1
|
Munaò G, Prestipino S, Costa D. Early stages of aggregation in fluid mixtures of dimers and spheres: a theoretical and simulation study. Phys Chem Chem Phys 2021; 23:22661-22672. [PMID: 34604896 DOI: 10.1039/d1cp03604a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We use Monte Carlo simulation and the Reference Interaction Site Model (RISM) theory of molecular fluids to investigate a simple model of colloidal mixture consisting of dimers, made up of two tangent hard monomers of different size, and hard spheres. In addition to steric repulsion, the two species interact via a square-well attraction only between small monomers and spheres. Recently, we have characterized the low-temperature regime of this mixture by Monte Carlo, reporting on the spontaneous formation of a wide spectrum of supramolecular aggregates [Prestipino et al., J. Phys. Chem. B, 2019, 123, 9272]. Here we focus on a regime of temperatures where, on cooling, the appearance of local inhomogeneties first, and the early stages of aggregation thereafter, are observed. In particular, we find signatures of aggregation in the onset of a low-wavevector peak in the structure factors of the mixture, as computed by both theory and simulation. Then, we link the structural information to the microscopic arrangement through a detailed cluster analysis of Monte Carlo configurations. In this regard, we devise a novel method to compute the maximum distance for which two spheres can be regarded as bonded together, a crucial issue in the proper identification of fluid aggregates. The RISM theory provides relatively accurate structural and thermodynamic predictions in comparison with Monte Carlo, but with slightly degrading performances as the fluid progresses inside the locally inhomogeneous phase. Our study certifies the efficacy of the RISM approach as a useful complement to numerical simulation for a reasoned analysis of aggregation properties in colloidal mixtures.
Collapse
Affiliation(s)
- Gianmarco Munaò
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
| | - Santi Prestipino
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
| | - Dino Costa
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
| |
Collapse
|
2
|
Martin TB, Gartner TE, Jones RL, Snyder CR, Jayaraman A. pyPRISM: A Computational Tool for Liquid-State Theory Calculations of Macromolecular Materials. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b00011] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Tyler B. Martin
- National Institute
of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | | | - Ronald L. Jones
- National Institute
of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Chad R. Snyder
- National Institute
of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | | |
Collapse
|
3
|
Rickayzen G, Heyes DM. Isotropic-nematic phase transition of uniaxial variable softness prolate and oblate ellipsoids. J Chem Phys 2017; 146:164505. [PMID: 28456193 DOI: 10.1063/1.4981887] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Onsager's theory of the isotropic-nematic phase separation of rod shaped particles is generalized to include particle softness and attractions in the anisotropic interparticle force field. The procedure separates a scaled radial component from the angular integral part, the latter being treated in essentially the same way as in the original Onsager formulation. Building on previous treatments of more idealised hard-core particle models, this is a step toward representing more realistic rod-like systems and also allowing temperature (and in principle specific chemical factors) to be included at a coarse grained level in the theory. The focus of the study is on the coexisting concentrations and associated coexistence properties. Prolate and oblate ellipsoids are considered in both the small and very large aspect ratio limits. Approximations to the terms in the angular integrals derived assuming the very large (prolate) and very small (oblate) aspect ratios limits are compared with the formally exact treatment. The approximation for the second virial coefficient matches the exact solution for aspect ratios above about 20 for the prolate ellipsoids and less than ca. 0.05 for the oblate ellipsoids from the numerical evaluation of the angular integrals. The temperature dependence of the coexistence density could be used to help determine the interaction potential of two molecules. The method works at temperatures above a certain threshold temperature where the second virial coefficient is positive.
