Specific excess surface energies

Second-order stress is difficult to observe and much less extensively studied. The causes of internal stress are still a matter for investigation. There are broad generalisations, e.g. frozen-in excess surface energy and a combination of edge dislocations of similar orientation , and more detailed mechanisms advanced to explain specific examples. 

The specific free surface energy of a material is the excess energy per unit area due to the existence of the free surface it is also the thermodynamic work to be done per unit area of surface extension. In liquids the specific free surface energy is also called surface tension, since it is equivalent to a line tension acting in all directions parallel to the surface. 

The units for surface tension and specific excess surface free energy are dimensionally equivalent and, for a pure liquid in equilibrium with its vapor. 

When the formation of new liquid surface is done reversibly and isothermally, the work needed to increase the liquid surface area by unity is called the specific excess surface free energy or, frequently, the specific surface free energy, having units J m and symbol 7 (specific here means per unit area). This is not the total energy of the molecules in unit area of the surface region (see section 7.3), but the excess which the molecules have over those in the bulk by virtue of being in the surface region. 

Stretching a solid changes both the surface area a and the specific excess surface free energy 7 . For a one-component, isotropic solid, let dw be the reversible isothermal work needed to extend the surface area by da. Then, if the surface is stretched in the same proportion in all directions ... 

The excess heat of solution of sample A of finely divided sodium chloride is 18 cal/g, and that of sample B is 12 cal/g. The area is estimated by making a microscopic count of the number of particles in a known weight of sample, and it is found that sample A contains 22 times more particles per gram than does sample B. Are the specific surface energies the same for the two samples If not, calculate their ratio. 

For example, if the property in Figure 7.13 was G and the dividing surface was placed so that the two shaded regions would be equal, then there would be no surface excess G The last term in Equation (30) would be zero. The Gibbs free energy is convenient to work with, however, so such a choice for x0 would not be particularly helpful. Until now we have not had any reason to identify the surface of physical phases with any specific mathematical surface. We had not, that is, until Equation (44) was reached. Now things are somewhat different. 

From the texturological point of view, formation of crystallizing PMs is different because of the existence of nucleation stages at each phase transformation, usually more than one. As a result each nucleation gives a new maximum value of specific surface area, which can only decrease until the next transformation. A set of successive phase transformations including both wet and dry stages is characteristic for numerous PMs. Thus, each new phase transformation starts with the maximum possible surface area with its successive decrease directed by the necessity to decrease excess free energy. 

The first test of this model is whether D is inversely proportional to the shear stress. This is indeed the case (Van der Linden et al. 1996). The second part of the test is to verify the proportionality constant, 4aeff. This effective surface tension, Oeff, has been calculated as follows (Van der Linden and Droge 1993). The effective surface tension is defined as the energy needed to deform a lamellar droplet, divided by the excess surface area needed to induce that specific deformation. Hence, one first needs to calculate the deformation energy for a given deformation and secondly divide that by the concomitant excess surface area. 

The first order wetting transition may occur if (-dfs/d< ))s does not change its sign when ( ) is varied. Then (-dfs/d< ))s may intersect the trajectory -2kV< )(< )) in a specific way depicted in Fig. 14b. Only two, out of four, intersection points — <]>ls and 2s - correspond to locally stable solutions of the variational problem. They describe two surface excess layers (see Fig. 14a) exhibiting partial (<]>1<( )ls t>2) and complete wetting (< )1<([)2 t>2s), respectively. The excess free energy Fe of these two composition profiles may be calculated with Eq. (27). Their energy differs by AFe presented in terms of the areas Sj and S2 in Fig. 14b ... 

Surface Tension. The presence of an interface between two phases goes along with an excess free energy that is proportional to the interfacial area. For a clean fluid interface the specific interfacial free energy (in J m 2) equals the surface or interfacial tension (in N-m-1). This is a two-dimensional tension acting in the direction of the interface, which tries to minimize the interfacial area. The surface tension of a solid cannot be measured. 

The excess concentration Ti of the adsorbed component i may also be called the surface coverage of i in imits of molecitles/cm. Eqiration (8) shows that the specific sitrface free energy is only equal to the sitrface energy y, if the sum over all chemical potentials on the r.h.s. of Eq. (8) is zero for a one-component system this reqitires Tj = 0. In other words, for a clean sitrface, free of adsorbates, the first layer of the substrate has no surface excess, hence f = y. 

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