Model Polymer Research Articles

A Physics-Guided Machine Learning Model for Predicting Viscoelasticity of Solids at Large Deformation.

Physics-guided machine learning (PGML) methods are emerging as valuable tools for modelling the constitutive relations of solids due to their ability to integrate both data and physical knowledge. While various PGML approaches have successfully modeled time-independent elasticity and plasticity, viscoelasticity remains less addressed due to its dependence on both time and loading paths. Moreover, many existing methods require large datasets from experiments or physics-based simulations to effectively predict constitutive relations, and they may struggle to model viscoelasticity accurately when experimental data are scarce. This paper aims to develop a physics-guided recurrent neural network (RNN) model to predict the viscoelastic behavior of solids at large deformations with limited experimental data. The proposed model, based on a combination of gated recurrent units (GRU) and feedforward neural networks (FNN), utilizes both time and stretch (or strain) sequences as inputs, allowing it to predict stress dependent on time and loading paths. Additionally, the paper introduces a physics-guided initialization approach for GRU-FNN parameters, using numerical stress-stretch data from the generalized Maxwell model for viscoelastic VHB polymers. This initialization is performed prior to training with experimental data, helping to overcome challenges associated with data scarcity.

Evolution equations for open systems and collective variables: Which equation would you like to solve by molecular dynamics simulation?

In molecular dynamics simulations, the Langevin equation is frequently used to model the dynamics of collective variables and of systems coupled to baths. Often, external forces are added to the Langevin equation (e.g., when using targeted or steered molecular dynamics in biomolecular simulation). It is also popular to add derivatives of thermodynamic potentials to the Langevin equation as effective forces (e.g., when using a potential of mean force in a coarse-grained polymer model). These practices can be adventurous. In this article, we recall derivations of different versions of the Langevin equation and we discuss why care is needed if one would like to make changes to the structure of the equation.

Dry polymer model for a string of pushers: Nontrivial scaling of tumbling time with shear rate

Understanding the dynamics of active polymers is an important component for modeling the dynamic response of biological cells and microorganisms when subjected to external forces. A minimal computational model of active filaments that captures all the essential features of activity-induced filament motion is required to study large systems of dense suspensions. In this paper we present a model of a dry active polymer, compare its steady-state static and dynamic properties with those of a polymer consisting of extensile stresslets, and show that the two models give very similar results. When subjected to shear flow, both models show two distinct regimes in the tumbling interval as a function of shear rate, with a diffuse crossover regime in between. At high shear rate, the active and passive polymers follow the same power law for the tumbling interval. However, the tumbling interval is smaller than that of the passive polymer for low shear rates and larger for the high shear rate. We show that activity-induced large bends increase the coupling of the polymer with the shear gradient in the low-shear-rate regime, leading to a decrease in the tumbling interval. However, in the high-shear-rate regime, the active forces on the folds at the end of the stretched polymer prevent it from tumbling, leading to a larger tumbling interval. We show that the critical shear rate, at which the tumbling interval versus the shear-rate curve of the active polymer crosses that of the passive polymer, is determined by the balance of bending and shear forces and increases with κ/N3, where κ is the bending coefficient and N is the length of the polymer. Published by the American Physical Society 2024

Exponential growth rate of lattice comb polymers

Abstract We investigate a lattice model of comb polymers and derive bounds on the exponential growth rate of the number of embeddings of the comb. A comb is composed of a backbone that is a self-avoiding walk and a set of t teeth, also modelled as mutually and self-avoiding walks, attached to the backbone at vertices or nodes of degree 3. Each tooth of the comb has ma edges and there are mb edges in the backbone between adjacent degree 3 vertices and between the first and last nodes of degree 3 and the end vertices of degree 1 of the backbone. We are interested in the exponential growth rate as t → ∞ with ma and mb fixed. We prove upper bounds on this growth rate and show that for small values of ma the growth rate is strictly less than that of self-avoiding walks.

SOP-MULTI: A Self-Organized Polymer-Based Coarse-Grained Model for Multidomain and Intrinsically Disordered Proteins with Conformation Ensemble Consistent with Experimental Scattering Data.

