Free volume and conductivity in polymer electrolytes

Positron annihilation lifetime spectroscopy (PALS) and impedance spectroscopy (IS) have been employed to study the effect of temperature and pressure on the DC conductivity (σ_DC) and the mean hole volume (V_h) of a NaPF₆ ethylene oxide based polyurethane electrolyte. The DC conductivity of the polymer electrolyte displayed a characteristic non-Arrhenius temperature dependence yielding acceptable values for both the “pseudo-activation energy” (B) and the “zero mobility temperature” (T₀) from a VTF fit. V_h(T) showed a linear increase of 0.53 cm³ (mol K)⁻¹. When extrapolating V_h(T) to 0 K a temperature very close to T₀ from the VTF fit was obtained, which suggests a free volume mediated conductivity mechanism. This suggestion is further supported by the linear dependence of ln(σ_DC(T)) on . Conductivity was measured as a function of pressure (σ_DC(P)) with ln(σ_DC(P)) showing a characteristic decrease with increasing pressure. The activation volumes (V_A) calculated from these measurements ranged from 45 to 20 cm³ mol⁻¹ over a temperature from 304 to 365 K. Critical volumes calculated from two current free-volume models were found to be unrealistic. Combining the extra volume required for ionic motion (V_A) with the available free volume (V_h) at the same temperature poses a realistic and ‘model-free’ figure of 117 cm³ mol⁻¹ for the critical volume at 304 K. This equates roughly to the volume of 3-4 EO units. The pressure dependence of free volume (V_h(P)) for a polymer electrolyte has been measured for the first time, and yielded a linear decrease in V_h with increasing pressure. A linear dependence of σ_DC(P) on was also found. A comparison of the isothermal and isobaric dependence of σ_DC on illustrates the contribution of factors other than free volume have on charge carrier number and mobility. This comparison shows that the variation of V_h with temperature and the variation of V_h with pressure affect the conductivity in very different ways. These results clearly show that free volume cannot be considered the sole factor responsible for conductivity in polymer electrolytes.     

Effect of pressure on the segmental dynamics of bisphenol-A-polycarbonate

The segmental dynamics of bisphenol-A-polycarbonate (BPA-PC) are studied as a function of temperature (in the range from 143 to 473 K) and pressure (0.1-300 MPa) within the frequency range from 3 × 10⁻³ to 1 × 10⁶ Hz using dielectric spectroscopy aiming at extracting the more relevant parameter associated with the liquid-to-glass transition. Rheological measurements are also made in the temperature range from 408 to 513 K for comparison. The dynamic results coupled with the equation of state reveal that both density and thermal energy control the segmental dynamics with density being the most important variable in the vicinity of the transition. This is documented by independent estimates of the value of the dynamic ratio E_V^∗/H^∗ (∼0.44). This low value of the dynamic ratio is discussed in terms of the packing irregularities and large monomer volume of BPA-PC. In addition, the pressure coefficient of T_g (dT_g/dP ∼ 0.52 K/MPa) is one of the highest for a polymeric substance.     

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.     

Laminar burning velocity and explosion index of LPG-air and propane-air mixtures

The determination of burning velocity is very important for the calculations used in hazardous waste explosion protection and fuel tank venting, which has a direct impact on environmental protection. The scope of the present study encompass an extensive study to map the variations of the laminar burning velocity and the explosion index of LPG-air and propane-air mixtures over wide ranges of equivalence ratio (Φ = 0.7-2.2) and initial temperature (T_i = 295-400 K) and pressure (P_i = 50-400 kPa). For this purpose a cylindrical combustion bomb was developed. The reliability and accuracy of the built up facility together with the calculation algorithm are confirmed by comparing the values of the laminar burning velocity obtained for a standard fuel (propane at normal pressure normal temperature conditions, NPT) with those available in the literature. The burning velocity was determined using different models depending on the pressure history (P-t) of the central ignition combustion process at the minimum ignition energy.The data obtained for the laminar burning velocity is correlated to S_L = S_L0(T/T₀)^α(P/P₀)^β where S_L0 is the burning velocity at NPT, α and β are the temperature and pressure exponents respectively. The value of β is observed to slightly vary with the equivalence ratio for both fuels. However, propane exhibits higher pressure dependency than that of LPG. The maximum laminar burning velocity found for propane is nearly 455 mm/s at Φ = 1.1, while that for LPG is nearly 432 mm/s at 4.5% fuel percent (Φ ≈ 1.5). The maximum explosion index, commonly called the “explosion severity parameter”, is calculated from the determined laminar burning velocity and is found to be 93 bar m/s for propane, and nearly 88 bar m/s for LPG.     

