Critical unbinding transition

The role of undulation on the equilibrium of lipid bilayers was also examined by Lipowsky and Leibler,18 who used a nonlinear functional renormalization group approach, and by Sornette,14 who employed a linear functional renormalization approach. It was theoretically predicted that a critical unbinding transition (corresponding to a transition from a finite to an infinite swelling) can occur by varying either the temperature or the Hamaker constant. However, the renormalization group procedures do not offer quantitative information about the systems, when they are not in the close vicinity of this critical point. 

In Figure 7 we present the free energy for an asymmetric Gaussian distribution (a = 1.4) as a function of distance for various values of the Hamaker constant (with all the other parameters unchanged). For H > 3.825 x 10-21 J, a stable minimum is obtained at a finite distance. For H < 3.825 x 10 21 J, the stable minimum is at infinite distance however, for 3.825 x 10-21c7 > H > 3.45 x 10-21 J, a local (unstable) minimum is still obtained at finite distance. For H = 3.825 x 10-21 J, a critical unbinding transition occurs, since the minima at finite and infinite distances become equal. However, these two minima are separated by a potential barrier, with a maximum height of 1.68 x 10 7 J/m2, located at a separation distance of 90 A. The results remained qualitatively the same for any combination of the interaction parameters. 

Fig. 6.36 Phase diagram calculated using SCFT for a blend of a symmetric diblock with a homopolymer with fl = 1 (see Fig. 6.32 for a blend with a diblock with / = 0.45) as a function of the copolymer volume fraction

The question arises as to the nature of the unbinding transition. There are two possibilities. As the temperature is raised, the wavelength of the lamellar phases increases continuously and finally diverges at some temperature, or the wavelength jumps dis-continuously to infinity at the transition. The former is denoted critical unbinding [170], the latter, first-order unbinding. In principle, either can occur [171]. This question was studied [82] for a particular system of a symmetrical (/ = 1/2) AB diblock copolymer in a solvent of A homopolymer of equal polymerization index. The result is that the... 

The RANI model remains less understood compared to the random medium problem. Exact renormalization analysis establish the marginal relevance of the disorder at d = 1, indicating a disorder dominated unbinding transition in d > 1. Several features including a generalization of the Harris criterion for this criticality via relevant disorder and aspects of unzipping have been discussed. 

Lipid membranes in a stack are bound together by attractive van der Waals forces. A systematic theory for the interplay of attractive forces and entropic repulsion leads to the theoretical prediction of a critical adhesion or unbinding transition. Such a transition was experimentally observed by Wolfgang Helfrich and Michael Mutz for stacks of sugar lipid membranes. 

Since the beta function is exact, we have obtained the exact correlation length scale exponent for the binding-unbinding critical transition. 

For a macroscopicly large slit of width L, capillary condensation is a first-order transition. The shift of the liquid-vapor coexistence curve P = Pi/l(.T) in the capillary relative to the bulk pressure P = Po(T ) is described by the Kelvin equation 8P = Po(T ) — i/t(f) 1/L. In the case of capped capillaries with a finite depth D and width L, capillary condensation becomes a continuous phase transition. There is a power law with corresponding critical exponents characterizing the unbinding of the meniscus from the bottom of the capped capillary if the pressure P approaches the... 

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