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Guerrero-García GI, Pérez-Guerrero D, Sarmiento Gómez E. Activation energy, spatial confinement, and mean first passage and escape times of a tracer in a wormlike micellar fluid: an effective potential approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:174006. [PMID: 35090139 DOI: 10.1088/1361-648x/ac4fe6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 01/28/2022] [Indexed: 06/14/2023]
Abstract
Wormlike micelles are long semiflexible cylindrical polymer structures formed by amphiphiles. In solution, these linear micelles percolate in multiconected entangled networks, where cross-links can break and recombine dynamically. Technological applications of wormlike micellar fluids include tunable encapsulation/delivery of molecules or colloids in biomedicine, oil industry, and/or cleaning processes. In this work, we propose that the experimental activation energy, the spatial confinement, and the mean first passage and escape times of a spherical tracer immersed in wormlike micellar network, in which caging effects are observed, can be estimated from economic Brownian dynamics simulations of a single particle interacting with an effective one-dimensional cosine-like potential of amplitudeU0and periodicityL. The proposed one-fitting parameter method has been used to characterize the long-time dynamics of wormlike micellar solutions formed by the self-assembly of a mixture of zwitterionic and anionic surfactants at several temperatures and different concentrations of surfactant and brine. The amplitudeU0has displayed a good agreement regarding the corresponding experimental activation energy at different temperatures. The periodicityLhas shown to be an upper bound of the mesh sizeξand of the same order of magnitude regarding the entanglement lengthle, obtained from rheology and microrheology experiments. The escape time of the tracer in the effective potentialτescapeand the timet*, at which a change of curvature in the mean square displacement occurs, are upper and lower limits, respectively, of the experimental relaxation time. Our method is simple and fast, and we foresee that it should be applicable to model the long-time behaviour of tracers in other polymer systems, in which caging effects are present.
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Affiliation(s)
- Guillermo Iván Guerrero-García
- Facultad de Ciencias de la Universidad Autónoma de San Luis Potosí, Av. Chapultepec 1570, Privadas del Pedregal, 78295, San Luis Potosí, México
| | - Daniela Pérez-Guerrero
- Instituto de Física de la Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, San Luis Potosí, México
| | - Erick Sarmiento Gómez
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León,México
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2
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Cho JH, Bischofberger I. Two modes of cluster dynamics govern the viscoelasticity of colloidal gels. Phys Rev E 2021; 103:032609. [PMID: 33862797 DOI: 10.1103/physreve.103.032609] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 03/05/2021] [Indexed: 11/07/2022]
Abstract
Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.
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Affiliation(s)
- Jae Hyung Cho
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Irmgard Bischofberger
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Taloni A, Flomenbom O, Castañeda-Priego R, Marchesoni F. Single file dynamics in soft materials. SOFT MATTER 2017; 13:1096-1106. [PMID: 28119987 DOI: 10.1039/c6sm02570f] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.
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Affiliation(s)
- Alessandro Taloni
- Center for Complexity & Biosystems, Physics Department, University of Milan "La Statale", Via Giovanni Celoria 16, 20133 Milano, Italy and CNR-ISC - Center for Complex Systems, Via dei Taurini 19, 00185, Roma, Italy.
| | | | - Ramón Castañeda-Priego
- Division of Science and Engineering, University of Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150, Leon, Gto., Mexico
| | - Fabio Marchesoni
- Dipartimento di Fisica, Universitá di Camerino, I-62032 Camerino, Italy.
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Bewerunge J, Ladadwa I, Platten F, Zunke C, Heuer A, Egelhaaf SU. Time- and ensemble-averages in evolving systems: the case of Brownian particles in random potentials. Phys Chem Chem Phys 2016; 18:18887-95. [PMID: 27353405 DOI: 10.1039/c6cp02559e] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Anomalous diffusion is a ubiquitous phenomenon in complex systems. It is often quantified using time- and ensemble-averages to improve statistics, although time averages represent a non-local measure in time and hence can be difficult to interpret. We present a detailed analysis of the influence of time- and ensemble-averages on dynamical quantities by investigating Brownian particles in a rough potential energy landscape (PEL). Initially, the particle ensemble is randomly distributed, but the occupancy of energy values evolves towards the equilibrium distribution. This relaxation manifests itself in the time evolution of time- and ensemble-averaged dynamical measures. We use Monte Carlo simulations to study particle dynamics in a potential with a Gaussian distribution of energy values, where the long-time limit of the diffusion coefficient is known from theory. In our experiments, individual colloidal particles are exposed to a laser speckle pattern inducing a non-Gaussian roughness and are followed by optical microscopy. The relaxation depends on the kind and degree of roughness of the PEL. It can be followed and quantified by the time- and ensemble-averaged mean squared displacement. Moreover, the heterogeneity of the dynamics is characterized using single-trajectory analysis. The results of this work are relevant for the correct interpretation of single-particle tracking experiments in general.
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Affiliation(s)
- Jörg Bewerunge
- Condensed Matter Physics Laboratory, Heinrich Heine University, 40225 Düsseldorf, Germany.
