Free energy surface excess

Since the surface areas of metal nanoclusters are enormous relative to their masses, they have an excess surface free energy comparable to the lattice energy, making them... 

The enormous surface area-to-volume ratio of nanopaiticles leads to excess surface free energy that is comparable to the lattice energy leading to structural instabilities. The nanoparticles have to... 

The free energy change can be altered by addition of excess surface free energy. 

It is clear from this equation that the solubility of a solid will increase exponentially with increasing surface area. For most solids, including carbonates, the influence of excess surface free energy is not large for particles unless they are under 0.1 microns in diameter (see Figure 2.6). It is important, however, to remember that... 

Here t is the unit tangent along C and t X k is drawn outward. Two kinds of displacement must be considered the virtual displacement, Sx, required for the element of virtual work, which is of a mechanical nature, and the actual boundary displacement, 8 x, which corresponds to the actual increase in area and applies to the free energy relationships. Since the identical parameter y appears in both types of work, it is demonstrated that y is simultaneously surface tension and possesses excess surface free energy properties. 

When a solution is in contact with another phase, the composition of the interphase is different from that of the bulk in such a manner as to minimize the excess surface free energy, y. 

To obtain WOg(cr) in a form soluble in the calorimetric solution, Spitsyn and Patsukova dehydrated H2W0 (cr) at the relatively low temperature of 250"C. The resulting WOg(cr) was a very fine lemon-yellow powder which may have excess surface free energy compared with the JANAF standard state. The latter is WO formed at high temperature in a calorimetric bomb. The actual enthalpy of formation of tungstic acid should be less negative if this effect is significant. 

It is also clear from Equation (5.2) that surface or interfacial tension - that is, the force per unit length tangential to the surface, measured in units of miUinewtons per metre - is dimensionally equivalent to an energy per unit area measured in millijoules per square metre. Eor this reason, it has been stated that the excess surface free energy is identical to the surface tension, but this is tme only for a single-component system - that is, a pure liquid (where the total adsorption is zero). 

The excess surface free energy per unit area of a plane-parallel him of thickness h is 54... 

Solids and liquids will always tend to minimize their surface area in order to decrease the excess surface free energy. For liquids, therefore, the equilibrium surface becomes curved, where the radius of curvature will depend on the pressure difference on the two sides of the interface and on the surface tension. Remember that we have considered the surface tension as a surface pressure exerted tangentially along the surface. Now we will also consider the role of the external and internal pressures that act normal to the interface on the properties of the surface. 

For nanomaterials, the excess surface free energy should be taken into consideration for the chemical potential, as shown in Eq. 6.5 ... 

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

FIGURE 2.4. The excess surface free energy of newly formed surface will depend on the nature of the new phase it contacts, (a) If the new surface contacts a vacuum, the excess free energy will be maximized, (b) If another phase is present (liquid or gas) the excess surface energy will be reduced by an amount depending on the new interactions. 

Surfactant molecules adsorb from a solution on hydrophobic solid-liquid (SL) and liquid-vapor (LV) interfaces, modifying the interfacial tensions (or excess surface free energies) of the SL and LV interfaces and contact angle. 

The gap between two colliding particles (bubbles, droplets, solid particles, surfactant micelles) in a colloidal dispersion can be treated as a film of uneven thickness. Then, it is possible to utilize the theory of thin films to calculate the energy of interaction between two colloidal particles. Deijaguin [276] has derived an approximate formula which expresses the energy of interaction between two spherical particles of radii and i 2 through integral of the excess surface free energy per unit area, f h), of a plane-parallel film of thickness h [see Eq. (161)] ... 

The driving force for sintering (a reduction in excess surface free energy) is translated into a driving force that acts at the atomic level (thus resulting in atomic diffusion) by means of differences in curvature that inherently occur in different parts of the three-dimensional compact. These differences in curvature create chemical potential and vacancy concentration differences, and thus control the direction of matter transport. The relationship that links surface energy, curvature and concentration differences is the Gibbs-Thomson equation ... 

As is the case for simple emulsions, multiple emulsions are thermodynamically unstable due to the excess free energy associated with the surface of the emulsion droplets. The excess surface free energy arises as a result of the cohesive forces between the molecules of an individual liquid being greater than the adhesive forces between the liquids (Banker and Rhodes, 1979 Martin et al., 1993). On dispersion, the interfacial area of the dispersed phase liquid increases considerably compared to that of the continuous phase liquid. Consider the interfacial free energy (1.1) associated with the interface between two immiscible liquids ... 

Excess surface free energy and surface tension of liquids... 

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. 

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