Linear chain surfactants at a planar interface: a comparative Monte Carlo study of several lattice models

Linear chain surfactants in a densely packed arrangement (such as alkane chains in lipid monolayers in the “uniform tilt” structures) are described by a crude coarse-grained model where the endgroups grafted on the interface form a regular lattice and the chains are described by the bond fluctuation model with chains containing N = 4 effective monomers only. Square-well interactions between the monomers are studied for both the attractive and repulsive case for three choices of the interaction range. None of these models exhibits a structure with uniform tilt. For attractive interactions the last bond has a strong tendency to fold back thus leading to a very high density close to the interface. Only when an intrachain-potential favoring stiff chain configurations also is included one can obtain configurations with uniform tilt order. Although related models (with much longer chain lengths and lower grafting densities) are very useful for the study of polymer brushes, the present case of very short chains in a high-density state clearly is plagued by various lattice artefacts and it is concluded that for modelling linear chain surfactants one should use an off-lattice model even on a coarse-grained level.     

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.     

Computer simulation of bottle-brush polymers with flexible backbone: good solvent versus theta solvent conditions

By molecular dynamics simulation of a coarse-grained bead-spring-type model for a cylindrical molecular brush with a backbone chain of N(b) effective monomers to which with grafting density σ side chains with N effective monomers are tethered, several characteristic length scales are studied for variable solvent quality. Side chain lengths are in the range 5 ≤ N ≤ 40, backbone chain lengths are in the range 50 ≤ N(b) ≤ 200, and we perform a comparison to results for the bond fluctuation model on the simple cubic lattice (for which much longer chains are accessible, N(b) ≤ 1027, and which corresponds to an athermal, very good, solvent). We obtain linear dimensions of the side chains and the backbone chain and discuss their N-dependence in terms of power laws and the associated effective exponents. We show that even at the theta point the side chains are considerably stretched, their linear dimension depending on the solvent quality only weakly. Effective persistence lengths are extracted both from the orientational correlations and from the backbone end-to-end distance; it is shown that different measures of the persistence length (which would all agree for Gaussian chains) are not mutually consistent with each other and depend distinctly both on N(b) and the solvent quality. A brief discussion of pertinent experiments is given.     

Mixtures of lattice polymers with structured monomers

The influence of monomer structure on the thermodynamic properties of lattice model polymer blends is investigated through Monte Carlo computations. The model of lattice polymers with monomer structure has been used extensively in the context of the lattice cluster theory (LCT), a thermodynamic theory for polymer mixtures in the liquid state. The Monte Carlo computations provide the first unequivocal test of the accuracy of the LCT predictions for binary mixtures of polymers with structured monomers. Four types of monomer structures are analyzed, corresponding to to the monomers of polyethylene, polypropylene, polyethylethylene, and polyisobutylene (PIB). Most computations use chains with M=12 and 24 beads and the total volume fraction of the beads is phi=0.6. Both structurally symmetric and asymmetric blends are investigated. For the symmetric case, the predictions of the LCT for the energies of mixing and the liquid-liquid coexistence curves are in qualitative agreement with the Monte Carlo computations, except for the PIB/PIB symmetric blend. For structurally asymmetric blends, the LCT does not capture contributions to the energy of mixing arising solely from structural differences between the components. Computational estimates of the nonideal entropy of mixing indicate that the LCT also underestimates the entropic cost of mixing chains with different structures, thus explaining some discrepancies between the theoretical and the Monte Carlo liquid--liquid coexistence curves.     

Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Exact sequence analysis for three-dimensional hydrophobic-polar lattice proteins

We have exactly enumerated all sequences and conformations of hydrophobic-polar (HP) proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the HP model, where only two types of monomers are distinguished, we determined and statistically analyzed designing sequences, i.e., sequences that have a nondegenerate ground state. Furthermore we were interested in characteristic thermodynamic properties of HP proteins with designing sequences. In order to be able to perform these exact studies, we applied an efficient enumeration method based on contact sets.     

