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Ramírez-Garza OA, Méndez-Alcaraz JM, González-Mozuelos P. Effects of the curvature gradient on the distribution and diffusion of colloids confined to surfaces. Phys Chem Chem Phys 2021; 23:8661-8672. [PMID: 33876027 DOI: 10.1039/d0cp06474b] [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
The properties and behavior of colloids confined to move on curved surfaces offer a fertile ground for analysis since the geometric constraints induce specific features that are not available in flat spaces. Given their pertinence for biological and physicochemical processes, both with potential useful applications, the development of the concepts and methodology necessary for a deeper understanding of these unconventional systems is indeed an essential pursuit. The present study discusses a general and rigorous algorithm for the implementation of Brownian dynamics simulations that solves underlying difficulties and shortcomings inherent to conventional first-order schemes. Still based on the Ermak-McCammon recipe, our approach complements it with the higher-order geodesical projections of the elementary jumps generated on the associated tangent plane. This strategy, which warrants the locally isotropic propagation of non-interacting particles, is tested with a model system of colloidal particles interacting through a screened Coulomb potential while confined to move on ellipsoidal surfaces. This allows us to measure the effects prompted by the curvature gradient on the static and dynamic properties of this system. The varying curvature thus induces energetically favorable configurations in which the particles maximize their Euclidean distancing by crowding the regions with the largest Gaussian curvature, while withdrawing from those with the lowest. In turn, these inhomogeneous distributions provoke the anisotropic self-diffusion of the confined colloids, which is examined by exploiting the pertinent geodesic radial coordinates. The proficient methods under consideration thus allows dealing with the rich and remarkable new phenomena generated by any distinctive surface geometry.
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Affiliation(s)
- O A Ramírez-Garza
- Departamento de Física, Cinvestav del I. P. N., Av. Instituto Politécnico Nacional 2508, Ciudad de México, C. P. 07360, Mexico.
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2
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Quintana C, González-Mozuelos P. Nanoparticles confined to a spherical surface in the presence of an external field: Interaction forces and induced microstructure. J Chem Phys 2018; 148:234901. [PMID: 29935519 DOI: 10.1063/1.5014991] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The structural response of a set of charged nanoparticles confined to move on a spherical surface under the influence of an external field is studied by Brownian Dynamics (BD) simulations and by an integral equation approach (IEA). Considering an identical nanoparticle as the source of the external field, we analyze the force exerted by the N confined particles on the external one, as well as the corresponding potential energy, focusing on their dependence on the distance of the external particle to the center of the sphere r0. The connection of the force and potential to the equilibrium local distribution of the adsorbed particles, that is, the microstructure within the spherical monolayer induced by the external nanoparticle, which is also dependent on r0, is elucidated by this analysis. It is found that the external particle needs to surmount a considerable potential barrier when moving toward the spherical surface, although much smaller than the one generated by a uniform surface distribution with an equivalent amount of charge. This is understood in terms of the correlation hole within the confined monolayer induced by the external particle. Another interesting conclusion is that the IEA provides an accurate, almost quantitative, description of the main features observed in the BD results, yet it is much less computationally demanding. The connection of these results with the overall chemical equilibrium of charged surfactant nanoparticles in the context of Pickering emulsions is also briefly discussed.
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Affiliation(s)
- C Quintana
- Departamento de Física, Cinvestav del I. P. N., Av. Instituto Politécnico Nacional 2508, Ciudad de México, C. P. 07360, Mexico
| | - P González-Mozuelos
- Departamento de Física, Cinvestav del I. P. N., Av. Instituto Politécnico Nacional 2508, Ciudad de México, C. P. 07360, Mexico
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Ramírez-Garza OA, Méndez-Alcaraz JM, González-Mozuelos P. Structural and dynamic inhomogeneities induced by curvature gradients in elliptic colloidal halos of paramagnetic particles. J Chem Phys 2017; 146:194903. [PMID: 28527452 DOI: 10.1063/1.4983496] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Paramagnetic colloidal particles distributed along an ellipse are used as a model system to study the effects of curvature gradients on the structure and dynamics of colloids in curved manifolds. Unlike what happens for circular and spherical systems, in the present case, the equilibrium one-particle distribution function displays inhomogeneities due to the changing curvature along the ellipse. The ensuing effects on the two-body correlations are also analyzed, leading to the observation of anisotropic and long-ranged effects. Another noticeable consequence is the slowing down of the self-diffusion of these particles, which for large eccentricities may induce metastable states; this is evaluated by means of the time-dependent self-distribution.
