Phase transitions, nonequihbrium

I. Jensen, R. Dickman. Nonequihbrium phase transitions in systems with infinitely many absorbing states. Phys Rev E 45 1710-1725, 1993. 

The evolution Eq. 13 of the order parameter has a similar form to the time-dependent Landau equation [17], which is fundamental in nonequihbrium phase transitions. The asymptotic value of the order parameter 4>i,oo is determined as the zero of the velocity 4>i- The main difference from the standard model of phase transitions lies in the time dependence in the coefficients Ait) and B(t) induced by that of the achiral concentration ait) and the total chiral concentration qft). Because the concentrations a and q are nonnegative, A(t) cannot exceed Bit) Ait) < Bit). 

In transferring from the precritical to the supracritical modes, the system symmetry changes spontaneously by analogy with thermodynamic phase transitions. This is why the transitions to form spatial dissipative structures in nonequihbrium systems are sometimes referred to as kinetic phase transitions. 

In conclusion, it should be also said that the origin of the hysteresis loop of the adsorption—desorption isotherms of porous polymers is stiU debated and can be interpreted in different ways. For example, there exists an opinion that hysteresis is not related to traditional capillary condensation in the pores, but may be a consequence of the out-of-equihbrium character of phase transitions in real disordered mesoporous polymers [255]. A failure to reach equilibrium under the given experimental conditions may be caused by the slow diffusion rate of the sorbate [256] or slow swelling of the polymeric sorbent on adsorption and slow relaxation of its swollen structure on desorption. Quite often, a subsequent adsorption on the same material results in larger adsorption capacity values. It is the so-called conditioning effect [256] that may imply a nonequihbrium character of the process. Even the reproducibihty of the shape and location of a hysteresis loop of the isotherms may indicate the estabhshment of fast... 

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