1188 28 The Structure of Solids, Liquids, and Polymersadded to the sum that is producing an average value. It was shown by Metropolis and
his coworkers that if sufficient terms are taken, this procedure produces averages that
are correctly weighted by the canonical probability distribution. In order to make the
system act somewhat like a piece of a larger system, periodic boundary conditions are
applied: If a move carries a particle out of the system, which is usually contained in
a cube, the particle is reintroduced into the system through the same location on the
opposite face of the cube.
The second simulation technique ismolecular dynamics.In this technique, which
was pioneered by Alder,^27 initial positions of the particles of a system of several hundred
particles are assigned in some way. Displacements of the particles are determined by
numerically simulating the classical equations of motion. Periodic boundary conditions
are applied as in the Monte Carlo method. The first molecular dynamics calculations
were done on systems of hard spheres, but the method has been applied to monatomic
systems having intermolecular forces represented by the square-well and Lennard–
Jones potential energy functions, as well as on model systems representing molecular
substances. Commercial software is now available to carry out molecular dynamics
simulations on desktop computers.^28
Both equilibrium and nonequilibrium information can be obtained by the molecular
dynamics technique. If the initial state of the system simulates a specific nonequilibrium
state, the relaxation of the system toward equilibrium can be studied, giving informa-
tion on transport properties.^29 After a sufficient time, the molecules will settle into
motions that simulate the motions of molecules in equilibrium liquids, and equilibrium
properties can be calculated.PROBLEMS
Section 28.5: The Structure of Liquids
28.31The density of ice at 0◦C is equal to 0.917 g mL−^1 , and
that of liquid water is equal to 1.000 g mL−^1. The water
molecules in the ice crystal have four nearest neighbors.
Estimate the number of nearest neighbors in liquid water
at 0◦C. Comment on your answer.
28.32At the normal melting temperature, 83.78 K, the molar
volume of solid argon is 0.0246 L mol−^1 and that of
liquid argon is 0.0282 L mol−^1.^30 Find the pressure
according to Eq. (28.5-5), and compare it with the correct
value, 1.00 atm.28.33The density of solid xenon is 3540 kg m−^3 and that of
liquid xenon is 3057 kg m−^3. Find the pressure according
to Eq. (28.5-5), and compare it with 1.00 atm, which is
the correct value at the normal melting temperature,
161.36 K.28.6 Approximate Theories of Transport
Processes in Liquids
Transport processes include diffusion, viscous flow, and heat conduction. There are a
number of approximate theories of transport processes in liquids, most of which are
based on classical statistical mechanics.(^27) B. J. Alder and T. E. Wainwright,J. Chem. Phys., 31 , 459 (1959).
(^28) Chem3D can carry out molecular dynamics calculations on laptop or desktop computers. It also carries
out molecular mechanics calculations. Information is available at http://www.cambridgesoft.com.
(^29) See W. G. Hoover,Ann. Rev. Phys. Chem., 34 , 103 (1983) for a review of work in this field.
(^30) K.-C. Kan,Chin. J. Phys., 17 , 32 (1979).