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Molecular chirality has traditionally been viewed as a binary property where a molecule is classified as either chiral or achiral, yet in recent decades, mathematical methods for quantifying chirality have been explored. Here, we use toy molecular systems to systematically compare the performance of two state-of-the-art chirality measures: (1) the Continuous Chirality Measure (CCM) and (2) the Chirality Characteristic (χ). We find that both methods exhibit qualitatively similar behavior when applied to simple molecular systems such as a four-site molecule or the polymer double-helix, but we show that the CCM may be more suitable for evaluating the chirality of arbitrary molecules or abstract structures such as normal vibrational modes. We discuss a range of considerations for applying these methods to molecular systems in general, and we provide links to user-friendly codes for both methods. We aim for this paper to serve as a concise resource for scientists attempting to familiarize themselves with these chirality measures or attempting to implement chirality measures in their own work. [ABSTRACT FROM AUTHOR]

Recent experiments by Brückner et al. [Science 380, 1357 (2023)] have observed an anomalous chain length dependence of the time of near approach of widely separated pairs of genomic elements on transcriptionally active chromosomal DNA. In this paper, I suggest that the anomaly may have its roots in internal friction between neighboring segments on the DNA backbone. The basis for this proposal is a model of chain dynamics formulated in terms of a continuum scaled Brownian walk (sBw) of polymerization index N. The sBw is an extension of the simple Brownian walk model widely used in path integral calculations of polymer properties, differing from it in containing an additional parameter H (the Hurst index) that can be tuned to produce varying degrees of correlation between adjacent monomers. A calculation using the sBw of the mean time τc for chain closure predicts—under the Wilemski–Fixman approximation for diffusion-controlled reactions—that at early times, τc varies as the 2/3 power of N, in close agreement with the findings of the Brückner et al. study. Other scaling relations of that study, including those related to the probability of loop formation and the mean square displacements of terminal monomers, are also satisfactorily accounted for by the model. [ABSTRACT FROM AUTHOR]

Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single-molecule experimental techniques and give insight into biologically relevant processes in vivo. In this paper, we determine the transverse position and bending correlation functions for a wormlike chain confined within slits and cylinders (with one and two confined dimensions, respectively) using a mean-field approach that enforces rigid constraints on average. We show the theoretical predictions accurately capture the statistics of a wormlike chain from Monte Carlo simulations in both confining geometries for both weak and strong confinement. We also show that the longitudinal correlation function is accurately computed for a chain confined to a slit and leverages the accuracy of the model to suggest an experimental technique to infer the (often unobservable) transverse statistics from the (directly observable) longitudinal end-to-end distance. [ABSTRACT FROM AUTHOR]

Polymer crystallization has long been a fascinating problem and is still attracting many researchers. Most of the previous simulations are concentrated on clarifying the universal aspects of polymer crystallization using model linear polymers such as polyethylene. We are recently focusing on a nearly untouched but very interesting problem of chiral selecting crystallization in helical polymers. We previously proposed a stepwise approach using two kinds of helical polymers, simple "bare" helical polymers made of backbone atoms only such as polyoxymethylene (POM) and "general" helical polymers containing complicated side groups such as isotactic polypropylene. We have already reported on the crystallization in oligomeric POM-like helix but have observed only weak chiral selectivity during crystallization. In the present paper, we investigate the crystallization of sufficiently long POM-like polymer both from the isotropic melt and from the highly stretched melt. We find in both cases that the polymer shows a clear chiral selecting crystallization. Specifically, the observation of a single crystal growing from the isotropic melt is very illuminating. It shows that the crystal thickness and the crystal chirality are closely correlated; thicker crystals show definite chirality while thinner ones are mostly mixtures of the R- and the L-handed stems. The single crystal is found to have a marked lenticular shape, where the thinner growth front, since being made of the mixture, shows no chiral selectivity. The final chiral crystal is found to be completed through helix reversal processes within thicker regions. [ABSTRACT FROM AUTHOR]

Hydrodynamic effect on the relaxation modes for a system of charged particles is reexamined. This effect is shown to produce a decrease in the diffusion coefficient due to the cloud of particles surrounding each charge. [ABSTRACT FROM AUTHOR]

Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper, we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in the statistics of the extruded loop, regardless of the specific time dependence of the extrusion velocity. In addition, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits. [ABSTRACT FROM AUTHOR]

The external voltage-driven polymer translocation through a conical pore (with a large opening at the entry and a small tip at the exit) is studied by using the Langevin dynamics simulation in this paper. The entire translocation process is divided into an approaching stage and a threading stage. First, the approaching stage starts from the polymer entering the large opening and ends up at a terminal monomer reaching the pore tip. In this stage, the polymer will undergo the conformation adjustment to fit the narrowed cross-sectional area of the pore, leading to three approaching modes: the non-stuck mode with a terminal monomer arriving at the pore tip smoothly, the weak-stuck mode for the polymer stuck inside the pore for a short duration with minor conformational adjustments, and the strong-stuck mode with major conformational changes and a long duration. The approaching times (the duration of the approaching stage) of the three approaching modes show different behavior as a function of the pore apex angle. Second, the threading stage describes that the polymer threads through the pore tip with a linear fashion. In this stage, an increase in the apex angle causes the reduction of the threading time (the duration of the threading stage) due to the increase in the driving force with the apex angle at the tip. Moreover, we also find that with the increase in the apex angle or the polymer length, the polymer threading dynamics will change from the quasi-equilibrium state to the non-equilibrium state. [ABSTRACT FROM AUTHOR]

