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Many device-scale phenomena rely,
at some level, on localised regions with very steep spatial
gradients of the director orientation and/or order parameter
due to the presence of a defect or an interface. Generally,
these regions with steep spatial gradients require a molecular
level description, whereas a continuum treatment is appropriate
for the (vastlylarger) remainder of the device volume.
In this project, we will develop distribution-matching techniques
through which molecular simulations
performed at surface or defect regions can be embedded within
a bulk continuum model. In this approach, recursive umbrella-sampling
calculations will be used to match the molecular and continuum
order tensor descriptions within an overlap region that
joins the two single-technique regions. Within the continuum
region, which will be able to span a large length scale,
on of two models will be used when appropriate. For systems
deep in a liquid crystal phase the appropriate model will
be Ericksen-Leslie theory which has been extremely successful
in modelling liquid crystal devices .
However, close to the nematic-isotropic or smectic-nematic
transition a Landau-de Gennes approach based on a Taylor
expansion of the thermotropic energy will be necessary .
The interaction from the molecular scale modelling will
come through the boundary conditions applied to the macroscopic
model which will be formed from spatial and temporal averaging.
Once developed this approach may also be used to inform
and model defect/surface behaviour in Projects 7,
8, 9
and 10.
P.I.C. Teixeira, A. Chrzanowska, G.D. Wall and D.J. Cleaver,
Density Functional Theory of a Gay-Berne Film Between Aligning
Walls, Molec. Phys., 99, 889
(2001).
A. Chrzanowska, P.I.C. Teixeira, H. Ehrentraut and D.J.
Cleaver, Ordering of Hard Particles Between Hard Walls,
J. Phys.-Condes. Matter, 13,
4715 (2001).
P. G. de Gennes and J. Prost,
A. Poniewierski and T.J. Sluckin, Theory of the nematic-isotropic
transition in a restricted geometry,
A. Poniewierski and T.J. Sluckin, On the free energy density
of non-uniform nematics,
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