Delu Zhao

A Molecular Model of the Elastic Behavior of Polymethylene Chains

In this paper, the elastic behavior of a polymethylene (PM) chain is investigated by using a realistic rotational-isomeric-state (RIS) model. In our calculation, the non-local interactions between pairs of segments in polymethylene chain are also considered, and the Lennard-Jones (L-J) potential function is adopted. Chain dimensions and thermodynamics statistical properties of PM chains with various elongation ratios λ are calculated. We find, that the elastic force increases slowly with elongation ratio for small λ, and abruptly for large λ. In the meantime, the energy contribution to elastic force is negative and significant, especially for large λ. Our calculations may provide some insight into the macroscopic phenomena of rubber elasticity.

Effects of the elastic deformation on the average conformations of polymethylene chains

Abstract The average conformation properties, such as the a priori probability P ξη and the segmental orientation function 〈 P 2 ( ζ )〉 of polymethylene chains with chain length from N =13 to N =21 are investigated by enumeration calculation method based on the rotational-isomeric state (RIS) model. Here non-local interactions of L–J potential are also considered. In the process of tensile deformation, the a priori probability P t increases with elongation ratio λ , meanwhile the a priori probability P g + (or P g − ) decreases with elongation ratio λ , and it leads the average energy per bond to decrease. The segmental orientation distribution function 〈 P 2 ( ζ )〉 of short deformed polymethylene chains may be expressed in the form of 〈P 2 (ζ)〉/(λ 2 −λ −1 )=a(λ 2 −λ −1 )+b where a and b only depend on PM chain length. Many conformations will vanish in the process of deformation. We also investigate the probability density distribution function of gyration radius P ( S ). For a given chain length, the maximum of P ( S ) increase with λ , and the distributed region of P ( S ) becomes smaller for large λ . Some comparisons with Flory–Fisk function of P ( S ) are also made. Our calculations may provide some insights into the rubber-like elasticity.

Predicting protein structure from long-range contacts.

Short-range and long-range contacts are important in forming protein structure. The proteins can be grouped into four different structural classes according to the content and topology of alpha-helices and beta-strands, and there are all-alpha, all-beta, alpha/beta and alpha+beta proteins. However, there is much difference in statistical property for those classes of proteins. In this paper, we will discuss protein structure in the view of the relative number of long-range (short-range) contacts for each residue. We find the percentage of residues having a large number of long-range contacts in protein is small in all-alpha class of proteins, and large in all-beta class of proteins. However, the percentage of residues is almost the same in alpha/beta and alpha+beta classes of proteins. We calculate the percentage of residues having the number of long-range contacts greater than or equal to (>/=) N(L)=5, and 7 for 428 proteins. The average percentage is 13.3%, 54.8%, 41.4% and 37.0% for all-alpha, all-beta, alpha/beta and alpha+beta classes of proteins with N(L)=5, respectively. With N(L) increasing, the percentage decreases, especially for all-alpha class of proteins. In the meantime, the percentage of residues having the number of short-range contacts greater than or equal to N(S) (>/=N(S)) in protein samples is large for all-alpha class of proteins, and small for all-beta class of proteins, especially for large N(S). We also investigate the ability of amino residues in forming a large number of long-range and short-range contacts. Cys, Val, Ile, Tyr, Trp and Phe can form a large number of long-range contacts easily, and Glu, Lys, Asp, Gln, Arg and Asn can form a large number of long-range contacts, but with difficulty. We also discuss the relative ability in forming short-range contacts for 20 amino residues. Comparison with Fauchere-Pliska hydrophobicity scale and the percentage of residues having large number of long-range contacts is also made. This investigation can provide some insights into the protein structure.

Dynamics of stiff chain

Abstract In this paper, the bending and stretching elastic potential energies are considered in calculating Hamilton actuating quantity. In the meantime, the mass density of the filament and the friction force are also considered. The normal mode analysis yields eigenfunctions and eigenvalues. In the dynamical equation of polymer chains without a Brownian force, two cases of ζ 2 −4 ρξ n >0 and ζ 2 −4 ρξ n ρ is the linear mass density of the filament, ζ is the friction constant per unit length of the filament, and ξ n is the eigenvalue. We discuss the dependence of the relaxation times on the persistence length. In the flexible limit, we obtain the relaxation times of the Rouse model. In the stiff-chain case, the relaxation times τ n are proportional to [ L /(2 n −1)] 4 .