Recent experiments on the return to equilibrium of solutions of entangled polymers stretched by extensional flows [Zhou and Schroeder, Phys. Rev. Lett. 120, 267801 (2018)] have highlighted the possible role of the tube model's two-step mechanism in the process of chain relaxation. In this paper, motivated by these findings, we use a generalized Langevin equation (GLE) to study the time evolution, under linear mixed flow, of the linear dimensions of a single finitely extensible Rouse polymer in a solution of other polymers. Approximating the memory function of the GLE, which contains the details of the interactions of the Rouse polymer with its surroundings, by a power law defined by two parameters, we show that the decay of the chain's fractional extension in the steady state can be expressed in terms of a linear combination of Mittag-Leffler and generalized Mittag-Leffler functions. For the special cases of elongational flow and steady shear flow, and after adjustment of the parameters in the memory function, our calculated decay curves provide satisfactory fits to the experimental decay curves from the work of Zhou and Schroeder and earlier work of Teixeira et al. [Macromolecules 40, 2461 (2007)]. The non-exponential character of the Mittag-Leffler functions and the consequent absence of characteristic decay constants suggest that melt relaxation may proceed by a sequence of steps with an essentially continuous, rather than discrete, spectrum of timescales. [ABSTRACT FROM AUTHOR]

The loop formation of a single polymer chain has served as a model system for various biological and chemical processes. Theories based on the Smoluchowski equation proposed that the rate constant (kloop) of the loop formation would be inversely proportional to viscosity (η), i.e., kloop ∼ η−1. Experiments and simulations showed, however, that kloop showed the fractional viscosity dependence of kloop ∼ η−β with β < 1 either in glasses or in low-viscosity solutions. The origin of the fractional viscosity dependence remains elusive and has been attributed to phenomenological aspects. In this paper, we illustrate that the well-known failure of classical kinetics of the loop formation results from the breakdown of the local thermal equilibrium (LTE) approximation and that the mutual information can quantify the breakdown of the LTE successfully. [ABSTRACT FROM AUTHOR]

The general theory of the construction of scale-consistent energy terms in the coarse-grained force fields presented in Paper I of this series has been applied to the revision of the UNRES force field for physics-based simulations of proteins. The potentials of mean force corresponding to backbone-local and backbone-correlation energy terms were calculated from the ab initio energy surfaces of terminally blocked glycine, alanine, and proline, and the respective analytical expressions, derived by using the scale-consistent formalism, were fitted to them. The parameters of all these potentials depend on single-residue types, thus reducing their number and preventing over-fitting. The UNRES force field with the revised backbone-local and backbone-correlation terms was calibrated with a set of four small proteins with basic folds: tryptophan cage variant (TRP1; α), Full Sequence Design (FSD; α + β), villin headpiece (villin; α), and a truncated FBP-28 WW-domain variant (2MWD; β) (the NEWCT-4P force field) and, subsequently, with an enhanced set of 9 proteins composed of TRP1, FSD, villin, 1BDC (α), 2I18 (α), 1QHK (α + β), 2N9L (α + β), 1E0L (β), and 2LX7 (β) (the NEWCT-9P force field). The NEWCT-9P force field performed better than NEWCT-4P in a blind-prediction-like test with a set of 26 proteins not used in calibration and outperformed, in a test with 76 proteins, the most advanced OPT-WTFSA-2 version of UNRES with former backbone-local and backbone-correlation terms that contained more energy terms and more optimizable parameters. The NEWCT-9P force field reproduced the bimodal distribution of backbone-virtual-bond angles in the simulated structures, as observed in experimental protein structures. [ABSTRACT FROM AUTHOR]

In this paper, molecular dynamics simulations are used to study the effect of molecular water and composition (Si/Al ratio) on the structure and mechanical properties of fully polymerized amorphous sodium aluminosilicate geopolymer binders. The X-ray pair distribution function for the simulated geopolymer binder phase showed good agreement with the experimentally determined structure in terms of bond lengths of the various atomic pairs. The elastic constants and ultimate tensile strength of the geopolymer binders were calculated as a function of water content and Si/Al ratio; while increasing the Si/Al ratio from one to three led to an increase in the respective values of the elastic stiffness and tensile strength, for a given Si/Al ratio, increasing the water content decreased the stiffness and strength of the binder phase. An atomic-scale analysis showed a direct correlation between water content and diffusion of alkali ions, resulting in the weakening of the AlO4 tetrahedral structure due to the migration of charge balancing alkali ions away from the tetrahedra, ultimately leading to failure. In the presence of water molecules, the diffusion behavior of alkali cations was found to be particularly anomalous, showing dynamic heterogeneity. This paper, for the first time, proves the efficacy of atomistic simulations for understanding the effect of water in geopolymer binders and can thus serve as a useful design tool for optimizing composition of geopolymers with improved mechanical properties. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations and measure the mean first-passage time t(z) for the free end to reach a certain distance z away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of t(z) are observed, with transition between them varying as a function of chain length. We use these simulation results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations leads us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more. [ABSTRACT FROM AUTHOR]

In this paper, we study a system of entangled chains that bear reversible cross-links in a melt state. The cross-links are tethered uniformly on the backbone of each chain. A slip-link type model for the system is presented and solved for the relaxation modulus. The effects of entanglements and reversible cross-linkers are modelled as a discrete form of constraints that influence the motion of the primitive path. In contrast to a non-associating entangled system, the model calculations demonstrate that the elastic modulus has a much higher first plateau and a delayed terminal relaxation. These effects are attributed to the evolution of the entangled chains, as influenced by tethered reversible linkers. The model is solved for the case when the linker survival time τs is greater than the entanglement time τe, but less than the Rouse time τR. [ABSTRACT FROM AUTHOR]

