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Polymer depletion-driven cluster aggregation and initial phase separation in charged nanosized colloids
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Image of FIG. 1.
FIG. 1.

Measured collective diffusion coefficient, , obtained by DLS as a function of the silica particle volume fraction, , for a salt concentration of .

Image of FIG. 2.
FIG. 2.

(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).

Image of FIG. 3.
FIG. 3.

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).

Image of FIG. 4.
FIG. 4.

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).

Image of FIG. 5.
FIG. 5.

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 .

Image of FIG. 6.
FIG. 6.

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.

Image of FIG. 7.
FIG. 7.

Initial aggregation time, , as a function of salt concentration , for .

Image of FIG. 8.
FIG. 8.

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 .

Image of FIG. 9.
FIG. 9.

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).

Image of FIG. 10.
FIG. 10.

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) , .

Image of FIG. 11.
FIG. 11.

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).

Image of FIG. 12.
FIG. 12.

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. : (◻); : (△) ; : (○) .

Image of FIG. 13.
FIG. 13.

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.

Image of FIG. 14.
FIG. 14.

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.

Image of FIG. 15.
FIG. 15.

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.

Image of FIG. 16.
FIG. 16.

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).

Image of FIG. 17.
FIG. 17.

Reduced total pair potential, , for , 0.15, and 0.2 mol/l with , , and . The inset shows the Coulomb barrier part.

Image of FIG. 18.
FIG. 18.

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.


Generic image for table
Table I.

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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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Polymer depletion-driven cluster aggregation and initial phase separation in charged nanosized colloids