Free volume and water uptake in a copolymer hydrogel series

A copolymer of 2-hydroxyethyl methacrylate (HEMA) with 2-ethoxy ethyl methacrylate (EEMA) was synthesized and the molecular mobility, free volume, and density properties examined as a function of composition. These properties were correlated with the equilibrium water uptake in order to determine which of the properties were most influential in causing high water sorption, as these materials are suitable candidates for hydrogel systems. It was found that the polar HEMA repeat unit results in a rigid, glassy sample at room temperature due to the high degree of hydrogen bonding between chains whereas high EEMA content leads to rubbery samples with subambient glass transition temperatures. The free volume properties on the molecular scale measured by positron annihilation lifetime spectroscopy (PALS) showed that higher HEMA content led to smaller, fewer holes and a lower free volume fraction than EEMA. Therefore the high water uptake of HEEMA-containing copolymers is largely related to the high polarity of the HEMA unit compared to EEMA, despite the low content of free volume into which the water can initially diffuse. Trends in density with copolymer composition, as measured on a macroscopic level, differs to that seen by PALS and indicates that the two techniques are measuring different scales of packing. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 463–471, 1998     

Sorption of small molecules in various polycarbonates and Kapton-H

Pressure-composition isotherms were determined at 20°C for CO₂ in Kapton and various substituted polycarbonates and for H₂O, Ar, N₂, CH₄, and acetone in bisphenol-A-polycarbonate. The isotherms are described by two parameters an average free energy of sorption and a width of a Gaussian distribution of free sorption energies. Within the framework of a recent model these parameters can be calculated assuming an elastic distortion of the polymer caused by the incorporation of solute atoms in preexisting holes. By comparing experimental values with predictions of the model the experimental width of the free energy distribution is only 30% smaller than the theoretical one. Functional relationships are obeyed between the sorption parameters on the one hand and glass transition temperature, average hole volume, and molecular volume of the solute on the other hand. Deviations occur for larger molecules like acetone and ethylene which are attributed to a viscoelastic distortion of the polymer. Comparing free energies of solution for the rubbery and glassy state of the polymer reveals more negative values for the glassy polymers despite their extra elastic distortion energy. This discrepancy is overcome by taking into account that the occupied volume has to be re-formed in the case of the rubbery or liquid polymer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 483–494, 1998     

Effect of water sorption on oxygen‐barrier properties of aromatic polyamides

Aromatic polyamides based on poly(m‐xylylene adipamide) (MXD‐based polyamides) and poly(hexamethylene isophthalamide) (HMD‐based polyamides) were examined. Insight into the excellent gas‐barrier properties was obtained by the characterization of the effect of water sorption on the thermal transitions, density, refractive index, free‐volume hole size, and oxygen‐transport properties. Reversing the carbonyl position with respect to the amide nitrogen substantially lowered the oxygen permeability of MXD‐based polyamides in comparison with that of HMD‐based polyamides by facilitating hydrogen‐bond formation. The resulting restriction of conformational changes and segmental motions reduced diffusivity. The primary effect of water sorption was a decrease in the glass‐transition temperature (T_g) attributed to plasticization by bound water. No evidence was found to support the idea that sorbed water filled holes of free volume. When the polymer was in the glassy state, the drop in T_g accounted for hydration‐dependent changes in the density, refractive index, and free‐volume hole size. The correlation of the oxygen solubility with T_g and density confirmed the concept of oxygen sorption as filling holes of excess free volume. In some cases, water sorption produced a glass‐to‐rubber transition. The onset of rubbery behavior was associated with a minimum in the oxygen permeability. The glass‐to‐rubber transition also facilitated the crystallization of MXD‐based polymers, which complicated the interpretation of oxygen‐transport behavior at higher relative humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1365–1381, 2005     

A free-volume hole-filling model for the solubility of liquid molecules in glassy polymers 2: Experimental validation

A model developed in a preceding paper for the solubility of liquids into glassy polymers has been validated with experimental results for a range of liquids in polycarbonate. The model gave good predictions for an average free-volume hole size of 65 cm³/mol and a free volume of 9%, which are consistent with measurements from other techniques. The fit was good apart from with water and small alcohols, and this is believed to be due to these molecules pairing or clustering within the free-volume holes. Infra-red spectroscopy confirmed the evidence of pairing and once this was included in the model, better predictions resulted. In all cases, the model was within an order of magnitude of the experimental value, which is considered very good as all parameters used are fundamental and quite accessible. The hole-size distribution previously used to fit gas sorption was found to give poor predictions, and reasons for this are discussed. The Flory-Huggins and Flory-Rehner theories produced predictions that are far too low as these only really apply to rubbery polymers.     

