The principle of free energy minimization

Most older theories rely more or less explicitly on the principle of free-energy minimization. This principle is well-known but, in order to apply it to polymer theory, we shall reformulate it precisely. 

Let us consider a system having the property that any configuration is defined by a set of vectors u1 . . . , uN and let us assume that a potential energy, . . . , Ujv) can be associated with each configuration. 

in the case of a chain with N links, the vector tij may define the direction and the length of the link of order j (with j = 1,. . ., N). In this case, the potential is frequently represented as the sum of two terms 

In general, a probability law P( i. uN) is associated with the various configurations 

A mean energy EN and an entropy S characterizing the disorder of the system correspond to this probability distribution 

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The change in state from liquid to solid as a material crystallizes, is driven by thermodynamics and the principle of free energy minimization, in turn this results from a trade between the total enthalpy and entropy of a system. 

The equilibrium state of a partially wetting droplet put in contact with a flat solid surface can be derived by using the principle of free-energy minimization. The optimum state is a hemispherical cap (see Figure 7.33), with a contact angle given by Young s equation ... 

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