Hysteresis loop characteristics

AP-24PDO (773-1273 K) and AP-25HDO (773-1073 K) materials exhibited Type IV N2 isotherms (not shown) with closed and well-defined HI hysteresis loops characteristic of mesoporous materials. After heating at 1273 K, AP-25HDO materials displayed, whatever the 24HDO/A1 molar ratio, reversible Type II isotherms that corresponded to non porous adsorbents. 

The polarization hysteresis loop measured at room temperature for the P (VDF-TrFE) 68/32 mol% copolymer changes with the irradiation dose (Cheng et al. 2002). With increased dosage, flie near square polarization hysteresis loop, characteristic for a normal ferroelectric material, is transformed to a slim polarization loop (at 75 Mrads). At very high dose (175 Mrads), the polymer becomes a Unear dielectric in which the crystallinity is near zero. 

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. 

It was noted earlier (p. 115) that the upward swing in the Type IV isotherm characteristic of capillary condensation not infrequently commences in the region prior to the lower closure point of the hysteresis loop. This feature can be detected by means of an a,-plot or a comparison plot (p. 100). Thus Fig. 3.25(a) shows the nitrogen isotherm and Fig. 3.25(h) the a,-plot for a particular silica gel the isotherm is clearly of Type IV and the closure point is situated around 0 4p° the a,-plot shows an upward swing commencing at a = 0-73, corresponding to relative pressures of 013 and therefore well below the closure point. 

If mesopores are present in addition to micropores, the isotherm will be of Type IV, with the characteristic hysteresis loop but, as explained in... 

A new classification of hysteresis loops, as recommended in the lUPAC manual, consists of the four types shown in the Figure below. To avoid confusion with the original de Boer classification (p. 117), the characteristic types are now designated HI, H2, H3 and H4 but it is evident that the first three types correspond to types A, E and B, respectively, in the original classification. It will be noted that HI and H4 represent extreme types in the former the adsorption and desorption branches are almost vertical and nearly parallel over an appreciable range of gas uptake, whereas in the latter they are nearly horizontal and parallel over a wide range of relative pressure. Types H2 and H3 may be regarded as intermediate between the two extremes. 

For perm anen t-m agnet materials where the coercivity is large, the demagaetizatioa curve, which correspoads to the secoad quadrant of the hysteresis loop, sometimes is plotted as the polarization J(= B — vs H(B — H vs H) to show the intrinsic characteristics of the material. The value of... 

The designer can use several approaches to prevent hysteresis failure. The first is material selection. The stiffer the material is, the smaller the strain is for a given stress level and the lower the hysteresis loss per cycle. Some materials are additionally fairly linear in stress-strain characteristics and have smaller hysteresis loops. These would be preferred in dynamic loading applications. 

In these polymeric species, the M,AT2-1,2,4-triazole linkage is rigid, and allows an efficient transmission of cooperative effects. Consequently, abrupt ST with broad thermal hysteresis loops have been observed [26, 32-34]. The absorption spectra of these compounds show a broad band at 520 nm corresponding to the Aig Trg d-d transition in the LS state whereas no band is found in the visible region in the HS state, the 5T2g-5Eg transition being located around 850 nm [7a]. The ST is thus accompanied by a thermochromic effect, purple (LS) and white (HS). These characteristics make these compounds potential candidates for practical applications, e.g. thermal display devices [7, 8, 17]. Such behaviour has been observed, for example, in the compound [Fe(4-amino-l,2,4-triazole)3](NC>3)2 [32] whose SCO is associated with a hysteresis loop of width 35 K, centred above room temperature [8]. 

The simulation results are shown in Figure 20. We can observe that the simulation can reproduce the characteristic feature, the hysteresis loop, observed in the dynamic n-A curves. 

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). 

The second category, time-dependent behaviour, is common but difficult to deal with. The best known type is the thixotropic fluid, the characteristic of which is that when sheared at a constant rate (or at a constant shear stress) the apparent viscosity decreases with the duration of shearing. Figure 1.21 shows the type of flow curve that is found. The apparent viscosity continues to fall during shearing so that if measurements are made for a series of increasing shear rates and then the series is reversed, a hysteresis loop is observed. On repeating the measurements, similar behaviour is seen but at lower values of shear stress because the apparent viscosity continues to fall. 

Existence of a large amount of mesopores usually results in the appearance of capillary condensation hysteresis loop. Type II AIs transform to type IV, and type III AIs transform to type V Type VI AIs are characteristic to low-temperature adsorption of some noble gases over energetically homogeneous surfaces. 

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. 

Magnetically soft Fe-Ni alloys can have their properties altered by heat treatment. The compound NisFe undergoes an order-disorder transformation at about 500°C. Since the susceptibility of the ordered phase is only about half that of the disordered phase, a higher susceptibility is realized when the alloy is quenched from 600°C, a process that retains the high-temperature, disordered structure. Heat treatment of Fe-Ni alloys in a magnetic field further enhances their magnetic characteristics (see Figure 6.61), and the square hysteresis loop of 65 Permalloy so processed is desirable in many applications. A related alloy called Supermalloy (see Table 6.19) can have an initial susceptibility of approximately one million. 

In between these tangencies, the curves R and L have three intersections, so the system has multiple stationary states (Fig. 7.3(b)). We see the characteristic S-shaped curve, with a hysteresis loop, similar to that observed with cubic autocatalysis in the absence of catalyst decay ( 4.2). 

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. 

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