THERMODYNAMIC FORM OF KINETIC
EQUATIONS AND AN EXPERIENCE
OF ITS USE FOR ANALYZING COMPLEX
REACTION SCHEMES
Valentin N. Parmon
Boreskov Institute of Catalysis
Novosibirsk State University
Novosibirsk, Russia, 630090,
parmon@catalysis.ru
May 30, 2012
Ghent, Belgium
1
Novosibirsk is the 3rd largest city in Russia
(behind Moscow and St-Petersburg)
Population >1,500,000
Universities and academies 30
Russia
St-Petersburg
Moscow
Siberia
Siberian Branch
of the Russian Academy of
Sciences
Great logistic center
(Trans-Siberian railway, International airport)
Novosibirsk
High-tech industries
The highest density of science in Russia
Novosibisrk Scientific Center – Akademgorodok
2
•
Population 130,000
•
35 academic research institutes of SB RAS with ca. 9,000 employees
•
7 chemical research institutes
•
Novosibirsk State University
The Siberian school of mathematicians in
chemistry (since the beginning of 60ths)
M.G. Slin’ko (1914–2008) – initiator of the wide application of
mathematical methods in catalysis
G.S. Yablonsky
A.N. Gorban’
– coupling of kinetic analysis with
thermodynamics
V.I. Bykov
– analysis of reaction schemes with
singularitues
M.Z. Lazman
3
– generalization of analysis of complex
reaction schemes
G.S. Yablonsky et al.
(1970s-2000s)
• Rigorous results based on assumed detailed
reaction mechanisms with the ideal mass-actionlaw dependences
(1) Linear Theory (1970s-1980s)
(2) Non-Linear Theory (1980s-2000s)
4
Linear theory
• ONE-ROUTE CATALYTIC REACTION with the linear mechanism
General expression for the steady state reaction rate
(Yablonsky, Bykov, 1976)
R  Cy 
where Cy is a “cyclic characteristics”
Cy = K+f+(C) – K–f–(C)
Cy corresponds to the overall reaction
 presents a complexity of complex reaction

pi
K
c
 j ji
j
i
• MULTI-ROUTE LINEAR MECHANISMS
(Yevstignejev, Yablonsky, Bykov, 1979)
5
Non-linear theory
KINETIC POLYNOMIAL
(Lazman, Yablonsky, 1980-2000s)
It is considered as the most generalized form which includes
Langmuir-Hinshelwood-Hougen-Watson equations and
equations of enzyme kinetics as particular cases
The kinetic polynomial of the one-route non-linear reaction
scheme is
BmRm +…+ B1R +B0Cy = 0
where R is the steady-state reaction rate, m are the integer
numbers
6
V.N. Parmon is a lecturer of Novosibirsk State University in
chemical kinetics and both classical (equilibrium) and, since
1995, non-equilibrium thermodynamics
7
Contents of the presentation:
8
•
Introducing the thermodynamic form of
kinetic equations
•
•
Some interesting one consequences
•
Few practical application
A problem of the “bottle neck” (limiting
step) and “rate controlling step” of a
stepwise reaction
A Thermodynamic Form of Kinetic Equations is
an Inevitable Step for the Successive Unifying
the Languages of Chemical Kinetics and
Chemical Thermodynamics
Chemical Kinetics: the main parameters are concentrations,
c, of reactants A and rate constants, ki,
d cα
vα =
= f  k i , c α   f  k i ,[A α ]
dt
Chemical Thermodynamics: the main parameters are
chemical potentials, , of thermalized reactants A
Note, however, that
 = f  α 
α = o  RTln   c 
where  is an activity coefficient
9
Introducing the Thermodynamic Form of
Kinetic Equations
   0
1
c  [A ] 
exp 

