A segment model for solutions of n-alkanes and n-alkenes

Abstract

Infinite-dilution activity coefficients of saturated and unsaturated normal hydrocarbons (C₅ to C₈)in n-alkane solvents (C₁₆ to C₂₈), mostly at 35°C, are discussed in terms of the segment version of the quasi-lattice model. The data were obtained by medium-pressure, packed-column G.L.C.; new values for n-alk-1-enes and for two (α,ω) n-alkadienes are included.

In the two-types-of-segment formalism as previously developed, the interactional part of the solute activity coefficient was calculated from a single adjustable parameter, the segment interchange energy. Here we extend the formalism to cover three different types of segment, with three characteristic segment interchange energies. The formalism is also generalized by allowing the number of segments per chain unit (e.g., the —CH₃ unit) to vary, thus increasing the number of adjustable parameters to five. The formalism has certain ambiguities, but data for the three types of solute, n-alkane, n-alk-1-ene, and (α,ω) n-alkadiene, in several n-alkane solvents, for example, should suffice to test the model.

Instead of finding the best-fit values of the five parameters by the conventional least-squares method, ranges of the parameters are scanned to produce contours of the standard deviation. This more powerful method reveals underlying functional relationships between the parameters. There does exist a region of the five-dimensional parameter space which correlates thirty low-temperature (below 50°C) results (sixteen different systems including all three types above) well within the estimated experimental uncertainty. Allowing a temperature variation of the segment interchange energies brings a further twelve high-temperature (55°C and above) n-alkane + n-alkane results (eight systems) into equally good correlation. The optimum values of the five parameters indicate that the —CH₃ and —CHCH₂ terminal chain units show similar interchange energies against the appropriate number of >CH₂ units, and also that, for the —CH₃ unit, this number is between 3 and 4.