1
Introduction

1.1 Overview

Chemistry is a complex science, especially for chemists. The etymology of the word "chemistry," the science of matter and its transformations, is a debatable issue [1]. It is very likely that it has been borrowed from the ancient name for Egypt, "Keme" the birthplace of alchemy. The word "complex" comes from the Latin word "complexus" the past participle of "complecti" (to entwine, encircle, compass, infold), from "com" (together) and "plectere" (to weave, braid).

Decoding complexity is considered one of the main scientific problems of the twenty-first century. In chemistry, this process of decoding aims at explaining the temporal evolution of a multicomponent chemical mixture. In this book, depending on the context, there are three different meanings of "time":

1. "Clock" time , or astronomic time , or "external" time of the system, t : This time relates to the change of chemical composition observed during some time interval.
2. "Internal" or "intrinsic" time: Typically, we consider this time when we are talking about the hierarchy of times of different chemical processes or reactions. For a first-order reaction, the intrinsic time, that is, the timescale at which the reaction occurs, is the reciprocal value of its rate coefficient that has the dimension per second.
3. Residence time: This time reflects the "transport time" of a chemical process, for example, in a plug-flow reactor () (see Chapter 3).

An excellent collection of the different meanings of time can be found in Ref. [2].

Formally, the non-steady-state model for a chemical process in a closed system (batch reactor) is identical to the steady-state model for the same chemical process in an open system in which the longitudinal profile of the chemical composition is taken into account, but the radial profile is neglected (see Chapter 3 for more details). In the latter model, the space time, which is proportional to the residence time, corresponds to astronomical time in the model for the batch reactor.

In the description of chemical complexity, the first key words are "many components," "many reactions" and "change," that is, a multicomponent chemical mixture changes in time and space. For example, in the homogeneous gas-phase oxidation of hydrogen

there are as much as nine different components and as much as 60 reactions involved. See Chapter 2 for more details.

In heterogeneous reactions, for example gas-solid reactions, the situation becomes even more complicated. Rephrasing Lewis Carroll's saying from Alice in Wonderland, "curiouser and curiouser," one can say "complexier and complexier." Over 90% of industrial chemical reactions occur with solid catalysts that can dramatically accelerate these reactions. Many catalysts are multicomponent solids, for example, mixed transition metal oxides on some support used in the selective oxidation of hydrocarbons. Catalysts can exist in different states that depend on the oxidation degree, water content, bulk structure, and so on. These states have different physicochemical properties and different abilities to accelerate reactions. Moreover, the catalyst composition changes in time under the influence of the reaction medium. This is the level of chemical complexity that needs to be decoded.

1.2 Decoding Complexity in Chemical Kinetics

Immediately, many questions regarding this decoding arise:

1. What are we going to decode?
2. Based on which experimental characteristics are we going to decode?
3. In which terms are we going to decode?

In this book, our answers are the following:

1. We are going to decode data mostly related to heterogeneous catalytic reactions.
2. We are going to decode these data based on experimental characteristics obtained during kinetic experiments, that is, measurements of rates of transformation of chemical components.
3. We are going to try and interpret these kinetic data based on the concept of reaction mechanism (or detailed mechanism), a detailed description of the steps leading from reactants to products of the reaction, which includes intermediates.

We consider this decoding to be an inherent feature of chemical kinetics, which can be defined as the science of rates and mechanisms of chemical reactions. One can hardly overestimate the role of chemical kinetics, both in understanding the "generative" character of chemical reactions and in designing new chemical processes and reactors.

1.3 Three Types of Chemical Kinetics

Presently, chemical kinetics is an area comprising challenges and adventures, in which at least four sciences overlap: chemistry, physics, chemical engineering, and mathematics. In fact, contemporary chemical kinetics itself is a complex combination of different areas. Depending on the goal of a kinetic analysis, one may distinguish between applied kinetics, detailed kinetics, and mathematical kinetics.

1.3.1 Applied Kinetics

The goal of applied kinetics is to obtain kinetic dependences for the design of efficient catalytic processes and reactors. Kinetic dependences are dependences of the rates of chemical transformations on reaction conditions, that is, temperature, pressure, concentrations, and so on. When expressed mathematically, these dependences are called kinetic models. A kinetic model is the basis of the mathematical simulation of a chemical process. A series of models needs to be developed for the simulation of a catalytic reactor: kinetic model model of catalyst pellet model of catalyst bed model of reactor. In this hierarchy of models, introduced by Boreskov and Slin'ko [3], the kinetic model represents the initial level, the foundation. No technologically interesting description of a chemical reactor can be given without reference to a kinetic model. Applied kinetic models are, as a rule, stationary; they are based on kinetic data obtained at steady-state conditions.

During the past 25?years, a lot of attention has been paid to the problem of selecting the best catalyst via so-called "combinatorial catalysis" procedures, which involve simultaneous steady-state testing of many different catalyst samples. However, the technique and methodology for precise kinetic catalyst characterization is still far from being complete, in particular for catalyst characterization at non-steady-state conditions. Such characterization is a critical issue in the design of a new generation of catalysts.

1.3.2 Detailed Kinetics

The study of detailed kinetics is aimed at reconstructing the detailed mechanism of a reaction, based on kinetic and non-kinetic (adsorption, desorption, spectrometric, etc.) data. The concept of a detailed mechanism may be used in a broad as well as a narrow sense. In its application to catalytic reactions, one should specify reactants, products, intermediates, reaction steps, surface properties, adsorption patterns, and so on.

In the practice of chemical kinetics, detailed kinetics is often used in a more narrow sense, as a set of elementary reaction steps. Each elementary step consists of a forward and a reverse elementary reaction, whose kinetic dependences are governed by the mass-action law.

1.3.3 Mathematical Kinetics

Mathematical kinetics deals with the analysis of various mathematical models that are used in chemical kinetics. As a rule, these are deterministic models consisting of a set of algebraic, ordinary differential or partial differential equations. There are also stochastic models that are based on Monte Carlo methods, for modeling adsorption or surface-catalytic reactions, reaction-diffusion processes in the catalyst pellet or in the catalyst bed, and so on.

Problems related to mathematical kinetics may be either direct kinetic problems or inverse kinetic problems. A direct kinetic problem requires the analysis of a given kinetic model, either steady-state or non-steady-state, with known kinetic parameters. In contrast, solving an inverse kinetic problem involves reconstructing the kinetic dependences and estimating their parameters based on experimental kinetic data, either steady-state or non-steady-state.

1.4 Challenges and Goals. How to Kill Chemical Complexity

We will address all three types of chemical kinetics mentioned. However, the focus will be on one big issue, which can be defined as "the correspondence between observed kinetic behavior and 'hidden' detailed mechanisms." This general problem will be posed and solved using the following three approaches to "killing chemical complexity":

1. thermodynamically consistent "gray-box" approach
2. analysis of kinetic fingerprints
3. non-steady-state kinetic screening.

1.4.1 "Gray-Box" Approach

Within the "gray-box" approach, a general structuralized form of the steady-state rate...