A rescaled MSA structure factor for dilute charged colloidal dispersions

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres

“…To calculate S(q) and g(r) based on the OMF pair potential with κ determined by Eq. (2), we have solved the Ornstein-Zernike integral equation using the well-established RogersYoung (RY) and rescaled mean spherical approximation (RMSA) schemes [3,[67][68][69]. The RY scheme is known for its excellent structure factor predictions within the OMF model (see subsection 3.1).…”

Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment

“…This undesired feature is absent in the case of an attractive Yukawa tail. As shown by Hansen and Hayter,46 this severe deficiency of the MSA can be remedied by increasing the hard-sphere diameter, σ , of the HSY spheres at fixed particle concentration to a larger value σ > σ , without altering the form of the Yukawa-tail of the pair potential. The rescaled effective diameter σ is determined from the physical constraint that the g(r ) in these systems must be continuous, i.e., from requiring the Gillan condition that g(r = σ + ; φ ) = 0 (Ref.…”

“…Negative values of g MSA (x) are found additionally also when the RMSA is applied to highly concentrated systems in the supercooled fluid regime at large values of the coupling parameter γ . 56 Hansen and Hayter 46 have provided a simple rescaling prescription which remedies the shortcoming of the MSA solution for strongly repelling particles where β u(x = 1 + ) 1 and consequently g(x = 1 + ) ≈ 0, i.e., for systems where the hard core plays no role. In the RMSA, one considers in place of the actual system a system of size-inflated spheres of rescaled hard-core diameter σ = σ/s, and rescaled volume fraction φ = φ/s 3 , where the inflation parameter s, with 0 < s ≤ 1, is determined by the Gillan condition g MSA (x = 1 + ; φ ) = 0 for x = x s = r/σ .…”

“…The diameter-rescaled MSA is referred to as the RMSA. 46 The RMSA scheme of Hansen and Hayter preserves the analyticity of the original MSA solution without sharing its deficiency at low φ and for strong Yukawa tail repulsion. This is the reason why the RMSA is widely used to this date as an efficient tool for calculating the pair structure, for fitting scattering data (see, e.g., its implementation in Ref.…”

Impact of polyethylene glycol on aqueous micellar solutions of sodium oleate studied by small-angle neutron scattering

“…To describe the micelle interaction peak, for which the S(q) function is responsible, we apply the rescaled mean spherical approximation for dilute charged colloidal dispersions developed by Hansen and Hayter [28]. Since the studied micelles consist of ionic surfactant molecules, the screened Coulomb potential is used in the model: Table 1 and Table 2, respectively.…”