Self-organisation and mesophases between liquid and crystal

Amphiphiles organise themselves because one end hates the solvent

Intuition

Think of a drop of washing-up liquid in water. Each molecule has a head that likes water and a tail that avoids it. When there are lots of them, the tails huddle together and the heads face outwards. Nobody tells them to. They self-organise to hide the tails.

An amphiphile has one solvophilic end (it likes the solvent). In the lecture’s example the Na⁺ dissociates, leaving a charged head. It also has one solvophobic end (it avoids the solvent), the fatty tail. At high concentration the molecules aggregate into 1-d, 2-d or 3-d structures to reduce how much tail touches the solvent. Tuning the solvent interactions and the relative volumes of head and tail gives a variety of lyotropic liquid crystals. The word comes from “lyo” meaning dissolve and “tropic” meaning change.

The slide 8 and 9 phase diagram plots temperature (°C) against amphiphile concentration (wt%, about 30 to 80). It has regions labelled I₁ (lowest concentration), H_I, V_I and L_α (lamellar, layers), with cartoons of hexagonal, la3d, cubic (I₁), micellar and lamellar structures pointing at the regions.

These are equilibrium phases, so they are not slowly aggregating into something else. The equilibrium phase depends on temperature and concentration. Without changing the molecule, you can also shift the diagram by altering pH or salt concentration. The same kind of process can occur between several components with specifically designed interactions. That is called self-assembly, and the lecture says it opens a lot of research in chemistry.

Mesophases sit halfway between a liquid and a crystal

Intuition

A liquid is like a crowd milling about in a car park, facing every which way. A crystal is like soldiers on parade, each in a fixed place, all facing the same way. A mesophase is like a crowd where everyone faces the same way but still wanders about. Some order, some freedom.

The lecture compares the two ends with this table.

Typical molecular liquid	Typical molecular crystal
Molecules free to diffuse in all 3 directions	Molecules vibrate around a specific site
Molecules free to rotate around all 3 axes	Molecules vibrate around a fixed orientation
Location of molecules has no long-range structure	Long-range translational order in all 3 directions
Orientation of molecules is isotropic	Long-range orientational order in all 3 directions

These microscopic properties decide many macroscopic ones: fluidity (response to shear), optical isotropy and interaction with electric fields. Mesophases are equilibrium phases that match some properties of liquids and others of crystals. Molecules that can form them are called mesogens. They do not need to be amphiphiles in a solvent. They can form in a single-component system, and the next lecture shows this can happen from molecular shape alone.

Rod shape and temperature decide which mesophase forms

The shape of a molecule and the temperature decide whether and how it acts as a mesogen. The director, written $\bar{n}$, is the average direction of the particle axis. The slide 13 heating sequence for rod-like molecules is Crystal, then SmC, SmA, N (nematic), then Isotropic. In SmC the rods are tilted at an angle $\Theta$ from the layer normal. Disc-shaped molecules can stack into columnar phases.

In short: smectic phases keep the rods in layers. The nematic phase keeps the rods pointing the same way but gives up the layers.

Cholesteric means the chiral nematic phase. If the mesogen is chiral, what looks like a nematic on a small scale may show a gradual rotation of the director on a longer scale. The pitch is the distance to rotate a full turn. Even with small molecules, the pitch can be long enough to match the wavelength of light and cause optical effects. In a very small temperature range, double-twist cholesteric cylinders pack to form a blue phase that can selectively reflect a colour.

Exam detail

Learn the heating sequence Crystal, SmC, SmA, N, Isotropic, the definition of the director, the pitch of a cholesteric, and the four-row liquid versus crystal table. These are the lecture’s own lists.

Anisotropy and electric fields are what make mesophases useful

Many of these phases have one, two or three different axes of symmetry over macroscopic distances. This is called anisotropy. As a result, physical and mechanical properties such as electrical and thermal conductivity, and light polarisation, can depend on the direction in which you measure them.

The charge distribution or polarisability of the molecules also means an external electric field can change the structure of a mesophase. The new equilibrium can be set up very quickly, although the speed depends on temperature and molecular interactions. Together with polarised light, this gives switchable transmission. The slide 17 applications are an LCD display and a photograph of a banana slug, with no text. The next lectures cover the display idea.

Pitfall

“Isotropic” and “anisotropic” are opposites. A liquid is isotropic, so its properties are the same in every direction. A nematic is anisotropic, so conductivity or light behaviour can change with direction.

Optional aside

The slide 8 and 9 phase diagram labels (I₁, H_I, V_I, L_α) are read from the figure. The slide text does not say which cartoon belongs to which region beyond the pointers, so no more detail is given here.

Recall

Why can a liquid crystal behave differently depending on the direction you look from?

Its molecules share an average direction (the director) over large distances. That gives the phase one or more preferred axes, which is anisotropy.