Diffusion Coefficients Of Polymers 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.

Application of Gaussian processes and transfer learning to prediction and analysis of polymer properties

Machine learning has shown superior performance in polymer properties prediction research. However, due to the complex experimental process or simulation process of polymers, it is not practical to obtain a large amount of data for fitting machine learning hyperparameters. This study aims to construct an effective performance prediction model using a small amount of data on polymers and the interaction between properties. In this paper we apply Gaussian Process Regression (GPR) and transfer learning for the establishment of polymer properties prediction models with few samples. Experiments show that when the algorithm is used to predict important properties such as diffusion coefficient and mechanical properties of polymers, the predicted value of the established model is close to the real value of the simulation, which verifies the validity of the model. Transfer learning can build a Gaussian model that describes the relationship between two performances, which not only improves the prediction accuracy of the prediction model, but also visualizes the relationship between performances and provides guidance for further experiments or simulations.

Kinetics of Surface Enrichment of a Polymer in a Glass-Forming Molecular Liquid

X-ray photoelectron spectroscopy has been used to measure the surface concentration and the surface enrichment kinetics of a polymer in a glass-forming molecular liquid. As a model, the bulk-miscible system of maltitol-polyvinylpyrrolidone (PVP) was studied. The PVP concentration is significantly higher at the liquid/vapor interface than in the bulk by up to a factor of 170, and the effect increases with its molecular weight. At a freshly created liquid/vapor interface, the concentration of PVP gradually increases from the bulk value at a rate controlled by bulk diffusion. The polymer diffusion coefficient obtained from the kinetics of surface enrichment agrees with that calculated from viscosity and the Stokes-Einstein equation. Our finding allows prediction of the rate at which the surface composition equilibrates in an amorphous material after milling, fracture, and a change in ambient temperature.

Combination of Hybrid Particle-Field Molecular Dynamics and Slip-Springs for the Efficient Simulation of Coarse-Grained Polymer Models: Static and Dynamic Properties of Polystyrene Melts.

A quantitative prediction of polymer-entangled dynamics based on molecular simulation is a grand challenge in contemporary computational material science. The drastic increase of relaxation time and viscosity in high-molecular-weight polymeric fluids essentially limits the usage of classic molecular dynamics simulation. Here, we demonstrate a systematic coarse-graining approach for modeling entangled polymers under the slip-spring particle-field scheme. Specifically, a frequency-controlled slip-spring model, a hybrid particle-field model, and a coarse-grained model of polystyrene melts are combined into a hybrid simulation technique. Via a rigorous parameterization strategy to determine the parameters in slip-springs from existing experimental or simulation data, we show that the reptation behavior is clearly observed in multiple characteristics of polymer dynamics, mean-square displacements, diffusion coefficients, reorientational relaxation, and Rouse mode analysis, consistent with the predictions of the tube theory. All dynamical properties of the slip-spring particle-field models are in good agreement with classic molecular dynamics models. Our work provides an efficient and practical approach to establish chemical-specific coarse-grained models for predicting polymer-entangled dynamics.

Constructing artificial respiratory chain in polymer compartments: Insights into the interplay between bo3 oxidase and the membrane.

Cytochrome bo3 ubiquinol oxidase is a transmembrane protein, which oxidizes ubiquinone and reduces oxygen, while pumping protons. Apart from its combination with F1Fo-ATPase to assemble a minimal ATP regeneration module, the utility of the proton pump can be extended to other applications in the context of synthetic cells such as transport, signaling, and control of enzymatic reactions. In parallel, polymers have been speculated to be phospholipid mimics with respect to their ability to self-assemble in compartments with increased stability. However, their usability as interfaces for complex membrane proteins has remained questionable. In the present work, we optimized a fusion/electroformation approach to reconstitute bo3 oxidase in giant unilamellar vesicles made of PDMS-g-PEO and/or phosphatidylcholine (PC). This enabled optical access, while microfluidic trapping allowed for online analysis of individual vesicles. The tight polymer membranes and the inward oriented enzyme caused 1 pH unit difference in 30 min, with an initial rate of 0.35 pH·min-1 To understand the interplay in these composite systems, we studied the relevant mechanical and rheological membrane properties. Remarkably, the proton permeability of polymer/lipid hybrids decreased after protein insertion, while the latter also led to a 20% increase of the polymer diffusion coefficient in polymersomes. In addition, PDMS-g-PEO increased the activity lifetime and the resistance to free radicals. These advantageous properties may open diverse applications, ranging from cell-free biotechnology to biomedicine. Furthermore, the presented study serves as a comprehensive road map for studying the interactions between membrane proteins and synthetic membranes, which will be fundamental for the successful engineering of such hybrid systems.

