Packings maximum density

An important phenomenon when considering the differences between ice I and liquid water is that water achieves its maximum density not in the solid state, but at 4 °C, i.e. in the liquid state. The reasons for this were first discussed by Bernal Fowler (1933). They noted that the separation of molecules in ice I is about 0-28 nm, corresponding to an effective molecular radius of 014 nm. Close packing of molecules of such radius would yield a substance of density 1-84 g cm" . To account for the observed density of 10 g cm" , it was necessary to postulate that the arrangement of molecules was very open compared with the disordered, close-packed structures of simple liquids such as argon and neon. 

The structure of ice is shown in the diagram. The crystal structure of ice is essentially tetrahedral. When water melts, the hydrogen bonds are progressively broken. The molecules pack closer together and so an initial reduction in volume of the liquid occurs before the usual expansion effect from raising the temperature is observed. Water, therefore, has its maximum density at 4°C. 

The packing particle density and fraction voids strongly affect the radial scale of turbulence (Ab) larger scales are found for beds containing denser particles at a given fraction voids. The scale of turbulence has a maximum value at e = 0.7. 

Densities of molecules adsorbed on surfaces are in moles per unit area, which we win give the symbol rij for species j. Typical units of nj are moles per cm. There is a maximum density rijo of molecules packed in a two-dimensional layer on a flat surface when all molecules touch or reach Hquidlike or soHdlike densities. We call this density a monolayer, whose density is approximately the inverse of the square of the molecular diameter, which is less than 1 x lO molecules/cm2 for all molecules (Figure 7-21). We wiU find it convenient also to define a coverage of adsorbed molecules as the fraction of the monolayer density dj,... 

Why do we obtain such complex rate expressions for such a simple process The answer is found simply in the 1 — 0 terms we added in the adsorption rate expression. We said that the density of adsorbed molecules could never exceed one monolayer because that was the maximum density with which molecules could be packed. The rate is assumed to be always proportional to the coverage of species A,... 

Aluminized expls exhibit a decrease in performance as their packing density approaches theoretical maximum density (TMD). This effect is more pronounced in compns of high A1 content. Table 9 (from Ref 17) shows equivalent weight ratios (WQd) and relative bubble energies (RBE) of two aluminized expls as a function of %TMD... 

Without exception the shock sensitivity of any expl increases as its packing density is decreased. At one extreme we have expl single crystals (ie, expls at their theoretical maximum density, TMD) and at the other extreme expl... 

It will be noted that the abscissae in Figure 33 are in terms of the ratio of diameters of the smallest to the largest sizes. The density of a packing will be affected by the number of components and by the size of the smallest and largest particles. Furnas also computed the number of components required to produce maximum density (minimum voids) for extreme size-ratios ranging from 0.00001 to 0.1. In general, values of the ratios of diameters greater than 0.003 require two components those from 0.0001 to 0.003 require three components and those less than 0.0001 require four components. 

We present here some of the highlights of Kitaigorodskii s considerations [88], First, the problem of dense packing is examined for the plane groups of symmetry. The distinction between dense-packed, densest-packed, and maximum density was introduced for the plane layer of molecules. The plane was called dense-packed when coordination of six was achieved for the molecules. The term densest-packed meant six-coordination with any orientation of the molecules with respect to the unit cell axes. The term maximum density was used for the packing if six-coordination was possible at any orientation of the molecules with respect to the unit cell axes while the molecules retained their symmetry. 

Fig. 3 Iso-density surfaces (about 15% of maximum density) for the two gap states per (2v X 2y/i) 2D unit cellassociated with a 25% concentration of vacancies in a close packed configuration, (a) on the left bonding combination of the two localized states trapped at the vacancy sites (b) on the right, antibonding combination. A top view of the surface is presented with oxygen atoms as black dots and magnesiums as light spheres. The location of the vacancies is indicated by black boxes, (from Ref. 69)...

Polyimide-Based Syntactic Foam (9). Three-phase syntactic foams were made using a polyimide solution (22% PI-2080 in DMF) and hollow glass microspheres (Type B-30-B, 3M Co.) which have a particle density of 0.25 to 0.30 cm and a bulk density of 0.182 g/cm . The solution and glass spheres were hand mixed and packed into a 5" x 5" mold and compacted under pressure. Variations of foam density were obtained by molding specific quantities of blend into different volumes ranging from Vi to 1" in thickness. Greater densities required higher pressures with the maximum density obtained at a pressure of about 100 psi. 

Since the most symmetrical arrangement of 12 neighbours (the icosahedral coordination group) does not lead to the densest possible 3D packing of spheres we have to enquire which of the infinite number of arrangements of twelve neighbours lead to more dense packings and what is the maximum density that can be attained... 

A wastewater flowrate of 180 m /day has a TOC (total organic carbon level) of 200 mg/L. A flxed-bed GAC adsorption column wiU be used to reduce the maximum effluent concentration to 8 mg/L. A breakthrough curve. Figure 7.12, has been obtained from an experimental pilot column operated at 2(BV)/hr. Other data concerning the pilot column are mass of carbon = 4.13 kg, water flowrate = 15 L/hr, and packed carbon density = 400 kg/m. Using the scale-up approach, determine the values of the following parameters for the design column ... 

Note that the volume density of closed pack spheres is about rfcpK, 0.74. The choice of t] = 0.45, which is about 6/10 of the maximum density, was chosen for convenience. In fact even at these densities converging of the Percus-Yevick equation is quite slow (see also Appendix E). 

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