Free Volume Behavior Research Articles

Free volume behavior in spincast thin film of polystyrene by energy variable positron annihilation lifetime spectroscopy

Free volume behavior in polystyrene thin films with thickness ranging from 22 to 1200nm on silicon substrates was studied by energy variable positron annihilation lifetime spectroscopy (EVPALS). The films were prepared by spincasting from toluene solutions of 0.5–5.0wt% polystyrene with Mw=1 090 000g/mol. Distinct deviations from bulk polystyrene in thermal expansion of the free volume holes and the glass transition temperature associated with free volume behavior were observed for the thinnest film with 22nm thickness, indicating its exclusively high chain mobility. Comparison of the polystyrene concentration in the precursor solution around the overlap concentration suggests that the high chain mobility is due to less entangled chains caused by rapid removal of the solvent from the diluted solution in order to prepare very thin film.

New relation between diffusion and free volume: II. Predicting vacancy diffusion

It has been suggested that physical aging is a result of vacancies (cavities, holes or pores) travelling to the external surface where they disappear and therefore cause density increase. The Doolittle relation D = A exp(− B/f) where f is the fractional free volume and A and B are constants, has been used in previous work to describe the diffusion coefficient D (diffusivity) for vacancy transport. In part I a new empirically determined relation has been suggested as an alternative to the Doolittle relation, and this new relation has been shown to accurately model gas permeability data over a wide range of polymeric free volume. This new relation takes the form D = α exp( βf) with α and β as constants. Here we show that when the Doolittle relation is replaced with the new relation an exact analytical solution exists to the differential equation that governs the fractional free volume behaviour throughout the sample during physical aging leading to an Empirically derived Vacancy Diffusion (EVD) model for physical aging. An approximate analytical solution based on the exact solution is then compared to experimental data and other popular models such as the Kovacs, Aklonis, Hutchinson and Ramos phenomenological model and the Curro, Lagasse and Simha vacancy diffusion model. This EVD model is also combined with a lattice contraction model to form a dual lattice contraction and vacancy diffusion model which is compared with McCaig, Paul and Barlow's experimental results, showing a good correlation. Further support for the new EVD model is revealed by its similarity with the early established constitutive kinetic equation. Previous aging models are complicated and difficult to implement, therefore, a model that is easy to implement and physically meaningful such as this EVD model is highly sought after. An application of the model reveals that vacancy diffusion to the external surface is the dominant aging mechanism within polysulfone thin films (<1 μm), but not within the thick films (>1 μm).

Correlations between free volume and pile-up behavior in nanoindentation reference glasses

Reliable interpretation of nanoindentation data often requires that corrections be made for geometric effects such as material pile-up. These corrections are often made with the assumption that the reference glasses used to calibrate the instrument are not susceptible to such effects. This letter presents the pile-up behavior of four silicate reference glasses, (a proprietary fused silica supplied by Hysitron, Inc., Corning 1737f, Corning 2947 (soda-lime-silica), and Schott BK-7, respectively), and correlates their tendency to pile-up with the free volume of their network structures. Irrespective of the reference glass that is used, shallow penetration depths (i.e., < 150nm) should be corrected for the errors induced by pile-up in the reference glass to avoid anomalous trends in modulus and hardness during nanoindentation studies.

Positron lifetime studies on the free volume changes during curing of rubber‐carbon black composites

AbstractThe free volume behavior as a function of time during curing of natural rubber‐carbon black composites studied by positron annihilation lifetime spectroscopy (PALS) is reported. The lifetime and intensity of the ortho‐positronium (o‐Ps) pick‐off annihilation, which correlate with the average size and the number of holes respectively, were measured as a function of curing time. The samples were cured at 160 °C, while all PALS measurements were made at room temperature. Results for curing D706 (Duradene‐706), a synthetic rubber is also reported and compared with those found from natural rubber (NR). (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Positron lifetime studies on the free volume changes during deformation of rubber‐carbon black composites

AbstractThe free volume behavior as a function of strain during deformation of natural rubber‐carbon black composites studied by positron annihilation lifetime spectroscopy (PALS) is reported. The lifetime and intensity of the ortho‐positronium (o‐Ps) pick‐off annihilation, which correlate with the average size and the number of holes respectively, were measured as a function of strain. The results show how PALS can detect the changes that occur in polymer composites samples and help explain the effect of carbon black on the properties of the composites when they are deformed under compression. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Temperature dependence of the free volume holes in polyhydroxybutyrate biopolymer: A positron lifetime study

