Crystallization hard condensed matter

Soft matter science is nowadays an acronym for an increasingly important class of materials, which encompasses polymers, liquid crystals, molecular assembhes building hierarchical structmes, and the whole area of colloidal sciences. Common to all of them is that fluctuations and thus the thermal energy T and the entropy play an important role. Soft then means that these materials are in a state of matter that are neither simple liquids nor hard solids of the type studied in hard condensed matter, hence sometimes soft matter firms also under the name complex fluids. 

Crystallization in Hard Condensed Matter Versus Self-Assembly of Soft Matter... 

The spring constants, a , should be chosen as to minimize the absolute value of integrand of Eq. (5.66) as a function ofX [112]. Note that in simple crystals in hard condensed matter, all particles fluctuate around the ideal lattice position by the same amount. The fluctuations of the fields, AW (c), in a self-assembled structure, however, depend on the spatial position, c. 

Within a particle-based model, there is no well-defined reference state for the self-assembled structure. However, one can try to relate the seF-assembled structure to a disordered melt (or a different self-assembled morphology) via a reversible path and calculate the change of the free energy by thermodynamic integration. Typically, transitions between disordered and ordered morphologies or between different self-assembled structures are of first order. Thus, in an analogy to crystallization of hard condensed matter, there is no path in the space of physical intensive variables - for example, temperature, incompatibility, or composition - that reversibly cormects disordered and ordered structures. 

Special simulation techniques have recently been devised to calculate free energies of these structure-forming fluids [43-45]. We have discussed several methods, which have been inspired by related approaches for calculating free energy of crystals in hard-condensed matter systems [43], rely on a field-theoretic representation via lattice-based fields [45] or exploit the possibility of simultaneously and accurately measuring the pressure and tdiemical potential due to the softness of the off-lattice potentials [44]. 

The study of phase transitions has played a central role in the study of condensed matter. Since the first applications of molecular simulations, which provided some of the first evidence in support of a freezing transition in hard-sphere systems, to contemporary research on complex systems, including polymers, proteins, or liquid crystals, to name a few, molecular simulations are increasingly providing a standard against which to measure the validity of theoretical predictions or phenomenological explanations of experimentally observed phenomena. 

Both polymers and liquid crystals belong to a class of matter, sometimes called condensed matter, complexing fluids, soft matter [32-34], extensively studied in recent years in terms of their behavior and physical-chemical properties. Unlike gases and liquids, soft materials exibit a certain form (polymer) or internal organization (liquid crystal) but, in contrast to "hard materials," they strongly respond to external mechanical (polymer) or electric (Uquid crystal) disturbances. 

Computer simulation techniques have become very important tools in the study of condensed matter systems since their development in the 1950s. Such simulations can study systems ranging from the very simple (hard spheres, Lennard-Jones particles) to the complex (for example, proteins and large biomolecules). The total number of atoms or molecules studied also varies greatly and depends upon the application - for the calculation of the bulk properties of simple systems, a few hundred particles is usually sufficient. Other systems such as interfaces and proteins require much larger simulations. In the case of the crystal-melt interface, simulations have an enhanced role owing to the difficulty of performing experiments that probe the interface. 

Speedy RJ. 1998. Pressure and entropy of hard-sphere crystals. Journal of Physics Condensed Matter 10 4387-4391. 

Fortini A and Dijkstra M. 2006. Phase behaviour of hard spheres confined between parallel hard plates Manipulation of colloidal crystal structures by confinement Journal of Physics Condensed Matter 18 L371-L378. 

---