Yablonsky, together with Lazman, developed the general form of steady-state kinetic description (the kinetic polynomial’), which is a non-linear generalization of many theoretical expressions proposed previously (the Langmuir –Hinshelwood and Hougen–Watson equations).^[2] Yablonsky also created a theory of precise catalyst characterization for the advanced worldwide experimental technique (temporal analysis of products) developed by John T. Gleaves at Washington University in St. Louis.^[3]

In 2008–2011, Yablonsky, together with Constales and Marin (Ghent University, Belgium), and Alexander Gorban (University of Leicester, UK), obtained new results on coincidences and intersections in kinetic dependences and found a new type of symmetry relation between the observable and initial kinetic data.^[4][5][6]

Together with Alexander Gorban, Yablonsky developed the theory of chemical thermodynamics and detailed balance in the limit of irreversible reactions.^[7][8]

Catalytic trigger and catalytic oscillator edit

A simple scheme for the nonlinear kinetic oscillations in heterogeneous catalytic reactions has been proposed by Bykov, Yablonsky, and Kim in 1978.^[9] The authors have started with the catalytic trigger (1976^[10][11]), the simplest catalytic reaction without autocatalysis that allows multiplicity of steady states.

${\displaystyle {\ce {{A2}+2Z <=> 2AZ}}}$

(1)

${\displaystyle {\ce {{B}+Z <=> BZ}}}$

(2)

${\displaystyle {\ce {{AZ}+BZ -> {AB}+2Z}}}$

(3)

Then they have supplemented this classical adsorption mechanism of catalytic oxidation by a "buffer" step

${\displaystyle {\ce {{B}+Z\rightleftharpoons (BZ)}}}$

(4)

Here, A₂, B, and AB are gases (for example, O₂, CO, and CO₂), Z is the "adsorption place" on the surface of the solid catalyst (for example, Pt), AZ and BZ are the intermediates on the surface (adatoms, adsorbed molecules, or radicals), and (BZ) is an intermediate that does not participate in the main reaction.

Let the concentration of the gaseous components be constant. Then the law of mass action gives for this reaction mechanism a system of three ordinary differential equations that describe kinetics on the surface.

${\displaystyle {\dot {x}}=2q_{1}z^{2}-2q_{5}x^{2}-q_{3}xy}$

(5)

${\displaystyle {\dot {y}}=q_{2}z-q_{6}y-q_{3}xy}$

(6)

${\displaystyle {\dot {s}}=q_{4}z-kq_{4}s}$

(7)

where z = 1 − (x + y + s) is the concentration of the free places of adsorption on the surface ("per one adsorption center"), x and y are the concentrations of AZ and BZ, correspondingly (also normalized "per one adsorption center"). and s is the concentration of the buffer component (BZ).

This three-dimensional system includes seven parameters. The detailed analysis shows that there are 23 different phase portraits for this system, including oscillations, multiplicity of steady states, and various types of bifurcations.^[12]

Reactions without the interaction of different components edit

Let the reaction mechanism consist of reactions.

${\displaystyle \alpha _{r}A_{i_{r}}\to \sum _{j}\beta _{rj}A_{j}\,,}$ 

where ${\displaystyle A_{i}}$  are symbols of components, r is the number of the elementary reaction and ${\displaystyle \alpha _{r},\beta _{rj}\geq 0}$  are the stoichiometric coefficients (usually they are integer numbers). (The components that are present in excess and the components with almost constant concentrations are not included.)

The Eley–Rideal mechanism of CO oxidation on PT provides a simple example of such a reaction mechanism without interaction of different components on the surface:

${\displaystyle {\ce {2Pt(+O2)<=>2Pt;\;\;{PtO}+CO<=>{Pt}+CO2\!\uparrow }}}$ .

