Isotherm determination

As already mentioned, the choice of the supercooled liquid as reference state has been questioned by some workers who use the saturation vapour pressure of the solid, which is measured at the working temperature in the course of the isotherm determination. The effect of this alternative choice of p° on the value of a for argon adsorbed on a number of oxide samples, covering a wide range of surface areas, is clear from Table 2.11 the average value of is seen to be somewhat higher, i.e. 18 OA. ... 

It must always be borne in mind that when capillary condensation takes place during the course of isotherm determination, the pore walls are already covered with an adsorbed him, having a thickness t determined by the value of the relative pressure (cf. Chapter 2). Thus capillary condensation occurs not directly in the pore itself but rather in the inner core (Fig. 3.7). Consequently the Kelvin equation leads in the first instance to values of the core size rather than the pore size. The conversion of an r value to a pore size involves recourse to a model of pore shape, and also a knowledge of the angle of contact 0 between the capillary condensate and the adsorbed film on the walls. The involvement of 0 may be appreciated by consideration... 

It has already been noted (p. 195) that some Type I isotherms exhibit a kind of hysteresis which persists to the lowest pressures (cf. Fig. 4.2) some adsorbate is retained even after prolonged outgassing ( lO Torr) at the temperature of the isotherm determination, and can only be removed if the pumping is carried out at an elevated temperature. Further examples are shown in Fig. 4.25, as well as in Fig. 4.23. 

A detailed study of the physical and chemical adsorption of water on three xerogels, ferric oxide, alumina and titania, as well as on silica (cf. p. 272) has been carried out by Morimoto and his co-workers. Each sample was outgassed at 600°C for 4 hours, the water isotherm determined at or near 20°C, and a repeat isotherm measured after an outgassing at 30 C. The procedure was repeated on the same sample after it had been evacuated at a... 

N, = amount of chemisorbed water formed during isotherm determination (OH groups per lOOA ). 

V, = hydroxyl content before isotherm determination (OH groups per 1(X) A ). 

The BET monolayer capacity N, calculated from the first water isotherm included both physisorbed and chemisorbed water, whereas that from the second isotherm iV, included only the physisorbed water. Thus the difference (iV, - N,) gave the amount of chemisorbed water taken up as hydroxyl groups during the isotherm determination. N, + iV ) was therefore the total concentration of hydroxyl groups on the surface when the second water isotherm was being measured. 

Carbon black adsorbed OLOA 1200 very strongly, eventually picking up 5% of its weight in dispersant. The first 2% adsorbed almost instantly, but additional increments adsorbed more and more slowly (see Figure 5). Such time-dependence in adsorption of large molecules is quite common (15), but is seldom studied. The adsorption isotherms determined after 48 hours of tumbling at 25°... 

Batch equilibrium tests used for sorption isotherm determinations involve solid suspensions (i. e., the full surface area of the solid particles is exposed to... 

Typically, adsorption isotherms are generated using a batch experiment at a fixed temperature and a fixed feed composition. These experiments include exposing a known amount of adsorbent to a known concentration of adsorbate at a constant temperature. Once equilibrium is established, the net adsorbate concentration in the liquid is measured. This process is repeated at multiple adsorbate concentrations and temperatures. A plot of adsorbate loading (g adsorbate/g adsorbent) versus adsorbate concentration reveals the adsorption isotherm with the shape of the isotherm determining the suitability of a particular adsorbent for a particular system [20]. 

Equations 10.47 through 10.49 constitute the basis for the method of isotherm determination by the perturbation method. The retention time of a small injection of a solute in a column equilibrated... 

Derivation of the Gibbs adsorption isotherm. Determination of the adsorption of surfactants at liquid interfaces. Laboratory project to determine the surface area of the common adsorbent, powdered activated charcoal. 

In a paper concerned primarily with the determination of neutral sugars, Richey and coworkers examined the O-trimethylsilyl derivatives of 2-acetamido-2-deoxy-D-glucose and 2-acetamido-2-deoxy-D-galactose.171 Similar methods for determining these compounds have also been used in studies on human milk,545 yeasts and bacteria,1,2 blood-group oligosaccharides,405 and urine.118 These methods were also included in a model study on the isothermal determination of sugars.256... 

