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Comments on the Eyring interpretation of the compensation effect
ELSEVIER
Polymer Degradation and Stability 50 (1995) 159-161 0 1995 Eisevier Science Liited Printed in Northern Ireland. ,411rights reserved 0141-3910/95/$09.50
0141-3910(95)00120-4
Comments
on the Eyring interpretation of the compensation effect F. TiidtW
& P. K. D&id
“Central Research Institute of Chemistry, Hungarian Academy of Sciences, H-1525 Budapest, PF 17, Hungary bInstitute of Chemical Technology, Etitviis Lbrrind University, H-1518 Budapest 112, Pf. 32, Hungary ‘H-2016, Lerinyfalu, Hunyadi 3, Hungary
(Received
19 April 1995; accepted 14 May 1995)
Numerous interpretations have already appeared concerning the compensation effect (CE). A recent proposal, associated with the study of polymers, suggests a linear relationship between Eyring’s activation enthalpy and activation entropy as an explanation of CE. The paper shows that these conceptual quantities give no additional or newer physical information than the Arrhenius parameters. Furthermore, they stem from the unjustified assumption of equilibrium for the transition state of reactions. Despite the ‘direct connection’ to material properties claimed for the Eyring interpretation, it will not prevent the occasional occurrence of a misleading apparent CE.
1 INTRODUCTION
not affect the essence and validity of our present train of thought, and secondly because it is often regarded as unity.* The aim of this paper is to consider the above in the following respects:
As is well known, the compensation effect (CE) is commonly understood as a linear correlation between the values of log Ai and Ei in the Arrhenius equation, ki = Ai . e-(Ei’RT) or logkj = logAi - 2 302RT
1. Do
the concepts AS+ and AH+ imply anything new compared to the Arrhenius parameters A and E? 2. The question of the equilibrium postulated concerning the activated state. 3. Is the stating of the enthalpy-entropy correlation a new novelty?
(1)
in a series of related reactions. There is no generally accepted explanation of CE in the literature even today. The essence of a recent claim to explain CE1 is to replace the Arrhenius equation (1) by
2 THE MEANING
OF THE CONCEPTS
h!?” AND AW
AS?
log~=logk+--h
2.303R
AH? 2.303RT
We show below that the replacement of the Arrhenius parameters A and E by Eyring’s AS+ and AH+ supplies no new information. This is easy to see by considering AHT=E,-RT or (3)
(2)
This ‘Eyring equation’ (2) was judged the more suitable, as an explanation of CE, by suggesting a linear relationship between As and AK, activation entropy and activation enthalpy respectively. For the sake of simplicity, we are not dealing here with the K transmission coefficient, firstly because this simplification does
Ei=AHf+RT
(4)
and ASr=RlogAi+Rlogh 1.59
ekT
or
(5)
160
F. Tiidh, A,
=
F.
eAS+,lR
relationships between the characteristic quantities of the two approaches.2,3 We can conclude that the functional relationships (3,4) and ($6) between the Eyring quantities on the one hand and the Arrhenius parameters on the other, consist of universal material constants and the (average) temperature T of the process. In other words, it is shown by the relationships (3,4) and (5,6) that the quantities AH,Zand Ei or As and Ai are mathematically convertible into each hence they do not carry different other, information. The seemingly different mathematical interpretations reflect, in fact, the same physical significance by using slightly different quantities.
3 THE QUESTION OF THE EQUILIBRIUM POSTULATED CONCERNING THE ACTIVATED
STATE
The fundamental postulate of the theory of absolute reaction rate.? is the assumption of thermodynamic equilibrium between Xf, the activated complex and its constituent starting molecules in the transition state of the A+B@X++C+D
(7)
of the process. The irreversible decomposition activated complex-to a lesser or greater extent, depending on its rate-disturbs the equilibrium. Therefore the assumption of the equilibrium value of [X’] also implies that the formation of X# goes much faster (more precisely, two or several orders of magnitude faster) than the rate at which it will be consumed by the unidirectional ‘decomposition’ reaction. The rates of the three elementary reactions cannot be commensurable, or more precisely, the reaction X+-+C+D
(8)
must proceed only at a negligibly low rate. (This is also recognized by Eyring himself: ‘This is one of the fundamental postulates of the theory developed here; it is supposed that the reaction does not appreciably disturb the equilibrium concentration of activated complexes.‘2) If, on the other hand, the rates of the three reactions are commensurable, equilibrium states or equilibrium concentrations cannot develop.
