Surface free energy defined

It is 0 (n) that accounts for the energy contribution of the nucleus-substrate and the nucleus-solution interface boundaries and has the physical meaning ofthe concept surface free energy defined in this general form by Stranski in 1936 [1.12, 1.13]. 

The integral A/, while expressible in terms of surface free energy differences, is defined independently of such individual quantities. A contact angle situation may thus be viewed as a consequence of the ability of two states to coexist bulk liquid and thin film. 

The excess energy associated with an interface is formally defined in terms of a surface energy. This may be expressed in terms either of Gibbs, G, or Helmholtz, A, free energies. In order to circumvent difficulties associated with the unavoidably arbitrary position of the surface plane, the surface energy is defined as the surface excess [7,8], i.e the excess (per unit area) of the property concerned consequent upon the presence of the surface. Thus Gibbs surface free energy is defined by... 

This is defined as the surface free energy per unit area projected onto the low index facet plane. The use of the projected free energy allows a direct analogy with the thermodynamics of a liquid-vapor system. See, e.g., Williams et al. for a clear discussion. 

The interface between two fluids is in reality a thin layer, typically a few molecular dimensions thick. The thickness is not well defined since physical properties vary continuously from the values of one bulk phase to that of the other. In practice, however, the interface is generally treated as if it were infinitesimally thin, i.e., as if there were a sharp discontinuity between two bulk phases (LI). Of special importance is the surface or interfacial tension, a, which is best viewed as the surface free energy per unit area at constant temperature. Many workers have used other properties, such as surface viscosity (see Chapter 3) to describe the interface. 

Surface Tension. Testing for surface tension is sometimes referred to as the contact-angle test (see Fig. 13.6). Surface free energy is defined by surface tension which is directly related to surface cleanliness. If an adsorbate (dirt) is present on a surface, the free energy-surface tension is reduced as energy is spent in bonding the adsorbate to the surface. In other words, the surface has become less clean... 

For a pure substance, we will represent the surface free energy per unit surface area1 as gs and define it as (dG/dA%)T p . Thus... 

There is also an interesting relation between AG and the surface free energy, y, defined by Gibbs [cf. Equations 514 and 675 of (6) ]. 

Surface Tension The contracting force per unit length around the perimeter of a surface. This force is usually referred to as surface tension if the surface separates gas from liquid or solid phases, and interfacial tension if the surface separates two nongaseous phases. Although not strictly defined the same way, surface tension can be expressed in units of energy per unit surface area. For practical purposes surface tension is frequently taken to reflect the change in surface free energy per unit increase in surface area. 

The contraction of the surface is spontaneous that is, it is accompanied by a decrease in free energy. The contracted surface thus represents a minimum free energy state and any attempt to expand the surface must involve an increase in the free energy. The surface free energy of a liquid is defined as the work, tv, required to increase the surface area A by 1 m ... 

A nanoparticle exposed to vacuum or a gas is less stable than a bulk coarse grained material. A surface free energy can be defined in terms of surface enthalpy and entropy contributions. 

A more precise picture of an SLP distribution in a porous network raises serious theoretical problems because of the difficulty in defining analytically the pore structure. Thermodynamically the total-surface free energy is compounded from contributions from three interfaces (19), where A is the total support... 

Second, in thermodynamics it is more common to define surface tension in terms of work or the amount of energy needed to increase the surface with one unit area (i.e., the energy needed to bring a certain amount of molecules from the bulk to the surface). In this context the surface tension has a character of a surface free energy per unit area. The latter definition is in fact equivalent to the unit force per unit length (i.e. Nmjvr = NIm). The energy interpretation is by many researchers in thermodynamics considered the more fundamental one, and thus this interpretation is usually adopted for theoretical derivations. The surface tension is then defined as [1] [166] ... 

Critical Micelle Concentration and Kraff Point Another important characteristic of a surfactant is critical micelle concentration (CMC). CMC is defined as the concentration of surfactants above which micelles are spontaneously formed. Upon introduction of surfactants (or any surface active materials) into the system, they will iifitiaUy partition into the interface, reducing the system free energy by (a) lowering the energy of the interface (calculated as area times surface tension) and (b) removing the hydro-phobic parts of the surfactant from contact with water. Subsequently, when the surface coverage by the surfactants increases and the surface free energy... 

In Table 5.4 we summarize the expressions for the surface free energy, F, and chemical potential pij, for several thermodynamic models of adsorption. We recall that the parameter F is defined in different ways for the different models. On the other hand, the parameter K is defined in the same way for all models, specifically by Equation 5.3. The expressions in Tables 5.2 through 5.4 can be generalized for multicomponent adsorption layers. - ... 

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