Molecular mobility in polymers studied with thermally stimulated recovery

Thermally stimulated recovery, TSR, like as thermally stimulated depolarisation currents, is a suitable technique that allows for the study of conformational mobility in polymeric systems. Due to its relatively low equivalent frequency and transient nature, the viscoelastic data obtained from this technique are complementary to conventional dynamic mechanical analysis (DMA). In this work TSR-like experiments, including TSR, thermally stimulated creep and thermal sampling (TS) experiments were carried out in the same commercial DMA equipment, allowing for the direct comparison of the data. Some advises for running TSR experiments are presented, such as the need of performing blank experiments and temperature calibrations. The analysis of the data to obtain the thermokinetic parameters of TS experiments is revised. In particular, from the direct fitting of the data, it is reported a tendency for a linear relationship between the pairs of values of (E _a, log τ₀) that best adjust any TS single experiment. It is concluded that the usual equation for describing TS experiments possesses an intrinsic compensation between these two thermokinetic parameters. This revised version was published online in August 2006 with corrections to the Cover Date.     

Determination of empirical polarity parameters of the cellulose solvent N,N-dimethylacetamide/LiCl by means of the solvatochromic technique

Empirical solvatochromic polarity parameters (α-, β-, and $ \pi ^* $, AN and DN, as well as E_T(30)-values) for cellulose, N,N-dimethylacetamide (DMA)/LiCl and cellulose dissolved in DMA/LiCl are presented. The following solvent polarity indicators were applied: 2,6-diphenyl-4-(2,4,6-triphenyl-1- pyridinio)-1-phenolate ( 1 ), bis(4-N,N-dimethylamino)-benzophenone (MK, 2 ), iron(II)-di-cyano-bis(1,10)-phenanthroline, Fe(phen)₂(CN)₂, ( 3 ), and copper(II)-N,N,N′,N′-tetramethyl-ethylendiamine-acetylacetonate tetraphenylborate/chloride/bromide (Cu(tmen)(acac)⁺ X⁻ ( 4 )). The solvatochromic shifts (ν_max) of the indicators 1 , 2 , 3 , and 4 adsorbed to cellulose or dissolved in DMA/LiCl reflect the corresponding properties of the surrounding, the dipolarity/polarizability ($ \pi ^* $), the hydrogen bond donating ability or Lewis acidity (α), and the hydrogen bond accepting ability or Lewis basicity (β), respectively. Any indicator employed is well characterized (r > 0.97) by a linear solvation energy relationship (LSER) taking the Kamlet and Taft parameter into account: ν_max(indicator) = ν_max,0 + s$ \pi ^* $ + aα + bβ. Cellulose, DMA/LiCl, and the cellulose/DMA/LiCl solution approach a similar polarity with an E_T(30) parameter about 52 to 53 kcal mol⁻¹. The hypothetical interaction strength parameter (acid-base interactions, dipolar–dipolar interactions) between cellulose and DMA/LiCl are calculated by means of the individual Kamlet–Taft parameters α, β, and $ \pi ^* $ of cellulose and DMA/LiCl via a multiparameter equation. The specific chloride/cellulose interaction plays a dominant role in the cellulose solvent DMA/LiCl. Comparison of the polarity parameters of DMA/LiCl with the polarity parameters of other mixtures—such as N,N-dimethyl- formamide/LiCl, DMA/NaCl, or DMA/LiBr—are presented as well. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1945–1955, 1998     

The relation between the nonlinear dielectric effect and solvent polarity

The relation between solvent polarity expressed through the Dimroth-Reichardt spectroscopic parameter E _T (30) and the nonlinear dielectric effect (NDE) expressed through the parameter /E² is demonstrated where is a change in the electric permittivity of a solvent in an external strong electric field E. Both E _T (20) and /E², determined in quite different ways, are extremely sensitive to the dielectric properties of a solvent which depend on molecular interactions. Linear correlations between /E² and E _T (30) have been found for n-alkanols representing hydrogenbond donor solvents, and for halogenobenzenes which are dipolar, aprotic, weakly-associated solvents.Part of this work was presented at The 22^nd International Conference on Solution Chemistry in Linz, Austria, July 1991.     

Zur Entmischung von kubischen Mehrstoffcarbiden

Zusammenfassung Die Mischungslücke in den Systemen: TiC–{ZrC, HfC} und VC-{NbC, TaC} wird im Bereich von 1200° C bis zur Temperatur des kritischen Punktes experimentell ermittelt und mit Hilfe der freien Exzeß-Enthalpie von der Form: G ^E =x(1–x) {(a ₀+a ₁ T)+(2x–1)(b ₀+b ₁ T)} berechnet.

