In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and splitting of metastable states, have non trivial effects on such networks and must be taken into account. We do this by means of a recently proposed renormalization procedure. This method is applied to analyze the topology of the network of metastable states for different polypeptidic sequences in a minimalistic polymer model. A smaller spectral dimension emerges as a hallmark of stability of the global energy minimum and highlights a non-obvious link between dynamic and thermodynamic properties.
We study the Directed Polymer model subject to a particular form of disorder, $η(x,t)=η_X(x) η_T(t)$, recently proposed in biological applications. We find that two new universality classes arise, depending on the the lattice geometry. Using an intermediate model linking the two different orientations continuously, we find that there is a phase transition separating two distinct scaling phases. For both phases we get a reasonable understanding of the nature and values of the exponents, corroborated with numerical results.
Polymorphism rationalizes how processing can control the final structure of a material. The rugged free-energy landscape and exceedingly slow kinetics in the solid state have so far hampered computational investigations. We report for the first time the free-energy landscape of a polymorphic crystalline polymer, syndiotactic polystyrene. Coarse-grained metadynamics simulations allow us to efficiently sample the landscape at large. The free-energy difference between the two main polymorphs, $α$ and $β$, is further investigated by quantum-chemical calculations. The two methods are in line with e…
We study the geometric properties of the energy landscape of coarse-grained, off-lattice models of polymers by endowing the configuration space with a suitable metric, depending on the potential energy function, such that the dynamical trajectories are the geodesics of the metric. Using numerical simulations, we show that the fluctuations of the curvature clearly mark the folding transition, and that this quantity allows to distinguish between polymers having a protein-like behavior (i.e., that fold to a unique configuration) and polymers which undergo a hydrophobic collapse but do not have a …
We have performed multicanonical chain-growth simulations of a polymer interacting with an adsorbing surface. The polymer, which is not explicitly anchored at the surface, experiences a hierarchy of phase transitions between conformations binding and non-binding with the substrate. We discuss the phase diagram in the temperature-solubility plane and highlight the transition ``path'' through the free-energy landscape.
Polydispersity is found to have a significant effect on the potential energy landscape; the the average inherent structure energy with temperature decreases with polydispersity. Increasing polydispersity at fixed volume fraction decreases the glass transition temperature and the fragility of glass formation analogous to the antiplasticization seen in some polymeric melts. An interesting temperature dependent crossover of heterogeneity with polydispersity is observed at low temperature due to the faster build-up of dynamic heterogeneity at lower polydispersity.
Alterations in Conformations of Poly(3-hexylthiophene) on Au(111) Induced by Annealing
Albert-Ludwigs-Universität Freiburg（弗莱堡大学）；Université de Haute-Alsace（上阿尔萨斯大学）；CNRS, Institut de Science des Matériaux de Mulhouse（法国国家科学研究中心，米卢斯材料科学研究所）
The motion of polymers with inhomogeneous structure through nanopores is discussed theoretically. Specifically, we consider the translocation dynamics of polymers consisting of double-stranded and single-stranded blocks. Since only the single-stranded chain can go through the nanopore the double-stranded segment has to unzip before the translocation. Utilizing a simple analytical model, translocation times are calculated explicitly for different polymer orientations, i.e., when the single-stranded block enters the pore first and when the double-stranded segment is a leading one. The dependence…
We consider the lattice model for an ideal-linear polymer chain to mimic the conformations of the semi-flexible homo-polymer chain. The polymer chain is assumed to confine in the fairly small area, such that the flexible chain conformations are easily polymerized in the nano-area. It has been described using analytical calculations that such a situation may lead to interesting and distinct theoretical findings of the thermodynamics of semi-flexible homo-polymeric macromolecules where the macromolecules are confined in the nano-length scale. We also discuss the characteristics of the persistent…
In this review we provide an organized summary of the theoretical and computational results which are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide an accessible, non-specialist introduction to the main topological concepts, polymer models, and theoretical/computational methods used to investigate dense and entangled polymer systems. The main body of our review deals with: (i) the effect that spatial confinement has on the equilibrium topological entanglement of one or more polymer chains and (ii) the m…
The translocation time of a polymer chain through an interaction energy gradient nanopore was studied by Monte Carlo simulations and the Fokker-Planck equation with double-absorbing boundary conditions. Both the simulation and calculation revealed three different behaviors for polymer translocation. These behaviors can be explained qualitatively from free-energy landscapes obtained for polymer translocation at different parameters. Results show that the translocation time of a polymer chain through a nanopore can be tuned by suitably designing the interaction energy gradient.