“Grafting through” polymerization involving surface-bound monomers

“Grafting through” polymerization represents copolymerization of free monomers in solution and polymerizable units bound to a substrate. Free polymer chains are formed initially in solution and can incorporate the surface-bound monomers, and thereby, get covalently bonded to the surface during the polymerization process. As more growing chains attach to the surface-bound monomers, an immobilized polymer layer is formed on the surface. We use a combination of computer simulation and experiments to comprehend this process for monomers bound to a flat impenetrable substrate. We concentrate specifically on addressing the effect of spatial density of the surface-bound monomers on the formation of the surface-attached polymers. We employ a lattice-based Monte Carlo model utilizing the bond fluctuation model scheme to provide molecular-level insight into the grafting process. For experimental validation, we create gradients of density of bound methacrylate units on flat silicon wafers using organosilane chemistry and carry out “grafting through” free radical polymerization initiated in bulk. We report that the proximity of the surface-bound polymerizable units promotes the “grafting through” process but prevents more free growing chains to “graft through'' the polymerizable units. The “grafting through” process is self-limiting in nature and does not affect the overall density of the surface-bound polymer layer, except in case of the highest theoretical packing density of surface-bound monomers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 263–274     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

Quasiparticle band structure of infinite hydrogen fluoride and hydrogen chloride chains

We study the quasiparticle band structure of isolated, infinite (HF)(infinity) and (HCl)(infinity) bent (zigzag) chains and examine the effect of the crystal field on the energy levels of the constituent monomers. The chains are one of the simplest but realistic models of the corresponding three-dimensional crystalline solids. To describe the isolated monomers and the chains, we set out from the Hartree-Fock approximation, harnessing the advanced Green's function methods local molecular orbital algebraic diagrammatic construction (ADC) scheme and local crystal orbital ADC (CO-ADC) in a strict second order approximation, ADC(2,2) and CO-ADC(2,2), respectively, to account for electron correlations. The configuration space of the periodic correlation calculations is found to converge rapidly only requiring nearest-neighbor contributions to be regarded. Although electron correlations cause a pronounced shift of the quasiparticle band structure of the chains with respect to the Hartree-Fock result, the bandwidth essentially remains unaltered in contrast to, e.g., covalently bound compounds.     

基于“点击反应”的官能化环酯单体的合成及聚酯性能研究进展

聚酯高分子材料在医药生物材料领域有很广泛的应用,尤其是可作为药物缓释材料应用在人体当中。作为药物缓释材料的聚酯,需要具有较多的修饰位点,便于药物分子或其它小分子的键合。为了能够简便地、高效地将小分子键合到聚酯链上,可采用目前热门的"点击反应"进行小分子键合,这就需要将涉及"点击反应"的官能团引入到聚酯链上。由于采用合成聚酯的方法多为开环聚合反应,就需制备出双键和叁键官能化环酯类单体,便于以开环聚合方法制备官能化聚酯。本文综述了近年来基于"点击反应"而合成的官能化环酯类单体,将酯类单体分为三类进行了合成方法的详细介绍,重点归纳了所得到的官能化聚酯的聚合结果及其所键合的分子,阐述了官能化聚酯所具有的新性质,最后对这类聚酯材料的应用前景做了展望。     

Topochemical Syntheses of Polyarylopeptides Involving Large Molecular Motions: Frustrated Monomer Packing Leads to the Formation of Polymer Blends

We report the topochemical syntheses of three polyarylopeptides, wherein triazolylphenyl group is integrated into the backbone of peptide chains. We synthesized three different monomers having azide and arylacetylene as end-groups from glycine, L-alanine and L-valine. We crystallized these monomers and the crystal structures of two of them were determined by single-crystal X-ray diffractometry. Due to the steric constraints, both of these monomers crystallized with two molecules, viz. conformers A and B , in the asymmetric unit. Consistently, in both cases, the A -conformers are antiparallelly π -stacked and B -conformers are parallelly slip-stacked, exploiting weak interactions. Though the arrangements of molecules in the pristine crystals were unsuitable for topochemical reaction, upon heating, they undergo large motion inside the crystal lattice to reach a transient reactive orientation and thereby the self-sorted conformer stacks react to give a blend of triazole-linked polyarylopeptides having two different linkages. Due to the large molecular motion inside crystals, the product phase loses its crystallinity.     

