Interface energies

Initially in ceramic powder processing, particle surfaces are created tliat increase tlie surface energy of tlie system. During shape fomiing, surface/interface energy and interiiarticle forces are controlled witli surface active additives. 

When the nucleus is formed on a solid substrate by heterogeneous nucleation the above equations must be modified because of the nucleus-substrate interactions. These are reflected in the balance of the interfacial energies between the substrate and the environment, usually a vacuum, and the nucleus-vacuum and the nucleus-substrate interface energies. The effect of these terms is usually to reduce the critical size of the nucleus, to an extent dependent on... 

Another velocity finally appears in a system where a liquid is in contact with an interface. The interface energy 7 then works as a static driving force. This can trigger a current which is damped by a dynamic force, the viscous friction, in the case of density difference between crystal and liquid. Taking the ratio... 

For a nonvolatile liquid, where transport through the gas phase is negligible, one could substitute the first term in the equation, -ysv, with -yso, which corresponds to the interface energy between the dry solid and vacuum. If 5 > 0, the liquid will wet the surface if 5 < 0, a finite contact angle will exist, determined by Eq. (1). 

From this we find that the interface energy yinterface is the same as that of the two separate surfaces... 

MV /MV " (HV is heptyl viologen and MV is methyl viologen). The specific effects of iodide on the electrochemical behavior of the layer-type compounds were compared, and the characteristics of several PEC cells were described. The interface energies for n-MoSe2 in contact with various redox couples were given as in Fig. 5.9. 

The equilibrium shape of a crystal is, as described above, a polyhedron where the size of the crystal facets is inversely proportional to their surface energy, ysg. In the present section we will consider other types of interfaces as well and we will show that the interface energies determine the equilibrium morphology of interfaces in general. 

FIGURE 3.3 Schematic of an organic-metal interface energy diagram (a) without and (b) with an interface dipole and (c) UPS spectra of metal and organic. (From Hung, L.S. and Chen, C.H., Mater. Sci. Eng., R39, 143, 2002. With permission.)... 

In addition to the previously mentioned driving forces that determine the bulk state phase behavior of block copolymers, two additional factors play a role in block copolymer thin films the surface/interface energies as well as the interplay between the film thickness t and the natural period, Lo, of the bulk microphase-separated structures [14,41,42], Due to these two additional factors, a very sophisticated picture has emerged from the various theoretical and experimental efforts that have been made in order to describe... 

In the case of t < Lo, it has been suggested that perpendicular lamellae are favored in the boundary-symmetric confined film because they avoid the entropic penalty associated with the compressed chain conformations in parallel-oriented microdomains [109]. In boundary-asymmetric substrate-supported films, various kinds of morphologies, including hybrid morphologies that combine surface-parallel and surface-perpendicular components, are predicted, as well as observed, depending on the film thickness difference and surface/interface energies [14,41,120]. 

By modifying the surface/interface energies in a periodic manner, chemically patterned surfaces have also been widely used to control the orientation of nanostructures over large areas (Fig. 6). Theoretical [138-145] and experimental [73-76,88,89,146] results have indicated that with the appropriate surface grating and boundary conditions, lateral control over nanostructures propagates microns away from the surface (deep into the film), thus providing true 3D control of the self-assembly process. Russell and coworkers [73,74]... 

Figure 4.22. Schematic of an organic semiconductor/metal interface energy diagram (a) A = 0 and (b) A 0.

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]. 

Figure 5. Isolate islands with different e under the infinite- and zero-torque conditions. The shear modulus of the substrate phase is twice that of the film (p = 2p), and all the interface energies are identical to each other. Large open arrow heads mark triple j unctions, and small solid ones indicate islands on the top of a main island.

Figure 4-2 Calculated nucleation rate for Vc = 46 x 10 m /mol, E = 250 kj/mol, A5m-c = 50 J-K -moP, Al = 5 x 10 m, the equilibrium temperature of 1500K for (a) and (b), and the equilibrium pressure of 3 GPa for (c). (a) The dependence of crystal nucleation rate on the interface energy. Note that for a small change in interface energy from 0.300 to 0.295 J/m, the peak nucleation rate increases by more than one order of magnitude. If the interface energy changes from 0.3 to 0.2 J/m, the peak nucleation rate would increase by 17 orders of magnitude, (b) The nucleation rate of crystal and melt as a function of temperature, (c) The nucleation rate of crystal and melt as a function of pressure.

The nucleation rate depends strongly on the Interface energy (Figure 4-2a). 

Homogeneous nucleation is very difficult because of the large interface energy involved. If there are already interfaces in the system, an embryo may grow from... 

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