Prediction of maxima and minima in the curve of total sorption parameter in ternary polymer systems. Influence of ternary interaction parameter

Flory-Huggins theory modified by Pouchly has been applied to predict maxima and minima in the curve of total sorption in ternary polymer systems formed by a polymer and two liquids. In this work, different diagrams based on experimental magnitudes easily obtained such as the difference in affinities of liquids, solvents and non solvents, and the solvent molar volume ratio. Total sorption parameter has been considered to be the decisive magnitude to define extrema conditions in both cosolvent and cononsolvent ternary polymer systems. The theoretical prediction is not altered by the inclusion of ternary interactions. Different examples of ternary systems dealing with vinyl polymers and polydimethyl siloxane have been used to test the above formalism.     

A thermodynamic approach to study hydrogen-bonding interactions in solvent/solvent/polymer ternary systems

A thermodynamic approach based on both the classical Flory-Huggins (FH) formalism and the association equilibria (AE) theory has been developed to study the solubility properties of a system formed by a proton-donor solvent (A), a proton-acceptor solvent (B) and a proton-acceptor polymer (C). The miscibility of this ternary system is attained by competitive specific interactions via hydrogen-bonding established between the hydroxyl and carbonyl interacting groups of either solvent-solvent (AB) or solvent-polymer (AC) system components. The binary AB and AC specific interactions and their dependence with the system composition as well as with the extent of the association equilibrium have been quantified by means of two new parameters, Δg_AB and Δg_AC. These excess functions have appeared to be equivalent to the combinatorial or entropic term of the Gibbs free energy of the complex formation process, which accounts for the entropy of mixing plus the intermolecular specific interactions. The theoretical predictions have reasonablely agreed with experimental data on preferential solvation of two systems taken from literature: methanol(A)/1,4-dioxane(B)/poly(alkyl methacrylate)(C) and n-alcohol(A)/heptan-3-one(B)/poly(vinyl pyrrolidone)(C).     

A Flory–Huggins thermodynamic approach for predicting sorption equilibrium in ternary polymer systems

The Flory–Huggins theory as modified by Pouchlý has been applied to calculate preferential (λ) and total (Y) sorption coefficients for a ternary polymer system. The ternary interaction function (?₁?₂?₃G_T(u₁, ?₃)) is described as the product of three independent binary functions. This expression allows prediction of λ and Y from binary interaction parameters χ, χ, g, g, and g₁₂(?₁₀). Three ternary polymer systems are used to check the validity of the expression. Moreover for polymer systems in which the parameters g and/or g are unknown, a procedure to evaluate them has been developed and verified on systems for which sufficient experimental information is available.     

Correlation of thermodynamic modeling and molecular simulations for liquid-liquid equilibrium of ternary polymer mixtures based on a phenomenological scaling method

In our previous study [S.Y. Oh, Y.C. Bae, J. Phys. Chem. B 114 (2010) 8948-8953], we presented a new method to predict liquid-liquid equilibria in ternary simple liquid mixtures by using a combination of a thermodynamic model and molecular simulations. As a continuation of that effort, we extend our previously developed method to ternary polymer systems. In the simulations, we used the dummy atoms to calculate the pair interaction energy values between the polymer segments and the solvent molecules. Furthermore, a thermodynamic model scaling concept is introduced to consider the chain length dependence of the energy parameters. This method was applied to ternary mixtures incorporating low to high molecular weight polymers. The method presented here well described the experimental observations using one or no adjustable parameters.     

Multifractal analysis. A new method for the characterization of the morphology of multicomponent polymer systems

It has been demonstrated that use of polymeric emulsifiers under usual processing conditions in the melt state is a powerful technique for preparing polymer alloys. Digitized representation of optical micrographs of thin sections of blends of a low-density polyethylene and polystyrene (20 wt % PE-80 wt % PS) containing 2 and 5 wt % of two hydrogenated polybutadiene-polystyrene block copolymers exhibit different degrees of homogeneity as well as different morphological structures which can be studied by a multifractal analysis. We show how these differences are reflected in the f(α) spectrum of singularities which can be obtained by a box counting method in the canonical approximation. We have found a correlation between the f(α) curves and the mechanical properties of the corresponding samples: the samples which area the less multifractals have the best mechanical properties. © 1993 John Wiley & Sons, Inc.     

