Volume fraction silica dispersions

Figure 6.5 Plot of the apparent storage and loss moduli as a function of strain for volume fractions of dispersions of silica particles (a — I50nm, c — 10 3 M)...

The adsorption of block and random copolymers of styrene and methyl methacrylate on to silica from their solutions in carbon tetrachloride/n-heptane, and the resulting dispersion stability, has been investigated. Theta-conditions for the homopolymers and analogous critical non-solvent volume fractions for random copolymers were determined by cloud-point titration. The adsorption of block copolymers varied steadily with the non-solvent content, whilst that of the random copolymers became progressively more dependent on solvent quality only as theta-conditions and phase separation were approached. 

Gillespie and Wiley used a cone-and-plate viscometer to measure F/A versus dv/dx for dispersions of silica and cross-linked polystyrene in dioctyl phthalate. At a volume fraction of 0.35 for both solids, the following results were obtained ... 

Polymeric fibers are popular for reinforcing concrete matrices because of their low density (more number of fibers for a prescribed volume fraction), high tensile strength, ease of dispersion, relative resistance to chemicals, and relatively low cost compared to other kinds of fibers. Polypropylene and polyolefin fibers are typically hydrophobic, resulting in a relatively poor bond with concrete matrices compared to some other types of fibers. Treatment of polypropylene with an aqueous dispersion of colloidal alumina or silica and chlorinated polypropylene enhances the affinity of these fibers toward cement particles. Treatment of polypropylene fibers with a surface-active agent provides better dispersion of the fibers and a stronger bond between cement and fiber. The earlier attempts at surface treatments of polypropylene fibers have had only limited success and have not been commercially attractive. 

Figure 7-6 shows the viscosity of thermoreversible dispersions (discussed in Section 7.2.4) of a 50-nm silica particles onto which octadecyl chains have been densely grafted in benzene at particle volume fractions 4> — 0.088-0.133, as a function of temperature T (Woutersen and de Kruif 1991). For T > 9 — 316 K, the viscosity relative to that of the solvent, rir = r /f]s, is independent of temperature, and its dependence on volume fraction 0 is exactly as expected for hard spherical particles without attractive interactions. As T is lowered below 9, however, the viscosity rises rapidly, because of the onset of attractive interactions. 

Figure 22. Variation of [ 17ou>s/i w7t toith total volume fraction of the dispersed phases for 9-pm silica sand. (Reproduced with permission from r erence 57. Copyright 1991 Pergamon Press.)...

Fig. 21 (a, b) The frequency dependencies of the storage G (a) and loss G" (b) moduli for different volume fractions of uncoated silica hard spheres (7 h = 210 nm) dispersed in ethylene glycol [238]. The solid lines represent MCT predictions, (c) Respective data (G solid square, G" open square for an aqueous glassy microgel suspension (PNIPAM-coated PS latex particles, overall radius 105.3 nm and effective volume fraction 0.585 at 10°C), along with the MCT lines [256]. The minimum of G" marks the inverse -relaxation time... 

Van der Werff and de Kruif (1989) examined the scaling of rheological properties of a hard-sphere silica dispersion (sterically stable monodisperse silica in cyclohexane) with particle size, volume fraction and shear rate. The shear-thinning behaviour was found to scale with the Peclet number Pe = 6nt]sa yl k-QT), or the ratio of shear time to structure-build-up time, where a is the particle radius, is the viscosity of the solution, y is the shear... 

Figure 13.13. Comparison of the behavior predicted from Equation 13.35 with the data tabulated by de Kruif et al [43] for the viscosity of dispersions of sterically stabilized hard silica spheres in cyclohexane. There are no adjustable parameters in Equation 13.35. Relative viscosity denotes r (dispersion)/r (cyclohexane). Relative volume fraction denotes 0/0. Couette and parallel refer to measurements with a Couette rheometer and a parallel plate rheometer, respectively. Zero and infinite refer to the limits y —>0 and y- < >, respectively.

