Gaussian PSD

Figure 6. Plot on probability paper of cumulative PSD data for a 5OOA Ultrastyragel column. The mean (p = l.TO) and standard deviation (a= O.I2) of the Gaussian PSD were determined graphically.

H ( ) is the average pore diameter We also applied the same treatment with a gaussian PSD 4. RESULTS AND COMMENTS... 

In this work, we did not identify any improvement of the average deviation when passing from a simple DR plot treatment to a gaussian PSD analysis. Anyway, this conclusion cannot be considered as general as it depends on the adosbent. 

Then, assuming that microporosity is composed of different pore sizes and that each type of adsorption can be described by the DA equation with exponent n equal to 3, we used the Stoeckli method [7] to determine the gaussian PSD,y(L) ... 

Prediction of Calibration Curves. If the PSDs of individual columns can be accurately represented by Gaussian distributions, then it should be possible to predict the PSD and cumulative PSD... 

According to experimental data, and assuming that PSD is Gaussian, Dubinin and Radushkevich obtained an equation, which relates the degree of micropore filling (9) with the differential molar work of adsorption ... 

As described earlier, one of the first methods used to obtain PSD from the Dubinin equation is the so-called Dubinin-Stoeckli method [38-43], For strongly activated carbons with a heterogeneous collection of micropores, the overall adsorption isotherm is considered as a convolution of contributions from individual pore groups. Integrating the summation and assuming a normal Gaussian equation for the distribution of MPV with respect to the K parameter (Equation 4.19), Stoeckli obtained an equation useful to estimate the micro-PSD. 

The methods depend on the theoretical treatment which is used. A majority of them are based on the Generalised Adsorption Isotherm (GAI) also called the Integral Adsorption Equation (LAE). The more recent approaches use the Monte Carlo simulations or the density functional theory to calculate the local adsorption isotherm. The analytical form of the pore size distribution function (PSD) is not a priori assumed. It is determined using the regularization method [1,2,3]. Older methods use the Dubinin-Radushkevich or the Dubinin-Astakhov models as kernel with a gaussian or a gamma-type function for the pore size distribution. In some cases, the generalised adsorption equation can be solved analytically and the parameters of the PSD appear directly in the isotherm equation [4,5,6]. Other methods which do not rely on the GAI concept are sometimes used the MP and the Horvath-Kawazoe (H-K) methods are the most well known [7,8]. 

An edditional measure of the PSD is the skewness parameter s. defined by Garden (1968b) as the exponent of the radius such that the PSD expressed in tbe size parameter (radius) is most nearly Gaussian. 

PSD turns out to be a Gaussian-like function of jco foo- The model applies equally well to the isotopically substituted formaldehydes (Fig. 39), for which the observed shift of PSD s to higher jco values is proportional to the square root of the reduced mass of the molecule. Chang et al. studied the decay of formaldehyde using classical trajectories on a semiempirical six-dimensional PES [315] starting the trajectories at the TS. Since the final step of the reaction is very fast, classical dynamics produce PSD s which agree well with the experiment. 

Figure 3 Comparison of PSDs obtained using the Dubinin-Stoeckli (DS), Horvalh-Kawazoe (HK), and density fitnctional theory (DFT) methods to interpret an isotherm generated from molecular simulation of nitrogen adsorption in a model carbon that has an Gaussian distribution of slit pore widths (18]. Results are shown for mean pore widths of 8.9 A (left) and 16.9 A (right).

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