A Hamiltonian Formulation of Colloid Electrostatic Theory
Application of Hamilton’s method in the calculus of variations to an electrostatic field model of a suspension of charged colloidal particles with selection of a Lagrangian to yield Poisson’s law as the Euler equation has led to the following results: (1) the potential energy of interaction of two parallel plates, representing colloidal particles in suspension, is derived without assuming a specific charge distribution in the domain, (2) the force between the particles is obtained as a result and therefore does not require independent derivation.
In the present theory, no artifact of a charging process to build up electrical double layers in the vicinity of the colloid particles is required. However, the interaction energy is the same as that described by previous investigators.
KeywordsSurface Charge Density Hamiltonian Formulation Helmholtz Free Energy Colloid Model Lyophobic Colloid
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