Polymer Diffusion Research Articles

Dynamics of Polymer Films on Polymer-Grafted Substrates: A Molecular Dynamics Simulation.

For substrate-supported polymer films, the tails of adsorbed chains are generally assumed to play important roles in the propagation of the substrate's effect inside polymer films. The effects of the grafting density and the rigidity of substrate-grafted polymers, the simplest model for the adsorbed tails, on the diffusivity of film polymers are investigated by performing molecular dynamics simulations. An optimal grafting density σo, around the critical grafting density for the transition from "mushroom" to "brush", is found with the most pronounced suppression of diffusivity on the film polymers; i.e., the penetration of the film polymers into the grafting layer reaches the maximum. However, at high grafting density, the crowded and vertically stretched brush excludes the coil-like film polymers, and the suppression is thus reduced. At σo, with an increase in the rigidity of the grafted polymers, the suppression is increased quickly at low rigidity but slowly at high rigidity. The dynamic suppression is attributed to the combination of the conformation change from stretching at low rigidity to tilted orientation at high rigidity and decelerated mobility induced by the rigidity. The stretching conformation enhances, whereas the tilted conformation weakens the interpenetration between the grafted polymers and the film polymers. Our results reflect the importance of both conformational variation and interchain interaction in the interface region.

Rigorous Models for Vapor Diffusion in Polymers with Immobilization and Chemical Potential Gradients.

Two key phenomena─immobilization and concentration-dependent mixing free energies─simultaneously alter the sorption thermodynamics and diffusion of vapors in materials. This interrelation is leveraged to fit a unified model simultaneously capturing both sorption dynamics and the equilibrium isotherms. This transport model incorporates quasi-equilibrated immobilization reactions and considers Fick's law rigorously in terms of chemical potential gradients rather than concentration gradients. Five material case studies are discussed with varying characteristics, including fillers that provide sites for surface sorption, pores for capillary condensation, and apparent clustering or pooling at high vapor concentrations. Each case study illustrates that intrinsic diffusivity is constant, while the effective diffusivity changes predictably because of immobilization or changing free energies of mixing.

Gas permeability, diffusivity, and solubility in polymers: Simulation-experiment data fusion and multi-task machine learning

Machine learning (ML) models for predicting gas permeability through polymers have traditionally relied on experimental data. While these models exhibit robustness within familiar chemical domains, reliability wanes when applied to new spaces. To address this challenge, we present a multi-tiered multi-task learning framework empowered with advanced machine-crafted polymer fingerprinting algorithms and data fusion techniques. This framework combines scarce “high-fidelity” experimental data with abundant diverse “low-fidelity” simulation or synthetic data, resulting in predictive models that display a high level of generalizability across novel chemical spaces. Additionally, this multi-task scheme capitalizes on known physics and interrelated properties, such as gas diffusivity and solubility, both of which are closely tied to permeability. By amalgamating high throughput generated simulation data with available experimental data for gas permeability, diffusivity, and solubility for various gases, we construct multi-task deep learning models. These models can simultaneously predict all three properties for all gases under consideration, with markedly enhanced predictive accuracy, particularly compared to traditional models reliant solely on experimental data for a singular property. This strategy underscores the potential of coupling high-throughput classical simulations with data fusion methodologies to yield state-of-the-art property predictors, especially when experimental data for targeted properties is scarce.

Understanding the influence of sodium chloride concentration on ion diffusion in charged polymers

Previous observations made on sulfonated polysulfones equilibrated with solutions of increasing salinity, where salt diffusion coefficients increase concurrently with reductions in water content driven by osmotic de-swelling, are currently unexplained. To further explain the molecular underpinnings of these observations, we characterized the influence of external salt solution concentration on the average salt and ion diffusion properties of two sulfonated polymers: a model cross-linked material (XLAMPS) and a series of sulfonated polysulfones (HQ:BP – XX). Analysis of the average salt and co- and counter-ion diffusion coefficients in these polymers suggest that the increase in charge screening (of electrostatic interactions between anionic sulfonate groups and co-ions) that occurs with increasing salinity affects the salt diffusion coefficients of sulfonated polysulfone in a manner that is different from what would be expected based on changes in water content alone and from what was observed for XLAMPS. Free volume theory describes the influence of these electrostatic effects on salt diffusion using a parameter related to the characteristic free volume element size necessary for diffusion. The results and analysis suggest that charge screening reduces the characteristic free volume element size necessary for diffusion in sulfonated polysulfone, which provides an explanation for the observed increase in average salt diffusion coefficients with increased salinity.