Organic materials with a high index of refraction (RI) are attracting considerable interest due to their potential application in optic and optoelectronic devices. However, most of these applications require an RI value of 1.7 or larger, while typical carbon-based polymers only exhibit values in the range of 1.3–1.5. This paper introduces an efficient computational protocol for the accurate prediction of RI values in polymers to facilitate in silico studies that can guide the discovery and design of next-generation high-RI materials. Our protocol is based on the Lorentz-Lorenz equation and is parametrized by the polarizability and number density values of a given candidate compound. In the proposed scheme, we compute the former using first-principles electronic structure theory and the latter using an approximation based on van der Waals volumes. The critical parameter in the number density approximation is the packing fraction of the bulk polymer, for which we have devised a machine learning model. We demonstrate the performance of the proposed RI protocol by testing its predictions against the experimentally known RI values of 112 optical polymers. Our approach to combine first-principles and data modeling emerges as both a successful and a highly economical path to determining the RI values for a wide range of organic polymers. [ABSTRACT FROM AUTHOR]

We present a theory of adsorption of flexible polyelectrolytes on the interior and exterior surfaces of a charged vesicle in an electrolyte solution. The criteria for adsorption and the density profiles of the adsorbed polymer chain are derived in terms of various characteristics of the polymer, vesicle, and medium, such as the charge density and length of the polymer, charge density and size of the vesicle, electrolyte concentration and dielectric constant of the medium. For adsorption inside the vesicle, the competition between the loss of conformational entropy and gain in adsorption energy results in two kinds of encapsulated states, depending on the strength of the polymer-vesicle interaction. By considering also the adsorption from outside the vesicle, we derive the entropic and energy contributions to the free energy change to transfer an adsorbed chain in the interior to an adsorbed chain on the exterior. In this paper, we have used the Wentzel-Kramers-Brillouin (WKB) method to solve the equation for the probability distribution function of the chain. The present WKB results are compared with the previous results based on variational methods. The WKB and variational results are in good agreement for both the interior and exterior states of adsorption, except in the zero-salt limit for adsorption in the exterior region. The adsorption criteria and density profiles for both the interior and exterior states are presented in terms of various experimentally controllable variables. Calculation of the dependencies of free energy change to transfer an adsorbed chain from the interior to the exterior surface on salt concentration and vesicle radius shows that the free energy penalty to expel a chain from a vesicle is only of the order of thermal energy. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the relaxation dynamics of Sierpinski hexagon fractal polymer. The relaxation dynamics of this fractal polymer is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, by performing real-space renormalization transformations, we determine analytically the complete eigenvalue spectrum of the connectivity matrix. Based on the eigenvalues obtained through iterative algebraic relations we calculate the averaged monomer displacement and the mechanical relaxation moduli (storage modulus and loss modulus). The evaluation of the dynamical properties in the Rousetype approach reveals that they obey scaling in the intermediate time/frequency domain. In the Zimm-type approach, which includes the hydrodynamic interactions, the relaxation quantities do not show scaling. The theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results. [ABSTRACT FROM AUTHOR]

In Paper I [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)] we derived a quantum transition-state theory (TST) by taking the t → 0+ limit of a new form of quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t → 0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that quantum TST (i.e., RPMD-TST) is exact if there is no recrossing (by the real-time quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the t → ∞ limit of the ring-polymer flux-side time-correlation function with that of a hybrid flux-side time-correlation function (containing a ring-polymer flux operator and a Miller-Schwarz-Tromp side function), and by representing the resulting ring-polymer momentum integrals as hypercubes. Together with Paper I, the results of this article validate a large number of RPMD calculations of reaction rates. [ABSTRACT FROM AUTHOR]

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH4→ H2 + CH3. The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach to study the probability distribution of the radius of gyration of freely jointed chains. In this approach, we study the joint distribution PN(Rg2,Rvector G), where Rg is the radius of gyration and Rvector G is the vector from the first bead to the center of the chain. We derive an iteration relation between the probability distributions of chains with lengths N and N+1. When the chain length is large, the iteration relation can be approximated by an evolution equation with integral determining condition. The equation is solved to obtain the probability distribution function, which yields the known result obtained by Fixman [J. Chem. Phys. 36, 306 (1962)] using the integral method. We hope the iteration method in this paper could be used to study the probability distribution of the structure factor of polymer molecules. [ABSTRACT FROM AUTHOR]

The nonlinear viscoelastic behavior of the Fraenkel-chain model is studied with respect to the constitutive equation of the Rouse model. Distinctly different from the results of the Rouse model, the Fraenkel-chain model gives the following characteristic nonlinear behavior: (a) The two distinct dynamic modes in the relaxation modulus GS(t,λ)—as observed in the linear region reported in Paper I [Y.-H. Lin and A. K. Das, J. Chem. Phys. 126, 074902 (2007), preceding paper]—or in the first normal-stress difference function GΨ1(t,λ) are shown to have different strain dependences: strain hardening for the fast mode and strain softening for the slow mode. (b) The Lodge–Meissner relation GS(t,λ)=GΨ1(t,λ) holds over the whole time range, which has been shown both analytically and by simulation. (c) The second normal-stress difference is nonzero, being positive in the fast-mode region and negative in the slow-mode region. The comparisons between orientation and stress for all tensor components consistently confirm the strong correlation of the slow mode as well as its entropic nature with the segmental-orientation anisotropy as shown in the linear region studied in Paper I. A consequence of this correlation is the applicability of the stress-optical rule in the slow-mode region. This also leads to the expectation that the damping function h(λ)=GS(t,λ)/GS(t,λ→0) and the ratio between the first and second normal-stress differences, N2(t,λ)/N1(t,λ), are described by the orientation tensor which has the same form as that given by Doi and Edwards [J. Chem. Soc. Faraday Trans. 2 74, 1789 (1978); 74, 1802 (1978)] with independent-alignment approximation for an entangled system. The similarity between the slow mode of an entanglement-free Fraenkel-chain system and the terminal mode of an entangled polymer system as observed in the comparison of theory, simulation, and experiment suggests that the close correlation of the entropic nature of the mode with the orientation anisotropy—as of the Fraenkel segment or the primitive step in the Doi–Edwards theory—is a generally valid physical concept in polymer viscoelasticity. [ABSTRACT FROM AUTHOR]