The modeling of conformations and dynamics of (bio)polymers is of primary importance for understanding physicochemical properties of soft matter. Although short-range interactions such as covalent and hydrogen bonding control the local arrangement of polymers, non-covalent interactions play a dominant role in determining the global conformations. Here we focus on how the inclusion of many-body effects in van der Waals dispersion affects the outcome of geometry optimizations and molecular dynamics simulations of model polymers. We find that delocalized force contributions are key to explore the…
Single molecule force spectroscopy provide details of the underlying energy surfaces of proteins which are essential to the understanding of their unfolding process. Recently, it has been observed experimentally that by pulling proteins in different directions relative to their secondary structure, one can gain a better understanding of the shape of the energy landscape. We consider simple lattice models which are anisotropic in nature to study the response of a force in unfolding of a polymer. Our analytical solution of the model, supported by extensive numerical calculations, reveal that the…
Polymer translocation through a nanopore in a membrane investigated theoretically. Recent experiments on voltage-driven DNA and RNA translocations through a nanopore indicate that the size and geometry of the pore are important factors in polymer dynamics. A theoretical approach is presented which explicitly takes into account the effect of the nanopore length and diameter for polymer motion across the membrane. It is shown that the length of the pore is crucial for polymer translocation dynamics. The present model predicts that for realistic conditions (long nanopores and large external field…
Polymer dynamics at large fields in Rubinstein-Duke repton model is investigated theoretically. Simple diagrammatic approach and analogy with asymmetric simple exclusion models are used to analyze the reptation dynamics of polymers. It is found that for polyelectrolytes the drift velocity decreases exponentially as a function of the external field with an exponent depending on polymer size and parity, while for polyampholytes the drift velocity is independent of polymer chain size. However, for polymers, consisting of charged and neutral blocks, the drift velocity approaches the constant limit…
Cracking the whip accelerates the tail of a chain to hit the air loudly and clearly. We proved that the similar acceleration effect causes coil deformation of driven chain-like polymers. We first preformed Monte Carlo simulations of a single driven polymer coil to demonstrate its deformation in company with faster or slower deviations of velocities. We then performed parallel Brownian Dynamics simulations to demonstrate that the coil deformation can be caused by the so-called "cracking-the-whip" effect due to non-synchronous biased Brownian motions of monomers inherited in Monte Carlo simulati…
We develop a theory describing density profile of the semi-flexible polymers absorbed onto a planar surface. The theoretical analysis consists of two parts. As a first part, we calculate a density profile of the adsorbed polymers by developing an extension of the Bethe-Peierls approximation to the case of nonhomogeneous systems. This approach relies on the combination of the single chain adsorption theory and the lattice version of the self-consistent field theory. Semi-flexibility of a chain is described by incorporating a finite coordination number of the lattice into the consideration, in t…
Jumps between neighboring minima in the energy landscape of both homopolymeric and heteropolymeric chains are numerically investigated by determining the average escape time from different valleys. The numerical results are compared to the theoretical expression derived by Langer [J.S. Langer, Ann. Phys. 54 (1969) 258] with reference to a 2N-dimensional space. Our simulations indicate that the dynamics within the native valley is well described by a sequence of thermally activated process up to temperatures well above the folding temperature. At larger temperatures, systematic deviations from …
High molecular weight polymer solutions have a powerful tendency to deposit adsorbed layers when exposed to even mildly attractive surfaces. The equilibrium properties of these dense interfacial layers have been extensively studied theoretically. A large body of experimental evidence, however, indicates that non-equilibrium effects are dominant whenever monomer-surface sticking energies are somewhat larger than kT, a common case. Polymer relaxation kinetics within the layer are then severely retarded, leading to non-equilibrium layers whose structure and dynamics depend on adsorption kinetics …
The Replica Exchange Wang-Landau Method is used to estimate the energy landscape of a polymer composed of a simple hydrophobic and polar sequence using the HP protein model. Calculations of state transitions between the energy levels of the derived energy landscape are made using an equation of motion from the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework. The SEAQT framework makes it possible to determine the unique kinetic paths from an arbitrary quasi-equilibrium or non-equilibrium initial state to stable equilibrium. Calculations performed with SEAQT require significantly…
