A Microscopic Perspective

Temperature and heat capacity are mo properties that are easy to measure, but not so easy to conceptualize. In this chapter, we develop a conceptual picture of temperature, heat capacity, and related quantities. We use two simple models—the ideal gas, and the two-state Schottky model of Chapter 10. Two-state systems can have negative temperatures (lower than T = OK). Negative temperatures help to illuminate the meanings of temperature and heat capacity in general. 

Temperature is a property of a single object. Equation (7.6) defines the temperature in terms of the entropy change that results when a system takes up or gives off energy. 

When energy enters the system as heat, it excites particles to move from the ground state to the excited state. The energy U of the system is proportional to the number n of molecules in the excited state, so 

Coin-flip statistics Equation (1.19) gives the multiplicity of states  

Equation (12.4) shows that the temperature of a two-state system depends on the energy spacing fo (the property that distinguishes one type of material from another), the number of particles N, and the total energy U through the quantity n. 

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Hochella, M. F. Jr. and Banfield, J. F. (1995). Chemical weathering of silicates in nature A microscopic perspective with theoretical considerations. In "Chemical Weathering Rates of Silicate Minerals" (A. F. White and S. L. Brantley, eds), pp. 353 06. Mineralogical Society of America Washington, DC, Reviews in Mineralogy 31. 

A. Gross, Theoretical Surface Science A Microscopic Perspective, Springer, Berlin, 2003. 

Benjamin, I. 1996. Chemical reactions and salvation at liquid interfaces A microscopic perspective. Chem. Rev. 96 (4) 1449-1475. 

I. Benjamin, Chemical reactions and solvation at liquid interfaces a microscopic perspective, Chem. Rev. (Washington, D. C.), 96 (1996) 1449-75 I. Benjamin, Theory and computer simulations of solvation and chemical reactions at liquid interfaces, Acc. Chem. Res., 28 (1995) 233-9 L. R. Martins, M. S. Skaf and B. M. Ladanyi, Solvation dynamics at the water/zirconia interface molecular dynamics simulations, J. Phys. Chem. B, 108 (2004) 19687-97 J. Faeder and B. M. Ladanyi, Solvation dynamics in reverse micelles the role of headgroup-solute interactions, J. Phys. Chem. B, 109 (2005) 6732 10 W. H. Thompson, Simulations of time-dependent fluorescence in nano-confined solvents, J. Chem. Phys., 120 (2004) 8125-33. 

To make Jello, powder containing gelatin (a protein), sugar and flavoring is dissolved in hot water and then placed in the refrigerator to cool. Describe, from a microscopic perspective, what happens in this process. 

Benjamin, I. Chemical Reactions and Solvation at Liquid Interfaces A Microscopic Perspective. Chem. Rev. 1996,96,1449-1475. 

We now turn attention to a completely different kind of supercritical fluid supercritical water (SCW). Supercritical states of water provide environments with special properties where many reactive processes with important technological applications take place. Two key aspects combine to make chemical reactivity under these conditions so peculiar the solvent high compressibility, which allows for large density variations with relatively minor changes in the applied pressure and the drastic reduction of bulk polarity, clearly manifested in the drop of the macroscopic dielectric constant from e 80 at room temperature to approximately 6 at near-critical conditions. From a microscopic perspective, the unique features of supercritical fluids as reaction media are associated with density inhomogeneities present in these systems [1,4],... 

A. GroB, in Theoretical Surface Science — a microscopic perspective. Springer, Berlin, 2002. 

We begin with an abstract of the physics that underlies the kinetics of bond dissociation and structural transitions in a liquid environment. Developed from Einstein s theory of Brownian motion, these well-known concepts take advantage of the huge gap in time scale that separates rapid thermal impulses in liquids (< 10 s) from slow processes in laboratory measurements (e.g. from 10 s to min in the case of force probe tests). Three equivalent formulations describe molecular kinetics in an overdamped liquid environment. The first is a microscopic perspective where molecules behave as particles with instantaneous positions or states x(t) governed by an overdamped Langevin equation of motion,... 

Hochella MF, Banfield JF (1995) Chemical weathering of silicates in nature a microscopic perspective with theoretical considerations. Rev Mineral 31 353-406 Jamnik J, Maier J (1997) Transport across botmdary layers in ionic crystals. Chem Phys 101 23-40 Khachaturyan AG (1983) Theory of Stractrrral Transformations in Solids. Wiley, New York, 574 p Krivoglaz MA (1969) Theory of X-ray and thermal nention scattering by real crystals. Plenum, New York, 405 p... 

If one aims at understanding this rather peculieir phase behavior from a microscopic perspective, one again needs to know the relevant thermodynamic potential. However, one is immediately confronted with a complication because a mechanical expression for thermodynamic potentials cannot be derived due to the low symmetry of the confined fluid (see also discassion in Section 1.6.2). Therefore, a different means of calculating these potentials must be devised. This alternative computational technique will be based on a perturbational approach to which the current section is devoted. 

In nature, water is often found to occur in contact with interacting surfaces which are larger than a water molecule in size. Examples include protein and DNA molecules, silica and mica surfaces, and water in zeolite pores, to name a few. Recently studies have been initiated to understand the nature of such water from a microscopic perspective. We have already discussed proteins and DNA in detail in previous chapters. In this section, we shall cover a few interesting non-biological susbstances. 

Bandyopadhyay G, Dutta S, Lahiri SC (2010) Determination of surface tension, stnictural, and related properties of aquo-alcohol mixtures at 298 K. Z Phys Chem (Munich) 224 729-742 Benjamin 1 (1996) Chemical reactions and solvation at liquid interfaces a microscopic perspective. Chem Rev 96 1449-1475... 

Grob A (2003) Theoretical surface science a microscopic perspective. Springer, New York... 

Interestingly, the freezing process can be much more easily simulated in the presence of an external electric field Svishchev, I. M. Kusalik, P. G. Electrofreezing of liquid water a microscopic perspective, J. Am. Chem. Soc. 1996, 118, 649-654. The timescale for the transformation is calculated to be a few hundred picoseconds, or three orders of magnitude faster than the timescale found in the study of ref. [21. 

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