論文

To study the establishment of homochirality observed in the crystal growth experiment of chiral molecules from a solution under grinding, we extend the lattice gas model of crystal growth as follows. A lattice site can be occupied by a chiral molecule in R or S form, or can be empty. Molecules form homoclusters by nearest neighbor bonds. They change their chirality if they are isolated monomers in the solution. Grinding is incorporated by cutting and shafling the system randomly. It is shown that Ostwald ripening without grinding is extremely slow to select chirality, if possible. Grinding alone also cannot achieve chirality selection. For the accomplishment of homochirality, we need an enhanced chirality change on crystalline surface. With this "autocatalytic effect" and the recycling of monomers due to grinding, an exponential increase of crystal enantiomeric excess to homochiral state is realized.

We study equilibrium shapes of adsorbate crystals by allowing a possibility of dislocations on an elastic substrate in a two-dimensional lattice model. The ground state energy is calculated numerically with the use of an elastic lattice Green's function. From the equilibrium shapes determined for various coverages, we infer the growth mode. As the misfit parameter increases, the growth mode changes from the Frank-van der Merwe (FM) to the Stranski-Krastanov (SK), further to the FM with dislocations for a parameter range of ordinary semiconductor materials. Conceivable growth modes such as the SK with dislocations appear in a parameter range between the SK and the FM with dislocations.

We propose a new mechanism for the achievment of homochirality in life without any autocatalytic production process. Our model consists of a spontaneous production together with a recycling cross inhibition in a closed system. It is shown that although the rate equations for this system predict no chiral symmetry breaking, the stochastic master equation predicts complete homochirality. This is because the fluctuation induced by the discreteness of population numbers of participating molecules plays essential roles. This fluctuation conspires with the recyling cross inhibition to realize the homochirality.

We study misfit dislocations in a two-dimensional elastic lattice model of epitaxy using Green's function. The interaction between the dislocations of the lattice model is compared with that of continuum elasticity theory. It is found that the behavior of the lattice model at a long distance agrees with that of standard continuum theory, but an additional interaction between dislocations due to extra forces around the dislocation core is important. The extra forces also lead to an increase in the dislocation interval. On a flat adsorbate surface with a periodic array of misfit dislocations, the preferential adsorption site is found to be either on the top or at the midpoint of the dislocations depending on the sign of the force dipole moment of the adatom and the sign of the misfit parameter.

Stochastic aspects of chemical reaction models related to the Soai reactions as well as to the homochirality in life are studied analytically and numerically by the use of the master equation and a directed random walk model. For systems with a recycling back reaction, a unique final probability distribution is obtained by means of detailed balance conditions. With a nonlinear autocatalysis the distribution has a double-peak structure, indicating the chiral symmetry breaking. This problem is further analyzed by examining eigenvalues and eigenfunctions of the master equation. In the case without recycling, final probability distributions depend on the initial conditions. In the nonlinear autocatalytic case, time-evolution starting from a complete achiral state leads to a final distribution which differs from that deduced from the nonzero recycling result. This is due to the absence of the detailed balance, and a directed random walk model is shown to give the correct final profile. When the nonlinear autocatalysis is sufficiently strong and the initial state is achiral, the final probability distribution has a double-peak structure, related to the enantiomeric excess amplification. It is argued that with autocatalyses and a very small but nonzero spontaneous production, a single mother scenario could be a main mechanism to produce the homochirality

The diffusion effect on chirality selection in a two-dimensional reaction-diffusion model is studied by Monte Carlo simulations. The model consists of achiral reactants A which turn into either of the chiral products R or S in a solvent of chemically inactive vacancies V. The reaction contains a nonlinear autocatalysis as well as a recycling process, and the chiral symmetry breaking is monitored by an enantiomeric excess (ee) . Without dilution a strong nonlinear autocatalysis ensures chiral symmetry breaking. By diluting a diffusionless system, the ee decreases and a racemic state is recovered below a critical concentration cc. When the diffusion is allowed, the steady value of increases and cc decreases. As for the relation between the ee and the concentration c, a formula interpolating between the diffusionless (D=0) and the homogeneous (D=) limits is proposed by incorporating the diffusional enhancement of the concentrations of chiral species. Diffusion also accelerates the development of the chiral order, and the time required to establish the order in a system of a size L2 is inversely proportional to the diffusion constant D as L2/D.