The polymerization dynamics of double-stranded polymers, such as actin filaments, is investigated theoretically using simple chemical kinetic models that explicitly take into account some microscopic details of the polymer structure and the lateral interactions between the protofilaments. By considering all possible molecular configurations, the exact analytical expressions for the growth velocity and dispersion for two-stranded polymers are obtained in the case of the growing at only one end, and for the growth from both polymer ends. Exact theoretical calculations are compared with the predi…
The theoretical formulation of driven polymer translocation through nanopores is complicated by the combination of the pore electrohydrodynamics and the nonequilibrium polymer dynamics originating from the conformational polymer fluctuations. In this review, we discuss the modeling of polymer translocation in the distinct regimes of short and long polymers where these two effects decouple. For the case of short polymers where polymer fluctuations are negligible, we present a stiff polymer model including the details of the electrohydrodynamic forces on the translocating molecule. We first show…
Theoretical derivation and numerical confirmation are provided for the scaling of pore-blockade times as $N^{2+ν}$ for unbiased translocation in two and three dimensions, with $N$ as the polymer length and $ν$ as the Flory exponent of the polymer. The polymer performs Rouse dynamics.
Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer science, social science and chemical synthesis. Examples include linear bio-polymers, linear signaling pathways in cells as well as topological sorts appearing in project management. Using a statistical mechanical treatment, we study circuit topology landscapes of linear polymer chains with intra-chain contacts as a prototype of linearly sorted objects with int…
Using molecular dynamic simulation, we study the stretching of an adsorbed homopolymer in a poor solvent with one end held at a distance $z_e$ from the substrate. We measure the vertical force $f$ on the end of the chain as a function of the extension $z_e$ and the substrate interaction energy $w$. The force reaches a plateau value at large extensions. In the strong adsorption limit, we show that the plateau value increase linearly in $w$ in good agreement with a theoretical model. In the weak adsorption limit, a polymer globule with a layered structure is formed and elastically deformed when …
We present a novel generating function (GF) method for the self-condensing vinyl polymerization (SCVP) system with any initial distribution of preexisted polymers. Such a method was proven to be especially useful to investigate the semi-batch SCVP system allowing a sequence of feeding operations during the polymerization. Consequently, the number-, weight-, and z-average molecular weights as well as polydispersity index of hyperbranched polymers can be explicitly given, which are determined by predetermined feeding details and conversions in each polymerization step. These analytical results a…
We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity of the target assembly. By considering the designed interactions separately from weaker, incidental interactions, our approach yields predictions for the equilibrium yield and nucleation barriers. These predictions are in good agreement with corresponding Monte Carlo simulations. We show that a few fundamental properties of the connectivity graph determine t…
. We consider three dimensional model of the Gaussian polymer chain in the presence of defects to understand the formation of a polymer aggregate where the aggregate is induced by the defects. The defects are acting as an attractive centres of the monomers and it induces aggregation of the monomers of the chain around the defects. It has been shown using the analytical calculations that the formation of a polymer aggregates are favoured when the defects have extensions in all the possible three dimensions. We have also calculated relevant other thermo-dynamical parameters (i. e. the average nu…
Neutral or charged polymers that are densely end-grafted to surfaces form brush-like structures and are highly stretched under good-solvent conditions. We discuss and compare relevant results from scaling models, self-consistent-field methods and MD simulation techniques and concentrate on the conceptual simple case of planar substrates. For neutral polymers the main quantity of interest is the brush height and the polymer density profile, which can be well predicted from self-consistent calculations and simulations. Charged polymers (polyelectrolytes) are of practical importance since they ar…
We present a theoretical approach which maps polymer blends onto mixtures of soft-colloidal particles. The analytical mesoscale pair distribution functions reproduce well data from united atom molecular dynamics simulations of polyolefin mixtures without fitting parameters. The theory exactly recovers the analytical expressions for density and concentration fluctuation structure factors of soft colloidal mixtures (liquid alloys).