P. K. D&id
Formulated from another angle: in the case of commensurable rates, the concentration of the activated complex is not an equilibrium concentration, but a commensurable one at most. However, the theory of absolute reaction rates still uses, instead of the real value, the concept of equilibrium concentration of the activated complex to deduce the corresponding kinetic equations. These relations, derived in this manner, have the appearance of exact formulae although on the basis of the above consideration, they are approximate equations, at best. The elimination of this contradiction, which has been built into the theory ‘unnoticed’ is not possible within the framework of the theory. It could be the subject of further discussion and investigation to what extent this inherent contradiction makes the theory of absolute reaction rates inaccurate. It is certainly evident that the accuracy of these relationships increases if the decomposition rate of the activated complex decreases and in the extreme case-at zero decomposition rate-the formulae become exact. There is another feature of the activated complex which differs from that of the starting components and end-products of the reaction. The latter-in the state of chemical equilibrium-belong to the minima of the corresponding chemical potential functions. However, the activated complex-as a function of the reaction coordinate-belongs to the maximum of the corresponding potential function, which in fact means an unstubfe (hence par excellence non-equilibrium) state. Also if the assumption of equilibrium is unjustified,4,5 enthalpy and entropy as ‘activation’ concepts are questionable, because the attribute ‘activation’ deprives the expressions enthalpy and entropy of their original meaning, which is associated with the concept of equilibrium.
4 NOVELTY OF THE ENTHALPYENTROPY CORRELATION The suggestion of an enthalpy-entropy correlation, as one of the explanations of CE, is not new. Its history goes back over a number of decades.+l’ Exner called CE an ‘enthalpyentropy correlation’,1*-14 which itself throws light upon the origin of the explanation’ cited above. As ThorrP has it, the enthalpy-entropy
The Eyring interpretation of the compensation effect
correlation-in connection with equilibria-is the consequence of the axiomatic foundations of the concerning Therefore thermodynamics. claims of Crine,l the existence of the linear AI-P--AS+ relation in itself, as an explanation of CE, cannot be accepted as a new finding.
161
Furthermore, we have pointed out that the naming, enthalpy-entropy correlation, concerning CE, is not new, but a technical term which has been used in the literature for several decades.
ACKNOWLEDGEMENT 5 CONNECTION OF THE QUESTION WITH POLYMER DEGRADATION It can be seen from the foregoing that there is no reason to criticizeI what has been previously polymer degradationpredicted,17 concerning introduced18 ageing compensation efect because it was presented originallyl’ using the Arrhenius model and not Eyring’s. It does not affect the validity of ACE correlation whether it is presented through the Arrhenius or Eyring plot.‘e2’ The latter differs from the Arrhenius plot only in an insignificant and disputable correction. The occasional deviations, in the light of normal experimental errors, are not significant numerically. The part of the criticism16 which claims physical significance only for Eyring’s representation does not hold either, since this CE, cited as example of physical significance,16 proved to be an apparent CE, without physical meaning.22,23 Thus, even Eyring’s interpretation is unable to protect its user from the occasional occurrence of a misleading apparent CE. With respect to the characteristics of the real and apparent CE (and ACE) and to their distinction, we refer to the method4 which considers the relative position of the isokinetic point on the temperature scale, compared to the temperature interval of experiments.
6 CONCLUSION Numerous interpretations have already appeared concerning the compensation effect (CE). A recent proposal’ recommends a linear relationship between Eyring’s” activation enthalpy (AH+) and activation entropy (AS”) as an explanation of CE. We have shown that while these concepts do not carry new or more information than the Arrhenius preexponent (A) and activation energy (E), they stem from the unjustified assumption of equilibrium for the transition state of reactions.
