Solvent Diffusion In Polymers Research Articles

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.

Solvent-Assisted Secondary Drying of Spray-Dried Polymers

PurposeThe purpose of this work is to introduce solvent-assisted secondary drying, a method used to accelerate the residual solvent removal from spray dried materials. Spray-drying is used to manufacture amorphous solid dispersions, which enhance the bioavailability of active pharmaceutical ingredients (APIs) with low aqueous solubility. In the spray-drying process, API and excipients are co-dissolved in a volatile organic solvent, atomized into droplets through a nozzle, and introduced to a drying chamber containing heated nitrogen gas. The product dries rapidly to form a powder, but small amounts of residual solvent (typically, 1 to 10 wt%) remain in the product and must be removed in a secondary-drying process. For some spray-dried materials, secondary drying by traditional techniques can take days and requires balancing stability risks with process time.MethodsSpray-dried polymers were secondary dried, comparing the results for three state-of-the-art methods that employed a jacketed, agitated-vessel dryer: (1) vacuum-only drying, (2) water-assisted drying, or (3) methanol-assisted drying. Samples of material were pulled at various time points and analyzed by gas chromatography (GC) and Karl Fischer (KF) titration to track the drying process.ResultsModel systems were chosen for which secondary drying is slow. For all cases studied, methanol-assisted drying outperformed the vacuum-only and water-assisted drying methods.ConclusionsThe observation that methanol-assisted drying is more effective than the other drying techniques is consistent with the free-volume theory of solvent diffusion in polymers.

A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis

The theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick's and Fourier's laws in the deformed (Eulerian) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous Cahn-Hilliard equations are used. The formulation of the problem uses Lagrangian (reference) configuration while the transport processes are pulled back. Except the static problem, the demagnetizing energy is ignored and only local non-selfpenetration is considered. The analysis as far as existence of weak solutions of the (thermo)dynamical problem is performed by a careful regularization and approximation by a Galerkin method, suggesting also a numerical strategy. Either ignoring or combining particular aspects, the model has numerous applications as ferro-to-paramagnetic transformation in elastic ferromagnets, diffusion of solvents in polymers possibly accompanied by magnetic effects (magnetic gels), or metal-hydride phase transformation in some intermetalics under diffusion of hydrogen accompanied possibly by magnetic effects (and in particular ferro-to-antiferromagnetic phase transformation), all in the full thermodynamical context under large strains.

Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

AbstractTheories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011

The use of THz time-domain reflection measurements to investigate solvent diffusion in polymers

Solvent diffusion into polymers is central to their performance, for example as controlled delivery pharmaceutical products. In this work, we present the novel application of terahertz (THz) time-domain reflectance spectroscopy to quantify the ingress of acetone into various polymer materials. Reflections from the top and bottom surfaces of the discs are temporally resolved, as is a reflection from the interface between acetone-wet polymer and dry polymer. These reflections enable both the polymer swelling and more importantly the position of the liquid diffusion front to be quantified as a function of time. Verification of these measurements is provided by equivalent magnetic resonance imaging (MRI) measurements, with which there is excellent agreement.

Visualization of Solvent Diffusion in Polymers by NMR Microscopy with Radio-Frequency Field Gradients

NMR microscopy by radio-frequency field gradients is especially well suited for studying solvent penetration in polymers, due to the weak sensitivity of the method to magnetic susceptibility variations caused by object heterogeneities and to its ability to accommodate short transverse relaxation times better than the conventional imaging procedure by static field gradients. It is shown in this paper that distinct features of the swelling process can be easily observed by this method from two-dimensional NMR images and from the diffusion profiles provided by cross-sections through that image. A specific application of the method concerns the stretched PVC for which solvent diffusion and swelling are strongly anisotropic.

Size effects on solvent diffusion in polymers

Capillary column inverse gas chromatography (CCIGC) has been used for the measurement of diffusion coefficients in polymer-solvent systems at conditions approaching on a solvent diffusion in two polymers, poly(methyl methacrylate) (PMMA) and poly(vinyl acetate) (PVAc, measuremnets of diffusion coeffiients were made at temperatures ranging from T g to 70 K above T g . Over 30 solvents were evaluated: alkanes, alkenes, aromatic hydrocarbons, and aliphatic esters.

A Theoretical Study of the Time‐Dependence of Solvent Diffusion in a Polymer

AbstractBased on experimental evidence in literature an attempt is made to theoretically derive an expression for the diffusion rate of a solvent in a polymer, a process by which the polymer can adopt a gellous state. In particular the movement of the solvent/gel interface is examined. With respect to the time dependence the solvent diffusion in polymers can be attributed to two cases Proportional to t (Alfrey's Case I) Proportional to √t (Alfrey's Case II) Both cases are mathematically treated particularly with respect to the different time‐dependence of solvent diffusion.

NMR Imaging of Solvent Diffusion in Polymers

Nuclear magnetic resonance (NMR) imaging is sensitive to the mobile protons of solvent molecules and, as such, is well suited for studying the solvent diffusion in polymers. The fundamentals of NMR imaging are described, providing a platform for application of NMR imaging to diffusion processes in polymers. The constraints on the imaging experiment imposed by the diffusion process are discussed with respect to sample geometry and the rate of diffusion. A fast imaging scheme known as FLASH is described as an alternative method which reduces the influence of the diffusion rate and NMR relaxation parameters. Example images are given with regard to each of the constraints. An example of the successful application of NMR imaging to the study of Case II diffusion in PMMA is also given. The advantages and disadvantages of NMR imaging as applied to diffusion in polymers, as well as examples of the diffusion process that NMR imaging is uniquely qualified to study, are given in the conclusion.

Influence of temperature on the diffusion of solvents in polymers above the glass transition temperature

Influence of temperature on the diffusion of solvents in polymers above the glass transition temperature

Kinetics of plasticizer migration between nitrocellulose and ethylcellulose in double‐base propellant systems

AbstractRecent experimental and theoretical work on the concentration‐dependent diffusion of solvents in polymers has led to a reasonably detailed understanding of the processes involved. The possibility exists of supplementing standard but costly surveillance testing with rapid laboratory‐scale measurements of plasticizer migration. Many solvent‐polymer systems conform rather closely to the assumption that the amount of material transferred by diffusion is a function of the composite variable t1/2/l. This means that any scale factor applied to the diffusion path length, in a one‐dimensional system, may be compensated for by applying the square of this factor to the time. It has been shown that this assumption can apply with reasonable accuracy to plasticizer diffusion in the propellant‐inhibitor systems. By approximating a particular 2 in. rocket charge with a one‐dimensional model, it is possible to predict the time required for the unit's inhibitor to reach specified levels of plasticizer migration at any storage temperature of interest. A large temperature coefficient appears to be associated with the equilibrium plasticizer migration in the system chosen for experiment, as well as with the rate. Unless suitable allowance is made, this can lead to serious misinterpretation of the results of the surveillance that has been accelerated by raising the storage temperature.