Statistical Mechanical Theory of Penetrant Diffusion in Polymer Melts and Glasses

Investigation towards nanomechanical sensor array for real-time detection of complex gases

This study presents the development and characterization of a nanomechanical gas sensor array with piezoresistive detectors for a wide range of applications. The sensors, made of silicon and polymers and integrated with the piezoresistive sensors on a silicon-on-insulator wafer, convert to electrical signals the stress caused by volume change of polymer induced by gas absorption. The fabrication of the sensors incorporates a process where Polymer A (Polyolefin), Polymer B (Fluorocarbon polymer) Polymer C (Acrylic resin), and Polymer D (Amino polymer), are deposited within silicon slits, demonstrating their distinct responses to various vapor species. These sensors show swift response times and efficient recovery periods, which makes them promising for real-time multiple gas and smell monitoring applications. An array of four nanomechanical sensors with polymers shows high repeatability and sensitivity when subjected to multiple gas exposure and turn-off cycles. The gas sensor arrays, effectively monitoring fish quality over several days, suggest a potential for determining optimal storage and early spoilage detection in perishables. The study demonstrates that the nanomechanical sensor array can accurately distinguish between different gas concentrations using principal component analysis, paving the way for real-time, automated multiple gas detection and analysis without human intervention.

The Influence of Local Constraints on Solvent Motion in Polymer Materials

The influence of obstacles in the form of polymer chains on the diffusion of a low-molecular-weight solvent was the subject of this research. Studies were performed by computer simulations. A Monte Carlo model-the Dynamic Lattice Liquid algorithm-based on the idea of cooperative movements was used. The tested materials were polymer networks with an ideal structure (with a uniform mesh size) and real, irregular networks (with a non-uniform mesh size) obtained numerically by copolymerization. The diffusion of the solvent was analyzed in systems with a polymer concentration that did not exceed 16%. The influence of the polymer concentration and macromolecular architecture structure on the mobility and character of the motion of the solvent was discussed. The influence of irregular network morphology on solvent dynamics appeared to be significantly stronger than that of regular networks and star-like polymers.

Does pervasive interconnected network of cellulose nanocrystals in nanocomposite membranes address simultaneous mechanical strength/water permeability/salt rejection improvement?

In this research work, we investigated the effect of two cellulose nanocrystal (CNC)-related parameters, namely aspect ratio and loading content on the mechanical and desalination performance of a cellulose diacetate (CDA) model membrane system. Dispersion of high aspect ratio (HAR) CNCs in the CDA resulted in different types of nanoassembly, represented by evaluating the mechanical efficacy coefficient (CFE), viscoelastic responses and separation performance of the nanocomposite membranes. Accordingly, 0.15 and 0.25 wt% showed random isolated dispersion and tight polymer-nanorod network, while 0.50 and 0.75 wt% conformed to nanorods' pervasive interconnected network (PIN) through side-by-side aggregation and intensive bundle alignment, respectively. Specifically, the nanocomposite membrane containing 0.50 wt% HAR-CNCs simultaneously demonstrated improved mechanical strength along with mitigated water permeability/salt rejection tradeoff for brackish water desalination. This concurrent boosting was attributed to the effective mechanical reinforcement mechanism induced by the percolating network along with its partial aggregation-caused bi-continuous and electrostatically-controlled nano-pathways, orchestrating the separation tradeoff. It confirmed our hypothesis that a nanocomposite membrane with metamaterial characteristic could be obtained via manipulating the dispersion state of CNC rods in the CDA, triggering coincided optimization of mechanical strength and desalination performance.

