Defining the Transfer Coefficient in Electrochemistry: An Assessment
Bibliographic record
Abstract
The transfer coefficient α is a quantity that is commonly employed in the kinetic investigation of electrode processes. In the 3rd edition of the IUPAC Green Book, the cathodic transfer coefficient αc is defined as –(RT/nF)(dlnkc/dE), where kc is the electroreduction rate constant, E is the applied potential, and R, T, and F have their usual significance. This definition is equivalent to the other, -(RT/nF)(dln|jc|/dE), where jc is the cathodic current density corrected for any changes in the reactant concentration at the electrode surface with respect to its bulk value. The anodic transfer coefficient αa is defined similarly, by simply replacing jc with the anodic current density ja and the minus sign with the plus sign. It is shown that this definition applies only to an electrode reaction that consists of a single elementary step involving the simultaneous uptake of n electrons from the electrode in the case of αc, or their release to the electrode in the case of αa. However, an elementary step involving the simultaneous release or uptake of more than one electron is regarded as highly improbable in view of the absolute rate theory of electron transfer of Marcus; the hardly satisfiable requirements for the occurrence of such an event are examined. Moreover, the majority of electrode reactions do not consist of a single elementary step; rather, they are multistep, multi-electron processes. The uncritical application of the above definitions of αc and αa has led researchers to provide unwarranted mechanistic interpretations of electrode reactions. In fact, the only directly measurable experimental quantity is dln|j|/dE, which can be made dimensionless upon multiplication by RT/F, yielding (RT/F)(dln|j|/dE). One common source of misinterpretation consists in setting this experimental quantity equal to αn, according to the above definition of the transfer coefficient, and in trying to estimate n from αn, upon ascribing an arbitrary value to α, often close to 0.5. The resulting n value is then identified with the number of electrons involved in a hypothetical rate-determining step or with that involved in the overall electrode reaction. A few examples of these unwarranted mechanistic interpretations are reported. In view of the above considerations, it is proposed to define the cathodic and anodic transfer coefficients by the quantities αc = –(RT/F)(dln|jc|/dE) and αa = (RT/F)(dlnja/dE), which are independent of any mechanistic consideration.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.021 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.006 | 0.016 |
| Open science | 0.006 | 0.006 |
| Research integrity | 0.004 | 0.010 |
| Insufficient payload (model declined to judge) | 0.003 | 0.003 |
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 source (direct Gemma or distilled Codex), 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".