Model Polymer Research Articles

Weak noise theory of the O'Connell-Yor polymer as an integrable discretization of the nonlinear Schrödinger equation.

We investigate and solve the weak noise theory for the semidiscrete O'Connell-Yor directed polymer. In the large deviation regime, the most probable evolution of the partition function obeys a classical nonlinear system which is a nonstandard discretization of the nonlinear Schrödinger equationwith mixed initial-final conditions. We show that this system is integrable and find its general solution through an inverse scattering method and a non-standard Fredholm determinant framework that we develop. This allows us to obtain the large deviation rate function of the free energy of the polymer model from its conserved quantities and to study its convergence to the large deviations of the Kardar-Parisi-Zhang equation. Our model also degenerates to the classical Toda chain, which further substantiates the applicability of our Fredholm framework.

Construction and parameter calibration of potato double‐layer flexible bonding model based on discrete‐element method

AbstractThe current discrete‐element simulation models for potatoes are multisphere polymer models derived from the Hertz–Mindlin (no slip) contact model in the discrete‐element simulation software (EDEM). These models oversimplify by considering potato peel and flesh as sharing identical mechanical properties within the structure. This oversimplification impedes a thorough investigation of the characteristics and mechanisms underlying potato peel‐breaking damage during mechanized harvesting, making in‐depth exploration challenging through simulation experiments. Consequently, this study conducted laboratory tests to determine the water content of potato peel and flesh, as well as the friction coefficients and collision recovery coefficients for various material pairs: flesh–steel, peel–steel, peel–peel, peel–flesh, and flesh–flesh. Subsequently, based on these findings, a double‐layer flexible bonding model for potato samples and whole stems under specific water content conditions was developed using EDEM software. The bonding parameters of the double‐layer flexible model for potato samples were refined through virtual shear calibration tests, leading to the identification of the optimal parameter combination: Flesh particle–flesh particle normal stiffness(tangential stiffness) per unit area X1 = 4.39 × 108 N/m3, peel particle–flesh particle normal stiffness(shear stiffness) per unit area X3 = 1.81 × 109 N/m3, peel particle–peel particle shear stiffness per unit area X6 = 1.99 × 109 N/m3, peel particle–peel particle critical normal stress X7 = 2.06 × 109 Pa. To validate the accuracy of the bonding parameters, shear and compression validation tests were conducted on entire potato stems. Comparison of the validation results from laboratory tests and simulation tests revealed an average relative error of e = 3.25%, signifying the feasibility of the constructed double‐layer flexible bond model for potatoes. This model meets the requirements for studying the characteristics and mechanisms of peel‐breaking damage in potatoes.Practical ApplicationsThe paper introduces a novel double‐layer flexible bonding model for potatoes using the discrete‐element method (DEM), which accurately simulates the mechanical properties and damage characteristics of potato peels and flesh. This research has significant practical applications in agricultural machinery design, improving the efficiency and reducing the damage during mechanical harvesting. By providing a more realistic simulation of potato behavior under mechanical stress, it can guide the development of gentler handling equipment, reduce waste, and enhance the quality of harvested potatoes. This contributes to optimizing the post‐harvest process, ensuring better storage, and extending the marketable life of potatoes.

A thermo-mechanically coupled constitutive model for semi-crystalline polymers at finite strains: Mechanical and thermal characterization of polyamide 6 blends

In the field of material modeling, thermoplastic polymers are often studied because of their complex material behavior and their prevalence in industry applications due to their low cost and wide range of applications. Nowadays, where reusability becomes more and more important, materials which can undergo reversible thermomechanical deformations are appealing for, e.g., the construction of car body components. To predict such complex forming processes with multiple influencing factors, such as temperature, strain rate or underlying material morphology, model formulations are needed that account for these influences simultaneously and are validated against experimental data. Unfortunately, up to now only a few contributions are available which consider all these phenomena. In addition, the range of process parameters considered is often narrow due to the experimental effort required for testing. This usually results in limited predictive capabilities of the model. To overcome these limitations, in this work, a thermo-mechanically coupled material model is developed that accounts for the underlying morphology in terms of the degree of crystallinity (DOC). The model formulation is derived in a thermodynamically consistent manner, incorporating coupled nonlinear visco-elastic and elasto-plastic material behavior at finite strains. To characterize and further validate the model, mechanical as well as thermal experiments are conducted for polyamide 6 (PA6). Here, a blending strategy of PA6 together with an amorphous co-polymer is introduced during specimen production to achieve a wider range of stable DOCs(approximately 15%). The model formulation is successfully applied to experimental results and its predictions are in good agreement with experimental observations.

