Forward scattering of light, X-rays and neutrons

The central points of this paper can now be summarized. We consider here, for simplicity only, vanishing particle concentration. In equilibrium sedimentation equation (6) applies. The density increment is a measurable quantity. It can either be introduced into equation (6) to calculate M2, or it can be analysed by equation (7) and (8) to provide additional information on specific volumes and solute interactions. Light scattering is determined by the analogous equation (20). The refractive index increment is also experimentally accessible and its structure (not considered here) is similar to that of the density increment Small angle X-ray scattering is determined by equation (31) and the electron density increment which appears in this equation cannot be directly determined by experiment. Yet it can be obtained in straight-forward fashion from the mass density increment, by equation (34). Similarly, in the case of neutron scattering (equation (38)), the scattering length density increment is obtained from the mass density increment by equation (40), or it may now be directly evaluated by neutron interferometry. It is thus possible to analyse all forward scattering phenomena on the bases of well established fluctuation theory. In this chapter the emphasis has been on forward scattering only, but the considerations should be taken ito account as well at finite values of the scattering vector q. Whereas the role of interparticle interactions diminishes at low concentrations and at short distances (increasing q), the composition of the 'invariant' particle (as required in the analysis of Luzzati & Tardieu, 1980) should, as before, be characterized by the thermodynamic analysis. Additional points discussed have dealt with the connection with the conventional particle contrast parameters (Section 4 and equations (44)-(48)), the effect of heterogeneity in particle composition and systems comprising two homomacromolecules (equations (21)-(24)), the effect of hydrogen-deuterium substitution on mass density and scattering length density increments (equations (42) and (43)). Numerical examples have been worked out for density increments and interaction parameters of CsDNA in CsCl (Table 1, Fig.3) and for properties of this system in hydrogen-deuterium mixtures (Table 2, Figs 4 and 6). The implications of these considerations for other systems have been considered.