Domain coarsening

S.M. Allen and J.W. Cahn. Microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall., 27(6) 1085-1095, 1979. 

Basic models for domain coarsening and pattern formation... 

Patterns usually appear due to the instability of a uniform state. However, such an instability does not necessarily lead to pattern formation. Let us consider, e.g., phase separation of a van-der-Waals fluid near the critical point Tc. For T > Tc, there exists only one phase, while for T < Tc, there exist two stable phases, corresponding to gas and liquid, and an unstable phase whose density is intermediate between those of the gas and the liquid. When an initially uniform fluid is cooled below Tc, the unstable phase is destroyed, and in the beginning one observes a mixture of stable-phase domains, i.e. hquid droplets and gas bubbles, which can be considered as a disordered pattern. However, the domain size of each phase grows with time (this phenomenon is called Ostwald ripening or coarsening). Finally, one observes a full separation of phases a liquid layer is formed in the bottom part of the cavity, and a gas layer at the top. Thus, the instabihty of a certain uniform state is not sufficient for getting stable patterns. Below we formulate some mathematical models that describe both phenomena, domain coarsening and pattern formation. 

Let us emphasize that there are no other spatially uniform stationary solutions except (p = 0. Thus, when the latter solution is unstable, the system tends to a non-uniform state, i.e. pattern formation takes place. A direct simulation shows that stripe patterns are formed [36], with the stripes wavelength near 2tt fkc- Note that because of the rotational invariance of problem (14) the orientation of the stripes is arbitrary. Initially, a disordered system of stripes is developed from random initial conditions, and then some large domains are developed with a definite orientation of stripes inside each domain. The mean domain size grows with time, i.e. domain coarsening takes place for differently oriented stripe patterns rather than for different uniform phases. 

This chapter is organized as follows. In section 1.1, we introduce our notation and present the details of the molecular and mesoscale simulations the expanded ensemble-density of states Monte Carlo method,and the evolution equation for the tensor order parameter [5]. The results of both approaches are presented and compared in section 1.2 for the cases of one or two nanoscopic colloids immersed in a confined liquid crystal. Here the emphasis is on the calculation of the effective interaction (i.e. potential of mean force) for the nanoparticles, and also in assessing the agreement between the defect structures found by the two approaches. In section 1.3 we apply the mesoscopic theory to a model LC-based sensor and analyze the domain coarsening process by monitoring the equal-time correlation function for the tensor order parameter, as a function of the concentration of adsorbed nanocolloids. We present our conclusions in Section 1.4. 

Rapid solvent evaporation and solidification of the electrospun fibers during electrospinning, decreases the domain coarsening, so there are fine and stretched phase domains in the nanofibers, and carbon nanofibers with a large amount of nanopores throughout the surface and the interior of the fibers were obtained. The nanopores in the fibers at about several tens of nanometers in widths are continuous. Great potential of the nanoporous carbon fiber obtained in this study make many interesting applications for them in different fields [8]. 

Mafik A, Sandy AR, Lurio LB, Stephenson GB, Mochrie SGJ, McNulty I, Sutton M (1998) Coherent X-ray study of fluctuations during domain coarsening. Phys Rev Lett 81(26) 5832-5835... 

---