Specific Free Volume Research Articles

Study of Acoustic Nature of Tetrapentylammonium Bromide in N,N-Dimethyl-Ethylmethyl Ketone Systems at Different Temperatures

Ultrasonic velocity, viscosity and density studies on solution of tetrapentylammonium bromide (Pen4NBr) in N,N-dimethylformamide, ethylmethylketone (EMK) and DMF-EMK solvent mixtures containing 0, 20, 40, 60, 80 and 100 mol % of DMF at 298, 308 and 318K have been reported. From the velocity, viscosity and density data values, various parameters namely, the adiabatic compressibility (β), Intermolecular free length (Lf), specific acoustic impedance (Z), free volume (Vf), internal pressure (πi) and relaxation time (τ) have been calculated. All these parameters have been discussed separately to throw light on the solute-solvent and solvent-solvent interactions.

Study of Acoustic Nature of Tetrapentylammonium Bromide in N,N-Dimethyl-Ethylmethyl Ketone Systems at Different Temperatures

Ultrasonic velocity, viscosity and density studies on solution of tetrapentylammonium bromide (Pen4NBr) in N,N-dimethylformamide, ethylmethylketone (EMK) and DMF-EMK solvent mixtures containing 0, 20, 40, 60, 80 and 100 mol % of DMF at 298, 308 and 318K have been reported. From the velocity, viscosity and density data values, various parameters namely, the adiabatic compressibility (β), Intermolecular free length (Lf), specific acoustic impedance (Z), free volume (Vf), internal pressure (πi) and relaxation time (τ) have been calculated. All these parameters have been discussed separately to throw light on the solute-solvent and solvent-solvent interactions.

A comparative structural, thermal and electrical study of Ca2 +, Sr2 + substituted BiMnO3

Bi1-xAxMnO3 (A=Sr, Ca; 0.40≤x≤0.55) systems have been synthesized by solid state reaction method to investigate the effect of two different cations substitution in place of Bi3+. All samples are monophasic as observed in X-ray diffraction. The Bi1-xSrxMnO3 shows the tetragonal symmetry whereas, Bi1-xCaxMnO3 shows orthorhombic as confirmed by Rietveld refinement. The Bi1-xSrxMnO3 system shows higher conductivity as compared to Bi1-xCaxMnO3. Bi0.50Sr0.50MnO3 exhibits highest conductivity of 180S/cm at 790°C which can be attributed to its higher specific free volume and uniform grain size with better distribution in entire structure. Sr2+ doped system has lower thermal expansion coefficient as compared to Ca2+ doped system.

Functional packaging materials: factors affecting the capacity and rate of water adsorption in desiccant composites

Ten different polymers were selected as possible matrices for zeolite-containing desiccant composites utilized in the preparation of functional packaging materials. Water uptake was determined at 100 % RH and the results were analyzed to identify factors influencing the capacity and rate of water adsorption. The results showed that the desiccant was able to adsorb a considerable amount of water in its free pores. The adsorption capacities of the composites depended linearly on the amount of desiccant present in the composite, but were independent of the type of polymer used. Water initially diffused rapidly into the composites, but this diffusion slowed over time and also with increasing desiccant content. The latter effect can be explained by the increase in the diffusion path as the zeolite content increases. The initial rate of diffusion depended solely on the specific free volume of the matrix, and this factor also strongly influenced the overall rate of water adsorption. However, the latter characteristic also depended on other factors, such as the dispersion of the desiccant in the matrix. Matrix type and zeolite content must be selected according to the task to be fulfilled; fast adsorption can only be achieved by using polymers with large free volumes.