AbstractThe size of the free volume holes and their distributuion in polyhydroxybutyrate (PHB) biopolymer have been studied using positron annihilation lifetime spectroscopy (PALS). The measurements were performed as a function of the temperature from 243 to 363 K. The temperature dependence of the free volume hole shows a glass transition temperature, Tg at 278 K. The free volume behaviour of PHB shows a small linear increase with temperature below Tg and a steeper increase above Tg. The thermal expansion coefficients of the free volume hole were determined to be 4.78 x 10–3 and 12.5 x 10–3 / K below and above Tg, respectively. The free volume hole distribution shows a narrow distribution below Tg. With increasing temperature, the maximum of the distributions of the free volume holes shifts to higher values. Meanwhile, widening of the distribution is smaller in lower temperature ranges and more pronounced at higher temperatures, especially above Tg. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Classical and recent free-volume models for polymer solutions: A comparative evaluation

In this work, two “classical” (UNIFAC-FV, Entropic-FV) and two “recent” free-volume (FV) models (Kannan-FV, Freed-FV) are comparatively evaluated for polymer–solvent vapor–liquid equilibria including both aqueous and non-aqueous solutions. Moreover, some further developments are presented here to improve the performance of a recent model, the so-called Freed-FV. First, we propose a modification of the Freed-FV model accounting for the anomalous free-volume behavior of aqueous systems (unlike the other solvents, water has a lower free-volume percentage than polymers). The results predicted by the modified Freed-FV model for athermal and non-athermal polymer systems are compared to other “recent” and “classical” FV models, indicating an improvement for the modified Freed-FV model for aqueous polymer solutions. Second, for the original Freed-FV model, new UNIFAC group energy parameters are regressed for aqueous and alcohol solutions, based on the physical values of the van der Waals volume and surface areas for both FV-combinatorial and residual contributions. The prediction results of both “recent” and “classical” FV models using the new regressed energy parameters are significantly better, compared to using the classical UNIFAC parameters, for VLE of aqueous and alcohol polymer systems.

Investigation of free volume, interfacial, and toughening behavior for cyanate ester/bentonite nanocomposites by positron annihilation

AbstractEffects of filler on microstructure and toughening behavior of cyanate ester (CE)/bentonite (BT) nanocomposites with different content of BT have been studied by positron annihilation lifetime spectroscopy, X‐ray diffraction, transmission electron microscopy, dynamic mechanical analysis, etc. The interesting results found by PALS indicate that the size and concentration of the free volume holes and the apparent free volume fraction increased with increasing the content of BT, which indicates that adding nano‐layers to thermosetting materials can lead to the high crosslinking density structure “looser.” The experimental results reveal that the increases in size of free volume holes and apparent free volume fraction are related to the increasing conversion of cure reaction. On the other hand, the mechanism of toughening (by adding the nano‐clay to the thermosetting material) has been discussed by combining free volume and interfacial property. It is shown that, for the high crosslinking thermosetting material‐based nanocomposites, both the property of free volume and dispersion state of nano‐layers are the two key factors in determining toughening property. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 1509–1515, 2006

Phase behavior and thermal dynamic properties of free volume on SMMA/SMA copolymer blend studied by PALS method

The temperature dependence of the free volume in SMMA/SMA (30/70) blend was investigated by the positron annihilation life spectroscopy (PALS) at different heating rates according to the free volume theory, and the thermodynamics characteristics of the phase behavior of the polymer blends was also explored. At temperatures above Tg, we found from the positron annihilation life spectra that when the structural relaxation time is comparable with the retention time, the temperature dependence of the free volume parameters obviously departs from the linear relation. Based upon the change tendency of the free volume concentration I3 with temperature, it is postulated that there is a growing stage of the phase separation in the same temperature range.

Free volume and the physico‐mechanical behaviour of polyurethane/polyacrylonitrile interpenetrating polymer networks: positron annihilation results

AbstractA series of semi‐interpenetrating polymer networks (SIPNs) of polyurethane (PU) and polyacrylonitrile (PAN) in the weight ratios 90/10, 70/30, 60/40 and 50/50 PU/PAN were prepared using polyethylene glycol, 4,4′‐diphenylmethane diisocyanate and acrylonitrile by sequential polymerization. Differential scanning calorimetry and scanning electron microscopy techniques were used to find the glass transition temperature and surface morphology of SIPNs. The tough and transparent SIPN films were characterized for physico‐mechanical properties such as density, surface hardness and tensile properties. Positron annihilation lifetime spectroscopy (PALS) was used to measure the free volume behaviour of the IPNs. The sorption behaviour of IPNs with benzene penetrant was also measured. An attempt was made to correlate the PALS results with the mechanical and sorption properties of the SIPNs. Copyright © 2005 Society of Chemical Industry

A free-volume term based on the van der Waals partition function for the UNIFAC model

The objective of this work was to develop a model that takes into account the unique free-volume effect of water. The free-volume percentage of water is less than that of most polymers. This is opposite to the free-volume behavior of most solvents with polymers. As a result, the free-volume term in the UNIFAC-FV model introduced by Oishi and Prausnitz fails for aqueous systems. In the new model a free-volume term derived from the generalized van der Waals partition function is added to the combinatorial and residual terms of UNIFAC. In UNIFAC the geometric parameters were generally obtained directly from the van der Waals values. For water, however, these parameters were regressed. With the new free-volume term better predictions were obtained when the standard van der Waals geometric parameters for water were used. The new model was compared with the UNIFAC-FV model of Oishi and Prausnitz and the Entropic-FV model of Elbro et al. The new model was found to give better predictions for the aqueous polymer systems as well as for the non-aqueous polymer systems.