Universal properties of branched copolymers in dilute solutions

We analyze the universal conformational properties of complex copolymer macromolecules, based on two topologies: the rosette structure containing fc linear branches and fr closed loops grafted to the central core, and the symmetric pom-pom structure, consisting of a backbone linear chain terminated by two branching points with functionalities f. We assume that the constituent strands (branches) of these structures can be of two different chemical species a and b. Depending on the solvent conditions, the inter- or intrachain interactions of some links may vanish, which corresponds to Θ-state of the corresponding polymer species. Applying both the analytical approach within the frames of direct polymer renormalization and numerical simulations based on the lattice model of polymer, we evaluated the set of parameters characterizing the size properties of constituent parts of two complex topologies and estimated quantitatively the impact of interactions between constituent parts on these size characteristics.

Mitotic chromosomes are self-entangled and disentangle through a topoisomerase-II-dependent two-stage exit from mitosis

The topological state of chromosomes determines their mechanical properties, dynamics, and function. Recent work indicated that interphase chromosomes are largely free of entanglements. Here, we use Hi-C, polymer simulations, and multi-contact 3C and find that, by contrast, mitotic chromosomes are self-entangled. We explore how a mitotic self-entangled state is converted into an unentangled interphase state during mitotic exit. Most mitotic entanglements are removed during anaphase/telophase, with remaining ones removed during early G1, in a topoisomerase-II-dependent process. Polymer models suggest a two-stage disentanglement pathway: first, decondensation of mitotic chromosomes with remaining condensin loops produces entropic forces that bias topoisomerase II activity toward decatenation. At the second stage, the loops are released, and the formation of new entanglements is prevented by lower topoisomerase II activity, allowing the establishment of unentangled and territorial G1 chromosomes. When mitotic entanglements are not removed in experiments and models, a normal interphase state cannot be acquired.

Footprints of loop extrusion in statistics of intra-chromosomal distances: An analytically solvable model.

Active loop extrusion-the process of formation of dynamically growing chromatin loops due to the motor activity of DNA-binding protein complexes-is a firmly established mechanism responsible for chromatin spatial organization at different stages of a cell cycle in eukaryotes and bacteria. The theoretical insight into the effect of loop extrusion on the experimentally measured statistics of chromatin conformation can be gained with an appropriately chosen polymer model. Here, we consider the simplest analytically solvable model of an interphase chromosome, which is treated as an ideal chain with disorder of sufficiently sparse random loops whose conformations are sampled from the equilibrium ensemble. This framework allows us to arrive at the closed-form analytical expression for the mean-squared distance between pairs of genomic loci, which is valid beyond the one-loop approximation in diagrammatic representation. In addition, we analyze the loop-induced deviation of chain conformations from the Gaussian statistics by calculating kurtosis of probability density of the pairwise separation vector. The presented results suggest the possible ways of estimating the characteristics of the loop extrusion process based on the experimental data on the scale-dependent statistics of intra-chromosomal pair-wise distances.

Stochastic kinetic theory applied to coarse-grained polymer model.

A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison with explicit Langevin equation simulations under conditions with analytical solutions. The polymers are modeled as Hookean dumbbells in one dimension, without including hydrodynamic interactions and polymer-polymer interactions. Stochastic moment equations are derived from full field theory. The accuracy of the field theory and moment equations is quantified using autocorrelation functions. The full field theory is only accurate for a large number of polymers due to keeping track of rare occurrences of polymers with a large stretch. The moment equations do not have this error because they do not explicitly track these configurations. The accuracy of both methods depends on the spatial degree of discretization. The timescale of decorrelation over length scales bigger than the spatial discretization is accurate, while there is an error over the scale of single mesh points.

