Polymer Diffusion Research Articles

ToF-SIMS Depth Profiling to Measure Nanoparticle and Polymer Diffusion in Polymer Melts

We apply time-of-flight secondary ion mass spectroscopy (ToF-SIMS) and cross-sectioned trilayer samples to separately measure nanoparticle (NP) and polymer diffusion on micrometer length scales in polymer melts. We fabricate polymer/diffusing medium/polymer trilayer samples and measure the cross section to extract the NP or deuterated polymer distribution in 3D using ToF-SIMS. After correcting the data for sample tilt, deconvoluting the beam resolution, and integrating the data to extract 1D concentration profiles, we fit the data to extract the diffusion coefficient. These results from cross-sectional ToF-SIMS are in excellent agreement with earlier studies using well-established ion beam methods. This work establishes ToF-SIMS as a reliable tool for measuring NP and polymer diffusion coefficients and opens the door to investigating diffusion in more complex polymer systems and across longer time and length scales.

Spatiotemporal Mapping of Hole Nucleation and Growth during Block Copolymer Terracing with High-Speed Atomic Force Microscopy.

As a platform for investigating two-dimensional phase separation, we track the structural evolution of block copolymer thin films during thermal annealing with environmentally controlled atomic force microscopy (AFM). Upon thermal annealing, block copolymer films with incommensurate thickness separate into a terraced morphology decorated with holes. With in situ imaging at 200 °C, we follow the continuous progression of terrace formation in a single region of a cylinder-forming poly(styrene-block-methyl methacrylate) thin film, beginning with the disordered morphology on an unpatterned silicon substrate and continuing through nucleation and coarsening stages. Topographic AFM imaging with nanoscale resolution simultaneously captures ensemble hole growth statistics while locally tracking polymer diffusion through measurements of the film thickness. At early times, we observe homogeneous hole nucleation and isotropic growth, with kinetics following the predictions of classical nucleation theory. At later times, however, we find anomalous hole growth which arises due to the combination of Ostwald ripening and coalescence mechanisms. In each case, our real-space observations highlight the importance of hole interactions for determining coarsening kinetics, mediated either through the interconnected phase for Ostwald ripening or through binary collision events for coalescence.

Brownian motion of flexibly linked colloidal rings.

Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on the conformation and diffusion of molecular ring polymers simultaneously are challenging due to their inherently small size. Here, we study an experimental model system for cyclic polymers, that consists of rings of flexibly linked micron-sized colloids with n=4-8 segments. We characterize the conformations of these flexible colloidal rings and find that they are freely jointed up to steric restrictions. We measure their diffusive behavior and compare it to hydrodynamic simulations. Interestingly, flexible colloidal rings have a larger translational and rotational diffusion coefficient compared to colloidal chains. In contrast to chains, their internal deformation mode shows slower fluctuations for n≲8 and saturates for higher values of n. We show that constraints stemming from the ring structure cause this decrease in flexibility for small n and infer the expected scaling of the flexibility as function of ring size. Our findings could have implications for the behavior of both synthetic and biological ring polymers, as well as for the dynamic modes of floppy colloidal materials.

Measuring thermal diffusivity when the principal axes are unknown a priori

The thermal diffusivity of polymers may develop anisotropy due material possessing or mechanical loading. The orientation of the anisotropy may not be visually apparent. An analytical study has been performed where the four non-zero components of the diffusivity tensor are estimated for a specimen with in-plane anisotropy. Sensitivity coefficients were calculated for each of the non-zero components of the diffusivity tensor at the four measurement locations. The amplitude of the sensitivity coefficients suggest that the signal received at each sensor is sufficient for estimating the parameters, while the character of the coefficients over time suggests that the parameters are independent. Small values of in-plane anisotropy lead to negligible errors (< 0.4%) in the estimated parameters when the off-diagonal diffusivity is neglected. Larger differences in anisotropy require the estimation of the off-axis terms, which is possible with the addition of a fourth sensor to the extended flash diffusivity method. This additional measurement may be used to verify assumptions of thermally orthotropic behavior in materials.

