isomeric state model. It is found that the mean-square radius of gyration of the chains may be expressed as 〈S 2 〉 1 2 =0.445·M 1 2 in agreement with experimental data 〈S 2 〉 1 2 M =0.45·M 1 2 This simulation can provide a method to investigate the mean-square radius of gyration of polymer chains.

Effect of side groups on dynamics of polymer chains

Abstract The dynamics of polymer chains, such as (ABRBR)x, are investigated by means of the equivalent linear polymer chains, (AB′B′)x, with the probability p of movement of bead B′, It is found that the relaxation times of the equivalent linear polymer chains obey the relation Tk(p) = Tk0 · p−βk, where β1 = 0.75, β2 = β3 = 0.85, in the absence of excluded volume, and Tk(p) = Tk0 · p−βk (excluding k = 1), where β2 = β3 = 0.90, in the presence of excluded volume, where Tk0 is the relaxation times Tk of linear polymer chains, or Tk0 = Tk(p = 1.0).

Dynamics of the improved body-centred cubic lattice model for polymer chains

Abstract 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 T R ( P ) ∼ ( N - 1) 2.05 / P 0.75 in the absence of excluded volume and the relation T R ( P ) ∼ ( N - 1) 2.33 / P 0.95 in the presence of excluded volume, also the relation T k ( P ) ∼ T k (1)/ P β k ( β 1 = β 2 = 0.77, β 3 = 0.90) in the absence of excluded volume. Comparisons with theoretical predictions are made.

The ratio 〈 S2p〉/〈 R2p 〉 for linear polymer chains☆

Abstract 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).

Effects of pore structure on the dynamics of lattice models for polymer chains

Abstract The dynamics of polymer chains confined in pores are investigated in order to examine the effects of pore structure on the dynamics of the lattice model. The dynamics are studied by calculation of the relaxation times of the autocorrelation function of the first three normal coordinates T k and of the end-to-end vector T R for various widths of an infinite parallel-plate and length of side of an infinite cuboid. It is found that the relaxation times T k and T R obey the scaling law: T ∼ ( N − 1) 2 . Comparisons with the dynamics of polymer chains confined in an infinite cylinder are made, and the results are almost the same.

Unperturbed chain dimensions of polysilane in the third-order interaction approximation

Abstract The configurational energies, the characteristic ratio and the temperature coefficient for a polysilane chain with the third-order interaction are calculated. The characteristic ratios (〈R2〉/nl2)∞ and (〈S2〉0/nl2)∞ are 3.57 and 0.575, respectively, and the temperature coefficient is −3.0 × 10−3 deg−1. These results are less than those in the second-order interaction approximation. The third-order interaction approximation are useful for calculating the dimensions of polymer chains.