Predicting chain dimensions from an artificial neural network model

Artificial neural network models are used to investigate polymer chain dimensions. In our model, the input nodes are glass transition temperature (Tg), entanglement molecular weight (Me), and melt density (ρ). The number of nodes in the hidden layer is eight. We found that the relative error for prediction of the characteristic ratio ranges from 0.77 to 7.5% and that the overall average error is 3.57%. Artificial neural network models may provide a new method for studying statistics properties of polymer chains.

A Monte Carlo study of polymer network dynamics

Abstract Junction fluctuations in a polymer network are investigated by using the Monte Carlo method. In our calculation, a modified bond-fluctuation model is adopted. In our model, the kuhnian bond lengths are set to vary between 2 and 4, which is different from the lengths between 2 and √ 10 of the standard model. It is found that the average fluctuations of junctions i and j may be expressed in the form of ΔR i 2 / r 2 0 = a (φ−1) +b(φ=3, 4, 5, 6) 〈ΔR i ΔR j 〉/ r 2 0 = a′ (φ−1) +b′(φ=3, 4, 5, 6) where a=0.83, b=−0.076, a′=0.06, b′= 0.0075, and 〈r2〉0 is the mean-square end-to-end distance of two adjacent junction points and φ is the junction functionality. Comparisons with the Cayley tree model are also made. Our method uses real, rather than phantom, chains, and this method can be used to investigate the dynamics of polymer network chains.

A molecular study on the reinforcement of polymethylene elastomers

Abstract Monte Carlo simulations are carried out on filled networks of polymethylene (PM), which are modeled as composites of PM chains and three-dimensional cubic lattices of filler particles. Calculations are carried out for PM chains with various chain lengths n and various cubic unit dimensions a. The elastic behavior is investigated by using a realistic rotational-isomeric-state (RIS) model and enumeration calculation method. The average conformations, such as a priori probability Pη and the segmental orientation function 〈P2(cosζ)〉 of PM chains are also calculated. In the process of tensile deformation, the a priori probability Pt increases with elongation ratio λ, however, it decreases with increasing cubic unit dimensions a. The segmental orientation distribution function 〈P2(cosζ)〉 of deformed PM chains decreases with increasing cubic unit dimensions a, especially in the region of large deformation. Average Helmholtz free energy per bond becomes small when increasing cubic unit dimensions a, and average energy per bond becomes large when increasing cubic unit dimensions a. We find that the elastic force increases with elongation ratio for small λ, and abruptly for large λ. In the meantime, the energy contribution to elastic force is negative and significant. It is also shown that the elastic force and the energy contribution to elastic force is almost the same with various cubic unit dimensions a. The ratio fu/f ranges from −0.4 to −0.6 at T=425 K. The reinforcement effects on the Helmholtz free energy 〈A〉 and energy 〈U〉 are important; however, the effect on the elastic force is insignificant. Our calculation may provide some insight into the macroscopic phenomena of rubber elasticity.

Folding lattice HP model of proteins using the bond-fluctuation model

In this paper, we find good amino acid sequences that fold to a desired target structure as a ground state conformation of lowest accessible free energy using the modified bond-fluctuation lattice model. In our protein lattice model, bond lengths are set to vary between one and √2 in three dimensions. Our results agree well with the native state energies E N . Comparisons with the putative native state (PNS) energy E PNS and the hydrophobic zippers (HZ) energy E HZ are made. For every sequence, the global energy minimum is found to have mulitple degeneracy of conformations, which is the same result as for the constraint-based hydrophobic core construction (CHCC) method. The interior conformations of the ground states are also discussed.

Elastic behavior of non-Gaussian polymethylene chains

Abstract In this paper, elastic behaviors of non-Gaussian polymethylene (PM) chains with chain length N =100 are investigated by rotational isomeric state model. Here the tetrahedral lattice of PM chain and the non-local interaction of Sutherland potential are adopted. In the metropolis movement of PM chain, a four-bond movement model is used. The average energy and average Helmholtz free energy with various elongation ratios λ are calculated by Monte Carlo simulation method. The average energy increases with elongation ratio λ and the average Helmholtz free energy decreases with elongation ratio λ . The elastic force f and the energy contribution to elastic force f u can be obtained from f =∂〈 A 〉/∂ r and f =∂〈 U 〉/∂ r . We find that the elastic force f increases with elongation ratio λ and the energy contribution f u decreases with elongation ratio λ , and f u is less than zero. The ratio f u / f is close to −0.21 for λ ⩽1.25, and −0.04 to −0.35 for λ >1.25 at T =364 K. In our calculation, the rubber elasticity may be discussed in terms of the chemical structure of polymer chains.