Enthalpy of dilution of polystyrene/diethyl ketone

The enthalpy of dilution at 298,15 K was measured for the system polystyrene/diethyl ketone with a recently constructed flow type microcalorimeter, and the heat interaction parameter, χ_h, was estimated. It was found that χ_h, for this system is very small and negative and that its absolute value decreases with increasing molecular weight of the polymer. By comparison with other ketone systems measured previously, it was found that a polar solvent makes the polystyrene molecule energetically stable in solution.     

The heats of dilution of polystyrene solutions

The heats of dilution of atactic polystyrene-anisole, -dibenzyl ether, and -acetophenone systems were measured in the concentration range of 0,168 to 0,02 in volume fraction of the polymer, by adding successively 1 ml of the solvent to the solution of a known concentration by using an isothermal calorimeter at 303K. The heats of dilution of all systems obtained proved to be exothermic. The interaction heat parameter depends considerably on the concentration of the polymer and also on the molecular weight of the polymer. In polystyrene-anisole and -dibenzyl ether systems an interesting fact was found: the χ₁-parameter is negative and its absolute value increases at first, reaches a maximum and then decreases as the molecular weight of the polymer increases.     

Polymer-cosolvent systems, 1. Polystyrene in acetone/cyclohexane mixtures

Attempts were made to explain the cosolvency or the solubilisation of polystyrene in cyclohexane/acetone mixtures at 30°C. Cyclohexane is a Φ-solvent for polystyrene at 35°C. and acetone is a non-solvent. The effective interaction parameter χ_ms of Scott has been determined for the optimum solvent composition from the slope of a Stockmayer-Fixman plot as modified by Yamakawa. The value of unperturbed dimension obtained for polystyrene at this solvent composition coincides very well with that obtained in cyclohexane (Θ-solvent). The binary interaction parameter χ₁₂, between the two liquids obtained from χ_ms shows a certain amount of incompatibility between them. The values of λ^*, the preferential adsorption coefficient, were calculated for the entire solvent spectrum assuming the binary interaction parameters χ_ij as being independent of solvent composition. The inversion point (λ^* = 0), the optimum solvent composition yielding [η]_max, and the importance of χ₁₂₃, the ternary interaction parameter, are discussed.     

Correlation of data on intrinsic viscosities in mixed solvents by means of the modified flory-huggins equation

An equation for the total sorption potential Y derived from the modified Flory-Huggins equation and containing concentration-dependent interaction parameters, including the ternary parameter χ_T, was used to correlate reported data on intrinsic viscosities in mixed solvents. Similarly to the evaluation of data on preferential sorption, the assumption of proportionality between the ternary parameter and the interaction parameter of components of the mixed solvent, g₁₂, was successfully applied to the case of total sorption. The assumption proved to be useful in the treatment of 12 ternary systems, if the single-liquid approximation was employed. The calculated proportionality constant between the ternary parameter and g₁₂ has properties similar to that evaluated from the data on preferential sorption. The conditions of occurrence of a maximum or minimum in the dependence of total sorption on composition are discussed.     

Thermodynamics of polymer blends based on poly(methyl acrylate) and poly(vinyl acetate) with different molecular weights

In this work a study on thermodynamics of polymer blends, based on poly(methyl acrylate) (PMA) and poly(vinyl acetate) (PVAc), was carried out. Our foremost aim was to examine the molecular weight effect on polymer compatibility. The results confirm our hypothesis: the interaction parameter χ₁₂, varies abruptly in a very restricted molecular weight range. In this way, it can be concluded that molecular weight, as well as other parameters (i.e. lateral group hindrance, chain functionalization, composition temperature and so on), influences greatly polymer miscibility.     

