arXiv subjects

Yukio Saito

Publications and source records attributed to Yukio Saito.

At least 19 recordsLinked to original sources

arXiv2009

Selection of Crystal Chirality: Equilibrium or Nonequilibrium?

To study the solution growth of crystals composed of chiral organic molecules, a spin-one Ising lattice gas model is proposed. The model turns out to be equivalent to the Blume-Emery-Griffiths model, which shows an equilibrium chiral symmetry breaking at low temperatures. The kinetic Monte Carlo simulation of crystal growth, however, demonstrates that Ostwald ripening is a very slow process with a characteristic time proportional to the system size: The dynamics is nonergodic. It is then argued that by incorporating grinding dynamics, homochirality is achieved in a short time, independent of the system size. Grinding limits cluster sizes to a certain range independent of system size and at the same time keeps the supersaturation so high that population numbers of average-sized clusters grow. If numbers of clusters for two types of enantiomers differ by chance, the difference is amplified exponentially and the system rapidly approaches the homochiral state. Relaxation time to the final homochiral state is determined by the average cluster size. We conclude that the system should be driven and kept in a nonequilibrium state to achieve homochirality.

cond-mat.stat-mech↗

arXiv2008

Chiral Crystal Growth under Grinding

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 rinding, an exponential increase of crystal enantiomeric excess to homochiral state is realized.

cond-mat.stat-mech↗

arXiv2008

Fluctuation Induced Homochirality

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.

physics.chem-ph↗

arXiv2007

Shape of Heteroepitaxial Island Determined by Asymmetric Detachment

Square lattice gas models for heteroepitaxial growth are studied by means of kinetic Monte Carlo simulations, in order to find a possible origin of anisotropic island shape observed in growth experiments of long organic molecules. When deposited molecules form clusters irreversibly at their encounter during surface diffusion, islands grow in a ramified dendritic shape, similar to DLA. Introduction of molecular detachment from edges makes islands compact with smooth edges. Tilting of adsorbed long molecules or steps in a vicinal substrate may induce orientation-dependence in the detachment rate of edge molecules from an island. In simulations with orientation-dependent detachment rates, a clear anisotropy in an island shape is observed. Shape anisotropy on a vicinal substrate is enhanced as steps get dense, in agreement to the experimental observation.

cond-mat.mtrl-sci↗

arXiv2007

Dewetting of a solid monolayer

We report on the dewetting of a monolayer on a solid substrate, where mass transport occurs via surface diffusion. For a wide range of parameters, a labyrinthine pattern of bilayer islands is formed. An irreversible regime and a thermodynamic regime are identified. In both regimes, the velocity of a dewetting front, the wavelength of the bilayer island pattern, and the rate of nucleation of dewetted zones are obtained. We also point out the existence of a scaling behavior, which is analyzed by means of a geometrical model.

cond-mat.soft↗

arXiv2007

Two-Dimensional Island Shape Determined by Detachment

Effect of an anisotropic detachment on a heteroepitaxial island shape is studied by means of a kinetic Monte Carlo simulation of a square lattice gas model. Only with molecular deposition followed by surface diffusion, islands grow in a ramified dendritic shape, similar to DLA. Introduction of molecular detachment from edges makes islands compact. To understand an anisotropic island shape observed in the experiment of pentacene growth on a hydrogen-terminated Si(111) vicinal surface, asymmetry in detachment around the substrate step is assumed. Edge molecules detach more to the higher terrace than to the lower terrace. The island edge from which molecules are easy to detach is smooth and the one hard to detach is dendritic. If islands are close to each other, islands tend to align in a line, since detached molecules from the smooth edge of the right island are fed to the dendritic and fast growing edge of the left island.

cond-mat.mtrl-sci↗

arXiv2006

Rate Equation Approaches to Amplification of Enantiomeric Excess and Chiral Symmetry Breaking