Effects of Molecular Weight and Surface Interactions on Polymer Diffusion in Confinement

Understanding the transport and thermodynamics of polymers in confined spaces is helpful for many separation processes like water purification, drug delivery, and oil recovery. Specifically, for water purification, dextran has been used as a "model" foulant. Uncovering how these polymers interact in confinement can reduce the fouling of organic membranes and will lead to better separation processes overall. We have determined the diffusion coefficient, D, of dextran and sodium polyacrylate in convex lens-induced confinement using differential dynamic microscopy. In this setup, the gap height ranges continuously from 0.077-21.8 μm. It was found that polymer diffusion becomes slower in higher confinement, which is consistent with a change in the increase of the hydrodynamic resistance to macromolecule motion and depends on the surface properties. These findings indicate that dextran diffusion changes in confinement and can lead to a better understanding of separation processes.

Post‐synthesis amination of polymer of intrinsic microporosity membranes for CO2 separation

AbstractMembrane separation is an energy‐saving technology for carbon capture. However, it is subjected to permeability‐selectivity trade‐off limitation. Although chemical functionalization is proposed to boost separation efficiency, controlling sorption–diffusion process remains extremely challenging. In this study, a facile, controllable, and versatile chemical vapor amination strategy is reported to simultaneously tune gas sorption and diffusion in polymer of intrinsic microporosity (PIM)‐based membranes for improving carbon capture performance. Through simple exposure in amine vapors under mild conditions, nucleophilic substitution of amines toward ether and halogen groups induce grafting, ring‐opening, terminal replacement, chain‐scission, and crosslinking of PIM‐1, thereby underpinning CO2‐philicity and tailoring passageway. The prepared CO2‐philic membranes exhibit substantially improved CO2/N2 selectivity over 30.8, about 226% as that of original one, accompanied by high CO2 permeability of 2590 Barrer, which can surpass the trade‐off upper bound of polymer membranes. Our results reveal that post‐synthesis amination is an effective route to obtain high‐performance membranes.

Visualizing ion transport in polymers via ion-chromic indicators.

There is growing interest in polymers with high ionic conductivity for applications including batteries, fuel cells, and separation membranes. However, measuring ion diffusion in polymers can be challenging, requiring complex procedures and instrumentation. Here, a simple strategy to study ion diffusion in polymers is presented that utilizes ion-chromic spiropyan as an indicator to measure the diffusion of LiTFSI, KTFSI, and NaTFSI within poly(ethylene oxide)-based polymer networks. These systems are selected, as these are common ions and polymers used in energy storage applications, however, the approach described is not specific to materials for energy storage. Specifically, to enabling the study of ion diffusion, these salts cause the spiropyran to undergo an isomerization reaction, which results in a significant color change. This colorimetric response enables the determination of the diffusion coefficients of these ions within films of these polymers simply by optically tracking the spatial-temporal evolution of the isomerization product within the film and fitting the data to the relevant diffusion equations. The simplicity of the method makes it amenable to the study of ion diffusion in polymers under a range of conditions, including various temperatures and under macroscopic deformation.

Simulation study on the effect of polydisperse nanoparticles on polymer diffusion in crowded environments.

The diffusion of polymer chains in a crowded environment with large and small immobile, attractive nanoparticles (NPs) is studied using Langevin dynamics simulations. For orderly distributed NPs on the simple cubic lattice, our results show that the diffusion of polymer chains is dependent on the NP-NP distance or lattice distance d. At low d where NPs are placed closely, subdiffusion occurs at a sufficiently high polydispersity of NPs, PD. Both the apparent diffusion coefficient and subdiffusion exponent of polymer chains decrease with increasing PD, attributed to the adsorption of polymers on NP clusters formed by larger NPs. At large d, normal diffusion is always observed, and the diffusion coefficient increases with increasing PD. The reason is that, at high PD, the difference between single large NP adsorption and double large NP adsorption is reduced, which increases the exchange of a polymer between the two adsorption states. Finally, the impact of size polydispersity of NPs on the diffusion of polymer chains in a crowded environment with randomly distributed NPs is also investigated. The results show that the position disorder of NPs enhances the subdiffusion of the system.

