Application of the Bjerrum Association Model to Electrolyte Solutions. III. Temperature and Pressure Dependencies of Association Constants

The Bjerrum association model, developed in 1926, is now incorporated in many conductance theories of electrolyte systems to extract ₀ and K _A from experimental data. The Bjerrum concept is simply a convenient way of taking into account short-range electrostatic interactions between ions. The equations of the Bjerrum model can be applied to the prediction of the temperature and pressure dependencies of K _A from the value of K _A at a reference T and P and from the dielectric properties of the solvent. This feature will be essential when the relaxation effect is taken into account when applying the model to heat capacities and compressibilities. These equations were tested against literature K _A values (obtained from treatment of conductance data by equations that incorporate the Bjerrum concept) in aqueous electrolyte solutions at high temperatures and pressures and in some electrolyte systems in acetonitrile, 2-butanone, propylene carbonate, -butyrolactone, and propanol. In the absence of specific interactions in solution, the agreement between experimental and predicted K _A are generally quite good. Notable exceptions are acids and bases in water, lithium perchlorate in most solvents, and the majority of electrolytes in propylene carbonate, suggesting that specific interactions in these systems may cause the model to fail.     

Electrical conductance,density and viscosity of the system lead(II) dodecanoate/dodecanoic acid

Data are presented for the densities, electrical conductances and viscosities of the molten system lead(II) dodecanoate/dodecanoic acid. Over the concentration range studied, molar volumes are linear functions of concentration at any selected temperature, although there are indications of deviations from ideal behaviour over the complete composition range from pure soap to pure acid. The molar volumes of the system lead(II) carboxylate/carboxylic acid for the even chain acids C₁₀ to C₁₈ are linear functions of chain length. As with other lead(II) dodecanoate systems, the Arrhenius plots for the conductance of the mixtures show curvature.Activation energies for conductance in the low temperature region show a steady decrease with increasing mole fraction of the acid. It is suggested that this arises largely from the increased mobility of the Pb²⁺ ion. The activation energies for viscous flow in the mixtures are similar to that of pure lead dodecanoate. Studies of the viscosities of the system lead(II) carboxylate/carboxylic acid as a function of the temperature for the even chain length acids C₁₀ to C₁₈ suggest a slight decrease in size of the unit of viscous flow when acid is present.     

NMR spin–spin relaxation in solid and molten polyethylene structures

The NMR spin-spin relaxation (T₂) spectra of high-density polyethylene (PE) has been investigated over a wide range of temperatures, both in the solid and molten states. Previous work in these laboratories has shown that the T₂ relaxation spectrum of molten polyethylene differs from that of other polymers studied in that (a) it cannot be decomposed into two relaxation spectra (T_2S and T_2L) and (b) there is some evidence of a memory effect. This paper attempts to elucidate these observations, and compare them with the spin-spin relaxation of polyethylene at lower temperatures. In the solid state, the T₂ decay comprises both a Gaussian distribution for the crystalline region, and an exponential decay for the amorphous component. The effects of crystallization conditions and of temperature were determined. In the molten state the T₂ decay is more complex, but can be resolved into three exponentials. The longest (T_2L) component arises as expected from the most mobile, low molecular weight fraction. The T_2S component is due to an entangled but mobile network, as in other polymers. In addition, a short relaxation component T_2X is observed, which is influenced by previous crystallinity and the processing history of the material, and is ascribed to some vestigial degree of structure in the molten phase.     

Temperature dependence of electric conductivity of molten binary mixtures of alkali and rare-earth metals chlorides

The temperature dependences of the specific and molar electric conductances of CeCl₃-MCl and LnCl₃-KCl (M=Li, Na, K, and Cs; Ln=Er and Yb) molten binary mixtures of various compositions were studied. The size of the cations of alkali and rare-earth metals was demonstrated to affect the intensity of the interactions of the components of the systems. Deviations of the molar conductance isotherms from additivity and dependence of the isotherms on the ratio between the mixture components were explained by the formation of complexes in the melts.     

