Fraction of covering

The rate of desorption will be proportional to the fraction of covered surface... 

In effect, this model considers that adsorption can be described as a localized condensation process that tends to progressively cover the entire surface when the gas pressure increases. A fluctuation in the fraction of covered surface necessarily induces a fluctuation in the energy of the contact between the two phases. This energy term is the product of an extensive quantity As, which is the contact surface between the two phases, with an intensive quantity Ps, which is comparable with a surface pressure. Ps is identified with the variation of the surface tension coefficient y during the covering, that is to say ... 

This hypothesis is perfectly satisfactoiy in case surface electrieal effects are present. In fact, the rigorous relationship that has been estabUshed between the fraction of covered surfaee and the heat of adsorption is not simple. It is however possible, using some hypotheses, to reaeh simpler solutions. That is how some linear approximation laws, for instance AH = AHq (1 - P0), were diseovered. The following expression was therefore reached ... 

Actually, according to a few other authors, the interactions between adsorbed molecules cause the dipole moment value p to vary depending on the fraction of covered surface. In the hypothesis of a high fraction of covered surface, a mutual depolarization of the dipoles occurs, which tends to lower the value of their dipole moments. 

However, this situation allows us to suppose that X2 is much larger then xi. Indeed, if we suppose that the medium fraction of covered surface is 0.5, and that the ratio of defects in the oxide is in the order of 1%, then the / Xj ratio is in the order of 20. 

On the other hand, for small initial cell densities (i.e. small fractions of covered electrode area, far from confluence) it is expected that the coplanar detection is more sensitive to the presence of cells in the volume between the fingers, with respect to the vertical condition in which Rgg is set by the electrode perimeter. At frequencies > /, the electric field intensity is more confined in the volume occupied by the cells in the coplanar geometry, in analogy to several successful examples of high speed cell detection in microfluidic flow cytometry [13]. 

However, as chemisorption is in general limited to a monolayer, we very often choose the fraction of covering 0 (or filling degree) of the surface. At a given time, this is the ratio of the amount of adsorbed gas to the total amount to obtain the monolayer. At equilibriirm, that is, at the end of a theoretically infinite time, this ratio will be 6. ... 

Indicate by the total number of sites per unit area before adsorption and by S the number of free sites at a given time, the amount of G - s is then S -S and the fraction of covering as ... 

However, the fractions of covering of the two entities are identical, from which ... 

It is noted that the ratio of the fractions of covering is proportional to the ratio of the partial pressures. 

On indicating by 6 and ff the fraction of covering of the two types of sites, the reactivity takes the form ... 

A quantity which is important from a catalytic point of view is the amount of gas which can be adsorbed at the surface. This is expressed in terms of the so-called adsorption isotherms. Langmuir [4] assumed that the adsorption rate was proportional to the fraction of free surface sites 1—6 and the desorption rate proportional to the fraction of covered surface 6, and he obtained the expression... 

Fig. X-3. Variation of contact angle with /oh. the fraction of the surface covered by HS(CH2)uOH in a mixture with HS(CH2)uCH3. Solid line is comparison with Eq. X-27, and dashed line is from Eq. X-28. (From Ref. 44.)...

While a thermodynamic treatment can be developed entirely in terms of f(P,T), to apply adsorption models, it is highly desirable to know on a per square centimeter basis rather than a per gram basis or, alternatively, to know B, the fraction of surface covered. In both the physical chemistry and the applied chemistry of the solid-gas interface, the specific surface area is thus of extreme importance. 

Since S /S equals 6, the fraction of surface covered, Eq. XVII-4 can be written in the form... 

Miller A R 1946 The variation of the dipole moment of adsorbed particles with the fraction of the surface covered Proc. Camb.Phil. See. 42 292-303... 

The model implies that at any pressure below the saturation vapour pressure, the fractions of the surface covered with 1, 2,. .., i molecules will be 6 02,.., 0i respectively, so that the thickness of the adsorbed layer will not be constant throughout. On the specific surface area A, therefore, the total number Z of molecules adsorbed will be... 

A series of consecutive time bins covers a length of time of a few milliseconds, with each bin representing a time of only a fraction of a nanosecond. When an ion arrives at the microchannel array detector, one time bin notes the resulting electronic pulse. 

In the simplest case, for which all adsorption sites are equivalent and do not interact with each other, the fraction of surface covered by adsorbate. 

Most synthetic latices contain 5—10 wt % of nonelastomeric components, of which more than half is an emulsifier or mixture of emulsifiers. One reason for this relatively high emulsifier concentration as compared with natural latex is that emulsifier micelles containing solubiHzed monomer play a principle role in the polymerization process. A high emulsifier concentration is usually necessary to achieve a sufficiently rapid rate of polymerization. Secondly, a considerable fraction of the surface of the polymer particles must be covered by adsorbed soap or equivalent stabilizer to prevent flocculation... 

Many chemical elements exhibit catalytic activity (5) which, within limits, is inversely related to the strength of chemisorption of the VOCs and oxygen, provided that adsorption is sufficiently strong to achieve a high surface coverage (17). If the chemisorption is too strong, the catalyst is quickly deactivated as the active sites become irreversibly covered. If the chemisorption is too weak, only a small fraction of the surface is covered and the activity is very low (17) (Fig. 2). 

The second conversion of GS to (GSi)r will be Case 4 of Table 5-10, the two-surface-zone enclosure with computation simphfied by assuming that the direct-view fac tor from any spot to a surface equals the fraction of the whole enclosure that the surface occupies (the speckled-furnace model). This case can be considered an ideahzation of many processing furnaces such as distilling and cracking coil furnaces, with parts of the enclosure tube-covered and part left refrac-toiy. (But the refractory under the tubes is not to be classified as part of the refractory zone.) Again, one starts with substitution into Eq. (5-173) of the terms GSi, GS, and S Si from Table 5-10, Case 4, with all terms first converted to their gray-phis-clear form. To indicate the procedure, one of the components, S Si, wil be formulated. 

Variable Variable ft e t/t, reduced time, fraction of surface covered by adsorbed ... 

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