Charge Redistribution in High-Entropy Perovskite Oxide Porous Nanotubes Boosts Nitrate Electroreduction to Ammonia.

High-entropy perovskite oxides are promising materials in the field of electrocatalysis due to their advantages such as large spatial composition regulation, entropy effects, and tunable material properties. However, the preparation of high-entropy perovskite oxides with stable and controllable structures still remains challenging. Herein, we fabricated a series of high-entropy perovskite oxide porous nanotubes (PNTs) by electrospinning as efficient electrocatalysts for the nitrate reduction reaction (NO3RR). We further revealed that the different diffusion and decomposition behaviors of metal ions and polymers during the calcination process are the key to the formation of high-entropy perovskite oxide PNTs. Especially, LaSrNiCoMnFeCuO3 PNTs show excellent performance of the NO3RR, achieving the maximum NH3 Faradaic efficiency of almost 100%, yield rate of 1657.5 μg h-1 mgcat.-1, and durable stability after successive cycling, being one of the best electrocatalysts for the NO3RR. The mechanism studies show that the charge redistribution induced by the multisite synergistic effect and abundant unsaturated sites in the high-entropy perovskite oxide PNTs favors the adsorption of NO3- and key intermediates and reduces the catalytic energy barrier, thus further achieving high NO3- conversion efficiency.

Interlayer enhancement of 3D printed CF/PLA composites via localized microwave welding and annealing-induced crystallization

Interlayer defects and insufficient diffusion are detrimental to the structural integrity of 3D printed composites. This study introduces a facile approach to enhance the interlayer adhesion and structural integrity of 3D printed carbon fiber/polylactic acid (CF/PLA) composites, utilizing graphene-coated CF/PLA filaments for localized microwave welding and annealing-induced crystallization. This method promotes localized PLA melting at the interlayer interfaces, facilitating polymer diffusion and transcrystallization, which are crucial for effective interlayer repair and enhancement. The unique microwave dissipation properties of graphene ensure selective heating at the interlayer interfaces without largely affecting the intralayer CF, which is crucial for maintaining the overall structural integrity. Combining microwave welding with post-annealing treatment promotes transcrystalline growth at interlayer interfaces, which results in a 26.4 % increase in 90° tensile strength of the 3D printed CF/PLA composites, demonstrating the effectiveness of our approach. These findings provide new insights into strategies for enhancing the mechanical properties of 3D printed carbon fiber thermoplastic composites through precise interlayer enhancement and interfacial defect repair.

Enhanced diffusion and universal Rouse-like scaling of an active polymer in poor solvent

Enhanced diffusion and universal Rouse-like scaling of an active polymer in poor solvent

Structural Color Out of the Blue: A Quantitative Framework for the Self-Assembly Kinetics of Cholesteric Cellulosic Mesophases.

Cholesteric mesophases based on cellulose ethers, such as ethyl cellulose and hydroxypropyl cellulose, have been studied widely for their remarkable ability to display macroscopic structural color. However, the typical time scales involved in the multiscale self-assembly of cholesteric liquid crystals, from individual nanoscale helical arrangements to discrete microscopic domains, and their dependence on the gel's viscoelastic properties remain underexplored. Here, we establish a quantitative relationship between the kinetics of structural color formation after shear deformation and cholesteric order development at the nano- and microscales. Utilizing rheology in tandem with static and time-resolved reflectivity measurements, we underscore the strong influence of polymer diffusivity and chain elasticity on self-assembly kinetics in cholesteric cellulose ether gels. We show that our phenomenological model can be employed to assess the structure-property relationships of multiple polysaccharide systems, elucidating key design guidelines for the development and processing of structurally colored cholesteric mesophases.

