Adsorption of a random heteropolymer with random self-interactions onto an interface

We consider the adsorption of a random heteropolymer onto an interface within the model of Garel et al. [#!gareletal89!#] by taking into account random self-interactions and ternary repulsive interactions between the monomers. Within the replica trick and by using a self-consistent preaveraging procedure we map the adsorption problem onto the problem of binding state of a quantum mechanical Hamiltonian. The analysis of the latter is treated within the variational method based on the 2nd Legendre transform. Our study reveals a complex behaviour of the localization of the heteropolymer. In particular, we predict a reentrant localization transition for moderate values of the asymmetry of the distribution function of the monomer sequences along the heteropolymer. Received 9 October 2001 and Received in final form 27 February 2002 Published online 6 June 2002     

Characterization of heteropolymer collapse

This paper proposes a method to enumerate and characterize the multidimensional rearrangement that a heteropolymer collapse represents. We follow the collapse using Langevin dynamics, and analyze folding pathways by measuring how matches to the final state develop, when viewed from each monomer in the polymer. The method is illustrated by following one specific heteropolymer, which was selected to have repeatable dynamical access to its final state. For this heteropolymer we found a nucleation event that precedes the correctly folded state. Received 28 October 1999     

Single chain force spectroscopy - Reading the sequence of HP protein models

We study the elastic properties of single A/B random copolymer chains, with a specific sequence and use them as theoretical model for so called HP proteins. HP proteins carry hydrophilic (P) and hydrophobic (H) monomers. We predict a rich structure in the force-extension relations which can be attributed to the information in the sequence. The variational method is used to probe local minima on the path of stretching and releasing for the chain molecules. At a given force, we find multiple configurations which are separated by energy barriers. A collapsed globular configuration consists of several domains which unravel cooperatively. Upon stretching, the unfolding path shows a stepwise pattern corresponding to the unfolding of each domain. While releasing, several cores can be created simultaneously in the middle of the chain, resulting in a different path of collapse. The long-range interactions and stiffness of the chain simplify the potential landscape given by the disorder in sequence. Received 5 March 2002 / Received in final form 16 May 2002 Published online 13 August 2002     

Fractal globule as a molecular machine

A fractal (crumpled) polymer globule, which is an unusual equilibrium state of a condensed unknotted macromolecule that is experimentally found in the DNA folding in human chromosomes, has been formed through the hierarchical collapse of a polymer chain. The relaxation dynamics of the elastic network constructed through the contact matrix of the fractal globule has been studied. It has been found that the fractal globule in its dynamic properties is similar to a molecular machine.     

X-ray studies of the structure of thermotropic copolyesters

This paper describes x-ray analysis of the structure of a group of wholly aromatic thermotropic liquid crystalline copolyesters, focusing on two systems: condensation copolymers of 4-hydroxy-benzoic acid (HBA) and 2-hydroxy–6-naphthoic acid; and of HBA, 2,6-dihydroxy-naphthalene, and terephthalic acid. The fiber diagrams of these copolymers contain a series of aperiodic meridional maxima that shift in position with the monomer ratio. We have shown that these characteristics are predicted by a structure consisting of an array of chains of completely random monomer sequence. The positions of the maxima are predicted by a simple model in which the monomers are represented by points, separated from their neighbors by the appropriate monomer lengths. Use of atomic models for the monomers leads to prediction of both the positions and the intensities of the maxima. Calculations for nonrandom sequence distribution show that all but minimal blockiness can be ruled out. From the breath of the meridional maximum at d = 2.1 Å it is possible to estimate the correlation or persistence length for the stiff chain conformation in the solid state.     

A semi-flexible attracting segment model of two-dimensional polymer collapse

Recently it has been shown that a two-dimensional model of self-attracting polymers based on attracting segments displays two phase transitions, a θ-like collapse between swollen polymers and a globular state and another between the globular state and a polymer crystal. On the other hand, the canonical model based on attracting monomers on lattice sites displays only one: the standard tricritical θ collapse transition. Here we consider the attracting segment model with the addition of stiffness and show that it displays the same phases as the canonical model.     