Mechanically alloyed Zr–Cu–Al–Ni–C glassy powders

Abstract In this contribution we report on the synthesis of glassy Zr55Cu30Al10Ni5 alloys with a carbon content up to 4 at.% by mechanical alloying which cannot be produced by casting techniques. X-ray analysis and differential scanning calorimetry, both in isochronal and isothermal mode, were carried out to assess the glassy nature of the powders. The viscosity was investigated by parallel plate rheometry and the crystallisation mechanism and kinetics are discussed in the framework of the Johnson–Mehl–Avrami (JMA) model. The comparison between carbon-free and carbon-containing alloys suggests a strong influence of increasing carbon content on the total free volume and viscous flow behaviour of the alloys and on the chemical and topological short-range order, affecting significantly the thermal stability and the crystallisation behaviour of the glassy phase and the supercooled liquid.

Ortho‐positronium lifetime distribution analyzed with MELT and LT and free volume in poly(ε‐caprolactone) during glass transition, melting, and crystallization

AbstractPositron annihilation lifetime spectroscopy (PALS) was used to study the free volume behavior in the temperature range between 100 and 370 K in semicrystalline poly(ε‐caprolactone) (PCL). For the analysis of the spectra we used the well‐known routine MELT as well as the new program LT8.0, which allows both discrete and log‐normal distributed annihilation rates. From experiments, confirmed by the analysis of simulated spectra, we found that MELT returns too large values for the o‐Ps lifetime τ3 associated with too small intensities I3. This is due to the underestimation of the width of o‐Ps lifetime distribution in MELT (the spectra analyzed contained 3 million counts). The same effects were observed in the parameters obtained from the discrete term analysis. LT, however, returns, when allowing the o‐Ps lifetime to be distributed, rather accurate values for τ3, I3, and the width (standard deviation σ3) of the o‐Ps lifetime distribution. The effect of the glass transition, melting, and crystallization on the annihilation parameters was observed. These results were compared with differential scanning calorimetry (DSC) and pressure–volume–temperature (PVT) experiments. From this comparison, the number density of holes and the fractional free (hole) volume have been estimated. At a “knee” temperature Tk ≈ 1.5 Tg, a leveling off of the o‐Ps lifetime τ3 and a distinct decrease in the width, σ3, of its distribution was observed; the latter effect was detected for the first time. Fast motional processes and/or the disappearance of the dynamic heterogeneity of the glass and the transition to a homogeneous liquid are discussed as possible reasons for these effects. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3077–3088, 2003

Miscibility, free volume behavior and properties of blends from cellulose acetate and castor oil-based polyurethane

A series of blend films from cellulose acetate (CA) and castor oil-based polyurethane (PU) were prepared. Morphology, miscibility, free volume behavior and properties of such blend films were investigated by wide-angle X-ray diffraction (WXRD), infrared, scanning electron microscopy (SEM), differential scanning calorimetry (DSC), positron annihilation lifetime spectroscopy (PALS), thermogravimetric analysis and tensile test. The results indicated that lager free volume cavities did not form at the interface of two polymers although a certain degree of phase separation was found by the studies of SEM and DSC. Strong intermolecular hydrogen bonding interactions at the interface, which was proved by Fourier transform infrared spectroscopy, favors even better molecular packing, that is, PU dispersed in CA continuous phase to form fine microphase separation domain in the CA-rich blends. Due to such special interactions in the fine microphase separation domain structure, optimized properties of tensile strength, breaking elongation and cold-resistivity were obtained in the blend film with 75wt% CA. The toughness of all the blend films was significantly higher than that of the film CA, owing to the plasticizing of PU elastomer in the blends.

