Hierarchical self-assembly: Self-organized nanostructures in a nematically ordered matrix of self-assembled polymeric chains

Abstract

We report many different nano-structures which are formed when model nano-particles of different sizes (diameter σn) are allowed to aggregate in a background matrix of semi-flexible self assembled polymeric worm like micellar chains. The different nano-structures are formed by the dynamical arrest of phase-separating mixtures of micellar monomers and nano-particles. The different morphologies obtained are the result of an interplay of the available free volume, the elastic energy of deformation of polymers, the density (chemical potential) of the nano-particles in the polymer matrix and, of course, the ratio of the size of self assembling nano-particles and self avoidance diameter of polymeric chains. We have used a hybrid semi-grand canonical Monte Carlo simulation scheme to obtain the (non-equilibrium) phase diagram of the self-assembled nano-structures. We observe rod-like structures of nano-particles which get self assembled in the gaps between the nematically ordered chains as well as percolating gel-like network of conjoined nanotubes. We also find a totally unexpected interlocked crystalline phase of nano-particles and monomers, in which each crytal plane of nanoparticles is separated by planes of perfectly organized polymer chains. We identified the condition which leads to such interlocked crystal structure. We suggest experimental possibilities of how the results presented in this paper could be used to obtain different nano-structures in the lab. There is persistent interest in the controlled self assembly and growth of nano-structures of predefined morphology and size starting from small constituent nanoparticles (NP) . A separate non-alligned interest of physicists is in the formation and properties of topological defects when large particles (large compared to the size and spacing between nematogens) are introduced in ordered liquid crystalline nematic and smectic phases [29][30][31][32][33][34][35][36][37][38][39][40][41]. Recents experiments have also explored the self organization of nano-particles in a background matrix of nematically ordered micellar phase, but constraints in the choice of size of NPs led to the following two scenarios: small NPs of 2 − 3 nm diameter pervade the nematic chains themselves and form a dispersion/solution, whereas, larger NPs of size 8 − 26 nm get expelled by the elastic energy of ordered nematic phases and aggregate at the grain boundaries between nematic domains [42][43][44]. The distance between adjacent nematic chains was 5.7 nm in the experiments.Our present study spans across these two different research domains and we use computer simulations to investigate the heirarchical self assembly of NPs in the free volume between parallel chains of nematically ordered worm-like micelles (WM). The micellar polymers are selfassembled themselves from monomeric beads and have a length and size distribution controlled by monomer density and temperature [45][46][47]. In a computer simulation, we are able to systematically vary the diameter, chemical potential of the spher...

Effect of the Strength of Attraction Between Nanoparticles on Wormlike Micelle- Nanoparticle System

“…Previous studies [47,48] using the same model (presented in the previous section) have reported the morphological transitions of nanoparticles with the increase in σ 4n . Those results were substantiated by showing the convergence of all ten independent runs to same morphological structures.…”

“…Using Monte Carlo technique, the system is allowed to equilibrate from a randomly initialized state. After around 5 × 10 5 − 6 × 10 5 iterations, the system evolves to form Wormlike chains of monomers having an exponential distribution of chain length [48]. With an increase in micellar density, an isotropic-to-nematic transition is observed, as has been reported in detail [48].…”

“…The model used in this paper is the same as the model used in [47,48] which is a modified version of the model presented in [49]. According to this model, the Wormlike micellar chains are coarse-grained as a chain of spherical beads.…”

“…After around 5 × 10 5 − 6 × 10 5 iterations, the system evolves to form Wormlike chains of monomers having an exponential distribution of chain length [48]. With an increase in micellar density, an isotropic-to-nematic transition is observed, as has been reported in detail [48]. A three-body potential V 3 is acting on a triplet with a central monomer (pink) bonded with two other monomers at distances of r 2 and r 3 , forming an angle θ at the central monomer and having a cutoff range of σ 3 .…”

Self assembled linear polymeric chains with tuneable semiflexibility using isotropic interactions

“…This enabled us to have a sharp potential peak at rather short distances near r = 1.3σ. In the past we have tried to get a sharp peak at such distances with Lennard Jones potential but without success [6,40]. Secondly, we used 2 kinds of particles A and B.…”