Gas Solubility, Diffusivity, Permeability, and Selectivity in Mixed Matrix Membranes Based on PIM-1 and Fumed Silica

The effects that the addition of fumed silica (FS) nanoparticles has on the gas permeability, solubility, diffusivity, and selectivity of a polymer of intrinsic microporosity (PIM-1) are modeled considering the density of the composite matrix as the key input information. PIM-1 is treated as a homogeneous glassy polymer endowed with a specific free volume that increases with the amount of nanoparticles loaded, as indicated by the experimental values of mixed matrix density. The solubility isotherms of H2, He, O2, N2, CH4, and CO2 in matrices of PIM-1 with different FS loadings are calculated with the nonequilibrium lattice fluid (NELF) model. The gas diffusivity and permeability variation due to FS addition are related to the fractional free volume of the polymer phase, according to the semiempirical free volume theory equation. Remarkably, the coefficient amplifying the free volume effect increases with the molecular size of the gas, expressed by the van der Waals volume, thus allowing an estimation of t...

Mixed gas and pure gas transport properties of copolyimide membranes

AbstractCopolyimides were synthesized from dianhydride of 4,4′‐(hexafluoroisopropylidene)diphthalic anhydride (6FDA) with various diamine contents of 4,4′‐oxydianiline (ODA) and 2,3,5,6‐tetramethyl‐1,4‐phenylenediamine (TeMPD) by chemical imidization in a two‐step procedure. Polyimides (PIs) were characterized using thermogravimetric analysis, Fourier transform infrared spectroscopy, differential scanning calorimetry, as well as specific volume and free volume. The gas transport properties for pure gas and blends of CO2 and CH4 for the homopolymers and 6FDA‐ODA/TeMPD copolymers were investigated at 35°C and 150 psi pressure. In pure gas permeation, permeability of CO2 and CH4 increased with increasing TeMPD content in the diamine moiety, whereas the ideal selectivity decreased with increasing TeMPD content. In the mixed gas permeation, permeabilities and separation factor were measured as a function of CO2 feed molar fraction for five PI membranes. The behavior of pure gas and mixed gas permeabilities and separation factor of CO2/CH4 mixtures as the chemical nature of the diamine and the CO2 molar fraction in the feed gas were varied and are discussed in detail. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2013

A-site-cation deficiency in the SrCe0.9Yb0.1O3−δ perovskite: effects of charge-compensation mechanism on structure and proton conductivity

Cation non-stoichiometry is now recognised to have a significant influence on the electrical-transport properties of proton-conducting oxides. The effects of A-site-cation deficiency in the Sr1−xCe0.9Yb0.1O3−δ perovskite system with potential use in electrochemical devices are examined. Electron diffraction is used to verify the orthorhombic perovskite structure (space group, Pnma) of compositions 0 ≤ x ≤ 0.06. Combined Rietveld refinements of high-resolution neutron and X-ray diffraction data confirm a previously reported anomalous evolution of the lattice parameters within the series, with a maximum in specific free volume observed for x = 0.04. Analysis of the ion-site occupancies indicates that A-site and oxygen vacancies form up to x = 0.04, with partial partitioning of the Yb dopant over the Sr and Ce sites taking place for higher levels of Sr deficiency. The change in defect chemistry is likely to be responsible for the anomalous evolution in structural parameters, and may arise from the alleviation of strain associated with substantial octahedral tilting which occurs for a high A-site vacancy content. In addition to lattice parameters, electrical transport and stability in CO2 are also affected by dopant partitioning. The proton conductivity appears to be well correlated with both the nominal oxygen-vacancy content and the specific free volume. The stability of the series towards carbonation is not correlated to the Sr chemical potential but, instead, is lowest for the composition of greatest specific free volume.

Predicting the diffusion coefficient of water vapor through glassy HPMC films at different environmental conditions using the free volume additivity approach

Prediction of diffusion coefficient of polymer materials is important in the pharmaceutical research and becomes the aim of this paper. This paper bases the prediction method on the estimation of the polymer fractional free volume at different environmental conditions. Focussing on glassy polymers, the free volumes of polymer films were estimated using the model of Vrentas et al. [J.S. Vrentas, J.L. Duda, H.-C. Ling, Antiplasticization and volumetric behavior in glassy polymers, Macromolecules 21 (1988) 1470–1475]. The required data are the moisture sorption and glass transition temperature data, which were measured on various hydroxypropyl methylcellulose (used as a model material) free films at different water activities. The temperature and molecular weight particularly determine the free volume of the polymer, while the sorbed water can either decease or increase the specific free volume of the polymer. At high water activity, the amount of water sorbed in the film increases to such level that the direct free volume addition by water becomes proportional to the contribution of the polymer itself. This confirms the importance of considering the environmental effect on the diffusivity of polymer during coating material selection. The presented approach enables the prediction of the diffusivity at any given relevant material variable and therefore has the potency to be used as a formulation development tool.

