Volume Filling intercept

In the case of the BET, a linear portion of the curve for the high-energy surfaces such as silica and alumina is at about 0.05-0.35 of P. For lower energy surfaces this does not hold. The DRK transformed plot usually has a very long linear portion. The DR theory is useful for determining pore volumes. The intercept of the ln(n ) axis should be a good indication of number of moles needed to fill the pore volume, For the DRK case it is an indication of the number of moles in a monolayer, n. ... 

Ramsay and Avery [82] investigated nitrogen adsorption in microporous silica compacts for 10-2>x>10-4 and found that < 7 kJ moI-1 for loose powder and increased with compaction and decrease in pore size. They found close agreement between amount adsorbed at monolayer coverage and intercept volume using the D-K equation, which indicated surface coverage as opposed to volume filling. 

For the ACs the data are representative of the samples after heat-treatment at all three temperatures since during their fabrication these materials have already been treated at temperatures in excess of 850°C. However, for the alumina and clay samples the surface areas and pore volumes are shown after treatment at each temperature as these materials undergo various phase transitions that lead to sintering of the samples and shifts in their relative pore size distributions with heat-treatment. The particle size was determined from the corresponding MIP curve for the powder raw material. The Sbet in the case of microporous ACs should be considered as an apparent surface area due to the micropore filling mechanism associated with these materials [15]. The external area and micropore volumes were calculated from the slope and intercept of the t-plots of the corresponding isotherms. The total pore volume was taken as the amount of gas adsorbed at a relative pressure of 0.96 on the desorption isotherm, equivalent to a pore diameter of 50 nm. The mesopore volume was calculated from the difference in the total pore volume and the micropore volume. 

Figure 3.7 Apparent partition coefficient of benzo[a]pyrene as a function of volume fraction of methanol with 95% confidence intervals. Salinity = 35%o suspension concentration = 10.8 g L. Filled squares denote apparent partition coefficients used for the regression and the intercept with the y axis (open circle) the cosolvent partition coefficient. [Reproduced with permission from W. J. M. Hegeman, C. H. van der Weijden, and J. P. G. Loch, Environ. Sci. Tecnol. 29, 363 (1995). Copyright 1995, American Chemical Society.]...

For simple cases, the relationship between three-dimensional sizes and L can be geometrically determined. It can be shown, for example, that uniformly sized spherical particles have a diameter given by = 1. 5L. Note also that the internal surface area per unit volume, Sy, is simply related to the mean lineal intercept for a three-dimensional structure of space-filling grains by the equation = 2/ Z. 

Figure 2.5 The dependence of-FT diffusion coefficient on diffusion time (A) and sanple volume at 373 K. NMR tubes of S mm io.d. were filled with rCompyrirNTfnI to a height of either 5 or 40 mm - the intercept provides the true diffusivity. The dry (<100 ppm HnOi ionic liquid was packed and sealed under an No atmosphere (<10 ppm HnOl. Measurements were performed on a 300 MFTz Broker Avance NMR spectrometer with a Diff30 diffusion prohe [481.

This equation shows the linear dependence of the left side on 1/T and p can be found from the intercept and slope of the experimental curve of temperature dependence of the system volume, V, the parameters e/K and Ino of Eq 4.20 and values Vh/kT and Ino + ei/kT of Eq 4.21. The parameters of Eq 4.20, found in this way, may be used to estimate the changes in enthalpy, H, entropy, S, and free energy, G, during the transition of polymer into a filled state. According to Smith, AH is determined as ... 

It was shown that, for filled and unfilled PMMA, the straight lines describing the dependence of Vg on Tg and Vp onTp (where Vp and Tp are specific volume and temperature of the secondary transition) have an intercept at the point with coordinates v and. The last values are limiting values of the specific volume of a melt and temperature, at which, due to the high hydrostatic pressure, the segmental mobility is fully suppressed and free volrune becomes zero. Using v = v for Eq 4.27, one can find sA-... 

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