Solid density definition

Density Types Density Definitions Solid Material Volume Volumes in Definition Closed- Open- Interparticle Pore Pore Void Volume Volume Volume ... 

The electronic density of states (DOS) describes energy of electrons in solids. By definition, the density of states p(B) is a value, which being multiplied by a small interval of energies dE equals to a number of the electronic states with energies in an interval from Eto E dE. In solids, the density distributions are not discrete like a spectral density but continuous. A high density of states at a specific energy level means that there are many states available for occupation. A density of states of zero means that no states can be occupied at that energy level. Local variations, most often due to distortions of the system, are often called local density of states (LDOS). 

Adsorbed concentration is not necessarily defined in terms of mole per unit surface area. It can be defined as mole per units solid volume as the surface area is not always available and moreover the adsorbed phase of practical solids is not defined as well structured surface. The adsorbed concentration is therefore conveniently defined as either mole per unit volume of the solid volume, which reflect the apparent space where adsorbed molecules reside, or mole per unit mass of the adsorbent. We shall use the definition of mole per unit solid volume as the other can be related to this by a factor of solid density. 

Generalizing to any two locations, 1 and 2, in the extruder and substituting in the definition of G the mass flow rate of solid followed by rearranging terms gives an extrusion model, which can predict the width of the solid bed at any location along the screw from knowledge of the melting rate, the solid bed barrel contact area, the solid density (function of solid temperature and internal pressure), the down chaimel solid velocity and the physical dimensions of the screw chaimel (Eq. 12.16). 

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. 

Depending on the application, models of molecular surfaces arc used to express molecular orbitals, clcaronic densities, van dor Waals radii, or other forms of display. An important definition of a molecular surface was laid down by Richards [182] with the solvent-accessible envelope. Normally the representation is a cloud of points, reticules (meshes or chicken-wire), or solid envelopes. The transparency of solid surfaces may also be indicated (Figure 2-116). 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

Microcellular elastomers16 bridge the gap between solid elastomers and low-density foams. Although they may appear to be noncellular, these materials have a microscopic cell structure and so are by definition high-density foams, with densities between noncellular solids and standard foams. The most commercially important applications include shoe soles, carpet backing, chair armrests,... 

This is an indication of the collective nature of the effect. Although collisions between hard spheres are instantaneous the model itself is not binary. Very careful analysis of the free-path distribution has been undertaken in an excellent old work [74], It showed quite definite although small deviations from Poissonian statistics not only in solids, but also in a liquid hard-sphere system. The mean free-path X is used as a scaling length to make a dimensionless free-path distribution, Xp, as a function of a free-path length r/X. In the zero-density limit this is an ideal exponential function (Ap)o- In a one-dimensional system this is an exact result, i.e., Xp/(Xp)0 = 1 at any density. In two dimensions the dense-fluid scaled free-path distributions agree quite well with each other, but not so well with the zero-density scaled distribution, which is represented by a horizontal line (Fig. 1.21(a)). The maximum deviation is about... 

Here, p is the density of the fluid, V is the relative velocity between the fluid and the solid body, and A is the cross sectional area of the body normal to the velocity vector V, e.g., nd1/4 for a sphere. Note that the definition of the drag coefficient from Eq. (11-1) is analogous to that of the friction factor for flow in a conduit, i.e.,... 

In this definition, ps and pt are the solid and fluid densities, respectively. The characteristic diameter of the particles is ds (which is used in calculating the projected cross-sectional area of particle in the direction of the flow in the drag law). The kinematic viscosity of the fluid is vf and y is a characteristic strain rate for the flow. In a turbulent flow, y can be approximated by l/r when ds is smaller than the Kolmogorov length scale r. (Unless the turbulence is extremely intense, this will usually be the case for fine particles.) Based on the Stokes... 

A gas suspended in a solid is also called a foam. This form of colloid is relatively rare in nature, unless we stretch our definition of solid to include rock, in which case pumice stone is a colloidal foam. Synthetic foams are essential for making cushions and pillows. There is also presently much research into forming metal foams, which have an amazingly low density. 

Although, the true density of solid phase p=m/Vp (e.g., g/cm3) is defined by an atomic-molecular structure (/ ), it has become fundamental to the definition of many texture parameters. In the case of porous solids, the volume of solid phase Vp is equal to the volume of all nonporous components (particles, fibers, etc.) of a PS. That is, Vp excludes all pores that may be present in the particles and the interparticular space. The PS shown in Figure 9.17a is formed from nonporous particles that form porous aggregates, which, in turn, form a macroscopic granule of a catalyst. In this case, the volume Vp is equal to the total volume of all nonporous primary particles, and the free volume between and inside the aggregates (secondary particles) is not included. 

Thus, there are two limitations of the pycnometric technique mentioned possible adsorption of guest molecules and a molecular sieving effect. It is noteworthy that some PSs, e.g., with a core-shell structure, can include some void volume that can be inaccessible to the guest molecules. In this case, the measured excluded volume will be the sum of the true volume of the solid phase and the volume of inaccessible pores. One should not absolutely equalize the true density and the density measured by a pycnometric technique (the pycnometric density) because of the three factors mentioned earlier. Conventionally, presenting the results of measurements one should define the conditions of a pycnometric experiment (at least the type of guest and temperature). For example, the definition p shows that the density was measured at 298 K using helium as a probe gas. Unfortunately, use of He as a pycnometric fluid is not a panacea since adsorption of He cannot be absolutely excluded by some PSs (e.g., carbons) even at 293 K (see van der Plas in Ref. [2]). Nevertheless, in most practically important cases the values of the true and pycnometric densities are very close [2,7],... 

The surface basicity of a solid catalyst can be defined in a way analogous to that applied to conventional bases. Thus, a surface Lewis base site is one that is able to donate an electron pair to an adsorbed molecule. If we take the definition of surface basicity in a more general way, it could be said that the active surface corresponds to sites with relatively high local electron densities. This general definition will include not only Lewis basicity but also single electron donor sites. We emphasize that the literature of heterogeneous catalysis often reports that both single-electron and electron-pair donor sites exist on basic catalysts. 

With only small differences in (Is)max the choice of the binder system is influenced by processability, physical properties, and propellant density. Thus, with the polyether binder an Is of 247 is reached with about 14% binder, but with the polyester the same Is is obtained with 11.5% binder, which is a definite disadvantage in terms of processability and mechanical properties. The higher Is with the polybutadiene binder is realized only at high solids loadings, but owing to its lower density, processability is still satisfactory. 

Compared at (Is)max, polyether and polybutadiene propellants have nearly identical densities since the higher density of the polyether binder, P = 1.0 (polybutadiene p 0.9), is offset by the lower solids content [p (NH4CIO4) = 1.95, p (Al) = 2.7]. At lower solids loadings the higher density of the polyether becomes a definite advantage. If nitro-plasticizers are used [p (nitroplasticizer) = 1.4] the 7S maN is shifted to appreciably lower solids loadings, so that the plasticizer is combined preferably with a polyether in order not to lose density. 

There are three definitions needed to accurately describe this process. (1) Compaction is the compression and consolidation of a two-phase (particulate solid/gas) system by the application of an external force (2) compression causes an increase in the apparent density (or a reduction in volume) by the displacement of air and (3) consolidation is defined as an increase in mechanical strength due to particle-particle interaction [1,2]. 

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