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EXISTING MODELS
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The need for "generic" models
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5CB, a popular liquid crystal molecule
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It may be modeled by 19+ LC centers, different in size and depth, and
positioned as shown
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Used for realistic simulations, to be compared to experiment
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Less suited for theory
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PMMA (= vinyl glass): more linear, but even more centers
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Multisite model
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Several (4...8) identical LJ sites
in regular distances
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Pro:
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captures some of the physics - see balls-and-sticks models
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Con:
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many interactions per pair
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not convex everywhere
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hard body limit (= fused hard spheres) afflicted by metastability
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But useful for gauging the Gay-Berne potential (see below)
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Kihara model
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Find the points of least mutual distance along
the two axes, then place an LJ center in each of these
"proxy points"
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Pro:
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very quick (only one LJ interaction)
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hard body limit is the well-studied spherocylinder (HSC)
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exhibits pronounced LC behaviour (nematic+smectic)
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Con:
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physics is wrong: side-by-side interaction is no
stronger than end-to-end (compare 4LJ: factor $\approx 5$)
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Gay-Berne model
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Great math, due to Berne-Pechukas; see
here
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But: fuzzy physics; see
here
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Gay-Berne: adapted Berne-Pechukas and defined standard
parameters by comparing to 4-Lennard-Jones model
(see above); later modified by Luckhurst.
See full GB formula
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The Gay-Berne potential has four adjustable parameters
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Pro:
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may be adjusted to represent anything from saucers
to cigars
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Con:
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parameters must be gauged anew for any shape;
not suited as reference potential
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Hard body limit: "Hard Gaussian
Overlap" (HGO) model;
has no definite shape; no pronounced LC phases
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vesely nov-2006
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