 RT
For a substance A
For an elementary reaction “ij”


vij  kij  ci

i 

i
ij
A  
   j A 

    0  
1
 kij   exp  i 
  
i
 
  RT  

   i 0
1


 kij   exp  
i
RT
 




where
i

  i  

 

exp


 RT





 i 



exp

  ijni
ij

RT




 is a “chemical potential” of reaction group i


0
 Gij0   Gi0



1

 kB T
i
ij  k ij 
exp  
exp  
  
i

RT
h
RT



 




 Gij0  
kB T

exp  

 RT 
h


10





0




1


exp   i   
   i  

i
 
 RT  
 




Properties of the Thermodynamic Form of
Equations for an Elementary Reversible Reaction
ij



 i A 
ji



j
A
If ij is the chemical variable for reaction “ij”
vij 
dij
dt

 vij  vij  ij  ni   ji  nj  ij ni  nj

since ij = ji !
Indeed, for partial equilibrium of reaction ij
when
i 
  i     j 

  j  
or

vij  0
thus ij = ji
11
 j 
  
exp  i   ni  exp 
  nj
RT
RT




New proprietary definitions:
 ij0 
kB T
ij   ji 
exp  



h
 RT 
– “truncated” rate constant of reaction ij
which depends only on the properties of TS
  
ni  exp  i 
 RT 
– thermodynamic “rush” of reaction group i
Why “rush” ?
vij  0 if ni  nj
vij  0 if ni  nj
vij  0 if ni  nj
i   i A

12
TS
j    j A

Some Related Properties
Inequality
ni  nj
is equivalent to the positive value of affinity Arij of reaction ij:
 j 
 i 
ni  exp 

  nj  exp 
RT
RT




at i   j
i   j 


i
     j    Arij  0

ni  nj is equivalent to Arij  0
ni  nj is equivalent to Arij  0
Direction of reaction ij coincides with the sign of Arij !
13
Thermodynamic Criterium of Kinetic
Irreversibility of a Reaction i  j

  j 
 i   j  
 i 
 i  




vij  ij exp 

exp


exp
1


 

  



ij
 RT 
 RT  

 RT  
 RT  





 Arij  


 ijni 1   
 

 RT  


So, the rate vij of reverse reaction
j  i is negligible in respect to
If Arij  RT (far from equilibrium)

 " can be substituted by single " 
In this case double " 
"

If Arij  RT
(the vicinity to equilibrium) then
vrij 
14
ijni
RT
Arij
vij
Consequence 1
For a set of stationary consecutive reactions which occur
from left to right
1
2
N
N1








 P:
R 
 Y1 
 Y2 ... 
 YN 
• obligatory R > Y1 > Y2 >...> YN > P!
• the number of single arrows " 
 " can not exceed the value of
Ar
m
!
RT


 P
Here Ar  R – P is affinity of stoichiometric stepwise reaction R 

15
Consequence 2
For any stoichiometric stepwise reaction “”



P
R 

which is linear in respect to its reaction intermediates Yi the rate is
expressed in the same way as for elementary reaction:
d 
v 
  nR  nP 
dt
where
 
 
nR  exp  R  , nP  exp  P 
 RT 
 RT 
R and P are initial and final reaction groups;
 is an algebraic combination of ij and, in some cases, thermodynamic
rushes of “external reactants” from either initial of final reactions groups
Note: Stoichiometric stepwise reaction means steady state occurrence of
the reaction in respect to its intermediates Yi
This relation in catalysis is known as a Horiuti–Boreskov equation!
16
Simple Example 1
Stepwise reaction


P
R 

occurs according to scheme
1


Y
R 

2

P
Y 

In the steady state in respect to Y
d[Y]
 1 R  Y  2 Y  P  0
dt
 R  2P
Y 1
1  2




d
d[R] d[P]


 1 R  Y  2 Y  P 
dt
dt
dt

1R  2P 
12
 1  R 
R  P   R  P
 







1
2
1
2



v 

where   
17
12
1  2






Simple Example 2



P
R1  R2 

Stepwise reaction
occurs according to scheme
1


Y
R1 

2

P
Y  R2 

In the steady state in respect to Y
d[Y]
 1 R1  Y  2 Y  R2  P  0
dt
 R  2P
Y 1 1
1  2R2




