Cavity size distributions in high free volume glassy polymers by molecular simulation

Two very permeable polymers, poly(1-trimethylsilyl-1-propyne) (PTMSP) and a random copolymer of tetrafluoroethylene and 2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole (TFE/BDD), have very similar and large fractional free volumes (FFV), but very different permeabilities. Using atomistic models, cavity size (free volume) distributions determined by a combination of molecular dynamic and Monte Carlo methods are consistent with the observation that PTMSP is more permeable than TFE/BDD. The average spherical cavity size in PTMSP is 11.2 Å whereas it is only 8.2 Å in TFE/BDD. These cavity size distributions determined by simulation are also consistent with free volume distributions determined by positron annihilation lifetime spectroscopy.     

Investigation of the chemical and morphological structure of thermally rearranged polymers

Reacting ortho-functional poly(hydroxyimide)s via a high-temperature (i.e., 350 °C–450 °C) solid-state reaction produces polymers with exceptional gas separation properties for separations such as CO₂/CH₄, CO₂/N₂, and H₂/CH₄. However, these reactions render these so-called thermally rearranged (TR) polymers insoluble in common solvents, which prevent the use of certain experimental characterization techniques such as solution-state nuclear magnetic resonance (NMR) from identifying their chemical structure. In this work, we seek to identify the chemical structure of TR polymers by synthesizing a partially soluble TR polymer from an ortho-functional poly(hydroxyamide). The chemical structure of this TR polymer was characterized using 1-D and 2-D NMR. By use of cross-polarization magic-angle spinning ¹³C NMR, the structure of the polyamide-based TR polymer was compared to that of a polyimide-based TR polymer with a nearly identical proposed structure. The NMR spectra suggest that oxazole functionality is formed for both of these TR polymers. Furthermore, gas permeation results are provided for the precursor polymers and their corresponding TR polymer. The differences in transport properties for these polymers result from differences in the isomeric nature of oxazole-aromatic linkages and morphological differences related to free volume and free volume distribution.     

Molecular dynamics simulation of diffusion of O2 and CO2 in blends of amorphous poly(ethylene terephthalate) and related polyesters

The diffusion of small molecules through polymers is important in many areas of polymer science, such as gas barrier and separation membrane materials, polymeric foams, and in the processing and properties of polymers. Molecular dynamics simulation techniques have been applied to study the diffusion of oxygen and carbon dioxide as small molecule penetrants in models polyester blends of bulk amorphous poly(ethylene terephthalate) and related aromatic polyesters. A bulk amorphous configuration with periodic boundary conditions was generated into a unit cell whose dimensions were determined for each of the simulated polyester blends in the cell having the experimental density. The diffusion coefficients for O₂ and CO₂ were determined via NVE molecular dynamics simulations using the Dreiding 2.21 molecular mechanics force field over a range of temperatures (300, 500 and 600 K) using up to 40 ns simulation time. We have focussed on the influence of the temperature, polymer dynamics, density and free volume distribution on the diffusion properties. Correlation of diffusion coefficients with free volume distribution was found.     

Role of free volume characteristics of polymer matrix in bulk physical properties of polymer nanocomposites: A review of positron annihilation lifetime studies

Polymer nanocomposites which have one or more nano-dimensional phases dispersed in polymer matrix show enhancement in bulk physical properties. In order to achieve the desired properties, a large number of polymer nanocomposites have been prepared by choosing different polymers and nanofillers. These studies showed that interfacial interaction between polymer molecules and nanofillers is the most important factor to achieve the synergistic effect towards enhancement in the bulk physical properties. The strong interfacial interaction also promotes the fine dispersion of nanofillers in a polymer matrix which consequently enables the preparation of polymer nanocomposites with higher loading of nanofillers. The polymer matrix constitutes a large volume fraction of polymer nanocomposites and hence the molecular packing of the polymer matrix itself plays a deterministic role in governing the physical properties of the nanocomposites. The strong interfacial interaction brings severe changes in the original molecular packing. In order to establish the structure-property relationships for polymer nanocomposites, characterization of molecular packing of polymer matrix in its nanocomposites is essential. In this aspect positron annihilation lifetime spectroscopy (PALS) is a highly suitable technique for characterization of free volume holes in polymers or polymer nanocomposites. The present review briefly describes the positron annihilation lifetime spectroscopy technique and relevant models for calculations of free volume hole’s size, density and their size distribution in polymer nanocomposites. We present a summary of the recent studies focussed on investigation of free volume structure (molecular packing) of polymer nanocomposites using PALS and its impact on transport, thermal and mechanical properties of the nanocomposites.     

