ТЕОРЕТИЧЕСКИЕ ОСНОВЫ ХИМИЧЕСКОЙ ТЕХНОЛОГИИ, 2014, том 48, № 5, с. 551-556
УДК 66.011
DECODING COMPLEXITY OF CHEMICAL REACTIONS
© 2014 G. S. Yablonsky
Parks College of Engineering, Aviation and Technology, Department of Chemistry, Saint Louis University, St. Louis, Missouri, USA gyablons@slu.edu Received 01.04.2014
Three approaches for grasping chemical complexity using data of kinetic measurements are presented, i.e. 'gray-box' approach, non-steady-state kinetic monitoring ("chemical calculus") and pattern analysis. All approaches are illustrated by original results.
Keywords: chemical complexity, gray-box approach, non-steady-state kinetic screening, temporal analysis of products (TAP), Y-procedure, analysis of kinetic fingerprints, chemical kinetics, kinetic models, catalytic reactions.
DOI: 10.7868/S0040357114050121
INTRODUCTION
Decoding complexity, which is considered one of the main scientific problems of the 21st century [1], aims in chemistry at explaining the temporal evolution of a multi-component chemical mixture. Three different meanings of "chemical time" can be distinguished [2]:
"Clock" time, or astronomic time, or "external" time of the system, t. This time relates to a change of chemical composition observed during some time interval.
"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 of a chemical reaction, i.e. the time scale at which it occurs, is the reciprocal value of its rate coefficient with dimension s-1.
Residence time. This time reflects the "transport time" of a chemical process, e.g. in a plug-flow reactor.
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. 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", i.e. a multi-component chemical mixture changes in time and space. For example, in the oxidation of hydrogen, a homogeneous gas-phase reaction,
2H2 + O2 2H2O
there are as much as nine different components and as much as 60 reactions elementary reactions (30 forward and 30 reverse ones, respectively) involved.
In heterogeneous reactions, e.g. 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 on solid catalysts, which can dramatically accelerate these reactions. Many catalysts are multi-component solids, e.g. 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, etc. 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 we have to decode.
In decoding complexity in chemical kinetics, immediately many questions regarding this decoding arise:
1. What are we going to decode?
2. What are the experimental characteristics based on which we are going to decode?
3. In which terms are we going to decode?
Typical answers are the following:
1. Most of chemical reactions can be considered complex, in particular catalytic reactions. Catalysis is a subject of special interest, both industrial and academic.
2. We are going to decode complex reactions based on kinetic experiments, i.e. measurements of rates of transformation of chemical components.
3. We are going to try and interpret kinetic data based on the concept of reaction mechanism (or detailed mechanism), which is a detailed description of the steps leading from reactants to products of the reaction, and including 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. It is difficult to overestimate the role of chemical kinetics both in understanding the "intimate" character of chemical reactions and in designing new chemical processes and reactors.
THREE TYPES OF CHEMICAL KINETICS
Presently, chemical kinetics is an area of 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 applied kinetics, detailed kinetics and mathematical kinetics [2].
Applied kinetics. The goal of applied kinetics is obtaining kinetic dependences for the design of efficient catalytic processes and reactors. Kinetic dependences are dependences of rates of chemical transformations on reaction conditions, i.e. temperature, pressure, concentrations, etc. 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 Boresk-ov 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 a kinetic model. Applied kinetic models are, as a rule, stationary, i.e. they are based on kinetic data obtained at steady-state conditions.
During the past 15 years, a lot of attention has been paid to the problem of selecting the best catalyst via so-called "combinatorial catalysis" procedures, i.e. 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.
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 both the broad and the narrow sense. In its application to catalytic reactions, one should specify reactants, products
and intermediates, reaction steps, surface properties, adsorption patterns, etc.
In the practice of chemical kinetics, detailed kinetics is often used in a more narrow sense, as a set of elementary steps. Each elementary step consists of a forward and a reverse elementary reaction, the kinetic dependences of which are governed by the mass-action law.
Mathematical kinetics. Mathematical kinetics deals with the analysis ofvarious mathematical models that are used in chemical kinetics. As a rule, these are deterministic models representing a set of algebraic, ordinary differential or partial differential equations. There are also stochastic models, which 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, etc.
Problems related to mathematical kinetics may be direct or inverse kinetic problems. A direct kinetic problem is an analysis of a given kinetic model, either steady-state or non-steady-state, with known kinetic parameters. On the other hand, an inverse kinetic problem is aimed at reconstructing the kinetic dependences and estimate their parameters based on experimental kinetic data, both steady-state and non-steady-state.
CHALLENGES AND GOALS
How to grasp chemical complexity? All three types of chemical kinetics mentioned can be addressed. However, the focus has to done 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 three approaches to "killing chemical complexity":
thermodynamically consistent "gray-box" approach;
analysis of kinetic fingerprints;
non-steady-state kinetic screening.
"Gray-box" approach. Within the "gray-box" approach, a general structurized form of the steady-state rate equation of the complex reaction is presented for linear reaction mechanisms [4, 5] and for nonlinear reaction mechanisms, the so-called "kinetic polynomial" [6].
This equation must contain some terms that can be written easily without any knowledge about the detailed mechanism, but only based on the overall equation of the complex reaction, including only reactants and products and no intermediates.
Nevertheless, this approach is not statistical modeling of the "black-box" type, as the kinetic models concerned are consistent from a thermodynamic point of view; if the reaction rate equals zero, the driving force equals zero as well, so thermodynamic relationships are fulfilled. That is why we call this approach a gray-box approach. In fact, it is a rigorous generaliza-
tion of results presented in the 1930s and 1940s by Horiuti, Boreskov and Hougen and Watson.
Lazman and Yablonsky [6] showed how the gray-box approach works for a general nonlinear mechanism, in which more than one intermediate can participate in an elementary reaction.
The kinetic polynomial for a single-route mechanism is rigorously represented as foll
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.