Detailed‐atomistic molecular modeling of small molecule diffusion and solution processes in polymeric membrane materials

Atomistic molecular modeling techniques have proven to be a very useful tool for the investigation of the structure and dynamics of dense amorphous membrane polymers and of transport processes in these materials. As illustrations, the results of extensive atomistic molecular dynamics investigations on the transport of different small molecules in flexible chain rubbery and stiff chain glassy polymers are discussed. For this purpose bulk polymer models and interface models for liquid feed mixtures in contact with the upstream site of the respective membrane have been employed. A comparison between the static structure and the dynamic behavior of the free volume in the simulated flexible chain rubbery polymers and stiff chain glassy polymers reveals qualitative differences which are decisive for experimentally observable differences in the diffusion of small molecules in these materials. The simulation results for the interface models reflect important features of experimentally well characterized pervaporation processes.     

Evolution of nanometer voids in polycarbonate under mechanical stress and thermal expansion using positron spectroscopy

Positron Annihilation Lifetime Spectroscopy (PALS) measurements were conducted on polycarbonate subjected to either thermal expansion or to tensile and compressive strains. It was found that thermal expansion affected both the nanometer hole size and the hole number density, whereas mechanical stress affected mainly the size of existing holes, and did not generate or eliminate holes in the quasielastic deformation region. The effect of stress on yield and postyield behavior of this glassy material was also investigated. The deduced hole volume fraction of this polymer at 25°C was 6.8 ± 0.5% from the thermal expansion experiment and 7.2 ± 1.2% from the mechanical loading experiment. When the specimen was under compression, the hole volume fraction was found to continuously decrease. This can be considered as evidence of the inability of the free volume concept in explaining the yield behavior of glassy polymers. ©1995 John Wiley & Sons, Inc.     

Partial molar volume of small molecules in glassy polymers

The sorption of atoms or molecules in glassy polymers is assumed to occur within a variety of sites belonging to the intermolecular volume and providing different space for the dissolved molecules. If the size of the small molecule is larger than the size of the site, the glassy polymer is elastically distorted during sorption of the solute molecules. Minimizing the total free energy yields the result that large sites are occupied first, giving rise to small volume changes only. By increasing the solute concentration, smaller sites have to be occupied as well and the corresponding volume changes are larger. Thus the molecules can be considered to act as probes for the intermolecular space. A quantitative analysis and comparison with experimental results provides information on the intermolecular space in a glassy polymer. Compared to the dual-sorption model, the model of this study is able to explain the nonlinear relationship between volume change of the polymer and the partial pressure of the solute. At large solute concentrations, swelling of the glassy polymer or its transformation into the rubbery state occurs, which gives rise to structural changes after desorption. © 1993 John Wiley & Sons, Inc.     

Sorption of CO2 in polymers observed by positron annihilation technique

Positron annihilation lifetimes were measured for several polymers in the atmosphere of high pressure CO₂ gas. At low CO₂ pressured both ₃ andI ₃ decreased due to the Langmuir-type sorption, and at higher pressures their values recovered because the Henry-type sorption takes over. The amount of sorbed CO₂ and dilation of the bulk volume were measured simultaneously, and the free volume fraction was determined at each CO₂ pressure. The free volume fraction became smaller (for polyimide and polycarbonate) or slightly larger (for polyethylene) with the progress of sorption. However, the size of the o-Ps hole estimated from the ₃ value increased regardless of the change of the free volume fraction. It appears that o-Ps is selectively looking at larger holes or expanding the holes in which it is accommodated. For polycarbonate, which remains to be glassy even at the largest CO₂ sorption attained in the experiment, the o-Ps hole size became larger than that before sorption. This implies that, even if the polymer is glassy as bulk, the sorption site is strongly prone to molecular displacement by the pressure of the penetrating Ps. Cautious consideration is evoked about directly correlating the o-Ps lifetime and intensity with the free volume in general.     

An analysis of molecular packing and chemical association in liquid water using quasichemical theory

We calculate the hydration free energy of liquid TIP3P water at 298 K and 1 bar using a quasi-chemical theory framework in which interactions between a distinguished water molecule and the surrounding water molecules are partitioned into chemical associations with proximal (inner-shell) waters and classical electrostatic-dispersion interactions with the remaining (outer-shell) waters. The calculated free energy is found to be independent of this partitioning, as expected, and in excellent agreement with values derived from the literature. An analysis of the spatial distribution of inner-shell water molecules as a function of the inner-shell volume reveals that water molecules are preferentially excluded from the interior of large volumes as the occupancy number decreases. The driving force for water exclusion is formulated in terms of a free energy for rearranging inner-shell water molecules under the influence of the field exerted by outer-shell waters in order to accommodate one water molecule at the center. The results indicate a balance between chemical association and molecular packing in liquid water that becomes increasingly important as the inner-shell volume grows in size.     