The authors acknowledge the support of this work by the Hungarian Research Foundation, Contract No. 2772,
REFERENCES J.-P., J. Macrornol. Sci.-Phys., B, 23(2) (1984) 201. Glasstone, S., Laidler, K. J. & Eyring, W., The Theory of Rate Processes. McGraw-Hill, New York, 1941. Schwetlick, K., Kinetische Methoden zur Vntersuchung van Reaktionsmechanismen. Deutscher Verlag der Wissenschaften, Berlin, 1971. Tiidijs, F., Proc IVPAC Int. Symp. Macromol. Chem., Budapest, 1969. Akademiai Kiad6, Budapest, 1971, p. 485. Simonyi, M. & TiidBs, F., The hydrogen atom abstraction reaction from O-H bonds, ‘m Advances in Physical Organic Chemistry, ed. V. Gold. Academic Press, London, 1971, p. 127. Cremer, E., Adv. Catal., 7 (195.5) 75. Venkataraman, H. S. & Hinshelwood, C. N., J. Chem. Sot. (London), Part I + II (1960) 4977. Leffler, J. E. & Grunwald, E., Rates and Equilibria of Organic Reactions. Wiley, New York, 1963. Ritchie, C. D. & Sager, W. F., Progr. Phys. Org. Chem., 2 (1964) 323. Galwey, A. K., Adu. Catal., 26 (1977) 24’7. Exner, O., Nature, 201 (1964) 488. Exner, O., Collection Czechoslovak Chem. Commun., 29 (1964) 1094. Exner, O., Collection Czechoslovak Chem. Commun.,
1. Crine,
2. 3.
4.
5.
6. 7. 8. 9. 10. 11. 12. 13.
37 (1972) 1425. O., Collection Czechoslovak Chem. Commun., 38 (1973) 781. 15. Thorn, R. J., J. Chem. Phys., S(8) (1969) 3582. 16. Crine, J.-P., IEEE Trans. Electrical lnsulation, 6(4) (1991) 811. 17. D&id, P. K., Proc. 4th Int. Symp. ENVIROEFFECT,
14. Exner,
Vol. I, p. 28. Czechoslovak Acad. Sci., Prague-Liblice, 197.5. 18. David, P. K., IEEE Trans. Electrical insulation, (3) (1987) 229.
G. C. & Dgvid, P. K., IEEE Trans. Electrical Insulation, 23(6) (1988) 1051. 20. DBvid, P. K., Proc. 5th Int. Conf Diel. Materials, Measurements and Appl., Canterbury, 1988, IEE Publ. 19. Montanari,
No. 289, p. 151. 21. D&vid, P. K. & Montanari,
G. C., Eur. Trans. Electrical Power Engng, 2(3) (1992) 187. 22. Dgvid, P. K., IEEE Trans. Electrical Insulation, S(5) (1993) 889. 23. David, P. K. & Montanari, G. C., Proc. 6th Int. Conf Diel. Materials, Measurements and Appl., Manchester, 1992, IEE Publ. No. 363, p. 378.
Polymer Degradation and Stability 50 (1995) 159-161 0 1995 Eisevier Science Liited Printed in Northern Ireland. ,411rights reserved 0141-3910/95/$09.50
0141-3910(95)00120-4
Comments
on the Eyring interpretation of the compensation effect F. TiidtW
& P. K. D&id
“Central Research Institute of Chemistry, Hungarian Academy of Sciences, H-1525 Budapest, PF 17, Hungary bInstitute of Chemical Technology, Etitviis Lbrrind University, H-1518 Budapest 112, Pf. 32, Hungary ‘H-2016, Lerinyfalu, Hunyadi 3, Hungary
(Received
19 April 1995; accepted 14 May 1995)
Numerous interpretations have already appeared concerning the compensation effect (CE). A recent proposal, associated with the study of polymers, suggests a linear relationship between Eyring’s activation enthalpy and activation entropy as an explanation of CE. The paper shows that these conceptual quantities give no additional or newer physical information than the Arrhenius parameters. Furthermore, they stem from the unjustified assumption of equilibrium for the transition state of reactions. Despite the ‘direct connection’ to material properties claimed for the Eyring interpretation, it will not prevent the occasional occurrence of a misleading apparent CE.
1 INTRODUCTION
not affect the essence and validity of our present train of thought, and secondly because it is often regarded as unity.* The aim of this paper is to consider the above in the following respects:
As is well known, the compensation effect (CE) is commonly understood as a linear correlation between the values of log Ai and Ei in the Arrhenius equation, ki = Ai . e-(Ei’RT) or logkj = logAi - 2 302RT
1. Do
the concepts AS+ and AH+ imply anything new compared to the Arrhenius parameters A and E? 2. The question of the equilibrium postulated concerning the activated state. 3. Is the stating of the enthalpy-entropy correlation a new novelty?
