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An isotropic phase has no preferred spatial direction. In a liquid crystal, its orientational nematic order parameter vanishes, although the molecules themselves may be anisotropic.

Awarded to Pierre-Gilles de Gennes for extending methods for studying ordering in simple systems to complex matter, especially liquid crystals and polymers.^[ref]

A liquid crystal flows while retaining partial molecular order. A nematic liquid crystal has long-range orientational order but no crystal-like positional lattice. Its local mean axis is the nematic director $\mathbf{n}$, with $\mathbf{n}\equiv -\mathbf{n}$ for an ordinary apolar nematic. Order leads to anisotropic optical and dielectric response and an elastic cost for director distortions.

Nematic order selects an axis, not a common molecular head direction or density-layer stack. The original sketch uses short rods as a coarse-grained orientation map.

Choose an asymmetric diblock copolymer in a cylinder-forming regime: minority cylinders lie in a continuous majority matrix. Form and anneal a film to develop microphase separation, control substrate and top-surface preferences or apply a suitable field to orient cylinders normal to the film, then selectively remove the minority phase. The retained majority matrix becomes the porous support. Infiltrate the channels with liquid crystal. The majority phase forms the channel walls; removing that continuous matrix would not generally leave a continuous nanoporous membrane.

With homeotropic anchoring, the director is radial at a cylindrical side wall. A strictly transverse radial texture has a line core, but an escaped radial texture can avoid it:The director turns axially at the center and is normal to the wall at radius $a$. The original axial-section sketch shows this three-dimensional escape. End conditions, channel dimensions and anchoring strength determine whether escape or a defect-containing profile is favored.

A liquid crystal has some molecular order while retaining liquid-like motion. The distinction between orientational and positional order separates its main phases.

A nematic liquid crystal has long-range orientational order about a nematic director $\mathbf{n}$, with $\mathbf{n}$ and $-\mathbf{n}$ equivalent for apolar molecules, but no periodic density lattice. Its nematic order parameter is $S=⟨(3{\cos }^2\theta -1)/2⟩$, where $\theta$ measures molecular alignment with the director. A cholesteric liquid crystal is a chiral nematic whose director rotates in space, producing a helical pitch while remaining locally nematic.

A smectic phase adds a periodic density modulation in one direction, forming layers with liquid-like motion within each layer. In a smectic A phase, the director is perpendicular to the layers; in a smectic C phase, it is tilted relative to the layer normal. A columnar liquid crystal instead has columns with a two-dimensional positional lattice and comparatively fluid motion along them.

These orders have different experimental signatures. Birefringence under crossed polarizers reveals orientational anisotropy, while X-ray diffraction can detect a smectic layer spacing $d$ through a peak near $q=2\pi /d$. Optical anisotropy alone does not establish a layer lattice.

A liquid crystal flows like a liquid while retaining some molecular order. In a nematic liquid crystal, elongated molecules have long-range orientational order but no ordinary positional lattice. The nematic director $\mathbf{n}$ specifies the preferred axis, with $\mathbf{n}$ and $-\mathbf{n}$ equivalent for head-tail-symmetric molecules. The nematic order parameter $S=⟨(3{\cos }^2\theta -1)/2⟩$ distinguishes an isotropic distribution, $S=0$, from perfect parallel alignment, $S=1$. A smectic phase additionally has a periodic layered density modulation, while molecules remain mobile within layers.

The broken rotational symmetry allows birefringence and distinct elastic costs for nematic splay, nematic twist and nematic bend. Under crossed polarizers, rotating a thin aligned sample changes the transmitted intensity because its two optical polarization components acquire different phases. Heating through a nematic-to-isotropic transition removes that orientational birefringence. An electric field can rotate the director if the dielectric anisotropy of a nematic favors alignment, explaining the optical switching principle of a liquid-crystal cell. Molecular shape, temperature, concentration and surface anchoring determine which ordered phase appears.

