Saturated, defined

Stoichiometric saturation defines equilibrium between an aqueous solution and homogeneous multi-component solid of fixed composition (10). At stoichiometric saturation the composition of the solid remains fixed even though the mineral is part of a continuous compositional series. Since, in this case, the composition of the solid is invariant, the solid may be treated as a one-component phase and Equation 6 is the only equilibrium criteria applicable. Equations 1 and 2 no longer apply at stoichiometric saturation because, owing to kinetic restrictions, the solid and saturated solution compositions are not free to change in establishing an equivalence of individual component chemical potentials between solid and aqueous solution. The equilibrium constant, K(x), is defined identically for both equilibrium and stoichiometric saturation. 

In protein-binding investigations the fractional saturation, defined as the fraction of protein molecules that are saturated with ligand is used as working function. 

The ratio of the slope to the MCD intensity at saturation defined by an intercept value, I, can be used to derive the expression ... 

While the general shape of curves obtained with various types of mixers is similar, different amounts of water are required to reach the specific saturations defining phases I to V. Figure 147 shows results for three mixers. In the case of 53 and Ss the absolute difference in liquid requirements is only 5ml/100g solids but in relation to 53 (the minimum amount of liquid required for granulation ) the difference is approximately lOO o. 

The fractional saturation, defined as the concentration L bound divided by total concentration cf sites for n sites, would give the equation... 

A soil parameter of historical importance is the percent base saturation, defined as... 

In the isotherm equtaion (6.6-1), P is the threshold pressure above which the surface is saturated, defined as below ... 

The different grade of saturation defining the two species A and B is of course reflected by their chemical reactivity. 

The relationship between pOj and blood oxygen saturation, defined by the value of p50 (pOj at which hemoglobin Is 50% saturated) is important in determining how tissue is oxygenated. It is generally... 

Using Y to represent the fractional saturation defined in Eq. (2), we have... 

For our needs, the saturation pressure of a mixture will be defined as the vapor pressure of a pure component that has the same critical constants as the mixture ( JT... 

The coverage of adsorbates on a given substrate is usually reported in monolayers (ML). Most often, 1 ML is defined as the number of atoms in the outemiost atomic layer of the umeconstmcted, i.e. bulk-tenuinated, substrate. Sometimes, however, 1 ML is defined as the maximum iiumber of adsorbate atoms that can stick to a particular surface, which is temied the saturation coverage. The saturation coverage can be much smaller... 

Then, the MW power is increased in order to partially saturate the EPR transition. The degree of saturation is provided by the saturation factor s defined earlier (see equation (bl.l5.13fi. 

However, many adsorbates caimot reach a coverage of 1 ML as defined in this way this occurs most clearly when the adsorbate is too large to fit in one unit cell of the surface. For example, benzene molecules nonnally lie flat on a metal surface, but the size of the benzene molecule is much larger than typical unit cell areas on many metal surfaces. Thus, such an adsorbate will saturate the surface at a lower coverage than 1 ML deposition beyond this coverage can only be achieved by starting the growdi of a second layer on top of the first layer. 

It is thus tempting to define the first saturated layer as being one monolayer, and this often done, causing some confiision. One therefore also often uses tenns like saturated monolayer to indicate such a single adsorbate layer that has reached its maximal two-dimensional density. Sometimes, however, the word saturated is omitted from this definition, resulting m a different notion of monolayer and coverage. One way to reduce possible confiision is to use, for contrast with the saturated monolayer, the tenn fractional monolayer for the tenn that refers to the substrate unit cell rather than the adsorbate size as the criterion for the monolayer density. 