We have studied the structure and free energy landscape of a semi-flexible lattice-polymer in the presence of a surface. At low temperatures coexistence of two-dimensional integer-folded crystals is observed. As the temperature is increased there is a transition from these crystalline configurations to a disordered coil adsorbed onto the surface. The polymer then gradually develops three-dimensional character at higher temperatures. We compute the free energy as a function of increasing crystallinity and compare with the free energy profiles assumed by the Lauritizen-Hoffman surface nucleation…
We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness throug…
Bottle brushes are polymeric macromolecules made of a linear polymeric backbone grafted with side chains. The choice of the grafting density σg, the length ns the grafted side chains and their chemical nature fully determines the properties of each macromolecule, such as its elasticity and its folding behaviour. Typically, experimental bottle brushes are systems made of tens of thousands of monomeric units, rendering a computational approach extremely expensive, especially in the case of bottle brush solutions. A proper coarse graining description of these macromolecules thus appears essential…
The process of adsorption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions is investigated. The performed scaling analysis is based on formal analogy between the polymer adsorption problem and the equivalent problem of critical phenomena in the semi-infinite $|ϕ|^4$ n-vector model (in the limit $n\to 0$) with a planar boundary. The whole set of surface critical exponents characterizing the process of adsorption of long-flexible polymer chains at the surface is obtained. The polymer linear dimensions parallel and perpendicul…
The dynamics of polymer-nanoparticle (NP) mixtures, which involves multiple scales and system-specific variables, has posed a long-standing challenge on its theoretical description. In this paper, we construct a microscopic theory for polymer diffusion in the mixtures based on a combination of generalized Langevin equation, mode-coupling approach, and polymer physics ideas. The parameter-free theory has an explicit expression and remains tractable on pair correlation level with system-specific equilibrium structures as input. Taking a minimal polymer-NP mixture as an example, our theory correc…
Here, we provide an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that can compete with the entropic tendency of a chain to crumple up into a random coil. Many studies on semiflexible polymers and their assemblies have been motivated by their importance in biology. Indeed, crosslinked networks of semiflexible polymers form a major structural component of tissue and living cells. Reconstituted networks of such biopolymers have emerged as a new class of biological soft matter systems with remarkable materi…
An extended theoretical study of interface potentials in adsorbed colloid-polymer mixtures is performed. To describe the colloid-polymer mixture near a hard wall, a simple Cahn-Nakanishi-Fisher free-energy functional is used. The bulk phase behavior and the substrate-adsorbate interaction are modelled by the free-volume theory for ideal polymers with polymer-to-colloid size ratios q=0.6 and q=1. The interface potentials are constructed with help from a Fisher-Jin crossing constraint. By manipulating the crossing density, a complete interface potential can be obtained from natural, single-cross…
The de Gennes' blob model is extensively used in different problems of polymer physics. This model is theoretically applicable when the number of monomers inside each blob is large enough. For confined flexible polymers, this requires the confining geometry to be much larger than the monomer size. In this manuscript, the opposite limit of polymer in nano-slits with one to several monomers width is studied, using molecular dynamics simulations. Extension of the polymer inside nanoslits, confinement force on the plates, and the effective spring constant of the confined polymer are investigated. …
We study the partitioning of cosolute particles in a thin film of a semi-flexible polymer network by a combination of coarse-grained (implicit-solvent) stochastic dynamics simulations and mean-field theory. We focus on a wide range of solvent qualities and cosolute-network interactions for selected polymer flexibilities. Our investigated ensemble (isothermal-isobaric) allows the network to undergo a volume transition from extended to collapsed state while the cosolutes can distribute in bulk and network, correspondingly. We find a rich topology of equilibrium states of the network and transiti…
We propose a field-theoretical approach to a polymer system immersed in an ideal mixture of clustering centers. The system contains several species of these clustering centers with different functionality, each of which connects a fixed number segments of the chain to each other. The field-theory is solved using the saddle point approximation and evaluated for dense polymer melts using the Random Phase Approximation. We find a short-ranged effective inter-segment interaction with strength dependent on the average segment density and discuss the structure factor within this approximation. We al…
