Hysteresis loops isotherms,adsorption

Adsorption/Desorption Mechanisms Isotherm Hysteresis Loops... 

The hydration shell is formed with the increasing of the water content of the sample and the NA transforms from the unordered to A- and then to B form, in the case of DNA and DNA-like polynucleotides and salt concentrations similar to in vivo conditions. The reverse process, dehydration of NA, results in the reverse conformational transitions but they take place at the values of relative humidity (r.h.) less than the forward direction [12]. Thus, there is a conformational hysteresis over the hydration-dehydration loop. The adsorption isotherms of the NAs, i.e. the plots of the number of the adsorbed water molecules versus the r.h. of the sample at constant temperature, also demonstrate the hysteresis phenomena [13]. The hysteresis is i( producible and its value does not decrease for at least a week. 

The basis of the classification is that each of the size ranges corresponds to characteristic adsorption effects as manifested in the isotherm. In micropores, the interaction potential is significantly higher than in wider pores owing to the proximity of the walls, and the amount adsorbed (at a given relative pressure) is correspondingly enhanced. In mesopores, capillary condensation, with its characteristic hysteresis loop, takes place. In the macropore range the pores are so wide that it is virtually impossible to map out the isotherm in detail because the relative pressures are so close to unity. 

A characteristic feature of a Type IV isotherm is its hysteresis loop. The exact shape of the loop varies from one adsorption system to another, but, as indicated in Fig. 3.1, the amount adsorbed is always greater at any given relative pressure along the desorption branch FJD than along the adsorption branch DEF. The loop is reproducible provided that the desorption run is started from a point beyond F which marks the upper limit of the loop. 

The model proposed by Zsigmondy—which in broad terms is still accepted to-day—assumed that along the initial part of the isotherm (ABC of Fig. 3.1), adsorption is restricted to a thin layer on the walls, until at D (the inception of the hysteresis loop) capillary condensation commences in the finest pores. As the pressure is progressively increased, wider and wider pores are filled until at the saturation pressure the entire system is full of condensate. 

Figure 3.26(a) and (h) gives results for nitrogen on a compact of silica. Curve (a) is a comparison plot in which the adsorption on the compact (ordinates) is plotted against that on the uncompacted powder (abscissae) there is a clear break followed by an increased slope, denoting enhanced adsorption on the compact, at p/p° = 0-15, far below the lower closure point ( 0-42) of the hysteresis loop in the isotherm (curve (b)). A second compact, prepared at 64 ton in" rather than 130 ton in", showed a break, not quite so sharp, at p/p° = 0-35. 

Fig. 3.28 The Kiselev method for calculation of specific surface from the Type IV isotherm of a compact of alumina powder prepared at 64 ton in". (a) Plot of log, (p7p) against n (showing the upper (n,) and lower (n,) limits of the hysteresis loop) for (i) the desorption branch, and (ii) the adsorption branch of the loop. Values of. 4(des) and /4(ads) are obtained from the area under curves (i) or (ii) respectively, between the limits II, and n,. (6) The relevant part of the isotherm.

Low-pressure hysteresis is not confined to Type I isotherms, however, and is frequently superimposed on the conventional hysteresis loop of the Type IV isotherm. In the region below the shoulder of the hysteresis loop the desorption branch runs parallel to the adsorption curve, as in Fig. 4.26, and in Fig. 4.2S(fi) and (d). It is usually found that the low-pressure hysteresis does not appear unless the desorption run commences from a relative pressure which is above some threshold value. In the study of butane adsorbed on powdered graphite referred to in Fig. 3.23, for example, the isotherm was reversible so long as the relative pressure was confined to the branch below the shoulder F. 

The first stage in the interpretation of a physisorption isotherm is to identify the isotherm type and hence the nature of the adsorption process(es) monolayer-multilayer adsorption, capillary condensation or micropore filling. If the isotherm exhibits low-pressure hysteresis (i.e. at p/p° < 0 4, with nitrogen at 77 K) the technique should be checked to establish the degree of accuracy and reproducibility of the measurements. In certain cases it is possible to relate the hysteresis loop to the morphology of the adsorbent (e.g. a Type B loop can be associated with slit-shaped pores or platey particles). 

The nitrogen adsorption isotherms for the onion-like Fe-modified MLV-0.75 materials are of type IV, although their hysteresis loops are of complex types, HI, H2, and H3. The H2-type hysteresis loop indicates the presence of bottle-shaped pores. The pore sizes obtained with the BJH method can be assigned to entry windows of mesopores. For pure MLV-0.75 and Fe-modified MLV-0.75 (x = 1.25), the pore size distributions exhibit two peaks (Fig. Id). The first peak appears at 9.0 and ca. 6 nm for MLV-0.75 and Fe-MLV-0.75, respectively. The shift of the broad peak maximum of the distribution curve... 

NaY yields a compietely reversible type I isotherm, characteristic of micropore filling common in many zeolites. However, USY-B and DAY yield an isotherm close to type IV. Similar differences in adsorption isotherms were observed for n-hexane, cyclohexane, n-pentane and benzene. Furthermore, many of the isotherms measured on DAY zeolites showed hysteresis loops (Figure 6). 

One of the most widely used methods for determining the pore size and surface area of zeolites is nitrogen physisorphon. From the shape of the nitrogen adsorption and desorption isotherm the presence and shape of the mesopores can be deduced. As shown in Figure 4.41 a faujasite without mesopores have a type I isotherm since the micropores fiU and empty reversibly, while the presence of mesopores results in a combination of type I and IV isotherms. The existence of a hysteresis loop in the isotherms indicates the presence of mesopores while the shape of this hysteresis loop is related to their geometric shape. 