The saturation coverage during chemisorption on a clean transition-metal surface is controlled by the fonnation of a chemical bond at a specific site [5] and not necessarily by the area of the molecule. In addition, in this case, the heat of chemisorption of the first monolayer is substantially higher than for the second and subsequent layers where adsorption is via weaker van der Waals interactions. Chemisorption is often usefLil for measuring the area of a specific component of a multi-component surface, for example, the area of small metal particles adsorbed onto a high-surface-area support [6], but not for measuring the total area of the sample. Surface areas measured using this method are specific to the molecule that chemisorbs on the surface. Carbon monoxide titration is therefore often used to define the number of sites available on a supported metal catalyst. In order to measure the total surface area, adsorbates must be selected that interact relatively weakly with the substrate so that the area occupied by each adsorbent is dominated by intennolecular interactions and the area occupied by each molecule is approximately defined by van der Waals radii. This... 

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

Striking confirmation of the conclusion that the BET area derived from a Type IV isotherm is indeed equal to the specific surface is afforded by a recent study of a mesoporous silica, Gasil I, undertaken by Havard and Wilson. This material, having been extensively characterized, had already been adopted as a standard adsorbent for surface area determination (cf. Section 2.12). The nitrogen isotherm was of Type IV with a well defined hysteresis loop, which closed at a point below saturation (cf. F, in Fig. 3.1). The BET area calculated from it was 290 5 0 9 m g , in excellent agreement with the value 291 m g obtained from the slope of the initial region of the plot (based on silica TK800 as reference cf. p. 93). 

Favorable and unfavorable equihbrium isotherms are normally defined, as in Figure 11, with respect to an increase in sorbate concentration. This is, of course, appropriate for an adsorption process, but if one is considering regeneration of a saturated column (desorption), the situation is reversed. An isotherm which is favorable for adsorption is unfavorable for desorption and vice versa. In most adsorption processes the adsorbent is selected to provide a favorable adsorption isotherm, so the adsorption step shows constant pattern behavior and proportionate pattern behavior is encountered in the desorption step. 

The equations of combiaed diffusion and reaction, and their solutions, are analogous to those for gas absorption (qv) (47). It has been shown how the concentration profiles and rate-controlling steps change as the rate constant iacreases (48). When the reaction is very slow and the B-rich phase is essentially saturated with C, the mass-transfer rate is governed by the kinetics within the bulk of the B-rich phase. This is defined as regime 1. 

The term aquifer is used to denote an extensive region of saturated material. There are many types of aquifers. The primary distinction between types involves the boundaries that define the aquifer. An unconfined aquifer, also known as a phraetic or water table aquifer, is assumed to have an upper boundary of saturated soil at a pressure of zero gauge, or atmospheric pressure. A confined aquifer has a low permeabiUty upper boundary that maintains the interstitial water within the aquifer at pressures greater than atmospheric. For both types of aquifers, the lower boundary is frequendy a low permeabihty soil or rock formation. Further distinctions exist. An artesian aquifer is a confined aquifer for which the interstitial water pressure is sufficient to allow the aquifer water entering the monitoring well to rise above the local ground surface. Figure 1 identifies the primary types of aquifers. 

The slope of the hysteresis loop in is also an important parameter. From this slope, the parameter S can be derived (17). In Figure 3 a part of the hysteresis loop (M as a function of the appHed field H) is given. The point at which M is constant as the function of the appHed field is defined as saturation magnetisation (M.). From the slope at can be written tan0 = = 1/ 1 — S ) ot dM/dH = — S ). Thus the S is defined in... 

At a field at which the particle is saturated perpendicular to the easy axis (oc = 90), = 2Kj. This field can be defined as the anisotropy... 

The most convenient mathematical method of describing pervaporation is to divide the overall separation processes into two steps, as shown in Figure 40. The first is evaporation of the feed Hquid to form a (hypothetical) saturated vapor phase on the feed side of the membrane. The second is permeation of this vapor through the membrane to the low pressure permeate side of the membrane. Although no evaporation actually takes place on the feed side of the membrane during pervaporation, this approach is mathematically simple and is thermodynamically completely equivalent to the physical process. The evaporation step from the feed hquid to the saturated vapor phase produces a separation, which can be defined (eq. 13) as the ratio of... 

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