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Affiliation(s)
- O A Ramírez-Garza
- Departamento de Física, Cinvestav del I. P. N., Ave. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, C.P. 07360, Mexico
| | - J M Méndez-Alcaraz
- Departamento de Física, Cinvestav del I. P. N., Ave. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, C.P. 07360, Mexico
| | - P González-Mozuelos
- Departamento de Física, Cinvestav del I. P. N., Ave. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, C.P. 07360, Mexico
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Castro-Villarreal P, Villada-Balbuena A, Méndez-Alcaraz JM, Castañeda-Priego R, Estrada-Jiménez S. A Brownian dynamics algorithm for colloids in curved manifolds. J Chem Phys 2014; 140:214115. [DOI: 10.1063/1.4881060] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pavel Castro-Villarreal
- Centro de Estudios en Física y Matemáticas Básicas y Aplicadas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata, Km. 8, Rancho San Francisco, C. P. 29050, Tuxtla Gutiérrez, Chiapas, México
| | | | | | - Ramón Castañeda-Priego
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Guanajuato, México
| | - Sendic Estrada-Jiménez
- Centro de Estudios en Física y Matemáticas Básicas y Aplicadas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata, Km. 8, Rancho San Francisco, C. P. 29050, Tuxtla Gutiérrez, Chiapas, México
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Fantoni R, Salari JWO, Klumperman B. Structure of colloidosomes with tunable particle density: simulation versus experiment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061404. [PMID: 23005093 DOI: 10.1103/physreve.85.061404] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2012] [Indexed: 06/01/2023]
Abstract
Colloidosomes are created in the laboratory from a Pickering emulsion of water droplets in oil. The colloidosomes have approximately the same diameter and by choosing (hairy) particles of different diameters it is possible to control the particle density on the droplets. The experiment is performed at room temperature. The radial distribution function of the assembly of (primary) particles on the water droplet is measured in the laboratory and in a computer experiment of a fluid model of particles with pairwise interactions on the surface of a sphere.
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Affiliation(s)
- Riccardo Fantoni
- National Institute for Theoretical Physics and Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa.
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Viveros-Méndez PX, Méndez-Alcaraz JM, González-Mozuelos P. Formation and structure of colloidal halos in two-dimensional suspensions of paramagnetic particles. J Chem Phys 2012; 136:164902. [PMID: 22559501 DOI: 10.1063/1.4704180] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Different Monte Carlo simulation approaches are used here to study the static structure induced by a spherical neutral substrate inserted in the midst of a two-dimensional suspension of paramagnetic particles. It is then observed that in some instances some of these particles are adsorbed to the surface of the substrate, forming colloidal halos. We investigate the necessary conditions for the formation of these halos and the dependence of the number of adsorbed particles on the relevant parameters of the system. The angular distribution of the adsorbed particles around the perimeter of the substrate is analyzed here too.
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Affiliation(s)
- P X Viveros-Méndez
- División de Ciencias e Ingenierías, Universidad de Guanajuato, León, Guanajuato, C. P. 37150, Mexico
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Guzowski J, Tasinkevych M, Dietrich S. Free energy of colloidal particles at the surface of sessile drops. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 33:219-242. [PMID: 21072554 DOI: 10.1140/epje/i2010-10667-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2010] [Accepted: 10/11/2010] [Indexed: 05/30/2023]
Abstract
The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals π/2 , a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free-energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.
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Affiliation(s)
- J Guzowski
- Max-Planck-Institut für Metallforschung, Stuttgart, Germany.
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Fortuna S, Colard CAL, Troisi A, Bon SAF. Packing patterns of silica nanoparticles on surfaces of armored polystyrene latex particles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2009; 25:12399-12403. [PMID: 19438175 DOI: 10.1021/la9010289] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Fascinating packing patterns of identical spherical and discotic objects on curved surfaces occur readily in nature and science. Examples include C(60) fullerenes, (1, 2) 13-atom cuboctahedral metal clusters, (3) and S-layer proteins on outer cell membranes. (4) Numerous situations with surface-arranged objects of variable size also exist, such as the lenses on insect eyes, biomineralized shells on coccolithophorids, (5) and solid-stabilized emulsion droplets (6) and bubbles. (7) The influence of size variations on these packing patterns, however, is studied sparsely. Here we investigate the packing of nanosized silica particles on the surface of polystyrene latex particles fabricated by Pickering miniemulsion polymerization of submicrometer-sized armored monomer droplets. We are able to rationalize the experimental morphology and the nearest-neighbor distribution with the help of Monte Carlo simulations. We show that broadening of the nanoparticle size distribution has pronounced effects on the self-assembled equilibrium packing structures, with original 12-point dislocations or grain-boundary scars gradually fading out.
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Affiliation(s)
- Sara Fortuna
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, UK
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