Linear polymer chain diffusion in semi-flexible polymer network: A dissipative particle dynamics study

Linear polymer chains transport in the crowded biological environment is profoundly important to biomedical engineering and nanotechnology. Cytoskeleton, which can be modeled as a semi-flexible polymer network, acts as a barrier when linear polymers diffuse inside the cell. The diffusion of linear polymers with length N in this polymer network is investigated by the dissipative particle dynamics (DPD) in the present study. Rouse theory is applied to analyze the conformational dynamics of the linear polymers based on the numerical results. It is found that the geometric constraint length Na is a crucial parameter to describe the role of the network of the polymer diffusion. Analyses on Rouse modes show that, in a short wavelength regime, the relaxation time obtained in numerical simulation follows the prediction of the Rouse theory. With the increasing wavelength, the linear polymer exhibits a transition from reptation behavior to the spatially homogeneous behavior at critical length scale Na, which is illustrated by different scaling laws dependent on wavelength. Based on the analyses on the Rouse modes and mean square displacements of the linear polymer, we present a non-dimensional conformational dynamics function dependent on time, with which a scaling law is proposed to predict the long time diffusivity of the linear polymer in a semi-flexible polymer network with different mesh sizes. It is shown that the prediction is well consistent with our DPD simulation results.

Cinematic reflectometry using QIKR, the quite intense kinetics reflectometer.

The Quite Intense Kinetics Reflectometer (QIKR) will be a general-purpose, horizontal-sample-surface neutron reflectometer. Reflectometers measure the proportion of an incident probe beam reflected from a surface as a function of wavevector (momentum) transfer to infer the distribution and composition of matter near an interface. The unique scattering properties of neutrons make this technique especially useful in the study of soft matter, biomaterials, and materials used in energy storage. Exploiting the increased brilliance of the Spallation Neutron Source Second Target Station, QIKR will collect specular and off-specular reflectivity data faster than the best existing such machines. It will often be possible to collect complete specular reflectivity curves using a single instrument setting, enabling "cinematic" operation, wherein the user turns on the instrument and "films" the sample. Samples in time-dependent environments (e.g., temperature, electrochemical, or undergoing chemical alteration) will be observed in real time, in favorable cases with frame rates as fast as 1Hz. Cinematic data acquisition promises to make time-dependent measurements routine, with time resolution specified during post-experiment data analysis. This capability will be deployed to observe such processes as in situ polymer diffusion, battery electrode charge-discharge cycles, hysteresis loops, and membrane protein insertion into lipid layers.

Polymer Brushes by Grafting to Reaction in Melt: New Insights into the Mechanism

AbstractUltrathin films of end‐tethered polymers, generally indicated as polymer brushes, have gained great interest for their ability to modify the surface interaction with the surrounding environment. One of the most common strategies to obtain polymer brushes is based on the reaction of end‐functional polymers with the substrate surface, in a process defined as grafting to. The two advantages of grafting to reactions are i) the functional polymer is prepared before the grafting reaction and therefore can be fully characterized and ii) the reaction has a self‐limiting nature, meaning that the number of grafted chains converges to a plateau value after a sufficiently long reaction time. The limit value of grafted chains is governed by the molecular weight of the employed polymer, thus allowing a fine control of the brush thickness. In this work, the origin of the self‐limiting nature of the grafting to reaction is discussed comparing theoretical models with experimental data. Furthermore, the kinetics of the process is discussed, considering both polymer diffusion and end‐group reactivity as the main drivers of the grafting to process. Finally, the effect of molecular weight dispersity on the brush characteristics is highlighted.

Dissolution Mechanisms of Amorphous Solid Dispersions: Role of Drug Load and Molecular Interactions

