Simple relationships for the estimation of melting temperatures of homologous series

The melting behavior of a homologous series is described in terms of the me lting of the parent molecule and of the polymer the series eventually forms . For those series characterized by a parent melting below the melting temp erature of the related polymer, the melting behavior can be described quant itatively by the hyperbolic function T-f(n) = T-f(infinity)[1 - 1/(mn + b)] , where T-f(n) refers to the melting temperature of a compound with n repea t units, T-f(infinity) is the melting temperature of the polymer, and m and b are two variables used in fitting the data. A plot of [1/(1 - T-f(n/T-f( infinity))] against n results in a straight line with slope m and intercept b. This linear relationship provided the analytical form of the equation d escribed above. For series with parents exhibiting melting temperatures hig her than those of the related polymer, a linear correlation is observed whe n [1/(1 - T-f(infinity)/T-f(n))] is plotted against (n). This resulted in t he hyperbolic relationship T-f(n) = T-f(infinity)/[1 - 1/(mn + b)]. These e quations appear applicable for the quantitative evaluation of the melting b ehavior of any homologous series, provided care is taken to consider compou nds characterized by the same symmetry number. Molecules containing odd and even numbers of repeat groups are generally treated separately. The hyperb olic behavior exhibited by the melting temperature in most series appears c haracteristic of molecules that seem to pack similarly in the solid state. Series with members exhibiting liquid-crystal behavior are successfully mod eled by these equations, provided the transition correlated is the temperat ure at which the liquid becomes isotropic. The usefulness of these equation s was tested by selecting three data points from each series to provide val ues for m and b. The melting temperatures of most compounds in the series w ere estimated using these parameters. This resulted in a standard deviation of +/-6.6 K between experimental and calculated values based on a total of 995 compounds.