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The miscibility gap within the systems: TiC–{ZrC, HfC} and VC—{NbC, TaC} has been experimentally determined in the region from 1200°C up to the temperature of the critical point. A calculation of the binodal curve has been carried out by means of an excess free enthalpy of the form: G ^E =x(1–x){(a ₀+a ₁ T)+(2x–1)(b ₀+b ₁ T)}.

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Mit 4 Abbildungen     

Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E ₁(t)=E ₁+exp(–a _n t+b _n ). In the limit of very large t, this becomes E ₁(t)=E ₁+exp(–a ₁ t+b ₁). A simple analysis shows that the parameters are a ₁=E ₂–E ₁ and b ₁=ln[(E ₂–E ₁)|c ₂|²/|c ₁|²]. Functions are introduced which allow determination of a ₁, b ₁ and lower bounds to E ₁.     

Electronic structures and MCD spectra of trigonal Cr(III)S6 systems

MCD, electronic absorption, external heavy atom, and crystal field data are presented for the low energy region (² E _g, ² T _1g, ⁴ T _2g) and high energy region (² T _2g, ⁴ T _1g) of Cr(dtp)₃, Cr(dtc)₃, and Cr(exan)₃. At low energy, MCD intensities of ² E(² E _g) and ² E(² T _g) are as large or larger than ⁴ T _2g, and the MCD technique is advantageous over electronic absorption in this respect. The MCD positions of ² E _g and ² T _1g are nearly the same for these molecules ( 13 kK and 13.6 kK) · ⁴ T _2g of this region appears trigonally split ( 500 cm^–1) in the MCD of dtp but to a smaller extent than in the electronic crystal spectrum of Lebedda and Palmer ( 600 cm^–1). MCD did not resolve such components for exan and dtc. The higher energy region includes ² T _2g and ⁴ T _1g, and the combined MCD and electronic absorption data of the three compounds taken together lead us to conclude the ordering ² A ₁(² T _2g)<² E(² T _2g)<⁴ E(⁴ T _1g). The potentially useful external heavy atom affect on the solution-observed electronic ² E and ⁴ E bands of Cr(dtp)₃ did not shed additional light on this order of E states. Finally, it is concluded that the order of ⁴ T _1g and ² T _2g cannot be decided from O _h crystal field calculations because of experimental uncertainties about choosing centers of gravity. In addition, ⁴ T _1g and ² T _2g are close together so that ordering ² E<⁴ E does not guarantee ² T _2g<⁴ T _1g. However, it can be concluded that the ratio C/B4 is not correct, whereas the larger 7<(C/B)<8 is consistent with the data of all three molecules because of small B parameters ( 0.4). Locating OO transitions may somewhat decrease C/B and Dq.

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Zusammenfassung In der vorliegenden Arbeit werden folgende Meßergebnisse mitgeteilt; MCD, elektronische Absorption, Einfluß eines äußeren schweren Atoms sowie Kristallfelddaten für den Bereich niedriger Energie (² E _g, ² T _1g, ⁴ T _2g) und den Bereich hoher Energie (² T _2g, ⁴ T _1g) von Cr(dtp)₃, Cr(dtc)₃ und Cr(exan). Bei niedriger Energie sind die MCD-Intensitäten von ² E(² E _g) und ² E(² T _1g) genau so groß, oder größer als ⁴ T _2g, und die MCD-Technik bietet Vorteile gegenüber der elektronischen Absorptionsmethode. Die MCD-Werte von ² E _g und ² T _1g sind für die genannten Moleküle etwa gleich ( 13 kK und 13,6 kK). ⁴ T _2g dieses Gebietes erscheint trigonal aufgespalten ( 500 cm^–1) bei MCD von dtp, aber in einem geringeren Maß als im elektronischen Kristallspektrum von Lebedda und Palmer ( 600 cm^–1) MCD löste solche Komponenten bei exan und dtc nicht auf. Der Bereich höherer Energie enthält ² T _2g und ⁴ T _1g, und aus der Kombination von Daten der MCD-Methode sowie der elektronischen Absorption schlossen wir auf die Anordnung ² A _1g(² T _2g)<² E(² T _2g)<⁴ E(⁴ T _1g). Der möglicherweise nützliche Effekt eines äußeren schweren Atoms auf die in Lösung beobachteten elektronischen ² E- und ⁴E-Banden von Cr(dtp)₃ brachte bezüglich dieser Anordnung der E-Zustände nichts Neues. Weiterhin wird gefolgert, daß die Ordnung von ⁴ T _1g und ² T _2g nicht aus O _h-Kristallfeldberechnungen entschieden werden kann, da experimentelle Unsicherheiten bezüglich der Wahl von Schwerpunkten bestehen. Außerdem liegen ⁴ T _1g und ² T _2g nahe zusammen, sodaß aus der Anordnung ² E<⁴ E nicht notwendig ² T _2g<⁴ T _1g folgt. Es kann jedoch gefolgert werden, daß das Verhältnis C/B4 nicht korrekt ist, während 7<(C/B)<8 konsistent mit den Daten aller drei Moleküle ist, da die B-parameter klein sind (0,4). Die Vokalisierung der OO-Übergänge könnten C/B und Dq etwas erniedrigen.