Mathematical Models for Estimating Diffusion Coefficients in Concentrated Polymer Solutions from Experimental Data

Diffusion processes in operations involving polymeric materials are of significant interest. Determining experimental values for diffusion coefficients is often challenging. Estimating these coefficients in concentrated polymer solution, polymer films, and membranes relies on experimental tests where the polymer is brought into contact with certain components/solvents. The diffusion coefficient values depend on the diffusion type, which is affected mainly by the nature of the polymer, concentration, and temperature. The literature presents an extensive amount of information regarding the diffusion phenomenon. This paper makes a particular contribution by showing how experimental data obtained from different applications can be processed to determine diffusion coefficients. The manuscript addresses some aspects regarding solvent diffusion in polymers, and illustrates how to determine the diffusion coefficients from experimental data. For specific cases of diffusion, several models for the predictive estimation of diffusion coefficients are also presented. Polymer–solvent systems such as polyvinyl alcohol (PVA)–water, cellulose acetate (CA)–tetrahydrofuran (THF) and cellulose triacetate (CTA)–dichloromethane (DCM) are investigated, with their diffusion mechanisms influenced by changes in structure caused by variations in concentration and temperature. The experimental data obtained through a gravitational technique allow for the highlighting of the diffusion mechanism and the selection of an appropriate mathematical model. A change in the structure of the polymer during the experiment leads to diffusion anomalies. Modeling the experimental data yielded diffusion coefficient values that vary based on the type of system investigated, composition and temperature. Thus, in the case of the CTA-DCM system, the diffusion coefficient at 303 K, at various concentration values, is in the range of 4.5 and 8·10−11 m2/s; for the PVA-H2O system, D = 4.1·10−12 m2/s at 303 K, and D = 6.5·10−12 m2/s at 333 K; while for the CA-THF system, the solvent–polymer diffusion coefficient has a value of 2.5∙10−12 m2/s at 303 K, and D = 1.75∙10−11 m2/s at 323 K. Mathematical models can be useful in studies regarding the drying of polymer films with complex structures, providing knowledge for designing or selecting suitable equipment.

Effect of Peptide-Polymer Host-Guest Electrostatic Interactions on Self-Assembling Peptide Hydrogels Structural and Mechanical Properties and Polymer Diffusivity.

Peptide-based supramolecular hydrogels are an attractive class of soft materials for biomedical applications when biocompatibility is a key requirement as they exploit the physical self-assembly of short self-assembling peptides avoiding the need for chemical cross-linking. Based on the knowledge developed through our previous work, we designed two novel peptides, E(FKFE)2 and K(FEFK)2, that form transparent hydrogels at pH 7. We characterized the phase behavior of these peptides and showed the clear link that exists between the charge carried by the peptides and the physical state of the samples. We subsequently demonstrate the cytocompatibility of the hydrogel and its suitability for 3D cell culture using 3T3 fibroblasts and human mesenchymal stem cells. We then loaded the hydrogels with two polymers, poly-l-lysine and dextran. When polymer and peptide fibers carry opposite charges, the size of the elemental fibril formed decreases, while the overall level of fiber aggregation and fiber bundle formation increases. This overall network topology change, and increase in cross-link stability and density, leads to an overall increase in the hydrogel mechanical properties and stability, i.e., resistance to swelling when placed in excess media. Finally, we investigate the diffusion of the polymers out of the hydrogels and show how electrostatic interactions can be used to control the release of large molecules. The work clearly shows how polymers can be used to tailor the properties of peptide hydrogels through guided intermolecular interactions and demonstrates the potential of these new soft hydrogels for use in the biomedical field in particular for delivery or large molecular payloads and cells as well as scaffolds for 3D cell culture.

