Critical temperatures of n-alkanes

The critical temperature may be considered to be a measure of the intensity of interaction between the n particles of a system, as produced by van der Waals forces. Although the critical temperature for n l is practically independent of the number of particles, there exists a possibility for estimating the influence of the number of i structural subunits composing a particle based on the value of the critical temperature of a macroscopic system. Critical temperatures are especially suitable for the comparison of numerical values within a homologous sequence because at these temperatures the systems are in corresponding states. 

If Tci and Tck are designated the critical temperatures of two different n-alkanes containing i and k carbon atoms, we may tentatively let the dimensionless ratio T cJT c.k be equal to the ratio of the two corresponding interaction functions wie and wk e in Eq. (6-9)  

Experimental values for the critical temperatures of n-alkanes are known up to eicosane (i=20) (Reid et al., 1987). For longer molecular chains the experimental determination of the critical temperature is not possible with sufficient accuracy due to the onset of thermal decomposition. 

The remarkable coincidence between the ratios of the critical temperatures, TCJTC within the homologous series and the ratios of the corresponding values of the interaction function w Jw supports the interpretation that this function is a measure of the energy density of interaction. 

Due to the translation and rotation of particles in the liquid state of a macroscopic system, the value of the interaction function may be assumed to be independent of the configuration of the particles within the system. Therefore, there is no need for data related to orientation. This is also valid for the i chainlike subunits of an alkane molecule. Due to the possibility of a free rotation of any of the i subunits around the bond axis with the neighboring subunits, a relative motion of segments of several subunits is also possible. 

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Figure 6-1 Critical temperatures of n-alkanes as a function of the number i of carbon atoms. Calculated values using Eq. (6-11) (—), measured values ( ) and limit value, Tc (-).

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