Fluid Phase Equilibria, 68 (1991) 35-46 Elsevier Science Publishers B.V., Amsterdam

35

Influence of size and shape effects on the solubility of hydrocarbons: the role of the combinatorial entropy *

Krzysztof Kniai Warsaw University of Technology, Division of Physical Chemistry, Noakowskiego 3, Warsaw 00-664 (Poland)

(Received January 3, 1991; accepted in final form July 4, 1991)

ABSTRACT

Kniai, K., 1991. Influence of size and shape effects on the solubility of hydrocarbons: the role of the combinatorial entropy. Fluid Phase Equilibria, 68: 35-46.

Solid-liquid equilibrium data of the n-alkanes from n-hexane to n-hexatriacontane dissolved in various alkane solvents have been used to determine the activity coefficients at infinite dilution. Comparison of the data obtained with vapour-liquid equilibriums, GLC and heat of mixing data suggests that almost ideal solubility in some systems results from an order/disorder phenomenon known as the Patterson effect. The importance of the combi- natorial entropy contribution for the solubility of hydrocarbons has been discussed.

INTRODUCTION

Solid-liquid equilibrium (SLE) has gained increasing interest in the recent decade. Besides its importance for technological processes such as crystallisation and purification, SLE provides a good tool for examining the thermodynamic nature of many systems.

The ultimate aim of this work is to investigate the influence of the solvent shape and size on the solubility of chain hydrocarbons.

The conclusions arrived at are based on sets of solubility data, extracted from the literature, including results recently reported by Domaiiska and Kniai (1990a,b) and the subsequent study has been deliberately confined to alkane mixtures, because of the importance of conformational effects in alkane thermodynamics.

* Work dedicated to Dr. Urszula Domadska from the Warsaw University of Technology.

0378-3812/91/$03.50 0 1991 Elsevier Science Publishers B.V. All rights reserved

36

n-Alkanes are highly ordered in the solid state, existing in many crys- talline phases which depend on the chain length (Broadhurst, 1962; Deni- co10 et al., 1983). In the liquid state they still retain much of their order, as was proved by Barbe and Patterson (1978). Using a light scattering tech- nique Tancrede et al. (1977) showed clearly that globular or spherical solvents destroy the conformational order in liquid long-chain hydrocar- bons, giving high positive values for the enthalpy and entropy of mixing. According to an early study by Patterson et al. (1972) the thermodynamic properties of alkane mixtures are made up of combinatorial, free volume and interactional (field forces + order destruction) contributions, as was shown when they considered the importance of each contribution to the activity coefficients at infinite dilution of many short or globular alkanes dissolved in long-chain n-alkanes.

Because of the high melting temperatures and low volatilities of the long chain paraffins, heat of mixing, GLC or VLE data for systems with high paraffin concentrations are very scarce. In this work SLE data have been used to determine the activity coefficients at infinite dilution for long-chain n-alkanes.

THE COMPUTATIONAL, PROCEDURE

The solubility of a solid in a liquid can be used to evaluate the activity coefficient of the solute component in the solution by eqn. (1).

In x, = - 2(+-l)+*(ln$+%-I)-lny (1)

This equation is valid if no phase transition takes place in the solid phase between the system temperature T and the solute melting temperature T,,.

When a phase transition takes place between T and Tml, eqn. (1) must be modified to include the effect of the transition point. For a first-order phase transition eqn. (1) has the form

In xi= - 2(-$-l)+*(ln-&+?-I)

AH,,, Tt,, -- -_ ( )

1 RTtr1 T

-1n y1

Experimental x1 vs. T data therefore permit evaluation of the activity coefficients of the solute y1 by using eqn. (1) or (2), provided that the necessary thermochemical properties of the solid are available (Table 1).

