The theoretical foundation laid out by Bruno Zimm [B. H. Zimm, "The scattering of light and the radial distribution function of high polymer solutions," J. Chem. Phys. 16, 1093 (1948); Ibid. "Apparatus and methods for measurement and interpretation of the angular variation of light scattering; Preliminary results on polystyrene solutions," J. Chem. Phys. 16, 1099-1116 (1948)] makes it possible to condense the results of the Rayleigh-Debye-Gans theory of light scattering into a simple equation. As described in the review article by Philip Wyatt [P.J. Wyatt, Anal. Chim. Acta 272, 1-40 (1993)] Zimm's development leads to the expression:

(1)

where:

• R(q,c) is the excess Rayleigh ratio of the solution as a function of scattering angle q and concentration c. It is directly proportional to the intensity of the scattered light in excess of the light scattered by the pure solvent.
• c is the solute concentration.
• M_w is the weight-averaged solute molar mass.
• A₂ is the second virial coefficient in the virial expansion of the osmotic pressure.
• K* is the constant 4p²(dn/dc)²n₀²/N_al₀⁴.
• N_a is Avogadro's number. This number always appears when concentration is measured in g/ml and molar mass in g/mol.
• P(q) describes the angular dependence of the scattered light, and can be related to the rms radius.

The expansion of P(q) to first order gives:

(2)

where n₀ is the index of refraction of the solvent, l₀ is the vacuum wavelength of the laser, and r_g is the rms radius. Here, the relation between the size and angular dependence of the scattered light is clear. For larger sizes (r_g greater than approximately 50 nm) it is necessary to include higher moments in the expansion of P(q).

The mean square radius, <r_g²>, may be calculated immediately from the slope at q = 0 of the measured ratios 1/R(q,c) with respect to sin²(q/2). If the macromoledule of mass M is made up of elements m_i, it may be shown that

(3)

where r_i is the distance of element m_i from the center of mass of the molecule of total mass M.
 

The basic light scattering equation holds true at ALL angles, not just one! With modern computers we can now collect all of the angular data and apply a Global Fit, since the relationship between mass, size, and the quantities measured is valid at all angles. The so-called “extrapolation,” to which some light scattering vendors may refer, consists actually of collecting a complete set of independent data points and using this full view of the scattering pattern to find the most accurate value of the molar mass, size and conformation. Wyatt performs, therefore, 18 simultaneous measurements with our 18-angle DAWN instrument.

Combining data obtained from more angles means greatly improved accuracy and precision. Nevertheless, some will argue that a measurement at a single low angle (in fact, the nosiest possible location!) is superior to a measurement over a range of angles. Clearly this argument is incorrect, as may be confirmed by the governing equations.