518 Classical time-dependent statistical mechanics
Fig. 13.6 Left: Standard periodic boundary conditions. Right: Lees–Edwards boundary con-
ditions.
across several layers until it dissipates into the bulk. However, in realistic applications,
the effect can persist for tens of angstroms before dissipating, so that very large system
sizes are needed in order to render this boundary effect negligible, leaving enough bulk
fluid to obtain reliable bulk properties.
As we discussed in Section 3.14.2, the effects of physical boundariesin equilibrium
molecular dynamics calculations can be eliminated by employing periodic boundary
conditions. Thus, it is interesting to ask if the idea of periodic boundary conditions
can be adapted for systems undergoing shear flow as a means of eliminating the phys-
ical plates. It is not immediately obvious how this can be accomplished,however, as
the plates are the very source of the driving force. One option is toreplace the usual
periodic array employed in equilibrium molecular dynamics calculations (see Fig. 13.6,
left) with an array in which layers stacked along they-axis move in thex-direction
with a speed equal toylγ, whereylis the position of thelth layer along they-axis. This
scheme is depicted in Fig. 13.6, right. Such time-dependent boundary conditions are
known asLees–Edwards boundary conditions(Lees and Edwards, 1972). As the right
panel in Fig. 13.6 suggests, it is the application of the Lees–Edwardsboundary condi-
tions that drives the flow and establishes the linear velocity profile required for planar
Couette flow. The combination of eqns. (13.3.6) and (13.3.7) with theLees–Edwards
boundary conditions is known as theSLLOD algorithm.^2 A serious disadvantage of
Lees–Edwards boundary conditions is its implementation for systems of charged par-
ticles employing Ewald summation techniques (see Appendix B), which are based in
reciprocal space. In such systems, no clear definition of the reciprocal-space vectors
exists under Lees–Edwards boundary conditions (Mundyet al., 2000).
An alternative to the Lees–Edwards approach drives the flow by evolving the box
(^2) For an explanation of the amusing origin of the “SLLOD” moniker, see Evans and Morriss (1984).
Suffice it to say, here, that SLLOD is not actually an acronym.