Swelling equilibrium and preferential sorption of crosslinked poly(methyl methacrylate) in the mixture acetonitrile + n-butanol

Measurements of preferential sorption,( ₃), determined by refractometry, and swelling equilibrium, ₃ ^–1, of PMMA networks have been carried out in the cosolvent mixture MeCN+BuOH at 25 and 49 C. With an intermediate mixture composition, ₃ ^–1 passes through a maximum at both temperatures. At 25 C MeCN is preferentially adsorbed by the network over most of the composition range, but a small inversion is detected. At 49 C MeCN is preferentially adsorbed over all the composition range.The behavior of the system crosslinked PMMA/MeCN + BuOH is compared with the results obtained for solutions of linear PMMA in mixtures formed by the same two solvents, MeCN and BuOH.     

Comparative thermodynamic analysis of the Pb-Au0.7Sn0.3 section in the Pb-Au-Sn ternary system

The results of comparative thermodynamic analysis of Pb-Au_0.7Sn_0.3 section in Pb-Au-Sn system are presented in this paper. Investigation was done comparatively by calorimetric measurements and thermodynamic calculation according to the general solution model. Thermodynamic parameters, such as partial and integral molar quantities, were determined at different temperatures. The comparison between experimental and calculated results showed mutual agreement. Demixing tendency of lead, presented in the positive deviation from ideal behavior, was confirmed through the study of concentration fluctuation in the long-wavelength limit. Also, chosen alloys in the investigated section were characterized using SEM-EDX analysis.     

Influence of the chemical nature of siloxanes on the thermodynamic characteristics of sorption for a series of linear and cyclic saturated hydrocarbons

The thermodynamic characteristics of sorption (Henry’s constants of sorption equilibrium K _sorp, heats of sorption q, and standard entropies of sorption ΔS°) were studied by gas chromatography to describe the behavior of linear and cyclic saturated hydrocarbons on phenylmethylsiloxane HP-5, fluoromethylsiloxane OV-210, and methylsiloxane OV-1. The K _sorp and q values and, correspondingly, the energy of dispersion interactions decrease in the series HP-5 > OV-1 > OV-210. The difference in structures of adamantane, trans-decalin, and decane molecules has almost no effect on the heats of sorption. Henry’s constants increase on going from decane to trans-decalin and, further, to adamantane. This effect becomes more pronounced with an increase in the sorbent polarity (OV-1 < HP-5 < OV-210). The entropy factor can play a key role in sorption processes on siloxanes.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 140–143, January, 2005.     

Construction of solid-liquid phase diagrams in ternary systems by titration calorimetry

Titration calorimetry was used to construct the solid-liquid equilibrium line in ternary systems containing the solute and an aqueous mixed solvent by measuring the heat of dissolution of the solid solute during successive additions of the liquid solvent. The plot of cumulated heats versus the mole ratio, n_solvent/n_solute, yields two (almost) linear increases of different slopes. These two lines represent successively the enthalpy of dissolution then the enthalpy of dilution of the medium; their intersection gives the solubility and the enthalpy of dissolution of the solute. Phase diagrams have been established over the whole concentration range for o-anisaldehyde, 1,3,5-trimethoxybenzene and vanillin, in water + methanol, +ethanol, or +n-propanol at 303, 313 and 318 K.     

Separation of minor macromolecular constituents from multicomponent polymer systems by means of liquid chromatography under limiting conditions of enthalpic interactions

Minor (<1%) macromolecular constituents may significantly affect physical/utility properties of the multicomponent polymer systems. Separation and molecular characterization of the small amounts of macromolecular additives from the dominant polymer matrices represents an exacting analytical problem. Recently a series of unconventional liquid chromatographic methods was developed for separation of the constituents of polymer blends; their generic name is Liquid chromatography under limiting conditions of enthalpic interactions, LC LC. The LC LC procedures employ the difference in elution rate of the low molecular substances and the macromolecules within the column packed with porous particles. Small molecules permeate practically all pores of the packing and therefore they elute slowly. Polymer species are partially of fully pore excluded and in absence of enthalpic interactions they are rapidly transported along the column. The appropriately chosen low molecular substances promote interactions of macromolecules within the column. If eluted in front of sample, the interaction promoting low molecular substance may create a sort of slowly eluting barrier that is “impermeable” for the interacting macromolecules and efficiently decelerates their fast transport. The blocking action of a barrier differs for macromolecules of distinct nature, which elute from the column with a different rate to be mutually separated irrespectively of their molar mass. In present work, different approaches to the LC LC separations are compared from the point of view of their applicability to complex polymer systems, in which one constituent is present at very low concentration, and also in light of sample recovery. The practical examples are the two- and three-component polymer blends of polystyrenes, poly(methyl methacrylate)s and poly(vinyl acetate)s of different molar mass averages and distributions, as well as the diblock copolymers polystyrene-block-poly(methyl methacrylate) that contain their parent homopolymers.     