Structural and electrical properties of (Ba1−xSrx)(Zr0.9M0.1)O3, M=Y, La, solid solutions

The aim of the work was to study the structural and electrical properties of the (Ba 1− x Sr x )(Zr 0.9 Y 0.1 )O 3 and (Ba 1− x Sr x )(Zr 0.9 Y 0.1 )O 3 solid solutions. The powders of different strontium content ( x = 0, 0.03, 0.05 and 0.1) were prepared by a thermal decomposition of organo-metallic precursors containing ethylenediaminetetraacetate acid. Some parameters describing stability and transport properties of the perovskite structure, such as tolerance factor, specific free volume and global instability index, were calculated. It was found that the introduction of strontium into both solid solutions caused the increase of specific free volume and global instability index—these structures became a little less stable but, on the other hand, better ionic conductor. All samples were cubic perovskite and the substitution of strontium for barium caused the decrease of respective lattice parameters. Electrical conductivity measurements were performed by the d.c. four-probe method in controlled gas atmospheres containing Ar, air, H 2 and/or H 2 O at the temperature from 300 to 800 °C. It was found that the conductivity depended on a chemical composition of the samples and the atmosphere. In general, the electrical conductivity was higher in wet atmospheres which contained oxygen, being in accordance with the model of a proton transport in the perovskite structure which assumed the presence of the oxygen vacancy. The solid solution containing 5 mol.% of strontium showed the highest conductivity and the lowest activation energy of conductivity regardless of the atmospheres.

Temperature Dependence of the Free Volume in Amorphous Teflon AF1600 and AF2400: A Pressure−Volume−Temperature and Positron Lifetime Study

The microstructure of the free volume and its temperature dependence were studied for amorphous Teflon AFs using pressure−volume−temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Two copolymers of tetrafluoroethylene and 2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole units with a composition of 35:65 (AF 1600, Tg = 160 °C) and 13:87 mol parts (AF 2400, Tg = 240 °C) were investigated after drying the as-received materials. The results are compared with those for CYTOP (Tg = 105 °C) and the perfluoroelastomer PFE (Tg = −2 °C) as well as for conventional (non-fluorinated) polymers. The PVT data were fitted by the Tait equation and the Simha−Somcynsky (S−S) equation of state (eos). From the latter one the hole fraction h and the specific hole free volume, Vf = hV, were determined. From the PALS data published recently by some of the authors (Rudel et al. Macromolecules 2008, 41, 788) the free volume hole size distribution characterized by its mean, ⟨vh⟩, and standard dev...

The free volume in two untreated, pressure-densified, and CO2 gas exposed polymers from positron lifetime and pressure-volume-temperature experiments

AbstractChanges in the microstructure of the free volume and its temperature dependence in ethylene-norbornene copolymer and bisphenol-A polycarbonate due to densification under pressure and swelling with CO2 gas have been examined using positron annihilation lifetime spectroscopy (PALS) and pressurevolume- temperature (PVT) experiments. Employing the Simha-Somcynsky equation of state the specific hole free and occupied volumes were estimated. From the PALS spectra analyzed with the new routine LT9.0 the size distribution of subnanometre holes and its mean and mean dispersion were calculated. Above Tg, the dispersion mirrors the thermal fluctuations in the free volume. From comparison of PALS and PVT data the specific number of holes was estimated. It was found that the occupied volume has a constant and identical compressibility in the glassy and rubbery state. It shows no memory for the history of the glass and mirrors only the pressure and temperature during the measurement. The change in the total volume due to the pre-treatments of the polymers occurs exclusively in the hole free volume Vf and the relative change in Vf is one order of magnitude larger than in the total volume. PALS data show that the mean hole size and its dispersion in the glassy state is decreased due to densification and increased due to swelling. PVT data show that the volume changes are frozen in the polymer glasses and that, when heating the samples, the volume begins to recover at temperatures ca. 50 K in gas swollen and 20 K in densified polymers below Tg. The PALS data show a corresponding behaviour.

