شيمي علمي براي زندگي امروز

(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.

These equations are used as the basis for rigorous fitting of the light scattering and concentration data by the ASTRA^® software to retrieve the molar mass, rms radius, and second virial coefficient for the macromolecules in solution.