Static and dynamic properties of polymer brush with topological ring structures: Molecular dynamic simulation

By defining a topological constraint value(rn),the static and dynamic properties of a polymer brush composed of moderate or short chains with different topological ring structures are studied using molecular dynamics simulation,and a comparison with those of linear polymer brush is also made.For the center-of-mass height of the ring polymer brush scaled by chain length h~N~v,there is no significant difference of exponent from that of a linear brush in the small topological constraint regime.However,as the topological constraint becomes stronger,one obtains a smaller exponent.It is found that there exists a master scaling power law of the total stretching energy scaled by chain length N for moderate chain length regime,F_(ene)~Np~v,for ring polymer brushes,but with a larger exponent v than 5/6,indicating an influence of topological constraint to the dynamic properties of the system.A topological invariant of free energy scaled by(c)~(5/4) is found.     

Molecular dynamics simulation of semiflexible polyampholyte brushes--The effect of charged monomers sequence

Planar brushes formed by end-grafted semiflexible polyampholyte chains, each chain containing an equal number of positively and negatively charged monomers, are studied using molecular dynamics simulations. Keeping the length of the chains fixed, the dependences of the average brush thickness and equilibrium statistics of the brush conformations on the grafting density and the salt concentration are obtained with various sequences of charged monomers. When similarly charged monomers of the chains are arranged in longer blocks, the average brush thickness is smaller and the dependence of brush properties on the grafting density and the salt concentration is stronger. With such long blocks of similarly charged monomers, the anchored chains bond to each other in the vicinity of the grafting surface at low grafting densities and buckle toward the grafting surface at high grafting densities.     

Polymer brushes near the crystallization density

In this paper, polymer brushes are studied via molecular-dynamics simulations at very high grafting densities, where the crossover between the brush regime and the polymer-crystal regime is taking place. This crossover is directly observed with the structure factor and pair-correlation function. With increasing grafting density, this crystallization is progressing from the core layer of the brush towards the surface layer. The same process is analyzed using the lateral fluctuations of the monomers as a signature of their diminishing mobility. Additionally, bond forces and the chain excess free energy indicate a transition from the brush regime to the overstretched regime, which is in agreement with predictions of a modified self-consistent field theory.     

Monte Carlo analysis of polymer translocation with deterministic and noisy electric fields

Polymer translocation through the nanochannel is studied by means of a Monte Carlo approach, in the presence of a static or oscillating external electric voltage. The polymer is described as a chain molecule according to the two-dimensional “bond fluctuation model”. It moves through a piecewise linear channel, which mimics a nanopore in a biological membrane. The monomers of the chain interact with the walls of the channel, modelled as a reflecting barrier. We analyze the polymer dynamics, concentrating on the translocation time through the channel, when an external electric field is applied. By introducing a source of coloured noise, we analyze the effect of correlated random fluctuations on the polymer translocation dynamics.     

Phase behaviour of polyethylene knotted ring chains

The phase behaviour of polyethylene knotted ring chains is investigated by using molecular dynamics simulations. In this paper, we focus on the collapse of the polyethylene knotted ring chain, and also present the results of linear and ring chains for comparison. At high temperatures, a fully extensive knot structure is observed. The mean-square radius of gyration per bond ² / (Nb²) and the shape factor <δ^*> depend on not only the chain length but also the knot type. With temperature decreasing, chain collapse is observed, and the collapse temperature decreases with the chain length increasing. The actual collapse transition can be determined by the specific heat capacity C_v, and the knotted ring chain undergoes gas-liquid-solid-like transition directly. The phase transition of a knotted ring chain is only one-stage collapse, which is different from the polyethylene linear and ring chains. This investigation can provide some insights into the statistical properties of knotted polymer chains.     