We introduce a new, topologically-based method for coarse-graining polymer chains. Based on the wavelet transform, a multiresolution data analysis technique, this method assigns a cluster of particles to a coarse-grained bead located at the center of mass of the cluster, thereby reducing the complexity of the problem by dividing the simulation into several stages, each with a fraction of the number of beads as the overall chain. At each stage, we compute the distributions of coarse-grained internal coordinates as well as potential functions required for subsequent simulation stages. In this paper, we present the basic algorithm, and apply it to freely jointed chains; the companion paper describes its applications to self-avoiding chains. [ABSTRACT FROM AUTHOR]

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

Knowledge of the conformational evolution of a polymer chain provides invaluable information for all polymer properties. However, the chain evolution is usually determined by monitoring single beads for short times only. In this paper, we numerically determine the configuration evolution over extended time periods by monitoring the eigenvalues of the gyration tensor and applying the scaling law methodology. Results of Brownian dynamics simulations of initially straight chains reveal that after the early free transverse diffusion, flexible polymers exhibit a transverse intermediate-time behavior of t[sup 3/4], while stiff polymers reveal two intermediate-time behaviors: an early t[sup 5/6] power law accompanied by a late t[sup 3/4] evolution. These results are associated with the inherent nonlinearity of the problem. The scaling law methodology we develop in this paper for monitoring the chain configuration should have wide applications in the study of polymer rheology. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The two pulse fluorescence bleaching experiments reported in an earlier paper [J. Chem. Phys. 117, 454 (2002)] are reanalyzed in the context of additional experiments. The fluorescence bleaching observed in that paper was originally ascribed to ground-state depletion. By analyzing the absorption saturation behavior and the magnitude of the pump–probe signal, we find that the absorption cross section of poly(phenylene vinylene) at 400 nm is two orders of magnitude too small to significantly deplete the ground state given the pump fluences used in that experiment. Instead, the observed depletion is due to a combination of exciton–exciton annihilation at early times and dark state luminescence quenching at later times. Different experiments have different sensitivities to the fluence-dependent quenching, with time-resolved experiments like transient emission and fluorescence decay time consistently underestimating the exciton–exciton annihilation rate. Experiments that measure the integrated fluorescence, such as fluorescence saturation and bleaching, result in a consistent value for the exciton–exciton annihilation constant of 6×10[sup -9] cm[sup 3]/s, while the dark state quenching constant is estimated to be at least 1.2×10[sup -8] cm[sup 3]/s. Indirect evidence based on the wavelength and sample dependence of the dark state formation suggest that the dark states are charge-separated polarons. The relatively large quenching constants are consistent with what has been observed in other conjugated polymers and suggest that the long-lived dark states in particular are effective quenchers, capable of quenching thousands of surrounding chromophores. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In an extension of earlier studies from this group on the application of the Jarzynski equality to the determination of the elastic properties of a finitely extensible Rouse model of polymers under flow [A. Ghosal and B. J. Cherayil, J. Chem. Phys. 144, 214902 (2016)], we derive several new theoretical results in this paper on the nature of the distribution function P(w) that governs the long-time limit t>>1 of the fluctuations in the work w performed by the polymer during flow-induced stretching. In particular, we show that an expression for the average of the nth power of the work, 〈wn(t)〉, can be obtained in closed form in this limit, making it possible to exactly calculate three important statistical measures of P(w): the mean μ, the skewness γ1, and the kurtosis γ2 (apart from the variance σ²). We find, for instance, that to leading order in t, the mean grows linearly with t at a constant value of the dimensionless flow rate Wi and that the slope of the μ−t curve increases with increasing Wi. These observations are in complete qualitative agreement with data from Brownian dynamics simulations of flow-driven double-stranded DNA by Latinwo and Schroeder [Macromolecules 46, 8345 (2013)]. We also find that the skewness γ1 exhibits an interesting inversion of sign as a function of Wi, starting off at positive values at low Wi and changing to negative values at larger Wi. The inversion takes place in the vicinity of what we interpret as a coil-stretch transition. Again, the finding exactly reproduces behavior seen in other numerical and experimental work by the above group Latinwo et al. [J. Chem. Phys. 141, 174903 (2014)]. Additionally, at essentially the same value of Wi at which this sign inversion takes place, we observe that the kurtosis reaches a minimum, close to 1, providing further evidence of the existence of a coil-stretch transition at this location. Our calculations reproduce another numerical finding: a power law dependence on Wi of the rate of work production that is characterized by two distinct regimes, one lying below the putative coil-stretch transition, where the exponent assumes one value, and the other above, where it assumes a second. [ABSTRACT FROM AUTHOR]

