Liquid-liquid and liquid-solid phase separation and flocculation for a charged colloidal dispersion
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Bibliographic record
Abstract
We model the intercolloidal interaction by a hard-sphere Yukawa repulsion to which is added the long-range van der Waals attraction. In comparison with the Derjaguin-Landau-Verwey-Overbeek repulsion, the Yukawa repulsion explicitly incorporates the spatial correlations between colloids and small ions. As a result, the repulsive part can be expressed analytically and has a coupling strength depending on the colloidal volume fraction. By use of this two-body potential of mean force and in conjunction with a second-order thermodynamic perturbation theory, we construct the colloidal Helmholtz free energy and use it to calculate the thermodynamic quantities, pressure and chemical potential, needed in the determination of the liquid-liquid and liquid-solid phase diagrams. We examine, in an aqueous charged colloidal dispersion, the effects of the Hamaker constant and particle size on the conformation of a stable liquid-liquid phase transition calculated with respect to the liquid-solid coexistence phases. We find that there exists a threshold Hamaker constant or particle size whose value demarcates the stable liquid-liquid coexistence phases from their metastable counterparts. Applying the same technique and using the energetic criterion, we extend our calculations to study the flocculation phenomenon in aqueous charged colloids. Here, we pay due attention to determining the loci of a stability curve stipulated for a given temperature T0, and obtain the parametric phase diagram of the Hamaker constant vs the coupling strength or, at given surface potential, the particle size. By imposing T0 to be the critical temperature T(c), i.e., setting k(B)T0 (=k(B)T(c)) equal to a reasonable potential barrier, we arrive at the stability curve that marks the irreversible/reversible phase transition. The interesting result is that there occurs a minimum size for the colloidal particles below (above) which the colloidal dispersion is driven to an irreversible (reversible) phase transition.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it