Microstructure of free volume in SMA copolymers I. Free volume from Simha-Somcynsky analysis of PVT experiments

The structure of the free volume and its temperature dependence between 25 and 200 °C of copolymers of styrene with maleic anhydride, SMA (0-35 mol% MA), is studied by pressure-volume-temperature (PVT) experiments and positron annihilation lifetime spectroscopy (PALS). In this first part of the work, PVT data are reported which were analysed with the Simha-Somcynsky equation of state to estimate the volume fraction of holes, h, which constitute the excess free volume. The temperature and pressure dependence of the specific volume V, the specific occupied and free volume, V_occ=(1−h)V and V_f=hV, and the corresponding isobaric expansivities and isothermal compressibilities for both the rubbery and glassy state are estimated. We obtained the unexpected results that (i) the occupied volume changes its coefficient of thermal expansion at T_g from α_occ,g≈0.5α_g≈1×10⁻⁴ K⁻¹ below T_g to almost zero (≈0.2×10⁻⁴ K⁻¹) above T_g and (ii) the isothermal compressibility of the occupied volume at zero pressure below T_g is rather high, κ_occ≈2.5×10⁻⁴ MPa⁻¹, and decreases only slightly at T_g to about 2×10⁻⁴ MPa⁻¹ above T_g. The variation of total, occupied, and free volume parameters with the composition of the SMA copolymers is discussed.     

Experimental electrical resistivity of liquid carbon in the temperature range from 4800 to ∼20,000 K

Specimens of high density pyrolytic graphite (2.2 g/cm³) were placed inside thick-walled sapphire tubes and heated over several microseconds by an electric current of 68 kA. The electrical resistivity of the liquid carbon was measured in a constant volume heating process. The transition of liquid carbon from semi-metal properties (resistivity decreasing with increase of input energy) to metal-like behavior (resistivity increasing with increase of input energy) was obtained at a high input energy (25-75 kJ/g) and at a high, but not measured, pressure. The transition temperature, T, was roughly estimated through the C_V value (heat capacity under constant volume). The relationship between the density and the transition temperature is as follows: for 1.88 g/cm³ density, the transition temperature T = 6300 K, for 1.76 g/cm³, T = 10,100 K, and for 1.1 g/cm³, T = 13,500 K. The estimated temperature at the maximum input energy (75 kJ/g) for liquid metal-like carbon (just before the destruction of the sapphire tube) is 23,000 K, with a corresponding measured electrical resistivity of 3000 μΩ cm.     

Free volume in poly(n-alkyl methacrylate)s from positron lifetime and PVT experiments and its relation to the structural relaxation

Free volume data from positron annihilation lifetime spectroscopy (PALS) experiments are combined with a Simha-Somcynsky (S-S) equation of state analysis of pressure-volume-temperature (PVT) data to model free volume contributions to structural mobility in a series of poly(n-alkyl methacrylate)s. From the PALS data the glass transition temperature, T_g, decreases (from 382 to 224 ± 5 K) and a given mean free volume is observed at lower temperatures as the side-chain length increases (going from methyl- to hexyl-). This is evidence of an internal plasticization whereby the side-chains reduce effective packing of molecules. By comparing PALS and PVT data, the hole number per mass unit, N_h′, is calculated using different methods; this varies between 0.54 and 0.86 × 10²¹ g⁻¹. It is found that the extrapolated free volume becomes zero at a temperature T₀′ that is smaller than the Vogel temperature T₀ of the α-relaxation. The α-relaxation frequencies can be fitted by the free volume theory of Cohen and Turnbull, but only when the free volume V_f is replaced by (V_f − ΔV) where ΔV( = E_f(T₀ − T₀′), E_f is the thermal expansivity of V_f) varies between 0.060 and 0.027 ± 0.003 cm³/g, decreasing with side-chain length, apart from poly(n-hexyl methacrylate) where ΔV increases to 0.043 ± 0.003 cm³/g. One possible interpretation of this is that the α-relaxation only occurs when, due to statistical reasons, a group of m or more unoccupied S-S cells are located adjacent to one another. m is found to vary between 8 and 2 for poly(methyl methacrylate) and poly(n-butyl methacrylate), respectively. We found that no specific feature in the free volume expansion was consistently in coincidence with the dynamic crossover.     