37

TABLE 1

Thermodynamic data of solutes

Solute *KY, AC,,, &I mol) (J/mol)

n-C, n-C,

n-Cl2 n-C,6 n-C,8 n-C,9 n-C20 n-C22 n-C,

n-c,, n-C28

n-C32

n-C 36

13.09 = 20.75 = 36.86 = 53.38 = 61.73 a 46.65 - 69.66 48.99 54.93 c 59.54 c 64.69 c 76.00 88.87

46.87 a 53.88 a 64.69 = 73.59 = 71.41=

332.6 d 85.56 d 58.50 f 66.60 f 50.50 f

118.90 f

177.83 a 216.37 a 263.58 a 291.45 b 301.40 b 304.65 = 309.40 = 317.05 a 323.75 e 329.55 e 334.45 e 342.10 349.05 c

- -

13.82

28.22 c 31.32 c 32.24 c 35.46 42.70 30.56 h 9.92

295.95 c

316.15 a 321.25 = 326.45 e 331.15 e 338.90 346.95 345.25

a Messerly et al., 1967. b Domariska and Kniti, 1990a. Schaerer et al., 1955. d Domariska et al., 1987a. Domahska et al., 1987b. f Domariska and Wyrzykowska, 1990. g Domanska and Kniai, 199Ob. h Hexatriacontane reveals two phase transitions in the solid state, data taken from Schaerer et al. (1955).

Thus, for each system the dependence of the activity coefficient on the solubility (mole fraction) has been obtained. Activity coefficients at infinite dilution (and corresponding temperatures) have been calculated using polynomial extrapolation of the first, second or third degree. The results, given as experimental, are listed in Tables 2 and 3.

The error in the activity coefficient estimation exceeds the error ob- tained from direct experimental techniques and varies from 25% for systems with lower alkanes as solutes (n-C,, n-C,, n-C,,) to 5% for sys- tems with higher paraffins as solutes (n-C,, n-C,,, . . . , n-C,,).

RESULTS AND DISCUSSION

Mixtures of short n-alkanes with long-chain paraffins reveal negative deviations from ideality, which become bigger as the difference between chain lengths of the components increases. Such properties of the systems under study were predictable, and have been confirmed by the results obtained from the GLC technique in reversed systems (see Table 3). Negative deviations from ideality are particularly big for mixtures of paraffins with cycloalkanes. The values based on SLE data for these

38

TABLE 2

Activity coefficients at infinite dilution for long-chain paraffin as solutes

Solute + Reference In ym 2; exp.