Humidity‐induced plasticization and antiplasticization of polyamide 6: A positron lifetime study of the local free volume

AbstractPolyamide 6 (PA6) was studied using positron annihilation lifetime spectroscopy (PALS). From theortho‐positronium lifetime τ3the size of local free volumes (holes) was estimated. In dry PA6 the mean hole volumevvaried between 70 Å3and 128 Å3when the temperature increased from 25 to 220°C. From the comparison of the coefficient of thermal expansion of macroscopic volume with that of hole volume a number density of holesNhof 0.8 nm−3was estimated. The mean hole volume of PA6 exposed to atmospheres of different relative humidity (RH) was compared with thev(T) behavior of dry PA6. We propose a phenomenological model in whichTgandvg, the glass transition temperature and the mean hole volume atTg, are allowed to vary withRH. AssumingTg(RH) as given in the literature, thevg(RH) were estimated from our experiments. In the range 0 &lt;RH&lt; 90%, thevgof the humid PA6 was always smaller than in the dry polymer, while nearRH= 100% both values became approximately identical. Two ranges of sorption behavior were observed. For small and mediumRH,vgdecreases by up to 19 Å3forRH= 45%, which corresponds to more than half of the volume of a water molecule. This behavior ofvgwas interpreted as antiplasticization (loss of free volume) of the glassy polyamide. For largerRH,vgincreases again toward the value of dry PA6, indicating a plasticization (gain of free volume) behavior that compensates and finally nullifies the former antiplasticization. The behavior of the local free volume in moist PA6 corresponds well to the known variation of the specific volume. Our results deliver experimental evidence for the decrease in the unrelaxed free volume of the (glassy) water–PA6 mixture with respect to that of the dry glassy polymer. The results are also discussed in terms of a simple hole‐filling model and of the hypothesis of firmly and loosely bound water molecules in polyamides. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 244–255, 2002; DOI 10.1002/app.10319

Bulk Volume Behavior of Pressure Densified Amorphous Polymers and Free Volume Behavior by Positron Annihilation Lifetime Measurement

Bulk Volume Behavior of Pressure Densified Amorphous Polymers and Free Volume Behavior by Positron Annihilation Lifetime Measurement

Characterization of thermotropic liquid crystalline polyester/polycarbonate blends: Miscibility, rheology, and free volume behavior

Miscibility, rheology, and free volume properties of blends of thermotropic liquid crystalline polymers (TLCPs) (Vectra A950) and polycarbonate (PC) are studied in this work. Despite the unusual increase in Tg of the PC phase, the blends are found to be generally immiscible. Transesterification may occur during blending and be the cause of the increase of Tg of the PC phase and the partial miscibility of the blends at high TLCP concentrations. With regard to the melt rheology of these materials, according to a three-zone model, dynamic moduli of Vectra A950 show plateau- and transition-zone behavior, while PC exhibits terminal-zone behavior. The blends show only terminal-zone behavior at low Vectra A950 contents (≤50%) and terminal- and plateau-zone behavior at higher Vectra A950 contents. The relaxation time of Vectra A950 is much longer than PC and the blends have relaxation times greater than additivity. Both the complex and steady shear viscosities of the blends increase with the addition of Vectra A950. This is attributed to interfacial association, which retards the reorientation and alignment of the Vectra A950 phase in the molten state. The Cox–Merz rule holds true for PC but not for Vectra A950 and the blends. Free volume properties on an angstrom scale evaluated by positron annihilation lifetime spectroscopy (PALS) indicate that Vectra A950 has smaller, fewer free volume cavities than PC and the variation of free volume behavior in the blends can be explained in terms of blend miscibility. The measured densities of the blends agree well with the free volume fractions of the blends determined from PALS. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 2319–2330, 2000

Studies on the free volume and the volume expansion behavior of amorphous polymers

In order to estimate the free volume contribution on the volume change, we investigated the relationship between the volume expansion behavior by Pressure–Volume–Temperature measurement apparatus and the free volume behavior by Positron Annihilation Lifetime Spectroscopy for some amorphous polymers. From these results, the free volume fraction of the amorphous polymers was calculated by assuming that the core volume increases at a constant rate with temperature. It was found that the amount of free volume was not constant even in the glassy state and it played a very important role in the volume expansion.

Miscibility and free volume behaviour of a number of polymer blends containing only thermotropic liquid crystalline polymers

An extensive study has been undertaken on a number of blends containing only thermotropic liquid crystalline polymers (TLCPs) as only components. The effect of the structure of the TLCPs on their miscibility and free volume properties (probed by positron annihilation lifetime spectroscopy) is presented in this work. Although all TLCPs studied are nematic and the experience with low molecular weight liquid crystals is that a common mesophase ensures miscibility, blends of TLCPs with each other show a wide range of miscibilities. The polymeric aspects of TLCPs such as their molecular chemistry, structure and conformation are also found to be important in determining miscibility in blends of such materials. Regardless of their various miscibilities, TLCP blends tend to display smaller, fewer free volume sites than expected from a weighted average. This is ascribed to the intrinsic affinity of nematic TLCPs. This differs from thermoplastic blends where it has been found that degree of blend miscibility alters free volume behaviour as a function of blend composition.

Characterization of thermotropic liquid crystalline polyester/polycarbonate blends: Miscibility, rheology, and free volume behavior

Characterization of thermotropic liquid crystalline polyester/polycarbonate blends: Miscibility, rheology, and free volume behavior