Thermodynamic free-energy barrier

The c,c,t-CDT and c,t,t-CDT production paths are shown to be not assisted by incoming butadiene, while the square-planar transition state involved along the all-t-CDT path is significantly stabilized by an axial coordination of butadiene. Hence, the all-t-CDT route becomes the most facile of the three CDT production paths with a free-energy barrier for reductive elimination of 23 kcal mol-1, that perfectly corresponds with experimental estimates.44 Accordingly, the production of C12-cyclo-oligomers requires moderate reaction conditions,9 although 7b represents a thermodynamic sink within the catalytic cycle. 

The "classical" theory of nucleation concentrates primarily on calculating the nucleation free energy barrier, AG. Chemical interactions are included under the form of thermodynamic quantities, such as the surface tension. A link with chemistry is made by relating the surface tension to the solubility which provides a kinetic explanation of the Ostwald Step Rule and the often observed disequilibrium conditions in natural systems. Can the chemical model be complemented and expanded by considering specific chemical interactions (surface complex formation) of the components of the cluster with the surface ... 

Using a similar approach, Notman et al. [81], determined the free energy for pore formation in bilayers composed of ceramide, as a model for the stratum corneum of the skin, both in the presence and in the absence of DMSO. Without DMSO, the bilayer was in the gel phase, and interestingly, a hydrophobic pore was observed with a high free-energy barrier ( 60 kj/mol). In the presence of DMSO, the bilayer was more fluid, and the more typical hydrophilic pore was observed, with a much smaller activation energy of 20kJ/mol. This work provided a thermodynamic and structural explanation for the enhanced permeability of skin by DMSO. 

All prebiotic polymerization reactions, which are dehydration reactions, are thermodynamically unfavorable. This free energy barrier can be overcome in two ways. The first is to drive the dehydration reaction by coupling it to the hydration of a high energy compound, and the second method is to remove the water by heating. In principle, visible or ultraviolet light could drive these reactions, but so far no one has demonstrated adequately such processes. 

Fig. 1.9 Calculated polymer-solvent phase diagram. The bimodal (continuous line) is the coexistence curve the points below it correspond to thermodynamically unstable states, which undergo phase separation. However, the pints between the bimodal and the spinodal (dashed line) are ki-netically stable, since there is a free-energy barrier to phase separation. C indicates the critical point the collapse temperature. The deviation of the low-concentration branch of the spinodal from the vertical axis below T is an artifact of the mean-field approximation. (From ref. [62])...

Barriers for inversion of configuration in chiral, overcrowded PAHs are relatively low. In hexabenzotriphenylene, a free energy barrier of 26.2 kcal mol-1 was found for isomerization of 53-C2 to the more thermodynamically stable 53 -D3. However, the free energy barrier for racemization in 53-C2, as determined from the 1H NMR coalescence temperature (AG rac = 11.7 kcal mol"1, Tc = 247 K, Av = 102 Hz at 500 MHz), was relatively low [95]. Pentacene 55 (Fig. 15.21), with a screw-type end-to-end twist of 144°, racemized slowly at room temperature (AG raCi25°c = 23.8 kcal mol-1) [97], that is, the barrier for racemization is similar to that in [5]helicene (AG rac = 24.1 kcal mol"1). 

Constrained Dynamics, Thermodynamic Integration, and Free-energy Barriers... 

Various methodologies have been developed to determine the free energy barriers from MD simulations. One of the common approaches applied in ab initio MD, known as the potential of mean force method has been derived from the thermodynamic integration technique. 34,35 In a canonical (NVT) ensemble the free energy difference, AA, between the two states, 0 and 1, can be calculated as the integral... 

In order to overcome the reaction barrier within current restrictions of computer time, the hydrogen coordination number of the hydroxylic oxygen was forced to decrease from unity to zero by applying a suitable constraint [47, 88, 89], By thermodynamic integration it is possible to determine the free energy barrier height for this process [19]. 

Mesoscopic non-equilibrium thermodynamics provides a description of activated processes. In the case considered here, when crystallization proceeds by the formation of spherical clusters, the process can be characterized by a coordinate y, which may represent for instance the number of monomers in a cluster, its radius or even a global-order parameter indicating the degree of crystallinity. Polymer crystallization can be viewed as a diffusion process through the free energy barrier that separates the melted phase from the crystalline phase. From mesoscopic non-equilibrium thermodynamics we can analyze the kinetic of the process. Before proceeding to discuss this point, we will illustrate how the theory applies to the study of general activated processes. 

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