Reduced potential energy

Mechanical compatibilization is accomplished by reducing the size of the dispersed phase. The latter is determined by the balance between drop breakup and coalescence process, which in turn is governed by the type and severity of the stress, interfacial tension between the two phases, and the rheological characteristics of the components [9]. The need to reduce potential energy initiates the agglomeration process, which is less severe if the interfacial tension is small. Addition... 

FIGURE 9.4 Reduced potential energy V (h) — Kl64nkT)V h) as a function of scaled plate separation Kh for the constant surface charge density model calculated with Eq. (9.125) for a = 0, 0.1, and 1 in comparison with V h) = (K/64nkT)V h) for the constant surface potential model calculated with Eq. (9.141). 

FIGURE 9.7 Reduced potential energy V = K/64nkT)V of the double-layer interaction per unit area between two parallel similar plates with constant surface potential as a function of the reduced distance Kh between the plates for several values of the scaled unperturbed surface potential ya = ze j/olkT. Solid lines are exact values and dotted lines represent approximate results calculated by Eq. (9.177). The exact and approximate results for To = 1 agree with each other within the linewidth. (From Ref. 13.)... 

In Fig. 13.9, we give the reduced potential energy V = (jcl64nkT)V of the double--layer interaction between two ion-penetrable semi-infinite similar membranes as a... 

FIGURE 14.10 Reduced potential energy V = 167tSrSoU/Kg of the image interaction between a hard plate (plate 1) and a hard sphere (sphere 2) of radius az with 2 = 0 as a function of kH for several values of the reduced radius ku2 of sphere 2. Solid lines = 0 dashed lines Si = ex (plate 1 is a metal). From Ref [14]. 

Taken together, the reduced potential energy and increased electron density between the nuclei demonstrate that tj/g describes a stable chemical bond, whereas i/ describes a state that is strictly repulsive everywhere and does not lead to bond formation. Therefore, we take the proper VB electronic wave function for a pair bond to be... 

Let us assume that the spectator C-F4 bond has a length X4 determined by the formation of the (QF4 H A hydrogen bond. This converts into a reduced potential energy function [761]... 

For any state (Tk, pk) the reduced potential energy U of the LJ system, when in a (reduced) configuration rw, is described by parameters s, a according to... 

Figure 6.10-1 shows a plot of the reduced potential energy cpn/sn versus the reduced distance r/ai2 Here we see the weak attraction for large separations and the strong repulsion for short separations. 

To show the effect of the collision diameter on the behaviour of the potential, we show on Figure 6.10-2 plots of the reduced potential energy versus r/a,2°, where ai2° is some reference collision diameter, and the parameter of the plot is a,2 12 = 0.95, 1, 1.1. The smaller is the collision diameter, the closer is the equilibrium position between the two atoms or molecules. 

Figure 6.10-7 Plots of the reduced potential energy versus z/a,2...

The reduced potential energy curves of the three heteroatomic pairs HeNe, HeAr and NeAr are included in Fig. 9.4. They are seen to have the same shape as the curves for homoatomic pairs. 

As mentioned in Sect. 6.2.1 (cf. Eq. 20), the accuracy of the contributions from the real and reciprocal spaces to the potential energy depends on a and Rcut and on a and cut. respectively. Figure 12 shows the absolute value of the difference between the reduced potential energy from the Ewald summation and the exact one as a function of a for fixed Kcut and ricut using an equilibrium configuration (filled symbols) and a random one but avoiding hard-sphere overlap (open symbols). The error estimates given by Eqs. 21 and 22 are also shown (curves). 

Fig. 12 Absolute truncation error of the reduced potential energy from the Ewald summation as a function of a at Rent = 13.0i M and cut = 14 using an equilibrium (filled spheres) and random (open spheres) configiuation of System IV. For a > 0.38J j, the symbols for the equilibrium and random configurations are indistinguishable. Nm = 80 and L = 32.224J m- The hard-sphere radii were retained when generating the random configuration. The corresponding estimated truncation errors of the real-space and reciprocal-space terms of the reduced potential energy according to Eqs. 21 and 22, respectively, are also shown (solid curves)...

Similar to the equation Er = EjA [Eq. (4.68)], we define the reduced potential energy function as... 

Understanding Reactivity with Reduced Potential Energy Landscapes Recent Advances and New Directions... 

---