Isotope effect in the diffusion of hydrogen and deuterium in polymers

Temperature dependences of diffusion and permeation coefficients of hydrogen and deuterium in glassy and rubbery polymer films have been measured. The size of the free volume element in rubbery polymers has been calculated according to the theory of Frisch and Rogers for the quantum isotope effect, but the free volume is too large for precise calculation below the glass-transition temperature. The cooperative movement of segments is also discussed using the ratio of preexponential factors for diffusion mechanisms above and below the glass-transition temperature.     

Understanding the effect of skin formation on the removal of solvents from semicrystalline polymers

The effect of glassy skin formation on the drying of semicrystalline polymers was investigated with a comprehensive mathematical model developed for multicomponent systems. Polymers with high glass‐transition temperatures can become rubbery at room temperature under the influence of solvents. As the solvents are removed from the polymer, a glassy skin can form and continue to develop. The model takes into account the effects of diffusion‐induced polymer crystallization as well as glassy–rubbery transitions on the overall solvent content and polymer crystallinity. A Vrentas–Duda free‐volume‐based diffusion scheme and crystallization kinetics were used in our model. The polymer–solvent system chosen was a poly(vinyl alcohol) (PVA)–water–methanol system. The drying kinetics of PVA films were obtained by gravimetric methods with swollen films with known water/methanol concentrations. The overall drying behaviors of the polymer system determined by our model and experimental methods were compared and found to match well. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3191–3204, 2005     

Network structure and plasticization of epoxy-based resins

The sorption behaviour of water molecules in epoxy-based thermosetting networks is discussed and related to the modifications of their properties. The hypothesized sorption modes and the corresponding mechanisms of plasticization are discussed on the basis of experimental vapor and liquid sorption tests, differential scanning calorimetry (DSC), thermomechanical analysis (TMA) studies, and dynamic mechanical analyses. Three modes of moisture sorption are assumed: increase in the free volume of the system, hydrogen bonding onto hydrophilic groups present in the network and adsorption onto the surfaces of “holes” which define the excess free volume of the glassy structure. The less stiff Diglycidyl ether of bisphenol-A (DGEBA) systems have no appreciable sorption via hydrogen bonding, but rather most of the moisture absorbed is due to the free volume increase and adsorption in the “holes”. On the other hand, the stiffer Tetraglycidyl Diaminodiphenyl Methane (TGDDM) systems absorb more moisture through significant hydrogen bonding rather than by the free volume increase. High plasticizations, evident as T_g depressions by 30 to 80°C, are possible being experimentally observed for the stiffer TGDDM resins. Relationships derived from the free volume theory or the classical thermodynamic treatment may be used to describe the dependence of T_g on the composition of miscible blends.     

The electronic structure of free water clusters probed by Auger electron spectroscopy

(H2O)(N) clusters generated in a supersonic expansion source with N approximately 1000 were core ionized by synchrotron radiation, giving rise to core-level photoelectron and Auger electron spectra (AES), free from charging effects. The AES is interpreted as being intermediate between the molecular and solid water spectra showing broadened bands as well as a significant shoulder at high kinetic energy. Qualitative considerations as well as ab initio calculations explain this shoulder to be due to delocalized final states in which the two valence holes are mostly located at different water molecules. The ab initio calculations show that valence hole configurations with both valence holes at the core-ionized water molecule are admixed to these final states and give rise to their intensity in the AES. Density-functional investigations of model systems for the doubly ionized final states--the water dimer and a 20-molecule water cluster--were performed to analyze the localization of the two valence holes in the electronic ground states. Whereas these holes are preferentially located at the same water molecule in the dimer, they are delocalized in the cluster showing a preference of the holes for surface molecules. The calculated double-ionization potential of the cluster (22.1 eV) is in reasonable agreement with the low-energy limit of the delocalized hole shoulder in the AES.     

Free volume studies in miscible polymer blend systems

This paper summarises the currently available literature concerned with measurement of free volume in miscible, amorphous polymer blends using positron annihilation lifetime spectroscopy (PALS) which probes excluded volume at the angstrom level. Previously reported data is compared with new data from a range of different blend systems. Miscible blends tend to show a negative deviation of free volume size (and to a lesser degree free volume fraction) on mixing due to the intimacy of packing of the blend component macromolecules. A largely immiscible system is also reported and shows a different behaviour (positive deviation of free volume size) and this is ascribed to additional free volume at the interface.     