The majority of physisorption isotherms (Fig. 1.14 Type I-VI) and hysteresis loops (Fig. 1.14 H1-H4) are classified by lUPAC [21]. Reversible Type 1 isotherms are given by microporous (see below) solids having relatively small external surface areas (e.g. activated carbon or zeolites). The sharp and steep initial rise is associated with capillary condensation in micropores which follow a different mechanism compared with mesopores. Reversible Type II isotherms are typical for non-porous or macroporous (see below) materials and represent unrestricted monolayer-multilayer adsorption. Point B indicates the stage at which multilayer adsorption starts and lies at the beginning of the almost linear middle section. Reversible Type III isotherms are not very common. They have an indistinct point B, since the adsorbent-adsorbate interactions are weak. An example for such a system is nitrogen on polyethylene. Type IV isotherms are very common and show characteristic hysteresis loops which arise from different adsorption and desorption mechanisms in mesopores (see below). Type V and Type VI isotherms are uncommon, and their interpretation is difficult. A Type VI isotherm can arise with stepwise multilayer adsorption on a uniform nonporous surface. 

As discussed in Section 1.4.2.1, the critical condensation pressure in mesopores as a function of pore radius is described by the Kelvin equation. Capillary condensation always follows after multilayer adsorption, and is therefore responsible for the second upwards trend in the S-shaped Type II or IV isotherms (Fig. 1.14). If it can be completed, i.e. all pores are filled below a relative pressure of 1, the isotherm reaches a plateau as in Type IV (mesoporous polymer support). Incomplete filling occurs with macroporous materials containing even larger pores, resulting in a Type II isotherm (macroporous polymer support), usually accompanied by a H3 hysteresis loop. Thus, the upper limit of pore size where capillary condensation can occur is determined by the vapor pressure of the adsorptive. Above this pressure, complete bulk condensation would occur. Pores greater than about 50-100 nm in diameter (macropores) cannot be measured by nitrogen adsorption. 

As discussed above, hysteresis loops can appear in sorption isotherms as result of different adsorption and desorption mechanisms arising in single pores. A porous material is usually built up of interconnected pores of irregular size and geometry. Even if the adsorption mechanism is reversible, hysteresis can still occur because of network effects which are now widely accepted as being a percolation problem [21, 81] associated with specific pore connectivities. Percolation theory for the description of connectivity-related phenomena was first introduced by Broad-bent et al. [88]. Following this approach, Seaton [89] has proposed a method for the determination of connectivity parameters from nitrogen sorption measurements. 

In the past it was very common to derive the mesopore size distribution from the desorption branch of the isotherm. The above considerations make it clear that this practice is questionable especially for Type H2 hysteresis loops, and can lead to misinterpretations [90]. Indeed a significant downward turn in the desorption branch of a N2 isotherm at p/po 0.4 leads to an apparent sharp maximum in the pore size distribution curve at 2 nm which is totally artefactual. Although no general guidelines exist on whether the adsorption or desorption branch should be used for computation, it should be understood that with Type H2 and H3 hysteresis loops, reliable results are much more Hkely to be obtained if the adsorption branch is used [21]. 

The shape of the hysteresis loop in the adsorption/desorption isotherms provides information about the nature of the pores. The loops have been classified according to shape as A, B and E (De Boer, 1958) or as HI - H4 by lUPAC (Sing et al, 1985). Ideally, the different loop shapes correspond to cylindrical, slit shaped and ink-bottle pores the loops in the isotherm IV and V of Figure 5.3 correspond to cylindrical pores. Wide loops indicate a broad pore size distribution (for an example see Fig. 14.9). The absence of such a loop may mean that the sample is either nonporous or microporous. These generalizations provide some initial assistance in assessing the porosity of a sample. In fact the adsorption/desorption isotherms are often more complicated than those shown in Figure 5.3 owing to a mixture of pore types and/or to a wide pore size distribution. 

Kiselev, using the above equation by graphical integration of the isotherm between the limits of saturation and hysteresis loop closure, was able to calculate surface areas for wide-pore samples in good agreement with BET measured areas. For micropores, the absence of hysteresis at the low-pressure end of the isotherm indicates that only adsorption and not condensation occurs, thereby rendering Kiselev s method inapplicable. 

Attempts to measure points on the desorption isotherm without first adsorbing near saturation will result in scanning the hysteresis loop from the adsorption to the desorption curve (see Fig. 15.13 and Section 15.6). 

The consequences of this type of activated physical adsorption is not only that the quantity adsorbed can lie off the isotherm but also that the measured quantity of adsorption is far less than the equilibrium value. No experiments have been conducted to illustrate whether or not the quantity adsorbed lies within the hysteresis loop. The occasional failure of the vacuum volumetric method to agree with the dynamic method, which is not subject to any pressure overshoot, may in part be attributed to this phenomenon. 

To scan the hysteresis loop from the adsorption to the desorption isotherm, the sample, immersed in the coolant, is equilibrated with a gas mixture with a relative pressure corresponding to the start of the scan on the adsorption isotherm. The adsorbate concentration is then reduced to a value corresponding to a relative pressure between the adsorption and desorption isotherms. When equilibrium is reached, as indicated by a constant detector signal, the coolant is removed and the resulting desorption signal is calibrated. Repetition of this procedure, each time using a slightly different relative pressure between the adsorption and desorption isotherms, yields a hysteresis scan from the adsorption to the desorption isotherm. 

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