Multidomain proteins with long flexible linkers and full-length intrinsically disordered proteins (IDPs) are best defined as an ensemble of conformations rather than a single structure. Determining high-resolution ensemble structures of such proteins poses various challenges by using tools from experimental structural biophysics. Integrative approaches combining available low-resolution ensemble-averaged experimental data and in silico biomolecular reconstructions are now often used for the purpose. However, extensive Boltzmann weighted conformation sampling for large proteins, especially for ones where both the folded and disordered domains exist in the same polypeptide chain, remains a challenge. In this work, we present a 2-site per amino-acid resolution SOP-MULTI force field for simulating coarse-grained models of multidomain proteins. SOP-MULTI combines two well-established self-organized polymer models─: (i) SOP-SC models for folded systems and (ii) SOP-IDP for IDPs. For the SOP-MULTI, we introduce cross-interaction terms between the beads belonging to the folded and disordered regions to generate conformation ensembles for full-length multidomain proteins such as hnRNP A1, TDP-43, G3BP1, hGHR-ECD, TIA1, HIV-1 Gag, polyubiquitin, and FUS. When back-mapped to all-atom resolution, SOP-MULTI trajectories faithfully recapitulate the scattering data over the range of the reciprocal space. We also show that individual folded domains preserve native contacts with respect to solved folded structures, and root-mean-square fluctuations of residues in folded domains match those obtained from all-atom molecular dynamics simulation trajectories of the same folded systems. SOP-MULTI force field is made available as a LAMMPS-compatible user package along with setup codes for generating the required files for any full-length protein with folded and disordered regions.

Features of the change in the thermal coefficient of electrical resistance upon heating electrically conductive composites of crystallizable polyolefins with carbon black

Objectives. To investigate electrically conductive polymer composite materials (EPCMs) based on crystallizable polyolefins and electrically conductive carbon black for the production of self-regulating heaters; to study the mechanism of the occurrence of positive and negative temperature coefficients (PTC and NTC) upon heating such composites.Methods. A comprehensive study of the structure and properties of crystallizable EPCMs with electrically conductive technical carbon was carried out. In order to measure the electrical characteristics of the composites, they were compacted into plates to model polymer heaters. Contact electrodes made of an ungreased brass mesh were embedded in their ends. The temperature dependencies of the electrical characteristics of the samples were investigated in a modified thermal chamber of an FWV 633.10 Vicat softening temperature meter. The change in the degree of crystallinity was analyzed by means of differential scanning calorimetry with a NETZSCH DSC 204 F1 Phoenix calorimeter. The dilatometric and rheological characteristics of the samples were studied using an IIRT-AM melt flow index tester.Results. It was determined that the self-regulation ability (an abnormally high positive thermal coefficient of electrical resistance) of selfregulating heaters made of composites of crystallizable polyolefins with electrically conductive technical carbon cannot be explained by the thermal expansion of EPCMs alone. It was shown that in crystallizable polyolefin-based EPCMs, the inversion of the thermal coefficients of electrical resistance (transition from PTC to NTC) is associated with a change in the aggregate state of EPCMs and the beginning of its transition to a viscous-flow state. A mechanism involving a sharp increase in the electrical resistance of self-regulating crystallizable polyolefin-based composite with electrically conductive technical carbon was proposed and substantiated. This mechanism takes into account the additional shear deformation effect produced on the crystalline phase of the EPCM by numerous expanding melt microvolumes formed at the early stages of the melting process with a minimum change in the degree of crystallinity.

Contrasting behavior of urea in strengthening and weakening confinement effects on polymer collapse.

Biomolecules inhabit a crowded living cell that is packed with high concentrations of cosolutes and macromolecules that result in restricted, confined volumes for biomolecular dynamics. To understand the impact of crowding on the biomolecular structure, the combined effects of the cosolutes (such as urea) and confinement need to be accounted for. This study involves examining these effects on the collapse equilibria of three model 32-mer polymers, which are simplified models of hydrophobic, charge-neutral, and uncharged hydrophilic polymers, using molecular dynamics simulations. The introduction of confinement promotes the collapse of all three polymers. Interestingly, addition of urea weakens the collapse of the confined hydrophobic polymer, leading to non-additive effects, whereas for the hydrophilic polymers, urea enhances the confinement effects by enhancing polymer collapse (or decreasing the polymer unfolding), thereby exhibiting an additive effect. The unfavorable dehydration energy opposes collapse in the confined hydrophobic and charge-neutral polymers under the influence of urea. However, the collapse is driven mainly by the favorable change in polymer-solvent entropy. The confined hydrophilic polymer, which tends to unfold in bulk water, is seen to have reduced unfolding in the presence of urea due to the stabilizing of the collapsed state by urea via cohesive bridging interactions. Therefore, there is a complex balance of competing factors, such as polymer chemistry and polymer-water and polymer-cosolute interactions, beyond volume exclusion effects, which determine the collapse equilibria under confinement. The results have implications to understand the altering of the free energy landscape of proteins in the confined living cell environment.

