Slit distribution function

Broekhoff, J.C.P. and De Boer, J.H. (1968). Pore systems in catalysts. XIV. Calculation of the cumulative distribution functions for slit-shaped pores from the desorption branch of a nitrogen sorption isotherm. J. Catal, 10(4), 391-400. 

V Vu w(a,p,y) w(N, r) W t) wq volume of a polymer segment. 6.1.1.3 scattering volume. 1.2.2 unit cell volume. 3.3.1 crystallite orientation distribution function. 3.6.3 end-to-end distribution of a Gaussian chain. 5.2.1 [5.12] slit-length weighting function. 5.6.1 constant value of W(t) with infinite slit approximation. 5.6.3... 

Given the slit-like shape of the pores, the pore size distribution function defined on a surface basis Fa(H) is related the corresponding function defined on a volume basis Fy(H) by Eq. (3) ... 

In this paper, we have presented and tested a model which allows the calculation of adsorption isotherms for carbonaceous sorbents. The model is largely inspired of the characterization methods based on the Integration Adsorption Equation concept. The parameters which characterize the adsorbent structure are the same whatever the adsorbate. In comparison with the most powerful characterization methods, some reasonable hypothesis were made the pore walls of the adsorbent are assumed to be energetically homogenous the pores are supposed to be slit-like shaped and a simple Lennard-Jones model is used to describe the interactions between the adsorbate molecule and the pore wall the local model is obtained considering both the three-dimension gas phase and the two-dimension adsorbed phase (considered as monolayer) described by the R lich-Kwong equation of state the pore size distribution function is bimodal. All these hypotheses make the model simple to use for the calculation of equilibrium data in adsorption process simulation. Despites the announced simplifications, it was possible to represent in an efficient way adsorption isotherms of four different compounds at three different temperatures on a set of carbonaceous sorbents using a unique pore size distribution function per adsorbent. 

The simplest method of determining the function S, in the visible region of the spectrum is to take photomultiplier readings when the entrance slit of the monochromator is illuminated by a tungsten lamp giving light of known spectral distribution. If RSL represents the values so obtained, the spectral sensitivity is then calculated from... 

Another approach to estimating spectral densities, which has the advantage of guaranteeing that the approximate functions are positive, can be based on the error bounds constructed in Section III-A for the spectral density broadened by a Lorentzian slit function. If we had a sufficient number of moments to make the error bounds very precise, then we could reduce the broadening as much as we like, so that the broadened distribution of spectral density becomes as close as we like to the true distribution. In order to estimate these higher moments, we should need to take advantage of some special feature of the distribution. For example, in the case of the harmonic vibrations of a crystalline solid, the distribution of frequencies lies between limits — co,nax and +comax, and is zero outside... 

We have calculated the energy 0 in this way for some polymers and separation conditions (Table 2) and, using the lattice-like model and a slit-like pore, we have found the distribution coefficients, K 1, for these macromolecules as a function of N, D, 0 and 0f 65). It turned out that for such a crude model not only the calculated KJj 1 values were close to the experimental ones, but also, which is especially important, that the chemical nature of the macromolecule, the functional groups and the separation conditions (the mobile phase composition) were correctly accounted for. Two examples of such calculations are given in Figs. 8 and 9. 

The formalism of nonlocal functional density theory provides an attractive way to describe the physical adsorption process at the fluid - solid interface.65 In particular, the ability to model adsorption in a pore of slit - like or cylindrical geometry has led to useful methods for extracting pore size distribution information from experimental adsorption isotherms. At the moment the model has only been tested for microporous carbons and slit - shaped materials.66,67 It is expected that the model will soon be implemented for silica surfaces. 

For any particular particle leaving the source S and ultimately striking the detection screen D, the value of

interaction with the detector at slit A. However, this value is not known and cannot be controlled for all practical purposes it is a randomly determined and unverifiable number. The value of

pattern observed on the screen is the result of a large number of impacts of particles, each with wave function xV(x) in equation (1.50), but with random values for probability density P,p(x) is just the sum of PA(x) and PB(x), giving the intensity distribution shown in Figure 1.9(b). 

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