Free energy landscape theory

In what follows, we use simple mean-field theories to predict polymer phase diagrams and then use numerical simulations to study the kinetics of polymer crystallization behaviors and the morphologies of the resulting polymer crystals. More specifically, in the molecular driving forces for the crystallization of statistical copolymers, the distinction of comonomer sequences from monomer sequences can be represented by the absence (presence) of parallel attractions. We also devote considerable attention to the study of the free-energy landscape of single-chain homopolymer crystallites. For readers interested in the computational techniques that we used, we provide a detailed description in the Appendix. ... 

Abkevich, V. I., Gutin, A. M., and Shakhnovich, E. I., Free energy landscape for protein folding kinetics Intermediates, traps, and multiple pathways in theory and lattice model simulations. J. Chem. Phys. 101, 6052 (1994). 

Our progress in understanding dissolution kinetics has been advanced from surfactant systems whose equilibrium phase behavior is well understood. Since phase formation is relatively fast, the kinetics are often simple and the dynamics are often controlled by collective diffusion. In cases where this breaks down and more complex behavior is observed free energy landscapes have provided us with important new insights. However, formation of instabilities such as myelins still remain a mystery and cannot be classified with well founded surfactant and polymeric instability theories. At present no theoretical explanation for their formation exists despite having been observed 150 years earlier by R. Virchow (5i). 

Polymer crystallization follows a typical nucleation-growth mechanism. According to the classical nucleation theory [1-3], nucleation implies a size threshold for the growth of the crystaUine phase, which is a consequence of rate competition between the body free-energy gain and the surface free-energy penalty. Thus, in the free-energy landscape, crystallization can be described as... 

The second tenet of this theory is that the breakdown from the transition state to products is the result of a vibration at the frequency v between two moieties in a locally flat energy profile at the saddle point corresponding to the transition from the reactant part to the product part of the free energy landscape. 

L. Sutto, M. D Abramo, and F. L. Gervasio,/. Chem. Theory Comput., 6(12), 3640—3646 (2010). Comparing the Efficiency of Biased and Unbiased Molecular Dynamics in Reconstructing the Free Energy Landscape of Met-Enkephahn. 

The transition state theory and the assumption of complex and rugged free-energy landscapes are still under debate. One reason is the inherent difficulty to identify the true relevant degrees of freedom Q which are typically highly system-specific. The problem is that the kinetic barrier frequently depends on the choice of Q which makes an experimental verification of a theoretically proposed free-energy landscape more difficult. Nonetheless, the free-energy landscape concept is helpful in understanding details of phase transitions (such as, e g., the occurrence of barriers that slow down the transition process) and to quantity these. 

There is a difference between experimentalists and theoreticians experimentalists observe the minima and maxima in free energy profiles—the experimental entities of intermediates and transition states—whereas theoreticians wish to calculate the entire energy surface of a reaction. Experimentalists talk about pathways, theoreticians about energy landscapes. Experiment and theory touch base around the ground and transition states that provide the milestones in the energy landscapes for the theoreticians to benchmark their calculations. The two views are reconciled in section G. 

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