不同边界条件下导电高分子电子结构的研究

用一维复式晶格作为反式聚乙炔的模型 ,在周期与非周期边界条件下 ,考虑链端效应并计及电子的非近邻跳跃 ,数值计算了格点数分别等于N =10、5 0、10 0和 2 0 0时聚乙炔的能谱和态密度 .讨论了不同格点数和结构参数对态密度及带宽的影响 ,并对两种边界条件下的计算结果进行了比较 .计算结果表明 ,当格点数N <5 0时 ,两者相差较大 ,这表明系统的边界将起很大作用 ;当格点数N≥ 5 0时 ,两者相差甚微 ,这时可利用周期性边界条件来研究有限系统问题 .     

Treatment of aperiodicity and correlation in polymers

The negative factor counting method (in its simple and matrix block form) for the determination of the density of states of disordered polymer chains and its applications to different aperiodic organic polymers are reviewed. The problems of the calculation of the correlation energy in large systems like polymers will be discussed. Different ways for the partitioning of an energy band into regions make it possible to perform Møller–Plesset perturbation theoretical calculations on polymers. Applications to hydrogen chains are presented. Finally, possible applications to disordered polymers are also discussed.     

The application of the extended negative factor counting method to deal with the electronic energy levels of pig insulin

The quantum-chemical calculation for pig insulin was done by the ENFC method in which the matrix elements were calculated in the ab initio level with the help of a minimal basis. The aqueous solution surrounding insulin was simulated by putting point charges around the residues that have electric charges. The electronic density of states (DOS) of insulin confirmed the conclusions obtained from aperiodic model peptide chains. It is shown that the frontier orbitals of the insulin were mainly localized on those residues which are involved in the expression of biological activity of insulin.     

Compatibility of coils and rods bearing flexible side chains

We present a theoretical treatment of nematic-isotropic phase equilibria in mixtures which consist of random coils and comblike polymers, the latter components being composed of a rigid backbone and flexible side chains. The mixing partition function is evaluated by using the Flory lattice model. The comblike component is characterized by the axial ratio x_r of its rigid main chain and the number of flexible side chains z, each containing m segments. The coiled component is described by its number of segments x_c. The net exchange energy of mixing is assumed to be zero; i.e., we consider athermal solutions. It is shown that the flexible side chains attached to the rigid main chains markedly enhance the compatibility in the isotropic phase. If the ratio of the volume fraction of the side chains to the volume fraction of the main chains is high enough, there is even a finite range of concentration where the random coils mix homogeneously with the comblike component. This is in contrast to mixtures of rods and coils, which have been shown by Flory to be incompatible over nearly the full range of composition. These conclusions hold true only when ordered states are involved. For comblike polymers with flexible backbones mixed with random coils in isotropic melts, the resulting free energy of mixing is given by the familiar Flory-Huggins expression.     

A revised worm‐like chain model for elasticity of polypeptide chains

The elasticity of polypeptide chains is usually characterized by the worm‐like chain model that was proposed first to describe the elasticity of double‐stranded DNA. However, the molecular dynamics simulation data on the elasticity of the polypeptide chains are deviated significantly away from the theoretical data obtained based on the worm‐like chain model. Here, we provide a revised worm‐like chain model by considering entropic, enthalpic, and hydrophobic effects and the effect of the compressing force applied to the polypeptide chains. The theoretical data obtained based on the revised model are in good agreement with the molecular dynamics simulation data. Additionally, we reveal that, besides the positive‐force regime in the elasticity of polypeptide chains, the negative‐force regime also plays important roles in the biological functions of proteins. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 297–307     

A quantitative study of tethered chains in various solution conditions using Langmuir diblock copolymer monolayers

This article summarizes our investigations of tethered chain systems using Langmuir monolayers of poly(dimethylsiloxane)‐polystyrene (PDMS‐PS) diblock copolymers on organic liquids. In this system, the PDMS block adsorbs strongly to the air surface while the PS block dangles into the subphase liquid. The air surface can be made either repulsive or attractive for the tethered PS chain segments by choosing a subphase liquid which has a surface tension less than or greater than that of PS, respectively. The segment profile of the PS block is determined by neutron reflection as a function of the surface density, the molecular weights of the PS and PDMS blocks, and the solution conditions. We cover the range of reduced surface density (Σ ) characteristic of the large body of data in the literature for systems of chains tethered onto solid surfaces from dilute solution in good or theta solvent conditions (Σ < 12). We emphasize quantitative comparisons with analytical profile forms and scaling predictions. We find that the strong‐stretching limit assumed in analytical self‐consistent field calculations (SCF) and scaling theories is not valid over this Σ range. On the other hand, over a large portion of this range (Σ ⪇ 5) tethered chain profiles are well described by a renormalization group theory for weakly interacting or noninteracting chains. Simultaneous with the study of the profile form, the free energy of the tethered chains is examined through the surface tension. A strong increase in the surface pressure is observed with increasing surface density which determines the maximum surface density which can be achieved. This effect is attributed to a combination of higher order osmotic interactions and configurational constraints. This effect may explain several outstanding discrepancies regarding the adsorption of end‐functionalized chains and diblock copolymers onto solid surfaces.     

