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Kim J, Wang Z, Lahlil K, Davidson P, Gacoin T, Kim J. Charge-driven liquid-crystalline behavior of ligand-functionalized nanorods in apolar solvent. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:86. [PMID: 37747573 DOI: 10.1140/epje/s10189-023-00345-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 09/05/2023] [Indexed: 09/26/2023]
Abstract
Concentrated colloidal suspensions of nanorods often exhibit liquid-crystalline (LC) behavior. The transition to a nematic LC phase, with long-range orientational order of the particles, is usually well-captured by Onsager's theory for hard rods, at least qualitatively. The theory shows how the volume fraction at the transition decreases with increasing aspect ratio of the rods. It also explains that the long-range electrostatic repulsive interaction occurring between rods stabilized by their surface charge can significantly increase their effective diameter, resulting in a decrease in the volume fraction at the transition, as compared to sterically stabilized rods. Here, we report on a system of ligand-stabilized LaPO4 nanorods, of aspect ratio ≈ 11, dispersed in apolar medium exhibiting the counter-intuitive observation that the onset of nematic self-assembly occurs at an extremely low volume fraction of ≈ 0.25%, which is lower than observed (≈ 3%) with the same particles when charged-stabilized in polar solvent. Furthermore, the nanorod volume fraction at the transition increases with increasing concentration of ligands, in a similar way as in polar media where increasing the ionic strength leads to surface charge screening. This peculiar system was investigated by dynamic light scattering, Fourier-transform infrared spectroscopy, zetametry, electron microscopy, polarized light microscopy, photoluminescence measurements, and X-ray scattering. Based on these experimental data, we formulate several tentative scenarios that might explain this unexpected phase behavior. However, at this stage, its full understanding remains a pending theoretical challenge. Nevertheless, this study shows that dispersing anisotropic nanoparticles in an apolar solvent may sometimes lead to spontaneous ordering events that defy our intuitive ideas about colloidal systems.
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Affiliation(s)
- Jeongmo Kim
- Laboratoire de Physique de la Matière Condensée, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France
| | - Zijun Wang
- Laboratoire de Physique de la Matière Condensée, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France
| | - Khalid Lahlil
- Laboratoire de Physique de la Matière Condensée, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France
| | - Patrick Davidson
- Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, 91405, Orsay Cedex, France.
| | - Thierry Gacoin
- Laboratoire de Physique de la Matière Condensée, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France.
| | - Jongwook Kim
- Laboratoire de Physique de la Matière Condensée, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France.
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Díaz-De Armas A, Martínez-Ratón Y. Role of length polydispersity in the phase behavior of freely rotating hard-rectangle fluids. Phys Rev E 2017; 95:052702. [PMID: 28618522 DOI: 10.1103/physreve.95.052702] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2017] [Indexed: 11/07/2022]
Abstract
We use the density-functional formalism, in particular the scaled-particle theory, applied to a length-polydisperse hard-rectangle fluid to study its phase behavior as a function of the mean particle aspect ratio κ_{0} and polydispersity Δ_{0}. The numerical solutions of the coexistence equations are calculated by transforming the original problem with infinite degrees of freedoms to a finite set of equations for the amplitudes of the Fourier expansion of the moments of the density profiles. We divide the study into two parts. The first one is devoted to the calculation of the phase diagrams in the packing fraction η_{0}-κ_{0} plane for a fixed Δ_{0} and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the η_{0}-Δ_{0} plane for fixed κ_{0} while Δ_{0} is changed. We characterize in detail the orientational ordering of particles and the fractionation of different species between the coexisting phases. Also we study the character (second vs first order) of the isotropic-nematic phase transition as a function of polydispersity. We particularly focus on the stability of the tetratic phase as a function of κ_{0} and Δ_{0}. The isotropic-nematic transition becomes strongly of first order when polydispersity is increased: The coexistence gap widens and the location of the tricritical point moves to higher values of κ_{0} while the tetratic phase is slightly destabilized with respect to the nematic one. The results obtained here can be tested in experiments on shaken monolayers of granular rods.
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Affiliation(s)
- Ariel Díaz-De Armas
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
| | - Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
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