Continuum, continuous structureless medium

If we now transfer our two interacting particles from the vacuum (whose dielectric constant is unity by definition) to a hypothetical continuous isotropic medium of dielectric constant e > 1, the electrostatic attractive forces will be attenuated because of the medium s capability of separating charge. Quantitative theories of this effect tend to be approximate, in part because the medium is not a structureless continuum and also because the bulk dielectric constant may be an inappropriate measure on the molecular scale. Eurther discussion of the influence of dielectric constant is given in Section 8.3. 

This is precisely what is meant when the medium is described as a structureless dielectric or continuum. In particular, when discussing the role of the solvent in electrolyte solutions it is often described as a continuous medium, or a structureless medium. Most of the theoretical discussions of electrolyte solutions formulate the theoretical equations in terms of factors which involve the macroscopic quantity, Use of this bulk quantity in the equations implicitly means a description in terms of the solvent being a strucmreless dielectric, with no microscopic or molecular structure. 

Although not rigorously correct, the approximation of water as a structureless homogeneous continuum dielectric medium is used by many simulative methodologies. Both Brownian dynamics (see the section entitled Implicit Solvation Brownian Dynamics) and electrodiffusive approaches (see the section on Flux-Based Simulation) include the water in the electrostatic picture as a continuous dielectric background with polarizability appropriately tuned... 

In the simplest model of solvation, the solvent is treated as a structureless and continuous medium of dielectric constant e. In 1920, Born developed the earliest polarizable continuum model. He treated the ion as a point charge q located in the center of a hollow sphere with radius R. The hollow charged sphere is embedded in a classical dielectric continuum having a relative dielectric constant s. The electrostatic contribution to the free energy, evaluated in Section 11.1.1.1, is given by... 

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