Thermodynamic minimum free-energy state

Self assembly involves the organization of molecules in a cluster or ordered system. The structure of the self assembled state is ordered and molecules interact through weak hydrophobic or hydrophilic interactions. Structural aspects are often important. Self assembly is a process that is driven by thermodynamics. The final state is a local or absolute minimum free energy state. 

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. 

Provided that v > v for most values of h then the form of curve shown in Figure 1 is obtained. When the magnitude of is substantial, say >> 10 kT, a stable dispersion is obtained. The form of the potential energy curve obtained by this approach shows immediately that the stability of a dispersion to electrolyte is kinetic in origin rather than thermodynamic, that is, the lowest free energy state is in the primary minimum and entry into this is prevented by the presence of the large activation energy represented by AV. A more sophisticated and detailed representation of these ideas can be found elsewhere (12,15,16). 

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 ... 

For processes in test tubes in laboratory heat baths, or processes open to the air, or processes in biological systems, it is not the work or heat flow that you control at the boundaries. It is the temperature and the pressure. This apparently slight change in conditions actually requires new thermodynamic quantities, the free energy and the enthalpy, and new extremum principles. S> stems held at constant temperature do not tend toward their states of maximum entropy. They tend toward their states of minimum free energy. 

The equilibrium state of a system at constant temperature and pressure is characterized by a minimum in the Gibbs free energy of the system according to the second law of thermodynamics. For a multicomponent, multiphase (bulk) system, the minimum free energy corresponds to uniformity of the chemical potential (yu,) of each component throughout the system as demonstrated below. For a binary system, the molar free energy (G) and chemical potentials are related by... 

This relation characterizes the thermodynamic state of a two-phase system with minimum free energy and is valid for the impermeable phase border between two immiscible bodies. Eq 2.52 is a condition of the minimization of the free energy of the system. A minimization of the work of cohesion of two phases Wes and Wep may be considered as an initial condition. From Eq 2.52, it follows that when any specific interaction at the phase border is absent, the thermodynamic work of adhesion is determined by the thermodynamic work of cohesion of the phase with lower cohesion energy. In this case, the adhesion may be enhanced by increasing cohesion strength of polymer. 

Because of the thermodynamic imperative to attain a state of minimum free energy for the system as a whole, surface units are subjected to a net inward attraction normal to the surface. Geometrically, that can be equivalent to saying that the surface is in a state of net lateral tension defined as a force acting tangent to the surface at each point on it. It is this apparent tangential force that leads to the concept of a surface tension. The units of surface tension and of the excess surface free energy are dimensionally equivalent and, for pure liquids in equilibrium with their... 

If the polymer system was able to exist in an equilibrium state only, then a strictly defined correlation between (a, ph) and (a, ph) would exist in particular conditions, according to minimum of free energy of system formation. Consequently, there would occur only one temperature at which process initiation is thermodynamically probable. In rare ca.ses there may occur different correlations between ( ph, a) and ( ph, a ), which display one and the same value of free energy minimum of system formation. 

The calculation is based on the rule of thermodynamics, which states that a system will be in equilibrium when the Gibbs free energy is at a minimum. Cl The objective then is the minimization of the total free energy of the system and the calculation of equilibria at constant temperature and volume or at constant pressure. It is a complicated and lengthy calculation but, fortunately, several computer programs are now available that considerably simplify the task. PI... 

The stable equilibrium thermodynamic state of a system at constant pressure and temperature is the one with the minimum Gibbs free energy, G. This thermodynamic condition is defined as ... 

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