Metastability states

Within this general framework there have been many different systems modelled and the dynamical, statistical prefactors have been calculated. These are detailed in [42]. For a binary mixture, phase separating from an initially metastable state, the work of Langer and Schwartz [48] using die Langer theory [47] gives the micleation rate as... 

Berezhkovskii A M and Zitserman V Yu 1992 Generalization of the Kramers-Langer theory decay of the metastable state in the case of strongly anisotropic friction J. Phys. A Math. Gen. 25 2077-92... 

The probability matrix plays an important role in many processes in chemical physics. For chemical reactions, the probability of reaction is often limited by tunnelling tlnough a barrier, or by the fonnation of metastable states (resonances) in an intennediate well. Equivalently, the conductivity of a molecular wire is related to the probability of transmission of conduction electrons tlttough the junction region between the wire and the electrodes to which the wire is attached. 

The first excited singlet state, 2 Sq, is also metastable in the sense that a transition to the ground state is forbidden by the Af selection rule but, because the transition is not spin forbidden, this state is not so long-lived as the 2 Si metastable state. 

Ideally, N is a long-lived, metastable state with an energy similar to that of the level of M which is being pumped. 

The reaction quotient may be measured, at least in principle, for the reacting system at any time. If Z is observed not to change, the system is at equiUbrium, or trapped in a metastable state that serves as a local equiUbrium. In informal work, a time-independent Z is identified directiy with the equiUbrium constant... 

Fig 5 3 Changes in the potential energy of a static mechanical system tell us whether it is in a stable, unstable or metastable state. 

AR Dinner, M Karplus. A metastable state m folding simulations of a protein model. Nature Struct Biol 5 236-241, 1998. 

Equation (3.32) demonstrates that the decay rate for a metastable state is equal to the inverse period of classical vibrations in the well ( attempt frequency ) times the barrier transparency. 

Now we take up the calculation of the rate constant for the decay of a metastable state. In principle it can be done by statistically averaging E from (3.32), but there is a more elegant and general way which relates the rate constant with the imaginary part of free energy. Recalling (3.19) we write the rate constant as... 

Returning to the tunneling, we assume a metastable state like that in fig. 19 and use the Im F method. The extremal trajectories for satisfy the instanton equation of motion (5Seff/5Q = 0),... 

To determine the position of the tricritical point and the structure of the ordered phases stable below the bifurcation we analyze the asymptotic form of Qeff for e 0. At local minima the functional derivative of Qeff with respect to all the OPs vanishes. From this condition and from (45), (58), (47), and (64) we find that at the metastable states... 

Here the nucleation barrier AO is the excess thermodynamic potential needed to form the critical embryo within the uniform metastable state, while the prefactor Jq is determined by the kinetic characteristics for the embryo diffusion in the space of its size a. Expressions for both AO and Jo given by Zeldovich include a number of phenomenological parameters. 

The probability du> a, r) to find an embryo of size a with its center at point r within the metastable state (treated as the equilibrium oue ) is related to the distribution function /(a,r) as... 

The validity of mean field theory for N —y oo has striking consequences for the initial stages of phase separation. " In a metastable state slightly inside the coexistence curve, the nucleation free energy barrier is due to spherical droplets with a radius R The free energy excess of a droplet is written in terms of bulk and surface terms " "... 

If 5v //v /coex is not small, the simple description Eq. (14) in terms of bulk and surface terms no longer holds. But one can find AF from Eq. (5) by looking for a marginally stable non-uniform spherically symmetric solution v /(p) which leads to an extremum of Eq. (5) and satisfies the boundary condition v /(p oo) = v(/ . Near the spinodal curve i = v /sp = Vcoex /a/3 (at this stability limit of the metastable states both and S(0) diverge) one finds "... 

These experiments illustrate an essential contribution to the plastic flow from phase transformations of metastable states. 

Amorphous alloys are in a thermodynamically metastable state, and hence essentially they are chemically more reactive than corresponding thermodynamically stable crystalline alloyIf an amorphous alloy crystallises to a single phase having the same composition as the amorphous phase, crystallisation results in a decrease in the activity of the alloy related to the active dissolution rate of the alloy . 

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