Bare particles

More sophisticated approaches to describe double layer interactions have been developed more recently. Using cell models, the full Poisson-Boltzmann equation can be solved for ordered stmctures. The approach by Alexander et al shows how the effective colloidal particle charge saturates when the bare particle charge is increased [4o]. Using integral equation methods, the behaviour of the primitive model has been studied, in which all the interactions between the colloidal macro-ions and the small ions are addressed (see, for instance, [44, 45]). 

PVA and TaM -for the 88%-hydrolyzed PVA. The same dependence was found for the adsorbed layer thickness measured by viscosity and photon correlation spectroscopy. Extension of the adsorption isotherms to higher concentrations gave a second rise in surface concentration, which was attributed to multilayer adsorption and incipient phase separation at the interface. The latex particle size had no effect on the adsorption density however, the thickness of the adsorbed layer increased with increasing particle size, which was attributed to changes in the configuration of the adsorbed polymer molecules. The electrolyte stability of the bare and PVA-covered particles showed that the bare particles coagulated in the primary minimum and the PVA-covered particles flocculated in the secondary minimum and the larger particles were less stable than the smaller particles. 

Transmission electron microscopy also gave evidence for bridging flocculation at partial coverage. Figure 3 shows electron micrographs of the bare particles and the particles covered partially with adsorbed Vinol 350. The partially covered particles are interconnected with fibrillar links, which are not observed in the bare-particle sample. 

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

Figure 4. Reduced viscosity ratio versus volume fraction of PS particles (o) bare particles (A) covered with Vinol 107 ( ) covered with Vinol 325 (A) covered with Vinol 205 (a) covered with Vinol 523.

Effect of PS Latex Particle Size on Adsorbed Layer Thickness. Figure 6 shows the variation of reduced viscosity with volume fraction for 190, 400, and HOOnm-size bare and PVA-covered PS latex particles. The viscosity variation of the different-size bare particles was the same, with an Einstein coefficient of ca. 3.0. The... 

It is interesting to compare these results with the electrophoretic measurements made under identical electrolyte concentrations. Figure 8 shows that the variation of electrophoretic mobility with sodium chloride concentration is different for the bare and the PVA-covered particles. For the bare particles, the mobility remains constant up to a certain salt concentration, then increases to a maximum and decreases sharply, finally approaching zero. The maximum in electrophoretic mobility-electrolyte concentration curve with bare particles has been explained earlier (21) by postulating the adsorption of chloride ions on hydrophobic polystyrene particles. In contrast, for the PVA-covered particles, the mobility decreases with increasing electrolyte concentration until it approaches zero at high salt concentration. 

Figure 7. W versus electrolyte concentration (NaCl) for different-size particles (o) 190nm particles ( ) 400nm particles open points for bare particles and closed points for particles covered withVinol 107 at saturation.

It was apparent that the dense adsorption layer of HPC which was formed on the silica particles at the LCST plays a part in the preparation of new composite polymer latices, i.e. polystyrene latices with silica particles in the core. Figures 10 and 11 show the electron micrographs of the final silica-polystyrene composite which resulted from seeded emulsion polymerization using as seed bare silica particles, and HPC-coated silica particles,respectively. As may be seen from Fig.10, when the bare particles of silica were used in the seeded emulsion polymerization, there was no tendency for encapsulation of silica particles, and indeed new polymer particles were formed in the aqueous phase. On the other hand, encapsulation of the seed particles proceeded preferentially when the HPC-coated silica particles were used as the seed and fairly monodisperse composite latices including silica particles were generated. This indicated that the dense adsorption layer of HPC formed at the LCST plays a role as a binder between the silica surface and the styrene molecules. 

Use the experimental value of [t/] for the bare particles and the relationship given in Example 13.5 to estimates 8RS for these particles. How do the layer thicknesses compare with 2Rg, for which the given radii of gyration were determined for the polymers in bulk solution ... 

In this way the three quantities (both the electric and the magnetic fine-structure constants at infinite momentum transfer and cxgut) would be equal. Furhermore, there would be a complete symmetry between electricity, magnetism, and strong force at the level of bare particles (i.e., at Q2 = oo) this symmetry would be broken by the effect of the quantum vacuum. 

Similarly, we have measured the thickness of an adsorbed synthetic polymer layer on titanium dioxide particles in a hydrocarbon medium. Since the polymer could not be removed from the particles once adsorbed, the values for the bare particles were obtained by centrifuging aqueous dispersions of the titanium dioxide stabilized with an ionic surfactant. 