Three-dimensional square water in the presence of an external electric field

In this work we study a tridimensional statistical model for the hydrogen-bond (HB) network formed in liquid water in the presence of an external electric field. This model is analogous to the so-called square water, whose ground state gives a good estimate for the residual entropy of the ice. In our case, each water molecule occupies one site of a cubic lattice, and no hole is allowed. The hydrogen atoms of water molecules are disposed at the lines connecting nearest-neighbor sites, in a way that each water can be found in 15 different states. We say that there is a hydrogen bond between two neighboring molecules when only one hydrogen is in the line connecting both molecules. Through Monte Carlo simulations with Metropolis and entropic sampling algorithms, and by exact calculations for small lattices, we determined the dependence of the number of molecules aligned to the field and the number of hydrogen bonds per molecule as a function of temperature and the intensity of the external field. The results for both approaches showed that, different of the two-dimensional case, there is no maximum in the number of HBs as a function of the electric field. However, we observed nonmonotonic behaviors as a function of the temperature of the quantities of interest. We also found the dependence of the entropy on the external electric field at very low temperatures. In this case, the entropy vanishes for the value of the external field for which the contributions to the total energy coming from the HBs and the field become the same.     

Spacer effect of novel bifunctional organophosphorus monomers in metal-imprinted polymers prepared by surface template polymerization

The interfacial activity and the molecular structure of functional monomers are critical factors that determine the success of synthesizing metal-imprinted polymers by surface template polymerization. From this point of view, first we prepared three distinct novel bifunctional organophosphorus monomers that are interspaced, in each case, by an alkyl spacer having a specific length. Each monomer carries two phosphonic acid groups and two aromatic groups in its molecular structures. Further, by using the synthesized bifunctional monomers, we prepared highly selective Zn(II)-imprinted polymers by the surface template polymerization initiated from a water-in-oil emulsion. To evaluate the template effect, we conducted diagnostic adsorption studies on Zn(II)-imprinted and unimprinted polymers with zinc ions. A high interfacial activity was found to be required for the functional monomers to create the predominant template effect. It became clear that Zn(II)-imprinted polymers having bifuctional monomers with 12-length alkyl chains (1,12-dodecanediol-O, O′-diphenyl phosphonic acid: DDDPA) yielded the best results. Moreover, analysis results of adsorption behavior supported a high-performance of the Zn(II)-imprinted polymers with DDDPA. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2727–2734, 1998     

Molecular simulation studies of the structure of phosphorylcholine self-assembled monolayers

We report a study of the structure of phosphorylcholine self-assembled monolayers (PC-SAMs) on Au(111) surfaces using both molecular mechanics (MM) and molecular dynamics (MD) simulation techniques. The lattice structure (i.e., packing densities and patterns) of the PC chains was determined first, by examining the packing energies of different structures by MM simulations in an implicit solvent. The chain orientation (i.e., antiparallel and parallel arrangements of the PC head groups) was then evaluated. The initial azimuthal angles of the PC chains were also adjusted to ensure that the optimal lattice structure was found. Finally, the two most probable lattice structures were solvated with explicit water molecules and their energies were compared after 1.5 ns of MD simulations to verify the optimal structures obtained from MM. We found that the optimal lattice structure of the PC-SAM corresponds to a radical7 x radical7 R19degree lattice structure (i.e., surface coverage of 50.4 A(2)molecule) with a parallel arrangement of the head groups. The corresponding thickness of the optimal PC-SAM is 13.4 A which is in agreement with that from experiments. The head groups of the PC chains are aligned on the surface in such a way that their dipole components are minimized. The P-->N vector of the head groups forms an angle of 82 degrees with respect to the surface normal. The tilt direction of molecular chains was observed to be towards their next nearest neighbor.     

Simple model of sickle hemogloblin

A microscopic model is proposed for the interactions between sickle hemoglobin molecules based on information from the protein data bank. A solution of this model, however, requires accurate estimates of the interaction parameters which are currently unavailable. Therefore, as a first step toward a molecular understanding of the nucleation mechanisms in sickle hemoglobin, a Monte Carlo simulation of a simplified two patch model is carried out. A gradual transition from monomers to one dimensional chains is observed as one varies the density of molecules at fixed temperature, somewhat similar to the transition from monomers to polymer fibers in sickle hemoglobin molecules in solution. An observed competition between chain formation and crystallization for the model is also discussed. The results of the simulation of the equation of state are shown to be in excellent agreement with a theory for a model of globular proteins, for the case of two interacting sites.     

