Energy-per-unit area

The total free energy of the system is then made up of the molar free energy times the total number of moles of the liquid plus G, the surface free energy per unit area, times the total surface area. Thus... 

The interfacial free energy per unit area is given by the adhesion force Fo/lrR", estimate the Hamaker constant responsible for the adhesion force in the crossed-cylinder geometry illustrated in the inset to Fig. VI-6. 

Referring to Section V-2, the double-layer system associated with a surface whose potential is some value j/o requires for its formation a free energy per unit area or a t of... 

In this relationship. S is alkane solubility, A is the cavity surface area and a is the hydrophobic free energy per unit area. Extensive fitting of this equation [24] yields a value of 88 kJ mol A for the proportionality constant a. This value corresponds to an unfavourable free energy of about 3.6 kJ mol for the transfer of a CH2 group to aqueous solution. 

As in the qualitative discussion above, let 7 be the Gibbs free energy per unit area of the interface between the crystal and the surrounding hquid. This is undoubtedly different for the edges of the plate than for its faces, but we... 

Fracture mechanics (qv) tests are typically used for stmctural adhesives. Thus, tests such as the double cantilever beam test (Fig. 2c), in which two thick adherends joined by an adhesive are broken by cleavage, provide information relating to stmctural flaws. Results can be reported in a number of ways. The most typical uses a quantity known as the strain energy release rate, given in energy per unit area. 

The combined effect of van der Waals and electrostatic forces acting together was considered by Derjaguin and Landau (5) and independently by Vervey and Overbeek (6), and is therefore called DLVO theory. It predicts that the total interaction energy per unit area, also known as the effective interface potential, is given by V(f) = ( ) + dl ( )- absence of externally imposed forces, the equiHbrium thickness of the Hquid film... 

Here,. Ai(X) is the partial SASA of atom i (which depends on the solute configuration X), and Yi is an atomic free energy per unit area associated with atom i. We refer to those models as full SASA. Because it is so simple, this approach is widely used in computations on biomolecules [96-98]. Variations of the solvent-exposed area models are the shell model of Scheraga [99,100], the excluded-volume model of Colonna-Cesari and Sander [101,102], and the Gaussian model of Lazaridis and Karplus [103]. Full SASA models have been used for investigating the thermal denaturation of proteins [103] and to examine protein-protein association [104]. 

The toughness is the energy per unit area to grow the craze to its maximum width so assuming that the stress along the craze is constant... 

We have seen how the concept of surface energy in principle relates to adhesion. The surface energy terms discussed (e.g. Eqs. 1-8) are all energies per unit area. We now need to consider carefully what we mean by the interfacial area. 

The surface energy term Fg is of the form surface excess energy per unit area of surface (cf. Eq. 1), so may be expressed as ... 

Metabolic energy is often normalized in terms of energy per unit area of skin (1 met = 58.2 W/m ) ... 

The interface free energy per unit area fi,u is taken to be that of a planar interface between coexisting phases. Considering a solution v /(z) that minimizes Eq. (5) subject to the boundary conditions vj/(z - oo) = - v /coex, v /(z + oo) = + vj/ oex one finds the excess free energy of a planar interface ... 

Adaptations to Habitats. Because of Eaith s geom-etiyf and the position of its axis, the equator receives more solar energy per unit area than the polar regions. Because Earth s axis is tilted relative to the plane of Earth s orbit around the Sun, this angle of incident radiation varies seasonally. These factors, combined with Earth s rotation, establish the major patterns of temperature, air circulation, and precipitation. 

The Alexander approach can also be applied to discover useful information in melts, such as the block copolymer microphases of Fig. 1D. In this situation the density of chains tethered to the interface is not arbitrary but is dictated by the equilibrium condition of the self-assembly process. In a melt, the chains must fill space at constant density within a single microphase and, in the case of block copolymers, minimize contacts between unlike monomers. A sharp interface results in this limit. The interaction energy per chain can then be related to the energy of this interface and written rather simply as Fin, = ykT(N/Lg), where ykT is the interfacial energy per unit area, q is the number density of chain segments and the term in parentheses is the reciprocal of the number of chains per unit area [49, 50]. The total energy per chain is then ... 

Where the particle of B contains m molecules, AGB is the bulk free energy change per molecule, a is the shape factor (4irr2 for a spherical interface) and y is the strain energy per unit area of interface. For a spherical nucleus, where vm is the volume of product per molecule ,... 

FIG. 15 Free energy per unit area as a function of surface separation for five different values of x-The parameters are Ng = 25, p = 0.04, N = 100, and Xsurf = 0. The cartoon on the left shows the reference state, where the grafted chains form a melt between the surfaces. In the cartoon on the right, the surfaces are separated by polymers that have localized between the interfaces. (From Ref. 100.)... 

The elastic energy (per unit area) consists of three contributions [78-80] ... 

The ratio of the surface energy produced by crushing to the energy consumed by the solid is the crushing efficiency, and is represented by T c. If e, is the surface energy per unit area,... 

Let e > 0 be the energy gain per segment in the nucleus (in units of kT) and a be the lateral surface free energy per unit area. The free energy Fm>/t per chain in the nucleus of Fig. 11 is given by... 

The conditions for propagating brush discharges may be quantified in terms of the thickness of the insulating layer d,ayer and the maximum allowable capacitive energy per unit area ue (in J/nr) where... 

The surface energy of a cluster is 75, where 7 is the surface energy per unit area. For a liquid metal 7 is identical to the surface tension. The ... 

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