Prediction of the density and viscosity in biodiesel blends at various temperatures

Biodiesel defined as mono-alkyl esters of vegetable oils and animal fats, has had a considerable development and great acceptance as an alternative fuel for diesel engines. Density and viscosity are two important physical properties to affect the utilization of biodiesel as fuel. In this work, mixtures of biodiesel and ultra low sulfur diesel (ULSD) were used to study the variation of density (ρ) and kinematic viscosity (η) as a function of percent volume (V) and temperature (T), experimental measurements were carried out for six biodiesel blends at nine temperatures in the range of 293.15-373.15 K. Both, density and viscosity increases because of the increase in the concentration of biodiesel in the blend, and both of them decrease as temperature increases. One empirical correlation was proposed to estimate the density: ρ = α·V + β·T + δ; and three empirical correlations were developed to predict the kinematic viscosity: η = exp[ln(γ) + ?·V + ω/T + λ·V/T²], η = exp[ln(γ) + ω/T + λ·V/T²] and η = exp[ln(γ) + ω/T + λ·V/T]. The corresponding parameters were optimized by the Levenberg-Marquardt method. The estimated values of density and viscosity are in good agreement with the experimental data because absolute average prediction errors of 0.02% and 2.10% were obtained in the Biodiesel(1) + ULSD(2) system studied in this work.     

Theoretical studies of the electronic structures and optical properties of stable blue-emitting polymer based on 4H-cyclopenta-[def]-phenanthrene

Geometries, ionization potentials (IPs), electron affinities (EAs) and optical properties of two series of π-conjugated oligomers (2,6-(4,4-bis(2-ethylthexyl)-4H-cyclopenta-[def]-phenanthrene))_nCPPn (2,6-(4,4-bis(2-ethylthexyl)-8,9-dihydro-4H-cyclopenta-[def]-phenanthrene))_nHCPPn (n = 1-4) were studied theoretically. The ground and the excited state geometries were optimized by B3LYP and CIS methods with 6-31G^∗ basis sets, respectively. The absorption and the emission spectra were calculated by TD-B3LYP method. The lowest-lying absorption is assigned to π → π^∗ transition, and the fluorescence can be described as originating from the ¹[ππ^∗] excited state. IPs, EAs, H-L gaps, absorption and emission properties of PCPP (n = ∞) and PHCPP (n = ∞) were obtained by extrapolation method. The fact that the lowest-lying absorption and the emission of PCPP are blue-shifted compared with those of PHCPP, can be interpreted by the smaller effective repeating units of PCPP. The extra absorption band at 289 nm of PCPP is contributed by the π → π^∗ transition involving the extra π-conjugation CC bond.     

Thermodynamics of sorption in and free volume of poly(5,6-bis(trimethylsilyl)norbornene)

Thermodynamics of sorption of n-alkanes C₄-C₁₁ in poly(5,6-bis(trimethylsilyl)norbornene) was studied using the Inverse Gas Chromatography (IGC). Temperature dependences of the specific retention volume V_g and solubility coefficient S of various alkanes were obtained in the range 60-140 °C. For solubility coefficients, the following equation holds: where T_c is the critical temperature of solutes, T is the experimental temperature and S is expressed in cm³(STP)/cm³ atm. The partial molar enthalpies ΔH_m and entropies ΔS_m of mixing of different n-alkanes in this glassy polymer vary in much wider range than in rubbers and display positive correlations: for more exothermic mixing process the larger negative ΔS_m values are observed. It was shown that the ΔH_m in poly(5,6-bis(trimethylsilyl)norbornene) pass through a minimum, when the size of solutes increases. The coordinates of ΔH_m at minimum versus solute size provide an estimate of the size of free volume elements in this polymer. This conclusion was supported by variation of permeability in different glassy polymers studied using IGC and by the results of other methods for probing free volume in glassy polymers.     

Microstructure of free volume in SMA copolymers II. Local free volume from PALS

The structure of the free volume and its temperature dependence between, at maximum 133 and 503 K of copolymers of styrene with maleic-anhydride, SMA (0-35 mol% MA), is studied by pressure-volume-temperature (PVT) experiments and positron annihilation lifetime spectroscopy (PALS). In this second part of the work, PALS data are reported from which the temperature dependence of the mean size and size distribution of local free volumes (subnanometer size holes) is analysed. The mean hole volume, ν_h, varies in PS between 80 Å³ (133 K) and 212 Å³ (503 K) and shows a systematic decrease with increasing MA content for a given temperature above T_g. The specific number of holes, N_h′, estimated from a comparison of PVT and PALS results, increases slightly with MA content from N_h′=(0.60±0.02)×10²¹ g⁻¹ to N_h′=(0.70±0.02)×10²¹ g⁻¹ which corresponds to N_h(T_g)=N_h′/V_g=0.62-0.82 nm⁻³ (V_g is the material's specific volume at T_g) and 1/N_h(T_g)=1.6-1.2 nm³ for the volume which contains one hole. The analysed size distributions of the holes above T_g follow the compressibility of the free volume as it is predicted by the theory of thermal volume fluctuation. We also comment on the connection between the hole size as measured by PALS and the size of a cluster of randomly distributed unoccupied cells as defined by the Simha-Somcynsky theory.     