A viscoelastic-viscoplastic thermo-mechanical model for polymers under hypervelocity impact

In hypervelocity impact (HVI) events, the thermo-mechanical behaviors of polymer materials are significantly influenced by viscous effects, thereby affecting energy absorption and shielding performance. A viscoelastic-viscoplastic thermo-mechanical model was newly developed to simulate the mechanical behavior and heat generation of polymer materials under HVI. The viscoelastic-viscoplastic constitutive equation and the Mie-Grüneisen equation of state (EOS) were applied to describe the deviatoric deformation and strongly nonlinear volumetric compression behavior. Moreover, the heat generation was calculated considering contributions from plastic work, irreversible entropy increase, and viscous dissipation which was not considered in the previous HVI numerical model. The temperature increase was calculated through adopting the apparent heat capacity method. The model was coded and seamlessly integrated into the LS-DYNA program through a user-defined material subroutine. Additionally, the FEM-SPH adaptive method was adopted to accurately simulate the fragmentation which always accompanies in the HVI event, wherein the finite element method (FEM) handles contact and deformation behavior, while the smoothed particle hydrodynamics (SPH) method addresses the formation and motion of debris clouds. Ultra-high molecular weight polyethylene (UHMWPE) was selected as the sample material, and its model parameters were calibrated based on the data from quasi-static and dynamic experiments. Good effectiveness and accuracy have been validated through comparing the simulation results and experimental results from the literatures. A noteworthy feature is that the model has the capability to capture the temperature distribution and various energy components induced by the impact, including viscous dissipation, plastic work, and residual energy. Finally, a comparison was made to explore the influence of viscosity on the impact response of UHMWPE plates. The analysis results indicate that material viscosity significantly improves energy absorption capabilities and overall shielding performance.

Crystallization of Poly(l-lactic acid) on Water Surfaces via Controlled Solvent Evaporation and Langmuir-Blodgett Films.

Solvent evaporation is one of the most fundamental processes in soft matter. Structures formed via solvent evaporation are often complex yet tunable via the competition between solute diffusion and solvent evaporation time scales. This work concerns the polymer evaporative crystallization on the water surface (ECWS). The dynamic and two-dimensional (2D) nature of the water surface offers a unique way to control the crystallization pathway of polymeric materials. Using poly(l-lactic acid) (PLLA) as the model polymer, we demonstrate that both one-dimensional (1D) crystalline filaments and two-dimensional (2D) lamellae are formed via ECWS, in stark contrast to the 2D Langmuir-Blodgett monolayer systems as well as polymer solution crystallization. Results show that this filament-lamella biphasic structure is tunable via chemical structures such as molecular weight and processing conditions such as temperature and evaporation rate.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties.

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

A phase-transition model of reprocessible thermadapt shape memory polymer

A new type of thermadapt shape memory polymer (SMP) has not only the processability of thermoplastic SMP, but also the excellent shape fixation of thermosetting SMP. To enhance the application of this thermadapt SMP within industrial sectors, a comprehensive constitutive model based on phase transition is being proposed as an indicative descriptor of the semi-crystalline thermadapt SMP’s salient features, predominantly related to its two-way shape memory effect (SME) and thermal reprocessability. The concept of cooling elongation is also introduced in this model for modeling the two-way SME during the crystallization process. The molecular mechanism of chain-packing has been studied and used to establish phenomenological formulas. In addition, to systematically assess the temperature-time dependence of the crystallization process, the Avrami equation is improved by incorporating the distribution of polymer chain segments. This strategy provides a detailed investigation into the evolving pattern of the crystallization process in response to various temperature and time conditions. Compared with the experimental results, it is found that our model can well capture mechanical behavior in multiple shape memory cycles, including the two-way SME and reshaping process caused by bond exchange reaction. Furthermore, the potential application of SMP in smart mandrels is explored because the cooling elongation feature is able to endow it with self-adaptive expansion ability.

The Effect of Thermal Residual Stress on the Stress State in a Short-Fiber Reinforced Thermoplastic

Upon their cooling and solidification, significant thermal residual stresses can develop in short-fiber reinforced thermoplastics due to the mismatch in coefficient of thermal expansion between fiber and matrix. In this study we set out to investigate this effect numerically. The build-up of thermal residual stresses is modeled by expanding a well-established constitutive model, the Eindhoven glassy polymer (EGP) model, with thermal expansion. The experimentally measured thermal residual stresses can be described using an effective glass-transition temperature and a constant coefficient of thermal expansion without the need for complex equilibrium kinetics associated with the glass transition itself. Subsequently, the influence of thermal residual stress on the deformation behavior for a short-fiber reinforced thermoplastic is studied employing multi-fiber representative volume elements (RVEs) for different fiber-weight fractions. The micromechanical models are evaluated on the importance of thermal residual stresses on the local and nominal stress state. From these analyses it can be concluded that the thermal residual stresses should be accounted for when assessing the quantitative local stress state and are therefore essential when local mechanisms are studied. In contrast, thermal residual stresses are not required to capture the nominal transient stress–strain response.

