118
5 3D Interphase of PVA Bionanocomposite Films
(SA inner Interface ) p = a 4 + b 4 L
2
p-effective + c 4 W
2
p-effective + d 4 H
2
p-effective
(5.4)
where L
Interphase-effective , W
Interphase-effective and H
Interphase-effective represent the
maximum length, width and thickness for effective interphases. L
p-effective, W
p-effective
and H
p-effective denote the maximum length, width and thickness for effective
nanoparticles. 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 using curving fitting. For instance, the constants of a 1 , b 1 ,
c 1 and d 1 in case of PVA/NBC bionanocomposites were determined to be 0.7439,
0.3627, 0.7006 and 0.9979, respectively, by fitting Eq. (5.1) with experimental data
in relation to surface area (SA
outer Interface ) f obtained from AFM measurements (see
more details in Appendix).
After obtaining surface area data, the associated results were employed in determining interphase/nanoparticle volume V p/Interphase and nanoparticles volume V p with
respect to fully and partially embedded nanoparticles according to modified equations
derived from Behmer and Hawkins [4] as follows:
(SA outer Interface ) f = e 1 V
f 1
p/Interphase
(5.5)
(SA outer Interface ) p = e 2 V
f 2
p/Interphase effective
(5.6)
(SA inner Interface ) f = e 3 V
f 3
p
(5.7)
(SA inner Interface ) p = e 4 V
f 4
p effective
(5.8)
e 1 , f 1 , e 2 , f 2 , e 3 , f 3 and e 4 , f 4 are constants determined using curving fitting. For
example, the constants of e 1 and f 1 in case of PVA/NBC phases were estimated to be
0.3824 and 0.3825, respectively, by fitting Eq. (5.5) with the data value of V p/Interphase
obtained from the AFM measurement (refer to Appendix for more details).
Final step is to determine interphase volume V Interphase for fully or partially
embedded nanoparticles in PVA nanocomposites shown in Figs. 5.1 as follows:
V Interphase
f
= V p/Interphase − V p
(5.9)
V Interphase
p
= V p/Interphase-effective − V p effective
(5.10)
Note that the aforementioned procedure applied to three PVA bionanocomposite
systems reinforced with NBCs, HNTs and Cloisite 30B clays used in this study
by considering interphase dimensions and properties (refer to Appendix for more
details).
5 3D Interphase of PVA Bionanocomposite Films
(SA inner Interface ) p = a 4 + b 4 L
2
p-effective + c 4 W
2
p-effective + d 4 H
2
p-effective
(5.4)
where L
Interphase-effective , W
Interphase-effective and H
Interphase-effective represent the
maximum length, width and thickness for effective interphases. L
p-effective, W
p-effective
and H
p-effective denote the maximum length, width and thickness for effective
nanoparticles. 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 using curving fitting. For instance, the constants of a 1 , b 1 ,
c 1 and d 1 in case of PVA/NBC bionanocomposites were determined to be 0.7439,
0.3627, 0.7006 and 0.9979, respectively, by fitting Eq. (5.1) with experimental data
in relation to surface area (SA
outer Interface ) f obtained from AFM measurements (see
more details in Appendix).
After obtaining surface area data, the associated results were employed in determining interphase/nanoparticle volume V p/Interphase and nanoparticles volume V p with
respect to fully and partially embedded nanoparticles according to modified equations
derived from Behmer and Hawkins [4] as follows:
(SA outer Interface ) f = e 1 V
f 1
p/Interphase
(5.5)
(SA outer Interface ) p = e 2 V
f 2
p/Interphase effective
(5.6)
(SA inner Interface ) f = e 3 V
f 3
p
(5.7)
(SA inner Interface ) p = e 4 V
f 4
p effective
(5.8)
e 1 , f 1 , e 2 , f 2 , e 3 , f 3 and e 4 , f 4 are constants determined using curving fitting. For
example, the constants of e 1 and f 1 in case of PVA/NBC phases were estimated to be
0.3824 and 0.3825, respectively, by fitting Eq. (5.5) with the data value of V p/Interphase
obtained from the AFM measurement (refer to Appendix for more details).
Final step is to determine interphase volume V Interphase for fully or partially
embedded nanoparticles in PVA nanocomposites shown in Figs. 5.1 as follows:
V Interphase
f
= V p/Interphase − V p
(5.9)
V Interphase
p
= V p/Interphase-effective − V p effective
(5.10)
Note that the aforementioned procedure applied to three PVA bionanocomposite
systems reinforced with NBCs, HNTs and Cloisite 30B clays used in this study
by considering interphase dimensions and properties (refer to Appendix for more
details).