Stretching of semiflexible polymers with elastic bonds

A semiflexible harmonic chain model with extensible bonds is introduced and applied to the stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study effects from bending rigidity, bond extension, discrete chain structure, and finite length of a semiflexible polymer in a unified manner. The interplay between bond extension and external force can be described by an effective inextensible chain with increased stretching force, which leads to apparently reduced persistence lengths in force-extension relations. We obtain force-extension relations for strong- and weak-stretching regimes which include the effects of extensible bonds, discrete chain structure, and finite polymer length. We discuss the associated characteristic force scales and calculate the crossover behaviour of the force-extension curves. Strong stretching is governed by the discrete chain structure and the bond extensibility. The linear response for weak stretching depends on the relative size of the contour length and the persistence length which affects the behaviour of very rigid filaments such as F-actin. The results for the force-extension relations are corroborated by transfer matrix and variational calculations.PACS: 87.15.-v Biomolecules: structure and physical properties - 87.15.Aa Theory and modeling; computer simulation - 87.15.La Mechanical properties     

Molecular dynamic simulations of elastomer structure and its influence on anisotropic stress under time-varying strain

We investigate the evolution of polymer structure and its influence on uniaxial anisotropic stress under time-varying uniaxial strain, and the role of external control variables such as temperature, strain rate, chain length, and density, using molecular dynamics simulation. At temperatures higher than glass transition, stress anisotropy in the system is reduced even though the bond stretch is greater at higher temperatures. There is a significant increase in the stress level with increasing density. At higher densities, the uncoiling of the chains is suppressed and the major contribution to the deformation is by internal deformation of the chains. At faster rates of loading stress anisotropy increases. The deformation mechanism is mostly due to bond stretch and bond bending rather than overall shape and size. Stress levels increase with longer chain length. There is a critical value of the functionality of the cross-linkers beyond which the uniaxial stress developed increases caused primarily by bond stretching due to increased constraint on the motion of the monomers. Stacking of the chains in the system also plays a dominant role in the behaviour in terms of excluded volume interactions. Low density, high temperature, low values of functionality of cross-linkers, and short chain length facilitate chain uncoiling and chain slipping in cross-linked polymers.     

Grafted polymers with annealed excluded volume: A model for surfactant association in brushes

We present an analytical self-consistent-field (SCF) theory for a neutral polymer brush (a layer of long polymer chains end-grafted to a surface) with annealed excluded volume interactions between the monomer units. This model mimics the reversible adsorption of solute molecules or aggregates, such as small globular proteins or surfactant micelles, on the grafted chains. The equilibrium structural properties of the brush (the brush thickness, the monomer density profile, the distribution of the end segments of the grafted chains) as well as the overall adsorbed amount and the adsorbate density profile are analyzed as a function of the grafting density, the excluded volume parameters and the chemical potential (the concentration) of the adsorbate in the solution. We demonstrate that, when the grafting density is varied, the overall adsorbed amount always exhibits a maximum, whereas the root-mean-square brush thickness either increases monotonically or passes through a (local) minimum. At high grafting densities the chains are loaded by adsorbed aggregates preferentially in the distal region of the brush, whereas in the region proximal to the grafting surface depletion of aggregates occurs and the polymer brush retains an unperturbed structure. Depending on the relative strength of the excluded volume interactions between unloaded and loaded monomers both the degree of loading of the chains and the polymer density profile are either continuous or they exhibit a discontinuity as a function of the distance from the grafting surface. In the latter case intrinsic phase separation occurs in the brush: the dense phase consists of unloaded and weakly extended chains and occupies the region proximal to the surface, whereas a more dilute phase consisting of highly loaded and strongly extended chains forms the periphery of the brush. Received 26 November 1998 and Received in final form 2 April 1999     

Molecular dynamics simulations of end-grafted centipede-like polymers with stiff charged side chains

We use molecular dynamics simulations to investigate centipede-like polymers with stiff charged side chains, end-grafted to a planar wall. The effect of the grafting density and the Bjerrum length on the conformational behaviour of the brush is examined in detail. In addition, we make a comparison of centipede-like polyelectrolyte (CPE) brushes with neutral centipede-like polymer (NCP) and linear polyelectrolyte (LPE) brushes. At weak electrostatic interaction, the main chains of the CPE chains adopt a strongly stretched conformation, and the monomer density profiles of side chains exhibit a clear oscillatory behaviour. With increasing Bjerrum length, the CPE brush undergoes a collapse transition. Compared to the CPE brushes, the counterion condensation effect is stronger for the LPE brushes, regardless of whether the electrostatic interaction is weak or strong and of whether the grafting density is low or high. Additionally, it is shown that the architecture of the grafted chains makes a weak contribution to the counterion condensation at strong electrostatic interaction. We also find that the electrostatic repulsion between charged side chains can enhance the stiffness of the main chains and thus limit the range of movement of the free-end monomers.     