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Presented in part at the 161st American Chemical Society National Meeting, Los Angeles, California, March–April, 1971.

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NDEA Pre-Doctoral Fellow.     

ESR studies on solvation by using <Emphasis Type="Italic">s</Emphasis>-butyl trifluoroacetyl nitroxide probe

Stable s-butyl trifluoroacetyl nitroxide (3) has been generated in electron-transfer reaction of O-benzoyl-N-s-butylhydroxylamine (1) and trifluoroacetyl peroxide (2) in F113 (CFCl₂CF₂Cl) solution at room temperature. ESR measurement of a _N and a _H values for 3 in 21 solvents has been carried out at 24~ 25°C. The a _N values for 3 in 12 aprotic solvents show a linear correlation with the cybotactic solvent parameters E _T and Z, i.e. a _N = 1.35×10-² E _T+6.84, a _N = 0.78×10-² Z+6.88. The physical significance for the slopes, slope × E _T or slope × Z, the extrapolated intercepts on the a _N axis are linked to the sensitivity of the nitroxide toward the solvation, the magnitude of the overall solvaton effect on the a _N values, and the intrinsic a _N value of 3 in the ideal gaseous state, respectively. The plots of a _N versus noncybotactic solvent constants, such as dipolar moment () and dielectric constant (), all show random cases.     

Generalized criterion of solvent polarity as a tool for control of chromatographic process

The generalized (reductive) criterion of solvent polarity was obtained by the method of multiparametric optimization of the Snyder index P", Hildebrand parameter _T , permittivity _r , and solvatochromism parameter E _T (30). Possibilities of employing this criterion for estimation of the elution power of normal and reversed mobile phases used in high-performance liquid chromatography were considered.     

Estimation of the Critical Temperature of Thermal Explosion for the Highly Nitrated Nitrocellulose Using Non-isothermal DSC

Two methods for estimating the critical temperature (T_b) of thermal explosion for the highly nitrated nitrocellulose (HNNC) are derived from the Semenov's thermal explosion theory and two non-isothermal kinetic equations, d/dt=Af()e^–E/RT and d/dt=Af()[1+E/(RT)(1–T_o/T)]e^–E/RT, using reasonable hypotheses. We can easily obtain the values of the thermal decomposition activation energy (E), the onset temperature (T_e) and the initial temperature (T_o) at which DSC curve deviates from the baseline of the non-isothermal DSC curve of HNNC, and then calculate the critical temperature (T_b) of thermal explosion by the two derived formulae. The results obtained with the two methods for HNNC are in agreement to each other.This revised version was published online in November 2005 with corrections to the Cover Date.     

Addition of organic and inorganic moieties to Fe2(CO)6(μ-EE′) and Fe3(CO)9(μ3-E)(μ3-E′) [E=Se,Te;E′=S,Se, Te]

Reaction of the iron chalcogen carbonyl clusters Fe₂(CO)₆(-EE) and Fe₃(CO)₉(₃-E)(₃-E), [E=Se, Te;E=S, Se, Te] with various inorganic and organic moieties produce a number of higher nuclearity clusters. The reactivity pattern of these iron chalcogen carbonyl compounds and the structure of the products formed are discussed.     

