Gaussian function heterogeneous

Subsequently, the parameters, T0 and AT, describe the desorption rate since, these parameters also represent the Gaussian function. Therefore, with the obtained results (Figure 4.40 and Table 4.9), it was shown that the parameter T, is associated with the adsorption energy of the adsorbate in the zeolite. In addition, the parameter AT was linked with the transport of molecules inside the zeolites channels during the nonisothermal desorption process as well with the heterogeneous character of adsorption in zeolites. 

As follows from Eqs. (2 ) and (3) the shape of the X(E) function depends on the local heterogeneity, Ak, of the particular patches of a heterogeneous surface. If the subsurfaces (patches) existing on the surface of the adsorbent radically differ in the Ak values, i.e. Ak i Ak then there are clear maxima in the global X(E) curve, as in the case of carbon-silica adsorbents (Fig. 1). However, if Ak-i Ak, the X(E) function can assume the shape of an exponential distribution, or become similar to the distribution X(E) for a non-modified silica gel (Fig.l). The X(E) function for this adsorbent can also be a superposition of several local quasi-gaussian functions. 

The mean field treatment of such a model has been presented by Forgacs et al. [172]. They have considered the particular problem of the effects of surface heterogeneity on the order of wetting transition. Using the replica trick and assuming a Gaussian distribution of 8 Vq with the variance A (A/kT < 1), they found that the prewetting transition critical point is a function of A and... 

The free induction decay following 90° pulse has a line shape which generally follows the Weibull functions (Eq. (22)). In the homogeneous sample the FID is described by a single Weibull function, usually exponential (Lorentzian) (p = 1) or Gaussian (p = 2). The FID of heterogeneous systems, such as highly viscous and crosslinked polydimethylsiloxanes (PDMS) 84), hardened unsaturated polyesters 8S), and compatible crosslinked epoxy-rubber systems 52) are actually a sum of three... 

In the Dubinin-Stoeckli (DS) method, a Gaussian pore size distribution is assumed for 7(B) in Eq. (39), based on the premise that for heterogeneous carbons, the original DR equation holds only for those carbons that have a narrow distribution of micropore sizes. This assumption enables Eq. (39) to be integrated into an analytical form involving the error function [119] that relates the structure parameter B to the relative pressure A = -RT ln(P/Po)-The structure parameter B is proportional to the square of the pore halfwidth, for carbon adsorbents that have slit-shaped micropores. 

Similar heterogeneous model has been used to develop a relaxation function by Chamberlin and Kingsbury (1994), who consider the localized normal modes to be involved in the relaxation process. Localized (domains) regions are assumed to be present between Tg and T. They are described as dynamically correlated domains (DCD). A Gaussian distribution of the domain sizes has been assumed, with each domain characterized by a Debye relaxation time. Expressions for the dielectric susceptibility have been derived and used to fit the experimental susceptibilities of salol, glycerol and many other substances with remarkable agreement over 13 decades of frequency (even when only one adjustable parameter is employed). 

This heterogeneity may, however, also be expressed in terms of polymer lifetimes instead of propagation rates. By assuming a Gaussian distribution of chain lifetimes Mussa (35) has been able to derive molecular weight distributions of the type observed experimentally. This treatment appears to imply a chain termination which has the form of an error function round a mean value. On the whole it seems that a variable propagation rate is the more likely. 

Tables 3 and 4 present the ranges of Ei value changes for individual systems. The shape of the curves of the thermodesorption energy distribution functions presented in Figure 12 are similar to Gaussian curves with one distinct peak indicating the existence of one main active centre on the surface of the adsorbents. The increase of desorption energy dmax for polar liquids (in kJ/mol 32.29< dmax<84.59 for water and 24.44< dmax<60.06 for n-butanol) is evidence of an increase of the adsorbent-adsorbate interaction forces. Broadening of bands on the desorption energy distribution curves indicates the increase of energetic heterogeneity of the studied materials.

To observe the film thickness dependence of u ) and Ao quantitatively, u and Ao at 230 K were plotted as a function of film thickness (Fig. 19). As the film thickness decreases, the non-Gaussian parameter increases, implying that the dynamic heterogeneity increases with a reduction in film thickness. Our smdies... 

Bersillon, J. -L., F. Villieras, F. Bardot, T. Corner, and J. -M. Cases. 2001. Use of the Gaussian distribution function as a tool to estimate continuous heterogeneity in adsorbing systems. Journal of Colloid and Interface Science 240, no. 2 400-411. doi 10.1006/ jcis.2001.7657. 

Identification of dynamics of a particular molecular fractions with diverse mobility Wider frequency range CP SS-NMR eases interpretation Analysis of NMR line width versus delay time (T profiles) using Gaussian-Lorentzian function (Gaussian part crystalline and Lorentzian amorphous fraction) for partially crystallinity Ambiguity about the source of biphasic spin relaxation decay profile (due to dynamic heterogeneity and/or hetero-nuclear coupling)... 

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