Quasiequilibrium state

The model based on formal kinetics was used to model the TPD curves of adsorbed CO molecules, based on the model previously reported [4], The desorption is strongly affected by the fast readsorption of CO on unoccupied Cu+ ions, thus, a quasiequilibrium state is a suitable approximation for the description of adsorption. A Langmuir type of adsorption isotherm was assumed for the CO adsorption on the Cu+ sites in zeolite, without considering lateral interactions among adsorbed molecules. 

Equation 1 was derived assuming that the nuclear spin magnetizations are at thermal equilibrium values prior to the start of the presaturation. In practice, due to time constraints on the instrument, this condition may not usually be reahzed and the nuclear spin magnetization can generally be in a quasiequilibrium state prior to presaturation. If (tj + t) is the delay between two consecutive 90° observe pulses, where t is the presaturation period and fa is the time delay before presaturation (this includes the data acquisition time for the previous pulse), then the appropriate expressions for STD and for control NMR spectra are given by ... 

Upon the formation of CdS colloids, at the point when the colloidal particles stop their growth and the system reaches the quasiequilibrium state, the total amount of cadmium is distributed over CdS particles and the aqueous phase of the solution, where it appears both as activated Cd2+ ion and as the compounds with complexing admixtures. One may assume the thermodynamic equilibrium is reached between the different possible forms of cadmium occurrence. Assuming the presence of only one complexing agent L, which participates in a stepwise complexing, we may describe the above equilibrium by a system of chemical equations ... 

Fig. 1. Reversible molecular association reactions involved in the assembly of crystals. Monomers initially combine into small aggregates (here, called chains). The association of monomers into chains leads to the formation of prenuclear aggregates that continue to grow by further addition of monomers or chains. The partition of molecules into monomers, chains, and prenuclear aggregates is called a quasiequilibrium state (Kam et al., 1978). When sufficient molecules associate in three dimensions, a thermodynamically stable critical nucleus is formed. The addition of monomers and/or chains to critical nuclei eventually leads to the formation of macroscopic crystals.

A basic assumption in sintering is that the particles are sintered under a quasiequilibrium state. This means that in the case of diffusion, the diffusion gradient is in a steady state and the time to achieve the steady state is negligible compared with that of a change in particle geometry. Therefore, atoms in any location are locally in equilibrium with a given capillary stress. Under this assumption, sintering kinetics is not controlled by the equilibration reaction and its kinetics at the interface but by atom movement. (This assumption does not apply to the evaporation/condensation mechanism described in Section 4.2.6.)... 

After the initial process (relaxation to the quasiequilibrium state) just described, a change in the number of micelles occurs, representing relaxation to the true... 

The results presented in this chapter clearly demonstrate that the state of the siuface is a dynamic process depending on kinetics of surface transformation temperatiue, reactant concentration, time on stream, even on the reactor used, all of which determine the structure and composition of the Pt surface. In short T-O-S experiments, in which the surface is not equilibrated, the conditions can be different than in long-term experiments, where the surface reaches a quasiequilibrium state. Comparison of results from different research groups requires detailed examination of all the conditions used to draw valid conclusions. Although this is a common-sense conclusion, researchers often compare results at quite different conditions, e.g., single crystal versus supported catalysts, to cite a common example. Often-heated arguments about which interpretation is the correct one are just a reflection of the surfaces being under different states due to the use of different experimental parameters. 

One can expect, therefore, that the fission product atoms in the fuel are in a quasiequilibrium state with regard to their environment. 

Let us now consider a feasible sequence of events during the cyclic functioning of membrane-bound ATPsynthase in the presence of a transmembrane pH difference. Position 1 in Fig. 5.27 corresponds to the enzyme quasiequilibrium state there are no phosphorylation substrates in the active center, the functional acid groups are protonated due to their contact with the acidic interior of a vesicle (pHj < pK ), and a is open a fast leakage of protons into the external aqueous phase via ATPsynthase is prevented by the barrier hindering the contact of the AH group with the exterior, symbolized in Fig. 5.27 by key b in the locked position. The attachment of phosphorylation substrates to the active center of the coupling factor (transition 1 2)... 

Similar linear dependences for SP - OPD with various were obtained in Ref. [7] and they testify to molecular mobility level reduction at decrease and extrapolate to various (nonintegral) values at = 1.0. The comparison of these data with the Eq. (1.5) appreciation shows, that reduction is due to local order level enhancement and the condition = 1.0 is realized at values, differing from 2.0 (as it was supposed earlier in Ref [23]). This is defined by pol5miers sfructure quasiequilibrium state achievement, which can be described as follows [24]. Actually, tendency of thermodynamically nonequilibrium solid body, which is a glassy polymer, to equilibrium state is classified within the fimneworks of cluster model as local order level enhancement or (p j increase [24-26], However, this tendency is balanced by entropic essence straightening and tauting effect of polymeric medium macromolecules, that makes impossible the condition (p j= 1.0 attainment. At fully tauted macromolecular chains = 1.0)

polymer structure achieves its quasiequilibrium state at d various values depending on copolymer type, that is defined by their macromolecules different flexibility, characterized by parameter C. ... 

Kozlov, G. V, Zaikov, G. E. (2002). The Concept of Quasiequilibrium State at Gross-Linked Polymers Physical Aging Description. Materialovedenie, 12,13-17. 