Collapse
Affiliation(s)
- G Rickayzen
- School of Physical Sciences, University of Kent, Canterbury, Kent CT2 7NH, United Kingdom
| | - D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 OEX, United Kingdom
| |
Collapse
|
4
|
Fraaije JGEM, van Male J, Becherer P, Serral Gracià R. Coarse-Grained Models for Automated Fragmentation and Parametrization of Molecular Databases. J Chem Inf Model 2016; 56:2361-2377. [DOI: 10.1021/acs.jcim.6b00003] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Johannes G. E. M. Fraaije
- Leiden
Institute of Chemistry, Leiden University, Einsteinweg 55, 2300 RA Leiden, The Netherlands
- Culgi BV, Galileiweg 8, 2333 BD Leiden, The Netherlands
| | - Jan van Male
- Culgi BV, Galileiweg 8, 2333 BD Leiden, The Netherlands
| | - Paul Becherer
- Culgi BV, Galileiweg 8, 2333 BD Leiden, The Netherlands
| | | |
Collapse
|
5
|
Munaò G, Costa D, Caccamo C. Development of molecular closures for the reference interaction site model theory with application to square-well and Lennard-Jones homonuclear diatomics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:414007. [PMID: 27548461 DOI: 10.1088/0953-8984/28/41/414007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Inspired by significant improvements obtained for the performances of the polymer reference interaction site model (PRISM) theory of the fluid phase when coupled with 'molecular closures' (Schweizer and Yethiraj 1993 J. Chem. Phys. 98 9053), we exploit a matrix generalization of this concept, suitable for the more general RISM framework. We report a preliminary test of the formalism, as applied to prototype square-well homonuclear diatomics. As for the structure, comparison with Monte Carlo shows that molecular closures are slightly more predictive than their 'atomic' counterparts, and thermodynamic properties are equally accurate. We also devise an application of molecular closures to models interacting via continuous, soft-core potentials, by using well established prescriptions in liquid state perturbation theories. In the case of Lennard-Jones dimers, our scheme definitely improves over the atomic one, providing semi-quantitative structural results, and quite good estimates of internal energy, pressure and phase coexistence. Our finding paves the way to a systematic employment of molecular closures within the RISM framework to be applied to more complex systems, such as molecules constituted by several non-equivalent interaction sites.
Collapse
Affiliation(s)
- Gianmarco Munaò
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| | | | | |
Collapse
|
6
|
Borówko M, Rżysko W, Sokołowski S, Staszewski T. Integral equations theory for two-dimensional systems involving nanoparticles. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1234079] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Małgorzata Borówko
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, Lublin, Poland
| | - Wojciech Rżysko
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, Lublin, Poland
| | - Stefan Sokołowski
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, Lublin, Poland
| | - Tomasz Staszewski
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, Lublin, Poland
| |
Collapse
|
7
|
Cigala G, Costa D, Bomont JM, Caccamo C. Aggregate formation in a model fluid with microscopic piecewise-continuous competing interactions. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1078006] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- G. Cigala
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina Viale , Messina, Italy
| | - D. Costa
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina Viale , Messina, Italy
| | | | - C. Caccamo
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina Viale , Messina, Italy
| |
Collapse
|
8
|
Lekkerkerker H, Tuinier R, Wensink H. Multiphase coexistence in mixed suspensions of large and small hard platelets. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1048319] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- H.N.W. Lekkerkerker
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University , Utrecht, the Netherlands
| | - R. Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology , Eindhoven, the Netherlands
| | - H.H. Wensink
- Laboratoire de Physique des Solides, Université Paris-Sud and CNRS , Orsay Cedex, France
| |
Collapse
|
9
|
Munaò G, Gámez F, Costa D, Caccamo C, Sciortino F, Giacometti A. Reference interaction site model and optimized perturbation theories of colloidal dumbbells with increasing anisotropy. J Chem Phys 2015; 142:224904. [DOI: 10.1063/1.4922163] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Affiliation(s)
- Gianmarco Munaò
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy
| | | | - Dino Costa
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy
| | - Carlo Caccamo
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy
| | - Francesco Sciortino
- Dipartimento di Fisica and CNR-ISC, Università di Roma “Sapienza,” Piazzale Aldo Moro 2, 00185 Roma, Italy
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S.Marta DD2137, Venezia I-30123, Italy
| |
Collapse
|
10
|
Wensink HH, Trizac E. Generalized Onsager theory for strongly anisometric patchy colloids. J Chem Phys 2014; 140:024901. [PMID: 24437905 DOI: 10.1063/1.4851217] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The implications of soft "patchy" interactions on the orientational disorder-order transition of strongly elongated colloidal rods and flat disks is studied within a simple Onsager-van der Waals density functional theory. The theory provides a generic framework for studying the liquid crystal phase behaviour of highly anisometric cylindrical colloids which carry a distinct geometrical pattern of repulsive or attractive soft interactions localized on the particle surface. In this paper, we apply our theory to the case of charged rods and disks for which the local electrostatic interactions can be described by a screened-Coulomb potential. We consider infinitely thin rod like cylinders with a uniform line charge and infinitely thin discotic cylinders with several distinctly different surface charge patterns. Irrespective of the backbone shape the isotropic-nematic phase diagrams of charged colloids feature a generic destabilization of nematic order at low ionic strength, a dramatic narrowing of the biphasic density region, and a reentrant phenomenon upon reducing the electrostatic screening. The low screening regime is characterized by a complete suppression of nematic order in favor of positionally ordered liquid crystal phases.