Comparative Molecular Simulation Study of Methane Adsorption in Metal−Organic Frameworks

A systematic Monte Carlo simulation has been performed on the adsorption of CH4 in a series of 10 metal−organic frameworks (MOFs) to confirm the desired characteristics of an optimal adsorbent for methane storage. The simulation shows that high isosteric heat of adsorption, specific accessible area, free volume, and low density of framework are all desirable properties for a material with high adsorption capacity. However, not all these properties are compatible, and there exists a complex interplay of these that influence the uptake of methane. We conclude that the accessible surface area and free volume play a main role in determining methane uptake at 298 K and 3.5 MPa from this simulation.

Temperature and pressure dependence of the free volume in the perfluorinated polymer glass CYTOP: A positron lifetime and pressure-volume-temperature study

The microstructure of the free volume was studied for an amorphous per- fluorinated polymer (Tg ¼ 378 K). To this aim we employed pressure-volume-temper- ature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha-Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, Vf ¼ hV and Vocc ¼ (1 � h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass Vocc has a particular high compressi- bility, while the compressibility of Vf is rather low, although h (300 K) ¼ 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, hvhi, and mean dispersion, rh, were calculated. From a comparison of hvhi with Vf a constant hole density of Nh 0 ¼ 0.25 3 10 21 g � 1 was estimated. The volume of the smallest representative freely fluctuating subsystem, hVSVi ! 1/rh 2 , is unusually small. This was explained by an inherent topologic disorder of this polymer. hvhi and rh show an exponential-like decrease with increasing pressure P at 298 K. The hole density, calculated from Nh 0 ¼ Vf /hvhi, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. V C 2007 Wiley

Fluctuation approach for the estimation of the dynamic heterogeneity in glass-forming liquids from the dispersion in o-Ps lifetimes: Free volume fluctuations in polymers

Positron annihilation lifetime spectra are analyzed with respect to the mean, τ3, and mean dispersion, σ3, of ortho-positronium lifetimes using the new routine LifeTime, version 9.0, which assumes a log-Gaussian distribution of annihilation rates λ=1/τ. From these data the size distribution of subnanometer local free volumes (holes) characterized by their mean, 〈vh〉, and mean dispersion, σh=〈δvh2〉1/2, is derived. Pressure–volume–temperature experiments are analyzed employing the Simha–Somcynsky equation of state in order to obtain the fractional, h, and the specific, Vf=hV, hole free volume and its expansivity and compressibility. From comparison of Vf with 〈vh〉 the specific number of holes Nh′ is estimated. It is assumed that the hole size dispersion mirrors directly the fluctuation in the free volume as long as the relaxation time of structural motion is larger than the ortho-positronium lifetime of a few nanoseconds. The mean fluctuation in the fractional and specific free volume is calculated. Starting from a fluctuation approach the mean size of the smallest subvolume 〈VSV〉 representative for structural relaxations is estimated. This volume is assumed to be closely related to the volume of a cooperatively rearranging region and to mirror the dynamic heterogeneity. Limits of this interpretation and specific features of PALS are discussed. The variation of the subvolume with temperature and pressure is analyzed. A different behavior of 〈vh〉 and σh is interpreted in terms of Donth’s theory of dynamic glass transition heterogeneity.

Structure of Latent Heavy Ion Tracks in Polyimide

ABSTRACT Employing small-angle X-ray scattering, we have confirmed that tracks along wakes of GeV heavy ions in polyimide possess a porous structure. Moreover, specific free volume of ∼ 20 nm3 per nm of track length, independent of track length, has been revealed along 5.5-nm-diameter 25 to 125 μm long tracks created by 2.19 GeV Au ions. Structural alteration involves, undoubtedly, highly-efficient material expulsion, and is attributed to a confined ion-induced radiolysis followed by removal of gaseous and volatile degradation products, most likely through the low-density tracks. Porosity enables selective track etching, doping, coating, or filling, which make tracks useful for nanotechnological applications.