In ym In ym solvent F-H S-G

In ym Im. F-H

c, + c-c, Goates et al. (1979) _a 0.161 - 0.006 0.009 - 0.003 c, +c-c, Ott and Goates (1983) _a 0.145 - 0.077 - 0.065 - o.q33 c, + n-c, Hoerr and Hatwood (1951) _a 0.111 - 0.038 - 0.037 - 0.016 c,, + n-c, Hoerr and Hatwood (1951) _a -0.113 - 0.258 - 0.252 - 0.106 c,, + c-c, Domanska and Kniai (199Ob) 218.3 - 0.368 - 1.130 - 1.124 - 0.429 c,, +2,2-c, Domanska and Kniai (1990a) 256.0 - 0.026 - 0.583 - 0.554 - 0.231 C,, +2,3-C, Domahska and Kniai (1990b) 253.6 - 0.073 - 0.583 - 0.571 - 0.231 c,, +2-c, Domahska and Kniai (1990b) 250.5 0.037 - 0.583 - 0.571 - 0.231 c 16 + 3-c, Domariska and Kniai (1990a) 259.5 - 0.194 - 0.583 - 0.571 - 0.231 c,, + n-c, Domanska and Kniai (1990a) _a - 0.089 - 0.583 - 0.570 - 0.231 c,, + n-c, Dernini and De Santis (1976) 250.8 - 0.058 - 0.583 - 0.570 - 0.231 c 16 + c-c, Domanska and Kniai (1990a) 243.6 - 0.747 - 0.757 - 0.751 - 0.295 c,, +2,2-c, Domadska and Kniai 0990a) 261.6 - 0.037 - 0.770 - 0.734 - 0.300 c,, +3-c, Domahska and Kniai (1990a) 262.8 - 0.232 - 0.770 - 0.754 - 0.300 c,, + n-c, Domahska and Kniai (1990a) 265.0 - 0.248 - 0.769 - 0.753 - 0.300 c,, + c-c, Domanska and Kniti (1990a) 257.4 - 0.284 - 0.977 - 0.971 - 0.375 c,, + n-c, Domanska et al. (1987a) 262.5 - 0.094 - 0.544 - 0.534 - 0.216 c,, + c-c, Domahska et al. (1987a) 271.3 - 0.430 - 1.091 - 1.086 - 0.415 c,, + n-c, Domanska et al. (1987a) 263.8 - 0.341 - 0.622 - 0.610 - 0.246 c,, +2,2-c, Domanska and Kniai (1990a) 269.9 - 0.030 - 0.948 - 0.925 - 0.372 c,, +3-c, Domanska and Kniai (1990a) 270.6 - 0.228 - 0.968 - 0.948 - 0.371 c,, + n-c, Domadska and Kniai (1990a) 269.1 - 0.163 - 0.967 - 0.947 - 0.371 c, + c-c, Domanska et al. (1987b) 264.1 - 0.409 - 1.208 - 1.203 - 0.456 c, + n-c, Domafiska et al. (1987b) 266.3 - 0.177 - 0.703 - 0.690 - 0.276 c,, + c-c, Domadska and Kniai (199Ob) 269.6 - 0.968 - 2.023 - 2.018 - 0.732 c,, +2,2-c, Domaiiska and Kniai (199Ob) 280.9 - 0.008 - 1.175 - 1.126 - 0.445 C,, +2,3-C, Domadska and Kniai (199Ob) 281.6 - 0.254 - 1.175 - 1.153 - 0.445 c,, +2-c, Domanska and Kniai (199Ob) 282.7 -0.116 - 1.175 - 1.151 - 0.445 c,, +3-c, Domanska and Kniai (199Ob) 277.9 - 0.245 - 1.175 - 1.151 - 0.445 c,, + n-c, Kniai (1991) 281.4 - 0.280 - 1.175 - 1.150 - 0.445 c,, + c-c, Kniai (1991) 268.1 - 0.479 - 1.449 - 1.445 - 0.540 c, + n-c, Demini and De Santis (1976) _a - 0.796 - 1.390 - 1.361 - 0.519 c, + c-c, Domanska et al. (1987b) 270.7 - 0.752 - 1.698 - 1.694 - 0.624 c, + n-c, Domanska et al. (1987b) 273.5 - 0.316 - 1.048 - 1.028 - 0.400 c, + c-c, Domanska et al. (1987b) 275.9 - 0.863 - 1.954 - 1.950 - 0.709 c, + n-c, Domatrska et al. (1987b) 273.3 - 0.316 - 1.230 - 1.208 - 0.464 c, + n-c, Lundager et al. (1976) 279.7 - 0.194 - 2.434 - 2.379 - 0.865 c, + c-c, Domahska and Kniai (199Ob) 274.5 - 1.283 - 2.988 - 2.984 - 1.039 c, +2,2-c, Domadska and Kniai (199Ob) 285.1 -0.155 - 1.840 - 1.769 - 0.671 C,, +2,3-C, Domariska and Kniai (1990b) 272.0 - 0.319 - 1.840 - 1.806 - 0.671 c,, +2-c, Domanska and Kniai (1990b) 297.3 - 0.056 - 1.840 - 1.804 - 0.671 c,, +3-c, Domanska and Kniai (1990b) 273.5 - 0.217 - 1.840 - 1.804 - 0.671 c,, + n-c, Domanska and Kniai (1990b) 277.4 - 0.217 - 1.840 - 1.802 - 0.671 c,, + c-c, Domariska et al. (1987b) 270.5 - 0.802 - 2.215 -2.211 - 0.794

39

TABLE 2 (continued)

Solute + solvent Reference

c, + n-c, c, + n-c,, c, + n-c,, c,, + n-c, c,, + n-c, c,, + c-c, c,, + n-c, c,, + n-c, c32 + n-Clll c32 + n-C,2

c,, + n-c,

c,, + n-c,

c,, + n-c,

c,, + n-c,

C36 + n-C,,

c36 + n-Cl2

Lundager et al. (1976) 279.4 Lundager et al. (1979) 275.9 Lundager et al. (1979) 278.6 Lundager et al. (1976) 281.4 Seyer (1938) 288.3 Seyer (1938) 288.9 Lundager et al. (1976) 282.5 Seyer (1938) 290.8 Seyer (1938) 294.6 Seyer (1938) 293.9 Lundager et al. (1976) 279.5 Lundager et al. (1976) 280.1 Lundager et al. (1976) 278.5 Lundager et al. (1976) 278.6 Lundager et al. (1976) 280.6 Lundager et al. (1976) 279.8

In ym

exp.