Change of network structure in agarose gels by aging during storage studied by NMR and electrophoresis

Changes of the network structure in agarose gels during storage were studied by measuring diffusion coefficient (D) of probe polymers. PGSTE 1H NMR was used to measure the D of pullulan added as a probe to show an increase with storage suggesting the formation of coarse network with thicker bundles of agarose aggregates. The hydrodynamic mesh size was estimated from the degree of restriction in the diffusion shedding light on the change of microscopic environment in the agarose gel during storage. From the gel electrophoresis, D of DNA was calculated from the friction on the DNA movement under the electric field to show an increase of D with storage suggesting the change of network structure in the aged agarose gels. The results provided a better understanding of the aging mechanism in agarose gels with the conformational changes which should be commonly observed in polysaccharides.

Investigation of the electrocaloric effect in ferroelectric polymer film through direct measurement under alternating electric field

The electrocaloric (EC) effect of ferroelectric polymer film was investigated at a high frequency. The analysis used the finite element method and revealed that the extractive heat density per unit of time increases and the thermal diffusion length decreases with an increase in the frequency of the driving electric field. Given the small thermal diffusion coefficient of ferroelectric polymers, the high-frequency drive of the EC effect for ferroelectric polymer film is promising for cooling devices. To discuss the EC effect under an alternating current (AC) electric field, the EC temperature change of the vinylidene fluoride-trifluoroethylene copolymer 75/25 P(VDF-TrFE) film with a thickness of 2 μm was characterized through direct measurement using a thin-film thermocouple. The EC temperature change increases with an increase in the electric field and frequency and reached up to 0.23 °C at 1.5 MV cm−1 and 10 kHz. The extractive heat density was estimated to be as high as 0.69 W cm−2.

Simulation of Melt Viscosity Effect on the Rate of Solidification in Polymer

Phase field model has been successfully derived from ordinary metal phase field equation to simulate the behavior of semi-crystalline polymer solidification phenomenon. To obtain the polymer phase field model, a non-conserved phase field equation can be expanded to include the unique polymer parameters, which do not exist in metals, for example, polymer melt viscosity and diffusion coefficient. In order to expand this model, we include free energy density and non-local free energy density based on Harrowel-Oxtoby and Ginzburg-Landau theorem for polymers. The expansion principle for a higher order of binary phase field parameter was employed to obtain fully modified phase field equation. To optimize the final properties of the products, the solidification phenomenon in polymers is very important. Here, we use our modified equation to investigate the effect of melt viscosity on the rate of solidification by employing ordinary differential equation numerical methods. It was found that the rate of solidification is related to the melting temperature and the kinetic coefficient.

Measurement and prediction of solubilities and diffusion coefficients of ethylene in rubbery propylene copolymers

For design of gas phase polymerization processes for propylene copolymers, it is essential to understand how monomer solubility and diffusivity in the polymer are affected by comonomer content and polymer crystallinity. Measurements of solubilities and diffusion coefficients of ethylene in four propylene-based (ethylene and 1-butene) copolymer (cPP) samples are reported with a gravimetric method at temperatures below and above the melting point temperatures of each cPP. Diffusion coefficients were correlated with free-volume-theory adopting the free volume fraction evaluated from PVT data and the glass transition temperature of polymer. In the polymer rubbery state, solubilities and diffusion coefficients of ethylene could be predicted with the cPP crystallinities and FVT parameters obtained from molten state data.

A free volume theory on the chain length dependence of the diffusivity of linear polymers.