Analytic solution for the linear rheology of living polymers

It is often said that well-entangled and fast-breaking living polymers (such as wormlike micelles) exhibit a single relaxation time in their reptation dynamics, but the full story is somewhat more complicated. Understanding departures from single-Maxwell behavior is crucial for fitting and interpreting experimental data, but in some limiting cases numerical methods for solving living polymer models can struggle to produce reliable predictions/interpretations. In this work, we develop an analytic solution for the shuffling model of living polymers. The analytic solution is a converging infinite series, and it converges fastest in the fast-breaking limit where other methods can struggle.

Lattice polymers near a permeable interface

Abstract We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on one side or by the application of a force to manipulate the polymer. Different combinations of these three effects give slightly different statistical mechanical behaviours. The canonical lattice model of polymers is the self-avoiding walk which we mainly study with Monte Carlo simulation to calculate the phase diagram and critical phenomena. For comparison, a solvable directed walk version is also defined and the phase diagrams are compared for each case. We find broad agreement between the two models, and most minor differences can be understood as due to the different entropic contributions. In the limit where the bulk solvent on one side is overwhelmingly preferred we see how the localisation transition transforms to the adsorption transition; the permeable interface becomes effectively an impermeable surface.

A microsphere-homogenized strain gradient elasticity model for polymers

A microsphere-homogenized strain gradient elasticity model for polymers

Molecular dynamics simulations of thermomechanical properties of silicone-modified phenolic polymer

The silicone-phenolic multicomponent polymers are typically employed as the matrix of fiber-reinforced nanocomposites developed for reentry vehicles due to their excellent thermal and mechanical properties. The thermomechanical properties of the silicone-phenolic multicomponent polymer system, which are greatly related to the processing and microstructures, were studied using molecular dynamics (MD) simulations combined with experiments. A multistep dynamic polymerization approach was utilized to form the crosslinked polymer model, which was also validated in terms of both microstructures and properties. The thermomechanical properties of the crosslinked polymer system were established as a function of crosslinking degree, component ratio, temperature, strain rate, and cooling rate, and the influence mechanisms of the processing parameters were revealed. The crosslinking degree can greatly influence the glass transition temperature and volumetric coefficient of thermal expansion, which is attributed to the constrained chain mobility. The crosslinking degree and the component ratio have a significant effect on the morphologies and vibrational density of states of the polymer system, respectively, which in turn affects the thermal conductivity. The failure mode during uniaxial tensile was investigated in terms of the atomic energy distribution through MD simulations. The elastic and plastic deformation stages are dominated by intermolecular non-bonding interactions, but less contributed by the bonding interactions. This work can guide the design of polymeric nanocomposites by establishing the relationship of processing-microstructure-thermomechanical properties.

A simplified load-slip model for composite FRP-to-concrete tie with anchors for lateral performance prediction of strengthened squat RCSWs

This study addresses the critical need to enhance the lateral performance of existing reinforced concrete shear walls (RCSWs) that have become vulnerable to lateral loads due to outdated design codes and seismic activities. The paper introduces a novel tri-linear constitutive model for composite fiber-reinforced polymer (FRP)-to-concrete ties to predict the lateral behavior of RCSWs subjected to lateral loads. A simplified strut-and-tie model (STM) was employed, integrating a novel tri-linear model for FRP-to-concrete ties with the bond-slip and anchorage effects. Non-linear pushover analysis was conducted to simulate the lateral performance of FRP-strengthened RCSWs. The conducted STM was validated through experimental and numerical data from existing studies to assess its accuracy. The tri-linear constitutive model effectively predicted the lateral load and displacement capacities of FRP-strengthened RCSWs, accurately simulating both diagonal shear and flexure failure modes. Moreover, this model is applicable to both cracked concrete substrates and full-scale walls, accommodating various types of FRP composites, and different anchoring configurations, offering a robust tool for the seismic assessment of existing structures. The model was also applied to multi-story buildings, proving robust in handling complex geometry and offering enhanced computational efficiency compared to finite element (FE) analysis. This study confirms the applicability of the proposed model for practical use in assessing and designing FRP-strengthened RCSWs, offering a faster alternative to complex finite element analysis without sacrificing accuracy.