Free energy landscape of protein-like chains with discontinuous potentials

In this article the configurational space of two simple protein models consisting of polymers composed of a periodic sequence of four different kinds of monomers is studied as a function of temperature. In the protein models, hydrogen bond interactions, electrostatic repulsion, and covalent bond vibrations are modeled by discontinuous step, shoulder, and square-well potentials, respectively. The protein-like chains exhibit a secondary alpha helix structure in their folded states at low temperatures, and allow a natural definition of a configuration by considering which beads are bonded. Free energies and entropies of configurations are computed using the parallel tempering method in combination with hybrid Monte Carlo sampling of the canonical ensemble of the discontinuous potential system. The probability of observing the most common configuration is used to analyze the nature of the free energy landscape, and it is found that the model with the least number of possible bonds exhibits a funnel-like free energy landscape at low enough temperature for chains with fewer than 30 beads. For longer proteins, the free landscape consists of several minima, where the configuration with the lowest free energy changes significantly by lowering the temperature and the probability of observing the most common configuration never approaches one due to the degeneracy of the lowest accessible potential energy.     

Properties of grafted amphiphilic chains. A computer simulation study

The model of a heteropolymer film formed by polypeptide chains was used for theoretical considerations. The linear chains consisting of amino acid residues were approximated by alpha carbon chains. Each chain was constructed on a very flexible [310] lattice. The inter- and intramolecular interactions consisted of the long-range contact potential between residues. The chains were built of hydrophilic and hydrophobic residues. Chains were terminally attached to an impenetrable surface with lateral motions possible. The Monte Carlo simulations of this model were carried out by using the Metropolis algorithm. The influence of the grafting density, the sequence of the amino acid residues, and the temperature on the static properties of the formed layer were studied and discussed. It was shown that homopolymer chains collapsed at higher temperature than the heteropolymers. The size of the polymers forming brush was smaller for homopolymers than for heteropolymers. The structure of the resulting polymer film and of its external surface was determined. The block copolymers formed well defined hydrophobic and hydrophilic layers, while for the amphiphilic case the composition of the brush layers changed continuously at high temperature. It was observed that the latter effect vanished at the collapsed amphiphilic copolymer.     

Synthesis and characterization of polyphenylenes with polypeptide and poly(ethylene glycol) side chains

We report a novel approach for fabrication of multifunctional conjugated polymers, namely poly(p‐phenylene)s (PPPs) possessing polypeptide (poly‐l ‐lysine, PLL) and hydrophilic poly(ethylene glycol) (PEG) side chains. The approach is comprised of the combination of Suzuki coupling and in situ N‐carboxyanhydride (NCA) ring‐opening polymerization (ROP) processes. First, polypeptide macromonomer was prepared by ROP of the corresponding NCA precursor using (2,5‐dibromophenyl)methanamine as an initiator. Suzuki coupling reaction of the obtained polypeptide and PEG macromonomers both having dibromobenzene end functionality using 1,4‐benzenediboronic acid as the coupling partner in the presence of palladium catalyst gave the desired polymer. A different sequence of the same procedure was also employed to yield polymer with essentially identical structure. In the reverse sequence mode, low molar mass monomer (2,5‐dibromophenyl)methanamine, and PEG macromonomer were coupled with 1,4‐benzenediboronic acid in a similar way followed by ROP of the L‐Lysine NCA precursor through the primary amino groups of the resulting polyphenylene. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1785–1793     

Intramolecularly ordered globules and the collapse of short chains

We investigate the poor-solvent collapse of short chains having different stiffness through self-consistent minimization of the intramolecular free energy under the constraint of fixed segment lengths between adjacent beads. At first the chains form the Random Gaussian Globule, where the beads are distributed at random at the same average distance from the centre of mass, while the segments show very little correlation. At a larger attractive potential, this collapsed globule undergoes a transition to one or more ordered compact states, depending on the chain stiffness. Under very strong contraction, all chains are described as a Compact Ordered Globule: the beads are again at a constant average distance from the centre of mass, while the segments jump back and forth at the globule's wall with a very large correlation. At intermediate contraction, the thinner and stiffer chains form the Oscillating Ordered Globule wherein the beads are alternatively distributed on two concentric on two concentric shells. In this case, we also find metastable states with nonsymmetrical conformations of the chain with respect to its ends. We also briefly discuss the thermodynamics of the coil-globule and globule-globule transitions, showing that in long polymer chains these ordered conformations cannot involve the whole chain. However, we suggest that they might still be found as local globules that form for kinetic reasons.     

