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Appendix: Interphase Dimension Measurement Via AFM
Fig. A3 Relationship between surface area of outer interface (SA outer Interphase ) and interphase
length (L Interphase ) for PVA/NBC phases in PVA/NBC bionanocomposites [1]
(SA inner Interface ) p = a 4 + b 4 L
2
NBC-effective + c 4 W
2
NBC-effective + d 4 H
2
NBC-effective
(A8)
where L
Interphase-effective , W
Interphase-effective and H
Interphase-effective represent the
maximum length, width and thickness for effective interphases. L
NBC-effective ,
W
NBC-effective and H
NBC-effective denote the maximum length, width and thickness
for effective NBCs. 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 were determined to be 0.7439, 0.3627, 0.7006 and 0.9979, respectively,
by fitting Eq. (A5) with measured surface area (SA outer Interface ) f obtained from
the AFM, as depicted in Fig. A3. Using such coefficients on the training set, the
average error was about 8.7% while the maximum error is 26.7%, which were
similar to those obtained from the validation sets.
• At the third step, the interphase volume was calculated based on the following
equation suggested by Erdo˘ gan [4]:
SA p = eV
f
p
(A9)
where V represents the volume of anisotropic particles and e and f are also
the constants to be determined by fitting experimentally acquired SA p with