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Reply to comment of Dr Meier on “Reactivity of Stressed molecules…” J. Mol. Struct. (Theochem) 677 (2004) 77–83
Journal of Molecular Structure: THEOCHEM 729 (2005) 237–238 www.elsevier.com/locate/theochem
Correspondence Reply to comment of Dr Meier on “Reactivity of Stressed molecules.” J. Mol. Struct. (Theochem) 677 (2004) 77–83 We are grateful to Dr R.J. Meier for his interest in the paper discussed. However, certain statements in his comments should be clarified. Indeed, “neither the application of semi-empirical quantum methods to deformation and scission of polyethylene macromolecules, nor the conclusion that chain reactivity changes significantly when stress is applied, is new”. Neither was it claimed new in the paper. The problem addressed in this paper was not to confirm that mechanical stress does affect chemical reactions of a polymer chain (This influence is well documented in the literature, the references given by Dr Meier included.) but to quantify this effect for different reactions. Our approach proposed earlier in a number of publications [1–3] was to compare the activation barrier for stressed and unstressed molecule. This approach applies to various reactions: side hydrogen abstraction [1,2], acidic hydrolysis [2,3], ozone addition to double bond [4], and chain scission. The approach used was to calculate potential energy of a molecular fragment as dependent on the reaction coordinate. The deformation of the fragment was imposed as a restriction on its length. In that respect, the calculations for a shorter model molecule (e.g. octane considered in the paper) and periodic boundary conditions are quite similar, since in both cases one needs a reaction fragment length that secures independence of the result from this length. The use of periodic n-beads boundary conditions means that the process considered is a reaction proceeding simultaneously on each n-th bond (for the chain scission, each nth bond is ruptured simultaneously). The use of periodic boundary conditions is well justified for the calculation of chain modulus or pre-rupture deformation (See Refs. 6 and 10 in the Comment) when the deformation is the same for each bond. For a chemical reaction, any realistic modeling must refer to a sufficiently long reaction fragment, which is representative of a polymer chain. The use of a computation method is always a tradeoff between its accuracy and computational expenses. It was DOI of original article: 10.1016/j.theochem.2004.02.022 0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.04.021
shown in a number of works (see for example, refs in the Comment) that calculations from first principles, from second principles (DFT), and semi-empirical methods provide reasonable agreement with the experimental elastic modulus for PE chain. This was the reasoning for the use of elastic deformation of a molecule as an indicator for how representative the modeling fragment was. Thus, the calculation of modulus in the paper was not considered as a new result but rather was used as a check for the reaction fragment being representative of the polymer chain. The applicability of semi-empirical methods for a reaction, which (as rightly noticed by Dr Meier) proceeds away from the parametric domain where semi-empirical methods are parametrized, needs to be checked. Unfortunately enough, the accuracy of existing ab initio quantum chemistry methods in this parametric domain also can not be taken for granted. The first principles calculation does not a priori guarantee reliable results. In [5], the computations of the dissociation energy for N–H and O–H bonds showed reasonable agreement of the PM3 and DFT results (and both with experiment). For hydrogen abstraction, the MNDO calculations of energy barrier was tested for cyclic molecules [1,2] for which direct experimental data are available. The comparison with experiment showed that the calculation well predicts the change in activation energy with deformation of the reaction center, whereas the absolute energy barrier is poorly reproduced. Thus, the computation errors for strained and non-strained molecules were the same and mutually canceled for consideration of the strain effect. Finally, concerning a comparison of the predictions of the computations to experiment. The problem of mechanistic ultimate strength of a polymer chain was extensively studied (to the best of our knowledge it was first solved by Ludwig Prandtl) at different levels (see Refs. [6] and [10] in the Comment). However, this problem is relevant only for dynamic fracture of a chain. The practically observed strength of polymers is usually determined by the different mechanisms such as chain slippage or thermally activated chain scission (see, e.g. the book [6]). So in our approach, the chain scission is considered as a thermally activated reaction of stressed (at small deformation) molecule and we calculated stress dependence of barrier of this reaction, which proceeds at stresses far below the mechanistic limit of chain stability. Therefore, a comparison of the results of calculation with experimental data for an oriented semicrystalline polymer (where the crystallites make ‘grips’ for
238
Correspondence / Journal of Molecular Structure: THEOCHEM 729 (2005) 237–238
extended chains) appears well justified. The data for such a comparison are available; e.g. the formation of free radicals in stressed oriented polymer (PP) was studied in detail in [7] by the free radicals trap method. The dependence of the rate of radicals production on the stress, temperature, and time was obtained and analytically described in the framework of model of chains distributed in lengths.
References [1] B.E. Krisyuk, E.V. Polianchik, Doklady Akademii Nauk (Sov. Physics, Doklady) 304 (1989) 1177. [2] B.E. Krisyuk, E.V. Polianczyk, Int. J. Polym. Mater. 23 (1993) 1.
* Corresponding author.
[3] [4] [5] [6] [7]
B.E. Krisyuk, E.V. Polianchik, Khim. Fiz. (in Russian) 12 (1993) 252. B.E. Krisyuk, Rus. J. Phys. Chem. 78 (2004) 2214. V.T. Varlamov, B.E. Krisyuk, Rus. Chem. Bul. 53 (2004) 1609. H.H. Kaush, Polymer Fracture, Springer, Berlin, 1978. B.E. Krisyuk, E.V. Polianchik, Yu. N. Rogov, et al., Vysokomolekulyarnye soedineniya (Sov. Polym. Sci.) 25 (1983) 2036.