- 0.218 - 0.124

0.035 - 1.121 - 0.752 - 1.878 - 1.049 - 1.076 - 0.813 - 0.774 - 0.685 - 0.681 - 0.713 - 0.921 - 0.794 - 0.623

In ym F-H

- 1.419 - 0.698 - 0.446 - 3.009 - 2.308 - 2.751 - 1.809 - 1.441 - 0.943 - 0.631 - 3.599 - 2.792 - 2.215 - 1.787 - 1.202 - 0.831

In ym S-G

- 1.393 - 0.689 - 0.441 - 2.942 - 2.263 - 2.748 - 1.778 - 1.418 - 0.930 - 0.624 - 3.520 - 2.738 - 2.177 - 1.759 - 1.186 - 0.822

In ym Im. F-H

- 0.529 - 0.274 -0.179 - 1.046 - 0.825 - 0.965 - 0.661 - 0.537 - 0.362 - 0.249 - 1.226 - 0.978 - 0.795 - 0.654 - 0.454 - 0.322

Error of temperature determination too large.

systems are in agreement with results obtained by Letcher and Jerman (1976) from GLC.

According to Barbe and Patterson (1978) mixtures of chain compounds with solvents globular in shape should reveal almost ideal behaviour (provided only aliphatic groups are present) owing to the positive contribu- tion arising from the destruction of order in the longer alkane. The data reported in this work corroborate this concept, since mixtures with branched isomers of hexane have very small In ym. It is remarkable, however, that values of In ym for 2,2-dimethylbutane and 2-methylpentane are closer to ideality than those for 2,3_dimethylbutane and 3-methylpentane. The de- struction of order caused by mixing with 2,2-C, and 2-C, should therefore be greater. This conclusion is in agreement with Barbe and Pattersons (1980) interpretation of the heat of mixing data for n-hexadecane with the isomers of hexane.

The role of the combinatorial entropy

In order to examine the importance of the combinatorial effects the experimental acitivity coefficients (obtained from SLE data and also from GLC) have been compared with values predicted using the well known

40

TABLE 3

Activity coefficients at infinite dilution for long-chain paraffins as solvents a

System Reference Temp. In ym In ym In ym In ym solute + solvent (K) exp. F-H S-G Im. F-H n-c, + n-c,, n-c, + n-c,, c-c, + n-c,, n-c, + n-c,, 2,2-c, + n-c,, 2,3-C, + n-C,, 2-c, + n-c,, 3-c, + n-c,, n-c, + n-c,, c-c, + n-c,, n-c, + n-c,, n-c, + n-c,, n-c, + n-c, n-c, + n-c, c-c, + n-c,, n-c, + n-c, n-c, + n-c,, n-c, + n-c,, c-c, + n-c,, n-c, + n-c,, n-c, + n-c, c-c, + n-c,, c-c, + n-c,,

Hicks and Young (1968) 303.15 - 0.087 -0.418 -0.411 - 0.206 Hicks and Young (1968) 303.15 -0.101 -0.316 -0.311 -0.154 Letcher and Jerman (1976) 298.15 - 0.233 - 0.382 - 0.380 - O.i87 Hicks and Young (1968) 303.15 7 0.074 - 0.236 - 0.233 -0.113 Cruickshank et al. (1968) 308.15 - 0.058 - 0.387 - 0.373 - 0.190 Cruickshank et al. (1968) 308.15 - 0.131 - 0.386 - 0.381 -0.190 Cruickshank et al. (1968) 308.15 - 0.094 - 0.386 - 0.381 -0.190 Cruickshank et al. (1968) 308.15 - 0.131 - 0.386 - 0.381 -0.190 Cruickshank et al. (1968) 308.15 - 0.131 - 0.386 - 0.380 -0.190 Letcher and Jerman (1976) 308.15 - 0.294 - 0.457 - 4.455 - 0.226 Hicks and Young (1968) 308.15 -0.113 - 0.300 - 0.296 - 0.146 Hicks and Young (1968) 308.15 - 0.090 - 0.231 - 0.228 -0.111 Hicks and Young (1968) 313.15 -0.186 - 0.568 - 0.558 - 0.284 Hicks and Young (1968) 313.15 -0.161 - 0.454 - 0.447 - 0.224 Letcher and Jerman (1976) 313.15 - 0.368 - 0.527 - 0.526 - 0.263 Hicks and Young (1968) 313.15 - 0.133 - 0.362 - 0.357 - 0.177 Hicks and Young (1968) 333.15 - 0.234 - 0.636 - 0.626 - 0.321 Hicks and Young (1968) 333.15 - 0.219 -0.517 -0.510 - 0.258 Letcher and Jerman (1976) 328.15 - 0.454 - 0.657 - 0.656 - 0.332 Hicks and Young (1968) 343.15 - 0.329 -0.818 - 0.807 - 0.420 Hicks and Young (1968) 343.15 - 0.308 - 0.691 - 0.682 - 0.350 Letcher and Jerman (1976) 338.15 - 0.531 - 0.773 - 0.773 - 0.395 Letcher and Jerman (1976) 343.15 - 0.631 - 0.878 - 0.878 - 0.453