High drug load amorphous solid dispersions (ASDs) have been a challenge to formulate partially because drug release is inhibited at high drug loads. The maximum drug load prior to inhibition of release has been termed the limit of congruency (LoC) and has been most widely studied for copovidone (PVPVA)-based ASDs. The terminology was derived from the observation that below LoC, the polymer controlled the kinetics and the drug and the polymer released congruently, while above LoC, the release rates diverged and were impaired. Recent studies show a correlation between the LoC value and drug-polymer interaction strength, where a lower LoC was observed for systems with stronger interactions. The aim of this study was to investigate the causality between drug-PVPVA interaction strength and LoC. Four chemical analogues with diverse abilities to interact with PVPVA were used as model drugs. The distribution of the polymer between the dilute aqueous phase and the insoluble nanoparticles containing drug was studied with solution nuclear magnetic resonance spectroscopy and traditional separation techniques to understand the thermodynamics of the systems in a dilute environment. Polymer diffusion to and from ASD particles suspended in aqueous solution was monitored for drug loads above the LoC to investigate the thermodynamic driving force for polymer release. The surface composition of ASD compacts before and after exposure to buffer was studied with Fourier transform infrared spectroscopy to capture potential kinetic barriers to release. It was found that ASD compacts with drug loads above the LoC formed an insoluble barrier on the surface that was in pseudo-equilibrium with the aqueous phase and prevented further release of drugs and polymers during dissolution. The insoluble barrier contained a substantial amount of the polymer for the strongly interacting drug-polymer systems. In contrast, a negligible amount was found for the weakly interacting systems. This observation provides an explanation for the ability of strongly interacting systems to form an insoluble barrier at lower drug loads. The study highlights the importance of thermodynamic and kinetic factors on the dissolution behavior of ASDs and provides a potential framework for maximizing the drug load in ASDs.

Prediction of Water Diffusion in Wide Varieties of Polymers with All-Atom Molecular Dynamics Simulations and Deep Generative Models.

Permeation through polymer membranes is an important technology in the chemical industry, and in its design, the self-diffusion coefficient is one of the physical quantities that determine permeability. Since the self-diffusion coefficient sensitively reflects intra- and intermolecular interactions, analysis using an all-atom model is required. However, all-atom simulations are computationally expensive and require long simulation times for the diffusion of small molecules dissolved in polymers. MD-GAN, a machine learning model, is effective in accelerating simulations and reducing computational costs. The target systems for MD-GAN prediction were limited to polyethylene melts in previous studies; therefore, this study extended MD-GAN to systems containing copolymers with branches and successfully predicted water diffusion in various polymers. The correlation coefficient between the predicted self-diffusion coefficient and that of the long-time simulation was 1.00. Additionally, we found that incorporating statistical domain knowledge into MD-GAN improved accuracy, reducing the mean-square displacement prediction outliers from 14.6% to 5.3%. Lastly, the distribution of latent variables with embedded dynamics information within the model was found to be strongly related to accuracy. We believe that these findings can be useful for the practical applications of MD-GAN.

Experimental Investigation and Numerical Verification on Diffusion of Permeable Polymers in Sandy Soils with Considering Grouting Parameters

Experimental Investigation and Numerical Verification on Diffusion of Permeable Polymers in Sandy Soils with Considering Grouting Parameters

Compression Relaxation of Multi-Structure Polymer Composites in Penetrating Liquid Medium.

Multi-structural polymer composites are widely used in the mechanical engineering, automotive, aviation and oil refining industries, as well as in the printing industry as a shock-absorbing deckle on the offset cylinders of printing machines. During offset printing, composites come into contact with inks and washing solutions, the components of which penetrate the material and cause the polymers to swell. This process degrades the print quality, and for this reason the study of its features is relevant. The prerequisites for this work are the study of the fundamental laws of diffusion and sorption of liquids by polymers with different micro- and macro-structures in different physical states and in different forms (e.g., films, sheets, fibers and fabrics). The combination of polymer materials in the composition of multi-structural fabric blankets makes it possible to obtain materials with unique mechanical properties and high resistance to liquid penetrating media and to use them in high-tech processes of multi-color printing with high resolution and color rendering. This article reports for the first time the kinetics and thermodynamics results obtained from the swelling of multi-structural polymeric blankets in solvents used in printing, and the effect of sorption of different polar liquids on the viscoelastic strain under compression during the operation of the damping systems of printing machines. Using mathematical models of activated liquid diffusion in polymers and deformation of a viscoelastic body, the swelling rate constants, solvent diffusion coefficients (the kinetic characteristics of the swelling process) and Flory−Huggins parameters (the thermodynamic characteristics of the interaction of the solvent with the composite) for composite−solvent systems with several chemical composition variants were determined. The elastic modulus and the viscosity coefficient of the composite under liquid saturation were calculated based on the experimental cyclic compression data. The range of change in the compression and restoration times of the polymeric blankets (0.09 s ÷ 0.78 s) was determined. It was shown that the composite swelled to a limited extent in all the studied liquids. All solvents used were thermodynamically poor (χ > 0.5). It has been established that rubber−fabric blankets coated with nitrile rubber are the least resistant to the action of dichloroethane, and that blankets with layers of polyolefins are not resistant to ethyl acetate. Water significantly affects the physicochemical properties of rubber−fabric blankets with a large proportion of cotton fabric layers. The data obtained can serve as a basis for optimizing the compositions of inks and cleaning solutions, as well as a theoretical basis for the thermodynamics of composite−solvent systems.

