Free energy barrier scaling

The fact that the final product 3-Tp Rh(CO)(H)(R) does not appear on the ultrafast time scale (<1 ns,) (Fig. 4) indicates a free energy barrier greater than 5.2 kcal/mol for the alkane C-H bond activation. Nanosecond step-scan FTIR experiments on the 3-Tp Rh(CO)2/cyclohexane system show that the remnant of the 2-Tp Rh(CO)(S) peak persists for 280 ns after photoexcitation, while the product CO stretch at 2032 cm-1 rises with a... 

J. E. Hunter and W. P. Reinhardt (1995) Finite-size-scaling behavior of the free-energy barrier between coexisting phases - determination of the critical-temperature and interfacial-tension of the Lennard-Jones fluid. J. Chem. Phys. 103, pp. 8627-8637... 

The infoiTnation provided here, which concentrates on energetic and structural aspects of the problem, represents only the first steps toward understanding the behavior of a hydroxide defect in ice. The next stage is to analyze the dynamics of hydroxide motion, which will require both microscopic and macroscopic approaches. The microscopic event consists of proton transfer from one of the three waters pictured at the bottom of Fig. 2 to the hydroxide. It would not be surprising if calculation of transition states requires levels of electronic structure theory beyond the modest levels of DFT that suffice for equilibrium structures. The energy and free energy barrier of this process sets the time scale for local hopping of the hydroxide ion. The macroscopic level is a description of defect diffusion within the disordered H-bond network. 

Quite recently, Lee and Strandburg have studied the finite size scaling behavior of the bulk free energy barrier between the solid and liquid states in the hard disk system, and have obtained the first unambiguous evidence for a first-order melting transition [1]. 

It is seen that the scale for the free energy barrier AF /kBT is set by the... 

The thermodynamic effects of finite size and the kinetic barriers, AG, for the formation of vapor phase have been fully developed [41-46]. Macroscopic thermodynamics predicts that when we have two non-polar surfaces immersed in a liquid and bring them closer together, at a critical distance, Dc, liquid will be replaced by vapor (2). Due to a considerable free energy barrier for confinement-induced evaporation, however, the liquid phase is often metastable below Dc [36, 41, 43, 45, 47]. Coarse-grained simulations confirmed [45] macroscopic scaling predictions [48, 49] ... 

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