Sequence effects on the forced translocation of heteropolymers through a small channel

By using a recently developed Monte Carlo algorithm and an exact numerical method, we calculate the translocation probability and the average translocation time for charged heterogeneous polymers driven through a nanopore by an external electric field. The heteropolymer chains are composed of two types of monomers (A and B) which differ only in terms of their electric charge. We present an exhaustive study of chains composed of eight monomers by calculating the average translocation time associated with the 256 possible arrangements for various ratios of the monomer charges (lambda(A)lambda(B)) and electric field intensities E. We find that each sequence leads to a unique value of the translocation probability and time. We also show that the distribution of translocation times is strongly dependent on the two forces felt by the monomers ( approximately lambda(A)E and approximately lambda(B)E). Finally, we present results that highlight the effect of having repetitive patterns by studying the translocation times of various block copolymer structures for a very long chain composed of N=2(18) monomers (all with the same number of A and B monomers).     

Mixtures of liquid-crystalline polymers

A density-functional expansion method is used to derive the free energy of a polymer mixture. The expression obtained includes the entropy of mixing, the entropy of configuration of the chains and the interactions (both isotropic and anisotropic ones). The chains are modelled as interacting elastic lines (bend curvature). The method is very general, and we only focus our attention on binary mixtures. The phase diagram and the order parameters are calculated. We show some results for two types of mixtures: a nematic polymer in a non-mesomorphic particle (polymer or solvent) and in another nematic liquid crystal (small-molecule or polymer). We discuss the influence of the molecular weights, the persistence length and the interactions on the phase separation.     

Influence of small rings on the thermodynamics of equilibrium self-assembly

The competition between the formation of linear chain clusters and ring structures in an equilibrium self-assembling system is reexamined by developing a new Flory-Huggins type theory that combines an estimate for the loss of configurational entropy ΔS(ring) upon ring formation with the standard treatment of the free energy of a polydisperse solution of linear chains. The excess entropy of ring formation ΔS(ring) is obtained from an analytical fit to exact enumeration data for self-avoiding chains and rings with 30 or fewer steps on a cubic lattice. Illustrative calculations of the spinodal curves and the extent and the average degree of self-assembly highlight the physical conditions for which the cyclic structures impact the thermodynamic characterization of equilibrium self-assembling systems.     

Exfoliation of a stack of platelets and intercalation of polymer chains: Effects of molecular weight,entanglement, and interaction with the polymer matrix

Exfoliation of a stack of sheets (a model for clay platelets) in a dynamic matrix of polymer chains is investigated by a computer simulation model. How the interplay between the thermodynamics (interaction-driven) and conformational (structural constraints) entropy affects the exfoliation of sheets is the subject of this study. A stack of four sheets with a small initial interlayer distance constitutes the layer on a discrete lattice. The layered platelets are immersed in a matrix represented by the mobile polymer chains which occupy a fraction (concentration) of the lattice sites. Both sheets and chains are modeled by the bond-fluctuation mechanism and execute their stochastic motion via Metropolis algorithm. An attractive and a repulsive interaction between the polymer matrix and platelets are considered. Exfoliation of the sheets is examined by varying the molecular weight of the polymer chains forming a dynamic network matrix with various degrees of entanglements. At low-molecular weight of the polymer, exfoliation is achieved with repulsive interaction and the exfoliation is suppressed with attractive matrix as sheets stick together via polymer mediated interaction introduced by intercalated polymer chains. Increasing the molecular weight of the polymer matrix suppresses the exfoliation of sheets primarily due to enhanced entanglement—at high-molecular weight (with the radius of gyration of polymer chains larger than the characteristic linear dimension of the platelets), the stacked (layered) morphology is arrested via entropic trapping and exfoliation ceases to occur. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2696–2710, 2008     

Adsorption from polymer mixtures. The effect of molecular mass

Two approaches are used to study the adsorption of components from polydisperse polymer melts. The distribution of components of binary mixture of homopolymers differing only in molecular masses near the neutral wall is studied using the Scheutjens-Fleer lattice model. An increase in the concentration of component with lower molecular mass near the wall observed under the considered conditions is caused by a decrease in the losses of configurational entropy of polymer chains. The adsorption of low-molecular-mass component is calculated for a large set of model parameters. The equation describing adsorption as a function of mixture concentration and parameter (N ₁/N ₂ ? 1) characterizing the difference in chain lengths of N ₁ and N ₂ components is proposed. The proposed equation is a specific case of equation, which was derived using Flory-Huggins lattice theory and the data on the dependences of surface tension on the composition of polydisperse melts.