Exchange Energy Parameter Research Articles

Determination of thermodynamic properties and phase transition temperatures of phenylbenzoate-based calamitic liquid crystals by inverse gas chromatography method

ABSTRACT In this study, Phenylbenzoate-based calamitic liquid crystals (LCs) were synthesized and characterized, and then the thermodynamic properties and phase transition temperatures were investigated by inverse gas chromatography (IGC) at infinite dilution. The phase transition temperatures of the LCs were determined in the range of 40–170°C by the IGC method. Finally, in the thermodynamic equilibrium region (the range of 160–200°C), Flory-Huggins theory and the equation of state theory with the LC-solvent interaction parameters, the effective exchange energy parameters, the weight fraction activity coefficient, and also the partial molar heat of mixing at infinite dilution of solvent, the molar heat of vaporization of solvent, and the partial molar heat of sorption of solvent were calculated.

Investigation of thermodynamic properties of Amine Modified Polystyrene and its use for separation of isomers

In this study, thermodynamic properties, glass transition temperature and isomer separation ability of PVBC (poly (vinyl benzyl chloride)) -Diethanol amine (PVBC-DEA) polymer was investigated by IGC method. For purpose, the retention diagrams were drawn using interactions between PVBC-DEA with selected isomer solvents (i-butyl acetate, n-butyl acetate and t-butyl acetate) at between 85 and 110°C. The glass transition temperature value of the polymer was determined from the retention diagrams as 76°C and the obtained value, it has been understood that this value is compatible with 75.2°C found by differential scanning calorimetry. The selectivity coefficients, ∝, of the isomer solvents were determined for the PVBC-DEA in the infinite dilution, according to the results obtained, it was revealed that the polymer can separate the isomers. The polymer-solvent interaction parameters for Flory-Huggins theory, χ12∞, and the equation of state theory, χ12*,the effective exchange energy parameters, χeff, the weight fraction activity coefficient, Ω1∞, and also the partial molar heat of mixing at infinite dilution of solvent, ΔH¯1∞, the molar heat of vaporization of solvent, ΔH¯v, and the partial molar heat of sorption of solvent, ΔH¯s, were calculated between 85 and 110°C. The obtained results were discussed.

Thermodynamic Characterization of Sodium Alginate by Inverse Gas Chromatography

This work addresses the surface properties and solubility parameters of sodium alginate (SA) using the inverse gas chromatography (IGC) technique. The dispersive component of the surface free energy,γSD, of the studied adsorbent surface was calculated in the infinite dilution region. The specific enthalpy of adsorption,ΔHS, the specific free energy of adsorption, ΔGS, and the specific entropy of adsorption, ΔSS, of solvents on SA were determined. The acidic KA and the basic KD parameters of the SA surface were calculated. The values obtained for KA and KD parameters indicated that the SA surface has a basic character. The interactions between 16 solvents and SA were investigated at a temperature range (373.2–398.2 K). The weight fraction activity coefficient,Ω1∞, Flory–Huggins interaction parameter, χ12∞, equation-of-state interaction parameter, χ12*, and effective exchange energy parameter, Xeff, of the SA–solvent system were estimated. The results indicated that all the studied solvents are poor solvents for SA. This means that it can be used in the packaging food and biomedical field. The solubility parameter of SA, δ2, was determined as 17.5 (cal/cm3)1/2.

Investigation of thermodynamic properties of 4-decyloxybiphenyl-4′-carboxylic acid liquid crystal and preparation of polymer dispersed liquid crystal composite

In this study, firstly, retention behavior of solvents on the liquid crystalline material 4-decyloxybiphenyl-4′-carboxylic acid (DBCA) has been studied by inverse gas chromatography (IGC) technique. Liquid crystal (LC) selectivity was investigated using the acetate isomers by the IGC method at temperatures between 333.2 K and 543.2 K. Later on, the interactions of LC with n-octane, n-nonane, n-decane, undecane, dodecane, tridecane, n-propyl benzene, isopropyl benzene, ethylbenzene, chlorobenzene and toluene between 518.2 K and 543.2 K were examined. LC-solvent interaction parameters for Flory-Huggins theory, χ12∞, and equation of state theory, χ12∗, effective exchange energy parameters, Xeff, the weight fraction activity coefficent, Ω1∞, the partial molar heat of mixing at infinite dilution of the solvent, ∆H1∞, molar heat of vaporization of solvent, ∆HV and the partial molar heat of sorption of the solvent, ∆H1, s were obtained.Secondly, polymer dispersed liquid crystal (PDLC) composite film in composition 20/80 poly(methyl methacrylate) (PMMA):DBCA by weight was synthesized by solvent-induced phase separation method. The mesomorphic behavior of DBCA and PDLC composite has been investigated by differential scanning calorimetry (DSC) and optical polarizing microscopy (PM).

