Size effect on competition of two diffusion mechanisms for drug molecules in amorphous polymers

Diffusion of drug molecules in polymer materials is of great importance in controlled drug release, and the investigation of the mechanism of drug release from the polymer matrix would help us to understand the release behavior of the controlled release system. In this work, molecular dynamics simulations were employed to investigate the diffusion mechanisms of penetrant molecules with different sizes in poly(lactic acid-co-ethylene glycol) (PLA-PEG). The size effect on the diffusion mechanism of penetrant molecules in polymer matrixes was discussed in detail. A competition mechanism in a two-step diffusion process-(1) motion within the cavities (free volumes), and (2) jumps between cavities or movement of the cavity itself originated from the wriggling of the polymer chains-was observed, and the contributions of these two factors to the diffusion coefficient were successfully separated. With the medium volume of penetrant molecules (e.g., benzene), a competition between these two steps was observed. Step (2) controlled the diffusion when penetrant molecules became bigger.     

Solvent diffusion in amorphous glassy polymers

In this article, a mathematical model is proposed for predicting solvent self‐diffusion coefficients in amorphous glassy polymers based on free volume theory. The basis of this new model involves consideration of the plasticization effects induced by small molecular solvents to correctly estimate the hole‐free volume variation above and below the glass‐transition temperature. Solvent mutual‐diffusion coefficients are calculated using free volume parameters determined as in the original theory. Only one parameter, which can be predicted by thermodynamic theory, is introduced to express the plasticization effect. Thus, this model permits the prediction of diffusion coefficients without adjustable parameters. Comparison of the values calculated by this new model with the present experimental data, including benzene, toluene, ethyl benzene, methyl acetate, and methyl ethyl ketone (MEK) in polystyrene (PS) and poly(methyl methacrylate) (PMMA), has been performed, and the results show good agreement between the predicted and measured values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 846–856, 2000     

Diffusion of large penetrant molecules in amorphous polymers

A new version of the free-volume theory of diffusion is modified to describe self-diffusion phenomena in polymer + solvent systems for solvents which do not move as single units. The free-volume equations are used to interpret data which appear to illustrate that some large solvent molecules do indeed move in a segmentwise manner. The dependence of the effective activation energy for diffusion on solvent size is examined, and the importance of energy effects on the diffusion process is considered.     

The rate of solvent diffusion in amorphous polymers

The present work is a contribution to our understanding of one aspect of the diffusion process, the diffusion rate. It attempts to show that all diffusion theories must satisfy the following: 1) the rate of diffusion at the initial stages of the process must be finite 2) the rate of diffusion must have square root time dependence at longer diffusion distances. Deviations of experimental data from these rules usually result from experimental inaccuracies. Whereas Fickian approach satisfies the second but not the first rule and Case II sorption the opposite, their combination satisfies neither. Two alternative explanations, which provide a very good correlation with the experimental data, are suggested: Limited diffusion rate and sorption kinetics.     

Holographic grating relaxation studies of probe diffusion in amorphous polymers

Probe diffusion of camphorquinone, thymoquinone, and diacetyl in polymers was studied by the laser-induced holographic grating relaxation (HGR) technique in polymers. The effects of changing the probe size and various parameters of the polymer, such as the molecular weight, chain conformation, and the glass transition temperature, on the probe diffusion coefficient have been investigated. Furthermore, effects of cross-linking and plasticizing the chains of the polymer host on the probe diffusion coefficient were also studied. Temperature-dependent studies show that except for the very low molecular weight poly(methyl methacrylate), all probe diffusion coefficient data above the glass transition temperature fit well to the WLF equation. ©1995 John Wiley & Sons, Inc.     

Dual-mode free volume model for diffusion of gas molecules in glassy polymers

The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist—one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737–1746, 1997     

Solvent diffusion in amorphous polymers: Polystyrene–solvent systems

The inverse gas chromatography (IGC) technique was used to obtain the partition and diffusion coefficients of solvents in polystyrene over a wide range of temperatures. Infinite dilution experiments were performed with three solvents: toluene, benzene, and hexane. Finite concentration data were measured for the polystyrene–toluene system at various concentrations from 110 to 180 °C. For the finite concentration region, the modified capillary column model used by Tihminlioglu and Danner (J Chromatogr A 1999, 845, 93–101) was used to calculate diffusion and thermodynamic data. Finite concentration thermodynamic data were also calculated with the retention theory approach and compared with the capillary column model. The experimental IGC results are in good agreement with data from other experimental techniques. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1965–1974, 2000     

Relation between amorphous structure of polymers and penetrant diffusion: A molecular dynamics simulation

Molecular dynamics simulation has been performed for studying the relation between amorphous structure of polymers and penetrant diffusion. The self-diffusion coefficients of O₂ and He in various polymer models, which differ from each other in view of the amorphous structure, were calculated above their glass transition temperatures. The amorphous structure was characterized by considering the percolation of the unoccupied volume. A good correlation was found between the self-diffusion coefficients and the number of clusters in the unoccupied volume at the critical point of the percolation. Based on the simulated cluster size distribution at the critical point, we defined a parameter into which effects of both the amorphous structure and the penetrant size are well incorporated. It was confirmed that the penetrant diffusion is intimately associated with the amorphous structure of polymers.     

