Large spheres

The net attraction of surface molecules to the interior of the liquid indicates that molecules are most stable when attractive forces are maximized by as many neighbor molecules as possible. Consequently, a liquid is most stable when the fewest molecules are at its surface. This occurs when the liquid has minimal surface area. Spheres have less surface area per unit volume than any other shape, so small drops of a liquid tend to be spheres. Large drops are distorted from ideal spheres by the force of gravity. 

Very large ratios for A (RNj+l/A (RNCS +) suggest inner-sphere. Large ratios of A (RSCN +)/A (RN3+) indicate outer-sphere and small ratios (<10) are probably inner-sphere. (Sec. 5.6(c)). 

Consider an electron in an s orbital on an atom. The s function does not depend on the angles, 9, (f). As a consequence we can represent the 5 function as a sphere, or in two dimensions as a circle. We can make the sphere large enough so that it include any desired fraction of the charge cloud. This sphere is called a boundary surface. 

Silica spheres, large pore diameter, impregnated and reimpregnated with orthophosphoric acid... 

For creeping flow (0 < Re < 1), the solutions of the conduction-convection equation with flow held of the Hadamard-Rybczynski or Stokes are given by numerical integration [1]. The numerical results show that the concentration contours are not symmetrical (Figure 5.1 and Figure 5.2) and that the how inside and outside the sphere largely inhuences heat or mass transfer. In the case of a sphere with weak viscosity ratio, the heat or mass transfer is facilitated. 

The term vacant site of requirement 3 needs some clarification. It does not simply mean that there be a gap in the coordination sphere large enough to accommodate the incoming ligand. There must also be an empty orbital ready to accept the p-H, or more exactly, the pair of electrons that constitutes the P-C—H bond. Another way of looking at this is to say that the electron count of the product alkene hydride is 2e more than that of the alkyl starting material. An 18e alkyl is much more reluctant to p-eliminate via a 20e intermediate than is a 16e alkyl, which can go via an 18e alkene hydride. Even if the alkene subsequently dissociates, which is often the case, we still have to stabilize the transition state leading to the alkene hydride intermediate if we want the reaction to be fast. An 18e alkyl, on the other hand, is said to be coordinatively saturated. By this we mean that an empty orbital is not... 

Recently, the multiple morphologies of block ionomers in solution have been investigated extensively (99-101). The equilibrium, near-equilibrium, and nonequilibrium morphologies observed to date are spheres, rods, bicontinuous rods, bilayers, lamellae, vesicles, inverse bicontinuous rods, large compound micelles, aggregates of spheres, large rod-shaped compound micelles, large compoimd vesicles, and many others (101). 

Determine the net DLVO interaction (electrostatic plus dispersion forces) for two large colloidal spheres having a surface potential 0 = 51.4 mV and a Hamaker constant of 3 x 10 erg in a 0.002Af solution of 1 1 electrolyte at 25°C. Plot U(x) as a function of x for the individual electrostatic and dispersion interactions as well as the net interaction. 

Figure Bl.8.4. Two of the crystal structures first solved by W L Bragg. On the left is the stnicture of zincblende, ZnS. Each sulphur atom (large grey spheres) is surrounded by four zinc atoms (small black spheres) at the vertices of a regular tetrahedron, and each zinc atom is surrounded by four sulphur atoms. On the right is tire stnicture of sodium chloride. Each chlorine atom (grey spheres) is sunounded by six sodium atoms (black spheres) at the vertices of a regular octahedron, and each sodium atom is sunounded by six chlorine atoms.

An important step in tire progress of colloid science was tire development of monodisperse polymer latex suspensions in tire 1950s. These are prepared by emulsion polymerization, which is nowadays also carried out industrially on a large scale for many different polymers. Perhaps tire best-studied colloidal model system is tliat of polystyrene (PS) latex [9]. This is prepared with a hydrophilic group (such as sulphate) at tire end of each molecule. In water tliis produces well defined spheres witli a number of end groups at tire surface, which (partly) ionize to... 

The first case is relevant in the discussion of colloid stability of section C2.6.5. It uses the potential around a single sphere in the case of a double layer that is thin compared to the particle, Ka 1. Furthennore, it is assumed that the surface separation is fairly large, such that exp(-K/f) 1, so the potential between two spheres can be calculated from the sum of single-sphere potentials. Under these conditions, is approximated by [42] ... 

A second case to be considered is that of mixtures witli a small size ratio, <0.2. For a long time it was believed tliat such mixtures would not show any instability in tire fluid phase, but such an instability was predicted by Biben and Flansen [109]. This can be understood to be as a result of depletion interactions, exerted on the large spheres by tire small spheres (see section C2.6.4.3). Experimentally, such mixtures were indeed found to display an instability [110]. The gas-liquid transition does, however, seem to be metastable witli respect to tire fluid-crystal transition [111, 112]. This was confinned by computer simulations [113]. 

Imhof A and Dhont J K G 1995 Experimental phase diagram of a binary oolloidal hard-sphere mixture with a large size ratio Phys. Rev. Lett. 75 1662-5... 

The above argument shows that complete overlap of coil domains is improbable for large n and hence gives plausibility to the excluded volume concept as applied to random coils. More importantly, however, it introduces the notion that coil interpenetration must be discussed in terms of probability. For hard spheres the probability of interpenetration is zero, but for random coils the boundaries of the domain are softer and the probability for interpenetration must be analyzed in more detail. One method for doing this will be discussed in the next section. Before turning to this, however, we note that the Flory-Huggins theory can also be used to yield a value for the second virial coefficient. 

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