a Exp, experimental; F-H, Flory-Huggins; S-G, Stavermann-Guggenheim; Im. F-H, im- proved Flory-Huggins.

Flory-Huggins expression for the combinatorial entropy:

the Stavermann-Guggenheim combinatorial term:

where

(3)

ai = xiri

q = xi41 2=4 x1r1 +x,r, x141 +x242

41

l.al -

1.m -

0.80 -

0.a .

0.40 .

am - l

0-M 0

-0.M ,e , 1

(5)

am @_I2 a25 0.Y a50 0.62 ai5 a@? 1.m 0

Fig. 1. Values of A In ym = In ~2, - In rCm,t vs. size factor OJ = rr / rz, where In r,,r has been calculated using the Flory-Huggins expression for combinatorial entropy. Filled circles represent mixtures of long-chain n-alkanes as solutes and short-chain, globular or cyclic alkanes as solvents (SLE data); open circles pertain to reversed systems (VLE or GLC data).

and the improved Flory-Huggins term (Kikic et al., 1980):

In $ = In : + 1 - : [ I 1 I

where

The values of the group volume and surface parameters (Y, g) applied in this paper have been taken from the work of Kehiaian and Marongiu (1988).

The results of the predictions are listed along with the experimental data in Tables 2 (SLE data) and 3 (GLC data). Figures 1, 2 and 3 present the difference between the experimental and predicted activity coefficients (A In y) vs. solvent/solute size ratio o. Filled circles represent systems in which a long-chain compound is the solute (SLE data), while open circles represent systems in which a long-chain compound is the solvent. Figures 1 and 2, presenting the results of the Flory-Huggins term and Stavermann- Guggenheim term respectively, are almost similar, indicating that both

1.w - . . ha am . a

b

0.a .

0.40 . l c ii,

oGL. am 0

-0.20 ,m ,

am au a25 0.27 am a62 ai5 a87 1-m 0

Fig. 2. Values of A In ym = In y&, -In y,,, vs. size factor w = rl /r2, where In yc,, has been calculated using the Stavermann-Guggenheim expression for combinatorial entropy. Filled circles represent mixtures of long-chain n-alkanes as solutes and short-chain, globular or cyclic alkanes as solvents (SLE data); open circles pertain to reversed systems WLE or GLC data).

0-m 0.12 ai3 0.33 a5I cl62 lx75 @.a? LDI w

Fig. 3. Values of A In ym = In y& -1n y,,, vs. size factor w = rl /r2, where In yc,r has been calculated using the improved Flory-Huggins (Kikic et al., 1980) expression for combinato- rial entropy. Filled circles represent mixtures of long-chain n-alkanes as solutes and short-chain, globular or cyclic alkanes as solvents (SLE data); open circles pertain to reversed systems (VLE or GLC data).

43

models overestimate the role of the combinatorial entropy, especially in the range 0 < o < 0.5. It is significant that the A In ym is much higher for systems with long-chain alkanes as solutes. There must be a positive contribution to the activity coefficient reflecting the destruction of the orientational order. In Fig. 3, however, the points are more scattered. The improved Flory-Huggins expression underestimates the combinatorial ef- fects in many systems: long-chain paraffins-cycloalkanes, cycloalkanes- long-chain paraffins, long-chain paraffins-long-chain solvents. Neverthe- less for many systems the predictions made by the improved Flory-Huggins model are very good, owing to the more suitable mathematical form of the model. One should remember that Kikic et al. (1980) altered the classical Flory-Huggins expression in an attempt to improve VLE and GLC data predictions. For the data reported in this work the modified Flory-Huggins model behaves similarly to the correlation functions like Wilson or UNI- QUAC if interaction parameters correlated for VLE data are applied to SLE systems (see, for example, Domanska (1986) or Domaiiska (1988)).

