Transition homogeneous

The existence of metastable states is caused by the activation character of the initial stage of a first-order phase transition. Homogeneous nucleation determines the upper boundary of the liquid superheat and supercooling. The appearance of a viable new-phase nucleus in a metastable liquid is connected with the performance of the work IT. determined by the height of the thermod5mamic potential barrier, which is to be overcome for the subsequent irreversible growth of a new phase. The dimensionless complex W, k T, where kg is the Boltzmann constant and T is the temperature, is the stability measure of the metastable phase. ... 

Liquid and vapor phases have in common that they deform and move when a shear stress is applied these states are often referenced together as fluid phases. The different regions are separated by lines which mark the phase transitions. Homogeneous (one phase) and heterogeneous regions, where two or even three phases coexist (e.g., at the triple point), can be distinguished. 

If the probability Tik(co) of absorption or emission of radiation with frequency a> causing a transition Ek is equal for all the molecules of a sample that are in the same level i ,, we call the spectral line profile of this transition homogeneously broadened. Natural line broadening is an example that yields a homogeneous line profile. In this case, the probability for emission of light with frequency u> on a transition with the normalized Lorentzian profile L (o—u>o) and central frequency coq is given by... 

Figure C3.5.9. Contributions to the homogeneous linewidth of a C=0 stretching transition of W(CO)g (Q 2000...

We consider a finite space, which contains the NA sample and is in contact with a bath of water or water vapor. That allows one to maintain the r.h. in the experimental space at a constant level and change it when necessary. Such a scheme corresponds to the real experiments with wet NA samples. A NA molecule is simulated by a sequence of units of the same type. Thus, in the present study, we consider the case of a homogeneous NA or the case where averaging over the unit type is possible. Every unit can be found in the one of three conformational states unordered. A- or B- conformations. The units can reversibly change their conformational state. A unit corresponds to a nucleotide of a real NA. We assume that the NA strands do not diverge during conformational transitions in the wet NA samples [18]. The conformational transitions are considered as cooperative processes that are caused by the unfavorable appearance of an interface between the distinct conformations. 

The conformational transitions in the presented model take place accord-itig to the all-or-nothing law, i.e. they occur at the certain r.h. value. The same behaviour has been observed, for example, for the helix-coil transition of the model double-stranded structure A(pA)i7-U(pU)i7 [24]. It is worth noting that this structure is homogeneous, the same is supposed in our model. 

Likewise, quantum mechanical calculation succeeds in giving a theoretical explanation of some facts that the resonance theory could not explain, for example, why bis(pyridine-2)monomethine cyanine and bis(pyridine-4)monomethine cyanine possess the same lowest energy transition contrary to the 2,2 - and 2,4 -quinoline monomethine dyes, together with a molecular coefficient extinction lower than that of the 4,4 -quinoline dye (11). Calculation shows also that there is no theoretical reason for observing a relationship between and pK in a large series of dyes with different nuclei as it has been postulated, even if limited observations and calculations in short homogeneous series could lead to this conclusion (105). 

Homogeneous alloys have a single glass transition temperature which is determined by the ratio of the components. The physical properties of these alloys are averages based on the composition of the alloy. 

Rate of polymerization. The rate of polymerization for homogeneous systems closely resembles anionic polymerization. For heterogeneous systems the concentration of alkylated transition metal sites on the surface appears in the rate law. The latter depends on the particle size of the solid catalyst and may be complicated by sites of various degrees of activity. There is sometimes an inverse relationship between the degree of stereoregularity produced by a catalyst and the rate at which polymerization occurs. 

Below a certain critical temperature, which varies with pressure and stoichiometry, cool flames for several hydrocarbons propagate from the wall inward above this temperature, they propagate from the center of the vessel (78). This transition is interpreted as evidence for a changeover from a predominantly heterogeneous preflame mechanism to a homogeneous one. 

G. N. Schrauzer, ed.. Transition Metals In Homogeneous Catalysis, Marcel Dekker, Inc., New York, 1971. 

G. W. ParshaH, Homogeneous Catalysis The applications and Chemistry of Catalysis by Soluble Transition Metal Complexes,Johm. Wiley Sons, Inc., New York, 1980, 240 pp. An excellent treatment of catalysis by coordination compounds. 

Polymerization of olefins such as styrene is promoted by acid or base or sodium catalysts, and polyethylene is made with homogeneous peroxides. Condensation polymerization is catalyzed by acid-type catalysts such as metal oxides and sulfonic acids. Addition polymerization is used mainly for olefins, diolefins, and some carbonyl compounds. For these processes, initiators are coordination compounds such as Ziegler-type catalysts, of which halides of transition metals Ti, V, Mo, and W are important examples. 

The expressions provide the limiting transition. When d Q for all j-phases, g rTf and the above expression transforms to the expression for a homogeneous sample. In case of the two-component powder, consisting of fluorescent and non-fluorescent par ticles, when size of the non-fluorescent par ticles d - Q, the above expression transforms to the expression for slurrylike substance (A.L. Finkelstein, T.N. Gunicheva, e. a. // X-Ray Spectrom. 1992. V. 21. p. 287-292). In case of the multicomponent powder with the equal size particles the expression transforms to the well-known Berry-Fumta-Rhodes formula. 

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