Surface Characteristics and Physicochemical Properties of Polystyrene-b-Poly(Acrylic Acid) Determined by Inverse Gas Chromatography

Surface and bulk properties of polystyrene-b-poly(acrylic acid) (PS-b-PAA) were determined by inverse gas chromatography (IGC) technique. The determined surface properties were dispersive component of surface energy, \( \gamma_{\text{S}}^{\text{D}} \), Lewis acid and base constants, \( K_{\text{A}} \) and \( K_{\text{D}} \), respectively. The dispersive component of surface energy ranged from 39.9 to 20.9 mJ m−2 at a temperature range from 303 to 343 K while \( K_{\text{A}} \) and \( K_{\text{D}} \) were found to be 0.083, and 0.781, respectively, at this temperature range. The higher \( K_{\text{D}} \) than \( K_{\text{A}} \) suggested the surface of the copolymer was basic. The bulk polymer interaction parameters such as weight fraction activity coefficient, \( \varOmega_{1}^{\infty } \), Flory–Huggins interaction parameter, \( \chi_{12}^{\infty } \), equation-of-state interaction parameter, \( \chi_{12}^{ * } \), and effective exchange energy parameter, \( X_{\text{eff}} \) of PS-b-PAA were determined using the retention data of several solvents at temperatures between 413 and 453 K.

Group estimation method for parameters of Flory–Orwoll–Vrij equation and free volume effects in polymer–solvent interaction parameters

The Flory–Orwoll–Vrij (FOV) equation is commonly used to analyze the interaction parameters of vapors in polymer melts. The theory considers the free volume effects and requires several pure component parameters, which can be determined from the pressure–volume–temperature (PVT) data of liquids. For polymers the specific volume can be predicted using three characteristic parameters over a temperature and pressure range. For low molecular weight liquids, molar core volume, V*, external degree of freedom, C, and interaction energy parameter, ET, which was introduced in this study, showed linear relationships with the carbon number for several series of homologues. A group calculation method to estimate characteristic parameters was proposed in this study. The free volume effect depended on the reduced volumes of solutes and polymers. It increased when the system temperature increased. Inverse gas chromatography (IGC) data of Flory–Huggins parameters, χ, of several polar solvents in poly(vinyl chloride) and poly(tetramethylene glycol) were positive, but the exchange energy parameters, X12, were negative and consistent with the molecular interaction consideration.

Investigation of thermodynamic and surface characterisation of 4-[4-(2-ethylhexyloxy)benzoyloxy]benzoic acid thermotropic liquid crystal by inverse gas chromatography

The inverse gas chromatography method was used to obtain thermodynamic and surface properties of the thermotropic liquid crystalline material, 4-[4-(2-ethylhexyloxy)benzoyloxy]benzoic acid (EBBA). The retention diagrams of undecane, dodecane, tridecane, ethyl acetate, n-butyl acetate, iso-butyl acetate, toluene, ethylbenzene, iso-propylbenzene, n-propylbenzene and chlorobenzene on EBBA were plotted at temperatures between 443.2 and 468.2 K. The specific retention volume, , Flory–Huggins interaction parameter, , equation-of-state interaction parameter, , and effective exchange energy parameter, , were determined. The dispersive component of the surface free energy, , of the studied adsorbent surface was estimated using retention times of different nonpolar organic solvents in the infinite dilution region. The specific free energy of adsorption, the enthalpy of adsorption, , and the entropy of adsorption, , of solvents on liquid crystal were determined. The values of were correlated with the donor and the acceptor numbers of the probes to quantify the acidic and the basic parameters of the liquid crystal surface. The values obtained for and parameters indicated an acidic character for the surface of EBBA.

A lattice model for thermally-sensitive core–shell hydrogels

A lattice molecular thermodynamic model for describing the swelling behavior of thermally-sensitive core–shell hydrogels was developed by integrating a close-packed lattice model for mixing free energy and a Flory Gaussian chain model for the elastic free energy. The thermodynamic model is characterized with two parameters: the temperature-dependent exchange energy parameter ε and the Topology-dependent size parameter V*. The input values of both parameters can be obtained by experimental results of pure polymer hydrogels. With the help of proposed model, swelling behaviors of two kinds of hydrogel systems were analyzed: one is a doubly thermally-sensitive core–shell hydrogels (with two LCSTs) and the other comprises a thermally-sensitive hydrogel shell with a hard internal core. We show that the calculated results are in good agreement with the experimental data.

