Energy per area

We define N as the total number of atoms, which is constant, so that the number of particles is N/n. The number of surface atoms on a given particle scales as the square of the particle radius, or as Thus, is proportional to the total surface area and scales as n [second part of Eq. (1)]. The surface energy per area (or the energy per surface atom) depends on the surface radius of curvature. The surface energy is taken to be a constant plus a term that is inversely proportional to the radius of curvature. Thus, the energy per surface atom (p — jl ) scales as C -I- where C and D are constants. Thus, we finally get Psuri = A l... 

This supplies a second definition of surface tension It equals the work per unit area required to produce a new surface. In terms of this definition, the units of 7 are energy per area — J m 2 in SI or erg cm"2 in the cgs system. 

The surface energy per area, 7, has the same units as a force per length and for some interfacial geometries can lead to an interfacial net force that is balanced by a difference in pressure between the two adjacent phases. If 7 is isotropic, this pressure difference is directly proportional to the interfacial curvature through the the Gibbs-Thomson equation (see Sections C.2.1 and C.4.1),... 

Every surface has an energy per area associated with it because molecules or atoms at a surface have different surroundings than those in the interior. The units of surface energy are J/m2. Surface tension, inN-m, is equivalent to surface energy. The work to create a surface can be thought of as a surface tension on a line, working through a distance. 

Consider the square lattice in Figure 12.3 and let the area of the surface equal 1. ForO < 0 < 90°, the number of missing vertical bonds is sin 0/a and the number of missing horizontal bonds is cos 9/a, so the total number of missing bonds is (sin 7 + cos 0)/a. Breaking these bonds creates two surfaces of total length = 2, so the surface energy per area is... 

Thus surface or interfacial tension can also reflect the change in Gibbs free energy per area, consistent with the idea that area expansion requires energy. 

De Boer had shown that, summed over the volumes of two parallel planar blocks whose separation Z was smaller than their depth and lateral extent, the —C/r6 energy became an energy per area that varied as the inverse square of the separation Z (1/Z2 for small Z) ... 

It is as though the energy per interaction between spheres is the energy per area between planes of the same materials but multiplied by a continuously varying area 2jtRiR2Z/(Ri + R2) that goes to zero as the spheres are brought into contact. 

Divide by 4jtR2 to create an energy per area kT A12A32 kT... 

For slabs of equal thickness, a = b, this energy per area is... 

Think of the interaction per unit area between two infinitesimally thin layers of A and B. N2 sin 9 is the number of rod-rod interactions per unit area in the two thin layers. Because g(l, 6) is the energy per interacting pair, N2 sin 9 g(l, 9) is an energy per area. 

Solution Feed Anam = 47 x 10 21 J, the Hamaker coefficient for tetradecane across vacuum, into the interaction energy per area — (AHam/l 2 r/2) of plane-parallel half-spaces of separation / = 3 x 1(T9 m ... 

Solution Look only at the 0-dependent part of the free energy per area G(Z, 0) multiplied by L2,... 

Thermodynamically, a solid surface is sufficiently characterized by two parameters surface energy (a scalar), with units of energy per area, and surface stress (a second-rank tensor), also with units of energy per area. For a liquid, these two are the same, but they can be very different for solids. We do not discuss the latter in this book, nor shall we distinguish between surface energy and surface tension, which is defined as the reversible work done in creating unit area of new surface. In one-component systems, surface energy and surface tension are numerically equal. 

In 1934 Derjaguin [29] published a method that transformed an additive force, F, between two curved bodies at a separation, b0, to the free energy per area between two flat surfaces, W(b0). The free energy per area, is calculated as the work to bring the two bodies from infinite separation to the actual separation, where the separation refers to the closest distance between the... 

According to the Derjaguin approximation (see Appendix B), the force between the surfaces is related to the free energy per area between two flat surfaces. Then, standard thermodynamics can be used to transform the free energy into the osmotic pressure ... 

Fig. 7. The change of free energy per area versus the change in gallery height based on the thermodynamic model presented in [26], for various surface-polymer affinities Ags=0,-2, -4 and -6 mj/m2. Both figures adopted from [26]...

The SCF [Eq. (39)] minimizes the free energy of the interfacial system. The Helmholtz free energy per area of segment for restricted equilibrium is... 

For pure particle erosion, a value of n of the order of 3 is frequently found. This can be explained by a consideration of the kinetic energy of the particles hitting the surface. The total impact energy per area unit and time unit is Vi mv. m is the sum of the particle mass per area and time unit. At constant concentration c, m is... 

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