Electronic structures around the local defects in all-trans-polyacetylene: An analysis by the cluster-series model

A new approach to analyze the electronic structure around the local defects in a polymer chain is developed based on the cluster-series model. In this approach, by extending the cluster molecule to both sides of the defect, the size effect on electronic structure can be estimated systematically and efficiently. Moreover, through the extension process, the periodicity of electronic structure can be extracted in the form of the periodic pattern of stationary orbitals, which are molecular orbitals unaltered by the extension of the cluster. Such periodic orbitals characterize the bulk states of periodic polymer and the energy band structure can be reconstructed from them. Illustrative analyses of some kinds of local defects in all-trans-polyacetylene are presented at the ab initio STO -3G level. The effects of local defects can be detected by the deviation from periodic bulk states. © 1993 John Wiley & Sons, Inc.     

A rapid and efficient algorithm for packing polypeptide chains by energy minimization

An improved algorithm for packing polypeptide chains with fixed geometry, which converges to a local energy minimum rapidly and efficiently, is described. The speed of convergence of the new algorithm is comparable to that of existing algorithms for minimizing the energies of single polypeptide chains, and it is several times greater than the speed of convergence of previous algorithms for minimizing the energy of structures consisting of several polypeptide chains. The algorithm has been used to minimize the energy of three-stranded (L -Ala)₈ β-sheets, three-stranded (L -Val)₆ β-sheets, and five-stranded (L -Ile)₆ β-sheets, starting from regular structures found previously; of the three-stranded regular and truncated (Gly-L -Pro-L -Pro)₄ structures used in earlier work to model collagen; and of the stacked β-sheet (L -Ala-GLy)₆ structures used to model silk. The antiparallel L -Ala β-sheet, and Gly-Pro-Pro triple helices, and the silk II structure remained nearly regular after energy minimization, but by contrast with results from earlier computations the other structures became significantly irregular. © 1994 by John Wiley & Sons, Inc.     

Interaction between polymers: Dispersion energy of two infinite linear chains

Using the newly developed discrete variant of the k · p perturbation theory for linear chains an expression is derived for the dispersion interaction between two infinite chains valid for both insulating and metallic polymers. It is shown that the formally divergent dispersion energy is also finite for metallic systems, but it may be considerably enhanced in polymers with partly filled bands as compared with insulting ones. The accuracy of the proposed k · p expansion is investigated on model chains through comparisons with direct ab initio Hartree–Fock crystal orbital calculations. Applying second order perturbation theory an explicit formula in terms of band parameters is given for the numerical calculation of the dispersion energy.     

Study on structure formation of short polyethylene chains via dynamic Monte Carlo simulation

Monte Carlo (MC) simulations of structure formation for short polyethylene chains at low temperature are performed based on a recent developed method that uses coarse-grained chains on a high coordination lattice. Local short-range interactions based on rotational isomeric state (RIS) model and long-range interactions obtained from Lennard–Jones (LJ) potential are introduced during the simulation. Properties evaluated from the simulations are the mean square dimensions, anisotropy of the radius of gyration tensor, local conformation determined by the occupancy of trans state and orientation correlation functions, energy of the system, and chain packing reflected by the pair correlation functions and structure factors. All of these parameters reveal an ordering process that produces an approximation to a hexagonal crystal phase. The hexagonal structure is imposed by the presence of a diamond lattice underlying the high coordination lattice on which the simulation is performed. Folding of the chains in the crystal is mandatory, because they have fully extended lengths in excess of the dimension of the simulated periodic box. Nevertheless, the simulations demonstrate that a high degree of crystallinity can be achieved in reasonable computer time. The simulation technique should be applicable to other choices of periodic boundary conditions that do not affect the results as strongly as in the present case.     