Morphology of symmetric ABCD tetrablock quaterpolymers in melt was studied by the Monte Carlo (MC) simulation, where the volume fractions of the block chains, f, kept the relationships of fA = fD and fB = fC, and the volume fraction of the two mid-blocks φ was defined as φ = fB + fC. Previous self-consistent field theory for ABCD reported morphological change including several structures; however, the scope was limited within a two-dimensional system. To the contrary, in this paper, MC simulations were carried out in three dimensions with changing the φ value finely, which resulted in finding a tetracontinuous structure in the range of 0.625 ⩽ φ ⩽ 0.75. Moreover the tetracontinuous structure has been found to be the gyroid structure, and the mean curvature of the B/C interface is nearly zero. We concluded that the B/C interface must be the Schoen gyroid surface, one of three-dimensional periodic minimal surfaces. The geometrical nature of the A/B interface should be equivalent to that of the C/D interface, and they stand as level surfaces to the Schoen gyroid surface. [ABSTRACT FROM AUTHOR]

We use the two solvation potentials discussed in the previous paper and polymer reference interaction-site model (PRISM) theory to calculate the mutually consistent single-molecule conformation and liquid structure of model linear flexible nonpolar polymers. We focus on the mean end-to-end distance R2 and radius of gyration Rg of the single chain as functions of polymer density. Our calculations are compared to computer simulations to assess their accuracy, and some aspects of the general trends with density predicted are discussed. Two methods of calculating the conformation of the single chain in the solvation potential are used, one is Monte Carlo simulation, the other, introduced in this paper, employs a generating functional. We cannot unambiguously confirm the accuracy of one solvation potential over the other; at low density they give identical results, and the exact values are too few at high density. However, we are inclined to question the accuracy of the hypernetted-chain (HNC) style potential at high densities because it seems to predict a strong contraction of the polymer chain that is not seen experimentally in real polymer melts. [ABSTRACT FROM AUTHOR]

In this paper, we continue investigations on the solution methods for the generalized Percus–Yevick equations for the pair correlation functions of polymers, which were formulated in the previous papers of this series [J. Chem. Phys. 99, 4084, 4103 (1993)]. Previously, they were reduced to recursive integral equations and solved numerically. In this paper, a translational invariance approximation is used to reduce the number of integral equations to solve. In this approximation, only N integral equations out of N2 integral equations are required for a polymer consisting of N beads (monomers). The behavior of an isolated polymer is studied with three different potential models, a soft sphere, a hard sphere, and a Lennard-Jones potential. The main motivation for considering these three potential models is in testing the idea of universality commonly believed to hold for some properties of polymers. We find that the universality holds for the power law exponent for the expansion factor of polymers at high temperatures. The end-to-end distance distribution functions, intermediate distribution functions, chemical potentials, the density distributions, and various expansion factors of the polymer chain are computed from the solutions of the integral equations in the case of coiled, ideal, and collapsed states of the polymer. The expansion factors in the collapsed regime are found to obey power laws with respect to the length of the polymer and [B(T)-B(θ)], where B(T) is the second virial coefficient and θ is a modified θ temperature. The values of these exponents approach those from the known theories of polymer collapse as the chain length becomes long and the ratio of bond length to bead radius becomes large. [ABSTRACT FROM AUTHOR]

The thermodynamics of symmetric polymer blends is investigated using the polymer reference interaction site model integral equation theory with the new molecular closures presented in the previous paper. In contrast to the atomic mean spherical approximation reported earlier by Schweizer and Curro [J. Chem. Phys. 91, 5059 (1989); Chem. Phys. 149, 105 (1990)] (in which the critical temperature is proportional to the square root of the degree of polymerization), the molecular closures predict a linear dependence of the critical temperature on the degree of polymerization, in agreement with classical mean field theory. Detailed numerical calculations using the reference molecular mean spherical approximation (R-MMSA) and the reference molecular Percus–Yevick (R-MPY) closures are presented for the intermolecular structure and effective chi parameter in symmetric blends of semiflexible chains. For the symmetric blend, the R-MMSA closure is almost an integral equation realization of mean field theory, consistent with the analytical results presented in the previous paper. With the R-MPY closure, at low densities, the effective chi parameter is significantly renormalized down from its mean field value and displays a strong composition dependence. As the density is increased, both the renormalization of the effective chi parameter and its composition dependence become weaker. These trends are consistent with recent computer simulations. The influence of chain aspect ratio and the precise choice of intermolecular potentials on blend thermodynamics and phase separation are also explored. With the exception of the composition dependence of the effective chi parameter in the R-MPY theory, the analytical thread calculations are shown to be in qualitative, and sometimes quantitative, agreement with all the numerical results for symmetric blends. [ABSTRACT FROM AUTHOR]

This paper is the first in a series of papers in which polymer adsorption on a surface is studied by computer simulation using the ‘‘scanning method.’’ This method is especially efficient to handle chain systems with finite interactions and geometrical constraints. Here we test the method by applying it to models of a single random walk (without excluded volume) on a simple cubic lattice, which are solved analytically; in the immediately following paper a self-avoiding walk model is treated. The scanning method is found to be extremely efficient, where walks of up to N=105 steps can be simulated reliably, leading thereby to very precise estimates of transition temperatures and critical exponents. In particular we test carefully for a lattice model the range of validity of scaling functions developed by Eisenrigler, Kremer and Binder [J. Chem. Phys. 77, 6296 (1982)] for a continuous model. We pay a special attention to corrections to scaling and demonstrate that they are strong above the transition temperature for ⊥, the perpendicular part of the mean-square end-to-end distance and for ρ(z), the monomer concentration profile. We show that at T=∞, the asymptotic regime, in which these corrections become negligible, is obtained for N≊40 000 for ⊥ but a significantly larger N is required for ρ(z). This means that this regime corresponds to a real polymer length that is not realized experimentally. [ABSTRACT FROM AUTHOR]

