SAXS result for the normalized mean scattered intensity obtained for silica spheres in DMF at the concentration of 150 mg/ml and with added LiCl (open circles). The solid line represents the calculated intensity . The form factor was calculated for a Gaussian size distribution of homogeneously scattering spheres of mean radius 85.5 nm and relative standard deviation of 1%.
[(a)–(c)] Results for , , and the reciprocal of the normalized obtained for the fixed colloid concentration samples of series H. The filled symbols are the data from the combined SAXS and XPCS measurements. The lines are RY-fit results of and the -scheme results for and based on the fitted input. The dashed lines for and in (a) are the RY and -scheme results obtained when the peak height of the experimental diffusion function is fitted instead of the peak in (see text for details). All system parameters used in the calculations are listed in Table I. Additional results on the series H are available in the supplementary material (Ref. 46) in Fig. S1.
[(a)–(c)] As in Fig. 2 but for more concentrated samples of series K. The salt concentrations are indicated in the plots. Additional results on this series are available in the supplementary material (Ref. 46) in Fig. S2.
[(a)–(c)] , , and the reciprocal of the normalized for the samples of series C, where is kept constant and the colloid weight concentration is varied. The filled symbols represent the combined SAXS and XPCS data and the lines are the RY-fit results for and the -theory results for and . The values of the silica weight concentration are indicated in the plots. Parameters used in the calculations are given in Table I.
(a) Fit values of the effective charge number and the charge number from the electrophoretic measurements, (b) maximum of the experimental , and (c) maximum of the -scheme-fitted of series H (◼) and K as a function of added salt concentration. In (a), the effective charge fit values from the high-charge branch of series H are also included (◻). The HS limits of for series H (solid line) and K (dashed line) are also shown in (c).
Series C results (filled symbols) for (a) fit values of the effective charge , (b) maximum of , and (c) maximum of as a function of colloid concentration for a fixed added salt value of . The solid line in (c) represents the hard-sphere result, .
-RMSA values of (a) and (b) of at salt-free conditions calculated as a function of for various values of as indicated (iso- lines). The upper limiting contour line in (b) is derived from the cutoff condition for the onset of freezing. The solid isocharge lines are obtained from the lower branch of RMSA effective charge values. The solid arrows point to growing values of .
Peak values of the hydrodynamic function as a function of the colloid volume fraction . Included are our data for series H, K, and C. Further shown are XPCS data for 0.5 mM (△) and 50 mM (○) of added 1-1 electrolyte (Ref. 6). Lower dashed line: HSs. Upper solid line: Limiting freezing contour line for de-ionized fluid systems redrawn from Fig. 7.
Parameters used in the -scheme calculations of and . The solvent is DMF at and , corresponding to a Bjerrum length . The radius obtained from the form factor measurement was used in all our calculations. The values for the effective charge were obtained from fitting the peak values of the RY and RMSA-, respectively, to the experimental ones (see Figs. 2–4). Three different series of samples have been studied. The samples in series H and K are for a fixed particle concentration but varying salinity, whereas in series C the salinity is fixed and the silica concentration is varied: -silica volume fraction; -silica weight concentration in mg/g; —added LiCl concentration, , and —effective charge numbers, in units of elementary charge , obtained, respectively, from the RMSA and RY structure factor peak height fits; and -inverse screening length calculated using . —effective charge number deduced from electrophoresis measurements on dilute samples . The missing input in the table for is due to the fact that for such a high amount of salt the peak height of is quite insensitive to .
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