However, the pH varies as well and might be the cause of the difference in sorption isotherms. Further investigations would be necessary. The sorption isotherms determined by Moulin et al. (1999) appear to be slightly lower for both Zn(II) (Fig. 6) and Pb(II) (Fig. 7), but the agreement is quite good. 

This type of adsorption is said to be reversible and the thermodynamic laws of the surface phenomena (e.g., isotherms, determination of AG°, AH°, and AS° as explained in Section 6.8.3) are valid. 

Water isotherms determined at 35°C. are shown in Figure 3. The amount of water sorbed by the Pittsburgh coal is about twice the amount taken up by Pocahontas coal. These isotherms represent equilibrium measurements. Hysteresis loops that do not close at relative pressures less than 0.3 are characteristic of water adsorption on coal. 

In Figure 4 for Pocahontas coal the methane isotherms at —195°, —78°, 0°, 30°, and 50°C., determined in the sequence indicated, are shown as solid curves, and the isotherms at 0°, —78° and —195°C. after the initial sequence are shown as dashed curves. For the Pittsburgh coal, only the isotherms in a rising series of temperatures were determined (Figure 5). Figures 4 and 5 show a plot of methane isotherms at —195°C. on a relative pressure basis (pressure of methane/vapor pressure) because the vapor pressure is only about 10 torr. Isotherms determined at —195°C. represent metastable equilibrium and those at 30°, 50°, and possibly 0°C. equilibrium. Adsorption was... 

The standard is weighed to an exact amount similar to the amount used in the isotherm determination (step 1). The standard is placed into the closed chamber which contains the unknown sample as the aw source and is equilibrated at a constant temperature. The key point is that equilibrium does not take as much time as the procedure using equilibration with saturated salt solutions (see Basic Protocol) i.e., the mass change can be determined in 24 hr if the calibration curve is also done with the same mass of standard and equilibrated for the same amount of time (step 3). 

In deriving the shapes of these isotherms, we first must define isotherms for ideal clays and ideal oxides. We then combine these ideal functions into overall isotherms and compare the derived functions to experimental isotherms determined for various adsorbents. We will show that observations which have been said to preclude ion exchange are, in fact, quite consistent with ion-exchange behavior. We will not attempt to derive actual values of equilibrium distribution coefficients, but rather we seek only to define the shapes of the isotherms. 

In Figure 6.22a, the MPSD of the DAY zeolite calculated with the help of the SF method is reported. The DAY zeolite has an FAU framework, with a 12MR three-dimensional channel system with apertures of 7.4 A (see Section 2.5.1) [83], The obtained PSD for the DAY zeolite shows a clear maximum at about 7 A. In Figure 6.22b, the S-F MPSD of the SWCNT is reported [80], The calculated PSD for the SWCNT indicates that this material has a slightly heterogeneous distribution of pores with a clear, and highly populated, maximum at 13.5 A [80], The adsorption study, in both cases, was carried out using N2 adsorption at 77 K isotherms, obtained with a Quantachrome Autosorb-1 equipment for adsorption isotherm determination by the volumetric method [21],... 

In principle, a continuous procedure can be used to construct the isotherm under quasi-equilibrium conditions the pure adsorptive is admitted (or removed) at a slow and constant rate and a volumetric or gravimetric technique used to follow the variation of the amount adsorbed with increase (or decrease) in pressure. A carrier gas technique, making use of conventional gas chromatrographic equipment, may be employed to measure the amount adsorbed provided that the adsorption of the carrier gas is negligible. In all types of measurement involving gas flow it is essential to confirm that the results are not affected by change in flow rate and to check the agreement with representative isotherms determined by a static method. 

The isosteric differential heats of physical adsorption of nitrogen near its boiling point on reduced and oxidized electropolishing single crystal copper surfaces can be evaluated from adsorption isotherms determined gravimetrically. 

Catalyst surface areas prior to reaction were determined by application of the BET method to nitrogen physisorption isotherms determined at 77K. 

The first step is devoted to the determination of adsorption isotherms. Several adsorption isotherm determination methods have been described [13], and we developed a laboratory apparatus allowing to determine very precise adsorption isotherms in supercritical fluids. 

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