The Time of Adsorption

In the previous section we related the time of adsorption, t, to the heat of adsorption, Qa  

This equation originates from Frenkel (190), who identified the constant to with the time of an oscillation of the adsorbed molecule, namely with the reciprocal frequency of the vibration perpendicular to the surface. 

The identification of t0 with the time of an oscillation of adsorbed molecules leads to the assumption that t0 will be about 10 13 sec., the latter being the time of oscillation of bound atoms (191). In many cases of adsorption t0, indeed, proves to be about 10 12 sec., although this has nothing to do with a time of oscillation of molecules. 

Frenkel s original derivation holds for the special case where the perpendicular vibration of the adsorbed molecules contributes to the entropy, that is, for the special case which Kemball (192) has termed supermobile adsorption. The adsorbed molecules, which in this case move freely over the surface, have not lost the third degree of transla-tory freedom altogether this freedom is transformed into a freedom of vibration, perpendicular to the surface. The reciprocal value of the frequency of the vibratory flight, which these molecules make over the surface, equals r0. 

In all other cases to has the dimensions but not the meaning of a reciprocal frequency (193). The time of adsorption can be calculated by means of statistical mechanics from the partition functions of the gaseous and the adsorbed molecule (193). The equilibrium condition for the adsorption may be written as 

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The adsorption process is examined on the basis of various assumptions regarding the relation between the time of relaxation of the surface and the time of adsorption. 

The time of adsorption, r, may be related to the heat of adsorption by the expression... 

Despite the somewhat larger heat of adsorption and the lower temperature, the time of adsorption of argon on charcoal therefore is practically the same as the corresponding figure for xenon on mercury. The higher the entropy, hence the more mobile the adsorbed molecule is, the longer is its time of adsorption, other quantities, such as heat of adsorption and temperature, being equal. 

A formal application of Eq. (51) leads to the conclusion that the time of adsorption appears to be dependent on the amount adsorbed and drops to zero for a fully occupied layer (200). This is caused by the assumption of the monolayer -conception, according to which molecules striking the occupied parts of that layer are supposed to reflect, without being adsorbed even for a moment. Equation (51), therefore, gives t as the average value for such an ideal monolayer. ... 

Despite the somewhat lower temperature and the higher heat of adsorption, the time of adsorption of the water molecules is roughly ten times shorter than that of ethyl chloride molecules. 

It is again the influence of the entropy on the free energy that causes this effect. The time of adsorption is higher the higher the mobility of the adsorbed molecule. 

Stephen et al have also reported the slow formation of a type of hydrogen which subsequently desorbed at 330 K. The magnitude of the desorption peak was dependent on the time of adsorption at 78 K. About 1 % of a monolayer of extra hydrogen is adsorbed in 10 minutes. 

The contact angle of CH2I2 on the monolayered slides increases linearly as the times of adsorption become greater, but it is no longer possible to estimate surface coverage. 

Fig. 12 (a) Number of adsorbed segments iVads(t) versus time t fm regular AB copolymers with length N = 256 and different block size M. The time interval of the transient shoulders is shown in the upper inset. The lower inset displays the variation in the scaling exponent a for the time of adsorption t oclV with block length M. (b) The same plot for a randmn copolymta- with N = 256 and different composition p p = l corresponds to the case of a homopolymer. The variation of a with p is shown in the inset. Reprinted with permission from [53]... 

The rate constant k can be calculated by the relationship between the amount and the time of adsorption, which have many t5rpes of expression. On the uniform surface, it can use Langmuir rate equation ... 

The effect of the time of adsorption following the formation of a suspension was determined by agitating the adsorption vessels for 18-185 hours. While the adsorbance did not change significantly for the conditions selected, the bound fraction decreased from 0.24 to 0.13 over this time period. This could be interpreted as a rearrangement toward a more extended conformation possible at very long adsorption times or as a mechanical degradation of the polymer. 

The resistance to mass transfer of solute from the fluid to the adsorbed state on the solid will include that residing in the gas surrounding the solid particles, that corresponding to the diffusion of solute throu the gas within the pores of the solid, and possibly an additional resistance at the time of adsorption. During physical adsorption, the last of these will probably be negligible. If the remaining resistances can be characterized by an overall gas mass-transfer coefficient Kyap based on the outside surface of the solid particles, the rate of solute transfer over the differential height of adsorber dZ (Fig. 11.30) can be written in the usual manner as... 

The initial degree of coverage surface by platinized platinum oiy- varied within rather wide limits, changing the time of adsorption accumulation Xads at the fixed adsorption potential Eads = 0.04 V, located in the double l er range and corresponding to the maximum of Giy-,E - dependences. The experiments on the study of the kinetics of adsorption accumulation on Pt (Pt) electrode are described in detail in [6-8],... 

The kinetics of heat release during adsorption can be monitored by the change in thermokinetic parameter t [14], The calorimetric signal decreases exponentially with the time of adsorption after the maximum of each adsorption peak. This can be expressed in the form D = where D and Dm are the deviation at time... 

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