Taking into account the well known correspondence between the field theoretical O(n)-vector model in the limit $n\to 0$ and the behavior of long-flexible polymer chains in a good solvent the investigation of ideal polymer chains adsorption onto structured surface like as a chemical step (where one part of a surface is repulsive for polymers and other part is at the adsorption threshold) was performed. The two-point correlation function of ideal polymer chain in the half - space bounded by structured surface with different adsorption energies $c_{1}$ and $c_{2}$ (with $c_{1}\neq c_{2}$) and the…
We propose a theoretical approach to quantitatively account for the role of entanglement in the nucleation of polymer melts, which is the unique feature of polymer differentiated from small molecules. By performing molecular dynamics simulations, we obtain the nucleation barriers of polymer systems with different entanglement densities, which exhibits an opposite trend compared to the prediction of the classic nucleation theory (CNT). To amend the deficiency of the CNT in polymer crystallization, we introduce the entanglement free energy to reflect the role of entanglement in polymer nucleatio…
Electrophoretic (EP) mobility reversal is commonly observed for strongly charged macromolecules in multivalent salt solutions. This curious effect takes place, e.g., when a charged polymer, such as DNA, adsorbs excess counterions so that the counterion-dressed surface charge reverses its sign, leading to the inversion of the polymer drift driven by an external electric field. In order to characterize this seemingly counterintuitive phenomenon that cannot be captured by electrostatic mean-field theories, we adapt here a previously developed strong-coupling-dressed Poisson-Boltzmann approach to …
We extend recent studies of the minimal energy packings of short flexible polymers with hard-core-like repulsions and short-range attractions to include bond-angle interactions with the aim of describing the collapsed conformations of `colloidal' polymers. We find that flexible tangent sticky-hard-sphere (t-SHS) packings provide a useful perturbative basis for analyzing polymer packings with nonzero bending stiffness only for {\it small} ratios of the stiffnesses for the bond-angle ($k_b$) and pair ($k_c$) interactions, i.e. $k_b^{\rm crit}/k_c \lesssim 0.01$ for $N<10$ monomers, and the criti…
A theoretical model of electromigrative, diffusive and convectivetransport polymer-gel composites is presented. Bulk properties are derived from the standard electrokinetic model with an impenetrable charged sphere embedded in an electrolyte-saturated Brinkman medium. Because the microstructure can be carefully controlled, these materials are promising candidates for enhanced gel-electrophoresis, chemical sensing, drug delivery, and microfluidic pumping technologies. The methodology provides `exact' solutions for situations where perturbations from equilibrium are induced by gradients of elect…
We propose a theoretical investigation of the physical adsorption of neutral comb-polymers with an adsorbing skeleton and non-adsorbing side-chains on a flat surface. Such polymers are particularly interesting as "dynamic coating" matrices for bio-separations, especially for DNA sequencing, capillary electrophoresis and lab-on-chips. Separation performances are increased by coating the inner surface of the capillaries with neutral polymers. This method allows to screen the surface charges, thus to prevent electro-osmosis flow and adhesion of charged macromolecules (e.g. proteins) on the capill…
Experimental observations and computer simulations have recently revealed universal aspects of polymer solution behaviour that were previously unknown. This progress has been made possible due to developments in experimental methodologies and simulation techniques, and the formulation of scaling arguments that have identified the proper scaling variables with which to achieve data collapse, both for equilibrium and nonequilibrium properties. In this review, these advances in our understanding of universal polymer solution behaviour are discussed, along with a brief overview of prior experiment…
We review recent results of the field theoretical renormalization group analysis on the scaling properties of star polymers. We give a brief account of how the numerical values of the exponents governing the scaling of star polymers were obtained as well as provide some examples of the phenomena governed by these exponents. In particular we treat the interaction between star polymers in a good solvent, the Brownian motion near absorbing polymers, and diffusion-controlled reactions involving polymers.
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 en…