Coupling between helix-coil and coil-globule transitions in helical polymers

We explore the coupling between the helix-coil and coil-globule transitions of a helical polymer using Monte Carlo simulations. A very rich state diagram is found. Each state is characterized by a specific configuration of the chain which could be a helix, a random coil, an amorphous globule, or one of various other globular states which carry residual helical strands. We study the boundaries between states and provide further insight into the physics of the system with a detailed analysis of the order parameter and other properties.     

Polymer localization in random potential

This work re-examines the classical problem of polymer collapse in a random system, using a Gaussian variational formalism to treat the “poor solvent” case. In particular we seek to clarify some of the disputed questions related to symmetry breaking between the replicas used to analyze such quenched systems, and the scaling of the globular collapse with the disorder strength. We map the random system to a chain with attractive interactions in the standard way, and conduct a variational analysis along with a detailed examination of the theory's stability to replica symmetry breaking. The results suggest that replica symmetry is in fact not broken by the collapse of the chain in a random-disordered system, and that inclusion of a positive third, or higher, virial coefficient is crucial to stabilize the theory. For three dimensions, we find the globule square radius falling as (α-2ω)², where α and ω are proportional to the second and third virial coefficients, respectively. This is in keeping with the earliest results of the replica-symmetric argument advanced by Edwards and Muthukumar [J. Chem. Phys. 89 (1988) 2435], but we anticipate a different scaling with dimensionality in other cases, with the globule square radius scaling as l(α,ω)^2/(d-2) for d<4, where l is some linear function. This result agrees a scaling argument regarding the chain in a random potential like that put forth by Cates and Ball [J. Phys. (France) 49 (1988) 2009], but with a repulsive third virial coefficient present.     

General theory of the long-range interactions in protein folding

The process of the globular structure formation from a long molecular chain is examined in a general sense. In the course of this process various regions of the chain interact with each other. The bonds formed during this process are classified as native and non-native ones. Native bonds are formed in native globular structure. All other bonds are “incorrect” (non-native). It is demonstrated that the globule formation can occur actually without production and subsequent decay of non-native contacts. The proposed model allows to avoid a search of numerous non-native variants since long-distance interactions with a high selectivity take place between the chain regions that form native bonds. The presence of these interactions prompts the chain regions which yield native contacts start to draw together and to interact. The databank data analysis shows that the developed model can be applied not only to the abstract structures but also to real polypeptide chains which are able to form both globular structures and helical fibrils.     

Supersymmetry approach to the random heteropolymer theory

The effective equation of motion that describes the different monomer alternation along the heteropolymer chain is proposed. On this basis the supersymmetry field scheme is built up to analyze memory and ergodicity breaking effects.     

Deformation of globular polysoaps: extension, confinement and extensional flow

A theoretical model of the extension and confinement of globular polysoaps predicts novel force laws. Polysoaps are polymers comprising of a flexible hydrophilic backbone incorporating, at intervals, amphiphilic monomers. The equilibrium configuration of long polysoaps, that form numerous spherical intrachain micelles, is a spherical globule of close packed micelles. The coupling of the deformation to the hierarchical self organization of the chain gives rise to a distinctive force law involving, for extension, two plateau regimes. When the chain is stretched by extensional flow the two regimes merge and the polysoap exhibits a single globule-stretch transition. Received 16 June 1998 and Received in final form 19 November 1998     

