Identification of the insertion sites Sample Clauses

Identification of the insertion sites. Considering the shape and size of DBT compared to anthracene, we examined substitutions of two or three host molecules. The initial orientation of DBT was parallel to the (b,c) crystal plane, with the long axis close to ’b’. Figure 4.5 shows the substitutions envisaged here, with replacement of two (substitutions III and V) or three (substitutions I, II, and IV) host molecules. Note that, for all of these, equivalent substitutions (noted I’-V’) are obtained by symmetry in a glide plane parallel to (b,c). Properties related by this symmetry, e.g. the tilts of the DBT long axis off the host’s ’b’ axis, will change sign on going from (I)-(V) to (I’)-(V’). Substitutions of two molecules along the ’a’ crystal axis was rejected on grounds of packing and hindrance by the host molecule at the centre of the (a,b) cell face. While sublimation crystal growth is a non-equilibrium process, it should be stressed that for the present purposes, it is nonetheless the equilibrium Xxxxx free energy differences between different substitutions under ambient conditions, rather than the minimised energies of optimised structures, that are more appropriate to judge which substitution sites are most likely. These free energies were estimated from 1 ns simulations of a variety of substitutions of two or three hosts by one DBT molecule. The models were subsequently quenched to 1 K (50 ps runs) for comparison with experimental data obtained at helium temperatures. Thus, it turns out that the structures with lowest potential energy at helium temperatures are not always the most probable at room temperature. Free energy differences between substitutions of the same number of an- thracene sites are just the differences in the total internal energies of the simulations. Differences between substitutions of different numbers of host molecules include an entropic contribution, estimated (cf. [105]) by assuming the doped crystal is in equilibrium with anthracene vapour: ∆G = ∆E + E − 2RT. (4.3) Taking the values of ∆G (at 300 K and 1 bar) for the substitution I as a reference, we found substitution II at 1.3 kcal/mol, substitution III at