Landau theory of phase transitions

Toledano J-C, Toledano P (1987) The Landau theory of phase transitions. World Scientific, Singapore... 

Kuchanov SI, Panyukov SV (2006) A new look at the Landau theory of phase transitions in polydisperse heteropolymer liquids (paper to be published)... 

This relation is analogous to the equation of state for spin systems in the famous Landau theory of phase transitions. It reads, H = A0(T — Tc)t]/ + u0ij/3, where H is a magnetic field and i// is an order parameter, A0 and u0 being constants. In our problem, the left hand side of Eq. (2.41), which is a function of T and corresponds to H in spin systems. On the right hand side, the coefficient Vic — Vi which is determined by the degree of ionization, corresponds to the temperature parameter A0(T — Tc) in spin systems. Therefore, at yt = yu, we find T — Tc cc — c a with 8 = 3 near the critical point of ionic gels, where T— Tc plays the role of H in spin systems. 

One sfrategy is phenomenological and rooted in the Landau theory of phase transitions. The basic idea is to assert that the homogeneous free energy density... 

Obviously the enthalpy expression x a b in Eq. (3) neglects any correlation effects in the occupancy of lattice sites the probability that on neighboring lattice sites A-B-pairs occur is simply taken as the product < >A< >B of the respective volume fractions. This is a special case of a mean-field approximation (MFA), which is known to yield a critical behavior described by the Landau theory of phase transitions [100], which differs from the correct critical behavior expected [73,74] in the universal regime close to the critical point Xcrm 4>cri in Fig. 2. We shall discuss these various types of critical behavior in Sect. 2.2. 

The behaviour of the effective activation energy can be predicted from the Landau theory of phase transitions. According to it, for a second-order transition, the temperature dependence of the relaxation time is given by [48] ... 

One can make the analysis a bit more quantitative by using the well-known Landau theory of phase transition where one expands the free energy F in terms of fluctuation in the order parameter as... 

Equations (10.38) and (10.39) give a nonlinear integro-differential equation for W, and its mathematical handling is not easy. A guidance of how to proceed is obtained from the phenomenological theory in nematics. De Gennes showed that the dynamics of nematics is essentially described by the Landau theory of phase transition and proposed a phenomenological nonlinear equation fof the order parameter tensor... 

DYNAMICAL FLUCTUATIONS THE ALLOY ANALOGY AND THE LANDAU THEORY OF PHASE TRANSITIONS... 

A new approach based on the phenomenological Landau theory of phase transitions has now been developed to identify physical quantities associated with order parameters (rf) that might drive the isostructural transformation according to the free energy expansion (F(t/)) [81] ... 

Fig. 4.10 a V/Vq plot for BagSi4 as a function of pressure (points) along with a third-order Birch-Mumaghan equation of state (line). The macroscopic order parameter corresponds to spontaneous i c., the Variation of the volume cmrected from the compressibility, b Aspo ,a eous as a function of pressure fits with the theoretical analysis based on the Landau theory of phase transition null before the transition pressure, a jump at the transition and a square-root evolution after the transition. Such a behaviOT is also observed for Si atomic displacement parameters that can be used as microscopic order parameter [82]. The correlation between these physical quantities underlines the relationships between the isostructural transition and disordering of the Si sub-lattice... 

The electroclinic or soft mode effect could be explained within the framework of the Landau theory of phase transitions [4]. We can write the expansion of the free energy density g of smectic A up to the 0 term as follows ... 

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