Direct visualization of pyrene diffusion in polyethylene and polyoxymethylene passive samplers

While passive sampling of ultra-low aqueous concentrations of hydrophobic organic compounds in environmental aqueous media has emerged as a promising analytical technique, there is a lack of good understanding of the fundamental diffusive processes. In this research, we used a fluorophore, pyrene, as a model compound to track diffusion in polymers through absorption and environmental media exchange processes. We directly tracked the penetration of pyrene into polyethylene (PE) and polyoxymethylene (POM) rods during absorption from water by sectioning the rod after different stages of absorption and observing the fluorescence signal through a microscope. Diffusion profiles of pyrene in polymers were simulated by numerical integration of Fickian diffusion. The results indicated that the uptake process in PE is governed by Fick's law and the absorption and desorption kinetics are similar in this polymer. However, the observed uptake profiles of pyrene in POM were non-Fickian and the release kinetics out of POM was slower compared to uptake into the polymer. We show that slower desorption from POM makes corrections for nonequilibrium using performance reference compounds (PRCs) problematic for deployments in water or sediment where there is significant advection. However, for static sediment deployments, the overall kinetics of exchange is controlled by slow transport through sediment and the hysteretic behavior of POM may not preclude the use of PRCs to interpret equilibrium status.

Magnetic resonance insights into the heterogeneous, fractal-like kinetics of chemically recyclable polymers.

Moving toward a circular plastics economy is a vital aspect of global resource management. Chemical recycling of plastics ensures that high-value monomers can be recovered from depolymerized plastic waste, thus enabling circular manufacturing. However, to increase chemical recycling throughput in materials recovery facilities, the present understanding of polymer transport, diffusion, swelling, and heterogeneous deconstruction kinetics must be systematized to allow industrial-scale process design, spanning molecular to macroscopic regimes. To develop a framework for designing depolymerization processes, we examined acidolysis of circular polydiketoenamine elastomers. We used magnetic resonance to monitor spatially resolved observables in situ and then evaluated these data with a fractal method that treats nonlinear depolymerization kinetics. This approach delineated the roles played by network architecture and reaction medium on depolymerization outcomes, yielding parameters that facilitate comparisons between bulk processes. These streamlined methods to investigate polymer hydrolysis kinetics portend a general strategy for implementing chemical recycling on an industrial scale.

Review of Developed Methods for Measuring Gas Uptake and Diffusivity in Polymers Enriched by Pure Gas under High Pressure.

Gas emission and diffusion through polymeric materials play crucial roles in ensuring safety and monitoring gas concentrations in technology and industry. Especially, the gas permeation characteristics for O-ring material should be investigated for sealing application in a hydrogen infrastructure. To accommodate the requirements of different environments, we first developed four complementary effective methods for measuring the gas absorption uptake from polymers enriched by pure gas under high pressure and determining the gas diffusivity. The methods included the gravimetric method, the volumetric method, the manometric method, and gas chromatography, which are based on mass, volume, pressure, and volume measurements, respectively. The representative investigated results of the developed methods, such as gas uptake, solubility, and diffusivity are demonstrated. The measuring principles, measuring procedures, measured results, and the characteristics of the methods are compared. Finally, the developed methods can be utilized for testing transport properties, such as the leakage and sealing ability, of rubber and O-ring material under high pressure for hydrogen fueling stations and gas industry.

Ion Conductivity in Salt-Doped Polymers: Combined Effects of Temperature and Salt Concentration.

We construct a coarse-grained molecular dynamics model based on poly(ethylene oxide) and lithium bis(trifluoromethane)sulfonimide salt to examine the combined effects of temperature and salt concentration on the transport properties. Salt doping notably slows the dynamics of polymer chains and reduces ion diffusivity, resulting in a glass transition temperature increase proportional to the salt concentration. The polymer diffusion is shown to be well represented by a modified Vogel-Fulcher-Tamman (M-VFT) equation that accounts for both the temperature and salt concentration dependence. Furthermore, we find that, at any temperature, the concentration dependence of the conductivity is well described by the product of its infinite dilution value and a correction factor accounting for the reduced segmental mobility with increasing salt concentration. These results highlight the important role of polymer segmental mobility in the salt concentration dependence of ion conductivity for temperatures near and above the glass transition.