Necessary and sufficient conditions for the appearance of extrema on concentration distribution curves in complex equilibrium systems

It is shown that species distribution curves with at least one minimum may be found in most equilibrium systems with three or more components. Whether such concentration minima are actually observed then depends on the values of the equilibrium constants and on the total (analytical) concentrations of the components. A general algorithm is given for the necessary and sufficient conditions for the appearance of extrema in multicomponent systems. Three-component systems are studied in more detail and special attention is given to the limiting case of a horizontal inflection, i.e., the point where the concentration minimum just disappears. Two well-studied chemical examples, the Cu(2+)-diethylenetriamine-OH(-) and Hg(2+)-Cl(-)-OH(-) systems are discussed, along with a simple model system showing as many as five extrema on a single distribution curve.     

Chemical equilibrium model for the thermodynamic properties of mixed aqueous micellar systems: Application to thermodynamic functions of transfer

Mixed micelles can be formed in water between various pairs of hydrophobic solutes such as surfactants, alcohols and hydrocarbons. These systems can often be studied through the thermodynamic functions of transfer of one of the solutes, usually kept near infinite dilution, from water to an aqueous solution of the other solute. When mixed micelles are formed, these functions change significantly, and often go through extrema, in the region where the binary system micellizes or undergoes some microphase transition.Three main effects are responsible for the observed trends: pair-wise interactions between both solutes in the monomeric form, a distribution of the reference solute between the aqueous and micellar phases and a shift in the monomer-micelle equilibrium in the vicinity of the reference solute. Simple equations can be derived for these three effects which can account for the sign and magnitude of the observed trends using parameters which are derived for the most part from the two binary systems.     

A procedure for predicting sorption equilibrium in ternary polymer systems from Flory–Huggins binary interaction parameters and the inversion point of preferential solvation

A procedure has been developed, based on the Flory–Huggins theory as generalized by Pouchlý, which permits the calculation of preferential (λ) and total (Y) sorption coefficients from previous information on the binary interaction parameters, χ, χ, and g₁₂(?₁₀) and on the mixture composition at which the sign of λ inverts. The expressions obtained were applied to 10 cosolvent polymer systems for which experimental values of λ and Y are known. Practically in all the studied systems, the theoretical predictions are in fair accordance with the experimental data.     

Spectra analysis for macromolecular systems: Chain‐length effects in polymer particles

A complete set of frequencies for the density of states spectrum g(ω) is obtained for 6000‐atom polymer particles involving all 18,000 degrees of freedom. We efficiently generate the particle using molecular dynamics and molecular mechanics, and systematically analyze the spectra and thermal properties as a function of chain lengths: from one to 100 monomers. The density of states spectrum g(ω) shows a higher number of low‐frequency modes for the polymer particle with a smaller chain length, which results in a higher heat capacity at low temperature. Gibbs free energy was also calculated for the formation of a particle from a crystal as a function of temperature to evaluate thermal stability of those systems. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1812–1823, 2000     

A new hybrid double divisor ratio spectra method for the analysis of ternary mixtures

A new spectrophotometric method was developed for the simultaneous determination of ternary mixtures, without prior separation steps. This method is based on convolution of the double divisor ratio spectra, obtained by dividing the absorption spectrum of the ternary mixture by a standard spectrum of two of the three compounds in the mixture, using combined trigonometric Fourier functions. The magnitude of the Fourier function coefficients, at either maximum or minimum points, is related to the concentration of each drug in the mixture. The mathematical explanation of the procedure is illustrated. The method was applied for the assay of a model mixture consisting of isoniazid (ISN), rifampicin (RIF) and pyrazinamide (PYZ) in synthetic mixtures, commercial tablets and human urine samples. The developed method was compared with the double divisor ratio spectra derivative method (DDRD) and derivative ratio spectra-zero-crossing method (DRSZ). Linearity, validation, accuracy, precision, limits of detection, limits of quantitation, and other aspects of analytical validation are included in the text.     

