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By Whittaker E.T.
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E. Evans and R. Skalak, Mechanics and Thermodynamics of Biomembranes (CRC Press, Boca Raton, 1980). 11. G. de Gennes and C. Taupin, J. Phys. Chem. 86, 2294 (1982). 12. Physics of Complex and Supermolecular Fluids, eds. A. A. Clark (John Wiley and Sons, New York, 1987). 13. Physics of Amphiphillic Layers, eds. J. Meunier, D. Langevin, and N. Boccara (Springer-Verlag, Berlin, 1987). 14. H. Fendler and P. Tundo, Acc. Chem. Res. 17, 3 (1984). 15. A. Blumstein, R. H. Vanderspurt, J. Colloid Interface Sci.
Above the (x, y) plane can be regarded as distinct (d = 2)-dimensional phases; the lines of steps separating them then correspond to (d = 1)-dimensional interfaces. Thus we have a two-dimensional system of dimensions, say, Lx × Ly , consisting of many asymptotically parallel but thermally ﬂuctuating interfaces. If the mean spacing of the steps/interfaces is ¯, the slope of the corresponding vicinal surface is just q ≡ (dz/dx) = a/¯l. 39) Since q varies microscopically along the proﬁle we need to know how the tension, Σ, of the vicinal face depends on q.
15). The resolution of the paradox lies in recognizing that the underlying bulk crystal eﬀectively imposes a periodic potential on the interface which is, thus, no longer truly free. 16) where p = 2π/a⊥ corresponds to the interlayer periodicity of the crystal normal to the face in question. Does such a perturbation change the wandering behavior? g. Ref. 22). 17) evaluated at the critical point in question satisﬁes the criterion ωX < d . 18) If ωX > d the perturbation is irrelevant; at ωX = d it is marginal.