146
5 Controversy of Thermodynamics Associated with Surface …
After rearrangement, Eq. (5.20) simply retrieves the generalized Lippmann equation
of Eq. (5.19) for an isotropic solid electrode in place of Eq. (5.17).
Consequently, the Shuttleworth equation cannot be an appropriate starting point
to obtain a formulation for
∂g
∂E
[15]. It is emphasized that Eq. (5.19) for a solid
electrode should be used as a starting point [15]. The Gokhshtein equation for an
isotropic solid electrode, i.e.,
∂g
∂E
ε
= −q −
∂q
∂ε
E
explicitly indicates that the
partial derivatives of
∂g
∂E
and
∂q
∂ε
are thermodynamically constrained to constant
elastic strain ε and potential E, respectively, as compared to Eq. (5.17). Furthermore,
Proost [15] pointed out that the thermodynamic constraint of constant elastic strain
does not keep for the surface stress measurement of a solid electrode as a function of
applied potential by a cantilever bending method since the curvature of the cantilever
electrode, i.e., the elastic strain changes with potential. According to Proost [15], it is
strictly inappropriate to use the equations associated with electrocapillarity of a solid
electrode derived under the constant elastic strain in order to interpret the surface
stress versus potential curve measured by a cantilever bending method. The average
value of
g
E
in some potential range obtained from the surface stress versus potential
curve by using the cantilever bending method does not meet the thermodynamic
constraint of constant elastic strain.
References
1. Láng G, Heusler KE (1994) J Electroanal Chem 377:1–7
2. Láng G, Heusler KE (1999) J Electroanal Chem 472:168–173
3. Láng GG, Barbero CA (2012) Laser techniques for electrode processes. chap 3. Springer, Berlin
4. Couchman PR, Davidson CR (1977) J Electroanal Chem 85:407–409
5. Linford RG (1978) Chem Rev 78:81–95
6. Schmickler W, Leiva E (1998) J Electroanal Chem 453:61–67
7. Callen HB (1960) Thermodynamics: an introduction to the physical theories of equilibrium
thermostatics and irreversible thermodynamics. chap 3. Wiley, New York
8. Gutman EM (1995) J Phys Condens Mater 7:L663–L667
9. Gutman EM (2014) J Solid State Electrochem 18:3217–3237
10. Gutman EM (2016) J Solid State Electrochem 20:2929–2950
11. Eriksson JC (1969) Surf Sci 14:221–246
12. Guidelli R (1999) J Electroanal Chem 472:174–177
13. Valincius G (1999) J Electroanal Chem 478:40–49
14. Kramer D, Weissmüller J (2007) Surf Sci 601:3042–3051
15. Proost J (2005) J Solid State Electrochem 9:660–664
16. Shuttleworth R (1950) Proc Phys Soc London A63:444–457
17. Bottomley DJ, Makkonen L, Kolari K (2009) Surf Sci 603:97–101
18. Ibach H (1997) Surf Sci Rep 29:193–263
19. Müller P, Saúl A (2004) Surf Sci Rep 54:157–258
20. Rusanov AI (1996) Surf Sci Rep 23:173–247
21. Rusanov AI (2005) Surf Sci Rep 58:111–239
22. Hermann R (1973) Geometry, physics, and systems. chap. 6. Marcel Dekker Inc, New York
23. Marichev VA (2009) Surf Sci 603:2345–2346
24. Bottomley DJ, Makkonen L, Kolari K (2009) Surf Sci 603:2347
5 Controversy of Thermodynamics Associated with Surface …
After rearrangement, Eq. (5.20) simply retrieves the generalized Lippmann equation
of Eq. (5.19) for an isotropic solid electrode in place of Eq. (5.17).
Consequently, the Shuttleworth equation cannot be an appropriate starting point
to obtain a formulation for
∂g
∂E
[15]. It is emphasized that Eq. (5.19) for a solid
electrode should be used as a starting point [15]. The Gokhshtein equation for an
isotropic solid electrode, i.e.,
∂g
∂E
ε
= −q −
∂q
∂ε
E
explicitly indicates that the
partial derivatives of
∂g
∂E
and
∂q
∂ε
are thermodynamically constrained to constant
elastic strain ε and potential E, respectively, as compared to Eq. (5.17). Furthermore,
Proost [15] pointed out that the thermodynamic constraint of constant elastic strain
does not keep for the surface stress measurement of a solid electrode as a function of
applied potential by a cantilever bending method since the curvature of the cantilever
electrode, i.e., the elastic strain changes with potential. According to Proost [15], it is
strictly inappropriate to use the equations associated with electrocapillarity of a solid
electrode derived under the constant elastic strain in order to interpret the surface
stress versus potential curve measured by a cantilever bending method. The average
value of
g
E
in some potential range obtained from the surface stress versus potential
curve by using the cantilever bending method does not meet the thermodynamic
constraint of constant elastic strain.
References
1. Láng G, Heusler KE (1994) J Electroanal Chem 377:1–7
2. Láng G, Heusler KE (1999) J Electroanal Chem 472:168–173
3. Láng GG, Barbero CA (2012) Laser techniques for electrode processes. chap 3. Springer, Berlin
4. Couchman PR, Davidson CR (1977) J Electroanal Chem 85:407–409
5. Linford RG (1978) Chem Rev 78:81–95
6. Schmickler W, Leiva E (1998) J Electroanal Chem 453:61–67
7. Callen HB (1960) Thermodynamics: an introduction to the physical theories of equilibrium
thermostatics and irreversible thermodynamics. chap 3. Wiley, New York
8. Gutman EM (1995) J Phys Condens Mater 7:L663–L667
9. Gutman EM (2014) J Solid State Electrochem 18:3217–3237
10. Gutman EM (2016) J Solid State Electrochem 20:2929–2950
11. Eriksson JC (1969) Surf Sci 14:221–246
12. Guidelli R (1999) J Electroanal Chem 472:174–177
13. Valincius G (1999) J Electroanal Chem 478:40–49
14. Kramer D, Weissmüller J (2007) Surf Sci 601:3042–3051
15. Proost J (2005) J Solid State Electrochem 9:660–664
16. Shuttleworth R (1950) Proc Phys Soc London A63:444–457
17. Bottomley DJ, Makkonen L, Kolari K (2009) Surf Sci 603:97–101
18. Ibach H (1997) Surf Sci Rep 29:193–263
19. Müller P, Saúl A (2004) Surf Sci Rep 54:157–258
20. Rusanov AI (1996) Surf Sci Rep 23:173–247
21. Rusanov AI (2005) Surf Sci Rep 58:111–239
22. Hermann R (1973) Geometry, physics, and systems. chap. 6. Marcel Dekker Inc, New York
23. Marichev VA (2009) Surf Sci 603:2345–2346
24. Bottomley DJ, Makkonen L, Kolari K (2009) Surf Sci 603:2347