Viscosity of aqueous and alkaline solutions of poly(ethylene oxide)

Viscosity measurements over a wide range of temperature were made on aqueous solutions of poly(ethylene oxide) samples of different molar mass and of low polydispersity. Above ca. 308 K the Mark-Houwink exponent decreases and tends to a value of 0,50 at a lower critical solution temperature of 376 ± 2 K. The same value for this θ-temperature is derived also as that at which the slope of Stockmayer-Fixman plots tends to zero. At 298 K the unperturbed dimensions [〈r²〉₀/M]^1/2 = 0,089 nm · g^?1/2 · mol^1/2 and their temperature coefficient d ln 〈r²〉₀/dT ≈ ? 1,5 (±0,5) · 10^?3 K^?1. In aq. KOH the intrinsic viscosity [η] is virtually uninfluenced by pH at low-medium pH, but at high pH, [η] falls sharply. Viscosity and phase separation measurements yield θ-conditions in 1,24 M aq. KOH at 298 K. The derived polymer-water interaction parameters χ increase from 0,449 at 276 K to 0,493 at 358 K, but the enthaplic component χ_H is incapable of yielding a meaningful value for the solubility parameter δ₂ of the polymer in such a hydrogen-bonding system. The calculated value of χ₂ was 18,9 (kJ · dm^?3)^1/2.     

Über die möglichkeiten zur bestimmung von mischungsenthalpien und -volumina aus der molekulargewichtsabhängigkeit der kritischen entmischungstemperaturen und -drücke am beispiel des systems trans-decahydronaphthalin/polystyrol

Cloud-point curves and critical curves (T_c = f(p)) have been measured for the system trans-decahydronaphthalene/polystyrene and three different molecular weights of the polystyrene component (2,5 · 10⁶; 3,9 · 10⁵; 1,1 · 10⁵). It turned out that by variation of the pressure the metastable region can be investigated up to the spinodal curve. A comparison of the theta-temperatures and the enthalpy contributions χ_H (to the Flory-Huggins interaction parameter χ) resulting from the measured critical temperatures according to Shultz-Flory, with the corresponding directly obtained literature data, demonstrates that, although the extrapolation of T_c to infinite molecular weight is feasible, χ_H obtained in this way is greater by a factor of approximately three, due to the concentration dependence of χ. The same is true for the determination of χ_V (the contribution of the work in change of volume to χ) from the molecular weight dependence of the critical pressure. The determination of χ_V from the slope of the critical curves and known χ_H is, however, possible; the results are in good agreement with direct measurements. The shape of the critical curves calculated theoretically according to Prigogine and Patterson, turns out to be very sensitive to the precise values chosen for the mechanical data of the pure components. By adjustment of the system-specific parameters the measured critical curves can be well represented analytically.     

Flory polymer-polymer interaction parameter between hemicellulose and lignin from hardwood

The interaction parameter between hemicellulose and lignin from beech wood was evaluated from vapor pressure osmometric measurements on solvent-polymer and solvent-polymer-polymer solutions. Dimethyl sulfoxide (DMSO) was used as a solvent. The interaction parameters between hemicellulose and DMSO (χ₀₁) and between lignin and DMSO (χ₀₂) increase with increasing temperature, and the change with temperature is proportional to inverse temperature. It was found for both polymers that DMSO becomes a “poor solvent” at higher temperature. This result was also derived from the free energy of dilution. The interaction parameter between hemicellulose and lignin (χ₁₂) was evaluated as a function of temperature from the activity of solvent in a solution of the three components. At 60°C, χ₁₂ is positive; it decreases with increasing temperature and becomes negative at 70–80°C where a minimum is found. Above 80°C, χ₁₂ increases again to become positive at 90°C. Thus, hemicellulose and lignin attract each other at 70–80°C, but there is repulsion between the polymers at higher and lower temperatures.     

Experimental verification of modern theory of molecular weight fractionation based on solubility difference

An attempt was made to verify the modern theory of molecular weight fractionation based on solubility behavior by experiment. Atactic polystyrene (PS) in methylcyclohexane (MCH) and in cyclohexane (CH) were employed for this purpose. The following quantities were determined experimentally and compared with theoretical values calculated with the aid of an electronic computer: The partition coefficient σ, volume ratio of polymer-lean phase to polymer-rich phase R, polymer volume fraction in the two phases, v_p(1) and v_p(2), weight-average molecular weight M?_w and the breadth of the molecular weight distribution (the ratio of weight- to number-average molecular weight, M?_w/M?_n and standard deviation σ′) of the polymers in both phases. The experimental data can be well explained in terms of theory if the concentration dependence of the polymer/solvent interaction parameter χ, expressed by p, is reasonably taken into account, i.e., p = 0,7 for PS in MCH and p = 0,6 for PS in CH. It was shown that σ depends slightly on molecular weight.     

