Donald Patterson

Volumes of mixing and theP* effect: Part I. Hexane isomers with normal and branched hexadecane

The Prigogine-Flory theory of solution thermodynamics has been used to interpret molar excess volume data, VE, for two series of alkane mixtures: the five isomers of hexane mixed with normal hexadecane (Data from Reeder, et al.) and the five hexane isomers mixed with a highly branched hexadecane isomer, 2,2,4,4,6,8,8-heptamethylnonane (this work). Values of VE are negative and similar for both series, but vary considerably with the hexane within a series. According to the theory, VE contains a ‘P* contribution’ not found in the excess enthalpy and entropy, which depends strongly on the internal pressures and the derived P* parameters of the components. Values of VE are well predicted for both series, the variation of VE corresponding to the different internal pressures or P* parameters of the hexanes.

Volumes of mixing and theP* effect: Part II. Mixtures of alkanes with liquids of different internal pressures

The Flory theory of solution thermodynamics is used to predict exess volumes for systems containing a series of n-alkanes mixed with liquids of higher P* parameter and internal pressure, i.e., cyclopentane, cyclohexane, carbon tetrachloride, benzene and dioxane as well as of lower P*, i.e., decamethyltetrasiloxane. Trends of VE, e.g. changes of sign with alkane carbon number are well predicted and indicate the importance of the P* contribution in VE. Mixtures of hexane isomers with liquids of much higher P* typically have large excess enthalpies through zero as an S-shaped curve against composition which is negative on the side of the high P* component. This behaviour is interpreted as arising from increasingly large negative P* contributions in VE.

The w-shape concentration dependence of CEp and solution non-randomness: Ketones + normal and branched alkanes

Abstract The excess heat capacity (CEp) has been measured for acetone + 2,2,4,4,6,8,8-heptamethylnonane (br-C16) (10 and 25°C), +n-C12 (15 and 25°C) and +n-C6 (25°C). CEp is large and positive but becomes negative at both extremes of the concentration range, i.e. it is W-shaped. It becomes rapidly more positive on loweringT, approaching phase separation at the UCST. br-C16 mixed with 2-butanone, 3-hexanone, 4-heptanone and 5-nonanone also give W-shapedCEp(x) curves although the negativeCEp appearing at very high ketone mole fraction (0.95) are extremely small, less than 0.05 J K−1 mol−1. As the length of the ketone molecule is increased, the W-shape becomes less pronounced and has disappeared for br-C16 + 4-decanone where CEp is negative throughout the composition range. The present systems, which show W-shapeCEp, and those in the literature, have large equimolarHE values, ⋍ 1000 J mol−1 or larger, and often are close to phase separation. It is suggested that the W-shape arises from twoCEp contributions. One is negative and of parabolic concentration dependence. The other, due to non-randomness and associated with extremely largeHE and GE values, is shown by the Guggenheim quasi-chemical theory to be positive, concave downwards in the middle of the composition range, but concave upwards at the extremes, i.e. it has the correct concentration dependence to give the W-shape. The excess volume has been measured for acetone + br-C16, +n-C12 and +n-C6. It is large and positive while dVE/dT, for systems near the UCST, is more positive than predicted by the Flory theory, i.e. its behavior is analogous to CEp. It is suggested that: (1) polar (but not H-bonded) systems where HE is very large, ⋍ 1000 J mol−1 or larger should exhibit the W-shapeCEp, becoming more pronounced with decrease of temperature, and (2) the curvature of HE/x1x2 againstx should be positive and large, increasing with decreasingT.

Interactions in alkane systems by depolarized Rayleigh scattering and calorimetry. Part 1.—Orientational order and condensation effects in n-hexadecane + hexane and nonane isomers

