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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]

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]

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 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]

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 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]

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]

The flow-induced coil-stretch transition of high molecular weight polymers has generally been held to be of first order. But evidence of significant slowing down in the rate at which the polymers relax to equilibrium in the vicinity of the transition suggests that the thermodynamic character of the transition may be less clear-cut. The above slowing down effect is actually characteristic of a second-order transition, and it points to the existence of a broad spectrum of conformational states in the transition region, analogous to the existence of fluctuations of all length scales at a critical point. In this paper, using a path integral approach based on a free-draining finitely extensible chain model, we calculate various polymer properties as a function of elongational flow as a way of exploring different statistical mechanical details of the coil-stretch transition. These properties include the molecular weight dependence of the flow-extension curve of the polymer, the distribution of its steady-state end-to-end distances, and the characteristic relaxation time τR of these distances. Among other findings, our calculations indicate that the coil-stretch transition is discontinuous in the N → ∞ limit, that the effective free energy of the chain is unimodal at all values of the flow, becoming broad and flat in the immediate vicinity of the transition, and that the ratio of τR to the Rouse relaxation time increases abruptly at the transition before eventually reaching a plateau value at large flow strengths. These aspects of the coil-stretch transition place it among a larger class of unconventional nominally first-order single chain transitions that include the adsorption transition of surface-tethered polymers and the escape transition of compressed polymers. [ABSTRACT FROM AUTHOR]