Fig. 9. Normalized UV-visible spectra of dilute dispersions of 640 nm latex spheres coated with five monolayers of Au Si02 nanoparticles. The thickness of the corresponding silica shells is indicated. The trends are consistent with the predictions of Eq. (15) but quantitative agreement is not possible due to the higher volume fraction of the shells in experiments...

In order to establish whether the gold core or the silica shell is primarily responsible for the observed colour changes, the spectra were measured at three different volume fractions. The first sample was a dispersion of Au—Si02—TPM particles in ethanol, the second was a dispersion of the same particles in a mixture of ethanol... 

The third term, which involves O (the volume fraction of silica), expresses the effect of increasing the silica concentration in decreasing the gel time. The expression 0/(1 - KO) is used instead of O itself as a concentration variable, since the particles will physically touch one another long before the silica volume fraction becomes one (corresponding to a 100% concentration). The constant in the denominator of this expression, which has the value of 2.58 for the particular sample of deionized Ludox used in these gelling experiments, is identical to the constant, which appears in the Einstein-Mooney equation for the viscosity of spherical colloidal particles. This will vary with the degree of hydration and aggregation, or the % solids in the dispersed phase, of the silica particles. 

Broadband dielectric spectroscopy is a powerful tool to investigate polymeric systems (see [38]) including polymer-based nanocomposites with different nanofillers like silica [39], polyhedral oligomeric silsesquioxane (POSS) [40-42], and layered silica systems [43-47] just to mention a few. Recently, this method was applied to study the behavior of nanocomposites based on polyethylene and Al-Mg LDH (AlMg-LDH) [48]. The properties of nanocomposites are related to the small size of the filler and its dispersion on the nanometer scale. Besides this, the interfacial area between the nanoparticles and the matrix is crucial for the properties of nanocomposites. Because of the high surface-to-volume ratio of the nanoparticles, the volume fraction of the interfacial area is high. For polyolefin systems, this interfacial area might be accessible by dielectric spectroscopy because polyolefins are nonpolar and, therefore, the polymeric matrix is dielectrically invisible [48]. 

In Section 23.2 was discussed the theory of reinforcement of polymer and elastomers which refers to the Guth-Gold-Smallwood equation (Equation (23.1)) to correlate the compound initial modulus (E ) with the filler volume fraction ( ). Moreover, it was already commented on the key roles played by the surface area and by the aspect ratio (/). Basic feature of nanofillers, such as clays, CNTs and nanographites, is the nano-dimension of primary particles and thus their high surface area. This allows creating filler networks at low concentrations, much lower than those typical of nanostructured fillers, such as CB and silica, provided that they are evenly distributed and dispersed in the rubber matrix. In this case, low contents of nanofiller particles are required to mutually disturb each other and to get to percolation. Moreover, said nanofillers are characterized by an aspect ratio /that can be remarkably higher than 1. Barrier properties are improved when fillers (such as clays and nanographites) made by... 

This relates the polymer activity (which determines B2) to the colloid volume fraction at the spinodal. De Hek and Vrij [56] could give a good description of the phase line of mixtures of polystyrene chains plus small volume fractions of (hard-sphere like) octadecyl silica spheres dispersed in cyclohexane [109]. 

To investigate the formation of microgel, a 15% silica sol of 6 nm particles was deionized by Her to pH 5.55 and aged at 30°C. Samples were taken at different times, diluted to 4% SiOj, and deionized to pH 3.5 (to leave little or no charge on particles), and the viscosity was determined. From this the volume percent of dispersed phase in the 4% sol was calculated from Figure 3.30 and then multiplied by 15/4 to find the volume fraction in the original sol before dilution. 

At the point where most of the monomer has been converted to particles but where these have not yet begun to aggregate, the viscosity of a sol may be calculated from the volume fraction of the dispersed phase, which is defined as the silica particl along with the water that adheres to the surface by hydrogen bonding. 

Knowing the silica content of a sol and the particle size one can calculate the volume fraction of the dispersed phase. jFor example. 1 ml of a 2% SiO, sol of 1.5 nm particles contains 0.022 ml of dispersed phase. From the Mooney equation (Figure 3.30) the value of/I, - 1 is 0.055. 

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