Boris E. Krisyuk* Eugene V. Polianczyk Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia Received 3 March 2005; Revised 20 April 2005; Accepted 23 April 2005 Available online 1 August 2005
Correspondence Reply to comment of Dr Meier on “Reactivity of Stressed molecules.” J. Mol. Struct. (Theochem) 677 (2004) 77–83 We are grateful to Dr R.J. Meier for his interest in the paper discussed. However, certain statements in his comments should be clarified. Indeed, “neither the application of semi-empirical quantum methods to deformation and scission of polyethylene macromolecules, nor the conclusion that chain reactivity changes significantly when stress is applied, is new”. Neither was it claimed new in the paper. The problem addressed in this paper was not to confirm that mechanical stress does affect chemical reactions of a polymer chain (This influence is well documented in the literature, the references given by Dr Meier included.) but to quantify this effect for different reactions. Our approach proposed earlier in a number of publications [1–3] was to compare the activation barrier for stressed and unstressed molecule. This approach applies to various reactions: side hydrogen abstraction [1,2], acidic hydrolysis [2,3], ozone addition to double bond [4], and chain scission. The approach used was to calculate potential energy of a molecular fragment as dependent on the reaction coordinate. The deformation of the fragment was imposed as a restriction on its length. In that respect, the calculations for a shorter model molecule (e.g. octane considered in the paper) and periodic boundary conditions are quite similar, since in both cases one needs a reaction fragment length that secures independence of the result from this length. The use of periodic n-beads boundary conditions means that the process considered is a reaction proceeding simultaneously on each n-th bond (for the chain scission, each nth bond is ruptured simultaneously). The use of periodic boundary conditions is well justified for the calculation of chain modulus or pre-rupture deformation (See Refs. 6 and 10 in the Comment) when the deformation is the same for each bond. For a chemical reaction, any realistic modeling must refer to a sufficiently long reaction fragment, which is representative of a polymer chain. The use of a computation method is always a tradeoff between its accuracy and computational expenses. It was DOI of original article: 10.1016/j.theochem.2004.02.022 0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.04.021
shown in a number of works (see for example, refs in the Comment) that calculations from first principles, from second principles (DFT), and semi-empirical methods provide reasonable agreement with the experimental elastic modulus for PE chain. This was the reasoning for the use of elastic deformation of a molecule as an indicator for how representative the modeling fragment was. Thus, the calculation of modulus in the paper was not considered as a new result but rather was used as a check for the reaction fragment being representative of the polymer chain. The applicability of semi-empirical methods for a reaction, which (as rightly noticed by Dr Meier) proceeds away from the parametric domain where semi-empirical methods are parametrized, needs to be checked. Unfortunately enough, the accuracy of existing ab initio quantum chemistry methods in this parametric domain also can not be taken for granted. The first principles calculation does not a priori guarantee reliable results. In [5], the computations of the dissociation energy for N–H and O–H bonds showed reasonable agreement of the PM3 and DFT results (and both with experiment). For hydrogen abstraction, the MNDO calculations of energy barrier was tested for cyclic molecules [1,2] for which direct experimental data are available. The comparison with experiment showed that the calculation well predicts the change in activation energy with deformation of the reaction center, whereas the absolute energy barrier is poorly reproduced. Thus, the computation errors for strained and non-strained molecules were the same and mutually canceled for consideration of the strain effect. Finally, concerning a comparison of the predictions of the computations to experiment. The problem of mechanistic ultimate strength of a polymer chain was extensively studied (to the best of our knowledge it was first solved by Ludwig Prandtl) at different levels (see Refs. [6] and [10] in the Comment). However, this problem is relevant only for dynamic fracture of a chain. The practically observed strength of polymers is usually determined by the different mechanisms such as chain slippage or thermally activated chain scission (see, e.g. the book [6]). So in our approach, the chain scission is considered as a thermally activated reaction of stressed (at small deformation) molecule and we calculated stress dependence of barrier of this reaction, which proceeds at stresses far below the mechanistic limit of chain stability. Therefore, a comparison of the results of calculation with experimental data for an oriented semicrystalline polymer (where the crystallites make ‘grips’ for
238
Correspondence / Journal of Molecular Structure: THEOCHEM 729 (2005) 237–238
extended chains) appears well justified. The data for such a comparison are available; e.g. the formation of free radicals in stressed oriented polymer (PP) was studied in detail in [7] by the free radicals trap method. The dependence of the rate of radicals production on the stress, temperature, and time was obtained and analytically described in the framework of model of chains distributed in lengths.
References [1] B.E. Krisyuk, E.V. Polianchik, Doklady Akademii Nauk (Sov. Physics, Doklady) 304 (1989) 1177. [2] B.E. Krisyuk, E.V. Polianczyk, Int. J. Polym. Mater. 23 (1993) 1.
* Corresponding author.
[3] [4] [5] [6] [7]
B.E. Krisyuk, E.V. Polianchik, Khim. Fiz. (in Russian) 12 (1993) 252. B.E. Krisyuk, Rus. J. Phys. Chem. 78 (2004) 2214. V.T. Varlamov, B.E. Krisyuk, Rus. Chem. Bul. 53 (2004) 1609. H.H. Kaush, Polymer Fracture, Springer, Berlin, 1978. B.E. Krisyuk, E.V. Polianchik, Yu. N. Rogov, et al., Vysokomolekulyarnye soedineniya (Sov. Polym. Sci.) 25 (1983) 2036.
Boris E. Krisyuk* Eugene V. Polianczyk Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia Received 3 March 2005; Revised 20 April 2005; Accepted 23 April 2005 Available online 1 August 2005