The Curtiss–Bird model of polymer melts has been extended to include polydisperse mixtures. The formula for the stress tensor derived in the last paper is used here to give explicit expressions for material functions in shear and elongational flow. Predictions are shown for viscosity, first normal stress coefficient, elongational stress growth viscosity, and steady elongational viscosity for Flory–Schulz and log–normal molecular weight distributions. It is also shown how generalizations that are observed experimentally for viscosity are predicted by the Curtiss–Bird model. In the next paper, these calculations are compared with experimental data. [ABSTRACT FROM AUTHOR]

Following the general scheme developed in the preceding paper (paper VII), dielectric and magnetic relaxation and fluorescence depolarization for flexible chain polymers in dilute solution are reinvestigated on the basis of the discrete helical worm-like chain in the higher-order subspace approximation. A comparison of theory with experiment is made with respect to the dielectric correlation time τD, the spin-lattice relaxation time T1, the spin–spin relaxation time T2, the nuclear Overhauser enhancement (NOE), the fluorescence emission anisotropy r(t), the average fluorescence anisotropy r, and the fluorescence correlation time τF. It is found that there is agreement between the diameters of the chains determined from these dynamic properties and those from chemical structures, better than in the previous crude subspace approximation, indicating that the theory is remarkably improved in the present approximation. The magnetic correlation time τM is in general not an observable, and therefore an empirical equation to be used for its determination from the observed T1 is constructed. It is then found that there is good correlation between the dynamic chain stiffness τX/τ0X and the static chain stiffness λ-1, where τ0X is the correlation time of the isolated subbody (monomer unit) with X=D, M, and F; τX/τ0X is a monotonically increasing function of λ-1 nearly independent of X as far as perpendicular dipoles are concerned. An explanation of this result is given. However, the dependence of τX on temperature cannot be explained very satisfactorily. [ABSTRACT FROM AUTHOR]

Recent experiments have shown that porous filters preadsorbed with polymer molecules exhibit an anomalously high pressure drop at high rates of flow. We have modeled the adsorbed polymers as dynamical systems and have found that the introduction of hydrodynamic interaction between molecules destabilizes at a high applied shear. As a direct result this instability will cause the molecules to unravel and stretch far into the cross section of the pore, and thus by inference, cause the observed anomalously high pressure drop. Although much of this paper is devoted to the stability characteristics of the deterministic system, Brownian motion is also considered, and an account of the statistics of the Brownian system when the deterministic system becomes unstable is given. The examples revealed in this paper are not of sufficient complexity to calculate with any accuracy the magnitude of this anomalous pressure drop. We simply present a procedure by which a large variety of more complex models could be undertaken and their ultimate effect clearly understood. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete nonlinear dynamics. It is found that Markovian treatments based on a Wilemski-Fixman approximation significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics. In addition, this analysis provides scaling laws of the mean first cyclization time (MFCT) with the polymer size N and capture radius b, which are identical in both Markovian and non-Markovian approaches. In particular, it is found that the scaling of the MFCT for large N is given by T - N3/2ln(N/b²), which differs from the case of the Rouse dynamics where T - N². The extension to the case of the reaction kinetics of a monomer of a Zimm polymer with an external target in a confined volume is also presented. [ABSTRACT FROM AUTHOR]

Although the Williams-Landell-Ferry (WLF) equation for the segmental relaxation time T(T) of glass-forming materials is one of the most commonly encountered relations in polymer physics, its molecular basis is not well understood. The WLF equation is often claimed to be equivalent to the Vogel-Fulcher-Tammann (VFT) equation, even though the WLF expression for T(T) contains no explicit dependence on the fragility parameter D of the VFT equation, while the VFT equation lacks any explicit reference to the glass transition temperature Tg, the traditionally chosen reference temperature in the WLF equation. The observed approximate universality of the WLF parameters C1(g) and C2(g) implies that T(T) depends only on T-Tg, a conclusion that seems difficult to reconcile with the VFT equation where the fragility parameter D largely governs the magnitude of T(T). The current paper addresses these apparent inconsistencies by first evaluating the macroscopic WLF parameters C1(g) and C2(g) from the generalized entropy theory of glass-formation and then by determining the dependence of C1(g) and C2(g) on the microscopic molecular parameters (including the strength of the cohesive molecular interactions and the degree of chain stiffness) and on the molar mass of the polymer. Attention in these calculations is restricted to the temperature range (Tg < T < Tg + 100 K), where both the WLF and VFT equations apply. [ABSTRACT FROM AUTHOR]

Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results. [ABSTRACT FROM AUTHOR]