Analysis of a Dilute Polymer Model with a Time-Fractional Derivative

Analysis of a Dilute Polymer Model with a Time-Fractional Derivative

Suitability of Polymers for 3D-Printing Laboratory Models for Shaking Table Experiments: Discussion and Indications.

This paper presents a comprehensive assessment of the suitability of seven commercially available polymers for crafting laboratory models designed for dynamic shaking-table tests using 3D-printing technology. The objective was to determine whether 3D-printed polymer models are effective for dynamic assessments of structures. The polymers underwent experimental investigations to assess their material properties, i.e., the elastic modulus, the mass density, and the limit of linear-elastic behaviour. The following methodology was applied to obtain the correct values of elasticity moduli and yield points of the polymers: (1) the uniaxial tensile test, (2) the compression test, and (3) the three-point loading test. The filament density was determined as the ratio of sample mass to its volume. The results indicate substantial variations in stiffness, density, and elasticity limits among them. For the similarity analysis, an existing reinforced concrete chimney 120 m high was chosen as a prototype. A geometric similarity scale of 1:120 for a laboratory mock-up was adopted, and a numerical model of the mock-up was created. The similarity scales were calculated for mock-ups made of each filament. Based on these scales, numerical calculations of natural frequencies and dynamic performance under a strong earthquake were carried out for models made of different polymers. Assessment of the polymers' suitability for laboratory models revealed positive outcomes. The agreement between field experiments, shaking-table tests, and numerical predictions in terms of natural frequencies was observed. Maximum stresses resulting from the earthquake indicated the satisfactory performance of the model below the linear-elastic limit. Despite differences in material properties, the selected polymers were deemed suitable for 3D-printing models for shaking-table tests. However, the discussion raised some important considerations. The upper frequency limit of the shaking-table imposes restrictions on the number of natural frequencies that can be determined. Numerical assessments of natural frequencies are recommended to prevent underestimation and to assess the feasibility of their determination. Additionally, resonance during natural frequency determination may lead to exceeding the linear-elastic limit, affecting filament properties, and making the similarity criteria invalid. Practically, this research contributes insights for planning shaking-table tests, aiding in selecting the most suitable filament and highlighting crucial considerations to ensure reliable and accurate dynamic assessments.

The thermo-optical coefficient as an alternative probe for the structural arrest of polymeric glass formers

The most important, yet independent susceptibilities to characterize the canonical glass transition include the thermal expansion, the specific heat and the shear modulus. At the glass transition, all these susceptibilities show a step-like behaviour as a function of temperature. However, in principle, different susceptibilities provide different perspectives on the glass transition. Due to the effect of sample history and considerable kinetic influences on the thermal glass transition behaviour, the best way to evaluate these different perspectives is to investigate them simultaneously. In this publication, different perspectives on the dynamical freezing process are obtained by a single experimental method: Temperature-modulated optical refractometry (TMOR). TMOR is used to simultaneously investigate the dynamic thermal expansion and, indirectly, the shear viscosity of a model polymer, both contributing to the thermo-optical coefficient. It will be discussed how this thermo-optical property couples to the structural arrest designated as one of the characteristics of the solidification process of polymers.

Blood compatibility of poly(propylene glycol diester) and its water structure observed by differential scanning calorimetry and 2H-nuclear magnetic resonance spectroscopy

Recently, we applied solution 2H-nuclear magnetic resonance spectroscopy (2H NMR) to analyze the water (deuterium oxide, D2O) structure in several biopolymers at ambient temperature. We established that polymers with good blood compatibility (i.e. poly(2-methoxyethyl acrylate) (PMEA)) have water observed at high magnetic fields (upfield) compared with bulk water. Polymers containing poly(propylene glycol) (PPG) or poly(propylene oxide) (PPO) exhibit good compatibility; however, the reason for this remains unclear. In addition, reports on the blood compatibility of PPO/PPG are limited. Therefore, PPG diester (PPGest) was prepared as a model polymer, and its blood compatibility and water structure were investigated. PPGest exhibited excellent blood compatibility. The water in PPGest was observed upfield by 2H NMR, and it was defined as non-freezing water via differential scanning calorimetry. Based on these observations, the relationship between the blood compatibility and water structure of PPGest is discussed by comparing with those of PMEA, and the reason for the good performance of PPG/PPO-based polymers is discussed.