Theoretical models and rate equations relevant to the Soai reaction are reviewed. It is found that in a production of chiral molecules from an achiral substrate autocatalytic processes can induce either enantiomeric excess (ee) amplification or chiral symmetry breaking. Former terminology means that the final ee value is larger than the initial value but depends on this, whereas the latter means the selection of a unique value of the final ee, independent of the initial value. The ee amplification takes place in an irreversible reaction such that all the substrate molecules are converted to chiral products and the reaction comes to a halt. The chiral symmetry breaking is possible when recycling processes are incorporated. Reactions become reversible and the system relaxes slowly to a unique final state. The difference between the two behaviors is apparent in the flow diagram in the phase space of chiral molecule concentrations. The ee amplification takes place when the flow terminates on a line of fixed points (or a fixed line), whereas symmetry breaking corresponds to the dissolution of the fixed line accompanied by the appearance of fixed points. Relevance of the Soai reaction to the homochirality in life is also discussed.

cond-mat.stat-mech↗

arXiv2006

Stochastic Approach to Enantiomeric Excess Amplification and Chiral Symmetry Breaking

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 random walk model. For systems with a recycling process, 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 process, 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.

cond-mat.stat-mech↗

arXiv2006

Diffusion Enhances Chirality Selection

Diffusion effect on chirality selection in a two-dimensional reaction-diffusion model is studied by the Monte Carlo simulation. 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 the nonlinear autocatalysis as well as recycling process, and the chiral symmetry breaking is monitored by an enantiomeric excess $ϕ$. Without dilution a strong nonlinear autocatalysis ensures chiral symmetry breaking. By dilution, the chiral order $ϕ$ decreases, and the racemic state is recovered below the critical concentration $c_c$. Diffusion effectively enhances the concentration of chiral species, and $c_c$ decreases as the diffusion coefficient $D$ increases. The relation between $ϕ$ and $c$ for a system with a finite $D$ fits rather well to an interpolation formula between the diffusionless(D=0) and homogeneous ($D=\infty$) limits.

cond-mat.stat-mech↗

arXiv2005

Chirality Selection in Open Flow Systems and in Polymerization

As an attempt to understand the homochirality of organic molecules in life, a chemical reaction model is proposed where the production of chiral monomers from achiral substrate is catalyzed by the polymers of the same enatiomeric type. This system has to be open because in a closed system the enhanced production of chiral monomers by enzymes is compensated by the associated enhancement in back reaction, and the chiral symmetry is conserved. Open flow without cross inhibition is shown to lead to the chirality selection in a general model. In polymerization, the influx of substrate from the ambience and the efflux of chiral products for purposes other than the catalyst production make the system necessarily open. The chiral symmetry is found to be broken if the influx of substrate lies within a finite interval. As the efficiency of the enzyme increases, the maximum value of the enantiomeric excess approaches unity so that the chirality selection becomes complete.

physics.bio-ph↗

arXiv2004

Random Deposition Model with a Constant Capture Length

We introduce a sequential model for the deposition and aggregation of particles in the submonolayer regime. Once a particle has been randomly deposited on the substrate, it sticks to the closest atom or island within a distance \ell, otherwise it sticks to the deposition site. We study this model both numerically and analytically in one dimension. A clear comprehension of its statistical properties is provided, thanks to capture equations and to the analysis of the island-island distance distribution.

cond-mat.stat-mech↗

arXiv2004

Chirality Selection in Crystallization

A cluster growth model is proposed to study chiral symmetry breaking in stirred crystallization from an achiral element. Achiral monomers are assumed to coagulate to form chiral clusters from dimers to hexamers. Due to the stirring, the hexamers break into dimers. The coagulation of two dimers into a tetramer also occurs. The fixed point analysis of coupled rate equations of cluster densities and their numerical integrations show that the chiral symmetry becomes broken if dimers are critical and able to dissociate back to achiral monomers. The chirality selection is understood by showing that, in a quasi-steady approximation, the rate equations reduce to those of dimers with nonlinear autocatalysis and decomposition.

cond-mat.other↗

arXiv2004

Chirality Selection Models in a Closed System

Recently the first chemical systems which show the amplification of enantiometric excess (ee) was found. Inspired by these experiments, we propose a few chemical reaction models in a closed system. The reactions consist of autocatalytic production of chiral molecules and their decomposition processes. By means of flow diagrams in the phase space of enatiometric concentrations, chiral symmetry breaking is studied. Without any destruction processes, the quadratic autocatalysis leads to the amplification of ee, but the flow is attracted to a fixed line, which is only marginally stable. The destruction processes alter the attractor structure completely. With a cross inhibition the linear autocatalysis is sufficient for the chiral symmetry breaking with a complete homochirality. With a back reaction, the quadratic autocatalysis is necessary to bring about the chiral symmetry breaking. The final ee is not complete if there is a racemization process.