CONCLUSIONS

Addition of a short, globular or cyclic solvent to an ordered long-chain paraffin leads to destruction of the conformational order. The values calculated from the Flory-Huggins (or Stavermann-Guggenheim) combi- natorial term are far more negative than the experimental results, indicat- ing that for systems in which a long-chain hydrocarbon is a solute the positive contribution from the Patterson effect must be considered. Systems in which the destruction of order is greatest (2,2-C, or 2-C,) reveal almost ideal solubility, owing to a larger-order contribution.

Classical formulae for the combinatorial entropy do not take into ac- count any order/disorder phenomena, giving rise to systematic deviations between calculated and experimental values. These deviations increase with the solute chain length. The frequently used Kikic version of the Flory-Huggins formula predicts the activity coefficient at infinite dilution with smaller error, but the results are still unsatisfactory.

Existing discrepancies between theory and experiment could be resolved either by introducing a new entropy formula similar to the expression of Kikic et al. (19801, but based on VLE, GLC and SLE data or by incorporat- ing into the classical entropy equations terms accounting for order/dis- order phenomena.

44

ACKNOWLEDGEMENTS

The author would like to express his highest gratitude to Professor D. Patterson and Professor H. Buchowski for their useful comments.

LIST OF SYMBOLS

AC, 2,2-c, 2,3-C, 2-c, 3-c, c-c, c-c, AHIn AK, 4

;

T, T,* x

heat capacity of melting at the melting point 2,2-dimethylbutane 2,3-dimethylbutane 2-methylpentane 3-methylpentane cyclopentane cyclohexane enthalpy of fusion enthalpy of phase transition relative molecular surface relative molecular volume gas constant at melting point temperature transition point temperature mole fraction (solubility)

Greek letters

Yrn the activity coefficient at infinite dilution YC the combinatorial part of the activity coefficient A In ym the difference between the experimental and calculated ym 6 Kikic-Alessi parameter 0 relative molecular surfaces ratio Q, relative molecular volumes ratio w solvent/solute size ratio

REFERENCES

Barbe, M. and Patterson, D., 1978. Orientational order and excess entropies of alkane mixtures. J. Phys. Chem., 82: 40-45.

Barbe, M. and Patterson, D., 1980. Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane. J. Solution Chem., 9: 753-769.

45

Broadhurst, M.G., 1962. An analysis of the solid phase behavior of the normal paraffins. J. Res. Nat. Bur. Stand. Sect. A., 66: 241-249.

Cruickshank, A.J.B., Gainey, B.W. and Young, C.L., 1968. Activity coefficients of hydrocar- bons C, to C, in n-octadecane at 35 C. Trans. Faraday Sot., 64: 337-348.

Denicolo, I., Doucet, J. and Craievich, A.F., 1983. X-ray study of the rotator phase of paraffins (III): Even numbered paraffins C,sH,s, C&H,,, C,,H,,, C,H,, and C,,HS,. J. Chem. Phys., 78: 1465-1469.

Dernini, S. and De Santis, R., 1976. Solubility of solid hexadecane and tetracosane in hexane. Can. J. Chem. Eng, 54: 369-370.

Domafiska, U., 1986. Vapour-liquid-solid equilibrium of eicosanoic acid in one- and two component solvents. Fluid Phase Equilibria, 26: 201-220.

Domatrska, U., 1988. Solubihty of 2,5_dimethylphenol and 3,4_dimethylphenol in binary solvent mixtures containing alcohols. Fluid Phase Equilibria, 40: 259-277.

Domanska, U. and Kniai, K., 1990a. Solid-liquid equilibria of some normal alkanes (C,,,

C,s, C,,)+ hexane, +3_methylpentane, + 2,2_dimethylbutane, or +cyclohexane. Int. Data. Series, Ser. A, Sel. Data Mixtures, 2: 83-93.