Flow dichroism of DNA can be quantitatively predicted via coarse-grained molecular simulations

We demonstrate the use of multiscale polymer modeling to quantitatively predict DNA linear dichroism (LD) in shear flow. LD is the difference in absorption of light polarized along two perpendicular axes and has long been applied to study biopolymer structure and drug-biopolymer interactions. As LD is orientation dependent, the sample must be aligned in order to measure a signal. Shear flow via a Couette cell can generate the required orientation; however, it is challenging to separate the LD due to changes in polymer conformation from specific interactions, e.g., drug-biopolymer. In this study, we have applied a combination of Brownian dynamics and equilibrium Monte Carlo simulations to accurately predict polymer alignment, and hence flow LD, at modest computational cost. As the optical and conformational contributions to the LD can be explicitly separated, our findings allow for enhanced quantitative interpretation of LD spectra through the use of an in silico model to capture conformational changes. Our model requires no fitting and only five input parameters: the DNA contour length, persistence length, optical factor, solvent quality, and relaxation time, all of which have been well characterized in prior literature. The method is sufficiently general to apply to a wide range of biopolymers beyond DNA, and our findings could help guide the search for new pharmaceutical drug targets via flow LD.

Correlations between adhesion and molecular interactions at buried interfaces of model polymer systems and in commercial multilayer barrier films.

Sum frequency generation vibrational spectroscopy (SFG) was applied to characterize the interfacial adhesion chemistry at several buried polymer interfaces in both model systems and blown multilayer films. Anhydride/acid modified polyolefins are used as tie layers to bond dissimilar polymers in multilayer barrier structures. In these films, the interfacial reactions between the barrier polymers, such as ethylene vinyl alcohol (EVOH) or nylon, and the grafted anhydrides/acids provide covalent linkages that enhance adhesion. However, the bonding strengths vary for different polymer-tie layer combinations. Here, using SFG, we aim to provide a systematic study on four common polymer-tie interfaces, including EVOH/polypropylene-tie, EVOH/polyethylene-tie, nylon/polypropylene-tie, and nylon/polyethylene-tie, to understand how the adhesion chemistry varies and its impact on the measured adhesion. Our SFG studies suggest that adhesion enhancement is driven by a combination of reaction kinetics and the interfacial enrichment of the anhydride/acid, resulting in stronger adhesion in the case of nylon. This observation matches well with the higher adhesion observed in the nylon/tie systems in both lap shear and peel test measurements. In addition, in the polypropylene-tie systems, grafted oligomers due to chain scission may migrate to the interface, affecting the adhesion. These by-products can react or interfere with the barrier-tie chemistry, resulting in reduced adhesion strength in the polypropylene-tie system.

Modeling the 3D Spatiotemporal Organization of Chromatin Replication

We propose a polymer model to investigate the dynamics of chromatin replication in three dimensions (PolyRep). Our results indicate that replication complexes, the replisomes, may self-assemble during the process and replicate chromatin by extruding it (immobile replisome) or by moving along the template filament (tracking replisome), reconciling previous discordant experimental evidence in favour of either scenario. Importantly, the emergence of one of the two morphologies depends in a major way on the replication origin distribution as well as on the presence of nonspecific interactions between unreplicated chromatin and firing factors—polymerases and other components of the replisome. Nonspecific interactions also appear instrumental to creating clusters of factors and replication forks, structures akin to the replication foci observed in mammalian cells . PolyRep simulations predict different mechanisms for foci evolution, including unanticipated loop-mediated fusion dynamics. We suggest that cluster formation, which our model suggests to be a generic feature of chromatin replication, provides a hitherto underappreciated but robust pathway to avoid stalled or faulty forks, which would otherwise diminish the efficiency of the replication process. Published by the American Physical Society 2024

The Logistic Function in Glass Transition Models of Amorphous Polymers: A Theoretical Framework for Isobaric Cooling Processes