physics.bio-ph↗

arXiv2004

Drift-Induced Step Instabilities Due to the Gap in the Diffusion Coefficient

On a Si(111) vicinal face near the structural transition temperature, the $1 \times 1$ structure and the $7 \times 7$ structure coexist in a terrace: the $1 \times 1$ structure is in the lower side of the step edge and the $7 \times 7$ structure in the upper side. The diffusion coefficient of adatoms is different in the two structures. Taking account of the gap in the diffusion coefficient at the step, we study the possibility of step wandering induced by drift of adatoms. A linear stability analysis shows that the step wandering always occurs with step-down drift if the diffusion coefficient has a gap at the step. Formation of straight grooves by the step wandering is expected from a nonlinear analysis. The stability analysis also shows that step bunching occurs irrespective of the drift direction if the diffusion in the lower side of the step is faster. The step bunching disturbs the formation of grooves. If step-step repulsion is strong, however, the step bunching is suppressed and the straight grooves appear. Monte Carlo simulation confirms these predictions.

cond-mat.mtrl-sci↗

arXiv2004

Homochirality proliferation in space

To understand the chirality selection in the biological organic system, a simple lattice model of chemical reaction with molecular diffusion is proposed and studied by Monte Carlo simulations. In addition to a simple stochastic process of conversions between an achiral reactant A and chiral products, R and S molecules, a nonlinear autocatalysis is incorporated by enhancing the reaction rate from A to R (or S), when A is surrounded by more than one R (or S) molecules. With this nonlinear autocatalysis, the chiral symmetry between R and S is shown to be broken in a dense system. In a dilute solution with a chemically inactive solvent, molecular diffusion accomplishes chirality selection, provided that the initial concentration is higher than the critical value.

physics.chem-ph↗

arXiv2003

Complete homochirality induced by the nonlinear autocatalysis and recycling

A nonlinear autocatalysis of a chiral substance is shown to achieve homochirality in a closed system, if the back-reaction is included. Asymmetry in the concentration of two enantiomers or the enantiometric excess increases due to the nonlinear autocatalysis. Furthermore, when the back-reaction is taken into account, the reactant supplied by the decomposition of the enantiomers is recycled to produce more and more the dominant one, and eventually the homochirality is established.

physics.chem-ph↗

arXiv2003

Two-Dimensional Nucleation with Edge and Corner Diffusion

The effect of edge and corner diffusions on the morphology and on the density of islands nucleated irreversibly on a flat substrate surface is studied. Without edge and corner diffusion, islands are fractal. As an edge diffusion constant $D_e$ increases, islands tend to take a cross shape with four needles in the $< 10 >$ direction. Additional corner diffusion with a diffusion constant $D_c$ yields square islands. When $D_e$ is small relative to the surface diffusion constant $D_s$, the square corner shows the Berg instability to produce hopper growth in the $<11>$ direction. The corner diffusion influences the island number density $n$. At a deposition flux $F$ with a small $D_c$, mainly monomers are mobile and $n \propto (F/D_s)^{1/3}$. At large $D_c$, dimers and trimers are also mobile and $n \propto F^{3/7} D_s^{-5/21} D_c^{-4/21}$. The $F$ dependence is in good agreement to the rate equation analysis, but the dependence on $D_c$ cannot be explained by the theory.

cond-mat.mtrl-sci↗

arXiv2002

Morphology of axisymmetric vesicles with encapsulated filaments and impurities

The shape deformation of a three-dimensional axisymmetric vesicle with encapsulated filaments or impurities is analyzed by integrating a dissipation dynamics. This method can incorporate systematically the constraint of a fixed surface area and/or a fixed volume. The filament encapsulated in a vesicle is assumed to take a form of a rod or a ring so as to imitate cytoskeletons. In both cases, results of the shape transition of the vesicle are summarized in phase diagrams in the phase space of the vesicular volume and a rod length or a ring radius. We also study the dynamics of a vesicle with impurities coupled to the membrane curvature. The phase separation and the associated shape deformation in the early stage of the dynamical evolution can well be explained by the linear stability analysis. Long runs of simulation demonstrate the nonlinear coarsening of the wavy deformation of the vesicle in the late stage.

cond-mat.soft↗