Packing interstices

Fig. 3.15 (a) A pore in the form of an interstice between close-packed and equal-sized spherical particles. The adsorbed him which precedes capillary condensation is indicated, (b) Adsorption isotherm (idealized). 

Titanium Dichloride. Titanium dichloride [10049-06-6] is a black crystalline soHd (mp > 1035 at 10°C, bp > 1500 at 40°C, density 31(40) kg/m ). Initial reports that the titanium atoms occupy alternate layers of octahedral interstices between hexagonaHy close-packed chlorines (analogous to titanium disulfide) have been disputed (120). TiCl2 reacts vigorously with water to form a solution of titanium trichloride andUberate hydrogen. The dichloride is difficult to obtain pure because it slowly disproportionates. 

Titanium Trichloride. Titanium trichloride [7705-07-9] exists in four different soHd polymorphs that have been much studied because of the importance of TiCl as a catalyst for the stereospecific polymerization of olefins (120,124). The a-, y-, and 5-forms are all violet and have close-packed layers of chlorines. The titaniums occupy the octahedral interstices between the layers. The three forms differ in the arrangement of the titaniums among the available octahedral sites. In a-TiCl, the chlorine sheets are hexagonaHy close-packed in y-TiCl, they are cubic close-packed. The brown P-form does not have a layer stmcture but, instead, consists of linear strands of titaniums, where each titanium is coordinated by three chlorines that act as a bridge to the next Ti The stmctural parameters are as follows ... 

In a packed column the individual solute molecules will describe a tortuous path through the interstices between the particles and some will randomly travel shorter routes than the average and some longer. The multi-path effect is diagramatically depicted in Figure 5. 

A liquid mobile phase is far denser than a gas and, therefore, carries more momentum. Thus, in its progress through the interstices of the packing, violent eddies are formed in the inter-particular spaces which provides rapid solute transfer and, in effect, greatly increases the effective diffusivity. Thus, the resistance to mass transfer in that mobile phase which is situated in the interstices of the column is virtually zero. However, assuming the particles of packing are porous (i.e., silica based) the particles of packing will be filled with the mobile phase and so there will... 

The PVC is simply P /Vf and is determined by the volume of filler added to the formulation. The CPVC occurs when the binder particles are close packed and Vv = 0. At the CPVC, there is Just enough binder to coat all of the filler particles and the substrate with at least monomolecular layer of binder, and fill the interstices between particles. 

Bead Size - The resins must be in the form of spherical granules of maximum homogeneity and dimensions so that they do not pack too much, the void volume among their interstices is constant for a given type, and the liquid head loss in percolation remains acceptable. Most ion-exchange resins occur as small beads or granules usually between 16 and 50 mesh in size. 

The elution of such gels is an example not of size exclusion but rather of hydrodynamic fractionation (HDF). However, it must be remembered that merely being able to physically fit an insoluble material through the column interstices is not the only criterion for whether the GPC/HDF analysis of an insoluble material will be successful. A well-designed HDF packing and eluant combination will often elute up to the estimated radius in Eq. (5), but adsorption can drastically limit this upper analysis radius. For example, work in our laboratory using an 8-mm-bead-diameter Polymer Laboratories aqueous GPC column for HDF found that that column could not elute 204 nM pSty particles, even though Eq. (5) estimates a critical radius of —1.5 jam. 

HdC separation also occurs in the interstices of a packed column, although the configuration of channels is not as simple as a microcapillary tube. The... 

In any crystal structure, the close-packed or closest-packed planes are the lowest energy planes. On all other planes, the density of atoms is lower, and the interatomic distance and the energy of the plane are greater. Contrary to intuitive expectations, the diameter of the largest holes or interstices between atoms in the close-packed f.c.c. structure is considerably greater than the diameter of the largest interstices between atoms in the non-close-packed b.c.c. structure. 

Even in a close-packed structure, hard spheres do not fill all the space in a crystal. The gaps the interstices—between the atoms are called holes. To determine just how much space is occupied, we need to calculate the fraction of the total volume occupied by the spheres. 

A solid emulsion is a suspension of a liquid or solid phase in a solid. For example, opals are solid emulsions formed when partly hydrated silica fills the interstices between close-packed microspheres of silica aggregates. Gelatin desserts are a type of solid emulsion called a gel, which is soft but holds its shape. Photographic emulsions are gels that also contain solid colloidal particles of light-sensitive materials such as silver bromide. Many liquid crystalline arrays can be considered colloids. Cell membranes form a two-dimensional colloidal structure (Fig. 8.44). 

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