Langevin Dynamics Simulation on the Diffusivity of Polymers in Crowded Environments with Immobile Nanoparticles

Langevin Dynamics Simulation on the Diffusivity of Polymers in Crowded Environments with Immobile Nanoparticles

Thermodiffusion of polymer solutions and colloidal dispersions in mixed solvents.

Two-color optical measurements of thermodiffusion in ternary mixtures frequently suffer from ill-conditioned contrast factor matrices, whose inversion leads to very large experimental errors. In this contribution, we show how the error amplification can be avoided in situations where a priori knowledge about the directions of the eigenvectors of the diffusion matrix is available. We present optical beam deflection experiments on solutions of the polymer polystyrene of Mw = 4880g/mol in a mixed solvent of toluene and cyclohexane. In this system, the two diffusion eigenvalues differ by almost one order of magnitude. The large eigenvalue can be attributed to the interdiffusion of the two solvents and the small one to the polymer diffusion relative to the mixed solvent. The pre-selection of the eigenvectors renders the method stable against fluctuations of the experimental parameters. Both the diffusion and the Soret coefficients attributed to the two modes agree very well with the respective values of corresponding binary mixtures.

Concerted ionic-electronic conductivity enables high-rate capability Li-metal solid-state batteries

Enabling the fast charge and discharge of Li-metal solid-state batteries paves the way towards their deployment in electro-mobility applications, which require high-energy and power with safety guaranteed. Solid-state batteries using polyethylene oxide as the polymer matrix are appealing candidates although currently limited to relatively slow rate capability arising from high solid-solid interfacial resistance and sluggish lithium-ion mobility at the solid electrolyte. In this work, the engineering design and optimization of composite electrodes with multi-walled carbon nanotubes lead to high performance Li metal solid-state cells, showing a high-capacity retention at rates up to 4C. The electrode formulations including the elongated architectures exhibit a concerted ionic-electronic diffusion in the catholyte polymer enabling fast Li-ion transport, enhancing the electronic percolation and increasing the interfacial reaction kinetics and exchange current density. The solid-state battery with LiFePO4 electrode shows an unprecedented capacity retention of 92% during 800 cycles at 2C. The promising performance at high-rates of this approach is also extended to electrodes with a high-voltage active material.

Diffusion and thermodiffusion of polymers in mixed solvents

Diffusion and thermodiffusion of polymers in mixed solvents

Development of Two-Dimensional Thermal Analysis Code for the Analysis of 3D Printed PLA Parts

Fused Deposition Modelling is one of the main 3D printing methods to manufacture plastic parts. The strength of the printed part by FDM is dependent on polymer diffusion between printed layers. The polymer diffusion between two neighboring layers occur not only during the extrusion of the hot top layer, but also during the production of consecutive layers due to thermal conduction. The heat diffusion from upper layers enhances the curing of polymers, which consequently affects the strength of the part. Therefore, the history of the temperature variations - curing time and curing temperature - should be analyzed to predict the strength of the part. The goal of this study is to develop a two-dimensional transient thermal analysis solver for the investigation of time-dependent thermal changes during the printing process. This solver is developed with the use of finite difference method employed under implicit scheme. The transient temperature pattern is qualitatively compatible to the experimental results in literature. The solver can be utilized for further thermal analyses to correlate temperature, polymer diffusion and strength with the inclusion of deposition path in the third dimension.