The characteristic curvature (Cc) definition and its use in assessing Cc for single ionic surfactants
Bibliographic record
Abstract
Abstract The hydrophilic–lipophilic‐difference (HLD) is a set of empirical equations that correlate the formulation conditions at phase inversion (HLD = 0). Based on partition studies for nonionic surfactants, the HLD can be interpreted as a normalized chemical potential difference between the surfactant dissolved in water and oil. The net‐average curvature (NAC) model extrapolates this interpretation into a curvature form that has been used to fit and predict the phase behavior of surfactant‐oil–water (SOW) systems. The curvature interpretation led to renaming the HLD surfactant parameter, sigma ( σ ), as the characteristic curvature (Cc). This work tests the validity of the curvature interpretation of the HLD, and the Cc concept, for single ionic surfactants and the use of this concept as a method to assess the Cc without the use of reference surfactants or alcohols. To this end, the net curvature of six anionic and two cationic surfactants was evaluated from solubilization data at the characteristic condition of 25°C, no added cosolvent, in the presence of an oil mixture with equivalent alkane carbon number (EACN) of zero, and as a function of salinity. These studies showed that the original HLD equation for ionic surfactant could not be interpreted as chemical potential or curvature because a salinity prefactor (coefficient) “bi” was missing. The revised equation, HLD bi = bi∙ln(S)‐k bi ∙EACN+Cc bi ‐a Tbi ∙(T‐25°C), could now be interpreted as a curvature expression, and it was demonstrated that Cc could be obtained from curvature using the expression Cc = Cc bi /bi. This single surfactant method produces uncertainties that, for most surfactants, ranged from 0.2 to 1 Cc units, similar to the uncertainty obtained with the conventional method of Cc determination using mixtures of test and reference surfactants.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".