 1R1  2P

d  d[P]
v 

 2 Y  R 2  P   2 
 P 
   R

dt
dt
 1
2 2

12

R1R 2  P    R1R 2  P
1  2R 2


where
18
 
12
1  2R 2




For an arbitrary set of monomolecular
transformations of intermediates there is a total
analogy with an electrotechnical equivalent
scheme!
Stepwise process occurs
according to scheme
Electrotechnical analog



P
R 


 {Y}

P
R 



i

vij  ij Yi  Yj
v Yi 
d[Yi ]

dt
Iij 
  Y  Y   0
ij
j

i
v   R  P


j

Ii 
1
Ui  Uj
R ij

1
R  U
j
I 
i
ij

 Uj  0
1
 UR  UP 
R
1
is calculated in the same way as
:
R
 is an algebraic combination of ij like R is that of Rij
19

Main basis for “linear” non-equilibrium
thermodynamics
Flux Ji of a parameter ai
dai
 Xi ,
dt
Ji 
where Xi is thermodynamic driving force for ai
For a complex system
Jj 
L
j
ij
Xi ,
where Lij are the Onsager’ coefficients of interrelation.
A sequence: existence of the Raleigh-Onsager dissipation function
P T
diS

dt
JX
i
i
i

 L
i
j
ij
Xi X j  0
According to the Prigogine theorem, P is the Lyapunov’ function which
reaches a positively defined minimum at the stationary state of the system
(when Jj = 0)
20
Consequence 3:
Existence of the Lyapunov’ functions  which are positively determined
and minimazing at the steady state in respect to intermediates even far
from equilibrium for any reaction schemes which are linear in respect to
intermediates
Example 1: Stepwise reaction



P
R 

occurs via the scheme

 {Y}

P
R 



i
where {Yi} means an arbitrary set of monomolecular transformations of Yi

i
v Yi 
21

 Ri R  Yi

2

1
ij Yi  Yj


2 i j


2


  jR Yj  P
j

2
d[Yi ]
1 

 Ri R  Yi   ij Yi  Yj  iP Yi  P  0
dt
2 Yi
j






Physical meaning of the Lyapunov’ function
for an arbitrary set of monomolecular reactions
far from equilibria
Stepwise process occurs
according to scheme
Electrotechnical analog



P
R 


 {Y}

P
R 



i

vij  ij Yi  Yj
v Yi 
d[Yi ]

dt

Iij 
  Y  Y 
j

ij
v   R  P
i
j
Ii 

1
Ui  Uj
R ij

1
j R Ui  Uj
ij
I 
Thus, the Lyapunov’ function  



1
 UR  UP 
R
   Y  Y 
2
i
j
ij
i
j
corresponds to the power W of the dissipation of Ohmic heat in the electrical circuit
2
1
W    Iij Ui  Uj   
Ui  Uj
i
j
i
j R ij
22




Example 2: Stepwise reaction


 P occurs via the scheme
R1  R2 

1


Y
R1 

2

P
Y  R2 


  1 R1  Y
vY 

2

2
R2
 Y R
2
P

2
d[Y]
1 

 1 R1  Y  2 Y  R2  P  0
dt
2 Y




Conclusions:
1. The Lyapunov function exists for any stepwise reactions which are linear in respect
to intermediates
2. Steady state of above reaction is stable
23
Consequence 4:
According to the Prigogine theorem all systems near thermodynamic
equilibrium have the stable steady state. All stepwise reactions linear in
respect to intermediates have their Lyapunov’ functions and thus are also
stable
A contrary example: Stepwise reaction