A mathematical model for stress-driven diffusion in polymers

A model for case II diffusion into polymers is presented. The addition of stress terms to the Fickian flux is used to produce the characteristics progressive front. The stress in turn obeys a concentration-dependent evolution equation. The model equations are analyzed in the limit of small diffusivity for the problem of penetration into a semiinfinite medium. Provided that the coefficient functions obey two monotonicity conditions, the solvent concentration profile is shown to have a steep front that progresses into the medium. The formulas governing the progression of the front are developed. After the front decays away, the long time behavior of the solution is shown to be a similarity solution as in Fickian diffusion. Two techniques for approximating the solvent concentration and the front position are presented. The first approximation method is a series expansion; formulas are given for the initial speed and deceleration of the front. The second approximation method uses a portion of the long time similarity solution to represent the short time solution behind the front.     

Study of the conformations of the molecules in amorphous polymers by computer simulation

Summary It is investigated by computer simulation whether space problems prevent a closing packing of chain molecules if the chain molecules are randomly coiled. Chains consisting of 100 beads were introduced into a primitive cubic lattice in such a way that each lattice point is occupied by not more than one bead. It was possible to occupy up to 88% of the lattice points. The average square end-to-end distance of the chains in the concentrated system is the same as for a single chain. Neither perfect chain bundles nor imperfect chain bundles occur in a considerable amount. This shows that it is possible to pack closely randomly coiled chains.

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Zusammenfassung Es wird durch Simulation auf einer Rechenmaschine untersucht, ob Probleme bei der Raumerfüllung ein dichtes Packen von Kettenmolekülen unmöglich machen, solange diese statistisch verknäult sind. Ketten, die aus 100 Kugeln bestehen, werden in ein primitives kubisches Gitter eingeführt in der Weise, daß auf jedem Gitterplatz höchstens eine Kugel zu liegen kommt. Es war möglich, bis zu 88% der Gitterpunkte zu besetzen. Der mittlere quadratische Fadenendenabstand der Ketten im konzentrierten System ist der gleiche wie der für eine einzelne Kette. Weder ideale Kettenbündel noch gestörte Kettenbündel treten in nennenswerten Maßen auf. Damit ist bewiesen, daß es möglich ist, statistisch verknäulte Ketten dicht zu packen.

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With 6 figures     

A generalized direct-particle-deletion scheme for the calculation of chemical potential and solubilities of small- and medium-sized molecules in amorphous polymers

The development, validation, and first applications of a generalized version of an inverse Widom method are described. It permits the calculation of solubility coefficients for molecules as large as, e.g., benzene in all polymers for which reasonable forcefield parameters exist. Predicting the solubility is a key to the knowledge-based design of materials utilized to solve permeability related problems. For long time, particle insertion methods, such as the Widom method, were the only way to predict solubilities from molecular models, but they, in most cases, only worked well for rather small penetrants (e.g., H2, O2, N2). Therefore, a few years ago, a new particle deletion algorithm "DPD" was introduced by Boulougouris, Economou, and Theodorou to overcome this problem in principle. The related computer code was, however, only applicable to special, relatively simple model systems. As application examples for the generalized version described here, solubility calculations for nitrogen, oxygen, and benzene in poly(dimethyl siloxane) are presented.     

Unified study of the different physical properties of amorphous polymers

Uptil now it has not been possible to explain the different physical properties of amorphous polymers using a model based on a single conceptual scheme. In this paper, a phenomenological model is proposed which tries to explain the mechanical, optical and thermal properties (both thermal conductivity and expansivity) of amorphous polymers. The model has similarities with the composite model, proposed by the present authors, which has proved to be successful in interpreting the different physical properties of semicrystalline polymers. The present model considers the bulk form of the polymer as an aggregate of microscopic units possessing intrinsic physical properties. On drawing, the development of anisotropy in different physical properties is supposed to be due to the development of preferred orientation of these units. The development of the preferred orientation has been estimated directly from birefringence data. The agreement between the calculated and experimental values of the elastic modulus, thermal conductivity and thermal expansivity of PVC, PMMA and PS is found to be reasonable good.     

