Liquid crystal glycolipids - Carbohydrate Chemistry: Chemical and Biological Approaches - page 316

where the volume of an individual alkyl chain is v, and the cross-
sectional area of the head group is a, and the length of the fully extended
chain is l.
There are then two ways to determine the number (N) of molecules in
the micelle, (i) surface area of the micelle divided by the area (a) of a head
group equals N, or (ii) volume (v) of the micelle divided by the volume (v)
of an individual molecule also equals N.

For the surface area (i) N = 4p(R mic ) 2 /a
For the volume (ii) N = 4p(R mic ) 3 /3v
Set the two values of N equal, then

R mic = 3v/a

If the radius of the micelle E equal to the molecular

length, l max
Then for a micelle (or micellar cubic phase)

1/3 = v/al max

The ratio determined for lamellar phase is v/al = 1, and for the
hexagonal phase is 1/3 o v/al o 1/2. However, caution has to be taken
using this model because the above predicted limits are relatively in-
sensitive to the exact values of v and a, but are strongly dependent upon
the choice of l. 8 Thus for n-octyl b- D -glucopyranoside, shown in Fig. 3, 1
heating from the crystal to the thermotropic liquid crystal state results in
the formation of a lamellar phase (SmA*) as predicted by the modelling.
Experimentally, it is possible to vary molecular shape, and hence alter
the packing constraints, by changing the substitution, location and
number of head groups with respect to the length and saturation of the
aliphatic chains. Thus, from a nano-engineering point of view, the syn-
thetic chemist can design materials in a predictive way in order to gen-
erate desired condensed phases of matter. In the following we describe
how each thermotropic liquid crystal phase, lamellar, bicontinuous cubic
and hexagonal, is related to glycolipid structure.

2 Lamellar phases
There are a number of possible molecular architectures that can form
rod-like molecular shapes. These include simple glycolipids with one
head group and one chain, bolaphiles that have two head groups joined
by a fatty chain, two simple glycolipids joined together, or multiple gly-
colipids joined together to give a dendrimer, as shown in Fig. 5. For these
structures the total head group area is similar to the total cross-sectional
areas of the aliphatic chains, and hence the curvature is low, and the
materials tend to form lamellar phases, as shown in Fig. 6.
One head group - one chain may seem a simple structural architecture
for an amphiphile, but for glycolipids the situation is complicated by the
variation of the structures of the sugar units available for head group
design, i.e. the head group may have an open chain structure, or a
pyranose or a furanose ring structure.
The simplest types of glycolipids to exhibit amphitropic properties are
the alkyl-substituted polyols. For these materials, the mesomorphic
properties have been investigated as a function of the aliphatic chain