Cooperative activated hopping dynamics in binary glass-forming liquids: effects of the size ratio, composition, and interparticle interactions

Slow dynamics in supercooled and glassy liquids is an important research topic in soft matter physics. Compared to the traditionally focused one-component systems, glassy dynamics in mixture systems adds in a rich set of new complexities, which are fundamentally interesting and also relevant for many technological applications. In this paper, we apply the recently developed self-consistent cooperative hopping theory (SCCHT) to systematically investigate the effects of the size ratio, composition and interparticle interactions on the cooperative activated hopping dynamics of matrix (in larger size) and penetrant (in smaller size) particles in varied binary sphere mixture model systems, with a specific focus on ultrahigh mixture packing fractions that mimic the deeply supercooled glass transition conditions for molecular/polymeric mixture materials. Analysis shows that in these high activation barrier cases, the long-range elastic distortion associated with a matrix particle hopping over its cage confinement always generates an elastic barrier of a nonnegligible magnitude, although the ratio between the elastic barrier and local barrier contribution is sensitively dependent on all three mixture-specific system factors considered in this work. SCCHT predicts two general scenarios of penetrant-matrix cooperative activated hopping dynamics: matrix/penetrant co-hopping (regime 1) or the penetrant mean barrier hopping time shorter than that of the matrix (regime 2). Increasing the penetrant-to-matrix size ratio or the penetrant-matrix cross-attraction strength is found to universally enlarge the composition window of regime 1. Diverse dynamical properties characterising different aspects of the cooperative activated hopping process, including the penetrant and matrix transient localization lengths, penetrant and matrix hopping jump distances, different types of local and elastic activated barriers, and matrix long-time diffusivity, relaxation time and dynamic fragility are quantitatively studied against a wide range of variations over the three system factors. Of particular interest is the universal "anti-plasticization" phenomenon achievable for sufficiently strong cross-attractive interactions. The prospects this work opens for the exploration of a wide variety of polymer-based mixture materials are briefly discussed at the end.

Elucidation of the physical factors that control activated transport of penetrants in chemically complex glass-forming liquids

Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, S0(T) (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of S0(T) and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how S0(T) decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.

Vitrimers: Using Dynamic Associative Bonds to Control Viscoelasticity, Assembly, and Functionality in Polymer Networks

Vitrimers have been investigated in the past decade for their promise as recyclable, reprocessable, and self-healing materials. In this Viewpoint, we focus on some of the key open questions that remain regarding how the molecular-scale chemistry impacts macroscopic physical chemistry. The ability to design temperature-dependent complex viscoelastic spectra with independent control of viscosity and modulus based on knowledge of the dynamic bond and polymer chemistry is first discussed. Next, the role of dynamic covalent chemistry on self-assembly is highlighted in the context of crystallization and nanophase separation. Finally, the ability of dynamic bond exchange to manipulate molecular transport and viscoelasticity is discussed in the context of various applications. Future directions leveraging dynamic covalent chemistry to provide insights regarding fundamental polymer physics as well as imparting functionality into polymers are discussed in all three of these highlighted areas.

Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses

We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical "slaving onset" stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.

Activated penetrant dynamics in glass forming liquids: size effects, decoupling, slaving, collective elasticity and correlation with matrix compressibility

We employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant-matrix pair correlation function and the penetrant-matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.

Defining the optimal criterion for separating gases using polymeric membranes

Polymeric membranes are efficient in separating gas mixtures, typically by exploiting the sieving mechanism. What controls the sieve size of a given polymer matrix is unclear, although one line of thought implies that the local cage size, defined by the dynamic motions of the glassy polymer matrix, is the relevant metric. Here, we use coarse-grained molecular dynamics simulations and show that the sieve size is defined by a static cavity size controlled by polymer chain stiffness (a packing-driven metric) combined with the local cage-like motions of the polymer host. The best separation performance for a pair of gases is when this combined metric is roughly half way between the diameters of the gases in question, with the static and dynamic quantities contributing roughly equally. For the various models simulated we find the existence of an upper bound correlation which passes through this optimal point and has a slope expected from the Freeman model, namely , where the d's correspond to the kinetic diameters of the gases in question. Our results thus demonstrate that the relevant free volume size that affects gas transport in these condensed phases is defined by both static and dynamic measures.

