fall 09 lm _12 - solids and liquids

fall 09 lm _12 - solids and liquids - Chem 481L Fall 2009 r...

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Prototype Solid Prototype Liquid r N(r) (4πr 2 r ) ρ r 1.0 Chem 481L Fall 2009 Lab Module #12 Due Date: Noon, Tuesday, December 8 Submit via Blackboard’s Digital Drop Box Goal: The purpose of this lab module is to use Virtual Substance to compare the short-range and long-range order (or disorder) of solid argon with its liquid counterpart. Research questions: Can the structures of solids and liquids be quantitatively modeled by Virtual Substance? How do the long-range and short-range orders differ between a solid structure and that if its liquid counterpart? Suggested reading: http://physchem.ox.ac.uk/~rkt/lectures/liqsolns/liquids.html Introduction The organization of particles in a liquid is qualitatively different from the solid state. At absolute zero, particles are at rest in a regular crystal lattice structure that extends infinitely in every direction. This perfect crystalline lattice is said to have infinite long-range order. As the temperature is raised, the particles gain kinetic energy and vibrate about their rest positions, but they remain locked in the lattice structure. The long-range order is maintained. At a certain temperature, the motion reaches a critical level and the ordered structure breaks down abruptly. This occurs at the melting point. In the liquid state, the particles have competing influences between the intermolecular forces, which tend to reproduce the ordered structure of the crystal lattice, and the kinetic energy, which tends to overcome the IM forces and work against the ordered structure. In liquids, the long- range structure is lost altogether. Despite this, a visible short-range order still exists in the liquid state. The strength of this remnant of the crystalline structure depends on the IM forces in the particular substance. Choosing a center particle in the liquid, one sees that the nearest neighbors are not randomly oriented about it; rather, they resemble, to some extent, the structure of the solid. The next- nearest neighbors demonstrate a smaller, yet visible, degree of order with respect to the center particle. At great distance, of course, there is no evidence of structure. Thus, liquids are said to exhibit some short-range order but no long-range order. The distance over which short-range order can be observed is on the order of particle diameters; this distance decreases as the temperature is raised because the particles have greater kinetic energy. The radial distribution function, g(r), is one method of quantifying the degree of long- and short- range order in a condensed phase system. The physical significance of g(r) can be visualized as follows: pick an atom in system, e.g. the red atom in the figure above. Then, the number of atoms N(r) in a spherical shell between r and r+ r away from the central atom, i.e. the red atom, is: where ρ is the bulk density and (4πr 2 dr) is the volume of the shell. If there was no spatial order, then the number of atoms inside the spherical shell would essentially be the bulk density (
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fall 09 lm _12 - solids and liquids - Chem 481L Fall 2009 r...

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