What happens at the crossroads between Chemical Engineering and Mathematics? Prof. Gregory S.Yablonsky
Parks College
Saint Louis University. USA
gyablons@slu.edu
Dept. of Chemical Engineering,
Washington University in St. Louis, USA
gy@che.wustl.edu
What happens at the crossroads between Chemical Engineering and Mathematics? Prof. Gregory S.Yablonsky
Parks College
Saint Louis University. USA
gyablons@slu.edu
Dept. of Chemical Engineering,
Washington University in St. Louis, USA
gy@che.wustl.edu
“I gave my mind a thorough rest by plunging into a chemical analysis” (Sherlock Holmes, “The Sign of Four”, Chapter 10)
Different points of view David Hilbert(1862-1943), the greatest German mathematician : “Chemical stupidity”…
Auguste Comte (1798-1857), the French philosopher, founder of sociology:
“Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry…if mathematical analysis should ever hold a prominent place in chemistry--an aberration which happily almost impossible--it would occasion of rapid and widespread degeneration of that science”
What is Mathematics? What is Chemistry? It is always difficult to answer simple questions.
One can say:
Mathematics is about special
symbolic reasoning or symbolic engineering
Chemistry is about transformation of substances
Or in another way:
Mathematics is Newton, Leibnitz, Hilbert,Hardy…
Chemistry is Lavoisier, Dalton, Avogadro, Mendeleev…
Chemical Engineering is Danckwerts, Damkoehler,
Aris, Amundson, Frank-Kamenetsky…
What is Chemical Engineering? Chemical Engineering = Chemistry + Transport + Material Properties Most of chemical processes (> 90%) occur with participation of special materials – catalysts, which composition is ill-defined. Main topics:
1) Chemistry
2) Transport
3) Catalyst properties
Mathematical Chemistry There are more than 6 millions of references on
“mathematical chemistry”(Internet)
Journal of Mathematical Chemistry (since 1987)
MaCKiE, “Mathematics in Chemical Kinetics and Chemical Engineering” (regular workshop
since 2002)
MATCH, Communications in Mathematics and Computer Chemistry
The mathematical impact into chemistry is growing Models of quantum chemistry (DFT-modeling)
Computational Fluid Dynamics
Monte-Carlo modeling
Statistical analysis
FT (Fourier Transformation) based experiment
The most important chemical problems
Sustainability Problems = Energy via Chemistry,
e.g. development of the efficient C1 transformation system (CO2 sequestration, CO+H2, CO2+CH4), photocatalytic system of water splitting, hydrocarbon oxidation system, etc.
These problems have to be solved urgently.
Revealing chemical complexity What is a chemical complexity?
There are many substances
which participate in many reactions.
Typically, chemical reactions
are performed over the catalysts.
Typically, chemical systems
are non-uniform and non-steady-state.
The chemical composition is changing in space and time.
Single Crystal Single Component
Polycrystalline Well-defined
Surface Structure Increasing Complexity
Increasing Pressure Technical Catalyst
Multi-component
Multi-scale
Polycrystalline
Heterogeneous Surface
Defects
Changes with Reaction Structure-Activity Relationships
“Materials-Pressure Gap” ?
One of the goals in our lab is to understand the relationship between catalyst structure and its activity. One way for us to understand this relationship is to bridge the pressure and materials gap. Under process conditions, it is often difficult to extract intrinsic properties of a catalyst. Intrinsic properties are properties that are directly related to the catalyst composition. Therefore, in order to extract these intrinsic properties, scientists must use surface science techniques under vacuum conditions to study single crystals. By performing single particle experiments using a single component polycrystalline material, we are developing an initial methodology to bridge this pressure and materials gap. Using the TAP reactor, we can define single particles as either single crystals or an industrial catalyst and perform identical experiments under the same conditions on both materials and directly compare the two results.
However we still are very far from revealing chemical complexity, from solving “chemical structure -activity”problem
Decoding Chemical Complexity: Questions Questions before the decoding:
What we are going to decode?
What are experimental characteristics based on which we are going to decode the complexity?
3. In which terms we are going to decode?
Examples of chemical reactions:
Overall Reactions:
2 H2 + O2 2H2O
2SO2 +O2 2SO3
According to chemical thermodynamics,
Keq(T) = C2H2 0/ (C2H2 C02)
Keq(T) = C2SO3 / (C2SO2 CO2)
Detailed Mechanism Detailed mechanism is a set of elementary reactions which law is assumed , e. g. the mass-action-law
An example:Hydrogen Oxidation 2H2 +O2 = 2H2O
1) H2 + O2 = 2 OH ; 2) OH + H2= H2O + H ; 3) H + O2 = OH + O;
4) O + H2 = OH + H ; 5) O + H20 = 2OH; 6) 2H + M = H2 + M ; 7) 2O + M = O2 + M;
8) H + OH + M = H2O + M; 9) 2 OH + M = H2O2 + M; 10) OH + O + M = HO2 + M;
11) H + O2 + M = HO2 + M; 12) HO2 + H2 = H2O2 + H;13) HO2 +H2 = H2O +OH;
14) HO2 + H2O = H2O2 + OH; 15) 2HO2 = H2O2 + O2; 16) H + HO2 = 2 0H;
17) H + HO2 = H2O + O; 18) H + HO2 = H2 + O2; 19) O + HO2 = OH +H;
20) H + H2O2 = H20 + OH; 21) O + H2O2 = OH +H02; 22) H2 + O2 = H20 + O;
23) H2 + O2 + M = H202 + M; 24) OH +M = O + H + M; 25) HO2+OH=H2O+O2;
26) H2 + O +M = H2O +M; 27) O + H2O + M = H202 + M; 28) O + H2O2 = H20 + O2;
29) H2 + H2O2 = 2H2O; 30) H + HO2 + M = H2O2 +M
A matrix is the mathematical image of
complex chemical system
( a chemical graph as well)
“Atomic”(“molecular” matrix)
Stoichiometric matrix
Detailed mechanism matrix
English mathematician Arthur Cayley (1821-1895), one of the first founders of linear algebra, applied its methods for enumerating isomers
Complexity 1. Catalytic reaction is complex itself E.g. mixed transition metal oxides used in the selective oxidation
+ support 2. Industrial catalysts are usually complex multicomponent solids 3. Catalyst composition changes in time under the influence of the reaction medium. Multi step character of the reaction
Including generation of different intermediates A specifically prepared catalyst can exist in different catalyst states
that are functions of oxidation degree, water content, bulk structure, etc.
that have different kinetic properties (activity and selectivity)
Chemical Kinetics = Reaction Rate Analysis Answers:
Our Holy Grail is the Detailed Mechanism
Our main experimental basis is
the Reaction Rate, R
(+data of some structural measurements)
Different goals of chemical kinetics: To characterize chemical activity of reactive media and reactive materials, particularly catalysts; to assist catalyst design
To reveal the detailed mechanism
To be a basis of kinetic model for reactor design and recommendations on optimal regimes
Different types of chemical kinetics Applied chemical kinetics
Detailed kinetics (Micro-kinetics)
Mathematical kinetics
Steady–state and non-steady-state measurements (1) In most of previous studies, a focus was done
on the steady-state experiments.
Convectional transport was used
as a ‘measuring stick’.
(2) In our studies, a focus was done
on non-steady-state experiments.
Diffusional transport was used
as a ‘measuring stick’.
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