Rotaxane liquid crystals with variable length: The effect of switching efficiency on the isotropic-nematic transition.

We examine a solution of non-adaptive two-state rotaxane molecules which can switch from a short state of length L to a long state of length qL, using statistical thermodynamics. This molecular switching is externally driven and can result in an isotropic-nematic phase transition without altering temperature and concentration. Here we concentrate on the limitation imposed by switching inefficiency, i.

Triangular cyclic rotaxanes: Size, fluctuations, and switching properties.

We examine one of the simplest cyclic rotaxanes-a molecule made from three rods with variable length between 0 and L. This [3]rotaxane, unlike a traditional molecule, shows significant size and shape fluctuations. We quantify these using a number of different measures.

Isotropic and nematic liquid crystalline phases of adaptive rotaxanes.

We describe the thermodynamics of a solution of rotaxanes which can change their length from a short state of length L to a long state of length qL in response to their surrounding environment. We call these rotaxanes "adaptive." We show that such a system can exhibit both isotropic and nematic liquid crystalline phases.

A Two-Stroke, Two-Cylinder Piston Rotaxane Motor.

We introduce a model for a rotaxane motor. This uses two major themes of rotaxane physics, that is, the ability to change the potential of different regions of the axle (switching) and the entropy associated with free rings. The motor is based on free rings being trapped and released by potential stripes or stations.

Threading a Ring or Tube onto a Rod: An Entropically Rare Event.

We calculate the entropy lost when a circular ring or a circular cylinder or tube is threaded onto a long rod in terms of the geometrical parameters, namely rod length and radius, the threaded ring radius, or the radius and length of a threaded tube. These formulas, constructed from a partition function, allow calculation of the fraction of rings/tubes threaded spontaneously onto rods. In all cases of practical interest, this fraction is very small and can be well represented by simple power laws depending strongly upon the geometrical parameters.

Fast switching from isotropic liquids to nematic liquid crystals: rotaxanes as smart fluids.

We examine a solution of rod-like piston-rotaxanes, which can switch their length by external excitation (for example optically) from a short state of length L to a long state of length qL. We show that this solution can exhibit a number of different behaviours. In particular it can rapidly switch from an isotropic to a nematic liquid crystalline state.

Conformational isomers of linear rotaxanes.

We examine a simple model of rotaxane structure, with 3 asymmetric rings interacting via repulsive power-law forces. This interlocked molecule exhibits conformational isomerisation which is different from that of molecules whose connectedness is through covalent bonds. The rings are free to translate along and rotate around the axle, and hence weak interaction forces between the rings can lead to distinct rotamer states.

A piston-rotaxane with two potential stripes: force transitions and yield stresses.

We examine a rod piston-rotaxane system, where the positions of several mobile rings on the axle are controlled by an external force acting on one of the rings. This allows us to access the translational entropy of the rings. For a simple rotaxane molecule with an axle that has uniform ring-axle interactions along its length, the molecule behaves like a miniature piston filled with a one-dimensional ideal gas.