Molecular modeling of polymers. 10. Characterization of conformational transitions of poly(acrylic acid) and poly(methacrylic acid) using dyad structures

The conformational profiles of nearest side-chain neighbors, methylene-dyad structures, of poly(acrylic acid), PAA, and poly(methacrylic acid), PMA, were determined as a function of tacticity, extent of ionization, and presence of counterion. The dominant backbone conformer states are quite similar for both isotactic and syndiotactic diads in a common charge state. Thus, the overall dimensional properties of isotactic syndiotactic and atactic chains of PAA or PMA, based upon dyad interactions, are predicted to be alike for a given charge state. Significant deviations from precise t, g⁺, and g^? states are found for the dyad minimum energy conformations. The rod-to-coil and coil-to-rod transitions observed in PAA and PMA, respectively, as a function of increasing counterion concentration can be explained, to a large extent, by the conformational profiles of the corresponding dyad model structures. © 1994 John Wiley & Sons, Inc.     

Titration curves of polypeptide chains by combined isoelectric focusing-electrophoresis in 8 M urea

Titration curves of reduced and alkylated polypeptide chains can be successfully performed in 8 M urea-polyacrylamide gel plates by electrophoresis perpendicular to a stationary stack of focused carrier ampholytes. All buffers and thiol reagents with pK values in the range pH 3--10 should be removed, since their pH-dependent ionization affects the migration and apparent pI values of the protein chains. No blurring of the patterns below pH 4.5 is observed, as usually found in titration curves in the absence of urea, thus allowing the direct titration of Glu and Asp residues. It is not possible by the present technique to titrate any group below pH ca. 3 and above pH ca. 10, due to the lack of suitable carrier ampholytes and to a "flooding" phenomenon, with concomitant identical electrophoretic mobility for all protein species, irrespective of their relative pI values and amino acid composition. The "electrophoretic titration curves" thus obtained were well correlated with the overall amino acid composition of the polypeptide chains analyzed.     

Comparison of surface properties of random, block, and graft copolymers having perfluoroalkyl and silicone-containing side chains

Fluorosilicone copolymers of random, block, and graft with both perfluoroalkyl and silicone-containing side chains were synthesized, and their surface properties and surface modification effects on PVC film were compared. It can be confirmed that the fluorosilicone copolymers of random, block, and graft exhibit very low surface free energies of 9-13 dyn/cm, depending on the perfluoroalkyl group content and their molecular structure. The inherent surface free energies of the fluorosilicone copolymers are significantly influenced by their molecular structure and perfluoroalkyl group content. It can also be found that the fluorosilicone copolymers are very effective for lowering surface free energy. The surface free energy of a copolymer/PVC blend strongly varies with perfluoroalkyl group content as well as molecular structure. The molecular structure of a fluorosilicone copolymer is as important as the perfluoroalkyl group content for their inherent surface free energies and surface modification of other polymers.     

Cluster CPA calculations for infinite and half–infinite chains and applications to coupled polymer chains

It is shown how the cluster CPA can be used to obtain the local density of states p(E) in a half-infinite or infinite random polymer chain. Calculations were performed for p(E) in a system composed of two coupled random chains with nearest neighbors interaction.     

Importance of chirality and reduced flexibility of protein side chains: a study with square and tetrahedral lattice models

Side chains of amino acid residues are the determining factor that distinguishes proteins from other unstable chain polymers. In simple models they are often represented implicitly (e.g., by spin states) or simplified as one atom. Here we study side chain effects using two-dimensional square lattice and three-dimensional tetrahedral lattice models, with explicitly constructed side chains formed by two atoms of different chirality and flexibility. We distinguish effects due to chirality and effects due to side chain flexibilities, since residues in proteins are L residues, and their side chains adopt different rotameric states. For short chains, we enumerate exhaustively all possible conformations. For long chains, we sample effectively rare events such as compact conformations and obtain complete pictures of ensemble properties of conformations of these models at all compactness region. This is made possible by using sequential Monte Carlo techniques based on chain growth method. Our results show that both chirality and reduced side chain flexibility lower the folding entropy significantly for globally compact conformations, suggesting that they are important properties of residues to ensure fast folding and stable native structure. This corresponds well with our finding that natural amino acid residues have reduced effective flexibility, as evidenced by statistical analysis of rotamer libraries and side chain rotatable bonds. We further develop a method calculating the exact side chain entropy for a given backbone structure. We show that simple rotamer counting underestimates side chain entropy significantly for both extended and near maximally compact conformations. We find that side chain entropy does not always correlate well with main chain packing. With explicit side chains, extended backbones do not have the largest side chain entropy. Among compact backbones with maximum side chain entropy, helical structures emerge as the dominating configurations. Our results suggest that side chain entropy may be an important factor contributing to the formation of alpha helices for compact conformations.