A molecular simulation study of cavity size distributions and diffusion in para and meta isomers

Polysulfone based on bisphenol A has been extensively used as a material for membrane-based gas separation. For polymers with aromatic rings in their backbones, such as polysulfones and polyimides, changing the connecting bond positions from meta to para seems to increase their permeability and diffusivity to gases. Cavity size distributions of three isomer pairs (PSF and 3,4′-PSF, PSF-P and PSF-M, 6FDA-6FpDA and 6FDA-6FmDA) are calculated through molecular simulation. The diffusivity of small molecules in these isomers is also obtained by molecular dynamics. For all three isomer pairs, the average cavity size in para isomers is larger than in meta isomers. The molecular dynamics determined diffusion coefficients of neon in para isomers are also larger than in meta isomers. These results are consistent with the experimental observation that room-temperature gas diffusion in para isomers is faster than in meta isomers.     

Drag reduction effectiveness of macromolecules

A working hypothesis has been developed to account for observed drag reduction properties of dilute polymer solutions. Drag reduction effectiveness of polymer solutes is attributed to their ability to form a deformable network structure which inhibits the formation of microvortices in the solvent and retards their ability to migrate through the fluid, coalesce, and result in fully developed turbulence centres. The size of microvortex precursors is tentatively set in the range of 100 Å, and it is assumed that the damping (drag reduction) effect of macromolecules is due to strong association between solvent molecules and polymer chains, immobilizing many of these active precursors. The hypothesis indicates that drag reduction effectiveness of polymers should depend strongly on polymer/solvent interactions in addition to the recognized variables of molecular weight, concentration and geometry of the flow-system. The hypothesis accounts for a number of published anomalous observations and leads to new predictions of drag reduction variations with polymer molecular weight distribution, and temperature. These and related predictions are the focal points of new experimental research studies of the drag reduction phenomenon.     

Influence of polyimide precursor synthesis route and ortho-position functional group on thermally rearranged (TR) polymer properties: Conversion and free volume

Thermal rearrangement of polyimides with ortho-position groups to polybenzoxazoles and related structures has been of recent interest for producing gas separation membranes. This study explores the influence of synthesis route and ortho-position functional group on the thermal rearrangement process and the fractional free volume of thermally rearranged (TR) polymers produced from polyimides derived from 3,3′-dihydroxy-4,4′-diamino-biphenyl and 2,2′-bis-(3,4-dicarboxyphenyl) hexafluoropropane dianhydride (HAB–6FDA). Acetate, propanoate, and pivalate ortho-position functional groups were considered. Thermogravimetric analysis (TGA) was used to study thermal rearrangement at temperatures between 350 and 450 °C, and evolved gases from TGA were analyzed via mass spectrometry to characterize the byproducts of thermal rearrangement and thermal degradation. CO₂ was the major byproduct of thermal rearrangement for all samples, and its evolution began well before the onset of thermal degradation. When non-hydroxyl ortho-position groups were present in the polymers, several byproducts other than CO₂ were also observed due to the loss of these ortho-position groups before thermal rearrangement. Free volume generally increased with increasing extent of thermal rearrangement, but precise values of free volume could not be accurately determined for polymers with propanoate and pivalate ortho-position functional groups due to uncertainties in the chemical structure of partially converted materials. For polymers with acetate and hydroxyl ortho-position groups, free volume could be determined within the uncertainty of density measurements. Thermal rearrangement behavior and free volume results for acetate containing polymers synthesized via different routes were very similar. Based on these results, the chemical structure of the ortho-position functional group has a larger impact on TR polymer properties than the polyimide precursor synthesis route.     

Rigid and microporous polymers for gas separation membranes

Microporous polymers are a class of microporous materials with high free volume elements and large surface areas. Microporous polymers have received much attention for various applications in gas separation, gas storage, and for clean energy resources due to their easy processability for mass production, as well as microporosity for high performance. This review describes recent research trends of microporous polymers in various energy related applications, especially for gas separations and gas storages. The new classes of microporous polymers, so-called thermally rearranged (TR) polymers and polymers of intrinsic microporosity (PIMs), have been developed by enhancing polymer rigidity to improve microporosity with sufficient free volume sizes. Their rigidity improves separation performance and efficiency with extraordinary gas permeability. Moreover, their solubility in organic solvents allows them to have potential use in large-scale industrial applications.     

