Molecular dynamics simulations of gas diffusion through polymer networks

Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.

Calculating diffusion coefficients from molecular dynamics simulations for foam extrusion modelling of polypropylene with CO2, N2 and ethanol

In foaming processes, the blowing agent has a significant influence on the material behaviour and the necessary processing parameters. Low-density polypropylene foam sheets are usually produced with aliphatic hydrocarbons or alkanes as physical blowing agent. Due to the necessary safety precautions and the environmental impact, there is great interest in using alternative blowing agents such as CO2. The sole use of CO2 often leads to corrugation, open cells or surface defects on the foam sheet and therefore requires modifications to the process technology. For this reason, blowing agent mixtures based on CO2 and organic solvents are used for the production of foam sheets. For developing a process model describing the melt flow in the extrusion die and the formation of cells, specific material data like diffusion coefficients are necessary. For CO2 and N2 as sole blowing agent, experimental data exist in the literature. Since no experimental data are available for co-blowing agents such as ethanol at elevated temperatures as they occur in the foam process, these data were calculated using molecular dynamics (MD) simulations. The benefit of MD simulations lies in their ability to reduce the experimental effort and, in particular, to provide data in cases where this data is not available through experimental measurements. The calculated diffusion coefficient values are compared to experimental data from the literature and presented for CO2, N2 and ethanol in polypropylene. The calculated diffusion coefficients of CO2 and N2 are compared with literature results and agree well with them. For the ethanol molecules, the diffusion coefficient is compared relative to the both aforementioned ones considered the larger size of the ethanol molecule compared to N2 and CO2. The results of the diffusion coefficients for ethanol are reasonable compared to the values found for the other two molecules.

Ultrafast Dynamics Experienced by Carbon Dioxide Diffusing through Polymer Matrices

Fourier transform infrared, pump-probe polarization anisotropy, and two-dimensional infrared spectroscopies were used to study the steady-state and time-dependent behavior of carbon dioxide dissolved in three different polymer systems. Gas reorientation dynamics in poly(methyl methacrylate), poly(methyl acrylate), and poly(dimethylsiloxane) were sensitive to the nature of chemical interactions between the gas and polymer, as well as whether the polymer was in a glassy or rubbery phase. The homogeneous dynamics experienced by the asymmetric stretching vibration were found to be fastest for rubbery polymers with weak, nonspecific gas-polymer interactions. Spectral diffusion was absent for the carbon dioxide vibrational mode in glassy poly(methyl methacrylate) but was activated for the chemically similar but rubbery poly(methyl acrylate). The vibrational dynamics are shown to have a direct correlation with the diffusivity of carbon dioxide through the polymer matrices.

Engineering (Bio)Materials through Shrinkage and Expansion

Although various (bio)fabrication technologies have achieved revolutionary progress in the past decades, engineered constructs still fall short of expectations owing to their inability to attain precisely designable functions. Shrinkable and expandable (bio)materials feature unique characteristics leading to size-/shape-shifting and thus have exhibited a strong potential to equip current engineering technologies with promoted capacities toward applications in biomedicine. In this progress report, the advances of size-/shape-shifting (bio)materials enabled by various stimuli, are evaluated; furthermore, representative biomedical applications associated with size-/shape-shifting (bio)materials are also exemplified. Toward the future, the combination of size-/shape-shifting (bio)materials and 3D/4D fabrication technologies presents a wide range of possibilities for further development of intricate functional architectures.

The role of ultrafast structural dynamics with physical and chemical changes in polydimethylsiloxane thin films by two-dimensional IR spectroscopy

Fourier transform infrared (FTIR) and two-dimensional IR (2D-IR) spectroscopies were applied to polydimethylsiloxane (PDMS) cross-linked elastomer films. The vibrational probe for the systems studied was a silicon hydride mode that was covalently bound to the polymer chains. The structure and dynamics reported by this mode were measured in response to a wide range of chemical and physical perturbations, including elevated curing temperature, increased curing agent concentration, mechanical compression, and cooling to near the glass transition temperature. The FTIR spectra were found to be relatively insensitive to all of these perturbations, and 2D-IR spectroscopy revealed that this was due to the overwhelming influence of heterogeneity on the spectral line shape. Surprisingly, the deconvoluted spectral line shapes showed that there were only slight differences in the heterogeneous and homogeneous dynamics even with the drastic macroscopic changes occurring in different systems. In the context of modeling polymer behavior, the results confirm that dynamics on the ultrafast time scale need not be included to properly model PDMS elasticity.