AbstractStudying the macroscopic‐phenomenological behavior of amorphous polymers at glass transition is often subject to limitations because the ordinary differential equations that describe the material behavior require numerical solution. To avoid these limitations, ad‐hoc‐formulated models of the glass transition have been proposed. However, their scope of application is expected to be limited due to insufficient theoretical foundation. This work establishes a theoretical framework for models that use the logistic function to approximate the macroscopic‐phenomenological behavior of amorphous polymers at glass transition. For this purpose, an exactly‐solvable Riccati equation is derived within thermodynamics with internal state variables. A closed‐form expression in terms of mathematical functions for the temperature derivative of a single internal state variable is the result. This closed‐form expression contains the logistic function thus featuring a continuous transition region centered around a pressure and cooling‐rate dependent transition temperature. Based on comparison of existing models with the exact solution derived from the Riccati equation, generalized models that approximate the thermal expansion coefficient and heat capacity at glass transition are proposed. This work thus demonstrates the validity of the logistic function in glass transition models of amorphous polymers and provides suggestions as to how existing models can be extended in their applicability.

The exchange dynamics of biomolecular condensates.

A hallmark of biomolecular condensates formed via liquid-liquid phase separation is that they dynamically exchange material with their surroundings, and this process can be crucial to condensate function. Intuitively, the rate of exchange can be limited by the flux from the dilute phase or by the mixing speed in the dense phase. Surprisingly, a recent experiment suggests that exchange can also be limited by the dynamics at the droplet interface, implying the existence of an 'interface resistance'. Here, we first derive an analytical expression for the timescale of condensate material exchange, which clearly conveys the physical factors controlling exchange dynamics. We then utilize sticker-spacer polymer models to show that interface resistance can arise when incident molecules transiently touch the interface without entering the dense phase, i.e., the molecules 'bounce' from the interface. Our work provides insight into condensate exchange dynamics, with implications for both natural and synthetic systems.

The exchange dynamics of biomolecular condensates

A hallmark of biomolecular condensates formed via liquid-liquid phase separation is that they dynamically exchange material with their surroundings, and this process can be crucial to condensate function. Intuitively, the rate of exchange can be limited by the flux from the dilute phase or by the mixing speed in the dense phase. Surprisingly, a recent experiment suggests that exchange can also be limited by the dynamics at the droplet interface, implying the existence of an ‘interface resistance’. Here, we first derive an analytical expression for the timescale of condensate material exchange, which clearly conveys the physical factors controlling exchange dynamics. We then utilize sticker-spacer polymer models to show that interface resistance can arise when incident molecules transiently touch the interface without entering the dense phase, i.e., the molecules ‘bounce’ from the interface. Our work provides insight into condensate exchange dynamics, with implications for both natural and synthetic systems.

Termination Kinetics of N‐Vinyl Formamide Radical Polymerization in Aqueous Solution

AbstractTermination kinetics of radical polymerization of N‐vinyl formamide (NVF) in aqueous solution has been measured via SP–PLP–NIR, i.e., single pulse (SP) initiation of pulsed laser polymerization (PLP) in conjunction with microsecond time‐resolved near‐infrared (NIR) detection of monomer concentration. Experiments are performed at initial NVF weight fractions from 0.20 up to bulk NVF, at monomer conversions up to 40%, and at temperatures from 40 to 70 °C as well as pressures from 500 to 2500 bar. Applying high pressure improves signal‐to‐noise quality. Data obtained upon pressure variation allow for extrapolation toward ambient pressure. The primary quantity from SP–PLP–NIR is kp/<kt>, i.e., the ratio of propagation rate coefficient, kp, to apparent chain‐length‐averaged termination rate coefficient, <kt>. With kp being available from literature, kp/<kt> yields <kt>. This quantity is relevant for modeling polymerization rate and polymer properties. Termination in the initial polymerization period turns out to be controlled by segmental diffusion and, at higher degrees of monomer conversion up to 40%, by translational diffusion.

Solvable toy model of negative energetic elasticity.

Recent experiments have established negative energetic elasticity, the negative contribution of energy to the elastic modulus, as a universal property of polymer gels. To reveal the microscopic origin of this phenomenon, Shirai and Sakumichi investigated a polymer model on a cubic lattice with the energy effect from the solvent in finite-size calculations [Phys. Rev. Lett. 130, 148101 (2023)0031-900710.1103/PhysRevLett.130.148101]. Motivated by this work, we provide a simple platform to study negative energetic elasticity by considering a one-dimensional random walk with the energy effect. This model can be mapped onto the classical Ising chain, leading to an exact form of the free energy in the thermodynamic or continuous limit. Our analytical results are qualitatively consistent with Shirai and Sakumichi's results. Our model serves as a fundamental benchmark for studying the elasticity of polymer chains.