Phase behaviour and miscibility window in UCST-type blends of poly(styrene-co-acrylonitrile) and tetramethylbisphenol A oligosulfones

Abstract The pressure–volume–temperature (PVT) behaviour of styrene–acrylonitrile (SAN) random copolymers and of tetramethylbisphenol A oligosulfones (TMOS) was studied using the Flory–Orwoll–Vrij (FOV) as well as the Sako–Wu–Prausnitz (SWP) equation-of-state (EOS). It was found that the SWP EOS is superior to the FOV theory in describing the PVT behaviour of the polymers, especially in the high-pressure range. Furthermore, blends comprising TMOS and SAN copolymers of varying acrylonitrile content were studied by means of cloud point measurements and differential scanning calorimetry. The system shows pronounced miscibility-window behaviour, i.e. the miscibility depends strongly on the copolymer composition. At the edges of the miscibility window, UCST (upper critical solution temperature) behaviour was observed and discussed in terms of the FOV EOS. The cloud point curves were exceptionally broad and could be reproduced neither by the Flory–Huggins nor by the FOV theory. However, taking the polydispersity of both components into account, the calculation of correct phase diagrams was possible using the FOV theory. Exchange energy parameters between the polymers, XAB, were obtained from fitting the critical points of the phase diagrams. Additionally, segmental exchange energy parameters Xi/j of the components were calculated.

Magnetisation reversal in cylindrical nickel nanobars involving magnetic vortex structure: A micromagnetic study

A three-dimensional, Fast-Fourier-Transformed (3D-FFT) micromagnetic simulation was employed to study the magnetization reversal mechanisms in cylindrical nickel nanobars possessing magnetic vortices. Individual Ni nanobars of height 150–250 nm with aspect ratio varying from 2.1 to 2.5 were considered, all of them supporting magnetic vortices domains. Magnetization reversal in these nanobars involves the vortex-creation–annihilation (VCA) mechanism with an inversion symmetry feature observed mid-way during reversal process. The effect of incidence angle of externally applied field on overall magnetization reversal process is examined in detail. The corresponding variations in coercivity, squareness, exchange energy and vortex parameters are described by the micromagnetic study that can shed insights for building practical Ni nanobars magnetic nanostructures/devices.

Dynamical coherent-potential approximation approach to excitation spectra in3dtransition metals

First-principles dynamical CPA (Coherent-Potential Approximation) for electron correlations has been developed further by taking into account higher-order dynamical corrections with use of the asymptotic approximation. The theory is applied to the investigations of a systematic change of excitation spectra in $3d$ transition metals from Sc to Cu at finite temperatures. It is shown that the dynamical effects damp main peaks in the densities of states (DOS) obtained by the local density approximation to the density functional theory, reduce the band broadening due to thermal spin fluctuations, create the Mott-Hubbard type bands in the case of fcc Mn and fcc Fe, and create a small hump corresponding to the `6 eV' satellite in the case of Co, Ni, and Cu. Calculated DOS explain the X-ray photoelectron spectroscopy data as well as the bremsstrahlung isochromat spectroscopy data. Moreover, it is found that screening effects on the exchange energy parameters are significant for understanding the spectra in magnetic transition metals.

Existence conditions for single-vertex structure of polarization in ferroelectric nanoparticles

The distribution of polarization in low-dimensional ferroelectric nanostructures appears to form vertex structures under open-circuit boundary conditions. A thermodynamics-based continuum phase field approach is employed to investigate the conditions for existence of single-vertex structure in two-dimensional (2D) square-shaped nanodots. It has been observed that, for a given material, such structure exists only in a certain range in dimension, which is associated to an exchange energy parameter in the model. It has been further noticed that, instead of a double-vertex structure, a single-vertex distribution remains in a 2D rectangular-shaped nanodot with initial conditions of polarization in favor of single-toroid shape.

