Jump-like

Jahn-Teller effect, 25 3 sites, 34 278 Jellium model, 34 139 Joule heating, 22 209, 220 Jump-like diffusion, 34 34... 

Who I must have jumped like a frog, because she eyed me oddly. 

For an athermal case, the continuous deswelling of the network takes place (Fig. 9, curve 1) which in the result of compressing osmotic pressure created by linear chains in the external solution (the concentration of these chains inside the network is lower than in the outer solution, cf. Ref. [36]). If the quality of the solvent for network chains is poorer (Fig. 9, curves 2-4), this deswelling effect is much more pronounced deswelling to strongly compressed state occurs already at low polymer concentrations in the external solution. Since in this case linear chains are a better solvent than the low-molecular component, with an increase of the concentration of these chains in the outer solution, a decollapse transition takes place (Fig. 9, curves 2-5), which may occur in a jump-like fashion (Fig. 9, curves 3-4). It should be emphasized that for these cases the collapse of the polymer network occurs smoothly, while decollapse is a first order phase transition. 

The most important prediction of the theory is the fact that in the region of a poor solvent the extension of a weakly charged polymer network can induce jump-like decollapse of the gel. In contrast, the compression of the swollen gel must induce the collapse of the network. 

It is worthwhile mentioning here some other predictions which follow from the consideration of Sect. 2.3. For the gel, which has charges of one sign, the phase transition induced by elongating force should be sharper than for the neutral network. For a polyampholyte network near the isoelectric point, this transition is always continuous and even less pronounced than for the neutral gel. Finally, for the gel near the transition point, very small values of the applied force can induce a collapse of the gel or a jump-like swelling of the gel sample. 

For the gels, which swell under the applied mechanical force, the dependence of deformation on the stress is characterized by some specific features. In particular, at some critical values of the applied force, the deformation can increase in a jump-like manner by hundreds of percent (Fig. 25). For the samples which are very close to the phase transition point even a very small increase in tension causes noticeable changes in the degree of swelling and in the dimensions of the gels. 

Finally, the study of the protons of the polymer chain measured by incoherent neutron scattering allows the identification of two distinct types of motion (a) a vibrational motion of the Debye-Waller type and (b) a slow jump-like diffusive motion of the whole chain confined within the volume restricted by... 

This is a very useful approach, which can be recommended for practical applications. A simplified version of this general treatment may also be useful. It is possible to consider vitrification of a material as a jump-like transition from a liquid to a solid state. This idea was advanced elsewhere, where residual stresses in inorganic glasses were calculated by treating vitrification as a sequential solidification of layers of a viscous liquid on the rigid surface of a previously solidified material. In a liquid layer (not yet solidified) at T > Tg, only flow deformations can occur. In the transition through Tg, this deformation is frozen in and cannot change later on. 

At the initial oxidation stages (in the induction period) active sites are accumulated. When their concentration reaches a definite level required for a jump-like acceleration of oxidation, either chain or catalytic transformation of the substrate begins at a high rate. 

To check these suggestions, the authors conducted an experiment with a peroxidase-mimetic sensor prepared on a new aluminum electrode under conditions corresponding to one of the minima in Figure 8.14. As shown by the plot of this experiment (point A in Figure 8.14), the minimum at C2H5OH concentration equal 10-3wt.% depends on aluminum foil conditions for a fresh electrode a sharp, jump-like increase of the potential is detected. 

I) If A > 0, then h2 < hi, and the reorientation of the second sublattice occurs in a field h = hn by a first-order phase transition. The total magnetization in this field has a jump-like change Am = 2. In the field interval h2 < h < h metastable states exist, and hysteresis is possible (Fig. 15a). 

II) At S 0 we have h2 i> hi, and the transition occurs continuously in the field interval Ah = h2 — h (Fig.15b). In this interval solution B) is realized. In an increased magnetic field a second-order phase transition takes place at h = hi and the magnetic susceptibility reveals a jump-like... 