A Monte Carlo simulation of tracer diffusion in amorphous polymers.

Tracer diffusion in amorphous polymers is a sought-after quantity for a range of technological applications. In this regard, a quantitative description of the so-called decoupling from the reverse proportionality between viscosity and diffusion coefficient into a fractional one remains a challenge requiring a deeper insight. This work employs a Monte Carlo simulation framework in 3 dimensions to investigate the consequences of different scenarios for estimating this fractional exponent on the diffusion coefficient of tracers in polymers near glass transition. To this end, we adopted a continuous-time random walk model for tracer diffusion in the supercooled liquid state. The waiting time distribution of the diffusants was computed based on the rotational correlation times of the polymer. This proposed procedure is of particular interest because it brings the quantity of waiting time (and its statistics) in connection with the measurable observable of rotational times. In the framework of our simulations the aforementioned fractional exponent appears in the relation between the diffusant's waiting time and the rotational time of the diffusion medium. A limited comparison with experimental diffusivities from the literature revealed a reasonable agreement with a fractional exponent on the basis of the molar volumes of the diffusant and the monomeric unit. Finally, an analysis of time-averaged mean squared displacement pointed to normal Brownian dynamics for tracer diffusion in polymers above the glass transition temperature.

Effects of charge asymmetry on the liquid-liquid phase separation of polyampholytes and their condensate properties.

Liquid-liquid phase separation (LLPS) is the mechanism underlying the formation of bio-molecular condensates which are important compartments regulating intra- and extra-cellular functions. Electrostatic interactions are some of the important driving forces of the LLPS behaviors of biomolecules. However, the understanding of the electrostatic interactions is still limited, especially in the mixtures of biomolecules with different charge patterns. Here, we focus on the electrostatic interactions in mixtures of charge-asymmetric and charge-symmetric polyampholytes and their roles in the phase separation behaviors. We build charge-asymmetric and charge-symmetric model proteins consisting of both glutamic acid (E, negatively charged) and lysine (K, positively charged), i.e. polyampholytes of E35K15 (charge asymmetric) and E25K25 (charge symmetric). Pure E25K25 can undergo LLPS. To investigate the effects of charge-asymmetric polyampholytes on the mixtures of E25K25/E35K15, we perform coarse-grained simulations to determine their phase separation. The charge-asymmetric polyampholyte E35K15 is resistant to the LLPS of the mixtures of E25K25/E35K15. The condensate density decreases with the molar fraction of E35K15 increasing to 0.4, and no LLPS occurs at the molar fraction of 0.5 and above. This can be attributed to the electrostatic repulsion between the negatively charged E35K15 polymers. We further investigate the effects of charge asymmetry on the conformations and properties of the condensates. The E35K15 polymers in the condensates exhibit a more collapsed state as the molar fraction of E35K15 increases. However, the conformation of E25K25 polymers changes slightly across different condensates. The surface tensions of condensates decline with the increase of the molar fraction of E35K15 polymers, while the diffusivity of polymers in the condensed phases is enhanced. This work elucidates the role of charge-asymmetric polyampholytes in determining the LLPS behaviours of binary mixtures of charge-symmetric and charge-asymmetric proteins as well as the properties of condensed phases.

All-atom molecular dynamics simulation of solvent diffusion in an unentangled polystyrene film.

The diffusion behavior of low molecular weight solvents within an unentangled polystyrene film below and above its glass transition temperature is investigated. The diffusion behavior in the glassy state exhibits a distinct behavior known as case II or class II diffusion, noticeably diverging from conventional Fickian diffusion observed above the glass transition temperature of the polymer film. In the context of case II diffusion, the primary experimental observation entails the emergence of a well-defined concentration front moving at a constant speed, delineating a swollen, rubbery region from a glassy region within the polymer system. Despite the prevalence of this phenomenon in experimental settings, simulating case II diffusion has posed a significant challenge, primarily due to the computationally intensive nature of the diffusion process. To address this, we have developed an all-atom molecular dynamics simulation approach for the observation of case II diffusion in glassy polymers. This method aims to unravel the intricacies of the diffusion process, providing valuable insights into the dynamic interactions between solvents and the polymer matrix.