Coarse-grained molecular dynamics simulation of activated penetrant transport in glassy polymers

Membrane separations of gas mixtures strive to maximize the permeability of a desired species while keeping out undesired ones. Permeability vs. selectivity data from many polymer membranes for a given gas pair with diameters d_A and d_B are typically collected in a "Robeson plot"', and are bound from above by a line with a slope λ = (d_B/d_A)² - 1. A microscopic understanding of this relationship, especially λ, is still missing. We perform molecular dynamics simulations of penetrant diffusion using three different coarse-grained polymer models over a wide range of penetrant sizes, temperatures, and monomer densities. The empirically relevant λ = (d_B/d_A)² - 1 is only found for polymers that are either supercooled liquids with caged segmental dynamics or glasses and when the penetrant size is approximately half the Kuhn length of the chains, for which the penetrant diffusion is an activated process.

Linking Silica Support Morphology to the Dynamics of Aminopolymers in Composites

A combined computational and experimental approach is used to elucidate the effect of silica support morphology on polymer dynamics and CO₂ adsorption capacities in aminopolymer/silica composites. Simulations are based on coarse-grained molecular dynamics simulations of aminopolymer composites where a branched aminopolymer, representing poly(ethylenimine) (PEI), is impregnated into different silica mesoporous supports. The morphology of the mesoporous supports varies from hexagonally packed cylindrical pores representing SBA-15, double gyroids representing KIT-6 and MCM-48, and cagelike structures representing SBA-16. In parallel, composites of PEI and the silica supports SBA-15, KIT-6, MCM-48, and SBA-16 are synthesized and characterized, including measuring their CO₂ uptake. Simulations predict that a 3D pore morphology, such as those of KIT-6, MCM-48, and SBA-16, will have faster segmental mobility and have lower probability of primary amine and surface silanol associations, which should translate to higher CO₂ uptake in comparison to a 2D pore morphology such as that of SBA-15. Indeed, it is found that KIT-6 has higher CO₂ uptake than SBA-15 at equivalent PEI loading, even though both supports have similar surface area and pore volume. However, this is not the case for the MCM-48 support, which has smaller pores, and SBA-16, whose pore structure rapidly degrades after PEI impregnation.

Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions

We formulate a microscopic, force-level statistical mechanical theory for the activated diffusion of dilute penetrants in dense liquids, colloidal suspensions, and glasses. The approach explicitly and self-consistently accounts for coupling between penetrant hopping and matrix dynamic displacements that actively facilitate the hopping event. The key new ideas involve two mechanistically (at a stochastic trajectory level) coupled dynamic free energy functions for the matrix and spherical penetrant particles. A single dynamic coupling parameter quantifies how much the matrix displaces relative to the penetrant when the latter reaches its transition state which is determined via the enforcement of a temporal causality or coincidence condition. The theory is implemented for dilute penetrants smaller than the matrix particles, with or without penetrant-matrix attractive forces. Model calculations reveal a rich dependence of the penetrant diffusion constant and degree of dynamic coupling on size ratio, volume fraction, and attraction strength. In the absence of attractions, a near exponential decrease of penetrant diffusivity with size ratio over an intermediate range is predicted, in contrast to the much steeper, non-exponential variation if one assumes local matrix dynamical fluctuations are not correlated with penetrant motion. For sticky penetrants, the relative and absolute influence of caging versus physical bond formation is studied. The conditions for a dynamic crossover from the case where a time scale separation between penetrant and matrix activated hopping exists to a "slaved" or "constraint release" fully coupled regime are determined. The particle mixture model is mapped to treat experimental thermal systems and applied to make predictions for the diffusivity of water, toluene, methanol, and oxygen in polyvinylacetate liquids and glasses. The theory agrees well with experiment with values of the penetrant-matrix size ratio close to their chemically intuitive values.