Hill equation definition

From this equation, we can construct an example that is extremely useful in visually examining receptor data, indeed any data fitting the simple mass action model of Eq. (19.1). This means that a toxicant under study is competing with the radioligand for one, and only one, population of sites. By definition, the Hill slope (often called nH) must equal 1. It turns out that by memorizing the numbers 9 and 91, one can do a very useful preliminary analysis of data fit to such a mass-action model. The reason for this is as follows ... 

We now return to the definition of the surface excess chemical potential fta given by Equation (2.19) where the partial differentiation of the surface excess Helmholtz energy, Fa, with respect to the surface excess amount, rf, is carried out so that the variables T and A remain constant. This partial derivative is generally referred to as a differential quantity (Hill, 1949 Everett, 1950). Also, for any surface excess thermodynamic quantity Xa, there is a corresponding differential surface excess quantity xa. (According to the mathematical convention, the upper point is used to indicate that we are taking the derivative.) So we may write ... 

The first differential is a standard definition of pressure, while the second determines the optimum free-volume content at constant V and T [Peek and Hill, 1950], These yield the S-S eos in the form of coupled equations ... 

Equation (3.4.1) follows directly from the definition of the process of solvation (see also Appendix G). The expression for the solvation, Gibbs or Helmholtz energy in terms of the process of inserting a particle at a fixed position is quite old, probably due to Kirkwood (1935) and later used in the scaled particle theory [see Sec. 3.8 and also Hill (1960) and Widom (1963,1982)]. 

Due to averaging no definite solution for the parameter A from equation (6) exists. Hence A (Figure 6, right) was determined by a least square method. The Hill parameters and A were used to calculate creep rates in 15 and 30 fiber orientation as well as for another temperature and stress. In Figure 7 and Figure 8 the results are depicted. 

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