Thermodynamics Of Polymer Solutions Research Articles

Polar effect in free volume theory for polymer solution thermodynamics

AbstractPolar effects on the thermodynamic properties of polymer solutions are treated within the framework of the free volume theory. The Sutherland potential and the dipole‐dipole interaction are assumed to represent intermolecular interaction in a polar system, with an approximation concerning the radial distribution function. Application of the treatment to some polar systems shows that the theoretical %‐parameters are smaller than the observed ones and than the calculated ones without regard to the polarity. The excess volume ratios are, however, nearer to the observed ones compared with those evaluated without the account of the polarity. Therefore, the present results are fairly good for strong polar solutions.

Phase diagrams and pulse‐induced critical scattering

AbstractRecent theoretical progress and major advances in computational methodology for spinodal and critical points make Pulse‐Induced Critical Scattering (PICS) a fast and reliable tool for examining statistical mechanical hypotheses, as expressed in the free energy of mixing function for solutions of linear polymers, and for measurement of the moments Mr = Σiwimir of the molecular weight distribution. Theoretical interpretation of measured phase diagrams has been hampered by 1) a lack of sufficiently reliable information on Mr(r = 1, 2, 3) of samples available from standard sources, and 2) the mental effort required in deriving spinodal and critical point equations from the increasingly complex free energy of mixing functions via the determinants of Willard Gibbs. Three strategies help to counter these difficulties: 1) Two molecular weight distributions (MWDs) are called r‐equivalent if they share at least the first r moments; computer software is available to determine the mixture of [r/2] sharp fractions which is r‐equivalent to a given MWD; thus the mixing of a small number of components gives access to an unlimited range of mixed samples whose moments are known (in terms of those of the components) to an accuracy set only by the analytical balance. 2) A spinodal truncation theorem (and critical point conjecture) exploits the concept of r‐equivalence since they determine the set of moments on which spinodal and critical point loci depend in addition to those moments featuring in the free energy expression. 3) Application of powerful algorithms of the QR‐type to the eigenvalue problems posed by the Gibbs spinodal and critical conditions have removed the necessity for prior excursions into the algebra of determinants by the human experimenter, since now spinodal and critical points can be numerically computed easily and directly from any postulated free energy function, especially when we employ the truncation theory and the notion of r‐equivalence. In consequence, the rapid feedback now possible with computer explorations of theoretical hypotheses is helpful in advancing the thermodynamics of polymer solutions and exploiting more fully the tools, such as PICS, for monitoring the relevant effects experimentally.

Thermodynamics of Polymer Solutions

I. INTRODUCTION The widely used Flory-Huggins theory of polymer solution thermodynamics was presented in the literature in 1942 [1, 2]. It is based upon the quasilattice theory of solutions [3], and leads to an equation for the free energy of mixing polymeric solute with monomeric solvent which contains a combinatorial entropy of mixing term and a regular solution theory enthalpy of mixing term. In its original form the theory contains only one adjustable parameter, characteristic of the intermolecular forces between molecules in solution. Hildebrand's solubility parameter concept [4] may be used to estimate the value of this parameter.

An Approximation for Nonrandomness in Polymer-Solution Thermodynamics

An Approximation for Nonrandomness in Polymer-Solution Thermodynamics

The Phase Separation Accompanied with Increasing Temperature : The Role of the Free Volume in the Thermodynamics of Polymer Solutions

The Phase Separation Accompanied with Increasing Temperature : The Role of the Free Volume in the Thermodynamics of Polymer Solutions

Free volume concept and polymer solutions thermodynamics

AbstractAfter briefly recalling previous work on thermodynamics of polymer solutions, we tentatively present a van der Waals‐like relationship for the excess enthalpy of mixing for polymer solutions, applied recently by Bagley et al. to simple mixtures and we derive the corresponding value of χH, the enthalpic part of the Flory‐Huggins parameter χ.

Gas—Liquid Chromatography on Polymers. II. Temperature Coefficients for Polyisobutylene—Hydrocarbons

Abstract Studies of the thermodynamics of polymer solutions by conventional static methods at very high concentrations of polymer are relatively few. Therefore, comparisons between enthalpy parameters obtained by the methods of glc and vapor sorption are limited to only a few cases. One other system for which comparable data are available is natural rubber and benzene. In this case, the glc value of κs is +0.18, while κs = 0.01 ± 0.1 has been obtained by vapor sorption. It appears from the somewhat sparse data collected to date that estimates of the residual enthalpy obtained by glc methods are as reliable as those obtained by static methods. Corrections for gas phase imperfection must be very carefully applied.

