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Gandhi P, Kuhnhold A. The effect of particle geometry and initial configuration on the phase behavior of twisted convex n-prisms. SOFT MATTER 2024; 20:5351-5358. [PMID: 38913010 DOI: 10.1039/d4sm00585f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/25/2024]
Abstract
We study the phase behavior of twisted convex n-prisms with n = 3 and 4, via Monte Carlo simulations. Biaxial phases, in untwisted prisms, can be induced by choosing specific geometries of the prisms. However, due to the convexity of the twisted particles, a strong twisting disables the formation of biaxial phases and stabilizes uniaxial nematic and smectic phases. Using the increased volume of the twisted convex particles, we define an effective aspect ratio of the twisted prisms and find a homogeneous phase behavior across the geometry of the prisms' cross-section and even across different shapes of the cross-section. In this representation biaxial phases are found for large aspect ratios, while the low aspect ratio behavior can be compared to the hard cylinder phase diagram. For 3-prisms with a small base angle, we show the influence of the initial configuration; a polar initial configuration results in a (polar) splay nematic phase, whereas a non-polar initial configuration results in a biaxial phase.
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Affiliation(s)
- Poshika Gandhi
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
| | - Anja Kuhnhold
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
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Dal Compare L, Romano F, Wood JA, Widmer-Cooper A, Giacometti A. Janus helices: From fully attractive to hard helices. J Chem Phys 2023; 159:174905. [PMID: 37921252 DOI: 10.1063/5.0168766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 10/05/2023] [Indexed: 11/04/2023] Open
Abstract
The phase diagram of hard helices differs from its hard rods counterpart by the presence of chiral "screw" phases stemming from the characteristic helical shape, in addition to the conventional liquid crystal phases also found for rod-like particles. Using extensive Monte Carlo and Molecular Dynamics simulations, we study the effect of the addition of a short-range attractive tail representing solvent-induced interactions to a fraction of the sites forming the hard helices, ranging from a single-site attraction to fully attractive helices for a specific helical shape. Different temperature regimes exist for different fractions of the attractive sites, as assessed in terms of the relative Boyle temperatures, that are found to be rather insensitive to the specific shape of the helical particle. The temperature range probed by the present study is well above the corresponding Boyle temperatures, with the phase behaviour still mainly entropically dominated and with the existence and location of the various liquid crystal phases only marginally affected. The pressure in the equation of state is found to decrease upon increasing the fraction of attractive beads and/or on lowering the temperature at fixed volume fraction, as expected on physical grounds. All screw phases are found to be stable within the considered range of temperatures with the smectic phase becoming more stable on lowering the temperature. By contrast, the location of the transition lines do not display a simple dependence on the fraction of attractive beads in the considered range of temperatures.
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Affiliation(s)
- Laura Dal Compare
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia Campus Scientifico, Edificio Alfa, Via Torino 155, 30170 Venezia Mestre, Italy
| | - Flavio Romano
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia Campus Scientifico, Edificio Alfa, Via Torino 155, 30170 Venezia Mestre, Italy
- European Centre for Living Technology (ECLT) Ca' Bottacin, 3911 Dorsoduro Calle Crosera, 30123 Venice, Italy
| | - Jared A Wood
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia
- The University of Sydney Nano Institute, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Asaph Widmer-Cooper
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia
- The University of Sydney Nano Institute, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia Campus Scientifico, Edificio Alfa, Via Torino 155, 30170 Venezia Mestre, Italy
- European Centre for Living Technology (ECLT) Ca' Bottacin, 3911 Dorsoduro Calle Crosera, 30123 Venice, Italy
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Tuinier R, Kuhnhold A. Equation of State of Charged Rod Dispersions. J Phys Chem B 2023; 127:9058-9065. [PMID: 37831936 PMCID: PMC10614191 DOI: 10.1021/acs.jpcb.3c04590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Revised: 09/15/2023] [Indexed: 10/15/2023]
Abstract
We study the accuracy of the theory of Stroobants, Lekkerkerker, and Odijk [Macromolecules 1986, 19, 2232-2238], called SLO theory, to describe the thermodynamic properties of an isotropic fluid of charged rods. By incorporation of the effective diameter of the rods according to SLO theory into scaled particle theory (SPT), we obtain an expression for the rod concentration-dependent free volume fraction and the osmotic pressure of a collection of charged hard spherocylinders. The results are compared to Monte Carlo simulations. We find close agreement between the simulation results and the SLO-SPT predictions for not too large values of the Debye length and for high rod charge densities. The deviations increase with rod density, particularly at concentrations above which isotropic-nematic phase transitions are expected.