In a recent paper [J. Chem. Phys., 121, 6064 (2004)] we developed a method to solve the wormlike chain model of semiflexible polymers. In this note we apply this method to evaluate the force-elongation relationship. It is found that our result agrees qualitatively with experimental data and the results obtained using three other theoretical treatments of semiflexible polymers for all values of the semiflexibility parameter. Quantitative comparisons are presented in the limit of long chains where good quantitative agreement with experimental data and two of the aforementioned theoretical studies are observed for elongations up to 60%, approximately. The limit of stiff chains was also studied and good quantitative agreement with other theoretical results is observed. These results complement the ones reported in our previous paper and show the robustness of our method.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The confinement of a polymer to volumes whose characteristic linear dimensions are comparable to or smaller than its bulk radius of gyration RG,bulk can produce significant changes in its static and dynamic properties, with important implications for the understanding of single-molecule processes in biology and chemistry. In this paper, we present calculations of the effects of a narrow rectangular slit of thickness d on the scaling behavior of the diffusivity D and relaxation time τr of a Gaussian chain of polymerization index N and persistence length l0. The calculations are based on the Rouse-Zimm model of chain dynamics, with the pre-averaged hydrodynamic interaction being obtained from the solutions to Stokes equations for an incompressible fluid in a parallel plate geometry in the limit of small d. They go beyond de Gennes' purely phenomenological analysis of the problem based on blobs, which has so far been the only analytical route to the determination of chain scaling behavior for this particular geometry. The present model predicts that D ∼ dN-1ln (N/d2) and τr ∼ N2d-1[ln (N/d2)]-1 in the regime of moderate confinement, where l0 < d < RG,bulk. The corresponding results for the blob model have exactly the same power law behavior, but contain no logarithmic corrections; the difference suggests that segments within a blob may actually be partially draining and not non-draining as generally assumed. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics of a simple bead-spring glass-forming polymer were studied with molecular dynamics simulations. The energy response to sinusoidal variations in the temperature was tracked in order to evaluate the dynamic heat capacity. The amplitude dependence of the response is the focus of the current paper where pronounced nonlinear behavior is observed for large amplitudes in the temperature 'driving force.' We generalize the usual linear response analysis to the nonlinear regime so that higher order terms in the Fourier series of the energy response can be compactly analyzed. This is done by grouping all Fourier terms contributing to entropy generation into a 'loss' contribution and the remainder yields the 'storage' term. Finally, the bead-spring system is mapped onto three simpler models. First is a potential energy inspired 'trap' model consisting of interconnected potential energy meta-basins and barriers. Second is the Tool-Narayanaswamy-Moynihan (TNM) model. Third is a version of the TNM model with a temperature dependent heat capacity. Qualitatively similar nonlinear behaviors are observed in all cases. [ABSTRACT FROM AUTHOR]

The growing importance of microfluidic and nanofluidic devices to the study of biological processes has highlighted the need to better understand how confinement affects the behavior of polymers in flow. In this paper we explore one aspect of this question by calculating the steady-state extension of a long polymer chain in a narrow capillary tube in the presence of simple shear. The calculation is carried out within the framework of the Rouse-Zimm approach to chain dynamics, using a variant of a nonlinear elastic model to enforce finite extensibility of the chain, and assuming that the only effect of the confining surface is to modify the pre-averaged hydrodynamic interaction. The results, along with results from the corresponding calculations of finitely extensible versions of both the Rouse and Rouse-Zimm models, are compared with data from experiments on the flow-induced stretching of λ-phage DNA near a non-adsorbing glass surface [L. Fang, H. Hu, and R. G. Larson, J. Rheol. 49, 127 (2005)]. The comparison suggests that close to a surface hydrodynamic screening is significant, and causes the chains to become effectively free-draining. [ABSTRACT FROM AUTHOR]

This paper presents the exact formula for the bivariate probability distribution function of a Brownian particle as a function of its position and velocity, whose orbit makes a specified number of turns around an infinite straight line. In the limit of large friction constant, the solution reduces to the well-known results for random Wiener paths. Topological entanglements of stiff polymers are discussed on the basis of this solution. The method to find the solution is applied to the velocity space of a Brownian motion, and the probability to find a closed path with a specified winding number is obtained. Hence, closed two-dimensional Brownian orbits are classified into regular homotopy classes, whose statistical weight is derived as a function of the total length and the friction constant. [ABSTRACT FROM AUTHOR]

In this paper, the cooperative effect of halogen bond with hydrogen bond has been used to make a halogen bond in FCl-CNH dimer vary from a chlorine-shared one to an ion-pair one. The halogen bond is strengthened in FCl-CNH-CNH trimer and its maximal interaction energy equals to -76 kJ/mol when the number of CNH in FCl-CNH-(CNH)n polymer approaches infinity. Once the free H atom in FCl-CNH-CNH trimer is replaced with alkali metals, the halogen bond becomes strong enough to be an ion-pair one in FCl-CNH-CNLi and FCl-CNH-CNNa trimers. An introduction of a Lewis acid in FCl-CNH dimer has a more prominent effect on the type of halogen bond. A prominent cooperative effect is found for the halogen bond and hydrogen bond in the trimers. FH-FCl-CNH-CNH and FH-FCl-CNH-CNLi tetramers have also been studied and the interaction energy of halogen bonding in FH-FCl-CNH-CNLi tetramer is about 12 times as much as that in the FCl-CNH dimer. The atoms in molecules and natural bond orbital analyses have been carried out for these complexes to understand the nature of halogen bond and the origin of the cooperativity. [ABSTRACT FROM AUTHOR]

Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry - the diffusion-limited cyclization of long chain polymers - is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time tc of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius d and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when d is much smaller than the size of the chain, tc ∼ Nd2, and that in case (b), tc ∼ N2/(2 - 2H), H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), tc ∼ N3.4, the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium. [ABSTRACT FROM AUTHOR]

