Measured collective diffusion coefficient, , obtained by DLS as a function of the silica particle volume fraction, , for a salt concentration of .
(a) TEM picture of a dried Ludox particles dispersion. (b) Size distribution of Ludox particles observed from image analysis. The mean particle radius is (see text for details).
Shear viscosity of a pure dextran solution as a function of the reduced concentration of polymer coils, , for three different molecular weights (see legend) at . The solid curve is a fit to the experimental data (see text).
Left: Collective diffusion coefficient, , of a Ludox silica dispersion at as a function of added dextran concentration, , , for , 0.1, and 0.2 mol/l, respectively. Right: Effective hydrodynamic radius, , obtained from the single-particle Stokes–Einstein relation using . The lower scale of the abscissa gives the polymer surface concentration, , that would result if all polymers did adsorb on the surface of the silica particles. As a rule of thumb, the surface is completely covered when (Ref. 48).
Normalized measured time-dependent (effective) collective diffusion coefficient of Ludox spheres as a function of the elapsed time after sample preparation, for varying (see legend) and .
Semilogarithmic plot of the reduced time-dependent effective hydrodynamic radius of colloid clusters deduced for several salt concentrations as a function of time for . The straight line segments are fits to the form , with the aggregation time . (▽): (a) , (b) ; (○): (c) , (d) ; (◇): (e) ; (◻): (f) , respectively.
Initial aggregation time, , as a function of salt concentration , for .
Effective colloid charge number as a function of added salt concentration, obtained from matching Eq. (5) to the experimentally determined initial aggregation time given in Fig. 7. The solid curve is a fit to the form , with , , and .
DLVO pair potential for parameters obtained from adjusting the effective colloid charge number , entering the calculation of , to the experimentally found initial aggregation time, for a system with at (see Table I).
Semilogarithmic plot of the effective hydrodynamic radius of aggregated colloidal clusters as a function of the elapsed time. The straight lines (a)–(f) are fits to the form , with the parameters and determined right after the sample preparation. The data for , and are replotted for comparison from Fig. 6. : (⌂, f) , ; (▲, e) , ; (▽, c) , ; : (◼, d) , ; (◇, b) , ; (◻, a) , .
Aggregation time, , as a function of inverse colloid volume fraction, for (○) and (◻). The dashed and solid curves are the theoretically predicted aggregation times for and 0.3 mol/l, respectively, calculated from Eq. (5), using in Eq. (4) (see also Fig. 9).
Semilogarithmic plot of the reduced effective hydrodynamic radius of colloid clusters as a function of elapsed time, for a mixture of Ludox silica spheres at and dextran at varying concentrations, with , and . The straight lines are fits to the form , with the characteristic time and the effective hydrodynamic radius measured right after sample preparation. For comparison, the data points for are replotted from Fig. 6. : (◻); : (△) ; : (○) .
The data points (symbols) give the experimentally determined aggregation time as a function of the reduced polymer concentration, in a mixture of dextran with varying range of attractions, , , and , respectively, and silica particles with and . The curves are the theoretically predicted based on the AOV potential and values of as explained in Sec. II B.
Total pair potential for , , and , with , , , , and fixed polymer concentration, . The black dashed curve is the repulsive electrostatic part, and the dashed-dotted (turquoise) curve the short-ranged vdW part of . The inset displays the Coulomb barrier part of located at smaller particle separations.
Photographs of samples containing a colloid-polymer mixture with [see also Fig. 16(c)], and polymer molar mass . The picture has been taken two days after sample preparation. Sample (i) with and has become turbid and forms a gel at later times. In sample (ii), where and , and sample (iii), where and , two phases are observed. The total height, , of the dispersion and the height, , of the more turbid bottom phase are indicated by arrows.
Nonequilibrium state diagrams of aqueous mixtures of Ludox silica particles and dextran for varying salt concentrations: [chart (a)] , (b) , (c) , (d) , and (e) for at room temperature. The phase diagrams of the samples have been recorded by visual inspection two weeks after sample preparation. Open circles (○) indicate fluidlike homogeneous mixtures. The half-filled circles describe samples, where a turbid viscous phase is observed at the container bottom. The triangles (▲) mark samples that form a gel throughout the sample. The solid dividing curves are guides to the eye, separating the single-fluid phase region from the region where phase separation or a system-spanning gel is observed after 2 weeks. For all salt concentration considered, these dividing curves are summarized in (f).
Reduced total pair potential, , for , 0.15, and 0.2 mol/l with , , and . The inset shows the Coulomb barrier part.
Time evolution of the nonequilibrium state diagram for an aqueous mixture of silica particles and dextran, with and . The gray (blue) symbols give the state of the sample two days after sample preparation. The black symbols describe the state after 2 weeks. The theoretically predicted binodal [dashed (green) curve] and spinodal [solid (red) curve] are obtained form GFVT on assuming -solvent conditions. The asterisks denote the critical point.
Parameters characterizing for several experimentally analyzed salt concentrations. The effective charge number, , has been adjusted to obtain the experimental values of without added polymers as described in the text.
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