1
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Schmidt R, Kiefer H, Dalgliesh R, Gradzielski M, Netz RR. Nanoscopic Interfacial Hydrogel Viscoelasticity Revealed from Comparison of Macroscopic and Microscopic Rheology. NANO LETTERS 2024; 24. [PMID: 38591912 PMCID: PMC11057034 DOI: 10.1021/acs.nanolett.3c04884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2023] [Revised: 04/02/2024] [Accepted: 04/03/2024] [Indexed: 04/10/2024]
Abstract
Deviations between macrorheological and particle-based microrheological measurements are often considered to be a nuisance and neglected. We study aqueous poly(ethylene oxide) (PEO) hydrogels for varying PEO concentrations and chain lengths that contain microscopic tracer particles and show that these deviations reveal the nanoscopic viscoelastic properties of the particle-hydrogel interface. Based on the transient Stokes equation, we first demonstrate that the deviations are not due to finite particle radius, compressibility, or surface-slip effects. Small-angle neutron scattering rules out hydrogel heterogeneities. Instead, we show that a generalized Stokes-Einstein relation, accounting for an interfacial shell around tracers with viscoelastic properties that deviate from bulk, consistently explains our macrorheological and microrheological measurements. The extracted shell diameter is comparable to the PEO end-to-end distance, indicating the importance of dangling chain ends. Our methodology reveals the nanoscopic interfacial rheology of hydrogels and is applicable to different kinds of viscoelastic fluids and particles.
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Affiliation(s)
- Robert
F. Schmidt
- Stranski-Laboratorium
für Physikalische und Theoretische Chemie, Technische Universität Berlin, Strasse des 17. Juni 124, 10623 Berlin, Germany
| | - Henrik Kiefer
- Fachbereich
Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Robert Dalgliesh
- STFC, ISIS, Rutherford
Appleton
Laboratory, Chilton, Oxfordshire OX11 0QX, United Kingdom
| | - Michael Gradzielski
- Stranski-Laboratorium
für Physikalische und Theoretische Chemie, Technische Universität Berlin, Strasse des 17. Juni 124, 10623 Berlin, Germany
| | - Roland R. Netz
- Fachbereich
Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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2
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Opdam J, Gandhi P, Kuhnhold A, Schilling T, Tuinier R. Excluded volume interactions and phase stability in mixtures of hard spheres and hard rods. Phys Chem Chem Phys 2022; 24:11820-11827. [PMID: 35508061 DOI: 10.1039/d2cp00477a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this paper we study excluded volume interactions, the free volume fraction available, and the phase behaviour, in mixtures of hard spheres (HS) and hard rods, modeled as spherocylinders. We use free volume theory (FVT) to predict various physical properties and compare to Monte Carlo computer simulations. FVT is used at two levels. We use the original FVT approach in which it is assumed that the correlations of the HS are not affected by the rods. This is compared to a recent, more rigorous, FVT approach which includes excluded volume interactions between the different components at all levels. We find that the novel rigorous FVT approach agrees well with computer simulation results at the level of free volume available, as well as for the phase stability. The FVT predictions show significant quantitative and qualitative deviations with respect to the original FVT approach. The phase transition curves are systematically at higher rod concentrations than previously predicted. Furthermore, the calculations revealed that a certain asphericity is required to induce isostructural fluid-fluid coexistence and the stability region is highly dependent on the size ratio between the rods and the spheres.
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Affiliation(s)
- Joeri Opdam
- 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.
| | - 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.
| | - Tanja Schilling
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
| | - 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.