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

Theories 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     

Connecting free volume with shape memory properties in noncytotoxic gamma‐irradiated polycyclooctene

The free volume holes of a shape memory polymer have been analyzed considering that the empty space between molecules is necessary for the molecular motion, and the shape memory response is based on polymer segments acting as molecular switches through variable flexibility with temperature or other stimuli. Therefore, thermomechanical analysis (TMA) and positron annihilation lifetime spectroscopy (PALS) have been applied to analyze shape recovery and free volume hole sizes in gamma‐irradiated polycyclooctene (PCO) samples, as a noncytotoxic alternative to more conventional PCO crosslinked via peroxide for future applications in medicine. Thus, a first approach relating structure, free volume holes and shape memory properties in gamma‐irradiated PCO is presented. The results suggest that free volume holes caused by gamma irradiation in PCO samples facilitate the recovery process by improving movement of polymer chains and open possibilities for the design and control of the macroscopic response. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1080–1088     

The temperature dependence of the local free volume in polyethylene and polytetrafluoroethylene: A positron lifetime study

Positron lifetime measurements, performed in the temperature range 80–300 K, are reported for polyethylene (PE) and polytetrafluoroethylene (PTFE). The lifetime spectra have been analyzed using the data processing routines LIFSPECFIT and MELT. Two long-lived components appear, which are attributed to pick-off annihilation of ortho-positronium in crystalline regions and at holes in the amorphous phase. The ortho-positronium lifetimes, τ₃ and τ₄, are used to estimate the crystalline packing density and the size of local free volumes in the crystalline and amorphous phases. The interstitial free volume in the crystals exhibits a weak linear increase with the temperature which is attributed to thermal expansion of the crystal unit cell. In the amorphous phase, the hole volume varies between 0.053 and 0.188 nm³ (PE) and between 0.152 and 0.372 nm³ (PTFE). Its temperature variation may be fitted by two straight lines, the intersection of which is used to estimate a glass transition temperature of T_g = 195 K for both PE and PTFE. The slopes of the free volume in the glassy and crystalline phases with the temperature correlate well with each other. The coefficients of thermal expansion of the hole volume are compared with the macroscopic volume change below and above the glass transition. From this comparison a fractional hole volume at T_g of 4.5 (PE) and 5.7% (PTFE) and a number of 0.73 (PE) and 0.36 (PTFE) × 10²⁷ holes/m³ is estimated. Finally, it is found that the intensity of o-Ps annihilation in crystals shows a different temperature dependence to that in the amorphous phase. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1513–1528, 1998     

Positron annihilation: a unique method for studying polymers

Positron annihilation is a unique technique for studying the local free volume of polymers. Employing the positron annihilation lifetime spectroscopy (PALS) the size and size distribution of subnanometer size holes which constitute the excess free volume may be studied. In combination with macroscopic volume data the fractional free volume and the number density of holes may be estimated. After presenting the principles of the method, some examples typically for the investigation of the free volume in polymers will be given. Moreover, the study of interdiffusion in demixed polymer blends and further applications are shortly reviewed     

Pure hydrocarbon sorption properties of poly(1-trimethylsilyl-1-propyne) (PTMSP), poly(1-phenyl-1-propyne) (PPP), and PTMSP/PPP blends

Propane and n-butane sorption in blends of poly(1-trimethylsilyl-1-propyne) (PTMSP) and poly(1-phenyl-1-propyne) (PPP) have been determined. Solubilities of propane and n-butane increased as the PTMSP content in the blends increased. This result is consistent with the higher free volume of PTMSP-rich blends and the better thermodynamic compatibility between PTMSP and these hydrocarbons. Propane and n-butane sorption isotherms were well described by the dual-mode model for sorption in glassy polymers. PTMSP/PPP blends are strongly phase-separated, heterogeneous materials. A noninteracting domain model developed for sorption in phase-separated glassy polymer blends suggests that sorption in the Henry's law regions (i.e., the equilibrium, dense phase of the blends) is consistent with the model. However, Langmuir capacity parameters in the blends are lower than predicted from the domain model, suggesting that the amount of nonequilibrium excess free volume associated with the Langmuir sites depends on blend composition. © 1996 John Wiley & Sons, Inc.     

Conformational rigidity and dielectric properties of polyimides

On the basis of two series of polyimides it was shown that the conformational rigidity and the presence of side voluminous substituents determine the packing of macromolecular chains in glassy state. The presence of hexafluoroisopropylidene groups leads to the increase of free volume of polymers due to the repulsion of such groups belonging to different macromolecular chains. The physical properties studied here, such as dielectric permittivity and electrets properties depend on the size of free volume. The normalized surface potential is determined by the mass fraction of fluorine content and by the conformational rigidity of those polymers.