Long-term permeation properties of poly(1-trimethylsilyl-1-propyne) membranes in hydrocarbon—Vapor environment

Poly(1-trimethylsilyl-1-propyne) (PTMSP), a high free-volume glassy di-substituted polyacetylene, has the highest gas permeabilities of all known polymers. The high gas permeabilities in PTMSP result from its very high excess free volume and connectivity of free volume elements. Permeability coefficients of permanent gases in PTMSP decrease dramatically over time due to loss of excess free volume. The effects of aging on gas permeability and selectivity of PTMSP membranes continuously exposed to a 2 mol % n-butane/98 mol % hydrogen mixture over a period of 47 days are reported. The permeation properties of PTMSP membranes are quite stable when the polymer is continuously exposed to a gas mixture containing a highly sorbing organic vapor such af n-butane. The n-butane/hydrogen selectivity was essentially constant for the 47-day test period at a value of 29, or 88% of the initial value of the as-cast film of 33. Condensable gases such as n-butane may serve as a “filler” in the nonequilibrium free volume of the polymer, thereby preserving the high level of excess free volume. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1483–1490, 1997     

Equation of state for Lennard–Jones flexible ring fluids

We present a new equation of state for Lennard–Jones (LJ) flexible ring fluids. We perform Monte-Carlo simulations for freely-jointed Lennard–Jones chain fluids (3-, 6- and 8-mer) in the canonical ensemble and obtain the intramolecular end-to-end pair correlation function data under extensive density and temperature conditions. We correlate these as a function of the density, the temperature and the number of segments in a chain. We apply this function to thermodynamic perturbation theory (TPT) and obtain a new equation of state for Lennard–Jones flexible ring fluids. We also compare existing simulation data [J. Chem. Phys. 104 (1996) 1729] with the results obtained using the newly derived equation of state.     

PVT properties of linear and dendritic polymers

The aim of this article is to examine the limits of applicability of the Simha‐Somcynsky (S‐S) equation of state (EOS) by comparing the pressure‐volume‐temperature (PVT) data and the derivatives (compressibility, κ, and thermal expansion coefficient, α) of anionic linear polystyrene (PS) with poly(benzyl ether) dendrimers (PBED). Fitting the PVT of PBED data to the S‐S EOS was similarly satisfactory as that of PS and the computed Lennard‐Jones (L‐J) interaction parameters showed similar errors of ca. 1%. Next, the experimental derivatives, α and κ of PS and PBED were compared with these functions computed from the S‐S EOS—good agreement was obtained for α at ambient pressure, P, indicating validity of the S‐S theory at least up to the first derivative. While the predicted κ = κ(P) dependence for PS and a linear PBED homologue was correct, for dendrimers the compressibility was higher at low pressure and it was lower at high P than theory predicts. Also the extracted values of the L‐J repulsion volume, v*, between a segment pair was smaller than expected. The specific architecture of dendrimer molecules is responsible for this behavior, since their 3D configuration is significantly different from the S‐S model with uniform segmental density and oxygen bonds in the main and side chains add flexibility. © 2009 NRC Canada. J Polym Sci Part B: Polym Phys 48: 322–332, 2010     

Ordering in thin films of asymmetric diblock copolymers

The time evolution of the free surface of asymmetric diblock copolymers of polystyrene and poly(methyl methacrylate) on a strongly interacting surface was studied with atomic force microscopy. The surface morphology underwent morphological transitions to satisfy commensurability conditions. These transformations were consistent with recent self‐consistent field arguments predicting the phase transitions of copolymers as a function of thickness (see M. J. Fasolka, P. Banerjee, A. M. Mayes, G. Pickett, & A. C. Balazs, Macromolecules 2000, 33, 5702). © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 663–668, 2001     

Phase equilibrium and diffusion of solvents in polybutadiene: A capillary‐column inverse gas chromatography study

The capillary‐column inverse gas chromatography method was used to measure the diffusion and partition coefficients of ethylbenzene, styrene, and acrylonitrile in polybutadiene (PBD) at infinite dilution of the solvents. Experiments were performed over a temperature range of 50–125 °C. At temperatures well above the glass‐transition temperature of PBD, the diffusivities were correlated using an Arrhenius expression. The Arrhenius parameters in turn were intercorrelated and shown to be a function of the occupied volume, thus providing a method for predicting the diffusion of other solvents in the same polymer. Further, the activation energy was predicted using the Duda‐Vrentas free‐volume approach. The activation energy thus obtained was compared with the activation energy of the Arrhenius approach. The weight‐fraction activity coefficient data were compared to the predictions of the group contribution, lattice‐fluid equation‐of‐state, and the UNIquac Functional‐group Activity Coefficient (UNIFAC) free‐volume models. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1046–1055, 2002     