Differential thermal analysis equipment for the study of molt nifluoride equilibria

Equipment constructed for phase investigations by differential thermal analysis DTA) is described. The samples, usually 1.5–2.5 g, are in platinum crucibles mounted in a nickel block inside a Kanthal-wired “thermal gradient free” laboratory furnace. The reference material is fired Al₂O₃. The temperature and the differential temperature are measured by Pt/Pt 10% Rh thermocouples. The differential thermocouple is immersed directly in the molten salt.The equipment has proved very well suited for phase investigations in molten and solid fluorides, including the detection of solidus curves in systems with solid solubility. A survey of the systems investigated is given.The equipment has also been tried for quantitative measurements. The enthalpies of fusion of the alkali metal cryolites, M₃AlF₆, were measured by DTA, and the results are compared with values obtained by calorimetry.     

Enthalpy Relaxation in Glasses: Regression analysis of integral DSC data

A new method of calculation of parameters of enthalpy relaxation models is proposed. Regression analysis treatment compares the experimental and calculated values of relaxation enthalpy. The experimental values of relaxation enthalpy are obtained by numerical integration of the difference between the two DSC curves. Contrary to the overall shape of the DSC curve the integral values are not affected by particular heat flow conditions during the DSC experiment. The Narayanaswamy's numerical model based on the Kohlrausch—William—Watts relaxation function was used to calculate the theoretical values of relaxation enthalpy. The application of the proposed method on the DSC experimental data of enthalpy relaxation of As₂Se₃ is shown.This revised version was published online in November 2005 with corrections to the Cover Date.     

Dielectric Relaxation of Some Rigid Molecules in Viscous Media

Abstract

The dielectric relaxation times(τ) have been evaluated from the measured values of dielectric constant(?′) and loss (?′′) of four rigid molecules in paraffin oil + benzene mixtures of varying viscosity extending from moderate to high values. Two of the rigid systems are nearly spherical in nature. An attempt has been made to find out the suitable viscosity term describing the dipolar rotation by applying the measured parameters to the earlier models as proposed by Debye, Hill and Kalman. Hill's model which describes the motion by a mutual viscosity (η_AB) term has been found to yield negative values showing its inadequacy for the systems rotating in high viscosity media. A comparison of Kalman's equation with Debye shows that the former gives better results for the region investigated both in high and low viscosity media. Even the systems having spherical symmetry give more satisfactory results when applied to Kalman's equation. In the process, the thermodynamical parameters and dipole moments of the molecules have also been evaluated and discussed.     

EMK-Messungen in binären unsymmetrischen Salzschmelzen aus Strontiumchlorid und Alkalimetallchloriden

The EMF of cells with transference of the type Cl₂, C/MeCl ? SrCl₂? MeCl(x)/C, Cl₂ is measured in the molten mixtures SrCl₂? MeCl (Me ? Li, Na, K, Rb, Cs). From the EMF-values and values of aktivities from another independent methods the transference numbers of the cations Sr²⁺ and Me⁺ relative to the chloride ion in the molten mixtures SrCl₂? LiCl, SrCl₂? NaCl and SrCl₂? KCl are calculated. The values of aktivities for the systems SrCl₂? LiCl and SrCl₂? NaCl are calculated from cryoscopic analysis of the eutectic phase diagrams.     