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Affiliation(s)
- Remco Tuinier
- Laboratory
of Physical Chemistry, Department of Chemical Engineering and Chemistry,
& Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Anja Kuhnhold
- Institute
of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
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Ding Y, Yang J, Wang C, Wang Z, Li J, Hu B, Xia C. Structural Transformation between a Nematic Loose Packing and a Randomly Stacked Close Packing of Granular Disks. PHYSICAL REVIEW LETTERS 2023; 131:098202. [PMID: 37721830 DOI: 10.1103/physrevlett.131.098202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2022] [Accepted: 06/29/2023] [Indexed: 09/20/2023]
Abstract
Packing structures of granular disks are reconstructed using magnetic resonance imaging techniques. As packing fraction increases, the packing structure transforms from a nematic loose packing to a dense packing with randomly oriented stacks. According to our model based on Edwards' volume ensemble, stack structures are statistically favored when the effective temperature decreases, which has a lower structural anisotropy than single disks, and brings down the global orientational order consequently. This mechanism identified in athermal granular materials can help us understand the nonergodic characteristics of disklike particle assemblies such as discotic mesogens and clays.
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Affiliation(s)
- Yunhao Ding
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Jing Yang
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Chenyang Wang
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Zhichao Wang
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Jianqi Li
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Bingwen Hu
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Chengjie Xia
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
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Banavar JR, Giacometti A, Hoang TX, Maritan A, Škrbić T. A geometrical framework for thinking about proteins. Proteins 2023. [PMID: 37565735 DOI: 10.1002/prot.26567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2023] [Revised: 07/16/2023] [Accepted: 07/21/2023] [Indexed: 08/12/2023]
Abstract
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity.
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Affiliation(s)
- Jayanth R Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon, USA
| | - Achille Giacometti
- Ca' Foscari University of Venice, Department of Molecular Sciences and Nanosystems, Venice, Italy
- European Centre for Living Technology (ECLT), Venice, Italy
| | - Trinh X Hoang
- Vietnam Academy of Science and Technology, Institute of Physics, Hanoi, Vietnam
| | - Amos Maritan
- University of Padua, Department of Physics and Astronomy, Padua, Italy
| | - Tatjana Škrbić
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon, USA
- Ca' Foscari University of Venice, Department of Molecular Sciences and Nanosystems, Venice, Italy
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Ding Y, Gong D, Yang J, Xu Z, Wang Z, Li J, Hu B, Xia C. Cubatic structural transformation of the packing of granular cylinders. SOFT MATTER 2022; 18:726-734. [PMID: 34874397 DOI: 10.1039/d1sm01440d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Packing structures of granular cylinders with the aspect ratio close to one have been reconstructed with the help of magnetic resonance imaging techniques. By controlling the container boundary conditions and preparation protocols, a structural transformation from a disordered liquid-like state to an orientationally ordered state with cubatic symmetry at a high packing fraction is observed. This ordering process is accompanied by the formation of more faceted contacts, which lower the elastic energy between jammed granular particles to drive the transformation. With the help of Edwards' volume ensemble theory, this granular structural transformation is explained using a phenomenological thermodynamic model and a self-consistent mean-field statistical mechanical model. Both models predict a sharp but continuous change of order parameter when the effective granular temperature is lowered. The intrinsic difference and connection between this granular structural transformation and the entropy-driven phase transition of conventional thermal hard-particle systems are discussed.
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Affiliation(s)
- Yunhao Ding
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Dianjinfeng Gong
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Jing Yang
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Zhen Xu
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Zhichao Wang
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Jianqi Li
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Bingwen Hu
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Chengjie Xia
- Shanghai Key Laboratory of Magnetic Resonance, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
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