Temperature and Pressure Dependence of the Free Volume in Polyisobutylene from Positron Lifetime and Pressure‐Volume‐Temperature Experiments

AbstractSummary: The microstructure of the free volume and its temperature and pressure dependence in PIB were studied by PVT experiments and PALS. Employing the Simha–Somcynsky equation of state, the hole‐free volume fraction h and the specific free and occupied volumes, Vf = hV and Vocc = (1 − h)V, respectively, and their expansivity and compressibility were calculated. From the PALS spectra analyzed using the LT9.0 software, the hole size distribution, the mean hole size 〈vh〉 and mean dispersion σh were calculated. From a comparison of 〈vh〉 with Vf, the hole density $N'_{\rm h}$ was obtained. It was found that PIB shows an unusual thermal expansion with glass‐like transitions at 210 K and 290 K (at 0 MPa). A similar behavior is observed for tan δ. It was found that at 296 K, 〈vh〉 decreases exponentially from 80 Å3 at 0.1 MPa to the extremely low value of 10 Å3 at 1 300 MPa. Starting from a fluctuation approach, the free‐volume fluctuations and the characteristic length scale (ξ) of dynamic heterogeneity of structural relaxation were estimated from σh. It was found that ξ increases from ≈1.5 nm to ≈1.9 nm when the temperature decreases from 293 K to the glass transition temperature Tg = 207 K (at 0 MPa) or the pressure increases from 0.1 MPa to 200 MPa (at 296 K).Fractional free volume and its mean fluctuation in PIB as determined from positron lifetime spectroscopy and PVT experiments analyzed with the Simha‐Somcynsky equation of state.imageFractional free volume and its mean fluctuation in PIB as determined from positron lifetime spectroscopy and PVT experiments analyzed with the Simha‐Somcynsky equation of state.

Free volume of an epoxy resin and its relation to structural relaxation: Evidence from positron lifetime and pressure-volume-temperature experiments

The microstructure of the free volume and its temperature dependence in the epoxy resin diglycidyl ether of bisphenol-A (DGEBA) have been examined using positron annihilation lifetime spectroscopy (PALS, 80-350K, 10(-5) Pa) and pressure-volume-temperature (PVT, 293-470 K, 0.1-200MPa) experiments. Employing the Simha-Somcynsky lattice-hole theory (S-S eos), the excess (hole) free volume fraction h and the specific free and occupied volumes, Vf=hV and Vocc=(1-h)V, were estimated. From the PALS spectra analyzed with the new routine LT9.0 the hole size distribution, its mean, <Vh>, and mean dispersion, sigma h, were calculated. <Vh> varies from 35 130 A3. From a comparison of <Vh>with V and Vf, the specific hole number N'h was estimated to be independent of the temperature [Nh(300 K)=N'h/V=0.65 nm-3]. From comparison with reported dielectric and viscosity measurements, we found that the structural relaxation slows down faster than the shrinkage of the hole free volume Vf would predict on the basis of the free volume theory. Our results indicate that the structural relaxation in DGEBA operates via the free-volume mechanism only when liquidlike clusters of cells of the S-S lattice appear which contain a local free volume of approximately 1.5 or more empty S-S cells. The same conclusion follows from the pressure dependency of the structural relaxation and Vf. It is shown that PALS mirrors thermal volume fluctuations on a subnanometer scale via the dispersion in the ortho-positronium lifetimes. Using a fluctuation approach, the temperature dependency of the characteristic length of dynamic heterogeneity, xi, is estimated to vary from xi=1.9 nm at Tg to 1.0 nm at T/Tg>1.2. A model was proposed which relates the spatial structure of the free volume as concluded from PALS to the known mobility pattern of the dynamic glass transition at low (cooperative alpha-relaxation) and high (alpha-relaxation) temperatures. We discuss possible reasons for the differences between the results of our method and the conclusion from dynamic heat capacity.

