Strong Phase Separation in a Model of Sedimenting Lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a 1-d lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels--- hence the term Strong Phase Separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses epsf, three ps figure

2,8'-Disubstituted-1,1'-Binaphthyls:A New Pattern in Chiral Ligands

The title binaphthyls 19 and 26, which are the positional isomers of 2-methoxy-2'-(diphenylphosphino)-1,1'-binaphthyl (MOP, 19) and 2-amino-2'-hydroxy-1,1'-binaphthyl (NOBIN, 26), have been synthesized by Suzuki coupling as the key step (10 + 15→18), followed by functional group transformations, involving C-P and C-N bond formation (18→19 and 18→23). Racemic intermediate 22 was resolved by cocrystallization with N-benzylcinchonidinium chloride and the absolute configuration determined by X-ray crystallography. These novel binaphthyls are configurationally stable and, as such, potentially usable as chiral ligands in asymmetric reactions. Michael addition of the glycine-derived enolate 40 to methyl acrylate, carried out in the presence of (R)-(-)-27 as the chiral phase-transfer catalyst, afforded L-glutamic acid (S)-(+)-43 of 92% ee (after hydrolysis of the primary product)