Transition, first-order cooperativity

Fig. 18. Heat capacity of a cooperative system as a function of the excess energy on aggregation. The critical temperature of a First order transition is reached with the last curve (parameter = 454). The parameter 0 corresponds to an isolated hindered rotator. Curves after data of Ref.ll0b)...

Conformational changes in biopolymers are commonly described by a model that has been derived by an application of the one-dimensional Ising model to the problem of cooperative transitions from random coil states into ordered mostly helical conformations of (homo)biopolymers (see e.g. Cantor and Schimmel, 1980). Although the threshold is mostly of the cooperative transition type, landscapes can be constructed for which the threshold corresponds to a first order phase transition. 

Both spin-crossover transitions (HS < LS, FO LS) are first order accompanied by definite jumps of populations, while the cooperative Jahn-Teller transition (HS FO) is weak first-order (very close to a second-order transition). It suggests a possibility of observation of hidden cooperative Jahn-Teller transition (the broken line in Fig. 7) between the metastable HS and FO phases, if the HS phase could be supercooled enough below the spin-crossover transition temperature Tc by a rapid cooling. 

Some complexes show a strong interdependence between crystal structure and spin-transition features. In the series of compounds [Fe(Rtz)6](BF4)2 (Rtz = 1-alkyltetrazole) the spin crossover behavior varies with the substituent R and is strongly influenced by cooperative effects. For example, the propyl derivative shows a quantitative spin transition, which is accompanied by a first-order crystallographic phase transition in the methyl and ethyl derivatives the Fe11 complexes occupy two nonequivalent lattice sites, only one of which shows a thermal spin transition.29... 

From the ratio AHyu/AHcai, the cooperative unit size (CUS) (in molecules) can be determined. The CUS is a measure of the degree of intermolecular cooperation between phospholipid molecules in a bilayer for a completely cooperative, first-order phase transition of an absolutely pure substance, this ratio should approach infinity, whereas for a completely noncooperative process, this ratio should approach unity. Although the... 

An extreme case that has received attention is that of a cooperative conformational transition examplified by the coil-helix (c h) transition that occurs in poly-a-aminoacids. Whereas the polypeptide chain is quite flexible when it exists as a random coil, the rigid helical form may bring about formation of a liquid crystalline phase, as discussed above, if its concentration is sufficient. The conformational transition and the phase transition may therefore be coupled. The helix-coil transition may then acquire the character of a first-order phase transition, owing to generation of the liquid crystalline phase. 

This conclusion was reached, tentatively, by Frenkel, Shaltyko and Elyashevich A phenomenological analysis presented by Pincus and de Gennes predicted a first-order phase transition even in the absence of cooperativity in the conformational transition. These authors relied on the Maier-Saupe theory for representation of the interactions between rodlike particles. Orientation-dependent interactions of this type are attenuated by dilution in lyotropic systems generally. In the case of a-helical polypeptides they should be negligible owing to the small anisotropy of the polarizability of the peptide unit (cf. seq.). Moreover, the universally important steric interactions between the helices, regarded as hard rods, are not included in the Maier-... 

A theoretical treatment has recently been carried out by the author in collaboration with Matheson along the lines discussed above with appeal only to the spatial requirements of hard rods as represented in the lattice model, orientation-dependent interactions being appropriately ignored. The two transitions, one conformational and the other a cooperative intermolecular transition, are found to be mutually affected each promotes the other as expected. The coil-helix conformational transition is markedly sharpened so that it becomes virtually discrete, and hence may be represented as a transition of first-order. These deductions follow from the steric interactions of hard rods alone intermolecular attractive forces, either orientation-dependent or isotropic, are not required. 

The square tiling model has some attractive features reminiscent of real glasses, such as cooperativity, a relaxation spectrum that can be fit by the KWW equation, and a non-Arrhenius temperature-dependence of the longest relaxation time (Fredrickson 1988). However, the existence of an underlying first-order phase transition in real glasses is doubtful, and the characteristic relaxation time of the tiling model fails to satisfy the Adam-Gibbs equation. 

Furthermore, the 2d RPM also yields a tricritical point, which, however, has a different physical basis [100], Here, tricriticality is founded on the insulator-conductor transition, which changes from second to first order. Notably, in real ionic solutions the conductivity shows two points of inflection one at low densities, which corresponds to the conductor insulator transition in 2d, and one near the criticality [38], Although accompanied by a maximum of the specific heat [68, 69], those changes of the conductivity are soft transitions determined by the mass action law and not cooperative A-transitions, required to allow for a tricritical point. 

The phenomenon of hysteresis is encountered in many areas of physics. It is associated with the delay of the dynamic response of cooperative systems to external perturbation. During a heating-cooling process in a system, thermal hysteresis (TH) commonly appears accompanying phase transitions. In particular, it is regarded as a signature of the first-order phase transition. But, the TH is less known than the magnetic hysteresis (MH), which is another type... 

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