Cell theory and equation‐of‐state of chain molecular systems: Application to polymer solids

We use the Lennard‐Jones and Devonshire cell theory without any ad hoc simplification of the cell potential to obtain the equation‐of‐state (EOS) for chain molecular systems. The interactions of the central segment with second and third shells of neighbors are taken into account. Numerical values of the cell integrals are given in tabular form along with interpolation expressions that cover the range of PVT variables appropriate to polymers. Results of comparison with EOS based on square‐well form are also discussed. Application of the theory to polymer glasses of diverse structures is found to be quite successful in explaining the PVT behavior over a wide range of temperatures both at atmospheric and elevated pressures. Further, scaled volume at the glass‐transition temperature is discovered to be a corresponding state property. Turning to crystals, the theory is generally in good accordance with the PVT data of three well‐studied polymers both at atmospheric and elevated pressures. For linear polyethylene the agreement is good up to 42 kbar for the room‐temperature isotherm. On the other hand, at higher temperatures where the data are limited to 5 kbar, the agreement is determined to be satisfactory for the three polymers. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 515–530, 2001     

Cross-linking of poly[1-(trimethylsilyl)-1-propyne] membranes using bis(aryl azides)

Cross-linkable poly[1-(trimethylsilyl)-1-propyne] (PTMSP) films were cast from toluene solutions containing PTMSP and either 4,4′-diazidobenzophenone or 4,4′-(hexafluoroisopropylidene)diphenyl azide. The composite films were clear and homogeneous and were cross-linked by UV irradiation at room temperature or thermal annealing at 180°C. Low levels of the bis(aryl azide) (1–5 wt %) were effective in rendering the films insoluble in toluene and THF, both good solvents for PTMSP. The process is simple and effective, and thus PTMSP can be readily converted to mechanically stable membranes with permeabilities and separation factors comparable or higher than those of poly(dimethylsiloxane). The films were characterized by measuring their density, their permeability toward O₂ and N₂, and their spectroscopic properties. Compared to PTMSP, films containing bis(aryl azide) cross-linkers had lower permeabilities and higher separation factors, consistent with a reduction in free volume. When the films were cross-linked photochemically, the permeabilities declined further and the separation factor increased. Films cross-linked thermally had permeabilities comparable to their PTMSP/azide precursors, and density and swelling measurements suggest that higher free volumes are obtained in thermally cross-linked films. All films stored in air suffered from a slow decline in permeability which may reflect slow surface oxidation of the films. When stored in vacuum, cross-linked films were stable and showed no loss in permeability, but the permeability of uncross-linked PTMSP films stored under the same conditions fell to 70% of their original value in 1 month. We attribute the permeability decline to densification accelerated by impurities and solvents. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 959–968, 1998     

Surfactant assisted polymerization of tetrafluoroethylene in supercritical carbon dioxide with a pilot scale batch reactor

Chain‐free radical polymerization of tetrafluoroethylene (TFE) was carried out in supercritical carbon dioxide (scCO₂), at 50 °C and 121–133 bar, with tertiary‐amyl‐per‐pivalate as a free radical initiator, using a 5‐L pilot scale batch reactor. Experiments were carried out both in the absence and in the presence of perfluoropolyether (PFPE) carboxylate surfactants. Stabilizers were employed under the free acid form and as sodium and calcium salts. An expanded fibrillated poly(TFE) was obtained in all experiments. In the case of surfactant‐free polymerizations, the product was mainly constituted by irregular shape macroparticles having size in the range 200–500 μm. Quite interestingly, when the free acid surfactant was used, a clear acceleration of the polymerization rate was observed and smaller polymer particles with more regular quasi‐spherical morphology were obtained. Melt fusion crystallinity of as‐polymerized poly(TFE) seemed not substantially affected by the presence of the stabilizers and was rather high (80–86%) suggesting that polymerization mainly occurs at polymer particle surface. All these elements suggest that FLUOROLINK® 7004H PFPE carboxylic acid decreases coagulation of primary polymer particles leading to an increase in polymer surface area. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 257–266, 2008     