Thermally stimulated currents in poly(bis(p-fluorophenoxy)phosphazene)

Thermally stimulated currents (TSC) were examined for poly(bis(p-fluorophenoxy)phosphazene) (PBFPP) film. TSC showed peaks at the glass transition temperature (Tg=–4 °C) and atT(1) (160 °C – 170 °C), where-form crystal phase transformed to mesophase of-form structure. Another peak was found atT _cc betweenTg andT(1). Linear relationship between polarization field and peak current ofT _cc -peak was found, which shows thatT _cc -peak was caused by motion of dipolar groups in crystalline phase. When heating (up to 200 °C) and cooling (down to 20 °C) thermal process was repeated,T _cc -peak shifted to higher temperature region approachingT(1) and simultaneously, the peak current ofT(1)-peak became smaller. Activation energy, time constant of dipolar relaxation and charge mobility were evaluated forT _cc -peak. From these results, it was concluded that-form and more ordered- form crystalline phases coexisted in PBFPP once heated aboveT(1) and the content of- form phase increased by repeated thermal hysteresis.     

Effect of finite extensibility on the viscoelastic properties of a styrene–butadiene rubber vulcanizate in simple tensile deformations up to rupture

Stress–strain and rupture data were determined on an unfilled styrene–butadiene vulcanizate at temperatures from ?45 to 35°C and at extension rates from 0.0096 to 9.6 min^?1. The data were represented by four functions: (1) the well-known temperature function (shift factor) a_T; (2) the constant strain rate modulus, F(t,T), reduced to temperature T₀ and time t/a_T, i.e., T₀F(t/a_T)/T; (3) the time-dependent maximum extensibility, λ_m(t/a_T); and (4) a function Ω(χ) where χ = (λ ? 1)λ_m⁰/λ_m, in which λ is the extension ratio and λ_m⁰ is the maximum extensibility under equilibrium conditions. The constant strain rate modulus characterizes the stress–time response to a constant extension rate at small strains, within the range of linear response; λ_m is a material parameter needed to represent the response at large λ; and Ω(χ) represents the stress–strain curve of the material in a reference state of unit modulus and λ_m = λ_m. The shift factor a_T was found to be sensibly independent of extension. At all values of t/a_T for which the maximum extensibility is time-independent, the relaxation rate was also found to be independent of λ. These observations indicate that the monomeric friction coefficient is strain-independent over the ranges of T and λ covered in the present study. It was found that λ_m⁰ = 8.6 and that the largest extension ratio at break, (λ_b)_max, is 7.3. Thus, rupture always occurs before the network is fully extended.     

The solubility and isotopic fractionation of gases in dilute aqueous solution. IIa. solubilities of the noble gases

A method for the analysis of precise gas solubility data is presented and applied to new determinations of the Henry constant, k₂, for He, Ne, Ar, Kr, and Xe. The values of k₂ are fitted to the same sets of temperature functions which we have tried for oxygen. Our previously proposed power series in 1/T, ln(k_2/P )=a₀+a₁/T+a₂/T² (Mark I), gives the best 3-term fit within the temperature range 0–60°C. For use over the full range to the critical temperature of water, we have discovered a new function given by (T^*)²ln(k_2/P )=A₀(T^*)²+A₁(1-T^*)^1/3+A₂(1-T^*)^2/3(Mark II), where T^*T/T _c1 . It fits our data from 0–60°C nearly as well as Mark I; it fits high temperature data from other sources; and at the critical temperature of water it satisfies theoretical requirements. Expansion of Mark II reveals the relationship between Mark II and Mark I and leads to a 4-term smoothing function, ln(k_2/P )=a_–2(T^*)^–2+a_–1(T^*)^–1+a₀+a₁T^* (Mark III), which we believe gives the best values only for the 0–60°C range. Mark III is used to calculate values for , and , 0–60°C, and a procedure is empolyed to estimate the errors. Agreement is excellent between these results and those obtained from precise microcalorimetric measurements made by others. With the inclusion of pressure correction terms, Mark II yields the four thermodynamic function changes for use at high temperatures. With increasing temperature, these changes suddenly turn upward toward plus infinity as T _c1 is approached. Essentially direct determinations of for argon by other workers are in excellent agreement with our results. The symmetrical activity coefficient at infinite dilution, ₂ ^° is examined and the hypothetical properties of k₂ are explored below 0°C. Mark II can be expressed in the reduced form (T^*)²ln(k ₂ ^* )=A₁(1-T^*)^1/3+A₂(1-T^*)^2/3, where k ₂ ^* k ₂/(p _c12c1). A₂ is a very good linear fit to A₁, which suggests a characteristic temperature for water at 287.3 K.     