Tuning the permeability of regular polymeric networks by the cross-link ratio

The amount of cross-linking in the design of polymer materials is a key parameter for the modification of numerous physical properties, importantly, the permeability to molecular solutes. We consider networks with a diamond-like architecture and different cross-link ratios, concurring with a wide range of the polymer volume fraction. We particularly focus on the effect and the competition of two independent component-specific solute-polymer interactions, i.e., we distinguish between chain-monomers and cross-linkers, which individually act on the solutes and are altered to cover attractive and repulsive regimes. For this purpose, we employ coarse-grained, Langevin computer simulations to study how the cross-link ratio of polymer networks controls the solute partitioning, diffusion, and permeability. We observe different qualitative behaviors as a function of the cross-link ratio and interaction strengths. The permeability can be tuned ranging over two orders of magnitude relative to the reference bulk permeability. Finally, we provide scaling theories for the partitioning and diffusion that explicitly account for the component-specific interactions as well as the cross-link ratio and the polymer volume fraction. These are in overall good agreement with the simulation results and grant insight into the underlying physics, rationalizing how the cross-link ratio can be exploited to tune the solute permeability of polymeric networks.

Tuning the selective permeability of polydisperse polymer networks

We study the permeability and selectivity ('permselectivity') of model membranes made of polydisperse polymer networks for molecular penetrant transport, using coarse-grained, implicit-solvent computer simulations. In our work, permeability P is determined on the linear-response level using the solution-diffusion model, P = KDin, i.e., by calculating the equilibrium penetrant partition ratio K and penetrant diffusivity Din inside the membrane. We vary two key parameters, namely the network-network interaction, which controls the degree of swelling and collapse of the network, and the network-penetrant interaction, which tunes the selective penetrant uptake and microscopic energy landscape for diffusive transport. We find that the partitioning K covers four orders of magnitude and is a non-monotonic function of the parameters, well interpreted by a second-order virial expansion of the free energy of transferring one penetrant from a reservoir into the membrane. Moreover, we find that the penetrant diffusivity Din in the polydisperse networks, in contrast to highly ordered membrane structures, exhibits relatively simple exponential decays. We propose a semi-empirical scaling law for the penetrant diffusion that describes the simulation data for a wide range of densities and interaction parameters. The resulting permeability P turns out to follow the qualitative behavior (including maximization and minimization) of partitioning. However, partitioning and diffusion are typically anti-correlated, yielding large quantitative cancellations, controlled and fine-tuned by the network density and interactions, as rationalized by our scaling laws. We finally demonstrate that even small changes of network-penetrant interactions, e.g., by half a kBT, modify the permselectivity by almost one order of magnitude.

Prediction and validation of diffusion coefficients in a model drug delivery system using microsecond atomistic molecular dynamics simulation and vapour sorption analysis

Diffusion of small to medium sized molecules in polymeric medical device materials underlies a broad range of public health concerns related to unintended leaching from or uptake into implantable medical devices. However, obtaining accurate diffusion coefficients for such systems at physiological temperature represents a formidable challenge, both experimentally and computationally. While molecular dynamics simulation has been used to accurately predict the diffusion coefficients, D, of a handful of gases in various polymers, this success has not been extended to molecules larger than gases, e.g., condensable vapours, liquids, and drugs. We present atomistic molecular dynamics simulation predictions of diffusion in a model drug eluting system that represent a dramatic improvement in accuracy compared to previous simulation predictions for comparable systems. We find that, for simulations of insufficient duration, sub-diffusive dynamics can lead to dramatic over-prediction of D. We present useful metrics for monitoring the extent of sub-diffusive dynamics and explore how these metrics correlate to error in D. We also identify a relationship between diffusion and fast dynamics in our system, which may serve as a means to more rapidly predict diffusion in slowly diffusing systems. Our work provides important precedent and essential insights for utilizing atomistic molecular dynamics simulations to predict diffusion coefficients of small to medium sized molecules in condensed soft matter systems.

Interdiffusion of solvent into glassy polymer films: A molecular dynamics study

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t(1/2) in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick's model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.

Molecular dynamics simulation of solvent–polymer interdiffusion: Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t(1/2), which is expected for Fickian diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self-diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.

Cooperative effects in the transport of small molecules through an amorphous polymer matrix

The transport of small molecules (penetrants) through polymer materials proceeds by a hopping mechanism: A penetrant typically dwells in a cavity of the polymer for a while and then performs a quick jump into an adjacent cavity. In this article we investigate a jump event in detail. Molecular graphics is used to identify if and how the motion of the penetrant is aided by the fluctuations of the polymer matrix. We employ both traditional molecular graphics techniques to show atomic motion and surface rendering methods to display the redistribution of penetrant-accessible volume in the polymer.