R 
P
occurs via the nonlinear autocatalytic scheme in respect to Y:
1


 2Y
R  Y 

2
Y 
P
The Lyapunov function does not exist !
There are two steady states
 0, any R

d[P]
v 
 2 Y   
2 
2
dt

R

,
R


 2

1
1 
 
The steady state in respect to Y can be nonstable !
Thus, the necessary conditions for loosing the stability of the steady state of a kinetic
scheme:
24
(1)
(2)
As least one elementary reaction has to be kinetically irreversible
This elementary reaction has to be non-linear in respect to the intermediates
Necessary conditions for oscillation of the
concentration of reaction intermediates:
25
" 
 " in the
•
far from equilibrium (at least one single
reaction scheme)
•
at least two reaction intermediates
•
at least one step which is nonlinear in respect to
intermediates
Consequence 5:
It is possible to write modified Onsager’ (the Horiuti-BoreskovOnsager) equations of interrelation of parallel stepwise chemical
reactions
A simple example:
Parallel step-wise reactions
occur via mechanism
1

 P1
R 

R
2

 P2
R 

At the steady state
Thus,






d[P1]
 2 Y  P1  11 R  P1  12 R  P2
dt

d[P2 ]
 3 Y  P2  21 R  P1  22 R  P2
dt








11 = 12/(1 + 2 + 3) > 0
22 = 13/(1 + 2 + 3) > 0
12 = 21 = -23/(1 + 2 + 3)
26
Y
d[Y]
 1 R  Y  2 Y  P1  3 Y  P2  0
dt

where
1


2
P1
3
P2
In a general case for parallel stepwise reactions
i

 Pi
R j 

v i 
Here
d  i

dt

  R
ij
j

R i  exp R j RT ,
   X
 Pj 
j

j
ij
j
Pi  exp Pi RT

ii > 0
Note: ij is not obviously symmetrical in respect to indexes i and j as it is
the case for reprocisity coefficients Lij in the classic Onsager equations in
the vicinity of equilibrium
Ji 
27
L
j
ij
Xj
The problem of “rate controlling” (“rate
determining”) step and “rate limiting” step (“bottle
neck” of the stepwise reaction)
An unambigous interpretation of the notion “rate determining”
(rate controlling) step by IUPAC
Rate controlling factor
  ln v 
CF  

  lnk 
ij k ,li,m j

lm
but
In the thermodynamic representation
  f Gij o 
kB T
ij 
exp  



h
RT


  ln v
CF  
  ln 
ij


28
  ln v 
CF  

  ln   , 

– contains parameters of only the thermalized
reactions groups and reactants
v   f ij ,n i



lm ,li,m j

vij  ij n i  nj
– contains parameters of only the transient states
  

  
ni  exp  i   exp   i  
 RT 
  RT 
Thus,
 r Gij0 
kij  k ji exp  

 RT 



– rate controlling factor of transient states
– rate controlling factor of the reactant
How to define correctly the
“rate limiting” step
(the “bottle neck”)?
29
The “rate determining step” and “bottle neck” in a
consequtive monomolecular reaction
1
2
3
n1











 P
R 
 Y1 
 Y2 
 ... 
 Yn 
v 
1
where


1
1


lim
i 1  i
d 
d[R] d[P]


  R  P
dt
dt
dt


n 1
  lim  mini 
So rate-determining step is the step with minimal i
Note:
in the steady state
Thus Yi  Yi1 

v  i Yi  Yi1
v
i
For i = lim the value of

Y  Y 
i
i 1
for i = 0,…, n+1
is maximal !
It means that the “bottle neck” (limiting step) is the step with the
maximum drop of Yi  Yi1 !
30
Application to catalytic reactions
A simple example:



 P
R 

occurs via catalytic Michaelis–Menten scheme
1


 K1
R  K 

2

 KP
K1 

where K and K1 are free catalytically active site and the catalytic intermediate
The balance equation
[K]  [K1]  [K]0
can be rewritten:
Thus
where K1
Here
31
 K0 
 K0 
 K0 
1
  K0 exp  
K exp  
  K1 exp  
 RT 


