Advances in Condensed Matter Physics

Volume 2015 (2015), Article ID 803480, 9 pages

http://dx.doi.org/10.1155/2015/803480

## Controlled Nanoparticle Targeting and Nanoparticle-Driven Nematic Structural Transition

^{1}Moscow State University of Instrument Engineering and Computer Science, Stromynka 20, Moscow 107996, Russia^{2}Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, SI-2000 Maribor, Slovenia

Received 21 November 2014; Revised 25 December 2014; Accepted 19 January 2015

Academic Editor: Ivan Smalyukh

Copyright © 2015 A. V. Dubtsov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We study experimentally and theoretically controlled targeting of specific nanoparticles (NPs) to different regions within nematic liquid crystal. Using a simple mesoscopic Landau-de Gennes-type model in terms of a tensor nematic order parameter, we demonstrate a general mechanism which could be exploited for controlled targeting of NPs within a spatially nonhomogeneous nematic texture. Furthermore, we experimentally demonstrate using polarising microscopy that even a relatively low concentration of localised appropriate NPs could trigger a nematic structural transition. A simple estimate is derived to account for the observed transition.

#### 1. Introduction

Recent years witness increased interest in soft nanocomposites consisting of soft matrices hosting specific nanoparticles (NPs) [1–3]. Appropriate combinations could yield quantitatively dramatically enhanced or qualitatively new behaviour that individual components do not exhibit on their own. Such systems are promising to trigger development of new nano-based practical applications. Furthermore, they could be also exploited as convenient testing ground for basic physics [1].

As soft matrices various liquid crystal (LC) phases and structures are often used [4–7]. In addition to softness (i.e., capability to exhibit strong response to even weak local perturbation), they are also optically transparent and in many cases stable close to room temperatures. Among others, these properties make them relatively easily accessible for experimental observations [5–7]. When various NPs are introduced to soft matrices several scenarios could be realized. In most cases it is of interest to obtain homogeneous mixtures of LCs and NPs and to avoid phase segregation or agglomeration of NPs [3]. If spatial nonhomogeneities exist within LC matrix, in most cases NPs tend to assemble in regions exhibiting relatively strong elastic distortions [1]. Furthermore, LC mediated interactions among NPs could enable their self-organization into different tunable superstructures [3].

In this paper, we study numerical targeting of specific NPs towards desired locations within spatially inhomogeneous nematic LC structures. Furthermore, we demonstrate experimentally that a relatively low concentration of localised NPs could be sufficient to trigger a global nematic structural transition.

The plan of the paper is as follows. In Section 2 we present the Landau-de Gennes mesoscopic model. In Section 3 we describe experimental setup. In Section 4 we theoretically study interactions between NPs and local LC ordering focusing on NP surface treatment. In Section 5 we present our experimental results demonstrating a nanoparticle-driven structural transition. A simple estimate is presented to explain the observed transition. In the last section, we summarize our findings. Some technical details are given in the appendix.

#### 2. Mesoscopic Modelling

At mesoscopic level, we describe a local nematic order in terms of the traceless and symmetric tensor order parameter [7, 8] as

The quantities and unit vectors determine eigenvalues and eigenvectors of , respectively. In case of uniaxial order, is commonly expressed as [7, 8]

Here, is the identity tensor, describes the nematic director field, and is the scalar uniaxial order parameter field. The unit vector field points along the local uniaxial ordering, where states are physically equivalent. Furthermore, quantifies the extent of fluctuations about . A local degree of biaxiality in is measured by the biaxial parameter [9] and . Uniaxial ordering corresponds to and maximal degree of biaxiality to .

The resulting free energy [7, 8] is expressed as
where *, *, , and stand for the condensation*,* elastic, confinement, and LC-NP interface free density contributions, respectively. The first integral is carried out over the LC volume. The second integral is performed over the surface area enclosing LC body and the third one over the NP-LC interface. In the lowest order approximation, which is needed to explain phenomena of our interest, they are expressed as

The condensation term enforces uniaxial nematic ordering. The quantities *, **,* and are material constants and is the bulk isotropic phase supercooling temperature. The elastic term is weighted by the positive elastic constants which tends to enforce homogenous ordering in . The interface term, where the superscript stands for* location*, determines conditions at the LC confining interface () or at the NP-LC interface (). The quantity is a surface strength constant, and is a surface normal unit vector [4]. For an interface enforcing homeotropic (isotropic tangential) ordering it holds ().

#### 3. Experimental Setup

In the experimental part of work, we used the nematic mixture LC ZhK 616. It consists of p-n-butyl-p-methoxyazoxybenzene (59%), p-n-butyl-p-heptanoylazoxybenzene (29%), and n-heptyl-benzoic acid n-cyano-phenyl ester (12%). The mixture possesses an optical anisotropy and relatively wide nematic phase window extending within the temperature .

Microdroplets of LC were dispersed in deionized water with a resistivity of 18.2 MΩ cm. The LC emulsion in water was formed by sequential cycles of sonication and vortex mixing of 2 *μ*L of LC and 2 mL of water at room temperature. Powdered phospholipid 1,2-diacyl-sn-glycero-3-phosphocholine (L-*α*-phosphatidylcholine, SIGMA Aldrich purity > 99%) was dispersed in deionized water at room temperature. Dispersion of the phospholipid powder in water at initial concentration of 10^{−3} g/mL was mixed by vortexing. Different dilutions were made to obtain concentrations ranging from 10^{−4} g/mL to 10^{−8} g/mL. A volume of 4 *μ*L of an aqueous dispersion of phospholipid was dispensed onto a glass substrate. A volume of 4 *μ*L of an LC emulsion was added to the water dispersion of the phospholipid. A polarized microscope with an objective of 100x magnification was used to monitor nematic order within LC droplets of diameters between 1 *μ*m and 10 *μ*m.

#### 4. Interaction between a Surface Treated Nanoparticle and Local Nematic Order

In this section we demonstrate a robust and simple NP targeting mechanism which could be exploited to assemble NPs within a desired region. For this purpose we study theoretically the impact of NP’s surface coating on interaction with its nematic surrounding using a simple confinement displaying cylindrical symmetry which can stabilize NLC structures displaying three distinctively different characteristic local nematic textures.

The geometry of the problem is sketched in Figure 1(a). We consider a nanoparticle immersed within a plan-parallel hybrid cell of thickness and radius . For the sake of simplicity, which does not affect general validity of results obtained, both the nanoparticle and the cell geometry exhibit the cylindrical symmetry. The cylindrical coordinate system is defined with the orthonormal triad of unit vectors .