Thermodynamic minimum free-energy

Folding, in essence, is based on a thermodynamic minimum free-energy criterion. The base pair is the most important stabilizing element of the... 

As compared to ECC produced under equilibrium conditions, ECC formed af a considerable supercooling are at thermodynamic equilibrium only from the standpoint of thermokinetics60). Indeed, under chosen conditions (fi and crystallization temperatures), these crystals exhibit some equilibrium degree of crystallinity at which a minimum free energy of the system is attained compared to all other possible states. In this sense, the system is in a state of thermodynamic equilibrium and is stable, i.e. it will maintain this state for any period of time after the field is removed. However, with respect to crystals with completely extended chains obtained under equilibrium conditions, this system corresponds only to a relative minimum of free energy, i.e. its state is metastable from the standpoint of equilibrium thermodynamics60,61). 

As we all know from thermodynamics, closed systems in equilibrium have minimum free energy and maximum entropy. If such a system were brought out of equilibrium, i.e. to a state with lower entropy and higher free energy, it would automatically decay to the state of equilibrium, and it would lose all information about its previous states. A system s tendency to return to equilibrium is given by its free energy. An example is a batch reaction that is run to completion. 

Equilibrium thermodynamics require a minimum free energy, F, for a stable system. Splitting F into contributions of the crystal volume and its surface gives... 

A cardinal thermodynamic principle is that systems change toward minimum free energy. The sign oiAG permits prediction of the behavior of a proposed chemical reaction with certainty... 

Recall that the secondary-structure model for RNA is a model - and a crude one at that. It neglects pseudo knots and other tertiary interactions, does not take deviations from the additive nearest neighbor energy model into account, and is based on thermodynamic parameters extracted from melting experiments by means of multidimensional fitting procedures. Thus, you cannot expect perfect predictions for each individual sequence. Rather, the accuracy is on the order of 50% of the base pairs for the minimum free energy structure. 

Rates of reaction vary with changes in temperature or concentration. All reactions are reversible (i.e., have a forward and a reverse reaction). When the rate of the forward reaction equals the rate of the reverse reaction, there is no net change in concentrations of any component, and the system is said to be at thermodynamic equilibrium. This condition represents a minimum free energy of the system and determines the limits of conversion. The overall rate of reaction equals zero at equilibrium. A relationship can be derived between the forward and reverse rate constants and the overall thermodynamic equilibrium constant. For example, consider the reaction... 

Proteins are dynamic molecules with respect to structure. The preferred folded structure for a given set of environmental conditions is that which has the minimum free energy. The driving force to assume a given folded structure is a thermodynamic force. In aqueous systems, the hydrophobic side-chains will endeavour to orient away from the surrounding water and towards the core of the molecule. However, for high surface activity, it is essential that the protein molecule should unfold and orient its hydrophobic side-chains towards the oil phase. A lack of hydrophilic residues usually does not restrict protein functionality at interfaces. Thus, flexible proteins can create a highly hydrated, mobile layer to stabilize an emulsion particle. 

A number of statistical thermodynamic theories for the domain formation in block and graft copolymers have been formulated on the basis of this idea. The pioneering work in this area was done by Meier (43). In his original work, however, he assumed that the boundary between the two phases is sharp. Leary and Williams (43,44) were the first to recognize that the interphase must be diffuse and has finite thickness. Kawai and co-workers (31) treated the problem from the point of view of micelle formation. As the solvent evaporates from a block copolymer solution, a critical micelle concentration is reached. At this point, the domains are formed and are assumed to undergo no further change with continued solvent evaporation. Minimum free energies for an AB-type block copolymer were computed this way. 

The intercalation of polymer or prepolymer from the solution is described via minimum free energy principle. The driving force of polymer intercalation is the entropy from the solvent desorption. Several researchers investigated the thermodynamics properties of PCN with homo polymeric systems in a confined geometry. However, Lim et al. investigated ternary systems, and explained that the intercalation distance of poly-(methyl methacrylate) (PMMA)/organic-modified clay (OMMT) nanocomposite is larger than that for the... 

This equation is equivalent to the statement that the surface tension is exactly equal to the Helmholz free energy per unit area. Thus, we may make use of the thermodynamic equilibrium statement that isolated systems tend toward the condition of lowest free energy to show that the stable state of a system is the one with minimum free energy, including the contribution of the surface free energy. 

In terms of thermodynamics, Torza and Mason [32] pioneered the study of the interfacial behaviour of systems containing various types of three mutually immiscible liquids. In their case, the thermodynamics of the system was influential in determining the final morphology since the liquid phase was highly mobile. The equilibrium state of the three phases will occur when the minimum free energy, Gs, defined below, is attained ... 

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