GPU implementations of the bond fluctuation model

We present two parallel implementations of the bond fluctuation model on graphics processors that outperform by a factor of up to 50 times an equivalent implementation on single CPU processor. The first algorithm is a parallelized version of an accelerated MC method published earlier in [S. Nedelcu, J.-U. Sommer, Single chain dynamics in polymer networks: a Monte Carlo study, J. Chem. Phys. 130 (2009) 204902]. In this first algorithm we use the parallel domain decomposition technique to avoid monomer collisions. In contrast, in the second algorithm we associate each monomer with a parallel process, where all monomers in the system are attempted to move simultaneously. In both cases, only monomer moves that result in allowed bonds and preserve lattice occupancy are accepted. To validate the correctness of the GPU algorithms we simulated monodisperse polymer melts at monomer number density 0.5 and compared static and dynamical properties with standard CPU implementations. We found good agreement between the CPU and the GPU results, which demonstrates the equivalence of the serial and parallel implementations. The influence of higher monomer number density is discussed.     

Structure of polymer solutions at interfaces: a Monte Carlo simulation study

The canonical ensemble Monte Carlo method is applied to study the structure of polymer solutions confined between surfaces. The polymer molecules are modeled as fused-sphere freely rotating chains with fixed bond length and bond angles and the solvent as hard spheres. The simulation results for the configurational and conformational properties of the chains are presented with varying interfacial distances, chain concentrations, and chain lengths. The chains are depleted at the wall at lower density, which, however, becomes less at higher density. With an increase in the interfacial distance, the enhancement/depletion of the chains at the wall becomes more marked. At all interfacial distances and chain lengths, increasing the concentration of the solvent makes the oscillation in the density profile of the chains more pronounced. Conformational properties provide important indications regarding the behaviour of chains as they approach surfaces.     

Dewetting as an investigative tool for studying properties of thin polymer films

Employing mass conservation, time-resolved dewetting experiments of thin polymer films allow to determine in real time the dynamic contact angle and the slippage length. Moreover, based on a systematic variation of interfacial properties of a polymer brush, dewetting makes it possible to calculate the force it needs to extract a single polymer chain from its own melt. In the visco-elastic regime close to the glass transition, the temperature and molecular weight dependence of the relaxation time of residual stresses resulting from film preparation by spin-coating can be obtained from the evolution of the shape of the dewetting rim. The presented examples demonstrate that dewetting represents a powerful approach for a sensitive characterization of rheological, frictional and interfacial properties of thin polymer films.     

Adsorption of hydrophobic polyelectrolytes onto oppositely charged surfaces

We present a scaling theory for the adsorption of a weakly charged polyelectrolyte chain in a poor solvent onto an oppositely charged surface. Depending on the fraction of charged monomers and on the solvent quality for uncharged monomers, the globule in the bulk of the solution has either a spherical conformation or a necklace structure. At sufficiently high surface charge density, a chain in the globular conformation adsorbs in a flat pancake conformation due to the Coulombic attraction to the oppositely charged surface. Different adsorption regimes are predicted depending on two screening lengths (the Debye screening length monitored by the salt concentration and the Gouy-Chapman length monitored by the surface charge density), on the degree of ionization of the polymer and on the solvent strength. At low bulk ionic strength, an increase in the surface charge density may induce a transition from an adsorbed necklace structure to a uniform pancake due to the enhanced screening of the intra-chain Coulombic repulsion by the counterions localized near the surface. Received 12 April 2001     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

甘氨酸直链寡肽振动光谱频移现象的理论研究

运用密度泛函理论,在6-31G(d)基组水平上对甘氨酸直链寡肽进行几何优化,并对其几何结构、平均结合能、振动频率进行计算。结果表明,平均结合能随着肽链增加单调变化,并趋于稳定;寡肽链键长的分析发现,链向与径向方向上变化趋势相反,存在各向异性。红外光谱的分析发现,位于肽键上同一基团的伸缩振动与弯曲振动分别发生红移和蓝移,并存在各向异性。这些现象源于：准一维的纳米结构导致了键长的各向异性;相同基团之间的诱导效应、耦合效应及氢键等因素导致了振动频率的红移和蓝移等现象。我们得出结论：甘氨酸直链寡肽链的生长利于结构的稳定性,在能量上,推测出寡肽链有自组装生长的趋势;在寡肽链的生长过程中,通过构象和光谱的现象,推断其物理化学属性存在尺寸效应。肽链端部基团的物理化学属性非常稳定,基本不受寡肽链长度的影响。该结果对应用红外光谱测量寡肽链的残基数及长度、特殊功能寡肽链的制备等工作具有指导意义。     

