Quasi-hard Sphere Phase Diagrams

In order to utilise our colloids as near hard spheres in terms of the thermodynamics we need to account for the presence of the medium and the species it contains. If the ions and molecules intervening between a pair of colloidal particles are small relative to the colloidal species we can treat the medium as a continuum. The role of the molecules and ions can be allowed for by the use of pair potentials between particles. These can be determined so as to include the role of the solution species as an energy of interaction with distance. The limit of the medium forms the boundary of the system and so determines its volume. We can consider the thermodynamic properties of the colloidal system as those in excess of the solvent. The pressure exerted by the colloidal species is now that in excess of the solvent, and is the osmotic pressure II of the colloid. These ideas form the basis of pseudo one-component thermodynamics. This allows us to calculate an elastic rheological property. Let us consider some important thermodynamic quantities for the system. We may apply the first law of thermodynamics to the system. The work done in an osmotic pressure and volume experiment on the colloidal system is related to the excess heat adsorbed d Q and the internal energy change d E  

For a reversible change the associated entropy change dS for the colloidal particles is given by applying the second law  

We can rewrite this in a new form at constant volume and entropy  

The simplicity of the form of these expressions suggests that S and V are natural variables of the internal energy E S,V). These expressions have demonstrated the first and second laws of thermodynamics for our colloidal system. However, it is not easy to perform an experiment at 

The Helmholtz free energy A(T,V) in excess of that of the medium is 

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