Exchange Energy Parameter Research Articles

Heat capacity of compensated F/AF bilayers

We report a theoretical study of the magnetic heat capacity, c V( T), of exchange coupled compensated ferromagnet/antiferromagnetic bilayers. We show that c V( T) may display a large peak at the temperature T R where the interface magnetic frustration induces a 90° reorientation of the F layer. We study Fe/FeF 2 bilayers and show that T R and the magnitude of the c V( T) peak depend on the strength of the interface exchange. We suggest how the sign of the interface exchange energy parameter can be investigated using features produced by external fields.

The ratio of crystallinity and thermodynamical interactions of polycaprolactone with some aliphatic esters and aromatic solvents by inverse gas chromatography

The retention diagrams of benzene, toluene, ethyl benzene, chloro benzene, n-propyl benzene, isopropyl benzene, methyl acetate, ethyl acetate, n-propyl acetate, n-butyl acetate and isoamyl acetate on the polycaprolactone were plotted at temperatures between 70 and 140oC by inverse gas chromatography technique. Percent crystallinity of polycaprolactone were obtained at temperatures below melting point from the retention diagrams of benzene, toluene and ethyl benzene. It was concluded that the data obtained by inverse gas chromatography were comparable those of obtained by differential scanning calorimetry. Specific retention volume, Vgo, Flory-Huggins polymer-solvent interaction parameters, χ12∞, the weight fraction activity coefficients of the solvents at infinite dilution, Ω1∞, effective exchange energy parameters, Xeff were determined. Later, the partial molar heat of sorption, ΔH1,sorp and the partial molar heat of mixing, ΔH1∞ were obtained from the slope of the logarithm of specific retention volume, Ln Vgo versus 1/T plot and from the slope of the logarithm of the weight fraction activity coefficients, Ω1∞versus 1/T plot, respectively.

Determination of Rate of Crystallinity and Thermodynamical Interaction Parameters of Polycaprolactone with Some Solvents by Gas Chromatography

AbstractThe retention diagram of polycaprolactone for tert‐butyl acetate was obtained by inverse gas chromatography method in the temperature range of 40‐140 °C. Rate of crystallinity was determined between 45.0 percent and 37.1 percent in the temperatures at 40 and 53 °C, respectively. Thermodynamic interaction parameters were determined for cyclopentane, cyclohexane, tetrahydrofuran and 1,4‐dioxane with polycaprolactone between 70 and 130 °C. Specific retention volumes, Vgo, Flory Huggins polymer‐solvent interaction parameters, χ12∞, equation of state polymer‐solvent interaction parameters, χ12*, weight fraction activity coefficients of the solvents at infinite dilution, Ω1∞, effective exchange energy parameters, X̄12were determined.

Optimized pulsed laser deposited barium ferrite thin films with narrow ferromagnetic resonance linewidths

Hexagonal M-type barium ferrite (BaM) films have been prepared by pulsed laser deposition. Optimal preparation conditions gave pure single phase films with the narrowest possible ferromagnetic resonance (FMR) linewidths. The films were deposited on c-plane sapphire substrates with a KrF excimer laser at wavelength of 248 nm and fluence of 1.7 J/cm2. The minimum linewidth films were obtained for an oxygen partial pressure of 300 mTorr and a substrate temperature of 910 °C, and were 0.85 μm thick. X-ray diffraction indicated pure single crystal BaM phase with local c-axis deviations less than 0.15°. Vibrating sample magnetometry data gave hysteresis loops with minimal hysteresis and small coercive force, saturation induction 4πMs of 4.2 kG and uniaxial anisotropy field HA of 16.4 kOe. The HA matches the anisotropy for bulk and the 4πMs is about 10% below literature values for the bulk. The FMR spectra were measured from 50 to 75 GHz by shorted wave guide techniques with the static field perpendicular to the film. The optimized film uniform mode half power FMR linewidth at 60.3 GHz was 27 Oe. This linewidth was a linear function of the frequency with a response coefficient of 0.5 Oe/GHz and nearly zero frequency intercept. Within experimental error, this linewidth response is the same as for bulk crystals. The FMR spectra show additional standing spin wave (SSW) resonances which could be indexed to give field positions that scale with the square of index n except for low order modes. The scaling gave a standard exchange energy parameter, Aex, of 6.4×10−7 erg/cm. The SSW linewidths scaled with n2. Application of the Kittel thickness variation model to the SSW linewidth data gave an estimated thickness variation of the film of about 7%.