A phase transition is a qualitative change of thermodynamic phase as control parameters such as temperature, pressure or chemical potential are varied. A genuine equilibrium singularity is a nonanalyticity of the appropriate thermodynamic potential in the thermodynamic limit; finite systems generally show rounded crossovers instead.

An order parameter is a macroscopic quantity that distinguishes the phases. It often vanishes in a symmetric disordered phase and becomes nonzero after spontaneous symmetry breaking, although density-driven transitions need not have that simple symmetry interpretation. It can be a scalar, vector or tensor. At a first-order phase transition an appropriate first derivative of the free energy is discontinuous, and the order parameter commonly jumps; at a continuous phase transition the order parameter can approach zero continuously while a susceptibility or a higher derivative becomes singular.

Three examples are:

These examples also illustrate why an order parameter must reflect the physical distinction between phases rather than merely be any quantity that changes with temperature.

Pierre-Gilles de Gennes developed connections between the physics of polymers and liquid crystals, using ideas from critical phenomenon studies. Long molecules and orientationally ordered fluids can have large collective responses even when their microscopic constituents differ greatly. Scaling and order-parameter descriptions identify which large-scale behavior follows from symmetry and connectivity rather than detailed molecular chemistry. His account of soft matter emphasizes this ability to move useful physical ideas between seemingly different materials, while retaining the experimental phenomena that distinguish them.^[ref]

A physicist who held the condensed matter physics chair at Collège de France from 1971 to 2004.^[ref]

Polymer physics connects the conformations and motion of long molecules to the properties of a material. A polymer can change shape through many segment rotations while its chemical backbone remains intact. This makes the competition between flow and relaxation important: the same chain can behave as a coil in one experiment and an extended object in another. Soft matter includes both these flexible structures and liquid crystals, whose orientational order produces a different route to strong mechanical and optical response.

A smectic phase is a layered liquid crystal with periodic density or composition variation along one direction and fluid-like positional organization within a layer. A simple order-parameter profile is $\varphi (\mathbf{r})=A\cos ({\mathbf{q}}_0\cdot \mathbf{r})$, with layer spacing $2\pi /|{\mathbf{q}}_0|$.

Layer displacement and orientational fluctuations are additional degrees of freedom, so a fixed cosine is only the simplest mean profile. A smectic A phase has average molecular alignment along the layer normal; a smectic C phase has a tilted director. Scattering can reveal the preferred layer spacing and orientation through peaks near ${\mathbf{q}}_0$. The layer structure does not imply a full three-dimensional crystal lattice of fixed molecular positions.

Soft matter studies materials whose large-scale structures respond strongly to modest mechanical or thermal disturbances, including polymers, liquid crystals and colloids. Polymer physics connects chain conformations to material response; the coil-stretch transition is one example.

A state of matter is a broad category of material behavior. A solid resists a sustained change of shape, a liquid flows while remaining difficult to compress, and a gas expands to fill its container. These distinctions are useful first descriptions, but they do not enumerate all thermodynamic phases. Plasma adds collective behavior of charged particles, while liquid crystals show that flow and structural order need not disappear together.

Distinguish three questions: what broad state of matter does the material resemble, which thermodynamic phase is present, and what are its temperature, pressure and other state variables? Two samples at different temperatures can be in the same liquid thermodynamic phase. Conversely, crystal polymorphism gives different solid thermodynamic phases of the same substance, distinguished by their crystal structures. A phase transition between them need not change the broad state-of-matter category.

For an imagined substance with crystalline forms A and B, melting A produces a solid–liquid phase transition, while converting A to B produces a solid–solid phase transition. A sample containing A and B has two thermodynamic phases even though all its material is solid. Cutting one uniform crystal into two pieces does not create a second thermodynamic phase: count distinct equilibrium forms, rather than pieces or grains. This distinction matters when applying the phase rule.

A phase diagram locates stable thermodynamic phases using temperature and pressure. Its liquid–gas phase coexistence curve ends at a liquid-gas critical point, around which a path connects liquid and gas without a first-order phase transition. Broad categories can therefore remain useful without a sharp boundary.^[ref]