Prediction of solvent‐diffusion coefficient in polymer by a modified free‐volume theory

Several versions of free‐volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation‐of‐state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T_g) is available from the SS equation. When above the T_g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free‐volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self‐diffusion coefficient and the solvent mutual‐diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000     

Side‐chain free aromatic polyimides containing anthracene units via Diels‐Alder precursors

Side‐chain free aromatic polyimides are expected to possess extraordinary mechanical properties and stability because of strong primary and secondary bonding forces. However, their low solubility makes it difficult to characterize, process, and obtain high molecular weight polymers. We have prepared highly stable thin films of side‐chain free aromatic polyimides from soluble Diels–Alder (DA) precursors. Heating the films of the precursors above 215°C induced retro‐DA reaction, which converted the precursors to the fully aromatic polyimides. The solid‐state retro‐DA reactions were monitored by attenuated total reflection Fourier transformed infrared (ATR‐FTIR) and UV‐Vis spectrometry. A critical issue for utilizing precursor chemistry in polymer synthesis is that it may result in porous and/or deformed materials. In this work, profilometry and atomic force microscope (AFM) were applied to study the surface and volume change. Our results showed that smooth and pin‐hole free films were obtained after the thermal treatment, while the volume decreased with a percentage close to the weight loss caused by the retro‐DA reaction. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Molecular dynamics simulation of diffusion of O2 and CO2 in amorphous poly(ethylene terephthalate) and related aromatic polyesters

The diffusion of small molecules through polymers is important in many areas of polymer science, such as gas barrier and separation membrane materials, polymeric foams, and in the processing and properties of polymers. Molecular simulation techniques have been applied to study the diffusion of oxygen and dioxide of carbon as small molecule penetrants in models of bulk amorphous poly(ethylene terephthalate) and related aromatic polyesters. A bulk amorphous configuration with periodic boundary conditions is generated into a unit cell whose dimensions are determined for each of the simulated aromatic polyesters in the cell to have the experimental density. The aim for this research is to explore and investigate the diffusion of gases through bulk amorphous poly(ethylene terephthalate) and related aromatic polyesters. The diffusion coefficients for O₂ and CO₂ were determined via NVE molecular dynamics simulations using the Dreiding 2.21 molecular mechanics force field over a range of temperatures (300, 500 and 600 K) using up to 30 ns simulation time. We have focussed on the influence of the temperature, polymer dynamics, number of aromatic rings, ortho-, meta-, para-isomers, density and free volume distribution on the diffusion properties. Correlation of diffusion coefficients with free volume, temperature, number of aromatic rings, ortho-, meta- and para-isomers was found.     

The Influence of Structure on Autohesion (Self-Tack) and other forms of Diffusion into Polymers

Autohesion is discussed emphasising in particular the influence of polymer chain structure on apparent rates of diffusion. The full range of autohesive levels which exists amongst rubbery polymers is rationalised by proposing a distinction between inter-chain free volume and “intra-chain” free volume, the latter being a collation of free volume regions “contained” in cavities associated with permanent polymer chain structural features which especially apply for certain polymer types. The coincidence of several such cavities plus the intervening inter-chain space causes the formation of holes which may attain sufficient size during normal chain thermal fluctuations to facilitate forward motion of an incoming chain.

The concept of free volume has been used to demonstrate the proposed model semi-quantitatively. Comparison with a simple model, involving inter-chain free volume only, is made throughout the calculation. The proposed model, in showing general agreement for several elastomers between free volume considerations and autohesive characteristics, provides an explanation for the large difference in tackiness which exists between natural rubber and ethylene propylene copolymers.

The relationship of the proposed model with chain co-operative motion is discussed, and its apparent correlation with the diffusion through polymers of a range of gases and solvents is discussed in some detail.     