A method for determination of thermodynamics and solubility parameters of polymers in dilute solutions from critical volume fractions

An equation using the critical volume fraction and segment number of polymer was proposed for the partial molar entropy change of a polymer for mixing in dilute solution. The partial molar enthalpy change of polymer for mixing was determined from the thermodynamic equilibrium property of two polymer phases at the critical temperature. The solubility or cohesion parameter of a polymer fraction at the critical temperature was calculated by using the partial molar enthalpy change and repeat unit volume of the polymer. The solubility parameter of high molar mass polymer at the theta temperature was determined by extrapolating solubility parameter values of the polymer fractions to high molar mass by using the solubility parameter-segment number relation of polymer fraction. This relation gives good straight line. The solubility parameter of the polymer at the theta temperature and the exchange energy parameter for polymer–solvent pair were obtained directly from the intercept and the slope of this line, respectively. These equations were applied to the critical point data of polystyrene (PS) in methylcyclohexane (MCH) and in cyclohexane (CH) solutions. The results obtained in this study coincide with the literature values for the solubility parameter of PS and exchange energy parameter for PS in CH solution. It was also found that the partial molar entropy change of a polymer for mixing at theta temperatures has about a constant value.

Blend formation between homo- and co-polymers at 298.15 k, PMMA-SAN blends

Solution heats in chloroform at 25 °C have been measured experimentally for poly(methylmethacrylate) (PMMA), samples of poly(styrene-co-acrylonitrile) (SAN) containing from 5 to 37 mass% of acrylonitrile, and some PMMA-SAN blends prepared inside the miscibility range. From these data the mixing enthalpies for blend formation were obtained. Use of the mixing heats values in the framework of the Prigogine-Flory-Patterson theory allowed to calculate values of the exchange energy parameters between the components of the blends much more negative than existing literature data. Calculation of binary interaction energy parameters between the single repeat units of the copolymer from the above data, and from model compounds, clearly indicates a strong increase of the intramolecular repulsive energy between nitrile and styrene units of SAN, as compared with the interaction between the corresponding free model molecules.

Determination of some thermodynamical interaction parameters of polycaprolactone with some solvents by inverse gas chromatography

AbstractThe retention diagrams of polycaprolactone (PCL) were obtained between 70 and 140 °C with solvents such as n‐pentane, n‐hexane, n‐heptane, n‐octane, n‐nonane, n‐decane, isopropyl acetate, isobutyl acetate and tert‐butyl acetate by an inverse gas chromatography technique. Some thermodynamical parameters, namely the weight fraction activity coefficient of the solvent at infinite dilution, $\Omega_{1}^{\infty}$, the Flory–Huggins interaction parameter, $\chi_{12}^{\infty}$, at infinite dilution of solvent, the hard‐core interaction parameter, $\chi_{t}^{\infty}$, at infinite dilution of solute, and the effective exchange energy parameters, X 12 in the equation‐of‐state theory, were determined for these polymer–solvent systems. In addition, the partial molar heat of sorption, Δ H 1, sorp, the partial molar heat of mixing, $\Delta \overline{H}_{1}^{\infty}$ of the solvents and the solubility parameter of the polymer, δ2, were determined for these systems. n‐Alkanes were particularly poor solvents but the esters studied were moderately good solvents for PCL. The solubility of the PCL did not change considerably with temperature in all the solvents studied. The values of interaction parameters were close to each other for PCL–ester systems studied. The solubility parameter of PCL, δ2, was found to be around 10 (cal cm−3)1/2 at room temperature and decreases linearly with temperature.© 2002 Society of Chemical Industry

Determination of the Pressure Dependence of Band‐Structure Parameters by Two‐Photon Spectroscopy

AbstractTwo‐photon spectroscopy has been used to determine the pressure dependence of band‐structure parameters such as band gap, exciton binding energy, biexciton binding energy, exchange energy, and Luttinger parameters. Compared to linear spectroscopy it yields not only a higher precision, but is often able to determine a larger number of parameters. Results are presented for ZnTe and CuCl nanocrystals in a LiCl matrix.