Are Hansen solubility parameters relevant in predicting the post-treatment effect on polyamide-based TFC membranes?

This study investigates the impact of solvent post-treatment on polyamide-based thin film composite (TFC) membranes, specifically examining the effect on commercial nanofiltration (NF) and reverse osmosis (RO) membranes. Na2SO4 rejection and increase in pure water permeance (PWP) were considered as the output parameters. The disparity in Hansen solubility parameters (HSP) between the post-treatment solution and the polyamide layer of the TFC membrane, denoted by Ra, is well adapted to understand the enhancement in water permeance through the membranes upon treatment. Aqueous solutions of dimethylformamide with a Ra value of 4, acetonitrile with a Ra value of 8.3, and ethanol with a Ra value of 12.7 were used as the post-treatment solutions. Our experimental design, based on the Box-Behnken design of Response Surface Methodology, incorporates variables such as the concentration of the solvent in the solution (% v/v), Ra value, and treatment time (s). Our findings demonstrate that the effect of post-treatment on the TFC membranes is not governed by the Ra value. Notably, while the post-treatment with the aqueous solution of acetonitrile, 80% v/v for 30 s, had considerable effects on NF membranes (124.5% enhancement in PWP; reduction of 3.5% in Na2SO4 rejection), its impact on RO membranes was negligible. Several factors explain this discrepancy, including the limitations of the HSP model for composite polymers, the inaccuracy of the PWP or salt rejection as a swelling indicator, variations in the HSP values of the polyamide layers for different membranes, and possible modifications in the interface between the support membrane and the polyamide layer. In summary, our study provides insights into the complex interactions between solvents and composite membranes, indicating that HSP alone is not a decisive factor in predicting post-treatment effects on polyamide-based TFC membranes.

Solution of steady state in the model polymer system with rupture and rebinding

In this paper, we study the steady state attained in our model polymer system that attempts to explain the relative motion between soft rubbing surfaces at the single polymer level. We generalize our one-dimensional model [Borah et al, 2016 Soft Matter 12 4406] by including the rebinding of interconnecting bonds between a flexible transducer (bead spring polymer) and a rigid fixed plate. The interconnecting bonds described as harmonic springs rupture and rebind stochastically when a constant force pulls the flexible transducer. We obtain a distinct steady state in stochastic simulations of the model when the bead positions and the bond states (closed or open) are independent of time, analogous to creep states in frictional systems and rupture termination states in earthquakes. The simulation results of the stochastic model for specific parameter sets agree with the numerical solution to the mean-field equations developed for analytical tractability. We develop an analytical solution for the steady state within the homotopy analysis method, which converges and agrees well with the numerical results.

A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution.

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.

An empirical predictive model for determining the aqueous solubility of BCS class IV drugs in amorphous solid dispersions

Context Determining solubility of drugs is laborious and time-consuming process that may not yield meaningful results. Amorphous solid dispersion (ASD) is a widely used solubility enhancement technique. Predictive models could streamline this process and accelerate the development of oral drugs with improved aqueous solubilities. Objective This study aimed to develop a predictive model to estimate the solubility of a compound from the ASDs in polymer matrices. Methods ASDs of model drugs (acetazolamide, chlorothiazide, furosemide, hydrochlorothiazide, sulfamethoxazole) with model polymers (PVP, PVPVA, HPMC E5, Soluplus) and a surfactant (TPGS) were prepared using hotmelt process. The prepared ASDs were characterized using DSC, FTIR, and XRD. The aqueous solubility of the model drugs was determined using shake-flask method. Multiple linear regression was used to develop a predictive model to determine aqueous solubility using the molecular descriptors of the drug and polymer as predictor variables. The model was validated using Leave-One-Out Cross-Validation. Results The ASDs’ drug components were identified as amorphous via DSC and XRD Studies. There were no significant chemical interactions between the model drugs and the polymers based on FTIR studies. The ASDs showed a significant (p < 0.05) improvement in solubility, ranging from a 3-fold to 118-fold, compared with the pure drug. The developed empirical model predicted the solubility of the model drugs from the ASDs containing model polymer matrices with an accuracy greater than 80%. Conclusion The developed empirical model demonstrated robustness and predicted the aqueous solubility of model drugs from the ASDs of model polymer matrices with an accuracy greater than 80%.