4.2 Particulate Silica Dispersion as Revealed by 3D-TEM
69
Fig. 4.12 Silica aggregate network and its parameters (from Fig. 4 in Ref. [11])
ture. Here, numbers of the cross-linked chains, the branched chains and the isolated
chains of the silica aggregates are designated as N.NdNd, N.NdTm, and N.TmTm,
respectively, and their fraction as F cross , F branch , and F isolate are defined as follows:
F cross = N.NdNd/(N.NdNd + N.NdTm + N.TmTm)
(4.1)
F branch = N.NdTm/(N.NdNd + N.NdTm + N.TmTm)
(4.2)
F isolate = N.TmTm/(N.NdNd + N.NdTm + N.TmTm)
(4.3)
The three fractions are calculated from the skeletonized 3D-TEM images in
Fig. 4.11, and the resulted F cross and F branch are plotted against the amount of compounded silica in Fig. 4.13 [8, 11]. Even though the results are scattered, temporarily the following tendencies are noted: Fraction of the cross-linked chain (F cross )
increased with silica amount, but RX silica seemed to show maximum at 60 phr.
Fraction of branched seemed to decrease with silica amount, but RX silica showed
minimum at 60 phr. Hydrophobic RX silica’s behaviors are similar to those of carbon
black (see the next section), and the behavior is in accordance with the gelation theory
to be described later. In other words, 60 phr may be assumed to be the gelling point
where the gel has fully extended. Hydrophilic VN silica’s behavior giving maximum
or minimum is explained by the gelling being completed earlier at 60 phr, and hence
80 phr data were post-gelling ones. After the gelling point, branching is predominant
over networking due to the steric hindrance.
Still more on the different behavior between the hydrophilic VN silica and the
hydrophobic RX silica, optical transparency was distinctively found and the disparity
69
Fig. 4.12 Silica aggregate network and its parameters (from Fig. 4 in Ref. [11])
ture. Here, numbers of the cross-linked chains, the branched chains and the isolated
chains of the silica aggregates are designated as N.NdNd, N.NdTm, and N.TmTm,
respectively, and their fraction as F cross , F branch , and F isolate are defined as follows:
F cross = N.NdNd/(N.NdNd + N.NdTm + N.TmTm)
(4.1)
F branch = N.NdTm/(N.NdNd + N.NdTm + N.TmTm)
(4.2)
F isolate = N.TmTm/(N.NdNd + N.NdTm + N.TmTm)
(4.3)
The three fractions are calculated from the skeletonized 3D-TEM images in
Fig. 4.11, and the resulted F cross and F branch are plotted against the amount of compounded silica in Fig. 4.13 [8, 11]. Even though the results are scattered, temporarily the following tendencies are noted: Fraction of the cross-linked chain (F cross )
increased with silica amount, but RX silica seemed to show maximum at 60 phr.
Fraction of branched seemed to decrease with silica amount, but RX silica showed
minimum at 60 phr. Hydrophobic RX silica’s behaviors are similar to those of carbon
black (see the next section), and the behavior is in accordance with the gelation theory
to be described later. In other words, 60 phr may be assumed to be the gelling point
where the gel has fully extended. Hydrophilic VN silica’s behavior giving maximum
or minimum is explained by the gelling being completed earlier at 60 phr, and hence
80 phr data were post-gelling ones. After the gelling point, branching is predominant
over networking due to the steric hindrance.
Still more on the different behavior between the hydrophilic VN silica and the
hydrophobic RX silica, optical transparency was distinctively found and the disparity