RT
RT






K  K1  K0
 K0  K0 
 and K0 corresponds to K at K  1
 exp 
 RT 


1


K  K0  RT ln 1  K1  K0  RT ln  K 
 
K1  K01  RT ln K1
Finally, at the steady state in respect to K1
d 
 
v 
 1 2
dt
1  2

K0 R  P

 1R  2P 
1 
    
2
 1

 

K0 R  P
1

K1
K
• At small extent of occupation of the active site with catalytic
intermediates K K
1


1
12
K R P
1  2 0

v 

0
and does not depend on standard thermodynamic parameters K1 of K1
• At large extent of occupation of the active site with catalytic

intermediates K K
1
v 
0
depends on K1
32

1
12
1R  2P
K0

 K0  K0
R  P exp  1
 RT








Note that for K K 1 one can have the situation when the
1
rate determining step does not coincide with the bottle neck !
v 
Let:
R
12
1R  2P
P and 1R
K0

 K0  K0
R  P exp  1
 RT






2P
In this situation
v  2K0

 K0  K0
R  P exp  1
 RT

independently on whether 1

2 or 1




2 !
So, the rate determining step is always step 2
But obligatory the “bottle neck” is the step with minimum i !
33
An unexpected conclusion:
there are situations when the rate-limiting
step can not be the rate-controlling step!
34
Conclusions
•
The thermodynamic form of kinetic equations allows a
dramatic simplification of analysis of complex reaction
schemes
•
Indeed, the main application of this approach is possibility to
extend fruitful and systematic analysis of chemical reaction
schemes for the area “far from equilibrium”
•
Among few principal problems which are resolving via this
approach this is a mathematically correct definition of the
“bottle neck” (the limiting step) of a stepwise reaction and
“rate determing step”
Unexpectedly, for some particular cases (e.g. for catalytic
reactions) these steps can not coinside
35
Few examples of practical interest
36
An example of a practical application:
Super low temperature of melting of active
component of operating metal catalysts due to
their oversaturation with carbon
Electron microscopy “in situ” videotape of Fe–C fluidized particles
migration over amorphous carbon support at 650 °C
time (sec):
300 A o
The melting temperature is
500 °C (!) lower than that
of the Fe–C eutectics
time (sec):
37
O.P.Krivoruchko, V.I.Zaikovskij, K.I.Zamaraev, Dokl.Akad.Nauk, v.329, 744 (1992) (in Russian)
Formation of Metastable Oversaturated
Solutions of Carbon in Metals at Catalytic
Graphitization of Amorphous Carbon
Camorph 
Cgraphite
met
G  –12 kJ/mol ( >RT)
Melting Temperatures, oC
Camorph
solution of C
in metal
Cgraphite
c(amorf) > c(in metal) > c(graphite)
Result: steady-state concentration of xC in metal >>
concentration of C in stable eutectics
equilibrium steady
pure
eutectics
metal
metal with graphite state
Fe
1539
1145
640
Co
1493
1320
600
Ni
1453
1318
670
If the rate determining step is formation of graphite from the melt:
xC (eq. with amorph. C) = xC (eq. with graphite)exp(–GR/RT) 
 4xC(eq. with graphite)  4xC (eq. eutectics)
ln 1  XC 
 mH  1 1 

 
  T  Teut  Tst  st  500 – 900 C !
R  T T0 
Hm and To are the melting heat and melting temperature for pure metal
38
V.N.Parmon. Catalysis Letters, 42, 195 (1996), O.P.Krivoruchko, V.I.Zaikovskij (1995)
Metastable Phase Equilibria for Fe–C
Systems during Occurrence
of the Catalytic Reaction
T, K
T
2000
Graphite liquids
Parameters, influencing the
melting temperature:
1. Oversaturation:
the Schröder equation
Solution of Fe in C
1600
Tx = TomH/{mH – RToln(1 – x)}
eutectics (T = 1420K, x = 0.173)
2. Metal particle size r:
Schröder
1200
Solution
of C in Fe
steady state (920K)
3. Size r’ of a crystallization
800
center (= size of the catalyst
particle)
Fe3C Fe2C
0
50
Content of C (mol. %)
39
 2Vm 
Tr  T exp 