Compatibility of poly(ethylene oxide) and poly(methyl methacrylate) chains in solutions of their blends,diblock and triblock copolymers

Solvent activity data were obtained from vapour pressure measurements at 50°C, 70°C, 100°C and reduced to χ-functions in systems consisting of benzene or toluene on the one hand and blends or block copolymers of poly(ethylene oxide) and poly(methyl methacrylate) on the other. The χ_BC-values are negative for all polymer subsystems, but miscibility on a segmental scale is somewhat different for block copolymers and blends. χ_BC depends on the concentration of solvent and is mainly influenced by the Δχ-effect in solution and correlated with the syndiotacticity of the PMMA chains. There is only a small influence of temperature and blend composition or block ratio.     

Theoretical evaluation of Kp in size‐exclusion chromatography from a thermodynamic viewpoint

The Flory‐Huggins formalism developed for a ternary solvent(1)‐polymer(2)‐polymer(3) system has been used to evaluate the binary and ternary interaction functions. The raw data are the two‐phase equilibrium compositions of the three components determined by liquid chromatography. These interaction functions have been used to evaluate theoretically the distribution coefficient of solute‐gel interactions in size exclusion chromatography (SEC), K_p. For a system solvent(1)‐polymer(2)‐gel matrix(3), a new expression for K_p has been obtained from a thermodynamic point of view. The proposed equation is a function of the fraction of gel matrix in the ternary phase, of the molar volumes of solvent and polymer and of the binary and ternary interaction functions. For the systems studied, values of K_p higher and lower than unity have been obtained at different hydrodynamic volumes which evidences the existence of secondary mechanisms. These calculations lead to a better understanding of the separation mechanism in chromatographic experiments.     

Investigation of exothermic polymer blends by neutron scattering

Provided a polymer is soluble, i. e., molecularly dispersed in another polymer irrespective of the molecular weight of the components, the solution is exothermic. By increasing the temperature two effects, both unfavourable to mixing become larger: (i) the excess entropy of mixing caused by contact interaction and (ii) the total effect from the difference of the free volumes of the pure components. So, an upper miscibility gap occurs. The thermodynamic properties of the mixture cannot be derived from the properties of the pure components. They can be described by the corresponding states theory of Prigogine, Flory, and Patterson with suitable values for the contact energy and contact entropy parameters X₁₂ and Q₁₂. The temperature of separation can be predicted from measurements on the mixture at low temperatures.     

Unperturbed dimensions of polymers in binary and ternary systems

The unperturbed dimensions parameter K_Θ is one of the most important characteristics of a polymer chain. For binary systems (polymer/solvent) and mostly for ternary systems (polymer/solvent(1)/solvent(2)) the K_Θ values show large discrepancies with respect to those under thetaconditions in a single solvent. These discrepancies can be explained by considering that the interaction parameter χ (and consequently the coil dimensions or the number of intramolecular contacts between polymer segments) changes with molecular weight M. Assuming this dependency, a modified Stockmayer-Fixman equation is proposed from which a unique value of K_Θ for a given polymer, independent of M, is obtained. The use for ternary polymer systems of an interaction parameter between polymer and the solvent mixture (χ_3M) which depends on M, allows to calculate a single K_Θ value for a polymer in different mixtures of solvents and justifies the proportionality found between K_Θ deviations and the excess Gibbs free energy between both solvents of the solvent mixture.     

A new theoretical approach to problems of the solution behaviour of ring-shaped polymers

In order to explain the difference in theta temperatures between ring-shaped polymers and their corresponding linear polymers, the Huggins parameters χ of ring-shaped polymers is assumed to obey the dependence χ = χ₁ (1 + σ ?₂) on local segment concentration as expressed by the volume fraction of the polymer ?₂, and σ being a constant. A comparison between theoretical results and light scattering measurements of Roovers and ourselves is satisfactory.     

