Surface charging parameters of charged particles in symmetrical electrolyte solutions
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Bibliographic record
Abstract
Surface electric charge of dispersed particles is an essential determinant of physicochemical properties, coagulation and flocculation processes, and stability of colloidal solutions. Size-dependence of surface potential, charge density, and total surface charge of suspended charged particles has recently received attention in the literature. Despite the clear significance of understanding such dependence, very few studies have been devoted to this problem, with contradictory results of the relationship type. Currently, there is no analytical formula to represent explicit relationships between surface charging parameters and particle size. This research work is directed at development of accurate physics-based formulas for quantification of curvature-dependence of surface potential, surface charge density, and total surface charge for cylindrical and spherical charged particles immersed in a symmetrical electrolyte solution. First, a non-dimensional approach is adopted to simplify the problems, overcoming the difficulty of dealing with multiple influential variables. Then, to reduce the degrees of freedom of the problems under consideration, Gauss's law is combined with the condition of electro-neutrality in an electrical double layer (EDL). Next, the resulting complex integral equations are solved to construct characteristic curves and to express the dimensionless surface charging parameters explicitly as a function of the dimensionless particle radius. The new theoretical expressions are founded on approximate analytical and numerical solutions of the nonlinear Poisson-Boltzmann (PB) equation in cylindrical and spherical geometries. Afterwards, the solutions of the non-dimensionalized problems are dimensionalized to derive accurate explicit closed-form expressions, describing how surface charging parameters are related to the radius of a charged particle, properties of the solution, and thermodynamic conditions. These analytical formulas enable researchers to properly determine surface potential, surface charge density, total surface charge, and radius of dispersed particles by characterizing only one of them. Finally, the validity of the commonly-held hypothesis that surface charge density is independent of particle size is examined at the end of this study.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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