A free volume theory was developed to account for the crossover of the chain length dependence of the center-of-mass self-diffusion coefficient of linear polymers from unentangled to entangled regimes. Similar to the original free volume theory of Cohen and Turnbull, this theory requires information about the free volume overlapping factor (α), critical free volume per bead (v), and mean free volume per bead (〈vf,i〉). However, one additional parameter is needed and it is the critical fraction of beads having free volume greater than or equal to αv termed as φ+. Here, α and v can be readily determined from the intermolecular and intramolecular radial distribution functions (i.e., g(r) and gintra(r)) obtained from molecular dynamics (MD) simulation and they were found to be 0.5 and 0.0257 nm3, respectively, for polyethylene melts and it is not dependent on N. 〈vf,i〉 was determined using the generic van der Waals (GvdW) equation of state and it had a value of 0.01 nm3 and the volume available to each bead can also be determined by Voronoi tessellation (VT) on the corresponding MD simulation trajectories. VT yielded exact probability of finding a certain amount of free volume and the free volume distribution was found in the form of the gamma distribution that is consistent with the positron annihilation lifetime spectroscopy observation. Finally, φ+ was calculated using the experimentally measured activation energies for diffusion per polyethylene molecule with different chain lengths and was found to be approximately 0.22 that was in line with what was found from MD simulations.

On the transport through polymer layer and porous arterial wall in drug-eluting stents

The safety and efficacy of drug-eluting stents are strongly influenced by the transport of the antiproliferative/anti-inflammatory drugs in the arterial wall. Dissolution in the polymer coating and specific binding in the artery wall play an important role in the process. We consider the model of dissolution, transport and binding of sirolimus on an axisymmetric domain representing the polymer coating layer and the porous artery wall in the vicinity of a stent strut. We employ the FEM on an unstructured mesh to discretize the governing equations. We employ a nonlinear dissolution model for the dynamics in the coating, and a nonlinear saturable binding model that includes both specific and non-specific binding in the arterial wall as separate phases, as proposed by McGinty and Pontrelli (J Math Chem 54:967–976, 2016). The arterial wall is considered an anisotropic porous media, and the flow is considered to be governed by Darcy flow. The permeability in the polymer coating is considered to be very small, but finite. The endothelium lamina, where present, is modelled as a no-flow boundary. The effect of slow and fast release polymers is considered, showing that the time evolution of the process can be efficiently controlled by the polymer diffusion coefficient. In fact, an order of magnitude decrease in the polymer diffusion coefficient results in an order of magnitude increase in the time of drug delivery. It is estimated that 52–54% of the sirolimus mass actually diffuses into the arterial wall. However, the spatial distribution of the sirolimus is greatly influenced by the flow and the arterial wall properties, being therefore susceptible to patient health conditions.

Predicting the Effects of Composition, Molecular Size and Shape, Plasticization, and Swelling on the Diffusion of Aromatic Additives in Block Copolymers

The rate of diffusion of small molecules within polymer matrices is important in an enormous scope of practical scenarios. However, it is challenging to perform direct measurements of each system of interest under realistic conditions. Free volume theories have proven capable of predicting diffusion coefficients in polymers but often require large amounts of physical constants as input. Therefore, we adapted a version of the Vrentas–Duda free volume theory of diffusion such that the necessary parameters may be obtained from a limited set of diffusion data collected at the temperature of interest using commercially available and automated sorption equipment. This approach correlates the size and shape of molecules to their trace diffusion coefficient, D, such that D of very large, solid diffusants can be predicted based on properties measured for condensable vapor diffusants. Our analysis was based on the volume-averaged transport properties of polyaromatic color additives within segmentally arranged poly(...

Electrospun Polymer Fiber Lasers for Applications in Vapor Sensing

A sensing approach based on laser emissionfrom polymer fiber networks is presented. Poly(methyl methacrylate) (PMMA) fibers doped with a laser dye are fabricated by electrospinning. They form random loop resonators, which show laser emission upon optical pumping. The shift of the spectral position of the narrow lasing modes upon uptake of alcohol vapors (model vapors are methanol and ethanol) serves as sensor signal. Thus, the high sensitivity related to the spectral line shifts of cavity‐based transducers can be combined with the fiber's large surface to volume ratio. The resulting optical sensors feature excellent sensing performance due to the large overlap (more than 80%) of light field and transducer. The shift of the laser modes results from the swelling of the polymer when exposed to solvent vapors. Due to distinctly different diffusion coefficients in polymers, the uptake dynamics reflected in the transient shift of the lasing peaks can be used to discriminate ethanol and methanol vapor in mixtures of them. The sensing mechanism is expected to be applicable to other solvent vapors that cause polymer swelling.

Enhanced Performance of Blended Polymer Excipients in Delivering a Hydrophobic Drug through the Synergistic Action of Micelles and HPMCAS.

