**Acknowledgments**

18 Recent Progress in Carbon Nanotube Research / Book 1

CNTs *<sup>γ</sup>*<sup>1</sup> <sup>=</sup> <sup>2</sup> <sup>∗</sup> 103 N/m<sup>2</sup> >> *<sup>γ</sup>*(*c*)

Φ2

respectively. I-isotropic, and N-nematic.

isotropic and nematic LC ordering.

*Replacement mechanism* [3, 34].

**4. Conclusions**

13.4x10-3

13.2 13.0 12.8 12.6 12.4

T-TNI=1.4K <sup>γ</sup>1=2\*104

<sup>γ</sup>2=104

and *coupled* regions that we have discussed previously.

N/m<sup>2</sup>

N/m<sup>2</sup>

In the case of a more realistic value of the coupling parameter between the LC molecules and

I

5x10-3 <sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>Φ</sup><sup>3</sup>

**Figure 10.** The (Φ3, Φ2) phase diagram in the *supercritical* regime for the bidisperse system, in the isotropic phase of LC,

The phase diagram is similar to that of Figure 9 showing again the existence of the *decoupled*

In the paper we analyze phase behavior of mixtures consisting of LC soft carrier matrix and immersed NPs. A relatively simple phenomenological modeling is used where we focus on

In the first part we consider isotropic NPs. We derive the effective free energy of the mixture from which we extract the effective Flory-Huggins parameter. Its structure reveals that on entering nematic ordering phase separation is very probable. However, it could be suppressed by LC-NP interfacial contribution providing that it promotes nematic ordering. From the structure of the average elastic free energy term we also conclude that NPs have in general tendency to assemble at localized sites exhibiting relatively strong elastic distortions. We proceed by studying interaction between a nanoparticle and a topological defect, which is a typical representative of localized strong elastic distortions. It is of interest to identify conditions for which NPs could be effectively trapped to tunable localized distortions. For example, in such a way phase separation could be prevented. In addition, localized elastic

As a model system we use a cylindrical hybrid cell possessing the boojum topological defect. We consider different surface treatment of the nanoparticle and analyze where it is placed in order to minimize total free energy of the system. We find out that a nanoparticle is attracted to a region the structure of which is compatible with configuration enforced by the nanoparticle. Therefore, one could trap NPs to topological defects if its surface enforces configuration resembling the defect core structure. We further show that condensation penalty of forming defects could be in this case significantly reduced due to the *Defect Core*

distortions could be exploited controlled positional trapping of immersed NPs.

bidisperse CNTs in the isotropic phase of LC (*T* − *TN I* = 1.4K is plotted in Figure 10.

<sup>1</sup> (*supercritical* regime, the <sup>Φ</sup>3, <sup>Φ</sup>2) phase diagram for the

I+N

N

V.P.-N. thanks to T. J. Sluckin for useful discussion, gratefully acknowledge the hospitality of l'Ecole Normale Supérieure de Lyon and the funding from CNRS. V.B. acknowledge support from the Romanian National Authority for Scientific Research, CNCS - UEFISCDI, project number PN-II-ID-PCE-2011-3-1007.