海底沉积物压缩波声速比与物理特性的关系

海底沉积物因组成结构复杂导致声学特性复杂多样,多种理论解释模型存在参数较多且各具适用性现象·通过运用体积平均和等效参数的方法对海底沉积物声波传播机理进行研究,提出一种少参数的海底沉积物与底层海水的压缩波声速比通用模型(General Model of Sound Speed Ratio,GMSSR).GMSSR模型包含弹性结构分布因子、孔隙度、等效密度比、等效弹性模量比4个物理特性参数。分析海底沉积物两相介质结构的串联和并联两种极限情况分析,基于弹性结构分布因子和串并联结构的体积平均分布建立一般情况下海底沉积物的等效弹性模量表达式·应用GMSSR合理地分析各海域测量的海底沉积物声速比经验模型的共性和解释南海实测数据分散的范围,表明:(1)表层海底沉积物主要是以串联结构为主,接近于悬浮液状态或者体积分量很少的并联堆积状态;(2)等效弹性模量比的影响因素大于等效密度比,结构变化往往通过影响弹性结构分布因子而影响等效弹性模量比,从而引起声速比的变化;(3)不同研究海域的声速比-孔隙度经验关系具有相似性,可以通过GMSSR模型分析得出;(4)基于弹性结构分布因子的差异,可以合理解释南海海域测量表层海底沉积物声速比较大的分散性。      

Stability of dense hydrophobic-polar copolymer globules: Regular,random and designed sequences

Stability of dense globular structures formed by amphiphilic copolymers consisting of hydrophobic (insoluble) units and a small fraction of single polar (soluble) monomer units is considered in the mean-field approximation for different types of unit distributions along the chain. Polar (P) units are located in a relatively thin surface layer due to their strong repulsion from hydrophobic (H) monomer units. We compared globules formed by different copolymer sequences with the same gross numbers of P- and H-units: regular HP-sequences (P-units separated by equal H-blocks), random copolymers (uncorrelated positions of P-units, i.e. Flory distribution of H-block lengths), proteinlike (PL) sequences (designed sequences involving both long H-blocks dominating by total mass, and short blocks dominating by number). We showed that PL-globules are more stable (lower free energy) and are characterized by a higher temperature of the coil-to-globule transition when compared with the other sequences mentioned above. We also considered HP-H-copolymers consisting of one long and many short hydrophobic blocks; we showed that it is these sequences that yield the dense globules corresponding to the lowest free energy.Received: 3 July 2003, Published online: 11 November 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling     

The supersymmetric theory of disordered heteropolymers

The effective equation of motion for describing the alternation of monomers of different sorts along a heteropolymer chain is proposed. This equation is used for constructing a self-consistent supersymmetric scheme that makes it possible to derive equations for the structure factor and the Green function. The effects of memory and ergodicity loss are studied as functions of the temperature and the intensity of the frozen disorder in the alternation of monomers. The phase diagram that determines the existence domains of nonergodic and frozen states is constructed.     

Thermodynamics of stiff macromolecules in the two-dimensional lattice model

The statistical-thermodynamic analysis of the compact structure (globule) of a flexural stiff macromolecule in the two-dimensional square lattice model is proposed. It is shown that the anisotropy of monomer direction distribution increases with increasing rigidity. The temperature dependence of the globule size turns out to be non-monotonic under fixed pressure.     

Holographic nanocomposites for recording polymer-nanoparticle periodic structures: II. Mechanism of formation of polymer-nanoparticle bulk periodic structure and effect of parameters of forming field on structure efficiency

We studied polymerizable nanocomposites for obtaining polymer-nanoparticle periodic structures by a holographic method. A general approach to choosing components of composites is developed that ensures a maximal contrast and high efficiency of structures for different types of nanoparticles. We found that the optimal monomeric component of a nanocomposite is a combination of single- and multifunctional monomers with substantially different reactivities. In this case, the low-reactivity monomer should posses a low viscosity, be a good solvent for nanoparticles, and have a low thermodynamic affinity to the polymer network formed upon the polymerization of the high-reactivity monomer. We developed a holographic composition based on known commercially produced monomers that ensures the formation of highly efficient periodic structures for nanoparticles of different types. We described the holographic properties of obtained nanocomposites, as well as parameters of bulk gratings recorded in them.     