Determination of crystallinity ratio and some physicochemical properties of poly(4‐methyl‐1‐pentene)

AbstractIt was determined that the thermal stability of poly(4‐methyl‐1‐pentene) (P4MP) was maintained up to 424°C in an inert atmosphere by thermogravimetric analysis. The retention diagrams of ethyl acetate, tert‐butyl acetate, and benzene on P4MP were plotted at temperatures between 30 and 280°C by inverse gas chromatography (IGC) technique. Melting temperature of the polymer was determined as 230 and 239.5°C by IGC and differential scanning calorimetry (DSC), respectively. The percent crystallinity of P4MP was obtained from the retention diagrams at temperatures below melting point. The percent crystallinity obtained by IGC is in good agreement with the ones obtained by DSC. Then, specific retention volume, V, weight fraction activity coefficient, Ω, Flory‐Huggins polymer‐solvent interaction parameter, χ, equation‐of‐state polymer‐solvent interaction parameter, χ, and effective exchange energy parameter, Xeff of octane, nonane, decane, undecane, dodecane, tridecane, n‐butyl acetate, isobutyl acetate, isoamyl acetate with P4MP, were determined between 240 and 280°C by IGC. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Micromagnetics of magnetisation reversal mechanism in Permalloy chain-of-sphere structure with magnetic vortices

Magnetisation reversal mechanism in a chain of closely spaced Permalloy nanospheres is presented using 3D micromagnetic simulation. While smaller spheres (d ∼ 20 nm) containing single domain reverses via domain switching mechanism, the larger sphere (d ∼ 50 nm) possessing magnetic vortices changes the orientation through vortex creation and annihilation (VCA) mechanism. The effect of total number of spheres (comprising the chain structure) and incidence angle of externally applied field on the VCA mechanism is explained in detail. The variation in coercivity, remanence, exchange energy and vortex parameters are discussed for the Permalloy chain-of-sphere system with uniform sphere size.

Determination of transition points and thermodynamic interaction parameters of poly(2,6-dimethyl-1,4-phenylene oxide)

The specific retention volumes Vg0 of n-butyl acetate, isobutyl acetate, isoamyl acetate, n-undecane, n-dodecane, n-tridecane, ethyl benzene, n-propyl benzene, isopropyl benzene and chloro benzene on poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) were obtained by inverse gas chromatography. Below glass transition temperature, two secondary transition points of PPO which occur at 90 and 130°C were observed from the retention diagrams of n-butyl acetate, isobutyl acetate and isoamyl acetate.Weight fraction activity coefficient at infinite dilution Ω1∞, Flory–Huggins polymer–solvent interaction parameter χ12∞, hard core polymer–solvent interaction parameter χ12* and effective exchange energy parameter Xeff were determined from the experimental Vg0 of studied solvents on PPO at temperatures above 220°C by inverse gas chromatography.

Detection of microphase separation in poly( tert-butyl acrylate- b-methyl methacrylate) synthesized via atom transfer radical polymerization by inverse gas chromatography

A trace amount of solvents such as n-octane, n-nonane, n-decane, ethyl acetate, n-propyl acetate, isoamyl acetate, toluene, ethyl benzene, n-propyl benzene, isopropyl benzene and chloro benzene was passed through the column of a gas chromatograph of which the stationary phase is poly( tert-butyl acrylate- b-methyl methacrylate), poly( tBA- b-MMA), block copolymer with low polydispersity, prepared via ATRP of tBA and MMA, respectively. The retention diagrams to determine the thermal transition of the polymer were obtained by plotting the logarithm of the specific retention volumes of isoamyl acetate and toluene against reciprocal values of absolute column temperatures between 40 and 170 °C by inverse gas chromatography (IGC) technique. Three glass transition temperatures, T gs of poly( tBA- b-MMA) were determined at 50, 70 and 105 °C by IGC indicating the phase separation of the polymeric blocks in the copolymer. The thermodynamical interaction parameters such as weight fraction activity coefficient of solvent at infinite dilution, Ω 1 ∞ , Flory–Huggins polymer–solvent interaction parameter, χ 12 ∞ , equation-of-state polymer solvent interaction parameter, χ 12 ∗ , effective exchange energy parameter, X eff, and solubility parameter of the copolymer, δ 2 were calculated at studied temperatures. The closeness of parameters of the poly( tBA- b-MMA) to those of the PMMA indicated that the continuous phase is MMA block in the microphase separated block copolymer. It seems that IGC is a reliable technique to study a phase separated block copolymer which contains nanosized domains.