Two different experimental studies of polymer dynamics based on single-molecule fluorescence imaging have recently found evidence of heterogeneities in the widths of the putative tubes that surround filaments of F-actin during their motion in concentrated solution. In one [J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchesner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)], the observations were explained in terms of the statistics of a worm-like chain confined to a potential determined self-consistently by a binary collision approximation, and in the other [B. Wang, J. Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010)], they were explained in terms of the scaling properties of a random fluid of thin rods. In this paper, we show, using an exact path integral calculation, that the distribution of the length-averaged transverse fluctuations of a harmonically confined weakly bendable rod (one possible realization of a semiflexible chain in a tube), is in good qualitative agreement with the experimental data, although it is qualitatively different in analytic structure from the earlier theoretical predictions. We also show that similar path integral techniques can be used to obtain an exact expression for the time correlation function of fluctuations in the tube cross section. [ABSTRACT FROM AUTHOR]

Recently, we developed a formalism for the scattering from linear and acyclic branched structures build of mutually non-interacting sub-units. [C. Svaneborg and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012)] We assumed each sub-unit has reference points associated with it. These are well-defined positions where sub-units can be linked together. In the present paper, we generalize the formalism to the case where each reference point can represent a distribution of potential link positions. We also present a generalized diagrammatic representation of the formalism. Scattering expressions required to model rods, polymers, loops, flat circular disks, rigid spheres, and cylinders are derived, and we use them to illustrate the formalism by deriving the generic scattering expression for micelles and bottle-brush structures and show how the scattering is affected by different choices of potential link positions and sub-unit choices. [ABSTRACT FROM AUTHOR]

Exciton dissociation and charge recombination processes in organic semiconductors, with thermal effects taken into account, are described in this paper. Here, we analyzed the mechanisms of polaron-excitons dissociation into free charge carriers and the consequent recombination of those carriers under thermal effects on two parallel π-conjugated polymers chains electronically coupled. Our results suggest that exciton dissociation in a single molecule give rise to localized, polaron-like charge carrier. Besides, we concluded that in the case of interchain processes, the bimolecular polaron recombination does not lead to an usual exciton state. Rather, this type of recombination leads to an oscillating dipole between the two chains. The recombination time obtained here for these processes are in agreement with the experimental results. Finally, our results show that temperature effects are essential to the relaxation process leading to polaron formation in a single chain, as in the absence of temperature, this process was not observed. In the case of two chains, we conclude that temperature effects also help the bimolecular recombination process, as observed experimentally. [ABSTRACT FROM AUTHOR]

Cargo transport through the nuclear pore complex continues to be a subject of considerable interest to experimentalists and theorists alike. Several recent studies have revealed details of the process that have still to be fully understood, among them the apparent nonlinearity between cargo size and the pore crossing time, the skewed, asymmetric nature of the distribution of such crossing times, and the non-exponentiality in the decay profile of the dynamic autocorrelation function of cargo positions. In this paper, we show that a model of pore transport based on subdiffusive particle motion is in qualitative agreement with many of these observations. The model corresponds to a process of stochastic binding and release of the particle as it moves through the channel. It suggests that the phenylalanine-glycine repeat units that form an entangled polymer mesh across the channel may be involved in translocation, since these units have the potential to intermittently bind to hydrophobic receptor sites on the transporter protein. [ABSTRACT FROM AUTHOR]

In this paper, the molecular mechanisms which determine the thermal conductivity of long chain polymer liquids are discussed, based on the results observed in molecular dynamics simulations. Linear n-alkanes, which are typical polymer molecules, were chosen as the target of our studies. Non-equilibrium molecular dynamics simulations of bulk liquid n-alkanes under a constant temperature gradient were performed. Saturated liquids of n-alkanes with six different chain lengths were examined at the same reduced temperature (0.7Tc), and the contributions of inter- and intramolecular energy transfer to heat conduction flux, which were identified as components of heat flux by the authors' previous study [J. Chem. Phys. 128, 044504 (2008)], were observed. The present study compared n-alkane liquids with various molecular lengths at the same reduced temperature and corresponding saturated densities, and found that the contribution of intramolecular energy transfer to the total heat flux, relative to that of intermolecular energy transfer, increased with the molecular length. The study revealed that in long chain polymer liquids, thermal energy is mainly transferred in the space along the stiff intramolecular bonds. This finding implies a connection between anisotropic thermal conductivity and the orientation of molecules in various organized structures with long polymer molecules aligned in a certain direction, which includes confined polymer liquids and self-organized structures such as membranes of amphiphilic molecules in water. [ABSTRACT FROM AUTHOR]

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles. [ABSTRACT FROM AUTHOR]

In this paper, Brownian dynamics simulation (BDS) studies are executed to demonstrate the distinctive influences of the extent of confinement on the collapsing mechanism and kinetics of a flexible hydrophobic polymer chain in a poor solvent. The collapsing behavior is quantified by the time of collapse, which below a critical dimension of the confinement (hc), encounters a drastic reduction with a further strengthening in the degree of confinement. For dimensions greater than this critical one, the collapse occurs through the well-known hydrodynamic interaction (HI) controlled multiple-globule-mediated mechanisms. However, for channel dimensions less than this critical one, the collapse mechanism is drastically altered. Under such circumstances, the collapse gets predominantly controlled by the confinement effects (with negligible contribution of the HIs) and occurs via the formation of a single central globule. This central globule rapidly engulfs the noncondensed polymer segments, and in the process largely hastens up the collapsing event. Under such circumstances, the collapse time is found to decrease linearly with decrements in the channel height. On the contrary, for channel heights greater than hc, the multiple-globule-mediated collapse is characterized by a collapse time that shows an exponential dependence on the channel height, rapidly attaining a state in which the confinement effect becomes inconsequential and HIs dictate the entire collapsing behavior. We further propose detailed arguments based on physical reasoning as well as free energy estimations to conclusively support the qualitative and quantitative nature of influences of the confinement on the polymer collapse. [ABSTRACT FROM AUTHOR]