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Tafel plot for an anodic process . The Tafel equation is an equation in electrochemical kinetics relating the rate of an electrochemical reaction to the overpotential. [1] The Tafel equation was first deduced experimentally and was later shown to have a theoretical justification. The equation is named after Swiss chemist Julius Tafel.
Such rates provide insights into the structure and bonding in the analyte and the electrode. For example, the exchange current densities for platinum and mercury electrodes for reduction of protons differ by a factor of 10 10, indicative of the excellent catalytic properties of platinum. Owing to this difference, mercury is the preferred ...
The slope of the potential vs. time graph is called the scan rate and can range from mV/s to 1,000,000 V/s. [3] The working electrode is one of the electrodes at which the oxidation/reduction reactions occur—the processes that occur at this electrode are the ones being monitored. The auxiliary electrode (or counter electrode) is the one at ...
The upper graph shows the current density as function of the overpotential η . The anodic and cathodic current densities are shown as j a and j c, respectively for α=α a =α c =0.5 and j 0 =1mAcm −2 (close to values for platinum and palladium).
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
In enzyme kinetics, a secondary plot uses the intercept or slope from several Lineweaver–Burk plots to find additional kinetic constants. [1] [2]For example, when a set of v by [S] curves from an enzyme with a ping–pong mechanism (varying substrate A, fixed substrate B) are plotted in a Lineweaver–Burk plot, a set of parallel lines will be produced.
Therefore, a plot of drain current versus gate voltage with drain, source, and bulk voltages fixed will exhibit approximately log-linear behaviour in this MOSFET operating regime. Its slope is the subthreshold slope. The subthreshold slope is also the reciprocal value of the subthreshold swing S s-th which is usually given as: [1]
For example, if the feed is a saturated liquid, q = 1 and the slope of the q-line is infinite (drawn as a vertical line). As another example, if the feed is saturated vapor, q = 0 and the slope of the q-line is 0 (a horizontal line). [2] The typical McCabe–Thiele diagram in Figure 1 uses a q-line representing a partially vaporized feed.