DESIGN, ASSEMBLY AND CHARACTERIZATION OF COMPOSITE ...

In the case of the aqueous carbon black gels studied here, no bridging flocculation
by polyelectrolyte is possible; and gelation is dependent on hydrogen bonding of the non-
ionic polymers, with the reinforcing effect of the carbon black particles. The polymer
concentration is significantly higher than in ceramic colloidal gels, partly because of the
higher specific surface area of smaller particles. The dissolved polymer Pluronic F-127
has a concentration enough to form a hydrogel without carbon black particles, but it
would be a much weaker one.
Enough hydrogen bonding sites must be present to allow gel behavior. In the
absence of extra polymer free in solution, the solid volume fraction of carbon black
dispersion has to be greater than a threshold value Φgel so that the inter-particle separation
may fall below twice of the surfactant layer thickness, resulting in compression and inter-
penetration of PEO chains of adsorbed NP4070 molecules. 98 After that, gel behaviors
replace viscous flow; elasticity increases as the particles network compacts further. It has
been shown that terminally anchored PEO tails (MW = 4800) may extend more than 30
nm in good solvent condition 111 . For the NP4070 surfactant with MW = 1600 PEO tails, a
value of around 10 nm is reasonable in water. Layer thicknesses for similarly-structured
nonylphenol polypropylene oxide-polyethylene oxide surfactants adsorbed on carbon
black in highly concentrated dispersions were calculated. 98 which also supports the
estimate of 10 nm thickness for the NP4070 surfactant. The average separation distance
between carbon black particles is estimated for different φsolids and packing types in Table
3.3. Considering the hierarchy structure of carbon black aggregates, 102 the maximum
packing density by weight for the carbon black gel is unlikely to be very high, much
volume must be occupied by the internal voids in those aggregates. This calculation
95