2.5 Dilatometric Detection of Strain Change for Nano-Porous Metal Electrode
65
surfaces, and (3) bi-continuous network structures with interpenetrating solid phase
and pore space. If Eq. (2.37) is applied to a nano-porous metal electrode, the changes
in mean surfaces stress g A can be determined from the relative changes in sample
length measured by dilatometry. The volumetric mean strain is given by
V
V
= −
P V
Y b
,
(2.38)
where Y b is the bulk modulus of the metal. For small strain, the following relationship
between the relative changes in volume and sample length holds:
V
V
=
3l
l o
,
(2.39)
where
l
l o
corresponds to the macroscopic strain of the sample. The specific surface
area per volume or mass can be measured by Brunauer–Emmett–Teller (BET) method
[55]. The substitution of Eqs. (2.38) and (2.39) into Eq. (2.37) leads to the relationship
between g A and
l
l o
[46, 47]:
g A = −
9Y b
2α
l
l o
= −
9Y b
2α m ρ
l
l o
,
(2.40)
where α is the specific surface area per volume
AV
−1
, α m the specific surface
area per mass (m
2 g
−1 ), and ρ is the mass density (g m
−3 ). We discuss the typical
application results of the in situ dilatometry in Sect. 3.4.4 of Chap. 3.
References
1. Láng GG, Barbero CA (2012) Laser techniques for the study of electrode processes. chaps. 4
and 5. Springer, Berlin
2. Gokhshtein AY (1976) Surface tension of solids and adsorption. Nauka, Moscow
3. Gokhshtein AY (1970) Electrochim Acta 15:219–223
4. Gokhshtein AY (1975) Russ Chem Rev 44:921–932
5. Valincius G (1998) Langmiur 14:6307–6319
6. Valincius G (1999) J Electroanal Chem 478:40–49
7. Malpus RE, Fredlein RA, Bard AJ (1979) J Electroanal Chem 98:171–180
8. Handley LJ, Bard AJ (1980) J Electrochem Soc 127:338–343
9. Seo M, Makino T, Sato N (1986) J Electrochem Soc 133:1138–1142
10. Seo M, Jiang XC, Sato N (1987) J Electrochem Soc 134:3094–3098
11. Dickinson KM, Hansen KE, Fredlein RA (1992) Electrochim Acta 37:139–141
12. Bode-Jr DD, Andeson TN, Eyring H (1967) J Phys Chem 71:792–797
13. Lin K-F, Beck TR (1976) J Electrochem Soc 123:1145–1151
14. Jiang XC, Seo M, Sato N (1991) J Electrochem Soc 138:137–140
15. Seo M, Aomi M (1992) J Electrochem Soc 139:1087–1090
65
surfaces, and (3) bi-continuous network structures with interpenetrating solid phase
and pore space. If Eq. (2.37) is applied to a nano-porous metal electrode, the changes
in mean surfaces stress g A can be determined from the relative changes in sample
length measured by dilatometry. The volumetric mean strain is given by
V
V
= −
P V
Y b
,
(2.38)
where Y b is the bulk modulus of the metal. For small strain, the following relationship
between the relative changes in volume and sample length holds:
V
V
=
3l
l o
,
(2.39)
where
l
l o
corresponds to the macroscopic strain of the sample. The specific surface
area per volume or mass can be measured by Brunauer–Emmett–Teller (BET) method
[55]. The substitution of Eqs. (2.38) and (2.39) into Eq. (2.37) leads to the relationship
between g A and
l
l o
[46, 47]:
g A = −
9Y b
2α
l
l o
= −
9Y b
2α m ρ
l
l o
,
(2.40)
where α is the specific surface area per volume
AV
−1
, α m the specific surface
area per mass (m
2 g
−1 ), and ρ is the mass density (g m
−3 ). We discuss the typical
application results of the in situ dilatometry in Sect. 3.4.4 of Chap. 3.
References
1. Láng GG, Barbero CA (2012) Laser techniques for the study of electrode processes. chaps. 4
and 5. Springer, Berlin
2. Gokhshtein AY (1976) Surface tension of solids and adsorption. Nauka, Moscow
3. Gokhshtein AY (1970) Electrochim Acta 15:219–223
4. Gokhshtein AY (1975) Russ Chem Rev 44:921–932
5. Valincius G (1998) Langmiur 14:6307–6319
6. Valincius G (1999) J Electroanal Chem 478:40–49
7. Malpus RE, Fredlein RA, Bard AJ (1979) J Electroanal Chem 98:171–180
8. Handley LJ, Bard AJ (1980) J Electrochem Soc 127:338–343
9. Seo M, Makino T, Sato N (1986) J Electrochem Soc 133:1138–1142
10. Seo M, Jiang XC, Sato N (1987) J Electrochem Soc 134:3094–3098
11. Dickinson KM, Hansen KE, Fredlein RA (1992) Electrochim Acta 37:139–141
12. Bode-Jr DD, Andeson TN, Eyring H (1967) J Phys Chem 71:792–797
13. Lin K-F, Beck TR (1976) J Electrochem Soc 123:1145–1151
14. Jiang XC, Seo M, Sato N (1991) J Electrochem Soc 138:137–140
15. Seo M, Aomi M (1992) J Electrochem Soc 139:1087–1090