Collapse
Affiliation(s)
- H H Wensink
- Laboratoire de Physique des Solides - UMR 8502, Université Paris-Sud and CNRS, 91405 Orsay Cedex, France
| | - E Trizac
- Laboratoire de Physique Théorique et Modèles Statistiques - UMR 8626, Université Paris-Sud and CNRS, 91405 Orsay Cedex, France
| |
Collapse
|
11
|
Wu L, Jackson G, Müller EA. Liquid crystal phase behaviour of attractive disc-like particles. Int J Mol Sci 2013; 14:16414-42. [PMID: 23965962 PMCID: PMC3759919 DOI: 10.3390/ijms140816414] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2013] [Revised: 07/24/2013] [Accepted: 07/25/2013] [Indexed: 11/17/2022] Open
Abstract
We employ a generalized van der Waals-Onsager perturbation theory to construct a free energy functional capable of describing the thermodynamic properties and orientational order of the isotropic and nematic phases of attractive disc particles. The model mesogen is a hard (purely repulsive) cylindrical disc particle decorated with an anisotropic square-well attractive potential placed at the centre of mass. Even for isotropic attractive interactions, the resulting overall inter-particle potential is anisotropic, due to the orientation-dependent excluded volume of the underlying hard core. An algebraic equation of state for attractive disc particles is developed by adopting the Onsager trial function to characterize the orientational order in the nematic phase. The theory is then used to represent the fluid-phase behaviour (vapour-liquid, isotropic-nematic, and nematic-nematic) of the oblate attractive particles for varying values of the molecular aspect ratio and parameters of the attractive potential. When compared to the phase diagram of their athermal analogues, it is seen that the addition of an attractive interaction facilitates the formation of orientationally-ordered phases. Most interestingly, for certain aspect ratios, a coexistence between two anisotropic nematic phases is exhibited by the attractive disc-like fluids.
Collapse
Affiliation(s)
- Liang Wu
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK; E-Mails: (L.W.); (G.J.)
| | - George Jackson
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK; E-Mails: (L.W.); (G.J.)
| | - Erich A. Müller
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK; E-Mails: (L.W.); (G.J.)
| |
Collapse
|
12
|
Munaò G, Costa D, Giacometti A, Caccamo C, Sciortino F. Structure and phase behavior of colloidal dumbbells with tunable attractive interactions. Phys Chem Chem Phys 2013; 15:20590-9. [DOI: 10.1039/c3cp52425f] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- G Munaò
- Dipartimento di Fisica, Università di Roma "La Sapienza", Piazzale Aldo Moro 2, 00185 Roma, Italy.
| | | | | | | | | |
Collapse
|
13
|
Fartaria RP, Javid N, Sefcik J, Sweatman MB. Simulation of scattering and phase behavior around the isotropic–nematic transition of discotic particles. J Colloid Interface Sci 2012; 377:94-104. [DOI: 10.1016/j.jcis.2012.03.046] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2011] [Revised: 03/13/2012] [Accepted: 03/14/2012] [Indexed: 10/28/2022]
|
14
|
Munaó G, Costa D, Sciortino F, Caccamo C. Simulation and theory of a model for tetrahedral colloidal particles. J Chem Phys 2011; 134:194502. [DOI: 10.1063/1.3582904] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
|
15
|
Munaò G, Costa D, Saija F, Caccamo C. Simulation and reference interaction site model theory of methanol and carbon tetrachloride mixtures. J Chem Phys 2010; 132:084506. [DOI: 10.1063/1.3314296] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
16
|
He P, Mejia AF, Cheng Z, Sun D, Sue HJ, Dinair DS, Marquez M. Hindrance function for sedimentation and creaming of colloidal disks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:026310. [PMID: 20365654 DOI: 10.1103/physreve.81.026310] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2009] [Indexed: 05/29/2023]
Abstract
We report the first measurement of the hindrance function for sedimentation or creaming of disk-shaped colloids via the analytical centrifugation. Disks align with the external flow right above a volume fraction of a few percent, and this effect is extremely sensitive to the aspect ratio of disks. Due to this alignment effect, disk sedimentation or creaming demonstrates distinct trends in dilute and semidilute regions.