Blends of hydroxypropyl methylcellulose acetate succinate (HPMCAS) and dodecyl (C12)-tailed poly(N-isopropylacrylamide) (PNIPAm) were systematically explored as a model system to dispense the active ingredient phenytoin by rapid dissolution, followed by the suppression of drug crystallization for an extended period. Dynamic and static light scattering revealed that C12-PNIPAm polymers, synthesized by reversible addition-fragmentation chain-transfer polymerization, self-assembled into micelles with dodecyl cores in phosphate-buffered saline (PBS, pH 6.5). A synergistic effect on drug supersaturation was documented during in vitro dissolution tests by varying the blending ratio, with HPMACS primarily aiding in rapid dissolution and PNIPAm maintaining supersaturation. Polarized light and cryogenic transmission electron microscopy experiments revealed that C12-PNIPAm micelles maintain drug supersaturation by inhibiting both crystal nucleation and growth. Cross-peaks between the phenyl group of phenytoin and the isopropyl group of C12-PNIPAm in 2D 1H nuclear Overhauser effect (NOESY) spectra confirmed the existence of drug-polymer intermolecular interactions in solution. Phenytoin and polymer diffusion coefficients, measured by diffusion-ordered NMR spectroscopy (DOSY), demonstrated that the drug-polymer association constant increased with increasing local density of the corona chains, coincident with a reduction in C12-PNIPAm molecular weight. These findings demonstrate a new strategy for exploiting the versatility of polymer blends through the use of self-assembled micelles in the design of advanced excipients.

Using Pyrene Excimer Fluorescence To Probe Polymer Diffusion in Latex Films

This study introduces a simple technique that can be used to quantitatively probe interparticle polymer diffusion (IPD) between adjacent particles in a latex film using pyrene excimer fluorescence (PEF). To demonstrate the validity of the technique, four latexes were prepared: two pyrene-labeled poly(n-butyl methacrylate) (Py-PBMA) latexes and two nonfluorescent PBMA latexes. The two pairs of Py-PBMA and PBMA latexes had similar distributions of polymer molecular weight and particle diameters. Mixtures of latex dispersions having a composition of 5 wt % Py-PBMA latex and 95 wt % nonfluorescent PBMA latex were cast into films. Fluorescence spectra of the films were acquired, and the ratio of the fluorescence intensities for the pyrene monomer (IM) and excimer (IE) was calculated to determine the IE/IM ratio. The latex films were then annealed at a constant temperature set between 75 and 119 °C. The fraction of mixing (fm), representing the amount of polymer having diffused out of a particle, was determined by monitoring the change in the IE/IM ratio as a function of annealing time. The fm profiles were then analyzed to yield the polymer diffusion coefficients, and the apparent activation energy (Ea) for diffusion was found to equal 179 ± 7 and 170 ± 12 kJ mol–1 for the high and low molecular weight chains, respectively. The c1 and c2 parameters in the WLF equation were calculated to be 11 ± 2 and 170 ± 30 K, respectively. The Ea values and c1 and c2 parameters were in close agreement with values previously found for PBMA by other techniques, suggesting that the PEF experiments provide a valid experimental means to probe IPD in latex films. The superiority of PEF over earlier procedures includes the extreme simplicity of the experimental method that involves the labeling of a single latex particle and the use of ratios of fluorescence intensity. It opens new research venues in the study of IPD during latex film formation.

Analysis of the transport properties of thermally rearranged (TR) polymers and polymers of intrinsic microporosity (PIM) relative to upper bound performance

A critical analysis comparing the diffusion selectivity, solubility selectivity, diffusivity, and solubility coefficients of thermally rearranged (TR) polymers and polymers of intrinsic microporosity (PIM), two types of polymers which consistently perform at or beyond the polymer upper bound for certain gas pairs (O2/N2 and CO2/CH4), is reported here. Although most polymers in these two classes exhibit transport properties in the range of typical glassy polymers, several variants offer exceptional performance. The diffusivity selectivity for O2/N2 and CO2/CH4 for TR polymers and PIM lies outside the range of the glassy polymer database. The solubility coefficients for O2 are at the upper end of the range of both TR and PIM polymers, as is also the case for CO2 solubility coefficients for PIM polymers. The O2/N2 and CO2/CH4 solubility selectivities for both PIM and TR polymers are in the range of typical glassy polymers. Thus, unique separation values for these polymers are a manifestation of maximizing diffusivity selectivity combined with very high gas solubility. Additionally, the previously determined diffusion gas kinetic diameters, dg, were found to correlate best with diffusion coefficients of PIM and TR polymers and serve to better analyze transport properties of upper bound materials.

