Local free energy minimum

Expanding this equation into powers into powers of and analyzing the stability of the local free-energy minimum at = 0 yields the Stoner-Wohlfarth coercivity... 

Two types of friction are commonly measured and calculated. The static friction Fj is defined as the minimum lateral force needed to initiate sliding of one object over a second, while the kinetic friction Fk v) is the force needed to maintain sliding at a steady velocity v. Observation of static friction implies that the contacting solids have locked into a local free-energy minimum, and Fj represents the force needed to lift them out of this minimum. It is a threshold rather than an actual force acting on the system, and it limits lateral motion in any direction. No work is done by the static friction, since no motion occurs. The kinetic friction is intrinsically related to dissipation mechanisms, and it equals the work done on the system by external forces divided by the distance moved. 

One central issue in tiibology is why static friction is so universally observed between solid objects. How does any pair of macroscopic objects, placed in contact at any position and orientation, manage to lock together in a local free energy minimum A second issue is why experimental values of Fj and tend to be closely correlated. The two reflect fundamentally different processes and their behavior is qualitatively different in many of the simple models described below. 

The PMF for Li+ adsorption shows two solvent-induced local minima. In bulk solution, the hydration shell of Li+ forms a rather rigid octahedral complex. Li+ and the water molecules in its hydration shell move cooperatively. Consequently, the hydration complex is sensitive to the barriers formed by the two pronounced layers of water molecules around z = —6k. and z = —3 A. This leads to a local free energy minimum on the solution side of each of the two maxima in the oxygen density profiles. There, molecules from the water layers can be part of the hydration eomplex (see below). 

Intermolecular repulsion forces will define a hard-sphere diameter for the molecules allowing the calculation and/or measurement of the density fluctuation as one moves away from the surface. As shown in Figure 4.86, the result is a damped density curve (density distribution versus distance in molecular diameters from the surface). For a liquid between two surfaces at short separation distances, the two effects will overlap producing an interference pattern as illustrated in Figure 4.9. When the distance of separation is some integral multiple of the hard sphere diameter, nAhs, reinforcement occurs producing a local free energy minimum. For separations that correspond to fractional... 

Random alloys do not necessarily have the minimum free energy. The ordered structure for intermetallics often represents the local free energy minimum, which may be affected by relative atomic size and electron negativity of the metal atoms [24], FePt nanoparticles with a face-centered tetragonal (fct) phase are among the most-studied intermetallics in recent years [25]. The colloidal FePt nanoparticles are hard to prepare under relatively mild synthetic conditions [25a, 26], An indirect approach is to thermally treat the disordered face-centered cubic (fee) FePt nanoparticles, which are synthesized from iron pentacarbonyl and platinum acetylacetonate in the presence of... 

At a chemical reaction, the system moves from a local free energy minimum of the reactants to another, lower free energy minimum of the products (Figure 8.1). In a slightly more advanced picture, there is a valley on the left, a pass at the top of the barrier in the middle of the figure, and another valley on the right. In a photochemical reaction, the dynamics takes place on an excited potential energy surface (PES). 

Over the course of the simulation, iVp(r) is kept constant (Xp = 0), while all other variables are driven towards the state corresponding to the local free energy minimum. In addition. Equation 10.11 is modified as follows ... 

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