Determination of Exchange Enthalpy andEntropy Parameters of Poly(dimethylsiloxane) with Somen-Alkanes by InverseGas Chromatography

The total interaction parameter at infinitely high polymer concentration, χ t ∞, and the effective exchange energy parameter, X 12 , of poly(dimethyl siloxane) with n-pentane, n-hexane, n-heptane and n-nonane were determined around room temperature using the inverse gas chromatography technique. The values of χ t ∞ are in agreement with corresponding literature values. The exchange enthalpy X 12 and entropy, Q 12 , parameters were determined at the same temperature. The X 12 parameters increase with the carbon number of the n-alkanes, while their temperature dependence is almost negligible. The Q 12 parameters are approximately independent of temperature and carbon number of the n-alkanes.

Determination of the exchange enthalpy and entropy parameters of the equation-of-state theory for poly(dimethyl siloxane) in various solvents

Abstract The interaction parameter χt∝ and the effective exchange energy parameter X 12 at infinite dilution of cyclohexane, benzene and chlorobenzene with poly(dimethyl siloxane) were determined around room temperature, according to relations given in the Flory formulation of the equation-of-state theory using the inverse gas chromatography technique. Then, the exchange enthalpy X12 and entropy Q12 parameters were determined by using a relation for the enthalpy interaction parameter χh of the equation-of-state theory, which is arranged for the inverse gas chromatography conditions. The values of the above-mentioned parameters are comparable with the values obtained earlier with other methods. The X12 and Q12 parameters of cyclohexane increase slightly with temperature, while those of benzene and chlorobenzene are almost independent of temperature.

Studies on miscibility in homopolymer/ random copolymer blends by equation of state theory

The miscibility of poly(methyl methacrylate) (PMMA) and styrene-acrylonitrile random copolymers (SAN) blends was investigated on the basis of the Flory—Orwoll—Vrij equation of state theory. To obtain the equation of state parameters ( P∗, V∗ sp , T∗: characteristic parameters ), the pressure—volume—temperature ( PVT) behaviour was measured for PMMA and a series of SANs with various acrylonitrile contents. The exchange energy parameter X ij was also calculated by fitting the theory to some phase diagrams of PMMA/SAN blends. The Flory—Huggins interaction parameter χ was separated into two contributions based on the equation of state theory for mixtures: the exchange energy term χ inter and the free volume term χ free. Both the temperature and copolymer composition dependences of χ inter and χ free were estimated by calculations using the equation of state parameters. There exists a region in which χ inter is negative, leading to a miscibility window in PMMA/SAN blends. However, the immiscibility at high temperatures in the blends cannot be explained only by χ inter; it is caused by the free volume contribution, χ free. The miscibility window behaviour in PMMA/SAN blends may be explained within the framework of the equation of state theory.

Determination of equation of state parameters of poly(dimethylsiloxane)-benzene system by intrinsic viscosity

The equation of state exchange energy ( X 12) and entropy ( Q 12) parameters and the ratio of contact sites ( S 2/ S 1) of the poly(dimethylsiloxane)-benzene system were determined using equation of state theory and intrinsic viscosity measurements. The values of X 12 and Q 12 parameters for S 2/ S 1=0.67 are found to be 16.64 J cm −3 and −0.0394 J cm −3 K −1, respectively.

Estimation of thermodynamic parameters for poly(ethyl methacrylate)/isopropyl alcohol system from intrinsic viscosity measurements

Intrinsic viscosities of poly(ethyl methacrylate) (PEMA) solutions in isopropyl alcohol (IPA) above and below the theta (θ) temperature (36.9°C) have been measured by using a capillary viscometer. The equation-of-state exchange energy ( X 12) and entroy ( Q 12) parameters were estimated as 62.82 J cm −3 and 0.03 J cm −3 K −1, respectively. The unperturbed dimension constant ( K θ ) and characteristic ratio ( C ∞) were determined as 5.91 × 10 −4 dl mol 1 2 g −3 2 and 9.3 using the intrinsic viscosity data obtained at the θ temperature for PEMA in IPA. The polymer-solvent interaction parameters ( x 1, x 2) were calculated from equation-of-state theory as a function of temperature. The value of the ratio of contact sites ( s 2 s 1 ) is found to be 0.73 for this PEMA-IPA pair.

Estimation of the equation of state exchange energy and entropy parameters of a polymer‐solvent pair by intrinsic viscosity measurements

AbstractThe intrinsic viscosity data of linear poly(4‐chlorostyrene) in n‐propylbenzene and isopropylbenzene were used to estimate the equation of state exchange energy (X12) and entropy (Q12) parameters. The quantities estimated for X12 were 6.7 and 8.1 J cm−3 and those of Q12 were −0.069 and −0.063 J cm−3 deg−1 in n‐propylbenzene and isopropylbenzene, respectively. The average values of the chain unperturbed dimension constant (Ko) and the characteristic ratio (Cx) were found to be 0.55 × 10−3 dl mol1/2g−3/2 and 10.54, respectively, from the intrinsic viscosities measured at the corresponding θ‐temperatures.