Molecular dynamics simulations to compute diffusion coefficients of gases into polydimethylsiloxane and poly{(1,5‐ naphthalene)‐co‐[1,4‐durene‐2,2′‐bis(3,4‐dicarboxyl phenyl)hexafluoropropane diimide]}

Diffusion coefficients of N₂, O₂, CO₂ and CH₄ at 298 K in polydimethylsiloxane (PDMS) and poly{[(1,5‐naphthalene)‐co‐[1,4‐durene‐2,2′‐bis(3,4‐dicarboxyl phenyl)hexafluoropropane diimide]} (6FDA‐1,5‐NDA) polymers have been estimated using molecular dynamics (MD) simulations. Estimated diffusion coefficients in PDMS decrease systematically with increasing size of the penetrant gas molecules following the experimental observations. For 6FDA‐1,5‐NDA polymer, diffusion coefficients decrease in the same order of magnitude, but differ in their sequential order, due to varying side group interactions of the polymer with the gaseous molecules. Cohesive energy density, solubility parameter and free volume of the polymers were determined using MD simulations. Reliability and accuracy of the simulations have been tested typically with the computed values of the diffusion coefficient of O₂ in PDMS polymer, which compare well with the literature data. X‐ray scattering profiles of 6FDA‐1,5‐NDA have been generated to understand the interrelationship between the morphology and diffusion coefficients. The radial distribution function was evaluated to find the contribution of atoms that are important in understanding the molecular interactions during gas diffusion in polymers. Copyright © 2007 Society of Chemical Industry     

A novel approach to polymeric microdispersions

Novel microdispersions of one polymer in another have been created by solvent devolatilization. Two incompatible polymers are first dissolved in a common solvent. The solvent is then rapidly evaporated, causing the residual polymeric solution to enter the two-phase region. Depending on the relative amounts of the two polymers and the rate of evaporation, polymer blends of widely differing morphologies are formed. Unlike previous methods employed for their production, polymer dispersions created by devolatilization have remarkably uniform particles, with the average size controllable in the range of 0.5 μm to 20 μm. If the solvent free volume fractions of the two polymers are more ore less equal, co-continuous networks are formed.     

A thermodynamically consistent, nonlinear viscoelastic approach for modeling glassy polymers

A thermodynamically consistent nonlinear viscoelastic constitutive theory is derived to capture the wide range of behavior observed in glassy polymers, including such phenomena as yield, stress/volume/enthalpy relaxation, nonlinear stress-strain behavior in complex loading histories, and physical aging. The Helmholtz free energy for an isotropic, thermorheologically simple, viscoelastic material is constructed, and quantities such as the stress and entropy are determined from the Helmholtz potential using Rational Mechanics. The constitutive theory employs a generalized strain measure and a material clock, where the rate of relaxation is controlled by the internal energy that is likewise determined consistently from the viscoelastic Helmholtz potential. This is perhaps the simplest model consistent with the basic requirements of continuum physics, where the rate of relaxation depends upon the thermodynamic state of the polymer. The predictions of the model are compared with extensive experimental data in the following companion paper.     

The Sizes of Polymer Molecules and the GPC Separation

Abstract

This introductory review explains in simplest terms the separation mechanism in GPC and the concept of size as its discriminant. Sample molecules permeate the gel to different degrees depending on their size and are kept out of the solvent stream in the interstices in correspondingly different time ratios. For rigid molecules the size is determined either by the volume or by the most prominent linear dimension. A better approximation seems to be Giddings's “mean external length.”

With polymers the decisive size parameter is the hydrodynamic volume. Its calculation from molecular weight must take into account the coiling of the polymer, its flexibility, and its interaction with the solvent. Another important consideration is the statistical nature of polymer properties which results in average values for molecular weight and size. Chain statistics yield polymer sizes that are compatible with pore dimensions of appropriate gels.     

Detection of glass transition in poly(ethylene terephthalate) and nylon-6 by positron annihilation

Positron annihilation lifetime spectroscopy (PALS) was used to investigate the phase transitions, mainly the glass transition, of poly(ethylene terephthalate) (PET) and nylon-6 during the thermal treatment of these polymers. The longest-lived component lifetime and intensity, indicative of ortho-positronium pick-off, exhibit thermal dependencies that can be attributed to the free-volume changes associated with structural transitions. Glass transition temperatures and the volume of intermolecular-space holes among polymer chains were obtained from the lifetime, τ₃ and intensity of formation, I₃, of the long-lived component of ortho-positronium. For PET, the free-volume fraction and thermal expansion coefficients related to the free-volume fraction were also obtained. Double glass transition behavior was noted in the analyzed polymers, which was consistent with their semicrystalline nature as revealed by differential scanning calorimetry. Increases in the slope of the lifetime-temperature plots for nylon-6 and PET were interpreted to suggest that glass transitions are followed by an increased free-volume cavity expansion as temperature is increased. The intensity response for PET was consistent with the association of glass transition with the reduction of crystalline consraint on segmental mobility in the amorphous phase. In contrast, the intensity behavior during the thermal treatment of nylon-6 seems to be governed more by the electronic effects occurring when the polymer chains acquire mobility than by free-volume changes. Since the sensitivity of PALS is in the order of nanometers, it is expected to give an alternative novel technique to estimate phase transitions and relaxations in polymers from the point of view of the free volume. © 1996 John Wiley & Sons, Inc.     