 r mH 
100
 2 Vm 
xr   x  exp 

 r RT 
Formation of Filamentous Carbon together with
Hydrogen at the Moderate-Temperature Catalytic
Pyrolysis of Methane and Low Hydrocarbons
catalysis
CnHm 
 C  2H2 
450650 C
o
500A
o
Ni-catalyst
1000 A
Ni/Cu-catalyst
The weight of the catalyst can be increased by a factor of 400 due to formation of
carbonaceous filamentous material
The growth of the filament corresponds to diffusion of carbon through the active component
with D>10–10 cm2/s
40
L.B.Avdeeva, V.A.Likholobov, G.G.Kuvshinov, at al. (1994)
Size effects in catalysis over metal
nanoparticles
2O3
CО + O2Au/Al

CO2
Pt/Al2O3
CН4 + 2 O2 
CO2 + 2 Н2О
430 °C
(s–1))10
TOF
УКА
10–4
(сек
-4
0.07
0.05
-1
TOF (s–1)
0.06
0.04
0.03
0.02
0.01
400 °C
140
120
100
80
60
40
20
0.00
0
0
2
4
<d>, nm
6
8
10
0
5
10
15
<d>, nm
<d>,
нм
20
Conclusion: There may occur size effects in catalytic reactions, which are many time
increase in the activity of metal catalysts upon a decrease of the active
component particles in size to several nanometers
I.41Beck, V.I. Bukhtiyarov, I.Yu. Pakharukov, V.I. Zaikovsky, V.V. Kriventson, V.N. Parmon, Journal of Catalysis 268 (2009) 60-67
25
Influence of the active component
particle size on the catalytic activity
(an energy correlation approach)

A
B
Mechanism:
A+K
K1
K1
B+K
(1)
(2)
The increment of chemical potential of a
nanoparticle of radius r

2 V
r =
r

Here  – surface excess energy,
V – molar volume of the catalyst active
phase,

TS1
 = æ r
æ < 1 is the Brønsted-Polyany correlation coefficient

 (1  æ )Δr 
v exp
Result:
TOF  vΣr

d[B]



dt 
Σ


RT
 æ Δr 
v
exp


 Σ
RT



42
V.N. Parmon, Doklady Physical Chemistry, vol. 413 (2007) 42-48


TS2
at low coverage with K1
at large coverage with K1
Correlation of the measured TOF values
for the complete CH4 oxidation over Pt/Al2O3
with the Pt size
at temperature 700 K and of the apparent activation energies Ea
with the reciprocal to the active component size (diameter) d
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,0
–1,0
140
120
log(TOF) (TOF in s–1)
–1,4
100
80
–2,2
60
40
–2,6
lg (TOF) = 3,304 (1/d) – 2,981
Ea, kJ/mol
–1,8
20
0,0
0
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,0
1/d, nm–1
For both lines the correlation coefficient is the same: æ  0.75
I.43Beck, V.I. Bukhtiyarov, I.Yu. Pakharukov, V.I. Zaikovsky, V.V. Kriventson, V.N. Parmon, Journal of Catalysis 268 (2009) 60-67
Thermodynamic conjugation of parallel chemical
transformations via a common catalytic
intermediate
K
B
A 

B
K
C
A 

C

A
X
The Horiuti-Boreskov-Onsager
coupling equations:
A
C* d[B]


[B] 
[C] 
 kBB[A]  1 

  kBC[A]  1 
dt
K
[A]
K
[A]

B

C


{X}
B
B
C
C
Reaction coordinate
{X} – catalytic intermediates


d[C]
[B] 
[C] 
 k CB[A]  1 

k
[A]
1




CC
dt
K
[A]
K
[A]