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Schella A, Melzer A, July C, Bechinger C. Effect of confinement on the mode dynamics of dipole clusters. SOFT MATTER 2015; 11:1197-1207. [PMID: 25563898 DOI: 10.1039/c4sm02333a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Dynamical properties of colloidal clusters composed of paramagnetic beads are presented. The clusters were trapped either in a parabolic trough or in a hard-wall confinement. In order to access the dynamics of the ensembles, the instantaneous normal mode (INM) approach is utilized, which uses cluster configurations as an input. The peaks in the mode spectra weaken when the system size is increased and when the coupling strength is lowered. The short-time diffusive properties of the clusters are deduced using the INM technique. It is found that angular diffusion is always larger than radial diffusion regardless of the shape of the external trap. Further, short-time diffusion seems to be almost independent of the coupling strength in the solid regime, but decreases with increasing packing fraction and size of the ensembles. In general, it is found that diffusion is larger for parabolically confined than for hard-wall trapped clusters.
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Affiliation(s)
- André Schella
- Institute of Physics, Ernst-Moritz-Arndt-University Greifwald, Felix Hausdorff Str. 6, 17489 Greifswald, Germany.
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Euán-Díaz EC, Herrera-Velarde S, Misko VR, Peeters FM, Castañeda-Priego R. Structural transitions and long-time self-diffusion of interacting colloids confined by a parabolic potential. J Chem Phys 2015; 142:024902. [DOI: 10.1063/1.4905215] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kumar AA. Crossover from normal diffusion to single-file diffusion of particles in a one-dimensional channel: LJ particles in zeolite zsm-22. Mol Phys 2014. [DOI: 10.1080/00268976.2014.989929] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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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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Hanes RDL, Schmiedeberg M, Egelhaaf SU. Brownian particles on rough substrates: relation between intermediate subdiffusion and asymptotic long-time diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062133. [PMID: 24483412 DOI: 10.1103/physreve.88.062133] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2013] [Indexed: 06/03/2023]
Abstract
Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or simulations. For the case of one-dimensional random potentials with Gaussian distributed energies, we present a detailed analysis of experimental and simulation data. It is shown that the asymptotic long-time diffusion coefficient can be related to the behavior at intermediate times, namely, the minimum of the exponent that characterizes subdiffusion and hence corresponds to the maximum degree of subdiffusion. As a consequence, investigating only the dynamics at intermediate times is sufficient to predict the order of magnitude of the long-time diffusion coefficient and the time scale at which the crossover from subdiffusion to diffusion occurs, i.e., when the long-time diffusive regime and hence thermal equilibrium is established. Inversely, theoretical predictions derived for the asymptotic long-time behavior can be used to quantitatively characterize the intermediate behavior, which hardly has been studied so far.
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Affiliation(s)
- Richard D L Hanes
- Condensed Matter Physics Laboratory, Heinrich Heine University, D-40225 Düsseldorf, Germany
| | - Michael Schmiedeberg
- Institute for Theoretical Physics 2: Soft Matter, Heinrich Heine University, D-40225 Düsseldorf, Germany and Department of Physics, University of Osnabrück, D-49076 Osnabrück, Germany
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, D-40225 Düsseldorf, Germany
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Herrera-Velarde S, Euán-Díaz EC, Córdoba-Valdés F, Castañeda-Priego R. Hydrodynamic correlations in three-particle colloidal systems in harmonic traps. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:325102. [PMID: 23838468 DOI: 10.1088/0953-8984/25/32/325102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We report on the hydrodynamic correlations between colloids immersed in a low Reynolds number fluid. We consider colloidal arrays composed of three particles; each colloid is trapped in a single harmonic potential and interacts with the other colloids only via hydrodynamic forces. We focus on the role of a third body in the two-body correlation functions. We give special attention to a collinear configuration of particles, although the salient features of an equilateral triangle configuration are outlined. The correlation functions are computed both by means of Brownian dynamics simulations, and by solving analytically and numerically the Langevin equation under the assumption of constant diffusion tensor; this approximation is validated through computer simulations. We explicitly show that the presence of a third body affects the auto- and cross-correlation functions and that their behaviour, in some specific conditions, can be different from that commonly seen in a two-particle system. In particular, we have found that the auto-correlation functions show a slower decay, while the cross-correlation ones exhibit a temporal shift and a weaker amplitude. Moreover, an unexpected behaviour related to a positive correlation and associated with the appearance of new dynamical modes is observed in the case of the collinear array of three particles. This interesting effect might be used to tune the degree of hydrodynamic correlation in few-body colloidal systems.
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Affiliation(s)
- Salvador Herrera-Velarde
- Subdirección de Postgrado e Investigación, Instituto Tecnológico Superior de Xalapa, Sección 5A Reserva Territorial s/n, 91096, Xalapa, Veracruz, Mexico
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Lucena D, Ferreira WP, Munarin FF, Farias GA, Peeters FM. Tunable diffusion of magnetic particles in a quasi-one-dimensional channel. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012307. [PMID: 23410331 DOI: 10.1103/physreve.87.012307] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2012] [Revised: 12/04/2012] [Indexed: 06/01/2023]
Abstract
The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous magnetic field. For a strong applied magnetic field, we find that the mobility of the system, the exponent of diffusion, and the crossover time among different diffusion regimes can be tuned by the orientation of the magnetic field. For weak magnetic fields, the exponent of diffusion in the subdiffusive regime is independent of the orientation of the external field.
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Affiliation(s)
- D Lucena
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil.
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