Evaluation of the free‐volume theory of diffusion

General characteristics of the free‐volume theory of diffusion are discussed, and a recent data‐theory comparison involving free‐volume theory is critically evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 501–507, 2003     

Theoretical study of tetrahydrofuran: Comparative investigation of spectroscopic and structural properties between gas and liquid phases

Rovibrational spectroscopic constant of tetrahydrofuran (THF) dimer have been calculated starting from three potential energy curves, each one obtained in a different way: (i) by ab initio calculations at MP2/aug‐cc‐pVDZ level; (ii) using Lennard‐Jones liquid parameters available in the literature, and (iii) from the pair obtained through Monte Carlo Simulation of liquid THF. The comparison among these results allowed the characterization of many solvent effect contributions. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Effect of physical aging of poly(1‐trimethylsilyl‐1‐propyne) films synthesized with TaCl5 and NbCl5 on gas permeability,fractional free volume,and positron annihilation lifetime spectroscopy parameters

The effect of physical aging on the gas permeability, fractional free volume (FFV), and positron annihilation lifetime spectroscopy (PALS) parameters of dense, isotropic poly(1‐trimethylsilyl‐1‐propyne) (PTMSP) films synthesized with TaCl₅ and NbCl₅ was characterized. As‐cast films were soaked in methanol until an equilibrium amount of methanol was absorbed by the polymer. When the films were removed from methanol, film thickness initially decreased rapidly and was almost constant after 70 h in air for both catalysts. This timescale was much longer than the timescale for complete methanol desorption (ca. 5 h). From the film‐thickness data, the reduction in FFV with time was estimated. For samples prepared with either catalyst, the kinetics of FFV reduction were well‐described by a simple model based on the notion either that free‐volume elements diffuse to the surface of the polymer film and are subsequently eliminated from the sample or that lattice contraction controls polymer densification. Methane permeability decreased rapidly during the first 70 h, which was the same timescale for the thickness change. The decrease in methane permeability was smaller in films prepared with NbCl₅ than with TaCl₅. The logarithm of methane permeability decreased linearly as reciprocal FFV increased, in accordance with free‐volume theory. The PALS results indicate that the concentration of larger free‐volume elements (as indicated by the intensity I₄) decreased with aging time and that the other PALS parameters were not strongly influenced by aging. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1222–1239, 2000     

Sorption and transport of hydrocarbon and perfluorocarbon gases in poly(1‐trimethylsilyl‐1‐propyne)

Pure gas solubility and permeability of H₂, O₂, N₂, CO₂, CH₄, C₂H₆, C₃H₈, CF₄, C₂F₆, and C₃F₈ in poly(1‐trimethylsilyl‐1‐propyne) (PTMSP) were determined as a function of pressure at 35°C. Permeability coefficients of the perfluorinated penetrants are approximately an order of magnitude lower than those of their hydrocarbon analogs, and lower even than those of the permanent gases. In striking contrast to hydrocarbon penetrants, PTMSP permeability to fluorocarbon penetrants decreases with increasing penetrant size. This unusual size‐sieving behavior in PTMSP is attributed to low perfluorocarbon solubilities in PTMSP coupled with low diffusion coefficients relative to those of their hydrocarbon analogs. In general, perfluorocarbon penetrants are less soluble than their hydrocarbon analogs in PTMSP. The difference in hydrocarbon and perfluorocarbon solubilities in high free volume, hydrocarbon‐rich PTMSP is much smaller than in hydrocarbon liquids and liquidlike polydimethylsiloxane. The low solubility of perfluorocarbon penetrants is ascribed to the large size of the fluorocarbons, which inhibits their dissolution into the densified regions of the polymer matrix and reduces the number of penetrant molecules that can be accommodated in Langmuir sites. From the permeability and sorption data, diffusion coefficients were calculated as a function of penetrant concentration. With the exception of H₂ and the C₃ analogs, all of the penetrants exhibit a maximum in their concentration‐dependent diffusion coefficients. Resolution of diffusion coefficients into a mobility factor and a thermodynamic factor reveals that it is the interplay between these two terms that causes the maxima. The mobility of the smaller penetrants (H₂, O₂, N₂, CH₄, and CO₂) decreases monotonically with increasing penetrant concentration, suggesting that the net free volume of the polymer–penetrant mixture decreases as additional penetrant is added to PTMSP. For larger penetrants mobility either: (1) remains constant at low concentrations and then decreases at higher penetrant concentrations (C₂H₆, CF₄, and C₂F₆); (2) remains constant for all concentrations examined (C₃H₈); or (3) increases monotonically with increasing penetrant concentration (C₃F₈). Presumably these results reflect the varying effects of these penetrants on the net free volume of the polymer–penetrant system. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 273–296, 2000     