Structural approach to the study of deformation mechanism of amorphous polymers

A new microscopic procedure for the visualization of structural rearrangements in amorphous polymers during their deformation to high strains is described. This approach involves the deposition of thin (several nanometers) metallic coatings onto the surface of the deformed polymer. Subsequent deformation entails the formation of a relief in the deposited coating that can be studied by direct microscopic methods. The above phenomenon of relief formation provides information concerning the deformation mechanism of the polymer support. Experimental data obtained with the use of this procedure are reported, and this evidence allows analysis of the specific features of structural rearrangements during deformation of the amorphous polymer at temperatures above and below its glass transition temperature under the conditions of plane compression and stretching, uniaxial tensile drawing and shrinkage, rolling, and environmental crazing. This direct structural approach originally justified in the works by Academician V.A. Kargin appears to be highly efficient for the study of amorphous polymer systems.     

Structural relaxation in amorphous polymers

A theoretical calculation based on the general solution of a multi-ordering-parameter model is found to be in good agreement with the measured volume relaxation of poly(vinyl acetate). This suggests that a limiting equilibrium state is eventually reached, which may resolve the disagreement between the behavior of the model and experiments discussed in the literature. In addition, the asymmetric character of the isothermal response and memory effect is satisfactorily calculated from the same basic equation. The distribution function and the temperature-structure dependence of relaxation times are discussed.     

Depolarization thermocurrents in amorphous polymers

The depolarization thermocurrent (DTC) method gives the dependence of the dielectric relaxation time on temperature. It has been used for investigations of relaxations obeying an Arrhenius-like law in crystalline polymers. The analysis of this method shows it is possible to study mechanisms described by the Williams-Landel-Ferry (WLF) equation. The critical temperature appearing in the free-volume theory of Cohen and Turnbull and also in the statistical thermodynamic theory of Adam and Gibbs can then be measured with good accuracy. The thermal coefficient of expansion of the free-volume and the WLF coefficient for any reference temperature can also be obtained. Since analysis of the experimental DTC spectrum is particularly simple, this method seems to be a very useful tool for examination of relaxation transitions in amorphous polymers. As an example, results obtained for poly(methyl methacrylate) are presented; they are consistent with published data.     

Theoretical models for diffusion in glassy polymers

A model is derived which incorporates and unifies many of the diverse observations occurring in diffusion in glassy polymers. This unification is made possible by explicitly formulating the common property of a glassy polymer in all its various modes, namely the finite relaxation time due to its slow response to changing conditions. The application and use of the model in various situations is discussed.     

Poled amorphous polymers for second-order nonlinear optics

Recent advances in poled amorphous polymers for second-order nonlinear optics are discussed with emphasis on stabilizing the frozen-in nonlinearity via chemical crosslinking under electric fields. Specific examples of a linear polymer and a crosslinked polymer, both with nitroaniline-type chromophores covalently attached as side groups, are presented and compared in their glass transition behavior, linear optical properties, poling dynamics, and stability of frozen-in nonlinearity. It is demonstrated that by employing chemical crosslinking under electric fields one can prepare highly efficient and stable poled polymers that exhibit no decay in nonlinearity at ambient conditions and no apparent tendency of decay even at 85°C as well as excellent optical properties. The historical development of organic materials for second-order nonlinear optics and recent advances in device fabrication based on poled polymers are also discussed briefly.     

Functionalized mesoporous materials for adsorption and release of different drug molecules: A comparative study

The adsorption capacity and release properties of mesoporous materials for drug molecules can be improved by functionalizing their surfaces with judiciously chosen organic groups. Functionalized ordered mesoporous materials containing various types of organic groups via a co-condensation synthetic method from 15% organosilane and by post-grafting organosilanes onto a pre-made mesoporous silica were synthesized. Comparative studies of their adsorption and release properties for various model drug molecules were then conducted. Functional groups including 3-aminopropyl, 3-mercaptopropyl, vinyl, and secondary amine groups were used to functionalize the mesoporous materials while rhodamine 6G and ibuprofen were utilized to investigate the materials’ relative adsorption and release properties. The self-assembly of the mesoporous materials was carried out in the presence of cetyltrimethylammonium bromide (CTAB) surfactant, which produced MCM-41 type materials with pore diameters of ∼2.7-3.3 nm and moderate to high surface areas up to ∼1000 m²/g. The different functional groups introduced into the materials dictated their adsorption capacity and release properties. While mercaptopropyl and vinyl functionalized samples showed high adsorption capacity for rhodamine 6G, amine functionalized samples exhibited higher adsorption capacity for ibuprofen. While the diffusional release of ibuprofen was fitted on the Fickian diffusion model, the release of rhodamine 6G followed Super Case-II transport model.