B

C


kij – formal rate constants
kB and KC – equilibrium constants
Conclusion: To change selectivity of a catalytic process one has to
generate some thermodynamic driving forces
44
V.N. Parmon, Thermodynamics of Non-Equilibrium Processes, Elsevier, 2010
Thermodynamic control of selectivity at the
decomposition of methanol
Two independent stepwise reactions – two channels of decomposition:
2 CH3OH
CH3OH
CH3OOCH + 2 H2
CO + 2 H2
{X}
Methylformate + 2 H2 (I)
2 CO + 4 H2 (II)
Reaction coordinate
Gibbs energy
Gibbs energy
2  Methanol
(I)
(II)
2  Methanol
{X}
2 CO + 4 H2 (II)
Methylformate + 2 H2 (I)
Reaction coordinate
{X} – catalytic intermediate
Conclusion: an increase in the partial pressure of CO has to result in
improving the selectivity in respect to methylformate
45
An example of an important practical
application:
Development of principally new one-step catalytic processes of direct insertion
of methane higher hydrocarbons
Usually: hydrocarbons
main products
CH4 as a byproduct
Due to existence of Onsager’s interrelation, one can reverse the direction of the
process of CH4 formation
Now:
hydrocarbons + CH4  heavier hydrocarbons
Examples:
Process “Bicyclar” CH4 + C3,C4 alkanes  aromatics + 5 H
Process “Biforming” CH4 + linear C5+  aromatics + 5 H2
46
Putative one-stage processes for conversion of light
paraffins CH4 and C3–C4 (methane and propanebutanes) to aromatic compounds
Reactions of light hydrocarbons
T*, K
1. 6 CH4
C 6H 6 + 9 H 2
1630
2. 2 C3H8
C 6H 6 + 5 C 2 H 6
760
3. 2 n-C4H10
p-C6H4(CH3)2 + 5 H2
4. C3H8 + n-C4H10
5. 3 C2H6
C6H5CH3 + 5 H2
C 6H 6 + 5 H 2
6. CH4 + 2 C3H8
8. CH4 + C2H6 + C3H8
9. CH4 + 3 C3H8
710
930
C6H5CH3 + 6 H2
7. CH4 + C3H8 + n-C4H10
800
p-C6H4(CH3) + 6 H2
C 6H 6 + 6 H 2
C10H8 + 10 H2
880
1060
940
830
Observation: Aromatization of C2–C4 paraffins is accompanied by the
methane co-production.
47
Yield of aromatic
hydrocarbons, t/t C4
Performance of the BICYCLAR process
depending on the C1/C4 ratio
CH4 + 2 C3H8
C6H5CH3 + 6 H2
CH4 + 3 C3H8
C10H8 + 10 H2
1.5
1.0
0.5
0
0
3
6
9
12
Molar ratio C1/C4
15
18
Catalyst Zn-ZSM-5, temperature 550 °C
The coupled conversion of butane and methane allows the yield of aromatic
hydrocarbons to be 2.5 times increased – up to 1.7 tonn per 1 tonn of involved C4
48
G.V.
Echevsky, E.G. Kodenev, O.V. Kikhtyanin, V.N. Parmon, Appl. Catal. A: General 258 (2004) 159-171
An example of a practical application:
Natural selection in simple autocatalytic systems at diminishing the concentration of food R
follows in one-directional progressive evolution of the system
i

 2Y
R  Yi 

i

ti
Yi 
P
There are two steady states:
Yi(1)  R 
 ti
 R  R cri
i
Yi(2)  0
At diminishing the concentration of food R, one Yi
proceeds a consecutive and irreversible (due to
disappearance of seeds) “death” of all autocatalysts
with the larger values of R cr   ti i
Y3(1)
Y2(1)
i
Thus, a one-directional and progressive (toward
diminishing the parameter Rcri) natural selection
takes place in the system. This is analogous to
appearance of a prototype of biological memory
Yi(2)
An extremely important conclusion: existence of a prototype of biological
memory in the absence of RNA or DNA !
49
V. Parmon, Doklady Phys. Chem., 377, 4 (2001) 510-515
Y1(1)
Thank you for your attention !
50