Probing the Molecular Mechanism of Viscoelastic Relaxation in Transient Networks.

Hydrogels, which have polymer networks through supramolecular and reversible interactions, exhibit various mechanical responsibilities to its surroundings. The influence of the reversible bonds on a hydrogel's macroscopic properties, such as viscoelasticity and dynamics, is not fully understood, preventing further innovative material development. To understand the relationships between the mechanical properties and molecular structures, it is required to clarify the molecular understanding of the networks solely crosslinked by reversible interactions, termed "transient networks". This review introduces our recent progress on the studies on the molecular mechanism of viscoelasticity in transient networks using multiple methods and model materials. Based on the combination of the viscoelasticity and diffusion measurements, the viscoelastic relaxation of transient networks does not undergo the diffusion of polymers, which is not explained by the framework of conventional molecular models for the viscoelasticity of polymers. Then, we show the results of the comparison between the viscoelastic relaxation and binding dynamics of reversible bonds. Viscoelastic relaxation is primarily affected by "dissociation dynamics of the bonds" and "network structures". These results are explained in the framework that the backbone, which is composed of essential chains supporting the stress, is broken by multiple dissociation events. This understanding of molecular dynamics in viscoelasticity will provide the foundation for designing transient networks.

Kinetics of Light-Responsive CNT / PNIPAM Hydrogel Microactuators.

Light-responsive microactuators composed of vertically aligned carbon nanotube (CNT) forests mixed with poly(N-isopropylacrylamide) (PNIPAM) hydrogel composites are studied. The benefit of this composite is that CNTs act as a black absorber to efficiently capture radiative heating and trigger PNIPAM contraction. In addition, CNT forests can be patterned accurately using lithography to span structures ranging from a few micrometers to several millimeters in size, and these CNT-PNIPAM composites can achieve response times as fast as 15ms. The kinetics of these microactuators are investigated through detailed analysis of high-speed videos. These are compared to a theoretical model for the deswelling dynamics, which combines thermal convection and polymer diffusion, and shows that polymer diffusion is the rate-limiting factor in this system. Applications of such CNT/hydrogel actuators as microswimmers are discussed, with light-actuating micro-jellyfish designs exemplified, and >1500 cycles demonstrated.

Properties of Low-Exothermic polymer grouting materials and its application on highway

Frost heaving and thawing settlement are the main problems in highways in permafrost regions. Non-aqueous reacting polymer is a relatively effective and environmentally friendly material to repair highways. However, its expansion and heat release influence on different strata in perma-frost areas remains unclear. Thus, a low-exothermic polymer was used to conduct grouting tests in different strata of frozen soil. The heat release characteristics and thermal conductivity of low exothermic polymers during the reaction were studied by laboratory experiments. Then it was applied to the protection of freeze-heave and thaw subsidence of highway in frozen soil area. Sensors were arranged to dynamically monitor the influence of polymer grouting, diffusion, expansion, and exothermic processes on different layers of frozen soil. The results showed that the thermal conductivity of low exothermic polymerwas affected by density, the higher the density, the higher the thermal conductivity. The maximum temperature, maximum displacement, and maximum pressure of polymer grouting on each layer were less than 36 °C, 1.4 mm, and 280 kPa, respectively, and the soil of each layer recovered to its initial state 60 min after grouting was completed. Polymer grouting had significant effects on the artificial road bases with a depth of more than 80 cm, and the affected depth of semi-rigid bases was less than 40 cm. Because of serious damage in the driving direction, the grout preferentially diffused to the driving side. Therefore, repairing roadbed diseased in the permafrost region using a low-exothermic polymer is feasible.