Using these general notions, the authors of Ref. [6, 7] offered the fractal models for polymers elastic constants description. The quasiequilibrium state of polymers structure is characterized by the criterion D = 3 [8, 9], where is dimension of excess energy localization domains. A loosely packed matrix is totality of such domains. The value can be determined within the frameworks of free volume fractal theory according to the equation [9] ... 

From the Eq. (3.5) together with the criterion (3.4) it follows, that at arbitrary Tthe definite value (tg ) will correspond to quasiequilibrium state, that is, this parameter is a function of temperature. Then relative deviation of loosely packed matrix (in which the entire fiuctuation free volume is concentrated [8, 9]) from quasiequilibrium state can be expressed as follows [6] ... 

The values for different polymers, A assessed by the Eq. (4.6) is about 2.5 A. The same distance, which a segment passes at shearing, when it occupies the position, shown in Fig. 4.1 b, that can be simply calculated from purely geometrical considerations. Hence, this assessment also indicates no reasons for assuming any sufficient free path length of dislocations in polymers rather than transition of a segment (or several segments) of macromolecule from one quasiequilibrium state to another [31]. 

The polymers physical aging represents itself the structure and properties change in time and is the reflection of the indicated materials thermodynamically nonequilibriiun nature [61, 62], As a rule, the physical aging results to polymer materials brittleness enhancement and therefore, the ability of structural characteristics in due course prediction is important for the period of estimation of pol5mier products safe exploitation. For cross-linked polymers the quantitative estimation of structure and properties changes in physical aging process was conducted in Refs. [63, 64] within the frameworks of fracture analysis [65] and cluster model of polymers amorphous state structure [7, 66]. The authors of Ref. [67] use the indicated theoretical models for the description of PC physical aging. Besides, for PC behavior closer definition in the indicated process such theoretical notions were drawn as structure quasiequilibrium state [68] and the thermal cluster model [69], which is one from variants of percolation theory. 

As it has been shown in Ref. [70], the value p.j. in the general case is a function molecular mobility level of polymer and p.j. > P, where P is the corresponding critical index of percolation cluster, the fomation oiwhich is controlled by geometrical interactions only [31]. The equality p.. = P is reached only in the case of completely inhibited molecular mobility., that is, in the case of quasiequilibrium state. 

Let us estimate further the value (p j at quasiequilibrium state reaching. This can be conducted according to the Eq. (10.31), determining the value = Pp as follows [32] ... 

Within the frameworks of the cluster model (p j estimation can be fulfilled by the percolation relationship (the Eq. (4.66)) usage. Let us note, that in the given case the temperature of polymers structure quasiequilibrium state attainment, lower of which (p j value does not change, that is, [32], is accepted as testing temperature T. The calculation (p j results according to the Eq. (4.66) for the mentioned above polymers are adduced in Table 15.2, which correspond well to other authors estimations. 

Actually, this equilibrium is never realized rigorously because of the presence of termination (and other side reactions that can affea the active chain concentration [P ]). It is a quasiequilibrium state in which eqn [2] only approximately holds when the rates of activation and deaaivation are much larger than those of termination (and other side reactions). 

Figure 6.43 The dependences of the fractal dimension d for structure of the quasiequilibrium state on the value of for epoxy polymer EP-3. 1 - the experimental data (Equation 5.4) 2 - calculation according to Equations 5.72, 5.73 3 -calculation according to Equations 5.49, 4.8 4 - approximation d = 2.5 [101]...

Adiabatic Calorimetry. An adiabatic calorimeter is, in principle, a straightforward device in which specific heat capacity is directly measured (Fig. 11). The temperature of the sample guard is controlled to be equal to that of the sample at any time. Under these conditions, there is no net heat flow between sample and sample guard, and all the energy delivered to the sample via the sample heater is effective in raising the temperature of the sample. If the temperature increase is small, the sample may be assumed to be in a quasiequilibrium state and the speciflc heat capacity can be directly calculated from the measured values of electrical energy, temperature increment, and sample mass. 

Although simple in concept, the adiabatic calorimetry method has numerous experimental problems associated with it. It is always difficult to match temperatures between a sample and its surrounding guard, which is especially critical in heat-capacity measurements. Furthermore, it is necessary to calibrate the specimen container. Both continuous and controlled step-change heating modes are employed, but both tend to be very slow as a quasiequilibrium state must be laboriously established at each temperature of interest. Finally, with polymer samples there may be problems in suitably casting or molding an electrical heater in the specimen. 

The proposed kinetic methods of the determination of the nitrate melt acidities are based on measurements of the rate of this reaction the rate of NO2 evolution from the melt depends only on their acidity. Further, during the course of reaction [9.2.45], the concentration of NO2 cation decreases this causes decrease in the rate of NO2 evolution. Finally, the latter becomes so slow that a series of sequential measurements of pO demonstrate that this parameter remains practically constant, i.e., the system passes to quasiequilibrium state. The pO value measured under these conditions is the upper limit of the melt acidity, which is independent of the composition of the added strong acid. This explains thermal dependence of the upper limit of acidity for nitrate melts observed elsewhere." The rise of the melt temperature results not only in the decrease of cation NO2 stability but also in the increase of the rate of reaction [9.2.45]. 

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