Untersuchungen zur Ursache der Entstehung von “Extended Chain”-Kristallen des Polyäthylens

Zusammenfassung Als Mechanismus für die Bildung von extended chain-Kristallen bei der Kristallisation von Polyäthylen unter hohen Drucken ist vorgeschlagen worden, daß sich zunächst Kristallite mit gefalteten Ketten bilden sollen, die sich dann infolge des Dickenwachstum zu Kristallen mit gestreckten Ketten umwandeln. Um diese Deutung zu überprüfen, wurden Polyäthylen-Einkristalle und orientierte Polyäthylenproben bei Drucken zwischen 1 und 4200 atm und bei Temperaturen zwischen 115 °C und 220 °C getempert. Die Proben wurden mit Hilfe der Röntgenkleinwinkelstreuung, der Elektronenmikroskopie und der Differential-Thermoanalyse untersucht. In keinem Fall konnte ein Hinweis auf eine Umwandlung zu extended chain-Kristallen gefunden werden. Vielmehr stellte es sich heraus, daß die Geschwindigkeit des Dickenwachstums offenbar nicht von der TempertemperaturT _a , sondern nur von der DifferenzT=T _m (p)–T _a zwischen SchmelzpunktT _m (p) und TempertemperaturT _a abhängt.

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Summary As a reason for formation of extended chain crystals of polyethylene during crystallization under high pressure the following mechanism has been proposed: At first a folded chain structure is formed and then isothermal thickening of those crystals occurs. In order to proof this explanation polyethylene single crystals and drawn polyethylene samples were annealed at pressures between 1 and 4200 atm and at temperatures between 115 °C and 220 °C. The properties of the annealed samples were studied by means of x-ray small angle scattering, electron microscopy, and differentialthermoanalysis. There was no evidence for transformation of folded chain crystals towards extended chain crystals. On contrary it was found that probably the rate of thickening depends on the temperature differenceT=T _m (p)–T _a between pressure depending melting pointT _m (p) and the annealing temperatureT _a.

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Wir danken den Herren Dr.G. F. Schmidt, Dr.H. Goddar und Dipl.-Phys.G. Hinrichsen für ihre Hilfe bei der Durchführung der Messungen und für wertvolle Ratschläge. Der Deutschen Forschungsgemeinschaft danken wir für die zur Verfügung gestellten Apparaturen.     

Possibility of deriving kinetic parameters from integrated DTA peaks

Three DTA peaks (two endo and one exothermic) were replotted in the form of peak area.a, or peak magnitude,T, as a function of temperature. The integral sigmoid curves were plotted in the form of logg() vs. 1/T or log logg()/T ² vs. 1/T. Both of the proposed summation methods gave satisfactory straight lines (F ₁ function), characterized by the same activation energies, correlation coefficients and standard deviations. Integration of the peak areas by Simpson's rule resulted in the same values as obtained by the summation procedure. Analysis by the suggested integral method resulted in activation energies that show a logarithmic divergence relative to the magnitude ofE _a estimated directly from the DTA peaks.     

Methanol adsorption by amorphous silica alumina in the critical temperature range

The methanol adsorption capacity of an amorphous silica-alumina was measured using an equilibrium technique. The experimental temperature range was of 140 to 260°C and the pure methanol pressure range was 0.1 to 1.2 MPa. A multilayer adsorption was found, also for temperatures above the critical temperature of the adsorbate. Based on the Jovanovic adsorption model, the mean residence times of the adsorbed molecules were calculated. Surprisingly, the heat of adsorption was found to be independent of the temperature in the multilayer adsorption range.Symbols Units a parameter defined by Equation (7) - a parameter defined by Equation (10) Pa - a(T) parameter in the Peng-Robinson equation Pa/(mol/m³)² - b parameter defined by Equation (8) - b parameter defined by Equation (11) Pa^–1 - b(T) parameter in the Peng-Robinson equation m³ mol^–1 - c constant in the BET equation - k Boltzmann constant, being 1.3806 · 10^–23 JK^–1 - K characteristic constant in the Peng-Robinson equation - m mass of one adsorbate molecule kg - p pressure Pa - q adsorption capacity g/g - Q heat of adsorption J mol^–1 - R gas constant, being 8.314 J mol^–1 K^–1 - T absolute temperature K - V molar volume m³ mol^–1 - x relative pressure (=p/p ₀) - active molecule area m² - residence time s - acentric factor     

