176
Appendix: Interphase Dimension Measurement Via AFM
A
B
kth plane
4 nm
Hk Cloisite30B
Hk Interphase
tHk1
tHk2
Interphase
Cloisite30B
tLj2
tLj1
LjCloisite30B
LjInterphase
A
B
jth plane
Cloisite30B
10 nm
Interphase
(a)
(b)
Fig. A10 Schematic diagrams of cross-sectional scanning of PVA/Cloisite 30B clay interphases
in PVA/Cloisite 30B clay bionanocomposites along, a longitudinal plane both in a top view, and
b height plane in a side view [2]
(SA inner Interface ) f = a
3 + b
3 L
2
Cloisite 30B + c
3 W
2
Cloisite 30B + d
3 H
2
Cloisite 30B
(A34)
(SA inner Interface ) p = a
4 + b
4 L
Cloisite 30B-effective + c
4 W
Cloisite 30B-effective
+ d
4 H
Cloisite 30B-effective
(A35)
a
1 , b
1 , c
1 , d
1 , a
2 , b
2 , c
2 , d
2 , a
3 , b
3 , c
3 , d
3 and a
4 , b
4 , c
4 , d
4 are constants determined via curving fitting. For instance, the constants of a
1 , b
1 , c
1 and d
1 were determined to be 0.6695, 0.3264, 0.7431 and 0.8981, respectively, as shown in Fig. A11
by fitting Eq. (A32) with measured surface area (SA outer Interface ) f obtained from the
AFM.
• At this step, the interphase volume in PVA/Cloisite 30B clay phases was calculated
in case of fully and partially embedded Cloisite 30B clays by rearranging Eqs.
(5.5)–(5.8) in Chap. 5 to yield:
(SA outer Interface ) f = e
1 V
f
1
Cloisite 30B/Interphase
(A36)
(SA outer Interface ) p = e
2 V
f
2
Cloisite 30B/Interphase-effective
(A37)
(SA inner Interface ) f = e
3 V
f
3
Cloisite 30B
(A38)
(SA inner Interface ) p = e
4 V
f
4
Cloisite 30B-effective
(A39)