A study on the thermodynamic properties of polyimide BTDA-ODA by adiabatic calorimetry and thermal analysis

Polyimide BTDA-ODA sample was prepared by polycondensation or step-growth polymerization method. Its low temperature heat capacities were measured by an adiabatic calorimeter in the temperature range between 80 and 400 K. No thermal anomaly was found in this temperature range. A DSC experiment was conducted in the temperature region from 373 to 673 K. There was not phase change or decomposition phenomena in this temperature range. However two glass transitions were found at 420.16 and 564.38 K. Corresponding heat capacity increments were 0.068 and 0.824 J g^–1 K^–1, respectively. To study the decomposition characteristics of BTDA-ODA, a TG experiment was carried out and it was found that this polyimide started to decompose at ca 673 K.This revised version was published online in November 2005 with corrections to the Cover Date.     

The influence of molecular conformation ofN-alkylsubstituted six-membered cyclic amines and alkylcyclohexanes on the thermodynamic characteristics of sorption in gas chromatography

The standard partial molar free energies, enthalpies, and entropies of sorption of the methylene units in the homologous series of alkylcyclohexanes andN-alkylsubstituted sixmembered heterocycles (piperidines, morpholines, and thiomorpholines) were determined on a capillary column with the methylsiloxane OV-101 stationary phase at 70–150°C. A characteristic feature of all series under study is an abnormally high increase in the values of thermodynamic parameters of sorption on going from the methyl to the ethyl homolog. This peculiarity is believed to be associated with the presence of thegauche butane orgauche methylethylamine fragments in the ethyl homolog. Thesegauche fragments have an increased sorption activity under conditions of gas chromatography in comparison with the correspondingtrans form. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 500–503, March, 1997.     

Fourier transform infrared study on the sorption of water to various kinds of polymer thin films

The state of sorbed water and the sorbing processes of water to various polymer thin films were studied with Fourier transform infrared (FTIR) spectroscopy. To prepare the polymer films, we used poly(ethylene glycol)s of different molecular weights and various kinds of vinyl polymers, such as poly(2‐methoxyethyl acrylate). The O? H stretching band of water sorbed in the films increased gradually on contact with water vapor at 50% relative humidity and leveled off. When O? H stretching bands of water sorbed to polymer films were compared, the peak positions and profiles of water sorbed to the polymeric materials with the same hydrogen‐bonding site were similar. A hybrid density‐functional method supported the assignment of the peaks. Furthermore, the diffusion coefficient (D) of water vapor in the polymer films was estimated by time‐resolved measurements of the sorbed water at the very initial stage (0–830 s). It was clearly shown that the D values of water vapor in the polymer materials with a strong hydrogen‐bonding site were smaller than those in hydrophobic polymers. The usefulness of the FTIR technique to investigate water sorption to polymer materials was definitely demonstrated. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2175–2182, 2001     

Determination of the intermolecular interaction parameters in the water-amide systems based on the data of the excess thermodynamic functions

The molar excess enthalpiesH ^E for the water +N-methyl-2-pyrrolidinone binary mixtures have been measured as functions of mole fraction at 298.15, 308.15 and 318.15 K, using isoperibol rotating calorimeter. A hydrogen bonding pairs model proposed by Luzar was fitted to the experimental dataH ^E,G ^E for the binary mixtures of water with hexamethylphosphoric triamide, N,N-dimethylformamide, N,N-dimethylacetamide and N-methyl-2-pyrrolidinone.     

多元气-液-固复杂体系相平衡

石油流体中含有气相、液相及可能遇到的固相包括水合物、石蜡和沥青质等,涉及多元气-液-固复杂体系的相平衡问题.为防止这些沉积物堵塞造成安全隐患,需要确定水合物、石蜡、沥青质沉积起始条件以及沉积量.本文针对化学热力学理论在含水合物、石蜡和沥青质的多元-多相平衡研究中的应用进行了综述.水合物相平衡模型较为成熟,主要有两类,其一为基于等温吸附理论的van der Waals-Platteeuw型热力学模型;其二为基于双过程水合物生成机理的Chen-Guo水合物热力学模型.石蜡沉积一般采用活度系数法、状态方程法及多固相模型描述.沥青质絮凝、沉积则可采用溶解度参数模型、状态方程法、胶体模型和标度理论模型进行计算.同时对多元气-液-固复杂体系的相平衡研究发展方向进行了展望.