Molecular optical anisotropies (γ2) have been obtained from depolarized Rayleigh scattering experiments on the 5 hexane isomers and 15 nonane isomers of widely varying degrees of branching. Values of γ2 have also been obtained for these molecules at high dilution in carbon tetrachloride. The latter values reflect the anisotropies of the molecular shapes of the isomers while the pure state values also contain a contribution due to correlation of the orientations of neighbouring molecules. Thus, for highly branched, isotropic isomers, the pure and dilute solution γ2 values are the same and are small. With increasing molecular anisotropy, the pure state value increases more rapidly than the dilute, the divergence reflecting the increasing correlation of molecular orientations. Values of γ2 have been found for n-hexadecane at high dilution in the hexanes and nonanes. They increase with the anisotropy of the solvent molecules and yield increasing values of the J12 parameter, which characterizes the correlation of orientations of the n-hexadecane and solvent molecules. The J12 values are given approximately by the geometric mean, (J11J22)½, of the order parameters of the pure liquids, indicating that the mixing of two liquids results in a net destruction of orientational order, i.e., ΔJ12=½(J11+J22)–J12 is positive. This change explains the variation in the heats of mixing of n-C16+ hexane systems. Molar heats of mixing have been measured at 25°C through the concentration range for n-C16 with 21 nonane isomers. With increasing nonane branching, ΔhM increases proportionally to ΔJ12. However, when nonane isomers have high degrees of steric hindrance, e.g., 3,3-diethylpentane or 2,3,3,4-tetramethylpentane, a new and large negative contribution is encountered in ΔhM. For example, ΔhM for n-C16+ 3,3-diethylpentane is S-shaped and negative at high nonane concentrations. Values of ΔvM and ΔsM also contain negative contributions for the few systems studied. The effect resembles a “condensation” of the less hindered alkane onto the large sterically hindered nonane, similar to the condensation effect found in cholesterol + lipid systems.

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies hE, Gibbs free energies gE and hence entropies sE have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C16. The hE and gE are negative while TsE are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to hE and TsE, counterbalanced in the case of TsE by the positive combinatiorial TsE for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of hE and TsE are now strongly positive, while those of gE are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C16 molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, hE and TsE are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C16 segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.

Order destruction and order creation in binary mixtures of non-electrolytes

Abstract Order-destruction and order-creation during mixing are discussed for binary mixtures of various liquids (component 1) with the n -alkane series (component 2). When component 1 is a spherical molecule liquid, e.g. cyclohexane, anomalous positive contributions occur in H E and S E , but negative ones occur in C P E , Δ C V , d V E /d T and other second-order quantities. The Flory theory is used as a first approximation to the prediction of these quantities. Thermodynamic effects, not included in the theory, are attributed to a net decrease in structure during mixing because of a destruction of short-range correlations of molecular orientations (CMO) in pure n -C n . When component 1 is a plate-like molecule, e.g. 1-chloronaphthalene, these effects are decreased and reversed in sign. This has been ascribed to a net increase in structure because of a hindrance to molecular motion or a change in molecular conformation. When component 1 is a linear or branched alcohol, the n -C n are relatively inert while component 1 is associated in both the pure and solution states leading to positive or negative effects in C P E depending whether the solution or pure component 1 is more structured. The Treszczanowicz-Kehiaian model for self-associated liquids + inert solvents explains these results and also provides a general framework for the discussion of both the process of order-creation and the process of order-destruction in solution.

Effect of molecular size on the W-shaped excess heat capacities: oxaalkane–alkane systems

Excess molar heat capacities, CEp, throughout the entire concentration range have been determined at 25 °C for the following oxaalkane–alkane systems: 2,5,8,11,14-pentaoxapentadecane (tetraglyme) with decane, nonane, octane and hexane; 2,5,8,11-tetraoxadodecane (triglyme) with hexadecane, pentadecane, tetradecane, dodecane, decane and hexane; 2,5,8-trioxanonane (diglyme) with 2,6,10,15,19,23-hexamethyltetracosane (squalane), 2,6,10,14-tetramethylpentadecane (pristane), hexadecane and decane; 2,5-dioxahexane (monoglyme) with squalane, pristane, decane and heptane; and 1,4-dioxacyclohexane (p-dioxane) with cyclohexane. For all these tures CEp has a W-shaped concentration dependence (two minima separated by a maximum). By increasing the molecular size of either component, the maximum in CEp is enhanced and displaced towards high concentrations of the smaller component. CEp behaviour correlates with degrees of non-randomness in the mixtures as quantified by the concentration–concentration correlation function Scc which is calculated using the Flory–Huggins theory with a group-interaction model and assuming interaction between molecular surfaces.