Liquid phase dynamics of molten M2S2O7 (M = K,Cs): A temperature dependent Raman spectroscopic study

The dynamics of M₂S₂O₇ (M = K, Cs) pyrosulfate salts in the liquid state is investigated by steady-state Raman spectroscopic experiments performed at temperatures up to 600 °C. The symmetric stretching modes of the S₂O₇²⁻ ions have been used as probes of the dynamics of these melts. Contrary to the most previous picosecond dynamics studies performed by means of Raman line profile analysis, we have employed in this work an approach that enables the extraction of valuable information concerning short-time dynamics by calculating time correlation functions of vibrational relaxation by fits in the frequency domain. The fitting method used enables the modeling of the real line profiles in a manner that is intermediate between Lorentzian and Gaussian by means of a function, which has an analytical counterpart in the time domain. The vibrational time correlation functions for both molten salts studied are rather adequately interpreted within the assumption of exponential modulation function concerning the environmental modulation in the context of Kubo–Rothschild approach and indicate that the system experiences an intermediate dynamical regime that gets only slower with increasing temperature. Continuous temperature dependence of the dephasing parameters is observed, while the temperature dependence of the dispersion parameter α indicates deviation from the simple liquid model and offers a complete picture of the way a complex liquid attains the condition of a simple one. The evolution of the dispersion parameter is indicative of the reduction of the coherence decay in the perturbation potential as a consequence of local short-lived aggregates. The experimental results are discussed in terms of theoretical models providing insight in the intermolecular coupling mechanisms.     

Ionic association in acetonitrile and in formamide

In a recent derivation of relaxation effects in the Debye-Hückel-Onsager theory of electrolyte conductance, with a length parameter a, terms are included which have been omitted in earlier treatments (see Appendix). The new expression was applied earlier in a reanalysis of conductance data for aqueous solutions and is applied here to solutions in acetonitrile and in formamide, representing respectively dielectric constants considerably lower and higher than water. As in aqueous solutions, a minimum standard deviation is found over a wide range of (K _A,a) pairs without much effect on A ₀ , so that only approximate determinations ofK _A are possible. On the whole, the most appropriate length parametera is the physical contact distance between counterions, not a fixed radius, independent of ionic size, such as the Bjerrum value, nor a much larger radiusR serving as a boudary between free and associated ions in the ionic atmosphere about a central ion. Relaxation effects calculated by the new analysis are smaller than those from previous expressions for equal values ofa, and this leads to considerably larger values ofK _A than in the original papers. As a consequence, specific short-range ion-ion and ion-solvent forces in most solutions predominate over electrostatic attraction between counterions in their contribution toK _A. A table of limiting equivalent conductance based on the A ₀ values obtained is presented; this differs little from previous tables since A ₀ values obtained by the new analysis are similar to those obtained originally.     

Thermal and radiation-induced polymerizations of N-tert-butylacrylamide and (N-tert-butylacrylamide)2–ZnCl2 complex

The thermal and radiation-induced in-source and postirradiation polymerizations of N-tert-butylacrylamide and (N-tert-butylacrylamide)₂–ZnCl₂ complex of this monomer were studied at various temperatures. In in-source, solid-state polymerizations of monomer and complex the conversion was about 95% at 21°C in about eight days. Their postirradiation polymerizations were also studied in solid state. The conversion-time curves of these two systems show an autoacceleration as in-source polymerization. In both types of polymerization the overall rate of polymerization of complex was higher than that of pure monomer at the same polymerization temperature. In investigations of the thermal polymerization of N-tert-butylacrylamide and ZnCl₂-complex it was observed that the ZnCl₂-complex system can be polymerized in air in the molten and solid state. The conversion of monomer to polymer reaches limiting values in solid state in about 1 hr. The thermal polymerization of ZnCl₂-complex in the molten state was also studied and 100% conversion was obtained in 30 min. The thermal polymerization of pure monomer was studied in vacuum and an appreciable amount of polymer was obtained in the molten state; however, the thermal polymerization of this monomer is negligible in solid state. In this work rates of polymerization for N-tert-butylacrylamide and (N-tert-butylacrylamide)₂–ZnCl₂ are compared under various experimental conditions and overall activation energies are calculated.     

