170
Appendix: Interphase Dimension Measurement Via AFM
• The final step represents the calculation of interphase volume V Interphase for fully
or partially embedded NBCs in PVA/NBC bionanocomposites based on Fig. 5.1a,
b in Chap. 5 given by
V Interphase
f
= V NBC/Interphase − V NBC
(A14)
V Interphase
p
= V NBC/Interphase-effective − V NBC-effective
(A15)
PVA/HNT Bionanocomposite Films
In a similar manner, real HNTs can show irregular shapes as well though they tend
to mainly possess hollow tubular structures. Non-uniform interphase thickness is
confirmed again for PVA/HNT interaction in corresponding bionanocomposites, as
presented in Fig. 5.6 in Chap. 5. As such, the determination of 3D interphase dimensions of PVA/HNT nanocomposites also follows the same procedure mentioned
earlier in PVA bionanocomposites reinforced with NBCs and Cloisite 30B clays as
follows:
• Two typical diameters were assumed for PVA/HNT phases, as shown in Fig. A5a,
consisting of the diameter along transverse section (DT iHNT ) and the diameter
along longitudinal plane section (DL jHNT ). Consequently, to determine W iInterphase
in PVA/HNT phases, they were scanned transversely, as depicted in Fig. A5 to
yield:
W iInterphase = DT iHNT + t Wi1 + t Wi2
(A16)
L jInterphase and H kInterphase of PVA/HNT phases were measured by scanning along
the jth longitudinal plane (j = 1, 2, 3, …) and along the kth height plane (k = 1, 2,
3, …), as shown in Fig. A6a, b, respectively. Accordingly, Eqs. (A2) and (A3) can
be rewritten as follows:
L jInterphase = L jHNT + t Lj1 + t Lj2
(A17)
H kInterphase = DL kHNT + t Hk1 + t Hk2
(A18)
• The next step is to determine interphase dimensions of PVA/HNT phases to
calculate
(SA outer Interface ) f , (SA outer Interface ) p , (SA inner Interface ) f and (SA inner Interface ) p as given
by:
(SA outer Interface ) f = a
1 + b
1 L
2
Interphase + c
1 W
2
Interphase + d
1 H
2
Interphase
(A19)
Appendix: Interphase Dimension Measurement Via AFM
• The final step represents the calculation of interphase volume V Interphase for fully
or partially embedded NBCs in PVA/NBC bionanocomposites based on Fig. 5.1a,
b in Chap. 5 given by
V Interphase
f
= V NBC/Interphase − V NBC
(A14)
V Interphase
p
= V NBC/Interphase-effective − V NBC-effective
(A15)
PVA/HNT Bionanocomposite Films
In a similar manner, real HNTs can show irregular shapes as well though they tend
to mainly possess hollow tubular structures. Non-uniform interphase thickness is
confirmed again for PVA/HNT interaction in corresponding bionanocomposites, as
presented in Fig. 5.6 in Chap. 5. As such, the determination of 3D interphase dimensions of PVA/HNT nanocomposites also follows the same procedure mentioned
earlier in PVA bionanocomposites reinforced with NBCs and Cloisite 30B clays as
follows:
• Two typical diameters were assumed for PVA/HNT phases, as shown in Fig. A5a,
consisting of the diameter along transverse section (DT iHNT ) and the diameter
along longitudinal plane section (DL jHNT ). Consequently, to determine W iInterphase
in PVA/HNT phases, they were scanned transversely, as depicted in Fig. A5 to
yield:
W iInterphase = DT iHNT + t Wi1 + t Wi2
(A16)
L jInterphase and H kInterphase of PVA/HNT phases were measured by scanning along
the jth longitudinal plane (j = 1, 2, 3, …) and along the kth height plane (k = 1, 2,
3, …), as shown in Fig. A6a, b, respectively. Accordingly, Eqs. (A2) and (A3) can
be rewritten as follows:
L jInterphase = L jHNT + t Lj1 + t Lj2
(A17)
H kInterphase = DL kHNT + t Hk1 + t Hk2
(A18)
• The next step is to determine interphase dimensions of PVA/HNT phases to
calculate
(SA outer Interface ) f , (SA outer Interface ) p , (SA inner Interface ) f and (SA inner Interface ) p as given
by:
(SA outer Interface ) f = a
1 + b
1 L
2
Interphase + c
1 W
2
Interphase + d
1 H
2
Interphase
(A19)