Measurement and prediction of solubilities and diffusion coefficients of carbon dioxide in starch–water mixtures at elevated pressures

AbstractThe solubility and diffusion coefficient of carbon dioxide in intermediate‐moisture starch–water mixtures were determined both experimentally and theoretically at elevated pressures up to 16 MPa at 50 °C. A high‐pressure decay sorption system was assembled to measure the equilibrium CO2 mass uptake by the starch–water system. The experimentally measured solubilities accounted for the estimated swollen volume by Sanchez–Lacombe equation of state (S‐L EOS) were found to increase almost linearly with pressure, yielding 4.0 g CO2/g starch–water system at 16 MPa. Moreover, CO2 solubilities above 5 MPa displayed a solubility increase, which was not contributed by the water fraction in the starch–water mixture. The solubilities, however, showed no dependence on the degree of gelatinization (DG) of starch. The diffusion coefficient of CO2 was found to increase with concentration of dissolved CO2, which is pressure‐dependent, and decrease with increasing DG in the range of 50–100%. A free‐volume‐based diffusion model proposed by Areerat was employed to predict the CO2 diffusivity in terms of pressure, temperature, and the concentration of dissolved CO2. S‐L EOS was once more used to determine the specific free volume of the mixture system. The predicted diffusion coefficients showed to correlate well with the measured values for all starch–water mixtures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 607–621, 2006

On the role of inter- and intra-molecular potentials in the simulation of vitrification with the bond fluctuation model

The glass transition of linear chain polymers was simulated by means of the bond fluctuation model, employing a Lennard–Jones inter-molecular potential and a bond-length intra-molecular potential. The influence of the balance between inter- and intra-molecular potentials on the model prediction was studied and an appropriate range was determined in order to simulate physical ageing. The relationship between molecular mobility and the dynamically accessible volume was shown in comparison with other definitions of specific volume or free volume. The temperature dependence of the dynamically accessible volume shows the vitrification of the material analogously to the temperature dependence of the lattice energy. Dynamically accessible volume has been proposed as a universal parameter to explain glass transition, but in the bond fluctuation model it does not give the same value for all simulated glass transitions. This fact could be corrected by including the Metropolis criterion in the dynamically accessible volume in order to extend the concept to thermal systems.

Glass transition and free volume in the mobile (MAF) and rigid (RAF) amorphous fractions of semicrystalline PTFE: a positron lifetime and PVT study

The structure of the free volume and its temperature dependence in poly(tetrafluoroethylene) (PTFE) and of its copolymer with perfluoro(propyl vinyl ether) (PFA) was studied by pressure–volume–temperature (PVT) experiments ( T=27–380 °C, P=0.1–200 MPa) and positron annihilation lifetime spectroscopy (PALS, T=−173–250 °C, P=10 −5 Pa). From the analysis of these experiments we conclude on the volumetric properties of the mobile (MAF) and rigid amorphous fractions (RAF) in these semicrystalline polymers. The specific volumes of the MAF and RAF, V MAF and V RAF, were estimated assuming that V MAF agrees with the specific volume of the melt extrapolated down to lower temperatures using the Simha–Somcynsky equation of state (S–S eos). V RAF was then estimated from the specific volume of the entire amorphous phase, V a, and the known V MAF. The specific free volume V f= V a− V occ was also estimated from V a using the S–S eos hole fraction h, V occ=(1− h) V a. From the analysis of PALS data with the routine LT9.0 the mean volume, 〈 v h〉, and the width, σ h, of the local free volume size distribution (holes of subnanometre size) were obtained. A comparison of 〈 v h〉 with V f delivered the hole density N ′ h . The volume parameters show that the RAF which is formed during crystallisation from the melt has a distinctly smaller specific free and total volume than the MAF. During cooling the contraction of the RAF slows down and finally, below room temperature, the RAF possesses a larger free volume than the MAF shows. Obviously, the restriction of the segmental mobility in the RAF by the crystals limits at high temperatures the free volume expansion and at low temperatures dense packing of the polymer chains. These conclusions from the analysis of the specific volume are confirmed by PALS experiments.