Electrical conductance,density, and viscosity of the molten system lead(II) dodecanoate/lead(II) oxide

Data are presented for densities, electrical conductances, and viscosities of the molten system lead(II) dodecanoate/lead(II) oxide concentrations up to 0.22 mole fraction of the oxide. Values of ?₀ obtained from extrapolation of graphs of density againts temperature are seen to decrease on adding small quantities of PbO, but to increase on adding further PbO. Results from thermal analysis suggest that this may be due to a change in structure of the liquid phase from small. spherical to long, cylindrical micelles. Over the concentration range studied, molar volumes are linear functions of concentration at any particular temperature. The molar volumes of the system lead(II) carboxylate/lead(II) oxide for the even chain acids C₁₀ to C₁₈ are linear functions of chain length. Arrhenius plots for the electrical conductance of the mixtures show curvature, as in other lead(II) dodecanoate systems. The activation energies for conductance in the low temperature region show a steady decrease with increasing PbO concentration and it is proposed that this arises from increased mobility of the charge carrier. The specific conductance at any temperature decreases with increasing mole fraction of oxide, indicating the oxide to be essentially undissociated in the melt. The activation energy for viscosity shows a dramatic increase on adding small amounts of PbO. This is suggested to arise from a change in the structure of the melt. Studies of the viscosities of the system lead(II) carboxylate/lead oxide as a function of chain length for the even chain acids C₁₀ to C₁₈ suggest a slight decrease in the size of the unit of viscous flow when oxide is present.     

1H NMR Relaxation Studies on Glycerine-Water and Dioxan-Water with Paramagnetic Ions

Abstract

The Proton magnetic Resonance (PMR) spin-lattice and spin-spin relaxation times (T ₁ and T ₂) were measured in highly viscous (glycerine - water) and less viscous (dioxan-water) systems at different temperatures. The values of relaxation times increase with increasing the temperature. This result is interpreted as due to the combined effect of viscosity and temperature in these solutions. The relaxation times were also measured in these solutions containing paramagnetic ions(PMI). The results indicate that the possibility of an anti-parallel bonding of the paramagnetic ions is higher in highly viscous solutions as compared to low viscous systems and the association in the above mixtures appears to be weak.     

Physical aging studies in epoxy resins. I. Kinetics of the enthalpy relaxation process in a fully cured epoxy resin

The physical aging of an epoxy resin based on diglycidyl ether of bisphenol-A cured by a hardener derived from phthalic anhydride has been studied by differential scanning calorimetry. The isothermal curing of the epoxy resin was carried out in one step at 130°C for 8 h, obtaining a fully cured resin whose glass transition was at 98.9°C. Samples were aged at temperatures between 50 and 100°C for periods of time from 15 min to a maximum of 1680 h. The extent of physical aging has been measured by the area of the endothermic peak which appears below and within the glass transition region. The enthalpy relaxation was found to increase gradually with aging time to a limiting value where structural equilibrium is reached. However, this structural equilibrium was reached experimentally only at an aging temperature of T_g-10°C. The kinetics of enthalpy relaxation was analysed in terms of the effective relaxation time τ_eff. The rate of relaxation of the system given by 1/τ_eff decreases as the system approaches equilibrium, as the enthalpy relaxation tends to its limiting value. Single phenomenological approaches were applied to enthalpy relaxation data. Assuming a separate dependence of temperature and structure on τ, three characteristic parameters of the enthalpic relaxation process were obtained (In A = ?333, E_H = 1020 kJ/mol, C = 2.1 g/J). Comparisons with experimental data show some discrepancies at aging temperatures of 50 and 60°C, where sub-T_g peaks appears. These discrepancies probably arise from the fact that the model assumes a single relaxation time. A better fit to aging data was obtained when a Williams-Watts function was applied. The values of the nonexponential parameter β were slightly dependent on temperature, and the characteristic time was found to decrease with temperature. © 1994 John Wiley & Sons, Inc.     

