An Improved Empirical Relation to Determine the Particle Number Density of Fluid-Like Ordered Charge-Stabilized Suspensions

Polystyrene as an archetypal charge-stabilized colloid model system was used in this work under well defined preparation conditions. A continuous preparation technique was used to control the suspension parameters salt concentration c and particle number density n. Measurements of n were performed using both conductivity in the completely deionized state and static light scattering. We found a significant deviation between the position of the first maximum of the static structure factor qmax=2π/L and an estimate identifying the relevant length scale L with the average inter-particle distance d¯=n−1/3. Instead, qmax was observed to follow the relation qmax=(2.20±0.03)π/d¯, which is equivalent to L=(0.91±0.02)d¯. Use of this led to consistent values for n in the crystalline and shear molten states and an improved precision in the fluid-like ordered state. Interestingly, qmax of the fluid phases was further observed to be very close to the Bragg peak of the corresponding crystal phase which was determined by the nearest neighbour distance dNN. This supports the idea that the local structure of the strongly correlated fluid is very similar to that of the crystalline phase.