Structural relaxation and diffusion in a model colloid-polymer mixture: dynamical density functional theory and simulation

Within the Asakura–Oosawa model, we study structural relaxation in mixtures of colloids and polymers subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self and distinct parts of the van Hove distribution function G(r,t) by means of dynamical density functional theory (DDFT) using an accurate free-energy functional based on Rosenfeld’s fundamental measure theory. In order to remove unphysical interactions within the self part, we extend the recently proposed quenched functional framework (Stopper et al 2015 J. Chem. Phys. 143 181105) toward mixtures. In addition, we obtain results for the long-time self diffusion coefficients of colloids and polymers from dynamic Monte Carlo simulations, which we incorporate into the DDFT. From the resulting DDFT equations we calculate G(r, t), which we find to agree very well with our simulations. In particular, we examine the influence of polymers which are slow relative to the colloids—a scenario for which both DDFT and simulation show a significant peak forming at r = 0 in the colloid–colloid distribution function, akin to experimental findings involving gelation of colloidal suspensions. Moreover, we observe that, in the presence of slow polymers, the long-time self diffusivity of the colloids displays a maximum at an intermediate colloid packing fraction. This behavior is captured by a simple semi-empirical formula, which provides an excellent description of the data.

Numerical simulation on polymer translocation into crowded environment with nanoparticles

The effects of crowded environment with nano particles are studied for polymer translocation through a small pore. The translocation time τ is simulated by Fokker-Planck equation at different free energy landscapes F and diffusion coefficients of polymer D. The free energy is calculated using the Rosenbluth-Rosenbluth method, and the diffusion coefficient is followed the relation $D \sim \frac {1}{N} e^{-\triangle F}$ . We find that the free energy is dependent on polymer-nanoparticle interaction, size of the nanoparticle, and position of the nanoparticle. The attractive nanoparticles at the trans side can provide a driving force to polymer by lowering the free energy, but the exclusive effect of nanoparticle can raise the free energy of polymer. There exists an optimum interaction that τ is roughly independent on the size and position of nanoparticles. It is found that these effects are related to the conformational change of polymer chain in crowded environment.

Determination of Concentration-Dependent Diffusion Coefficients in Polymer–Solvent Systems: Analysis of Concentration Profiles Measured by Raman Spectroscopy during Single Drying Experiments Excluding Boundary Conditions and Phase Equilibrium

Diffusion coefficients in polymer solutions are strongly dependent on composition and temperature. In many cases sufficient data are not available due to time-consuming measurements and a high number of material systems of interest. In this work a new method is proposed that allows determination of concentration-dependent diffusion coefficients directly from spectroscopic data of single film drying experiments. The quantitative data of concentration profiles in the sample are used to calculate diffusion coefficients by Fick’s law. The results are independent of boundary conditions in the gas phase. Two polymer solutions of poly(vinyl acetate) (PVAc) and the solvents methanol and toluene are investigated. The results are compared to diffusion data from the literature. Experimental proof of the independence from boundary conditions is provided. Diffusion coefficients down to values of approximately 10–14 m2 s–1 are accessible. The diffusion data are in good agreement with literature data and suitable for mo...

A free-volume interpretation of the decoupling parameter in bioactive-compound diffusion from a glassy polymer

Delivery of techno- and biofunctionality in all-natural processed foods is an area of steadily increasing fundamental and technological interest. We prepared a range of condensed biopolymer-vitamin systems and monitored the kinetics of bioactive compound release as a function of environmental temperature. Distinct patterns of structural relaxation were noted for the polymer matrix and microconstituent above the glass transition temperature of the high-solid sample. Then, there was a qualitative agreement between fractional free-volume of polymer and effective diffusion coefficient of vitamin within the glass transition region. These observations encouraged us to develop for the first time a mathematical expression that argues for linearity in the relationship between diffusion coefficient and inverse of fractional free volume yielding the so-called decoupling parameter of polymeric motion and small-molecule diffusion. Quantifying the cooperativity of vitamin and biopolymer interaction allows informed manipulation of bioactivity release, and the generic nature of the fundamental treatise invites validation in systems beyond the current range.