Collapse
Affiliation(s)
- Peng He
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, USA
| | | | | | | | | | | | | |
Collapse
|
17
|
|
18
|
Munaò G, Costa D, Caccamo C. Reference interaction site model investigation of homonuclear hard dumbbells under simple fluid theory closures: Comparison with Monte Carlo simulations. J Chem Phys 2009; 130:144504. [DOI: 10.1063/1.3098551] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
19
|
Munaò G, Costa D, Caccamo C. Thermodynamically consistent reference interaction site model theory of the tangent diatomic fluid. Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2009.01.064] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
20
|
Bolisetty S, Rosenfeldt S, Rochette CN, Harnau L, Lindner P, Xu Y, Müller AHE, Ballauff M. Interaction of cylindrical polymer brushes in dilute and semi-dilute solution. Colloid Polym Sci 2008; 287:129-138. [PMID: 19816531 PMCID: PMC2755784 DOI: 10.1007/s00396-008-1962-3] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2008] [Revised: 10/24/2008] [Accepted: 10/29/2008] [Indexed: 10/29/2022]
Abstract
We present a systematic study of flexible cylindrical brush-shaped macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and by dynamic light scattering (DLS) in dilute and semi-dilute solution. The SLS and SANS data extrapolated to infinite dilution lead to the shape of the polymer that can be modeled in terms of a worm-like chain with a contour length of 380 nm and a persistence length of 17.5 nm. SANS data taken at higher polymer concentration were evaluated by using the polymer reference interaction site model (PRISM). We find that the persistence length reduce from 17.5 nm at infinite dilution to 5.3 nm at the highest concentration (volume fraction 0.038). This is comparable with the decrease of the persistence length in semi-dilute concentration predicted theoretically for polyelectrolytes. This finding reveals a softening of stiffness of the polymer brushes caused by their mutual interaction.
Collapse
|
21
|
|
22
|
Bier M, van Roij R. Nonequilibrium steady states in fluids of platelike colloidal particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:021401. [PMID: 18352025 DOI: 10.1103/physreve.77.021401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2007] [Indexed: 05/26/2023]
Abstract
Nonequilibrium steady states in an open system connecting two reservoirs of platelike colloidal particles are investigated by means of a recently proposed phenomenological dynamic density functional theory [M. Bier and R. van Roij, Phys. Rev. E 76, 021405 (2007)]. The platelike colloidal particles are approximated within the Zwanzig model of restricted orientations, which exhibits an isotropic-nematic bulk phase transition. Inhomogeneities of the local chemical potential generate a diffusion current which relaxes to a nonvanishing value if the two reservoirs coupled to the system sustain different chemical potentials. The relaxation process of initial states towards the steady state turns out to comprise two regimes: a smoothening of initial steplike structures followed by an ultimate relaxation of the slowest diffusive mode. The position of a nonequilibrium interface and the particle current of steady states depend nontrivially on the structure of the reservoirs due to the coupling between translational and orientational degrees of freedom of the fluid.
Collapse
Affiliation(s)
- Markus Bier
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, Utrecht, The Netherlands.
| | | |
Collapse
|
23
|
Bier M, van Roij R. Relaxation dynamics in fluids of platelike colloidal particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021405. [PMID: 17930037 DOI: 10.1103/physreve.76.021405] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2007] [Revised: 06/08/2007] [Indexed: 05/25/2023]
Abstract
The relaxation dynamics of a model fluid of platelike colloidal particles is investigated by means of a phenomenological dynamic density functional theory. The model fluid approximates the particles within the Zwanzig model of restricted orientations. The driving force for time dependence is expressed completely by gradients of the local chemical potential, which in turn is derived from a density functional-hydrodynamic interactions are not taken into account. These approximations are expected to lead to qualitatively reliable results for low densities like those within the isotropic-nematic two-phase region. The formalism is applied to model an initially spatially homogeneous stable or metastable isotropic fluid which is perturbed by switching a two-dimensional array of Gaussian laser beams. Switching on the laser beams leads to an accumulation of colloidal particles in the beam centers. If the initial chemical potential and the laser power are large enough, a preferred orientation of particles occurs, breaking the symmetry of the laser potential. After switching off the laser beams again, the system can follow different relaxation paths: It either relaxes back to the homogeneous isotropic state or it forms an approximately elliptical high-density core which is elongated perpendicular to the dominating orientation in order to minimize the surface free energy. For large supersaturations of the initial isotropic fluid, the high-density cores of neighboring laser beams of the two-dimensional array merge into complex superstructures.
