Delplot analysis

Start with the question

Imagine feeding a molecule A to a catalyst and detecting several products. A product list alone does not tell you whether each compound formed directly from A or appeared later, after another product reacted. Delplot analysis is a way to use measurements taken at different conversions to estimate the formation rank of observed products.

Think of it as a disciplined clue about reaction order—not a photograph of the catalyst surface and not, by itself, proof of a complete mechanism. The original method was developed to complement kinetic model discrimination by helping infer product rank from yield and conversion data. [1]

The quantities and the plot

Choose one reference reactant, A, and define conversion and product yield consistently. For a feed containing no product P initially, a common molar basis is:

Here, A₀ and A are the inlet and unreacted amounts (or molar flow rates), P is the amount of product, X_A is conversion, Y_P is yield, and S_P is selectivity on this basis. If the feed already contains P, subtract its inlet amount when calculating net product yield. For non-1:1 stoichiometry, define a stoichiometrically consistent yield basis and state it.

A rank-r Delplot graphs:

At rank 1, the vertical quantity is selectivity: Y_P/X_A. For higher ranks, divide yield by the corresponding higher power of conversion. A finite, non-zero limiting intercept at rank r is evidence that product P has Delplot rank r under the method's assumptions. A zero intercept at rank 1 says the product is not observed as a primary product by this test; alone, it does not identify the exact later route. [1]

What “rank” means

These labels summarize observed product formation order, not necessarily the number of elementary surface events. An actual catalytic route may contain unmeasured adsorbed intermediates, parallel branches, reversibility, or multiple ways to make the same molecule. The original work distinguishes the rank detected by Delplot from a network's underlying rank; treat “primary/secondary” as an operational inference, not an absolute mechanistic identity. [1]

How to do it in practice

1. Define the system and basis. Name the reference reactant, stoichiometry, conversion definition, product yield basis, and any inlet products. Use the same conventions at every condition.
2. Collect a conversion series. In a flow reactor, vary contact time or space velocity; in a batch reactor, vary reaction time. Keep temperature, pressure, feed composition, catalyst state, and other relevant conditions controlled.
3. Include low-conversion points. Rank is inferred by extrapolating toward zero conversion. Ensure product quantitation is sensitive and precise enough in this region; avoid relying on a few scattered high-conversion points.
4. Calculate conversion and yield for every observation. Use consistent mole balances and report analytical uncertainty and carbon balance where appropriate.
5. Plot rank 1 first. For each product, plot Y_P/X_A against X_A. A reproducible finite, non-zero intercept supports primary formation.
6. Test higher ranks cautiously. For products with no supported rank-1 intercept, plot Y_P/X_A², then higher powers if the data quality and chemistry justify it. Compare candidate ranks across the same low-conversion region.
7. Build a candidate network, then challenge it. Check whether the ordering fits product-time trends, stoichiometry, plausible chemistry, and kinetic fits. Seek independent evidence for intermediates or surface steps.

A simple illustration

For the hypothetical sequence A → B → C, B is formed directly from A. At sufficiently low conversion, its yield can scale approximately with conversion, so Y_B/X_A can approach a finite non-zero value: evidence for rank 1. C requires further reaction of B; in the ideal simple case its yield grows approximately as conversion squared near zero, so Y_C/X_A² can approach a finite non-zero value: evidence for rank 2. This suggests B forms before C. It does not establish the catalyst's elementary steps, active site, or rate law.

What it explains—and why catalysis researchers use it

Delplot helps answer a focused question: which detected products appear to be formed directly from the feed, and which emerge only after additional transformations? This can narrow candidate reaction networks, flag plausible intermediates, guide which compounds to test as feeds, and help plan kinetic experiments. It is especially useful when several products are present and a selectivity value measured at only one conversion cannot reveal formation order.

It does not by itself explain why a catalyst prefers a route, identify a molecular mechanism, reveal invisible surface intermediates, prove an active site, or uniquely determine rate constants. Its value is as an independent, relatively simple diagnostic to pair with kinetic modeling and mechanistic experiments.

Catalysis example: GVL hydrodeoxygenation

In a study of γ-valerolactone (GVL) hydrodeoxygenation over Ni₂P/MCM-41, the proposed network placed pentanoic acid and 2-methyltetrahydrofuran (2-MTHF) among the initial products, with other products—including pentanal, butane, and pentane—appearing later in the proposed sequence. The first-rank analysis supported the two initial products, but higher-rank plots did not reliably recover the full sequence. The authors attributed this limitation to a later step consuming pentanal much faster than preceding steps: under those kinetics, pentanal could look primary to the analysis and distort assignment of subsequent products. [2]

This is a valuable teaching example: a plausible first-rank result does not guarantee the higher-rank results will work. Compare the plot-based inference with contact-time data and kinetic modeling.

Important limitations

• Very different step rates can mislead. A rapidly consumed intermediate may build little concentration or make downstream products appear to have a lower rank than expected. The GVL case demonstrates this issue. [2]
• Low-conversion measurements are demanding. Product signals are small, and uncertainty can dominate the extrapolated intercept. Sparse measurements make higher ranks particularly fragile. [2]
• Products may have mixed origins. One molecule can form both directly and through a secondary route. It may not have one clean rank, so inspect the shape and chemistry rather than forcing a single label. [3]
• Unobserved adsorbates matter. In benzofuran hydrodeoxygenation on CoPd phosphide/KUSY, Delplot agreed with simpler networks built from observed gas-phase species but not with more detailed networks containing adsorbed intermediates. The study linked the problem to strong adsorbate formation equilibria. [4]
• Rank is not mechanism. The method organizes observable product behavior. It cannot uniquely reconstruct hidden intermediates or elementary chemistry.

Take-home message

Delplot turns a series of product-yield-versus-conversion measurements into a structured hypothesis about the order in which observable products form. Use consistent definitions, measure low conversion well, and interpret rank assignments across the whole network. Then test the proposed pathway with kinetic modeling and independent mechanistic evidence. When rates are widely separated or adsorbed intermediates dominate, report Delplot as inconclusive or limited—not as a definitive reaction sequence.