Theoretical analysis on geometries and electronic structures of antiaromatic pentalene and its N‐substituted derivatives: monomer,oligomers and polymer

The antiaromatic compounds have received a great deal of attention for several decades because of their unusual electronic structures. The electronic structures and properties of antiaromatic pentalene and its six nitrogen heterocyclic derivatives were systematically studied by the density functional theory at the Becke, three‐parameter, Lee–Yang–Parr level with 6‐31G* basis set. The results indicated that all the monomers have stable singlet states and remarkable bond‐length alternations. From the dimer to polymer in those molecules, pentalene(P), cyclopenta[b]pyrrole(CPP), cyclopenta[d]imidazole(CPI), pyrrolo[2,3‐b]pyrrole(PP1) and pyrrolo[3,2‐d]imidazole(PI) are stable diradical structures; pyrrolo[3,2‐b]pyrrole (PP2) and imidazo[4,5‐d]imidazole(II) are stable singlet ground states. The electronic properties including bond length, bond‐length alternation, electron density at bond critical points, Wiberg bond index and nucleus‐independent chemical shift were analyzed. It was found that in diradical molecules the bond‐length alternations are diminished, the charge tends to equilibrate, the π‐electron delocalization and conjugation are strengthened. The electronic properties of singlet ground state molecules have nearly no variations from monomers to polymers. The band structure analysis shows that diradical structure molecules have small band gaps (<1.0 eV), wide bandwidth and small effective masses of holes and electrons which suggest that diradical structure molecules are very good candidates for conductive materials. Copyright © 2011 John Wiley & Sons, Ltd.     

Morphologies of a spherical bimodal polyelectrolyte brush induced by polydispersity and solvent selectivity

It is commonly realized that polydispersity may significantly affect the surface modification properties of polymer brush systems. In light of this, we systematically study morphologies of bidisperse polyelectrolyte brush grafted onto a spherical nanocolloid in the presence of trivalent counterions using molecular dynamics simulations. Via varying polydispersity, grafting density, and solvent selectivity, the effects of electrostatic correlation and excluded volume are focused, and rich phase behaviors of binary mixed polyelectrolyte brush are predicted, including a variety of pinned-patch morphologies at low grafting density and micelle-like structures at high grafting density. To pinpoint the mechanism of surface structure formation, the shape factor of two species of polyelectrolyte chains and the pair correlation function between monomers from different polyelectrolyte ligands are analyzed carefully. Also, electrostatic correlations, manifested as the bridging through trivalent counterions, are examined by identifying four states of trivalent counterions. Our simulation results may be useful for designing smart stimuli-responsive materials based on mixed polyelectrolyte coated surfaces.     

Mechanism for the Self-Assembly of Hollow Micelles from Rod-Coil Block Copolymers

The mechanism for the self-assembly of hollow micelles from rod-coil diblock copolymers is proposed. In a coilselective solvent, the diblock copolymers self-assemble into a layered structure. It is assumed that the rigid rods form an elastic shell whose properties are dictated by a bending energy. For a hollow micelle, the coils outside the micelle form a brush, while the coils inside the micelle can be in two different states, a brush or an adsorption layer, corresponding to symmetric or asymmetric configurations, respectively. The total energy density of a hollow micelle is calculated by combining the interfacial energy, elastic bending energy and the stretching energy of the brushes. For the asymmetric configuration with a polymer brush on one side, the competition between the elastic bending energy and the brush stretching energy leads to a finite spontaneous curvature, stabilizing hollow spherical micelles. Comparison of the free energy density for different geometries demonstrates that transitions for the different geometry micelles are controlled by the degree of polymerization of the coils and the length of the rods. These results are in agreement with the experimental results.     

Collapse of polyelectrolyte brushes: Scaling theory and simulations

We investigate polyelectrolyte brushes using both scaling arguments and molecular dynamics simulations. As a main result, we find a novel collapsed brush phase. In this phase, the height of the brush results from a competition between steric repulsion between ions and monomers and an attractive force due to electrostatic correlations. As a result, the monomer density inside the brush is independent of the grafting density and the polymerization index. For small ionic and monomer radii (or for large Bjerrum length) the brush undergoes a first-order phase transition from the osmotic into the collapsed state. Received 26 September 2000