TY - JOUR

T1 - Nucleation in systems with multiple stationary states

AU - Nitzan, A.

AU - Ortoleva, P.

AU - Ross, J.

N1 - Funding Information:
To conclude this section we should note that even though the dynamics of nucleus growth as given by eqn (3.16) or fig. 5 give important information on the rate of nucleation of one phase within another the rate of this process depends also on the rate of formation of nuclei by spontaneous fluctuations which is not discussed in the present work. We thank John M. Deutch for helpful discussions. This work was supported in part by the National Science Foundation and Project SQUID Office of Naval Research.

PY - 1974

Y1 - 1974

N2 - We consider a reaction diffusion system, far from equilibrium, which has multiple stationary states (phases) for given ranges of external constraints. If two stable phases are put in contact, then in general one phase annihilates the other and in that process there occurs a single front propagation (soliton). We investigate the macroscopic dynamics of the front structure and velocity for two model systems analytically and numerically, and for general reaction-diffusion systems by a suitable perturbation method. The vanishing of the soliton velocity establishes the analogue of the Maxwell construction used in equilibrium thermodynamics. The problem of nucleation of one phase imbedded in another is studied by a stochastic theory. We show that if the reaction dynamics is derived from a generalized potential function then the macroscopic steady states are extrema of the probability distribution. We use this result to obtain an expression for the critical radius of a nucleating phase and confirm the prediction of the stochastic theory by numerical solution of the deterministic macroscopic kinetics for a model system.

AB - We consider a reaction diffusion system, far from equilibrium, which has multiple stationary states (phases) for given ranges of external constraints. If two stable phases are put in contact, then in general one phase annihilates the other and in that process there occurs a single front propagation (soliton). We investigate the macroscopic dynamics of the front structure and velocity for two model systems analytically and numerically, and for general reaction-diffusion systems by a suitable perturbation method. The vanishing of the soliton velocity establishes the analogue of the Maxwell construction used in equilibrium thermodynamics. The problem of nucleation of one phase imbedded in another is studied by a stochastic theory. We show that if the reaction dynamics is derived from a generalized potential function then the macroscopic steady states are extrema of the probability distribution. We use this result to obtain an expression for the critical radius of a nucleating phase and confirm the prediction of the stochastic theory by numerical solution of the deterministic macroscopic kinetics for a model system.

UR - http://www.scopus.com/inward/record.url?scp=0001600449&partnerID=8YFLogxK

U2 - 10.1039/FS9740900241

DO - 10.1039/FS9740900241

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AN - SCOPUS:0001600449

SN - 0301-5696

VL - 9

SP - 241

EP - 253

JO - Faraday Symposia of the Chemical Society

JF - Faraday Symposia of the Chemical Society

ER -