Let the reaction mechanism have the conservation law

${\displaystyle \alpha _{r}m_{i_{r}}=\sum _{j}\beta _{rj}m_{j}{\text{ for some }}m_{j}>0{\text{ and all }}r,}$ 

and let the reaction rate satisfy the mass action law:

${\displaystyle W_{r}=k_{r}c_{i_{r}}^{\alpha _{r}},}$ 

where ${\displaystyle c_{i}}$  is the concentration of ${\displaystyle A_{i}}$ . Then the dynamic of the kinetic system is very simple: the steady states are stable^[13] and all solutions ${\displaystyle \mathbf {c} (t)=(c_{i}(t))}$  with the same value of the conservation law ${\displaystyle m(\mathbf {c} )=\sum m_{i}c_{i}}$  monotonically converge in the weighted ${\displaystyle l_{1}}$  norm: the distance between such solutions ${\displaystyle \mathbf {c} ^{(1)}(t),\mathbf {c} ^{(2)}(t)}$ ,

${\displaystyle \|\mathbf {c} ^{(1)}-\mathbf {c} ^{(2)}\|=\sum _{i}m_{i}|c_{i}^{(1)}-{c}_{i}^{(2)}|,}$ 

monotonically decreases in time.^[14]

This quasithermodynamic property of the systems without interaction of different components is important for the analysis of the dynamics of catalytic reactions: nonlinear steps with two (or more) different intermediate reagents are responsible for nontrivial dynamical effects like multiplicity of steady states, oscillations, or bifurcations. Without interaction between different components, the kinetic curves converge into a simple norm, even for open systems.

The extended principle of detailed balance edit

The detailed mechanism of many real physico-chemical complex systems includes both reversible and irreversible reactions. Such mechanisms are typical in homogeneous combustion, heterogeneous catalytic oxidation, and complex enzyme reactions. The classical thermodynamics of perfect systems is defined for reversible kinetics and has no limit for irreversible reactions.^[8] On the contrary, the mass action law gives the possibility to write the chemical kinetic equations for any combination of reversible and irreversible reactions. Without additional restrictions, this class of equations is extremely wide and can approximate any dynamical system with preservation of positivity of concentrations and the linear conservation laws. (This general approximation theorem was proved in 1986.^[15]) The model of real systems should satisfy some restrictions. Under the standard microscopic reversibility requirement, these restrictions should be formulated as follows: A system with some irreversible reactions should be at the limit of the systems with all reversible reactions and the detailed balance conditions.^[7] Such systems have been completely described in 2011.^[7] The extended principle of detailed balance is the characteristic property of all systems that obey the generalized mass action law and is the limit of systems with detailed balance when some of the reaction rate constants tend to zero (the Gorban-Yablonsky theorem).

The extended principle of detailed balance consists of two parts:

• The algebraic condition: The principle of detailed balance is valid for the reversible part. This means that for the set of all reversible reactions, there exists a positive equilibrium where all the elementary reactions are equilibrated by their reverse reactions.
• The structural condition is that the convex hull of the stoichiometric vectors of the irreversible reactions has an empty intersection with the linear span of the stoichiometric vectors of the reversible reactions. (Physically, this means that the irreversible reactions cannot be included in oriented cyclic pathways.)

The stoichiometric vector of the reaction ${\displaystyle \sum _{i}\alpha _{i}A_{i}\to \sum _{j}\beta _{j}A_{j}}$  is the gain minus loss vector with coordinates ${\displaystyle \gamma _{i}=\beta _{i}-\alpha _{i}}$ .

(It may be useful to recall the formal convention: the linear span of an empty set is 0; the convex hull of an empty set is empty.)

The extended principle of detailed balance gives an ultimate and complete answer to the following problem: how to throw away some reverse reactions without violating thermodynamics and microscopic reversibility? The answer is that the convex hull of the stoichiometric vectors of the irreversible reactions should not intersect with the linear span of the stoichiometric vectors of the reversible reactions, and the reaction rate constants of the remaining reversible reactions should satisfy the Wegscheider identities.

