The two modeling scales

With the characteristic functions not being directly accessible from the experiment, there are two possible methods to calculate them the first method, called macroscopic modeling, is based on the macroscopic variables the second method, called microscopic modeling, is based on molecular data 

In macroscopic modeling, these functions are obtained from a certain amount of data including state equations, thermomechanical coefficients, heat capacities, variations in surface tensions. Young s modulus and all variables which are classed under thermodynamic coefBcients, themselves grouped into characteristic matrices. This will be the focus of Chapter 2, in which we introduce these concepts and study this method. 

Microscopic modeUng is based on the statistics of collections of discernible or indiscernible objects, the introduction of canonical and molecular partition functions and the use of data about the molecule obtained from spectroscopy. Chapters 3, 4, 5 and 6 will develop these concepts and follow onto microscopic modeling. 

To form potential functions in macroscopic modeling, one must be able to calculate the characteristic function of a phase from experimental data. Here the challenge is to determine which experimental data must be used for a given phase with a selected ensemble of variables. To solve this, we will introduce the concepts of characteristic matrix and thermodynamic coefficient. 

We will associate with each characteristic function, and thus each ensemble of variables, a characteristic matrix formed from the associated thermodynamic coefficients. A certain number of matrix properties reduced the number of terms needed to define a thermodynamic state. These terms will therefore be the only ones required to solve arty problem regarding the transformation of the studied phase. 

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