Here A is the surface to surface separation between the bare particles and 6 is the thickness of the adsorbed layer. For distances of separation A > 26, the free energy of mixing of the chains is zero. Assuming constant segment density distribution in the adsorbed layers, Evans and Napper (15) derived the following expression for the free energy in the interpenetration domain, which is due only to the mixing of the chains ... 

In one of the limiting cases, the free polymer is allowed to penetrate the adsorbed layer around the particles. One may note that when the free polymer and the adsorbed polymer are both present in the steric layer around the particle, the interactions between the two must be taken into account while evaluating the in-terparticle forces. However, in the absence of a detailed knowledge of the structure of the adsorbed layer, it is difficult to evaluate this contribution to the interaction potential. Then, the situation is similar to the one considered by Asakura and Oosawa (16), and the force of attraction between two bare particles of radius a in the presence of free polymer molecules of radius / can be expressed as the product of the osmotic pressure Pmm and the area of the intersection of the two overlapping volumes ... 

It is a matter of course that the different surfactant coverages are also reflected in the corresponding surface tensions y of the latexes (see Fig. 4b). An increase of the surface tension with increasing diameter is observed. The miniemulsions based on polystyrene particles exceeding 100 nm have a surface tension of close to the one of pure water (72 mN nr1)- This is due to the fact that the bare particle surface is so large that adsorption equilibrium ensures a very low surfactant solution concentration. Smaller particles with their higher sur-... 

The effective volume fraction can be obtained from the intrinsic viscosity (rj) of the dispersion. According to Einstein s viscosity relation, the product of (ijl and the mass concentration c is proportional to the particle volume fraction, which is bigger for covered particles than for bare ones. The ratio (t 1 / n. where (rjlg is the intrinsic viscosity of the dispersion of bare particles, is therefore equal to the ratio between the volume of a covered pcutlcle and that of a bare one, l.e., it equals (l + d /a) . This method has been used by several authorsespecially in older work. 

Lionberger and Russel (1994) suggested that the stabilizing layers on the spheres of van der Werff et al. produce different lubrication forces than those between bare particles, such as those of Shikata and Pearson, and that this accounts for the differences between the high-frequency moduli of these two systems. Thus, it would appear, perhaps not surprisingly, that the high-frequency behavior of concentrated suspensions is sensitive to the details of interactions between spheres in near contact. 

While experimental evidence for polaronic relaxation is extensive, other experiments render the polaron models problematic (i) the use of the Arrhenius relation to describe the temperature dependence of the mobility (see above) leads to pre-factor mobilities well in excess of unity, and (ii) the polaron models cannot account for the dispersive transport observed at low temperatures. In high fields the electrons moving along the fully conjugated segments of PPV may reach drift velocities well above the sound velocity in PPV.124 In this case, the lattice relaxation cannot follow the carriers, and they move as bare particles, not carrying a lattice polarization cloud with them. In the other limit, creation of an orderly system free of structural defects, like that proposed by recently developed self-assembly techniques, may lead to polaron destabilization and inorganic semiconductor-type transport of the h+,s and e s in the HOMO and LUMO bands, respectively. 

It can be observed that with an increase in solvent polarity the dispersion stability displays a maximum, which corresponds to a minimum in the normalized setthng rate the normalization is done to account for differences in the density and the viscosity of the solvents. The normalized setthng rate equals the observed settling rate times the solvent viscosity/(particle density minus the solvent density). The maximum stabihty in this case is observed in moderately polar solvents (20 < e < 45). Bare particles suspended in a hquid medium are in constant Brownian motion and can flocculate rapidly on colhsion if the 1 is larger than about 15 kT. Stabilization can usually be achieved by decreasing the van der Waals attractive forces. The potential energy due to the van... 

Although the average value of T would be the same as in the former case, copious aggregation occurs due to bridging. A bare particle that meets a particle with a polymer layer will immediately stick to it, because some segments of a protruding polymer chain can adsorb onto the bare surface. 

Both bare particle and coated particle samples are injected manually. With a low flow rate, 0.2 mL/min, add 5 pL of sample and maintain the flow for 30 seconds. 

Such effectively independent, yet interacting particles, are called quasiparticles, or as we sometimes used to say, bare particles dressed up by the interactim with others. 

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