From 1997 to 2007, Yablonsky was a research associate professor in the department of energy, environmental, and chemical engineering at Washington University in St. Louis. Since 2007, Yablonsky has been an associate professor at Saint Louis University's Parks College of Engineering, Aviation, and Technology as well as in the department of chemistry.

During his career, Yablonsky has organized many conferences and workshops at national and international levels. Yablonsky frequently participates in interdisciplinary dialogues involving mathematicians, chemists, physicists, and chemical engineers.^[vague]

Yablonsky was selected in 2013 for the James B. Eads Award,^[16][17] which recognizes a distinguished individual for outstanding achievement in engineering or technology.

• Lifetime Achievement Award, in recognition of outstanding contributions to the research field of chemical kinetics, Mathematics in Chemical Kinetics and Engineering, MaCKiE, 2013
• James B. Eads Award, Academy of Science of St. Louis Outstanding Scientist Award (2013).^[18]
• Honorary Doctor Degree from the University of Ghent, Belgium (2010)^[19]
• Chevron Chair Professorship at the Indian Institute of Technology (IIT), Madras (2011)
• Honorary Fellow of the Australian Institute of High Energetic Materials, Gladstone, Australia (2011)

Yablonsky has numerous international designations as an honorary professor, fellow, doctor, and member of prestigious science academies and universities in Belgium, India, China, Russia, and Ukraine.

• 1996–present: American Institute of Chemical Engineers
• 2011–present: American Chemical Society
• 2011–present: Member of the Scientific Council on Catalysis at the Russian Academy of Sciences
• 2013–present: Fellow, Academy of Science of St. Louis

Yablonsky is the author of seven books, most recently^{[as of?]} Kinetics of Chemical Reactions: Decoding Complexity Wiley-VCH (2011) (together with Guy B. Marin), and more than 200 papers.

• Yablonsky, G.S.; V.I. Bykov; A.N. Gorban'; V.I. Elokhin (1991). Kinetic Models of Catalytic Reactions. Amsterdam–Oxford–New York–Tokyo: Elsevier.
• Marin, G.B.; G.S. Yablonsky (2011). Kinetics of Complex Reactions. Decoding Complexity. Wiley-VCH. p. 428. ISBN 978-3-527-31763-9.
• Estathiou, A.M.; G.S. Yablonsky; Gleaves, J. T. (2012). "Transient Techniques: Temporal Analysis of Products and Steady State Isotopic Transient Kinetic Analysis". Transient Techniques: Temporal Analysis of Products (TAP) and Steady-State Isotopic Transient Kinetic Analysis (SSITKA). Vol. 1 & 2. pp. 1013–1073. doi:10.1002/9783527645329.ch22. ISBN 9783527645329.
• Gleaves, J.T.; G.S. Yablonsky; P. Phanawadee; Y. Schuurman (14 October 1997). "TAP-2. Interrogative Kinetics Approach". Applied Catalysis A: General. 160 (1): 55–88. doi:10.1016/S0926-860X(97)00124-5.
• Grigoriy, Yablonsky; M. Olea; G. Marin (May–June 2003). "Temporal Analysis of Products: Basic Principles, Applications, and Theory". Journal of Catalysis. 216 (1–2): 120–134. doi:10.1016/S0021-9517(02)00109-4.
• Yablonsky, Grigoriy; I.M.Y. Mareels; M. Lazman (November 2003). "The principle of critical simplification in chemical kinetics". Chemical Engineering Science. 58 (21): 4833–4842. Bibcode:2003ChEnS..58.4833Y. doi:10.1016/j.ces.2003.08.004.
• Feres, R.; G.S. Yablonsky (2004). "Knudsen Diffusion and Random Billiards". Chemical Engineering Science. 59 (7): 1541–1556. doi:10.1016/j.ces.2004.01.016.

• Chemical reaction network theory

• Yablonsky's faculty profile at Parks College of Engineering, Aviation and Technology