Accurate estimation of solvation free energy using polynomial fitting techniques

This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem, 2009, 30, 2297). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and nonequidistant λ values, the solvation free energy can be estimated with high accuracy without using soft‐core scaling and separate simulations for Lennard‐Jones and partial charges. The results from our study suggest that these polynomial techniques, especially with use of nonequidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software . © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Poly[1‐(trimethylgermyl)‐1‐propyne] and poly[1‐(trimethylsilyl)‐1‐propyne] with various geometries: Their synthesis and properties

The polymerization of 1,2‐disubstituted acetylenes [1‐(trimethylgermyl)‐1‐propyne and 1‐(trimethylsilyl)‐1‐propyne] initiated by Nb‐ and Ta‐based catalytic systems was studied within a wide temperature range (?10 to +80 °C) with solvents (cyclohexane, CCl₄, toluene, anisol, and n‐chlorobutane) with variable dielectric constants (2.023–7.390). Conditions ensuring the synthesis of poly[1‐(trimethylsilyl)‐1‐propyne] (PTMSP) containing 20–80% cis units and poly[1‐(trimethylgermyl)‐1‐propyne] (PTMGP) containing 3–65% cis units were determined. The PTMSP and PTMGP samples were amorphous, exhibited a two‐phase structure characterized by the presence of less ordered regions and regions with an enhanced level of ordering, and differed in solubility. A correlation was found between the cis/trans ratio and the morphology, the geometrical density of PTMSP and PTMGP films, and the gas permeability of the polymers. The gas permeability and solubility behavior of PTMSP and PTMGP were examined in terms of the molecular characteristics of the polymer samples (the thermodynamic Kuhn segment and the Kerr electrooptic effect). It was demonstrated that the gas permeability, as well as the solubility of the polymers, was defined by their supramolecular ordering, which depended on the lengths of continuous sequences composed of units of analogous microstructures and on the flexibility of macrochains. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2133–2155, 2003     

The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations

We consider some fundamental aspects of the calculation of the pressure from simulations by performing volume perturbations. The method, initially proposed for hard-core potentials by Eppenga and Frenkel [Mol. Phys.52, 1303 (1984)] and then extended to continuous potentials by Harismiadis et al. [J. Chem. Phys. 105, 8469 (1996)], is based on the numerical estimate of the change in Helmholtz free energy associated with the perturbation which, in turn, can be expressed as an ensemble average of the corresponding Boltzmann factor. The approach can be easily generalized to the calculation of components of the pressure tensor and also to ensembles other than the canonical ensemble. The accuracy of the method is assessed by comparing simulation results obtained from the volume-perturbation route with those obtained from the usual virial expression for several prototype fluid models. Monte Carlo simulation data are reported for bulk fluids and for inhomogeneous systems containing a vapor-liquid interface.     

Sorption of methanol,dimethyl carbonate,methyl acetate,and acetone vapors in CTA and PTMSP: General findings from the GAB Analysis

Sorption of vapors of four organic compounds in two glassy polymers, cellulose triacetate (CTA) and poly[(trimethylsilyl)propyne] (PTMSP), has been reported and analyzed in terms of Guggenheim‐Anderson‐De Boer (GAB) model. These two structurally and physicochemically different glassy polymers both independently showed that one sorption site was formed by about three monomeric units. This finding held true for vapors of all characterized compounds; that is, for methanol, for its derivatives dimethyl carbonate and methyl acetate, and for acetone. The “rule of three” might thus also be applicable to other sorbates and glassy polymers. Further, an original modification of the GAB model for the sorption of alcohols in PTMSP was derived and successfully tested. Overall, the analyses of the sorption isotherms, heats of sorption and diffusion coefficients supported the view that the sorption of vapors in glassy polymers has adsorptive nature. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 561–569     

