Recent experiments [Rodarte et al 2013] have reported the assembly of micron-sized shells formed by nanoparticles dispersed in isotropic 5CB when cooled into the nematic phase. We present a theoretical model to explain this phenomenon that couples a Landau-de Gennes free energy for the liquid crystal with a new global free-energy expression for a square-well (SW) fluid. We derive the phase separation kinetic equations for the system [Elder et al 1991] and identify the conditions leading to the assemblage of particles in various phases: Firstly, we perform a linear-stability analysis of a uniform stationary state to discriminate among the Fourier modes with increasing and decreasing amplitudes. Secondly, we solve numerically the kinetic equations for the nematic-order-parameter and SW concentration fields and investigate how the interplay between the isotropic-nematic and liquid-vapour transitions can be used to guide self-assembly. We further exhibit the patterns obtained by varying the SW interaction parameters. In doing so, we profit from an explicit SW free-energy equation valid for all ranges and densities, and an ample temperature interval; this equation was derived via Singular Value Decomposition [Hoppe 2013] from simulation data �[Espíndola-Heredia et al, 2009; Zhou and Solana 2013] and known analytical behavior [Ponce and Renon 1976; del Río and Lira 1987; Benavides and del Río 1989].
This work was supported by CONACYT (Mexico) project FDC 2015-02-1450.
References:
AL Rodarte et al, J Matter Chem C, 1, 5527 (2013).
KR Elder et al, Phys Rev B, 44, 6673 (1991).
T Hoppe, PLOS ONE, 8, 10, e75792 (2013).
R Espindola-Heredia, F del Río and A Malijevsky, J Chem Phys, 130, 024509 (2009).
S Zhou and JR Solana, J Chem Phys, 138, 244115 (2013).
L Ponce and H Renon, J Chem Phys, 64, 638 (1976).
F del Río and L Lira, J Chem Phys, 87, 7179 (1987).
AL Benavides and F del Río, Molec Phys, 68, 983 (1989)
Engineered self-assembly , Non-equilibrium thermodynamics , Challenges and advances in fluid phase equilibria
