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Comment on "Simple thermodynamic derivation of the electrocapillary equations" by E.M. Gutman [Surf. Sci. 639 (2015) L5–L8]
SUSC-20517; No of Pages 2
May 24, 2015;
Model: Gulliver 5
Surface Science xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
Surface Science journal homepage: www.elsevier.com/locate/susc
Reply to Comment on “Simple thermodynamic derivation of the electrocapillary equations” by E.M. Gutman [Surf. Sci. xxx (2015) xxx-xxx]
Keywords: Thermodynamics Electrochemistry Surface tension Capillary phenomena Residual stresses
1. Introduction Gutman [1] presents strongly worded criticism on the recent effort to simplify the derivations of the electrocapillary equations by a clearcut thermodynamic analysis [2]. It is outlined here that the points raised by Gutman [1] are misunderstandings of the purpose and the details of the criticized paper [2].
2. Purpose of the simple derivations The approach taken by Makkonen [2] was to make different hypotheses on the free parameters of the thermodynamic system of a surface, and then find out what follows from these hypotheses. This was made by simplifying the analysis to the bone, using a strictly thermodynamic approach, without any other type of assumptions of the system properties. The purpose was to demonstrate from which basic assumptions the commonly claimed electrocapillary equations result, and which of them do not correctly result from any assumptions, using the thermodynamic formalism. The idea behind the method of hypothesis testing has escaped from Gutman [1], who repeatedly criticizes the correctness and relevance of the hypothesis utilized in [2] in the case of a double electric layer. The correctness of the hypothesis for the specific case, discussed by Gutman [1] at length, was entirely outside the scope of the paper [2], where great care was made not to make any kind of pre-claims on the hypothesis, since the purpose was to test them. Reflecting this, the closing sentence of the paper [2] was “Whether such systems exist is an issue of present dispute”. Gutman [1] also argues that the equations that result from the analysis [2] are not new, again misinterpreting the purpose of the paper. Contrary to Gutman's assertion, it was not claimed in [2] that the resulting equations are new. Instead, the purpose was to show which of the previously presented equations are justified and which are not, under the different assumptions on the free parameters of the thermodynamic system.
3. The derivations Gutman [1] claims that there is “confusion of thermodynamic potentials” in [2], not noting that, since no volume term appears in the interfacial equations, there is no distinction here between the surface Helmholtz and Gibbs free energies (see [3], p. 22). For considering the effect of the free parameters of the thermodynamic system, the fundamental equations, Eqs. (7) and (9) in [2], were constructed, and it was clearly stated that they represent two different thermodynamic systems. Gutman [1], nevertheless, insists that they can somehow be related by Legendre transformations. Whether this is formally true or not it is irrelevant to constructing the fundamental thermodynamic relations, since they are for two different systems. Furthermore, the attempt to show how such transformations can be made is incorrectly performed in [1], since a thermodynamically inappropriate definition of the specific surface charge is used throughout that analysis. As discussed in [2], the specific surface charge must be defined as q = dQ/dA, not qs = Q/A, to be compatible with the thermodynamic theory (see also [4]). Therefore, obtaining Eq. (11) from Eq. (10) in [2], is not “a mathematical mistake”, as claimed by Gutman [1], but directly results from the thermodynamically correct definition of the specific surface charge q. Gutman [1] points out that the difference between q and qs is not relevant when q is independent of A. However, this difference is very relevant to the derivations when no such pre-assumption is made, and is the most common reason for the erroneous equations often presented, as demonstrated by Gutman's [1] derivation of his Eq. (10). Gutman discusses the referencing in [2] with an apparent misunderstanding. The sentence [2] “If one instead follows [references] and considers a system where E is the independent variable …” means, of course, that in these references E is considered as the independent variable, not the contrary as interpreted by Gutman. Perhaps for the same reason, at the end of his comment, Gutman confuses his Eq. (1) with the case where q and E are linked, although this equation (Eq. (7) in [2]) is given as the fundamental thermodynamic relation specifically for the case where this is not so.
4. Conclusions None of the critical comments by Gutman [1] on the paper that he discusses [2] are valid.
Acknowledgements This work was supported in part by the Academy of Finland grant no. 268925.
http://dx.doi.org/10.1016/j.susc.2015.05.014 0039-6028/© 2015 Elsevier B.V. All rights reserved.
Please cite this article as: L. Makkonen, Reply to Comment on “Simple thermodynamic derivation of the electrocapillary equations” by E.M. Gutman [Surf. Sci. xxx (2015) xxx-xxx], Surf. Sci. (2015), http://dx.doi.org/10.1016/j.susc.2015.05.014
2
L. Makkonen / Surface Science xxx (2015) xxx–xxx
References [1] E.M. Gutman, Surf. Sci. (2015) (in press). [2] L. Makkonen, Surf. Sci. 635 (2015) 61. [3] C.C. Lang, C.A. Barbero, Laser Techniques for the Study of Electrode Processes, Springer, 2012. [4] D.J. Bottomley, L. Makkonen, K. Kolari, Surf. Sci. 604 (2010) 2066.