The influence of axial pressure on relaxor properties of BaBi2Nb2O9 ceramics

On the basis of our studies it results that dielectric properties of BaBi₂Nb₂O₉ ceramics are sensitive to axial pressure applied. The pressure causes an increase of dispersion in the real part of dielectric permittivity ?′(T,f) and a rise in the temperature T_m at which the maximum in ?′(T,f) dependence occurs. The applied pressure induces in the ?′(T) dependence an additional step-like anomaly, which appears at the temperature T_A < T_m. The applied pressure shifts both T_m and T_A at the same rate, i.e. dT_A/dX = dT_m/dX = +14 °C/kbar at high axial pressure range, above the threshold pressure X_thresh. The Vogel–Fulcher relationship is employed to determine the axial pressure influence on relaxor properties of BBN ceramics. The simulated order parameter q takes non-zero values below Burn‘s temperature T_B, where the polar clusters appear on cooling. For pressures higher than 0.8 kbar, the T_B changes at the rate dT_B/dX = −200 °C/kbar. The decrease in the difference between Burn's T_B and the freezing T_f temperatures induced by the applied axial pressure is observed. This could be ascribed to the narrowing of temperature range of relaxor behavior.     

Gas solubilities in ionic liquids using a generic van der Waals equation of state

A family of modified van der Waals equations of state (vdW EOS) is extremely useful for many industrial applications. For example, the generic Redlich-Kwong (RK) EOS or its modification by Soave (SRK EOS) and Peng-Robinson (PR EOS) are still of popular use in industry to the present day. These two most popular (“cubic”) EOSs are based on modifications [1/(V² + bV), or 1/(V² + 2bV − b²)] of the volume dependence on the attractive part of the original van der Waals EOS [1/V²] and also modifications of the temperature dependence of the attractive “a(T)” parameter of the original EOS (constant a). It is extremely rare in actual EOS applications to use the volume dependence of the original van der Waals EOS. In the present phase equilibrium calculations, we employ such a generic vdW EOS, P = RT/(V − b) − a(T)/V², with our well-tested mixing rule for multi-component mixtures. Using the same form of the “a(T)” parameter and the mixing rule, it has been found that all generic RK, PR, and vdW EOSs can present the phase behaviors (temperature-pressure-composition diagrams) equally well. It is shown that experimental gas solubility data (CO₂, CF₃-CFH₂, SO₂, and NH₃) in room-temperature ionic liquids are well correlated with the present EOS model, and also that the phase behaviors such as LLE (liquid-liquid separations) are satisfactorily predicted.     

Power law of molecular weight dependence of lateral growth rate of isotactic polypropylene

Molecular weight (M) dependence of the lateral growth rate (V) of α form crystal of isotactic polypropylene (iPP) was studied. Reliable equilibrium melting temperature determined in our previous study was used for the analysis of supercooling dependence of V. A power law of M of V, , was obtained, where H is a small constant (H = 0.7). The small H, which is similar to that of the hexagonal phase of polyethylene (H = 0.7) in comparison with the value of H = 1.7 for the orthorhombic phase of polyethylene, confirmed our prediction of smaller H for “rod like” chain polymers because of easier chain sliding within the interface between the crystalline phase and the melt. Thus, the universality of the important role of topological nature in polymer crystallization was confirmed. Lateral surface free energy (σ) of the α form of iPP was obtained as σ ≅ 1.59 × 10⁻⁶ J/cm².     

Synthesis, characterization, and high gas permeability of poly(diarylacetylene)s having fluorenyl groups

Diarylacetylenes having fluorenyl groups and other substituents (trimethylsilyl, t-butyl, bromine, fluorine) (1a-1) were polymerized with TaCl₅-n-Bu₄Sn. Monomers 1a-l produced high molecular weight polymers 2a-l (M_w 5.1 × 10⁵-1.3 × 10⁶) in 12-59% yields. All of the polymers were soluble in common organic solvents, and gave tough free-standing membranes by the solution casting method. The onset temperatures of weight loss of polymers 2a-l in air were over 400 °C, indicating considerably high thermal stability. All the polymer membranes showed high gas permeability; e.g., the oxygen permeability coefficient (PO₂) of 2a was as large as 4800 barrers. Membrane 2d possessing two fluorine atoms at meta and para positions of the phenyl ring showed the highest oxygen permeability (PO₂ = 6600 barrers) among the present polymers.     