Graft polymerization of vinyl acetate onto silica

The free‐radical graft polymerization of vinyl acetate onto nonporous silica particles was studied experimentally. The grafting procedure consisted of surface activation with vinyltrimethoxysilane, followed by free‐radical graft polymerization of vinyl acetate in ethyl acetate with 2,2′‐azobis(2,4‐dimethylpentanenitrile) initiator. Initial monomer concentration was varied from 10 to 40% by volume and the reaction was spanned from 50 to 70°C. The resulting grafted polymer, which was stable over a wide range of pH levels, consisted of polymer chains that are terminally and covalently bonded to the silica substrate. The experimental polymerization rate order, with respect to monomer concentration, ranged from 1.61 to 2.00, consistent with the kinetic order for the high polymerization regime. The corresponding rate order for polymer grafting varied from 1.24 to 1.43. The polymer graft yield increased with both initial monomer concentration and reaction temperature, and the polymer‐grafted surface became more hydrophobic with increasing polymer graft yield. The present study suggests that a denser grafted polymer phase of shorter chains was created upon increasing temperature. On the other hand, both polymer chain length and polymer graft density increased with initial monomer concentration. Atomic force microscopy–determined topology of the polymer‐grafted surface revealed a distribution of surface clusters and surface elevations consistent with the expected broad molecular‐weight distribution for free‐radical polymerization. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 300–310, 2003     

Gel permeation chromatography of polyoxymethylene

Gel permeation chromatography of polyoxymethylene has been studied using N,N-dimethylformamide as the solvent. Polyoxymethylene samples used here are a copolymer of tetraoxane with 1,3-dioxolane and a commercial polyoxymethylene whose molecular weight distributions are moderately broad. Their intrinsic viscosities [η] range from 1.4 to 2.8 dl/g. Factors affecting chromatograms are discussed, and the operating conditions were determined by using the analytical scale GPC. On the basis of these operating conditions, the molecular weight fractionation of polyoxymethylene was carried out by using the preparative scale GPC. It was found that polyoxymethylene can be effectively fractionated to give seven to ten fractions each of them containing the fractionated polymer ranging in weight from 0.2 to 8 mg when 40 mg polymer sample was used for a run of the measurement. The fractionated polymers were also found to have a narrow molecular weight distribution within a single peak, and their M_w/M_n values decrease with increasing molecular weight.     

High performance gel permeation chromatography of polystyrene

Microparticulate crosslinked polystyrene packings in short columns have been investigated with high performance liquid chromatography instrumentation. Reliable molecular weight data for six polystyrene standards having narrow molecular weight distributions and for a polystyrene having a broad distribution have been obtained by optimizing the injection procedure, using a constant flow pump, and incorporating an internal standard into each injected solution. Experimental determinations of the dependence of the polydispersity for polystyrene standards on eluent flow rate and polymer diffusion coefficient were in agreement with a relation predicted from theoretical considerations of chromotogram broadening. Because of the dependence of chromatogram broadening on polystyrene molecular weight, high efficiency separations for high polymers were only obtained at low eluent flow rates. For low polymers, high efficiency separations may be performed at fast eluent flow rates. It was concluded that accurate molecular weight distributions can only be determined from chromatograms obtained at low eluent flow rates, which was supported by experimental measurements of polydispersity on polystyrene sample prepared by a radical polymerization at low monomer conversion. A differential weight distribution calculated from an experimental chromatogram for the polydisperse polystyrene determined at the lowest eluent flow rate (0.1 cm³min^?1) was compared with distributions predicted theoretically for polystyrenes prepared by radical polymerization. It was concluded that the experimental distribution contained a small contribution from chromatogram broadening and that most of the radicals in the polymerization of styrene terminated by combination.