Nine trialkylamines, triethyl- to trihexylamine trioctyl-, tridodecyl, tri(methyl-2-butyl)-, and dimethyldodecylamine have been used for heats of mixing of the following systems at 298 K: A, fourteen systems made of all the possible binary mixtures (except one) of the six shorter amines; B, twelve systems made of a long chain amine, trioctyl-, tridodecyl- or dimethyldodecylamine with the four shorter members of the series; C, two systems consisting of the mixture of two long-chain compounds, trioctylamine with tridodecyl- and dimethyldodecylamine. Heats for the class A systems are less than or equal to 40 J/mol, indicating no net effect of the small polarity of the shorter members of the series. The experimental HE of these mixtures are compared with two theories. The Monte Carlo approach gives good predictions but the heats calculated with the Snider–Herrington theory are too negative. Heats of the class B systems are suitable for the investigation of two new contributions to the heats of mixing, the positive heat of disordering of long-chains HE(dis.) and the negative heat found in systems where one of the components is sterically hindered, HE(ster.hindr.). HE(dis.) found with the long-chain amines indicates an orientational order larger than in the case of the n-alkane of the same chain-length but equivalent to that found in the tetraalkyltin compounds of the same length. Recent work has shown that the tetrapropyl and tetraethyltin derivatives when mixed with long-chain alkanes or tin derivatives give rise to a HE(ster.hindr.) contribution. From this work and the present study, the steric hindrance contributions of five sterically hindered compounds tetraethyltin and tetrapropyltin, triethyl- and tripropylamine, and 3,3-diethylpentane mixed with different second components are calculated. The steric hindrance contribution is found proportional to the volume of the second component and increasing in the following order of the sterically hindered component: triethyl- < tripropylamine < tetraethyl- < tetrapropyltin < 3,3-diethylpentane. Heats of the class C systems are small without significant contribution of HE(dis.) due to the fitting of the long-chains in solution.
Discrete-lattice model approach to the tunneling between d-wave superconductors: Interference of tunnel bonds