(1)
in a series of related reactions. There is no generally accepted explanation of CE in the literature even today. The essence of a recent claim to explain CE1 is to replace the Arrhenius equation (1) by
2 THE MEANING
OF THE CONCEPTS
h!?” AND AW
AS?
log~=logk+--h
2.303R
AH? 2.303RT
We show below that the replacement of the Arrhenius parameters A and E by Eyring’s AS+ and AH+ supplies no new information. This is easy to see by considering AHT=E,-RT or (3)
(2)
This ‘Eyring equation’ (2) was judged the more suitable, as an explanation of CE, by suggesting a linear relationship between As and AK, activation entropy and activation enthalpy respectively. For the sake of simplicity, we are not dealing here with the K transmission coefficient, firstly because this simplification does
Ei=AHf+RT
(4)
and ASr=RlogAi+Rlogh 1.59
ekT
or
(5)
160
F. Tiidh, A,
=
F.
eAS+,lR
relationships between the characteristic quantities of the two approaches.2,3 We can conclude that the functional relationships (3,4) and ($6) between the Eyring quantities on the one hand and the Arrhenius parameters on the other, consist of universal material constants and the (average) temperature T of the process. In other words, it is shown by the relationships (3,4) and (5,6) that the quantities AH,Zand Ei or As and Ai are mathematically convertible into each hence they do not carry different other, information. The seemingly different mathematical interpretations reflect, in fact, the same physical significance by using slightly different quantities.
3 THE QUESTION OF THE EQUILIBRIUM POSTULATED CONCERNING THE ACTIVATED
STATE
The fundamental postulate of the theory of absolute reaction rate.? is the assumption of thermodynamic equilibrium between Xf, the activated complex and its constituent starting molecules in the transition state of the A+B@X++C+D
(7)
of the process. The irreversible decomposition activated complex-to a lesser or greater extent, depending on its rate-disturbs the equilibrium. Therefore the assumption of the equilibrium value of [X’] also implies that the formation of X# goes much faster (more precisely, two or several orders of magnitude faster) than the rate at which it will be consumed by the unidirectional ‘decomposition’ reaction. The rates of the three elementary reactions cannot be commensurable, or more precisely, the reaction X+-+C+D
(8)
must proceed only at a negligibly low rate. (This is also recognized by Eyring himself: ‘This is one of the fundamental postulates of the theory developed here; it is supposed that the reaction does not appreciably disturb the equilibrium concentration of activated complexes.‘2) If, on the other hand, the rates of the three reactions are commensurable, equilibrium states or equilibrium concentrations cannot develop.
P. K. D&id
Formulated from another angle: in the case of commensurable rates, the concentration of the activated complex is not an equilibrium concentration, but a commensurable one at most. However, the theory of absolute reaction rates still uses, instead of the real value, the concept of equilibrium concentration of the activated complex to deduce the corresponding kinetic equations. These relations, derived in this manner, have the appearance of exact formulae although on the basis of the above consideration, they are approximate equations, at best. The elimination of this contradiction, which has been built into the theory ‘unnoticed’ is not possible within the framework of the theory. It could be the subject of further discussion and investigation to what extent this inherent contradiction makes the theory of absolute reaction rates inaccurate. It is certainly evident that the accuracy of these relationships increases if the decomposition rate of the activated complex decreases and in the extreme case-at zero decomposition rate-the formulae become exact. There is another feature of the activated complex which differs from that of the starting components and end-products of the reaction. The latter-in the state of chemical equilibrium-belong to the minima of the corresponding chemical potential functions. However, the activated complex-as a function of the reaction coordinate-belongs to the maximum of the corresponding potential function, which in fact means an unstubfe (hence par excellence non-equilibrium) state. Also if the assumption of equilibrium is unjustified,4,5 enthalpy and entropy as ‘activation’ concepts are questionable, because the attribute ‘activation’ deprives the expressions enthalpy and entropy of their original meaning, which is associated with the concept of equilibrium.
4 NOVELTY OF THE ENTHALPYENTROPY CORRELATION The suggestion of an enthalpy-entropy correlation, as one of the explanations of CE, is not new. Its history goes back over a number of decades.+l’ Exner called CE an ‘enthalpyentropy correlation’,1*-14 which itself throws light upon the origin of the explanation’ cited above. As ThorrP has it, the enthalpy-entropy
The Eyring interpretation of the compensation effect
correlation-in connection with equilibria-is the consequence of the axiomatic foundations of the concerning Therefore thermodynamics. claims of Crine,l the existence of the linear AI-P--AS+ relation in itself, as an explanation of CE, cannot be accepted as a new finding.
161
Furthermore, we have pointed out that the naming, enthalpy-entropy correlation, concerning CE, is not new, but a technical term which has been used in the literature for several decades.