Holographic nanocomposites for recording polymer-nanoparticle periodic structures: I. General approach to choice of components of nanocomposites and their holographic properties

We studied polymerizable nanocomposites for obtaining polymer-nanoparticle periodic structures by a holographic method. A general approach to choosing components of composites is developed that ensures a maximal contrast and high efficiency of structures for different types of nanoparticles. We found that the optimal monomeric component of a nanocomposite is a combination of single- and multifunctional monomers with substantially different reactivities. In this case, the low-reactivity monomer should posses a low viscosity, be a good solvent for nanoparticles, and have a low thermodynamic affinity to the polymer network formed upon the polymerization of the high-reactivity monomer. We developed a holographic composition based on known commercially produced monomers that ensures the formation of highly efficient periodic structures for nanoparticles of different types. We described the holographic properties of obtained nanocomposites, as well as parameters of bulk gratings recorded in them.     

Randomly crosslinked macromolecular systems: Vulcanization transition to and properties of the amorphous solid state

As Charles Goodyear discovered in 1839, when he first vulcanized rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equilibrium phase transition, the liquid state, in which all macromolecules are delocalized, is transformed into a solid state, in which a non-zero fraction of macromolecules have spontaneously become localized. This solid state is a most unusual one: localization occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanization transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter.

In this article we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanization transition. This approach rests firmly on techniques from the statistical mechanics of disordered systems pioneered by Edwards and co-workers in the context of macromolecular systems, and by Edwards and Anderson in the context of magnetic systems. We begin with a review of the semi-microscopic formulation of the statistical mechanics of randomly crosslinked macromolecular systems due to Edwards and co-workers, in particular discussing the role of crosslinks as quenched random variables. Then we turn to the issue of order parameters, and review a version capable, inter alia, of diagnosing the amorphous solid state. To develop some intuition, we examine the order parameter in an idealized situation, which subsequently turns out to be surprisingly relevant. Thus, we are motivated to hypothesize an explicit form for the order parameter in the amorphous solid state that is parametrized in terms of two physical quantities: the fraction of localized monomers, and the statistical distribution of localization lengths of localized monomers. Next, we review the symmetry properties of the system itself, the liquid state and the amorphous solid state, and discuss connections with scattering experiments. Then, we review a representation of the statistical mechanics of randomly crosslinked macromolecular systems from which the quenched disorder has been eliminated via an application of the replica technique. We transform the statistical mechanics into a field-theoretic representation, which exhibits a close connection with the order parameter, and analyse this representation at the saddle-point level. This analysis reveals that sufficient crosslinking causes an instability of the liquid state, this state giving way to the amorphous solid state. To address the properties of the amorphous solid state itself, we solve the self-consistent equation for the order parameter by adopting the hypothesis discussed earlier. Hence, we find that the vulcanization transition is marked by the appearance of a non-zero fraction of localized monomers, which we compute, the dependence of this fraction on the crosslink density indicating a connection with random graph theory and percolation. We also compute the distribution of localization lengths that characterizes the ordered state, which we find to be expressible in terms of a universal scaling function of a single variable, at least in the vicinity of the transition. Finally, we analyse the consequences of incorporating a certain specific class of correlations associated with the excluded-volume interaction.     

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     

非一致随机分布复合材料力学参数预测的统计二阶双尺度方法

通过建立统计的二阶双尺度计算方法,预测了非一致随机分布复合材料结构的力学参数,包括刚度参数和弹性极限强度参数.所谓非一致随机分布复合材料结构,是指在整个结构中夹杂随机分布,但分布特征并不是处处相同,而是逐渐变化的,从而导致材料在宏观上具有随着位置连续变化的力学性能.描述了一致和非一致随机分布复合材料结构的特征及其细观表征方法,并建立了统计的二阶双尺度计算公式,讨论了材料的弹性极限强度准则.最后,针对不同的非一致随机分布复合材料,预测了材料的力学参数并与实验数据进行了对比.结果表明,统计的二阶双尺度方法对于预测非一致随机分布复合材料的力学参数是有效的. 关键词： 统计二阶双尺度方法 非一致随机分布 复合材料结构