Equilibrium conditions in the presence of an external field

In all of the studies of thermodynamic equilibrium that have been presented in the previous chapters, we have neglected the effects of an external field on the equilibrium properties of a system. This has been justified because the field may be present only in specific cases, the effect of the field may be negligible, or the position of the system in the field may be unchanged. The conditions of equilibrium in the presence of a gravitational or centrifugal field, an electrostatic field, and a magnetic field are developed in this chapter. 

A distinction must be made between gravitational effects for which the presence of material in the field does not change the intensity of the field, and the electrostatic and magnetic effects for which the presence of material within the field does alter the intensity. A complete treatment of electrostatic and magnetic effects would require a discussion of electromagnetic theory and the use of Maxwell s equations. However, we wish only to illustrate the thermodynamic effects of electric and magnetic fields. We therefore accept the results of a complete treatment and apply the results to simple systems. 

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First, we denote averages taken over equilibrium trajectories with the notation ( )o and those in the presence of an external field with ( -)e. Imagine needing to calculate (B)e, with the condition that (B)q = 0, where B is a quantity of interest. In the event that B does not satisfy this condition, one can always define a quantity B, such that B = B - B)q, thereby making B )q = 0. 

In the presence of an external field, such as a static electric field, may have a part that depends on the field. When no field is present, is entirely due to diffusion in Chapters 18 and 19 we shall study such dijfusion-reaction systems under far-from-equilibrium conditions in some detail. 

Before outlining the effect of fields on the orientation of the director, it must be emphasized that surface interactions and boundary conditions are usually of importance. The models applied here assume that there is a well-defined director distribution in the absence of any external field, and in practice this can only be provided by suitable treatment of boundary surfaces. The strength of surface interactions must also be considered as this will influence the equilibrium director configuration in the presence of a field. For the simplest description of field effects in liquid crystals it is usual to assume an infinite anchoring energy for... 

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