Diffusion in glassy polymers

Two versions of the free‐volume theory of diffusion are compared by considering differences in the predictions for the activation energy for the diffusion process. A number of data‐theory comparisons for free‐volume theory are discussed and evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 785–788, 2003     

Oscillatory surface tension due to finite-size effects

The simulation results of surface tension at the liquid-vapor interface are presented for fluids interacting with Lennard Jones and square-well potentials. From the simulation of liquids we have reported [M. González-Melchor et al., J. Chem. Phys. 122, 4503 (2005)] that the components of pressure tensor in parallelepiped boxes are not the same when periodic boundary conditions and small transversal areas are used. This fact creates an artificial oscillatory stress anisotropy in the system with even negative values. By doing direct simulations of interfaces we show in this work that surface tension has also an oscillatory decay at small surface areas; this behavior is opposite to the monotonic decay reported previously for the Lennard Jones fluid. It is shown that for small surface areas, the surface tension of the square-well potential artificially takes negative values and even increases with temperature. The calculated surface tension using a direct simulation of interfaces might have two contributions: one from finite-size effects of interfacial areas due to box geometry and another from the interface. Thus, it is difficult to evaluate the true surface tension of an interface when small surface areas are used. Care has to be taken to use the direct simulation method of interfaces to evaluate the predicted surface tension as a function of interfacial area from capillary-wave theory. The oscillations of surface tension decay faster at temperatures close to the critical point. It is also discussed that a surface area does not show any important effect on coexisting densities, making this method reliable to calculate bulk coexisting properties using small systems.     

On the phase equilibrium Stockmayer fluids

The fluid phase equilibrium of the Stockmayer fluid is investigated using a thermodynamic perturbation theory approach. The reference and the perturbation potential are the Lennard–Jones potential and the dipolar–dipolar interactions, respectively. They are assumed to be represented by the modified Benedict–Webb–Rubin equation of state [J.K. Johnson, J.A. Zollweg, K.E. Gubbins, Mol. Phys. 78 (1993) 591–618] and the Padé approximant [G. Stell, J.C. Rasaiah, H. Narang, Mol. Phys. 27 (1974) 1393–1414], respectively. The asymmetry found in an analogous study [M.E. van Leeuwen, B. Smit, E.M. Hendriks, Mol. Phys. 78 (1993) 271–283] based on the BWR equation of state [J.J. Nicolas, K.E. Gubbins, W.B. Streett, D.J. Tildesley, Mol. Phys. 37 (1979) 1429–1454] is now not observed on the vapour–liquid equilibrium coexistence curves of Stockmayer fluids with dipolar strength of μ^*2 = 1, 2, 3, and 4. Results agree with computer simulations for dipolar strength of μ^*2 = 1; however as strength dipole increases, liquid densities are over-estimated.     

Effect of biaxial orientation on dielectric and breakdown properties of poly(ethylene terephthalate)/poly(vinylidene fluoride‐co‐tetrafluoroethylene) multilayer films

Polymer films with enhanced dielectric and breakdown properties are essential for the production of high energy density polymer film capacitors. By capitalizing on the synergistic effects of forced assembly nanolayer coextrusion and biaxial orientation, polymer multilayer films using poly(ethylene terephthalate) (PET) and a poly(vinylidene fluoride‐co‐tetrafluoroethylene) [P(VDF‐TFE)] copolymer were produced. These films exhibited breakdown fields, under a divergent field using needle/plane electrodes, as high as 1000 kV mm^?1. The energy densities of these same materials, under a uniform electric field measured using plane/plane electrodes, were as high as 16 J cm^?3. The confined morphologies of both PET and P(VDF‐TFE) were correlated to the observed breakdown properties and damage zones. On‐edge P(VDF‐TFE) crystals induced from solid‐state biaxial stretching enhanced the effective P(VDF‐TFE) layer dielectric constant and therefore increased the dielectric contrast between the PET and P(VDF‐TFE) layers. This resulted in additional charge buildup at the layer interface producing larger tree diameters and branches and ultimately increasing the breakdown and energy storage properties. In addition to energy storage and breakdown properties, the hysteresis behavior of these materials was also evaluated. By varying the morphology of the P(VDF‐TFE) layer, the low‐field dielectric loss (or ion migration behavior) could be manipulated, which in turn also changed the observed hysteresis behavior. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 882–896