Upper and lower critical solution temperatures for polystyrene in methyl cyclopentane and in dimethyl cyclohexane

Abstract The demixing of polystyrene in methyl cyclopentane, and in dimethyl cyclohexane has been investigated, and the upper and lower critical solution temperatures established for several polymer molecular weights. In the former solvent both upper and lower θ temperatures can be defined, but not in the latter where cloud point curves for the upper and lower critical temperatures coalesce for high molecular weights. The Patterson theory of polymer solutions has been applied to the data, and the characteristic free volume and exchange energy parameters have been evaluated. The lower critical solution temperatures are nearly the same in cyclopentane and methyl cyclopentane due to a compensation between the free volume and contact interaction terms. Solvent size effects are considered in order to explain the differences in the interaction of solvent with polymer.

Exchange energy, magnetization, and Raman scattering of (Cd,Mn)Se

The exchange-energy parameter $\ensuremath{\alpha}{N}_{0}$ for conduction-band electrons in ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Se}$ was determined at $T=1.9$ K for $0.05\ensuremath{\le}x\ensuremath{\le}0.2$. For this range of $x$, $\ensuremath{\alpha}{N}_{0}$ is independent of $x$ and has the value (258\ifmmode\pm\else\textpm\fi{}5) meV. These results were obtained by comparing Raman scattering data for the spin splitting of donor electrons with magnetization data on the same crystals. The Raman data were obtained for $0.01\ensuremath{\le}x\ensuremath{\le}0.2$, and the magnetization data were taken for $0.05\ensuremath{\le}x\ensuremath{\le}0.3$. The magnetization was measured at temperatures $T$ between 1.5 and 4.2 K in magnetic fields $H$ up to 83 kOe. These data were fit to a parametrized Brillouin function. One of the fitting parameters gave an effective concentration ${\overline{x}}_{s}$ of magnetically active ${\mathrm{Mn}}^{2+}$ ions. The second fitting parameter ${T}_{0}$ was a measure of the average antiferromagnetic interaction between the Mn spins. The low-field magnetic susceptibility ${\ensuremath{\chi}}_{0}$ was fit to a Curie-Weiss law, which yielded the analogous parameters ${\overline{x}}_{C}$ and ${T}_{\mathrm{AF}}$ for low fields. As $x$ increased from 0.05 to 0.3, the fraction of magnetically active ions, $\frac{{\overline{x}}_{s}}{x}$, decreased from 0.6 to 0.1, and ${T}_{0}$ increased from 1.5 to 7 K. These trends are caused by the increase in the average antiferromagnetic interaction between the Mn spins as the average distance between them decreases with increasing $x$. Results of spin-flip Raman scattering from donor-bound electrons show that the Zeeman splitting $\ensuremath{\Delta}E$ of the donor's energy is large ($\ensuremath{\Delta}E\ensuremath{\gtrsim}10$ meV) for fields above 40 kOe. The splitting $\ensuremath{\Delta}E$ is approximately proportional to the magnetization, except at low $H$ where there is an additional contribution due to the difference between the local magnetization within the donor's orbit and the average bulk magnetization. This effect decreases for both increasing $H$ and decreasing $x$.

Vapor‐pressure osmometry and inverse gas chromatography in the analysis of thermodynamic properties of polymer solutions

AbstractThe primary objective of this work is to check the utility of vapor‐pressure osmometry as an experimental technique in obtaining thermodynamic data on polymer/solvent systems. The second objective is to obtain experimental values for the exchange energy parameters ΔP, X, and ζ of the theory of Sanchez and Lacombe. With respect to the first objective, solvent activities of polyiso‐butylene/benzene mixtures have been measured at several concentrations up to 600 g/kg of the solvent and at two temperatures. From the activities, it is possible to determine free energies, entropies, and enthalpies and their concentration dependence. Satisfactory agreement has been found between the results obtained and data provided by other techniques such as membrane osmometry and the Cahn electrobalance. These and other data obtained by inverse gas chromatography for the same mixture in the range 35–200°C have been used in calculating the exchange energy parameter of the lattice fluid theory at different concentrations and temperatures.

