chemistry

Neopolarogram

Neopolarogram is a chemistry topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Neopolarogram rather than just read about it. In short: The term neopolarogram refers to mathematical derivatives of polarograms or cyclic voltammograms that in effect deconvolute diffusion and electrochemical kinetics. This is achieved by analog or digital implementations of fractional calculus.

Key takeaways

Neopolarogram belongs to chemistry; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Neopolarogram to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Neopolarogram from memory before moving on to harder problems.

Reference excerpt

The term neopolarogram refers to mathematical derivatives of polarograms or cyclic voltammograms that in effect deconvolute diffusion and electrochemical kinetics. This is achieved by analog or digital implementations of fractional calculus. The implementation of fractional derivative calculations by means of numerical methods is straight forward. The G1- (Grünwald–Letnikov derivative) and the RL0-algorithms (Riemann–Liouville integral) are recursive methods to implement a numerical calculation of fractional differintegrals. Yet differintegrals are faster to compute in discrete fourier space using FFT.

Applications The graphs below show the behaviour of fractional derivatives calculated by different algorithms for ferrocene in acetonitrile at 100mV/s, the reference electrode is 0.1M Ag+/Ag in acetonitrile (+0.04V vs. Fc).

1st derivative of the "Semiderivative" or 1.5th order derivative in voltammetry 1.5th order derivative of a voltammogram hits the abscissa exactly at the point where the formal potential of the electrode reaction is found.

"Semiderivative" or numerical Grünberg-Letnikov derivative in voltammetry The G1 algorithm produces a numerical derivative that has the shape of a bell curve, this derivative obeys to certain laws, for example the G1 derivative of a cyclic voltammogram is mirrored at the abscissa as long as the electrochemical reaction is diffusion controlled, the planar diffusion approximation can be applied to the electrode geometry and ohmic drop distortion is minimal. The FWHM of the curve is approximately 100 mV for a system that behaves in the described manner. The maximum is found at the value of the formal potential, this is equivalent to the 1.5th order semiderivative hitting the abscissa at this potential. Moreover, the semiderivative scales linearly with the scanrate, while the current scales linearly with the square root of the scanrate (Randles–Sevcik equation). Plotting the semiderivatives produced at different scanrates gives a family of curves that are linearly related by the scanrate quotient in an ideal system.

"Semiintegral" or numerical Riemann-Liouville integral in voltammetry The shape of the semiintegral can be used as an easy method to measure the amount of ohmic drop of an electrochemical cell in cyclic voltammetry. Essentially the semiintegral of a cyclic voltammogram at a planar electrode (an electrode that obeys to the rules of planar diffusion) has the shape of a sigmoid while the original data is gauss-sigmoid convoluted. This enables the operator to optimize parameters necessary for positive feedback compensation in an easy manner. If ohmic drop distortion is present the two sigmoids for the forward and the backward scan are far away from congruence, the ohmic drop can be calculated from the deviation from congruence in these cases. In the example shown slight distortion is present, yet this does not have adverse effects on data quality.

Merits of FFT techniques The implementation differintegral calculation using fast fourier transform has certain benefits because it is easily combined with low pass quadratic filtering methods. This is very useful when cyclic voltammograms are recorded in high resistivity solvents like tetrahydrofuran or toluene, where feedback oscillations are a frequent problem.

References

Illustrations

Worked examples

Example 1 — a first encounter with Neopolarogram

Start with the simplest possible case. Write down what Neopolarogram claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Neopolarogram before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Neopolarogram ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Neopolarogram

In research: Neopolarogram appears in chemistry research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Neopolarogram in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Neopolarogram is common in secondary-school and first-year university syllabi. It links to neighbouring topics Electroanalytical chemistry, so understanding it makes those chapters shorter.
In everyday life: Look for Neopolarogram outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Neopolarogram in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Neopolarogram means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Neopolarogram out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Neopolarogram in simple terms?

Why does Neopolarogram matter?

Because it connects several chemistry ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Neopolarogram?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Neopolarogram.