Chain walking copolymerization of ethylene with cyclopentene - Effect of ring incorporation on polymer chain topology

Chain walking ethylene copolymerizations with cyclopentene (CPE) as the ring-forming comonomer were carried out in this study to investigate the tuning of polyethylene chain topology via the unique strategy of ring incorporation. Four sets of polymers containing five-membered rings on the polymer backbone at various low contents (in the range of 0-7.5 mol%) were synthesized by controlling CPE feed concentration at four different ethylene pressure/temperature combinations (1 atm/15 °C, 1 atm/25 °C, 1 atm/35 °C, and 6 atm/25 °C, respectively) using a Pd-diimine catalyst, [(ArNC(Me)-(Me)CNAr)Pd(CH₃)(NCMe)]⁺SbF₆⁻ (Ar = 2,6-(iPr)₂C₆H₃). The polymers were characterized extensively using ¹³C nuclear magnetic resonance (NMR) spectroscopy, triple-detection gel permeation chromatography (GPC), and rheometry to elucidate the chain microstructures and study the effect of ring incorporation on polymer chain topology. It was found that CPE was incorporated in the copolymers primarily in the form of isolated cis-1,3 ring units, along with a small fraction in the form of isolated cis-1,2 ring units. Significant linearization of polymer chain topology was achieved with ring incorporation in each of the three sets of polymers synthesized at 1 atm on the basis of the incrementally raised intrinsic viscosity curves in the Mark-Houwink plot and the significantly enhanced zero-shear viscosity of the polymer melts with the increase of ring content despite the decreasing polymer molecular weight. For the set of polymers synthesized at 6 atm/25 °C, the effect of ring incorporation on polymer chain topology was negligible or weaker due to their linear chain topology resulting at this polymerization condition. The results obtained in this study support the proposed blocking effect of backbone-incorporated rings on catalyst chain walking, and demonstrate that effective tuning of polyethylene chain topology from hyperbranched to linear can be conveniently achieved via CPE incorporation while without changing ethylene pressure or polymerization temperature.     

Study on physical and electrostatic interactions of counterions in poly(perfluorosulfonic) acid matrix: Characterization of diffusion properties of membrane using radiotracers

The self-diffusion coefficients of water and ions were used to study the physical (tortuosity) and electrostatic interactions of counterions in poly(perfluorosulfonic) acid membrane (Nafion-117) matrix. The self-diffusion coefficients of water were measured in the water swollen Nafion-117 membrane with Zn²⁺, Ca²⁺, Sr²⁺, and Fe²⁺ counterions by analyzing the experimental exchange rates between tritium tagged water (HTO) in membrane and equilibrating water. In order to study the effects of equilibrating solution, the HTO-desorption rate profiles between the membrane samples in H⁺ or Cs⁺ forms and equilibrating solution containing CsCl or HCl (0.25 mol/L) were measured. It was observed that the HTO-exchange rate profile was slower in case of membrane sample in Cs⁺-from equilibrated with salt/acid solution than that equilibrated with deionized water in same ionic form. However, HTO-exchange rate profile did not alter in case of H⁺-form of membrane on equilibration with salt or acid solution. The variation of ln  with polymer volume function V_p/(1 − V_p), where V_p is polymer volume fraction, indicated that: (i) in the membrane with multivalent counterions was lower than that reported for membrane with monovalent counterions at same V_p, and (ii) the linear trends observed in variation of ln  with V_p/(1 − V_p) for multivalent and monovalent counterions were significantly different. The values of in membrane normalized with at V_p = 0 were taken as an estimate of the tortuosity factor for self-diffusion of ions in the membrane matrix. The self-diffusion coefficients of ions reported in the literature along with tortuosity factor obtained from in the corresponding ionic forms of the membrane were analyzed to obtain the charge (Z_i) independent electrostatic interaction parameter g(φ) of monovalent and divalent ions in the membrane. This analysis indicated that g(φ) also vary exponentially as a function of V_p/(1 − V_p) irrespective of charge on counterions. In order to study the influence of V_p on diffusional transport rates of Na⁺ and Cs⁺ ions in membrane, a permeation experiment was carried out using H⁺-form of membrane having high water volume fraction. The diffusional transport rates of Cs⁺ and Na⁺ in H⁺-form of membrane were found to be similar indicating that the water volume fraction in membrane has strong influence on the parameters that govern the diffusion across the Nafion-117 membrane.