Lasse Makkonen. VTT Technical Research Centre of Finland, Espoo, 02044 VTT, Finland E-mail address: lasse.makkonen@vtt.fi. 11 May 2015 Available online xxxx
Please cite this article as: L. Makkonen, Reply to Comment on “Simple thermodynamic derivation of the electrocapillary equations” by E.M. Gutman [Surf. Sci. xxx (2015) xxx-xxx], Surf. Sci. (2015), http://dx.doi.org/10.1016/j.susc.2015.05.014
May 24, 2015;
Model: Gulliver 5
Surface Science xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
Surface Science journal homepage: www.elsevier.com/locate/susc
Reply to Comment on “Simple thermodynamic derivation of the electrocapillary equations” by E.M. Gutman [Surf. Sci. xxx (2015) xxx-xxx]
Keywords: Thermodynamics Electrochemistry Surface tension Capillary phenomena Residual stresses
1. Introduction Gutman [1] presents strongly worded criticism on the recent effort to simplify the derivations of the electrocapillary equations by a clearcut thermodynamic analysis [2]. It is outlined here that the points raised by Gutman [1] are misunderstandings of the purpose and the details of the criticized paper [2].
2. Purpose of the simple derivations The approach taken by Makkonen [2] was to make different hypotheses on the free parameters of the thermodynamic system of a surface, and then find out what follows from these hypotheses. This was made by simplifying the analysis to the bone, using a strictly thermodynamic approach, without any other type of assumptions of the system properties. The purpose was to demonstrate from which basic assumptions the commonly claimed electrocapillary equations result, and which of them do not correctly result from any assumptions, using the thermodynamic formalism. The idea behind the method of hypothesis testing has escaped from Gutman [1], who repeatedly criticizes the correctness and relevance of the hypothesis utilized in [2] in the case of a double electric layer. The correctness of the hypothesis for the specific case, discussed by Gutman [1] at length, was entirely outside the scope of the paper [2], where great care was made not to make any kind of pre-claims on the hypothesis, since the purpose was to test them. Reflecting this, the closing sentence of the paper [2] was “Whether such systems exist is an issue of present dispute”. Gutman [1] also argues that the equations that result from the analysis [2] are not new, again misinterpreting the purpose of the paper. Contrary to Gutman's assertion, it was not claimed in [2] that the resulting equations are new. Instead, the purpose was to show which of the previously presented equations are justified and which are not, under the different assumptions on the free parameters of the thermodynamic system.
3. The derivations Gutman [1] claims that there is “confusion of thermodynamic potentials” in [2], not noting that, since no volume term appears in the interfacial equations, there is no distinction here between the surface Helmholtz and Gibbs free energies (see [3], p. 22). For considering the effect of the free parameters of the thermodynamic system, the fundamental equations, Eqs. (7) and (9) in [2], were constructed, and it was clearly stated that they represent two different thermodynamic systems. Gutman [1], nevertheless, insists that they can somehow be related by Legendre transformations. Whether this is formally true or not it is irrelevant to constructing the fundamental thermodynamic relations, since they are for two different systems. Furthermore, the attempt to show how such transformations can be made is incorrectly performed in [1], since a thermodynamically inappropriate definition of the specific surface charge is used throughout that analysis. As discussed in [2], the specific surface charge must be defined as q = dQ/dA, not qs = Q/A, to be compatible with the thermodynamic theory (see also [4]). Therefore, obtaining Eq. (11) from Eq. (10) in [2], is not “a mathematical mistake”, as claimed by Gutman [1], but directly results from the thermodynamically correct definition of the specific surface charge q. Gutman [1] points out that the difference between q and qs is not relevant when q is independent of A. However, this difference is very relevant to the derivations when no such pre-assumption is made, and is the most common reason for the erroneous equations often presented, as demonstrated by Gutman's [1] derivation of his Eq. (10). Gutman discusses the referencing in [2] with an apparent misunderstanding. The sentence [2] “If one instead follows [references] and considers a system where E is the independent variable …” means, of course, that in these references E is considered as the independent variable, not the contrary as interpreted by Gutman. Perhaps for the same reason, at the end of his comment, Gutman confuses his Eq. (1) with the case where q and E are linked, although this equation (Eq. (7) in [2]) is given as the fundamental thermodynamic relation specifically for the case where this is not so.
4. Conclusions None of the critical comments by Gutman [1] on the paper that he discusses [2] are valid.
Acknowledgements This work was supported in part by the Academy of Finland grant no. 268925.
http://dx.doi.org/10.1016/j.susc.2015.05.014 0039-6028/© 2015 Elsevier B.V. All rights reserved.
Please cite this article as: L. Makkonen, Reply to Comment on “Simple thermodynamic derivation of the electrocapillary equations” by E.M. Gutman [Surf. Sci. xxx (2015) xxx-xxx], Surf. Sci. (2015), http://dx.doi.org/10.1016/j.susc.2015.05.014
2
L. Makkonen / Surface Science xxx (2015) xxx–xxx
References [1] E.M. Gutman, Surf. Sci. (2015) (in press). [2] L. Makkonen, Surf. Sci. 635 (2015) 61. [3] C.C. Lang, C.A. Barbero, Laser Techniques for the Study of Electrode Processes, Springer, 2012. [4] D.J. Bottomley, L. Makkonen, K. Kolari, Surf. Sci. 604 (2010) 2066.
Lasse Makkonen. VTT Technical Research Centre of Finland, Espoo, 02044 VTT, Finland E-mail address: lasse.makkonen@vtt.fi. 11 May 2015 Available online xxxx
Please cite this article as: L. Makkonen, Reply to Comment on “Simple thermodynamic derivation of the electrocapillary equations” by E.M. Gutman [Surf. Sci. xxx (2015) xxx-xxx], Surf. Sci. (2015), http://dx.doi.org/10.1016/j.susc.2015.05.014