Transition, first-order Subject

Ethylene dioxytetrathiafalvulene (EDO) 445 PE6 salt shows a first-order metal insulator transition at around 280 K <2003SM643>. The subject is expanding, and plenty of other reports on such compounds have been made... 

Fig. 3. Energy level diagram for a spin f nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels. Frequency of the central transition (shown in bold lines) is independent of the quadrupolar interaction to first order, but is subject to second-order quadrupolar effects (see text).

The collagen gelatin transformation in solution has been recognized as a reversible first-order phase transition, subject to the same physical laws which govern the crystalline amorphous phase transitions observed in systems of linear polymers. The direct relationship between the transition in solution and the well-known thermal shrinkage phenomenon exhibited by collagen fibers has also been established. 

Several cautions are, however, in order. Polymers are notorious for their time dependent behavior. Slow but persistent relaxation processes can result in glass transition type behavior (under stress) at temperatures well below the commonly quoted dilatometric or DTA glass transition temperature. Under such a condition the polymer is ductile, not brittle. Thus, the question of a brittle-ductile transition arises, a subject which this writer has discussed on occasion. It is then necessary to compare the propensity of a sample to fail by brittle crack propagation versus its tendency to fail (in service) by excessive creep. The use of linear elastic fracture mechanics addresses the first failure mode and not the second. If the brittle-ductile transition is kinetic in origin then at some stress a time always exists at which large strains will develop, provided that brittle failure does not intervene. 

Note that it is not a true change in the phase transition (second order to first order). If such a change occurs, a new scaling relation appears and the curves with different N should cross at approximately the same point. This point is a particular case of critical point, called multicritical point in theory of phase transition [25], Multicritical points in few-body systems is the subject of the next subsection. 

Water exchange on first row di- and trivalent transition metal ions has been the subject of extensive experimental studies and has been widely reviewed [15, 23). Table 4.1 summarizes the experimental first order rate constants and the activation parameters. 

NADH or aldehyde) in excess of the other reactant. Under these conditions, the chemical conversion of aldehyde to alcohol occurs with a (saturated) apparent first-order rate constant of 200 to 400 sec i. This process, as measured either by the disappearance of NADH or by the disappearance of chromophoric aldehyde, has been shown by McFarland and Bernhard (80) to be subject to a primary, kinetic isotope effect ksjkj) =2 to 3 when stereospecifically labeled (4-R)-deuterio NADH is compared to isotopically normal NADH. Shore and Gutfreund (84) earlier had investigated substrate kinetic isotope effects on the pre-steady-state phase of ethanol oxidation. Their studies demonstrated that the rate of the presteady-state burst production of NADH is subject to a primary kinetic isotope effect, kulkj) 4—6 when 1,1-dideuterio ethanol is compared to isotopically normal ethanol, and that there is no primary kinetic isotope effect on the steady-state rate. It can be concluded from these studies (a) that the rate of interconversion of ternary complexes e.g., Eq. (19) above], as already mentioned, is rapid relative to turnover, and (b) that the transition-state for the rate-limiting step in the interconversion of ternary complexes involves carbon-hydrogen bond scission and/or carbon-hydrogen bond formation. 

---