Limiting Electroconductivity and Structure of Molten Chlorides of Alkaline-Earth Metals

It is established experimentally that the electroconductivity of individual molten chlorides of calcium, strontium, and barium increases with the electric field strength and reaches limiting values, which are dependent on the salt nature and the temperature. The limiting electroconductivity of molten calcium and strontium chlorides satisfactorily obeys the Nernst–Einstein relationship. The relaxation kinetics of excess conductivity induced by high-voltage pulsed discharges is studied. The relaxation time is equal to about 10⁴ s.     

Viscosity of molten NaCI,NaBF4 and KBF4

Abstract

The viscosities of molten NaBF₄ and KBF₄ were determined over a 120°C interval and the viscosity of molten NaCl was redetermined over a 200°C interval by use of an oscillating cup viscometer. The viscosities of all three samples followed an Arrhenius type temperature dependence. The measured viscosity for NaCl agreed better with predicted values and the trend established by the other sodium and potassium halides than did previous determinations. The Batchinskii free volume concept of viscosity held for the sodium and potassium halides and the two MBF₄ salts. An equation based upon a hard-sphere model predicted viscosity values in agreement with experimental values for the alkali metal halides and KBF₄ but was not suitable for NaBF₄.     

Temperature dependence of rotational correlation times in tribromobenzene

The ¹³C relaxation times and nuclear Overhauser enhancements of the protonated carbons in 1,3,5-tribromobenzene were measured as a function of temperature in the solvent benzene-d₆. Rotational correlation times, τ_C(CH), calculated by the Microviscosity/Free Rotor and Hu-Zwanzig “slip” models are substantially below the measured values. In contrast, correlation times predicted by the Hynes—Kapral—Weinberg model are in near quantitative agreement with experiment at all temperatures studied.     

Analysis of viscoelastic behavior and dynamic mechanical relaxation of copolyester based layered silicate nanocomposites using Havriliak–Negami model

The solid‐state viscoelastic properties are examined for intercalated nanocomposites based on a copolyester and (2‐ethyl‐hexyl)dimethyl hydrogenated‐tallow ammonium montmorillonite. The nanocomposites are prepared via the direct melt intercalation technique using a conventional twin‐screw extruder. Dynamic mechanical thermal analysis of the nanocomposites is conducted using two different test setups. The dynamic mechanical relaxation spectra show an increase in the storage modulus of the nanocomposite over the entire temperature range under study as compared to the pristine polymer (except in the transition region from 70 to 80 °C). These results are analyzed using the empirical Havriliak–Negami (HN) equation. The four temperature independent HN parameters (α, β, E₀, and E_∞) and one temperature dependent parameter (τ, the relaxation time) are determined by solving the HN equation for each temperature over the range of temperatures. The calculated moduli results fit well with the experimental values of the relaxation spectra for the nanocomposites. This study shows that the HN model can be applied to polymer layered silicate nanocomposites, and it can be used to predict their dynamic mechanical properties over a wide range of temperatures and frequencies a priori. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2657–2666, 2004     

Low‐Temperature Molten‐Salt Production of Silicon Nanowires by the Electrochemical Reduction of CaSiO3

Silicon is an extremely important technological material, but its current industrial production by the carbothermic reduction of SiO₂ is energy intensive and generates CO₂ emissions. Herein, we developed a more sustainable method to produce silicon nanowires (Si NWs) in bulk quantities through the direct electrochemical reduction of CaSiO₃, an abundant and inexpensive Si source soluble in molten salts, at a low temperature of 650 °C by using low‐melting‐point ternary molten salts CaCl₂–MgCl₂–NaCl, which still retains high CaSiO₃ solubility, and a supporting electrolyte of CaO, which facilitates the transport of O²⁻ anions, drastically improves the reaction kinetics, and enables the electrolysis at low temperatures. The Si nanowire product can be used as high‐capacity Li‐ion battery anode materials with excellent cycling performance. This environmentally friendly strategy for the practical production of Si at lower temperatures can be applied to other molten salt systems and is also promising for waste glass and coal ash recycling.