Thermal properties of paramagnetic solid helium-3

It was shown in recent work that over a limited molar volume range and at asymptotically high temperatures the thermal modulations of the pressure along isochores of paramagnetic solid3He could be accounted for through the formalism of the Heisenberg model of an antiferromagnetically interacting localized spin-1/2 system. The internal consistency of this formalism requires the characteristic exchange-interaction parameter of the model derived from pressure modulation data to be identical with that appearing in the other thermal properties of this quantum solid. In a restricted temperature region where the spin excitations are the dominant thermal excitations of the solid, heat capacity data yield exchange-interaction parameters in fair agreement with those derived from pressures along isochores of larger molar volume. At higher temperatures, within well-defined limitations, thermal excitations involve both spin and phonon excitations. Here, because of the opposite temperature variations of the spin and phonon heat capacity components, the ensuing heat capacity minimum determines exactly the exchange-energy parameter and the relevant limiting Debye temperature as a function of the measured temperature location and value of the heat capacity extremum along the experimentally explored isochore. The exchange-energy parameters so derived display larger deviations from their predicted pressure-based values than those resulting from the lower temperature but still asymptotic spin-only heat capacities. At the present time, ambiguities in the experimental determinations of the characteristic Weiss temperatures of the asymptotic paramagnetic susceptibilities prevent one from deriving exchange-energy parameters with them. The present work leads to the prediction, within the limitations of the model formalism, of thermal properties of magnetized solid3He. Experimental investigations of these properties offer new approaches for probing the validity of the model formalism applied to paramagnetic solid3He.

Model formalism of paramagnetic solid helium-3

The statistical-thermodynamic formalism of a collection of localized spin-1/2 atoms whose spin Hamiltonian refers to the isotropic antiferromagnetic Heisenberg exchange-interaction scheme is applied here to account for a set of important equilibrium-thermodynamic measurements on paramagnetic solid3He performed some time ago by University of Florida investigators. The measured properties were the temperature-dependent modulations of the pressure, which were proved earlier to arise overwhelmingly from the nuclear spin system. The present formalism of the pressure modulations or of the spin pressures, along specified isochores of the solid, includes the density- or molar-volume-dependent microscopic exchange energy parameter and its derivative. In this paper we have derived directly hitherto unavailable exact values of these parameters from spin pressure data on magnetized solid3He, as well as indirectly through the intermediary of spin pressures in the absence of a magnetic field. The directly derived exact parameters result from a single characteristic equilibrium-thermodynamic state of the solid in the presence of a constant and uniform magnetic field of adequate strength. The indirectly derived but exact parameters, of possibly somewhat lower accuracy, require the knowledge of a single directly derived exchange-energy parameter together with a set of spin pressures of asymptotic high-temperature equilibrium states in the absence of a magnetic field. The indirectly derived microscopic parameters along two of the three experimentally explored magnetized solid isochores yielded calculated spin pressures in fair and acceptable agreement, respectively, with their measured values. The directly derived exact parameters used in calculating the spin pressures along the third experimentally investigated isochore, in the absence of a magnetic field and at three different field strengths, led to complete agreement with the data. These results lend support to the tentative proposition advanced in early work that over a range of temperatures and molar volumes of paramagnetic solid3He, the statistical-thermodynamic formalism based on the antiferromagnetic exchange-interaction scheme may give an acceptable account of the spin pressures as well as of other thermal properties of this quantum solid.

Volatility of solvents from polysulfone melt

The equilibrium volatilities and solvent–polymer interaction indices are measured for 23 solvents in molten polysulfone. On the basis of the results, the solvents are ranked in the order of their effectiveness: phenol, pyridine, N-methylpyrrolidone, dimethylacetamide, methylene chloride, cyclohexanone, chlorobenzene, dimethylformamide, fluorobenzene, diglyme, toluene, xylene, chloroform, sulfolane, methyl ethyl ketone, acetonitrile, methanol, ethanol, carbon tetrachloride, dimethyl sulfoxide, decane, octane, and heptane. In determining the solvency power, the basic interpretative concept is that a large value of the Flory-Huggins interaction parameter indicates an unfavorable interaction, a low positive value indicates slightly favorable interaction, and a negative value indicates a rather strong specific interaction. Two other interaction indices, namely, the exchange energy parameter of Flory, X12, and χ*, the Flory-Huggins interaction parameter based on an hypothetical characteristic state, do not yield the same order as listed above. The data presented permits calculation of Henry's law constant and equilibrium volatilities at the temperature range of 250–300°C, a processing range for polysulfone.