Thermodynamic properties for binary liquid mixtures of 1-chlorobutane+n-alkanes

Isothermal compressibilities K and isobaric thermal expansion coefficients _p have been measured at 25 and 45°C for pure components and the following binary mixtures: 1-chlorobutane+normal alkanes (n-C_n) where n=6, 8, 10, 12, 14 and 16. With these results and other thermodynamic data from literature the next mixing quantities have also been reported: (V ^E/T)_P, – (V)^E/P)_T, K _S ^v , H ^E/P)_T, (_pVT and C_v. The obtained results have been compared at 25°C with the calculated values by using the Prigogine-Flory-Patterson theory of liquid mixtures. The theory predicts the excess volume V^E and V ^E/P)_T values rather well, the C _P ^E quite poorly, while for V ^E/T)_P and V ^E/P)_T it is only predicted the trend with the chain length of the n-alkane. The last two quantities show deviations between theoretical and experimental, slightly higher in systems with longer n-alkanes than for shorter ones. Our conclusion is that a nonrigid linear molecule, like 1-chlorobutane, has a low ability as a breaker of the pure n-C_n orientation correlations, in between that which we found for toluene and p-xylene and much smaller than for cyclohexane or benzene.     

Study of approximate coupled cluster methods for first-order static properties

In this paper, we analyse the algebraic structure of the equations for calculating the first order static properties using several approximate versions of Coupled Cluster (CC) methods. In particular, the non-variational and the variational method using a CC wavefunction corresponding to an appropriately defined perturbed Hamiltonian as well as the simple expectation value expression using a CC stationary state are studied under different approximations. Two different models are proposed: (a) use of maximum overlap orbitals where the pertinent approximations are TT ₂, T ⁽¹⁾ T ₂ ⁽¹⁾, (b) use of Hartree-Fock orbitals and T(T ₁+T ₂), T ⁽¹⁾(T ₁ ⁽¹⁾ +T ₂ ⁽¹⁾ ) approximations. It is analytically shown that in both these models certain approximate versions of the methods under purview yield identical results for first order static properties.NCL Communication No. 3725     

Modification of the Pitzer model to calculate the mean activity coefficients of electrolytes in a water-alcohol mixed solvent solution

The approach tested in this work consists in adapting the Pitzer model, initially designed for aqueous solutions of electrolytes, to the case of solutions with a mixed solvent, without systematically readjusting the coefficients. This modified model was applied successfully to the calculation of the mean activity coefficients of NaBr in the mixed solvent H₂O+MeOH, H₂O+EtOH and compared with the experimental values obtained from electrode potential measurements.General D dielectric constant - G ^ex excess Gibbs energy - I ionic strength - k Boltzman's constant - m _i molality - N _o Avogadro's number - n _w number of kilograms of water - R gas constant - T temperature (K) - T _c critical temperature - T _cm critical temperature of mixed solvent - x _i molar fraction - z _i ionic charge - electronic charge - osmotic coefficient - ± mean activity coefficient of electrolyte - number of moles of ions given by one mole of electrolyte - _M number of moles of cations given by one mole of electrolyte - _X number of moles of anions given by one mole of electrolyte - _W density of water Debye- Hückel Model A Debye-Hückel parameter - a distance of closest approach of ions in solution - B Debye-Hückel parameter Pitzer Model b numerical parameter of model - numerical parameter of model - ₁, ₂ numerical parameters of model, used in the case of 2:2 electrolyte - _MX ⁽⁰⁾ numerical parameter of electrolyte MX - _MX ⁽¹⁾ numerical parameter of electrolyte MX - _MX ⁽²⁾ numerical parameter of 2:2 electrolyte MX - C _MX numerical parameter of electrolyte MX - binary interaction parameter - ternary interaction parameter     

Excess volumes of binary mixtures of ethylbenzene with octanol,nonanol and dodecanol from 50 to 100°C and 0.1 to 7.5 MPa

The excess volume V ^E of binary mixtures of octanol, nonanol and dodecanol in ethylbenzene have been calculated from the densities measured with a vibrating tube densimeter at temperatures from 50 to 100 °C and at pressures from 0.1 to 7.5 MPa. The values of V ^E are positive for all the three mixtures in the complete temperature, pressure and mole fraction ranges studied. The maxima in V ^E is observed at 0.4 mole fraction of alkanol. The results are discussed in terms of specific interactions present in the binary mixtures. The second order thermodynamic quantities (V ^E /T)_p,(V ^E /P)_T and (V _E /P)_T which have been derived from the effect of temperature and pressure on V ^E , indicate an overall net creation of order in the binary mixtures of ethylbenzene with higher homologues of alkanols.