The branching angle effect on the properties of rigid dendrimers studied by Monte Carlo simulation.

We studied the properties of rigid dendrimers with different branching angles by means of Monte Carlo simulations on a coarse-grained level. It was found that the terminal groups of dendrimers with both rigid and flexible spacers could locate near the center of the molecule. In flexible dendrimers, the wide distribution is attributed to the back folding of flexible spacers, while in rigid dendrimers, it is caused by the branching angle effect that a branch will grow laterally due to the restriction of a non-zero branching angle. It has been established that the branching angle is a key parameter for rigid dendrimers, which can be applied to tune the properties of rigid dendrimers: decreasing branching angle is helpful to obtain dendrimers with a larger size, lower density, and more terminal groups locating at periphery.

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.e., on the case where molecular switching is not quantitative, leading to a solution of rotaxanes in different states. We present switching diagrams that can guide in the design of rotaxanes which affect a macroscopic phase change.

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. In particular, we show that the average angles are [Formula: see text], and [Formula: see text] and the most populated lengths lie at [Formula: see text], and [Formula: see text] The triangles are usually obtuse. We discuss the area allowed within the triangle for inclusion compounds. Inspired by the linear rotaxane switches, we also consider the statistical mechanics of switching when stations with attractive interactions promote small-cycle areas.

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. The system shows several interesting kinds of behaviour. First we predict that the fraction of short-length rotaxanes increases linearly with concentration and is a maximum at the critical concentration that marks the isotropic to nematic transition. Second, the critical concentration shows a minimum at a certain value of q. Our model suggests that the effect of adaptive length changes is most dramatic at small q and where the long state is slightly favoured.

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. We calculate the power produced by such a motor, which is in the femtoWatt range. The power is proportional to the square of the number of rings.

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. There is a minimum ratio q* = 1.13 for which transitions from a pure isotropic state to a pure nematic state are possible. We present a phase-switching diagram, which gives the six possible behaviours for this system. It turns out that a large fraction of the phase switching diagram is occupied by the transition from a pure isotropic to a pure nematic 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. We use energy minimisation to determine these states exactly, and show that there can be transitions from asymmetric to symmetric states by varying the bond lengths. We also use classical statistical mechanics to show the effect of thermal noise.

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. We then examine the effect of two stripes on the axle, having different ring-axle interactions with the mobile rings, so that one section is of high energy (repulsive) for the rings and another section is of lower energy (or attractive). This kind of rotaxane can exhibit rapid changes in displacement or force, and in particular, this molecule can exhibit a yield stress in which the piston suddenly compresses under a small increase in the applied force.

Single chains of block copolymers in poor solvents: handshake, spiral, and lamellar globules formed by geometric frustration.

A single multiblock copolymer chain in poor solvent undergoes microphase separation within its own globule, driven by the same kind of forces operating in the bulk system. However, the necessity of packing a large AB interface into a small volume leads to novel convoluted geometries. Long block lengths form a double droplet. Very short block lengths exhibit bulk behavior, forming a lamellar globule. With intermediate block lengths, the AB interface buckles to form a hand shake or spiral dicluster. An order-disorder transition is reported for short block lengths.

Globule transitions of a single homopolymer: a Wang-Landau Monte Carlo study.

The temperature-independent Wang-Landau Monte Carlo approach is implemented for an off-lattice model of flexible homopolymers and applied to the coil-globule and solidification transitions based on chain sizes up to N=300. An intermediate transformation from low-density liquid globule to high-density liquid globule is suggested. A scheme for identifying polymer structures representative of particular temperatures in the course of the simulation is presented and applied to illustrate intermediate states in the coil-globule transition. Transition temperatures are calculated and used to obtain a theta point of at least Theta=1.96, distinctly higher than the solid-liquid transition temperature T(M)=1.26.

An off-lattice Wang-Landau study of the coil-globule and melting transitions of a flexible homopolymer.

The Wang-Landau Monte Carlo approach is applied to the coil-globule and melting transitions of off-lattice flexible homopolymers. The solid-liquid melting point and coil-globule transition temperatures are identified by their respective peaks in the heat capacity as a function of temperature. The melting and theta points are well separated, indicating that the coil-globule transition occurs separately from melting even in the thermodynamic limit. We also observe a feature in the heat capacity between the coil-globule and melting transitions which we attribute to a transformation from a low-density liquid globule to a high-density liquid globule.