Three-segment interactions

This Hamiltonian has a ground state with 50=l/2. Therefore, if for the strip we take into account only interactions between nearest segments (i.e., a two-particle approximation) we obtain the ferromagnetic ground state. Only the inclusion of three-segment interactions leads to the correct ground state spin of the lattice strip. 

Fig. 9.2. Diagrammatic structure underlying Eq, (9,32) The shaded blob represents a factor of tlie average segment density coupling to a three-body interaction.

The interaction of the BM3/FMN domain with the BMP domain involves four segments of the former and three segments of the latter (Figure 5). The largest such segment of BM3/FMN is the pi to al loop and... 

Thus, with each polymer segment, we can associate an orientation and a wave vector q. In the same way, with each interaction line, we can associate an orientation and a wave vector. Each wave vector can be considered to be transferred in the direction of the arrow which defines the corresponding orientation. We note that a two-body interaction transfers one wave vector q, whereas a three-body interaction transfers two wave vectors q and q". We also remark that the orientation of each line is arbitrary, but if the vector q is associated with an orientation, the vector - q must be associated with the opposite orientation. On a polymer, it is generally convenient to choose the direction in which s increases to define the orientations. Finally, we note that a factor (27i)"d corresponds to the introduction of each wave vector. 

Although the lattice model of the liquid state, upon which equations (26) and (27) are based, is open to criticism the treatment does describe a well-defined procedure for dividing a molecule into segments, counting the segment interactions of various kinds, and relating these to the thermodynamic properties of the mixture. The lattice model has frequently been applied at any one of three... 

The process of polymer adsorption involves a number of interactions that need to be carefully considered. Three main interactions are obvious, i.e. the surface/solvent, the chain/solvent and the chain/surface. For adsorption to take place, then unfavourable entropy loss when a polymer molecule approaches a surface must be compensated for by an energy of adsorption term. One usually describes the adsorption energy in terms of the value per segment in direct contact with the surface, addition, the polymer molecule... 

Simulations on a cubic lattice have been used to study the self-assembly into micelles by diblock copolymers with Na segments of block A and Nb segments of block B. Previous work has shown these simulations can be used to measure the critical micelle concentration (cmc). In the present work, the pairwise interactions cause the medium to behave as a poor solvent for block A and a good solvent for block B. The purpose is to determine the relative importance of the three pairwise interactions between different species, denoted by Eas E ab and Egg, for the cmc. Here ExY denotes the dimensionless pairwise interaction, Uxv/ Ty where UxY is the pairwise interaction energy of segments of species X and Y. The three species involved here are segments of A, segments of B, or solvent (S). Hence we examine all E xy where X Y. The results are compared with previous work that focused attention on the dominant pairwise interaction parameter, E as The effects of E ab bs important for asym-... 

At the intramolecular level, the shift of the 9 point must be observed with a rather large w and provided that the segment concentration in a coil is quite high, which depends on coil topology. Eg. three-particle interactions are most probable in branching (star-like) macromolecules with other conditions being equal. 

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