Collapse
Affiliation(s)
- Markus Bier
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584CE Utrecht, The Netherlands.
| | | |
Collapse
|
24
|
Harnau L, Rosenfeldt S, Ballauff M. Structure factor and thermodynamics of rigid dendrimers in solution. J Chem Phys 2007; 127:014901. [PMID: 17627363 DOI: 10.1063/1.2750339] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The "polymer reference interaction site model" (PRISM) integral equation theory is used to determine the structure factor of rigid dendrimers in solution. The theory is quite successful in reproducing experimental structure factors for various dendrimer concentrations. In addition, the structure factor at vanishing scattering vector is calculated via the compressibility equation using scaled particle theory and fundamental measure theory. The results as predicted by both theories are systematically smaller than the experimental and PRISM data for platelike dendrimers.
Collapse
Affiliation(s)
- L Harnau
- Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
| | | | | |
Collapse
|
25
|
Bier M, Harnau L, Dietrich S. Surface properties of fluids of charged platelike colloids. J Chem Phys 2006; 125:184704. [PMID: 17115776 DOI: 10.1063/1.2360939] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.
Collapse
Affiliation(s)
- Markus Bier
- Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, 70569 Stuttgart, Germany.
| | | | | |
Collapse
|
26
|
Rosenfeldt S, Karpuk E, Lehmann M, Meier H, Lindner P, Harnau L, Ballauff M. The Solution Structure of Stilbenoid Dendrimers: A Small-Angle Scattering Study. Chemphyschem 2006; 7:2097-104. [PMID: 16977668 DOI: 10.1002/cphc.200600231] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
The spatial structure of a stilbenoid dendrimer is investigated by small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) in dilute solution. All measurements are performed in toluene. The dendrimer consists of a stilbenoid scaffold with appended hexyloxy chains. SAXS is mainly sensitive to the dendrimer scaffold whereas SANS intensity, measured in fully deuterated toluene, derives from the solute molecules. The resulting SAXS and SANS intensities are analyzed by comparison with various models. It is found that the model of a circular disk gives the best description of the data. SAXS data demonstrate that the stilbenoid scaffold is flat as expected for benzene rings conjugated through vinylene units. Thus, it can be described by a circular disk with a radius of 1.6 nm and a thickness of 0.7 nm. SANS, on the other hand, shows that the hexyloxy chains are not confined in the plane defined by the core. This is derived from modeling the SANS data with a much thicker circular disk (radius: 2.4 nm, thickness: 1.8 nm). The structure factor S(q), describing the interaction of the dendrimers at higher concentrations, is modeled quantitatively with the "polymer reference interaction site model" (PRISM) integral equation formalism for hard plates such as particles. Here the structural data obtained from the analysis of the SANS data are used so that no new adjustable parameter is necessary for this description.
Collapse
Affiliation(s)
- Sabine Rosenfeldt
- Physikalische Chemie I, Universität Bayreuth 96440 Bayreuth, Germany
| | | | | | | | | | | | | |
Collapse
|
27
|
Li L, Harnau L, Rosenfeldt S, Ballauff M. Effective interaction of charged platelets in aqueous solution: investigations of colloid laponite suspensions by static light scattering and small-angle x-ray scattering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:051504. [PMID: 16383608 DOI: 10.1103/physreve.72.051504] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2005] [Indexed: 05/05/2023]
Abstract
We study dilute aqueous solutions of charged disklike mineral particles (laponite) by a combination of static light scattering (SLS) and small-angle x-ray scattering (SAXS). Laponite solutions are known to form gels above a certain critical concentration that must be described as nonequilibrium states. Here we focus on the investigation by SLS and SAXS at concentrations below gelation (c<0.016 g/L) and at low concentrations of added salt (0.001M and 0.005M). Thus, we have obtained the scattering function of single Laponite platelets as well as the structure factor describing their interaction at finite concentration. A detailed analysis of the combined sets of data proves that the solutions are in a well-defined equilibrium state. Moreover, this analysis demonstrates the internal consistency and accuracy of the scattering functions obtained at finite concentrations. We find that laponite particles interact through an effective pair potential that is attractive on short range but repulsive on longer range. This finding demonstrates that Laponite solutions exhibit only a limited stability at the concentration of added salt used herein. Raising the ionic strength to 0.005M already leads to slow flocculation as is evidenced from the enhanced scattering intensity at smallest scattering angles. All data strongly suggest that the gelation occurring at higher concentration is related to aggregation.
Collapse
Affiliation(s)
- Li Li
- Physikalische Chemie I, University of Bayreuth, 95440 Bayreuth, Germany
| | | | | | | |
Collapse
|