Surface undulations

Fig. 6.15 Dynamic structure factor from the junction-labelled triblock copolymer for different Q-values. T=433 K filled circles Q=0.20 A y filled squares Q=0.18 A open triangles down Q=0.14 A open triangles up Q=0.114 A open circles Q=0.08 A open squares Q=0.05 A T=473 K filled circles Q=0.20 A open triangles up Q=0.10 A open circles Q=0.08 A open squares Q=0.05 A"k The solid lines are result of the fit with the complete structure factor for surface undulations and Rouse motion. (Reprinted with permission from [284]. Copyright 2002 EDP Sciences)...

Let us examine the instability oi strained thin films. In Fig. 3, thin films of30 ML are coherently bonded to the hard substrates. The film phase has a misfit strain, e = 0.01, relative to the substrate phase, and the periodic length is equal to 200 a. The three interface energies are identical to each other = yiv = y = Y Both phases are elastically isotropic, but the shear modulus of the substrate is twice that of the film (p = 2p). On the left-hand side, an infinite-torque condition is imposed to the substrate-vapor and film-substrate interfaces, whereas torque terms are equal to zero on the right. In the absence of the coherency strain, these films are stable as their thickness is well over 16 ML. With a coherency strain, surface undulations induced by thermal fluctuations become growing waves. By the time of 2M, six waves are definitely seen to have established, and these numbers are in agreement with the continuum linear elasticity prediction [16]. 

Bloom, M. and Evans, E. (1991). Observation of surface undulations on the mesoscopic length scale by NMR. In L. Peliti, ed. Biologically Inspired Physics. Plenum Press, New York, p. 137. 

The surface undulation can be erased by nonpolarized UV-light irradiation at a very low light doses (200 mJ cm ) at room temperature. Ffeating at 100°C (isotropic phase of the hybrid film) for. 30 min also erased the surface structure. 

Engelhardt, H., Duwe, H.P., and Sackmann, E. (1985) Bilayer bending elasticity measured by Fourier analysis of thermally excited surface undulations of flaccid vesicles. Journal of Physics Letters, 46 (8). L395-L400. 

Once such method of controlling the surface undulations is through stress-guided self-assembly. Stress-driven self-assembly is a promising route to either induce ripples in a desired pattern [12] or guide undulation growth such that a specific corrugation is produced [4]. 

Figure 3. Plot of surface undulations in nanometers for a film of dimenions 2562/mi2 after 5 minutes. The undulations have grown due to van der Waals driven instabilities, but, as yet, the top and bottom surfaces are still separated by the fluid layer.

We now turn our attention to the latter stages in the evolution of these ultrathin solid-fluid-solid films. At some point during the growth of the surface undulations, the top and bottom solid layers meet and fluid is expelled from... 

Figure 2. Schemes for using piezoelectric quartz crystals. A. Quartz crystal microbalance configuration, standing shear wave between facing Au electrode contacts B. Surface acoustical mode configuration, surface undulation caused by bias between metal fingers C. Horizontal shear plate mode.

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