ACKNOWLEDGEMENT 5 CONNECTION OF THE QUESTION WITH POLYMER DEGRADATION It can be seen from the foregoing that there is no reason to criticizeI what has been previously polymer degradationpredicted,17 concerning introduced18 ageing compensation efect because it was presented originallyl’ using the Arrhenius model and not Eyring’s. It does not affect the validity of ACE correlation whether it is presented through the Arrhenius or Eyring plot.‘e2’ The latter differs from the Arrhenius plot only in an insignificant and disputable correction. The occasional deviations, in the light of normal experimental errors, are not significant numerically. The part of the criticism16 which claims physical significance only for Eyring’s representation does not hold either, since this CE, cited as example of physical significance,16 proved to be an apparent CE, without physical meaning.22,23 Thus, even Eyring’s interpretation is unable to protect its user from the occasional occurrence of a misleading apparent CE. With respect to the characteristics of the real and apparent CE (and ACE) and to their distinction, we refer to the method4 which considers the relative position of the isokinetic point on the temperature scale, compared to the temperature interval of experiments.
6 CONCLUSION Numerous interpretations have already appeared concerning the compensation effect (CE). A recent proposal’ recommends a linear relationship between Eyring’s” activation enthalpy (AH+) and activation entropy (AS”) as an explanation of CE. We have shown that while these concepts do not carry new or more information than the Arrhenius preexponent (A) and activation energy (E), they stem from the unjustified assumption of equilibrium for the transition state of reactions.
The authors acknowledge the support of this work by the Hungarian Research Foundation, Contract No. 2772,
REFERENCES J.-P., J. Macrornol. Sci.-Phys., B, 23(2) (1984) 201. Glasstone, S., Laidler, K. J. & Eyring, W., The Theory of Rate Processes. McGraw-Hill, New York, 1941. Schwetlick, K., Kinetische Methoden zur Vntersuchung van Reaktionsmechanismen. Deutscher Verlag der Wissenschaften, Berlin, 1971. Tiidijs, F., Proc IVPAC Int. Symp. Macromol. Chem., Budapest, 1969. Akademiai Kiad6, Budapest, 1971, p. 485. Simonyi, M. & TiidBs, F., The hydrogen atom abstraction reaction from O-H bonds, ‘m Advances in Physical Organic Chemistry, ed. V. Gold. Academic Press, London, 1971, p. 127. Cremer, E., Adv. Catal., 7 (195.5) 75. Venkataraman, H. S. & Hinshelwood, C. N., J. Chem. Sot. (London), Part I + II (1960) 4977. Leffler, J. E. & Grunwald, E., Rates and Equilibria of Organic Reactions. Wiley, New York, 1963. Ritchie, C. D. & Sager, W. F., Progr. Phys. Org. Chem., 2 (1964) 323. Galwey, A. K., Adu. Catal., 26 (1977) 24’7. Exner, O., Nature, 201 (1964) 488. Exner, O., Collection Czechoslovak Chem. Commun., 29 (1964) 1094. Exner, O., Collection Czechoslovak Chem. Commun.,
1. Crine,
2. 3.
4.
5.
6. 7. 8. 9. 10. 11. 12. 13.
37 (1972) 1425. O., Collection Czechoslovak Chem. Commun., 38 (1973) 781. 15. Thorn, R. J., J. Chem. Phys., S(8) (1969) 3582. 16. Crine, J.-P., IEEE Trans. Electrical lnsulation, 6(4) (1991) 811. 17. D&id, P. K., Proc. 4th Int. Symp. ENVIROEFFECT,
14. Exner,
Vol. I, p. 28. Czechoslovak Acad. Sci., Prague-Liblice, 197.5. 18. David, P. K., IEEE Trans. Electrical insulation, (3) (1987) 229.
G. C. & Dgvid, P. K., IEEE Trans. Electrical Insulation, 23(6) (1988) 1051. 20. DBvid, P. K., Proc. 5th Int. Conf Diel. Materials, Measurements and Appl., Canterbury, 1988, IEE Publ. 19. Montanari,
No. 289, p. 151. 21. D&vid, P. K. & Montanari,
G. C., Eur. Trans. Electrical Power Engng, 2(3) (1992) 187. 22. Dgvid, P. K., IEEE Trans. Electrical Insulation, S(5) (1993) 889. 23. David, P. K. & Montanari, G. C., Proc. 6th Int. Conf Diel. Materials, Measurements and Appl., Manchester, 1992, IEE Publ. No. 363, p. 378.