A study of some equation‐of‐state parameters of poly(methylhydrosiloxane‐co‐dimethylsiloxane) with some solvents by gas chromatography

AbstractTrace amount of methyl acetate, ethyl acetate, tert‐butyl acetate, pentane, hexane, and heptane were passed through the chromatographic column loaded with poly(methylhydrosiloxane‐co‐dimethylsiloxane) coated on Chromosorb W. The retention diagrams of the solvents on the copolymer were plotted by means of specific retention volumes at temperatures between 40 and 80°C by inverse gas chromatography technique. In this study, some thermodynamic interaction parameters such as Flory–Huggins polymer–solvent interaction parameter, equation‐of‐state polymer–solvent interaction parameter, effective exchange energy parameter, and weight fraction activity coefficients at infinite dilution of the solvent were determined. Then, the exchange enthalpy parameter and entropy parameter were determined by using a relation for the enthalpy interaction parameter of the equation‐of‐state theory, which is arranged for the inverse gas chromatography conditions. Later, the partial molar heat of sorption and the partial molar heat of mixing were obtained. The solubility parameter of this copolymer was determined as 6.64 (cal/cm3)1/2 at room temperature. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1627–1631, 2007

Studies on Equation-of-State Parameters and Linear Polymer Dimensions of Poly(p-chlorostyrene) in Diethylene Glycol Monobutyl Ether by Intrinsic Viscosity Measurements

Intrinsic viscosities, [η], of poly(p-chlorostyrene) (PPCS) in diethylene glycol monobutyl ether (DGMBE) which exhibits an exothermic solubility behavior with the polymer were measured using an Ubbelohde type capillary viscometer between 25 and 85°C. Polymer solvent interaction parameters at infinite dilution (χ1), exchange energy parameter \((\bar{X}_{12})\), exchange enthalpy (X12), and entropy parameters (Q12), of the PPCS/DGMBE pair were found at studied temperature range according to equation-of-state theory.

Thermodynamic interactions of a copolyester of bisphenol A with terephthalic acid and isophthalic acid with some solvents

AbstractThe retention diagrams of n‐octane, n‐nonane, n‐decane, n‐butyl acetate, isobutyl acetate, and isoamyl acetate on the polyarylate Ardel D‐100, a copolyester of bisphenol A with terephthalic acid and isophthalic acid, were plotted at temperatures between 120 and 260°C by an inverse gas chromatography technique. The glass‐transition temperature of the copolymer was determined to be 190°C from the discontinuity of these diagrams. The retention diagrams of benzene, ethyl benzene, n‐propyl benzene, isopropyl benzene, and chlorobenzene were also plotted between 200 and 260°C. The specific retention volume, weight fraction activity coefficient, Flory–Huggins polymer–solvent interaction parameter, hard‐core polymer–solvent interaction parameter, and effective exchange energy parameter were determined for the studied solvents. The parameters suggest that the studied aromatic hydrocarbons and aliphatic esters are moderately good solvents and chlorobenzene is a very good solvent for this copolyester, but the n‐alkanes are very poor solvents. The solubility parameter of this copolymer was determined to be 11.6 (cal/cm3)1/2 at room temperature by extrapolation of the values of the solubility parameters from the studied temperatures to 25°C. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 2365–2368, 2005

Determination of secondary transitions and thermodynamic interaction parameters of poly (ether imide) by inverse gas chromatography

The retention diagrams of poly(ether imide) for ethyl benzene, n-propyl benzene, isopropyl benzene, chloro benzene, n-butyl acetate, tert-butyl acetate, isoamyl acetate, n-nonane, n-decane, n-undecane, n-dodecane and n-tridecane were obtained by inverse gas chromatography technique. In this work, the slope changes on the diagram were assigned as secondary transitions. The secondary transition temperatures obtained by inverse gas chromatography technique are in good agreement with the ones obtained by thermally stimulated depolarization current in the literature. Specific retention volume, V g 0, the weight fraction activity coefficients of the solvents at infinite solution, Ω1∞, Flory-Huggins polymer-solvent interaction parameters,χ12∞, equation-of-state polymer-solvent interaction parameters,χ12*, effective exchange energy parameters, X eff were determined. Later, the partial molar heat of sorption, $\Delta\bar{H}_{1,sorp}$ and the partial molar heat of mixing, $\Delta\bar{H}_1^{\infty}$ were obtained. The solubility parameter of poly(ether imide), δ2 was determined as 10.7 (cal/cm3)1/2 by extrapolation of the δ2 values obtained by considering the free volume effects from studied temperature range to room temperature.