Multiple scattering and the scattering of light by large or small molecules in solution

Abstract

The scattering equations for two-component fluids are formulated so that individual scattering processes take place in vacuo. A gauge transformation is made which transforms these processes to ones taking place in a medium of refractive index m. Certain previously controversial factors apparently associated with the internal field are thereby isolated and shown to be multiple scattering terms. The formulae for the scattered intensity and turbidity of a two-component fluid of small molecules are calculated by an entirely molecular argument; they agree with the forms usually quoted as Einstein’s formulae except that the additional term reported previously is confirmed. It is conjected that a very precise identity exists between the phenomenological and molecular treatments of scattering when multiple scattering is properly included. It is shown that the concept of an excess molecular polarizability in a two-component system of small molecules is valid only up to an approximation of single scattering: but the concept of excess scattering remains valid in the multiple scattering theory of such systems. It is also shown that without additional assumptions both these concepts cease to be valid even in the single scattering approximation when the solute molecules are large. These assumptions amount to a ‘uniform distribution’ (in a sense here specified) of the solvent round the solute in regions of radius of the order of iA: they can be interpreted as hydration (or solvation) conditions. From a crude model of a macromolecular solution it is suggested that the Debye corrections which derive from a finite molecular size to estimates of molecular weights determined by light scattering, could be in error by as much as 100% (~ 5% of molecular weights) or perhaps even more: estimates of molecular size by dissymmetry can also be in similar error. For a given solute, both these and the molecular weight corrections should vary from solvent to solvent. As this has not been reported experimentally, solutions of large molecules may satisfy the hydration conditions which are indeed shown to be both necessary and sufficient for the formal reduction of the scattering equations to Debye’s form. It may therefore, be possible to use light scattering to investigate the state of hydration of such molecules in a solvent and to investigate the three two-particle correlation functions of such systems.