Thus, this calculation of the magnitude of the field, induced at the site by a single ion, and its dependence on distance explain the experimental observation of the jump-like magnetization changes at h = h and h = hi. As a result of the first phase transition, the reversed spins form a close-packed structure with a period ro 10 7cm. 

On other surfaces both the concentration and strength of bonding of the spiltover species will vary. The rate-controlling step may shift, and since the activation energies of the individual steps are not equal, the rate control can shift with temperature. For example, the diffusion coefficient may behave as T312 Ti/2 for two-dimensional diffusion as a surface gas. If a jump-like diffusion occurs from point to point, the dependence may contain an appropriate activation energy. 

Fig. 3.57 shows two IT(/j) isotherms of NaDoS films obtained at two electrolyte concentrations. The CBF/NBF transition zone is clearly seen. The right hand side of the curves refer to CBF and indicate that their thickness h decreases with increase in pa. When thickness of 7.1 nm is reached at nmax 105 Pa, the CBF transforms through a jump-like transition into NBF of h = 4.3 + 0.2 nm. The region of CBF/NBF transition is marked with dashed lines in the upper part of the isotherms. 

As it is known, the black film thickness h is a function of the electrolyte concentration (Fig. 3.62). Such a dependence has been studied in detail for microscopic foam films from sodium oleate solutions [14,73,96]. It has given the first quantitative evidence for the existence of the two types of black films. After a monotonous decrease in film thickness upon increasing electrolyte concentration up to 0.8 mol dm 3, a jump-like change in its thickness is observed (Fig. 3.62,a). An about twice thinner film is formed which does not change in thickness at a further increase in Cei. Thus Cei,cr was precisely determined and the concentration range in which the two types of black films are stable at a given temperature (21°C) was established. 

The region of jump-like changes in the dAsurface tension (see Fig. 3.77). This jump [364,365] is explained with a phase transition in the adsorption layer. Other authors have also noticed the flexion in Ao(C) isotherm and have considered it to be a transition from liquid-crystalline to gel state of the adsorption layer, e.g. in solutions of dodecylamine hydrochloride [374]. This transition can be found experimentally also from AV(C) dependence. As it is seen from Fig. 3.77 the minimum of AV coincides with the flexion point of Ao(lgC) isotherm. 

It is known [41] that NBF/CBF transition occurs in a foam from NaDoS solution with constant electrolyte concentration (more than 0.3 mol dm 3 NaCl) within the temperature range from 30 to 35°C (see Section 3.4.2). To confirm that the difference in flow rates is related to the foam film type studies were performed to establish the temperature dependence of the foaming solution flow rate through NaDoS foam with NBF (in the presence of 0.4 mol dm 3 electrolyte). The results from this series of experiments show that with the change in temperature from 20 to 25°C, vexp increases in accord with the decrease in solution viscosity. Further temperature rise (30-35°C) leads to a jump-like increase in flow rate (Fig. 5.2. - (x) points lay on curve 2 which is for CBF). Obviously, this coincides with the NBF/CBF transition. 

The flow rate dependences obtained are in good qualitative agreement with previous studies. It has been established [14,43-45] that NaDoS solution flow rate through foam is influenced strongly by the dodecanol concentration and a jump-like increase in the flow rate is also observed within the temperature range of 31 to 42°C. This transition temperature is a function of the NaDoS/dodecanol concentration ratio [14,43]. For instance, a sharp flow rate change in a solution containing 0.1 % NaDoS and 0.001% dodecanol occurs at 41°C, while at 0.2% NaDoS and 0.001% dodecanol solution the jump is at 21°C [45]. Data reported by... 

The studies performed reveal that the lower concentration limit of surfactant extraction using the foam separation technique is determined by the course of the surfactant stabilising ability versus surfactant concentration curves (lifetime dependences of films and foams, and probability for black spot formation on surfactant concentration). If there is a jump-like increase in the film (foam) lifetime with concentration, then VF IVg = f(C) and the accumulation ratio also undergoes a jump-like increase VF/Vg - from 0 to 1, and - from 1 to more than 1, corresponding to the lower concentration limit. 

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