Domanska, U. and Kniai, K., 1990b. Solid-liquid equilibria of some normal alkanes (C,,, C 22, C,,) + 2-methylpentane, + 3-methylpentane, + 2,2_dimethylbutane, or + cyclohe- xane. Int. Data. Series, Ser. A, Sel. Data Mixtures, 3: 194-206.

Domanska, U. and Wyrzykowska, D., 1990. Enthalpies of fusion and solid-solid transition of even-numbered paraffins C,,H,,, C,H,,, C&H,,, C,,H,s. Thermochim. Acta., submitted for publication.

Domatiska, U., Hofman, T. and Rolinska, J., 1987a. Solubility and vapour pressures in saturated solutions of high-molecular weight hydrocarbons. Fluid Phase Equilibria, 32: 273-293.

Domanska, U., Rolinska, J. and Szafrafiski, A.M., 1987b. Solid-liquid equilibria in some normal alkanes (C,,-C,)+ heptane or +cyclohexane. Int. Data. Series, Ser. A, Sel. Data Mixtures, 4: 269-276.

Goates, J.R., Ott, J.B., Moellmer, J.F. and Farrell, D.W., 1979. (Solid+liquid) phase equilibria in n-hexane + cyclohexane and benzene + p-xylene. J. Chem. Thermodyn., 11: 709-711.

Hicks, C.P. and Young, C.L., 1968. Activity coefficients of C,-Cs in C,,-C,, n-alkanes. Trans. Faraday Sot., 64: 2675-2682.

Hoerr, C.W. and Harwood, H.J., 1951 Solubihties of high molecular weight aliphatic compounds in n-hexane. J. Org. Chem., 16: 779-791.

Kehiaian, H.V. and Marongiu, B., 1988. A comparative study of thermodynamic properties and molecular interactions in mono- and polychloroalkane + n-alkane or + cyclohexane mixtures. Fluid Phase Equilibria., 40: 23-78.

Kikic, I., Alessi, P., Rasmussen, P. and Fredenslund, Aa. 1980. Can J. Chem. Eng., 58: 253. Kniai, K., 1991. Solubility of long-chain hydrocarbons in various alkanes. Experiments and

prediction. J. Chem. Eng. Data, in press. Letcher, T.M. and Jerman, P., 1976. Activity coefficients of cyclohexane+ n-alkane mix-

tures. J. Chem. Thermodyn., 8: 127-131. Lundager Madsen, H.E. and Boistelle, R., 1976. Solubility of long-chain n-paraffins in

pentane and heptane. J. Chem. Sot. Faraday Trans. 1, 72: 1078-1081. Lundager Madsen, H.E. and Boistelle, R., 1979. Solubility of octacosane and hexatriacon-

tane in different n-alkane solvents. J. Chem. Sot. Faraday Trans. 1, 75: 1254-1258. Messerly, J.F., Guthrie, G.B., Todd, S.S. and Finke, H.L., 1967. Revised thermodynamic

functions for the n-alkanes C,-C,,. J. Chem. Eng. Data, 12: 338-346.

Ott, J.B. and Goates, J.R., 1983. (Solid+liquid) phase equilibria in binary solutions containing benzene, cycloalkanes, n-alkanes and tetrachloromethane. An equation for representing (solid + liquid) phase equilibria. J. Chem. Thermodyn., 15: 267-278.

Patterson, D., Tewari, Y.B. and Schreiber, P., 1972. Interpretation of activity coefficients in alkane systems. J. Chem. Sot. Faraday Trans. 1, 68: 885-894.

Schaerer, A.A., Busso, C.J., Smith, A.E. and Skinner, L.B., 1955. Properties of pure normal alkanes in the C,, to C,, range. J. Am. Chem. Sot., 77: 2017-2019.

Seyer, W.F., 1938. Mutual solubilities of hydrocarbons. II. The freezing point curves of dotriacontane (dicetyl) in dodecane, decane, octane, hexane, cyclohexane and benzene. J. Am. Chem. Sot., 50: 827-830.

Tancrede, P., Bothorel, P., De St. Romain, P. and Patterson, D., 1977. Interactions in alkane systems by depolarized Rayleigh scattering and calorimetry. J. Chem. Sot. Faraday Trans. 2., 73: 15-28.