Viscosities of dilute solutions of poly (methyl methacrylate) and poly (ethyl methacrylate) in organic solvents

Poly(methyl methacrylate) and poly(ethyl methacrylate) prepared by a benzoylperoxide catalysed polymerization process were fractionated. The variation of the intrinsic viscosity and HUGGINS ' constant with temperature, molecular weight and solvent was studied. From the viscosity data the thermodynamic interaction parameters χ, ψ, k etc., and the solubility parameter of the polymers were evaluated and discussed.     

Composition-dependent Flory-Huggins parameters: molecular weight influences at high concentrations

Flory-Huggins interaction parameters χ were determined by means of equilibrium vapor pressures (measured via a combination of a head-space sampler with a gas chromatograph) and light scattering as a function of composition and temperature for the systems cyclohexanone/polystyrene [CHO/PS] and cyclohexanone/poly(butyl methacrylate) [CHO/PBMA]. The investigation of molecular weight influences on χ with the system CHO/PBMA demonstrates that they persist almost up to the pure polymer. In order to rationalize this result, it is postulated (in accord with experimental findings and theoretical predictions) that the dimensions of polymer chains may vary upon the addition of solvent even in highly concentrated solutions. From the information concerning χ(T) the inter action parameters were split into their enthalpy and entropy part. In the case of CHO/PS these quantities vary considerably with composition and turn out to be linearly interrelated.     

Enhancement of miscibility between hemicellulose and lignin by addition of their copolymer,the lignin-carbohydrate complex

The miscibility between hemicellulose and lignin from beech wood was investigated from observation of their glass transition temperature, along with the effect of addition of their copolymer, the lignin-carbohydrate complex (LCC). The binary and ternary blend systems of hemicellulose, lignin and LCC change from immiscible to miscible by increasing the temperature. This behavior shows that this blend system has an upper critical solution temperature (UCST). The binodal temperature decreases with increasing amount of LCC added. This behavior was analyzed by the temperature and composition dependence of the Flory polymer-polymer interaction parameter (χ₁₂). The value of χ₁₂ estimated from the phase diagrams indicates that χ₁₂ decreases with an increase in both the lignin content and the temperature.     

Unperturbed dimensions of polytetrahydrofuran

Phase separation techniques have been utilised to establish the following theta-conditions for polytetrahydrofuran : isopropanol at 44.6°C, di-ethyl malonate at 33.5°C and a mixture of ethyl acetate/n-hexane (22.7/77.3 wt.-%) at 30.4°C. The entropy, enthalpy, and free energy pair interaction parameters ψ₁, ?₁, and χ₁ were also obtained. Light scattering measurements were conducted in isopropanol alone and the second virial coefficient found to be zero, thus verifying theta-conditions. For all three solvent systems the KUHN -MARK -HOUWINK viscosity exponent ν was confirmed to be 0.50, but a unique value was not exhibited by the corresponding K_Θ. Some reasons are proposed to account for this. From each K_Θ the steric factor σ is calculated to be 1.67 (in isopropanol), 1.69 (in di-ethyl malonate) and 1.75 (in the mixed solvent). These values lie between those for polyethylene oxide and polyethylene.     

Thermodynamic studies based on corresponding states theory for solutions of polystyrene in ethyl methyl ketone

The polymer solution theory on the corresponding state principle developed by FLORY was examined by comparing the thermodynamic parameters calculated theoretically with experimental results. The osmotic pressure of the polystyrene/ethyl methyl ketone system was determined for solutions of polymer concentrations 10 to 30% at 10 to 55°C. Using X₁₂ and Q₁₂ parameters best fitting to these data, the calculated parameters were compared with experimental results. Both the entropy parameter ψ₁ and enthalpy parameter χH, 1 were negative and decreased with increasing temperature. FLORY'S theory elucidates appreciably well the thermodynamic quantities with the use of the adjustable parameters X₁₂ and Q₁₂, but there seems to remain still some disagreement with experimental results. SHULTZ-FLORY'S method for determining the Θ-temperature was discussed based on this theory.     

Free volume concept and polymer solutions thermodynamics

After 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 χ_H, the enthalpic part of the Flory-Huggins parameter χ.