Gas-Liquid Chromatography on Polymers. II. Temperature Coefficients for Polyisobutylene-Hydrocarbons

Abstract Studies of the thermodynamics of polymer solutions by conventional static methods at very high concentrations of polymer are relatively few. Therefore, comparisons between enthalpy parameters obtained by the methods of glc and vapor sorption are limited to only a few cases. One other system for which comparable data are available is natural rubber and benzene. In this case, the glc value of κs is +0.18, while κs = 0.01 ± 0.1 has been obtained by vapor sorption. It appears from the somewhat sparse data collected to date that estimates of the residual enthalpy obtained by glc methods are as reliable as those obtained by static methods. Corrections for gas phase imperfection must be very carefully applied.

Upper and lower critical solution temperatures in the cosolvent system acetone(1)+ diethyl ether(2)+ polystyrene(3)

Phase diagrams for different molecular weight fractions of polystyrene in the mixed solvent system acetone + diethyl ether have been obtained. The system shows a variation of upper and lower critical solution temperatures with solvent composition which indicates the cosolvent nature of the mixed solvent. No solvent composition is found which can dissolve high molecular weight poly-styrene (M106). The separation of critical solution temperatures can be predicted by the Prigogine theory of polymer solution thermodynamics, but not the absolute values.

Derivation of the thermodynamics of polymer solutions through use of the free volume concept. B. Heat of mixing

Derivation of the thermodynamics of polymer solutions through use of the free volume concept. B. Heat of mixing

Thermodynamics of concentrated polymer solutions containing polyethylene, polyisobutylene, and copolymers of ethylene with vinyl acetate and propylene

AbstractGas‐liquid chromatography is used to measure polymer‐solvent interactions in polymer solutions where the solvent is at infinite dilution. Experimental data are presented for 24 binary polymer‐solvent systems in the temperature range 50° to 150°C. A simple relation exists between the experimental retention volume data and the infinite dilution volatility; this volatility can be used to calculate the solvent vapor pressure over the polymer solution up to about 0.1 weight fraction solvent. Using concepts from the Prigogine‐Flory theory of polymer solutions, Flory‐Huggins X parameters for some polymer‐hydrocarbon systems were correlated with the hydrocarbon's normal boiling temperature.

Thermodynamic Properties of Liquids, Including Solutions. IX. Thermodynamic Properties of Polymer Solutions

The writer’s new theoretical approach to polymer solution thermodynamics is outlined and the results of its application to four types of polymer solutions (rubber–benzene, polyisobutylene–benzene, polyisobutylene–cyclohexane, poly(propylene oxide)–CCl4) are presented and briefly discussed. The parameters of the theory are precisely related to the compositions, properties and interactions of the chemical units (segments) in the component molecules. The enthalpy part of the interaction parameter, χh, depends on an equilibrium between the different types of contact between segment “surfaces.” The entropy part of χ is the sum of a correction for non-randomness of distribution of the intersegment contacts and a contribution measuring the concentration dependence of the randomness of segment orientations and motions.

Surface thermodynamics of polymer solutions

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSurface thermodynamics of polymer solutionsK. S. Siow and D. PattersonCite this: J. Phys. Chem. 1973, 77, 3, 356–365Publication Date (Print):February 1, 1973Publication History Published online1 May 2002Published inissue 1 February 1973https://doi.org/10.1021/j100622a012RIGHTS & PERMISSIONSArticle Views284Altmetric-Citations58LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts

Application of Gas-Liquid Chromatography to the Thermodynamics of Polymer Solutions