Self-association of alcohols in inert solvents. Apparent heat capacities and volumes of linear alcohols in hydrocarbons

Apparent molar heat capacities, ϕC, and volumes, ϕV, have been measured for methanol, hexan-1-ol and decan-1-ol in n-alkane solvents between xROH= 0.001 and 0.2 at 10, 25 and 40 °C. The apparent molar heat capacities show a maximum against concentration which increases and moves to lower alcohol concentrations as the temperature decreases. This leads to a negative dϕC/dT at low alcohol concentrations, changing sign at higher alcohol concentrations. The Treszczanowicz–Kehiaian model for self-associated liquids + inert solvents explains these concentration and temperature dependences in terms of alcohol self-association through hydrogen bonds. Tetramers are the predominant species, dimers being almost absent even at very low alcohol concentrations. The excess heat capacity, CEp, and dCEp/dT of the mixtures are of different sign in the following approximate concentration ranges: (I) for xROH > 0.01, CEp and dCEp/dT > 0, (II) for 0.005 0 and dCEp/dT < 0 and (III) for xROH < 0.005, CEp and dCEp/dT < 0. This behaviour is explained quantitatively by the Treszczanowicz–Kehiahian theory and is believed to occur in all associated + inert liquid systems. The apparent molar volumes increase rapidly as the concentration of alcohol decreases, corresponding to a destruction of the tetramers. ϕC and ϕV have also been measured for methanol dissolved in an active solvent, methyl acetate. The radically different results indicate that hydrogen bonding between the alcohol and the solvent has replaced self-association as the predominant influence on the thermodynamics.

Interactions in alkane systems by depolarized Rayleigh scattering and calorimetry. Part 2.—Orientational order in systems containing hexadecane isomers of different structure

Depolarized Rayleigh scattering has been used to obtain values of the molecular optical anisotropy (γ2) for the following hexadecane isomers at high dilution in carbon tetrachloride : 2,2,4,4,6,8,8-heptamethylnonane, 6-, 4- and 2-methylpentadecane, 6-pentylundecane and n-hexadecane. The values increase moderately through the series corresponding to increasingly anisotropic molecular shapes. Values of γ2 have also been obtained for the hexadecane series in their pure liquid states. These increase rapidly relative to the dilute solution values, indicating the development of short-range orientational order or correlations of molecular orientations. The pure liquid results with 6-, 4- and 2-methylpentadecane show that orientational order depends strongly on the methyl position and length of the straight-chain part of the alkane molecule. Values of γ2 for the hexadecane isomers have been found for high dilution in cyclohexane, 2,2-dimethylbutane and n-hexane which indicates that the hexadecanes can correlate their orientations to only a limited extent with these hexane solvents. Heats of mixing have been measured at 25°C through the concentration range for the hexadecane isomers mixed with cyclohexane, 2,2-dimethylbutane and n-hexane. For each hexane, the heats increase through the series of hexadecane isomers. This corresponds to the increase of orientational order in the pure hexadecane isomers and the destruction of order in the hexadecane on mixing with the hexane. The magnitudes and concentration dependences of the heats for the n-C6+ C16 isomer systems are similar to those for n-C6+ n-C16 heats at different temperatures. This is explained by changing temperature having the same effect on the order of n-C16 as changing molecular shape on the order of the C16 isomers at 25°C.

Thermodynamics of mixtures containing alkanes

Abstract Binary mixtures of various liquids (components 1) with the n-alkane series (components 2) have given many results for the following excess or mixing functions (X E or ΔX). Of particular interest are: (1) the trend of X E with n; (2) change of X E when the n-C n are replaced by the corresponding series of highly-branched alkane isomers, and (3) comparison with theoretical predictions. Certain theories, e.g. van der Waals 1, fail in their present form due to neglecting the Prigogine number of external degrees of freedom, c, whereas the Flory, incorporating c, gives useful predictions which form a “base-line” against which to see special effects. For instance, when component 1 is a quasi-spherical inert molecule, e.g. cyclohexane or CCl 4 , anomalous positive contributions occur in H E , S E and V E , but negative in C P E , ΔC v and ΔαγVT, dV E /dT and ΔγVT, while G E and dV E /dP seem little affected. These effects are usually attributed to a net decrease of structure during mixing due to a destruction of short-range orientational order in n-C n . When component 1 is a plate-like molecule, e.g. 1,2,4-trichlorobenzene or chloronaphthalene these effects are decreased or reversed in sign. This has been ascribed to a net increase of structure due to a change of molecular conformation or a hindrance of molecular motion. When component 1 is an alcohol, the n-C n are relatively inert while component 1 is associated in both the pure and solution states leading to + or - effects in C P E depending on whether the solution or pure component 1 is the more structured. Recently Grolier, Wilhelm and Inglese have shown that when component 1 is an ether or ketone, C P E may show an unusual concentration dependence with a double minimum, perhaps again due to molecular association or to conformational changes.