Abstract It has been well established that gas—liquid chromatography (glc) can give accurate thermodynamic data on binary solutions where the components differ considerably in volatility or molecular weight. The substance of lower molecular weight (component 1) is injected into the moving gas phase and dissolves at effectively infinite dilution in the stationary liquid phase. This is formed by the higher molecular weight material, for example, squalane, biphenyl, dinonyl phthalate, glycerol, or the higher n-alkanes such as C16, C24, C36, etc. The convenience of the technique is such that activity coefficient data have already been obtained for hundreds of systems. In contrast, activity data are available for far fewer high polymer systems, in part certainly because of the need to use the laborious vapor sorption technique. While that technique gives activity data as a function of concentration, it would still be desirable to have data at infinite dilution for a variety of systems in order to test contemporary theories of polymer solution thermodynamics. Recently Guillet and coworkers have applied the glc technique to systems in which the stationary phase is a high polymer. (J. E. Guillet and coworkers refer to the gas-phase component as the molecular “probe”. This avoids the glc teminology in which that component is the solute and the stationary-phase polymer would be the solvent. This terminology is confusing to polymer chemists used to solutions where the polymer is the solute, being present at low, rather than high, concentrations.) Their primary interest has been to demonstrate the versatility of the technique in determining first- and second-order phase transitions, degrees of crystallinity, and other physical characteristics of the polymer, while the present communication considers the determination of thermodynamic quantities. It has been prompted by comments from several workers who have noted the difficulty of applying the usual thermodynamic equations of glc which yield γ1∞, the activity coefficient of component 1 at infinite dilution [Equations (5) and (6)]. The equations require an exact value of the molecular weight of component 2, making difficult their use for polymer systems. Our main objective is to resolve this problem. However, we also wish to stress the utility of the technique in providing data with which to test contemporary theories of polymer solution thermodynamics. We therefore comment on equations which directly relate experimental glc data to the interaction parameter, χ, of polymer solution thermodynamics.

Thermodynamic Interaction in Poly(Dimethylsiloxane)—Hydrocarbon Systems from Gas—Liquid Chromatography

Abstract Poly(dimethyl siloxane) has been used as the stationary phase in gas—liquid chromatography. Retention volumes have been used to calculate the thermodynamic interaction parameters for a series of linear and branched alkanes and aromatic hydrocarbons interacting with the polymer. Values of the χ parameter have been compared with results for the same systems obtained from equilibrium (static) vapor-absorption experiments, and found to be in excellent agreement. The successful comparison indicates the potential value of the glc route as the source of rapidly obtained thermodynamic data at infinite dilution of the volatile phase. A number of the prerequisites are established for useful application of the glc method to polymer solution thermodynamics.

Thermodynamics of polymer solutions as functions of pressure and temperature

The construction of a light scattering photometer for use at different temperatures and pressures up to 1000 atm permits measurement of the chemical potential and the second osmotic virial coefficient for high polymer solutions. From this one can determine entropy, enthalpy, and volume changes of solvent on dilution. Measurement of the scattered intensity at several wavelengths (the scattering angle being held constant) gives the dimensions of the dissolved molecules. The above-mentioned quantities are determined for polystyrene and polyisobutylene in different solvents as functions of pressure, temperature and molecular weight. The total number of experiments shows the following results: 1. 1. The enthalpies of dilution are shifted in the same direction with increasing pressure. All endothermal systems become more endothermal with increasing pressure and all exothermal ones become less exothermal. Both for endothermal and exothermal pseudoideal systems the appropriate 0 temperatures (A2 = 0) increase with growing pressure. 2. 2. Calculation of volume changes of solvent on dilution (by measuring the pressure dependence of light scattering) shows that these volume changes are positive for endothermal systems and negative for athermal and exothermal ones. A theoretical treatment is made on the basis of the excluded volume theory and the principle of corresponding states.

Derivation of the thermodynamics of polymer solutions through use of the free volume concept. A. Entropy of mixing

Derivation of the thermodynamics of polymer solutions through use of the free volume concept. A. Entropy of mixing

Thermodynamics interactions in dilute polymer solutions: the virial coefficients

Abstract

Role of free volume in polymer solution thermodynamics

Abstract

Application of Gas-Liquid Chromatography to the Thermodynamics of Polymer Solutions

Abstract It has been well established that gas—liquid chromatography (glc) can give accurate thermodynamic data on binary solutions where the components differ considerably in volatility or molecular weight. The substance of lower molecular weight (component 1) is injected into the moving gas phase and dissolves at effectively infinite dilution in the stationary liquid phase. This is formed by the higher molecular weight material, for example, squalane, biphenyl, dinonyl phthalate, glycerol, or the higher n-alkanes such as C16, C24, C36, etc. The convenience of the technique is such that activity coefficient data have already been obtained for hundreds of systems. In contrast, activity data are available for far fewer high polymer systems, in part certainly because of the need to use the laborious vapor sorption technique. While that technique gives activity data as a function of concentration, it would still be desirable to have data at infinite dilution for a variety of systems in order to test contempo...