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3
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Unni M, Savliwala S, Partain BD, Maldonado-Camargo L, Zhang Q, Narayanan S, Dufresne EM, Ilavsky J, Grybos P, Koziol A, Maj P, Szczygiel R, Allen KD, Rinaldi-Ramos CM. Fast nanoparticle rotational and translational diffusion in synovial fluid and hyaluronic acid solutions. SCIENCE ADVANCES 2021; 7:eabf8467. [PMID: 34193423 PMCID: PMC8245030 DOI: 10.1126/sciadv.abf8467] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Accepted: 05/17/2021] [Indexed: 05/13/2023]
Abstract
Nanoparticles are under investigation as diagnostic and therapeutic agents for joint diseases, such as osteoarthritis. However, there is incomplete understanding of nanoparticle diffusion in synovial fluid, the fluid inside the joint, which consists of a mixture of the polyelectrolyte hyaluronic acid, proteins, and other components. Here, we show that rotational and translational diffusion of polymer-coated nanoparticles in quiescent synovial fluid and in hyaluronic acid solutions is well described by the Stokes-Einstein relationship, albeit with an effective medium viscosity that is much smaller than the macroscopic low shear viscosity of the fluid. This effective medium viscosity is well described by an equation for the viscosity of dilute polymer chains, where the additional viscous dissipation arises because of the presence of the polymer segments. These results shed light on the diffusive behavior of polymer-coated inorganic nanoparticles in complex and crowded biological environments, such as in the joint.
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Affiliation(s)
- Mythreyi Unni
- Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
| | - Shehaab Savliwala
- Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
| | - Brittany D Partain
- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611, USA
| | | | - Qingteng Zhang
- X-ray Science Division, Argonne National Laboratory, Lemont, IL 60439, USA
| | - Suresh Narayanan
- X-ray Science Division, Argonne National Laboratory, Lemont, IL 60439, USA
| | - Eric M Dufresne
- X-ray Science Division, Argonne National Laboratory, Lemont, IL 60439, USA
| | - Jan Ilavsky
- X-ray Science Division, Argonne National Laboratory, Lemont, IL 60439, USA
| | - Pawel Grybos
- AGH University of Science and Technology, av. Mickiewicza 30, Kraków 30-059, Poland
| | - Anna Koziol
- AGH University of Science and Technology, av. Mickiewicza 30, Kraków 30-059, Poland
| | - Piotr Maj
- AGH University of Science and Technology, av. Mickiewicza 30, Kraków 30-059, Poland
| | - Robert Szczygiel
- AGH University of Science and Technology, av. Mickiewicza 30, Kraków 30-059, Poland
| | - Kyle D Allen
- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611, USA
| | - Carlos M Rinaldi-Ramos
- Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA.
- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611, USA
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4
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Potier M, Tea L, Benyahia L, Nicolai T, Renou F. Viscosity of Aqueous Polysaccharide Solutions and Selected Homogeneous Binary Mixtures. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c02157] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mathieu Potier
- Le Mans Université, IMMM UMR-CNRS 6283, 72085 Le Mans Cedex 9, France
| | - Lingsam Tea
- Le Mans Université, IMMM UMR-CNRS 6283, 72085 Le Mans Cedex 9, France
| | - Lazhar Benyahia
- Le Mans Université, IMMM UMR-CNRS 6283, 72085 Le Mans Cedex 9, France
| | - Taco Nicolai
- Le Mans Université, IMMM UMR-CNRS 6283, 72085 Le Mans Cedex 9, France
| | - Frederic Renou
- Le Mans Université, IMMM UMR-CNRS 6283, 72085 Le Mans Cedex 9, France
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5
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Hess M, Gratz M, Remmer H, Webers S, Landers J, Borin D, Ludwig F, Wende H, Odenbach S, Tschöpe A, Schmidt AM. Scale-dependent particle diffusivity and apparent viscosity in polymer solutions as probed by dynamic magnetic nanorheology. SOFT MATTER 2020; 16:7562-7575. [PMID: 32716420 DOI: 10.1039/c9sm00747d] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
In several upcoming rheological approaches, including methods of micro- and nanorheology, the measurement geometry is of critical impact on the interpretation of the results. The relative size of the probe objects employed (as compared to the intrinsic length scales of the sample to be investigated) becomes of crucial importance, and there is increasing interest to investigate the dynamic processes and mobility in nanostructured materials. A combination of different rheological approaches based on the rotation of magnetically blocked nanoprobes is used to systematically investigate the size-dependent diffusion behavior in aqueous poly(ethylene glycol) (PEG) solutions with special attention paid to the relation of probe size to characteristic length scales within the polymer solutions. We employ two types of probe particles: nickel rods of hydrodynamic length Lh between 200 nm and 650 nm, and cobalt ferrite spheres with diameter dh between 13 nm and 23 nm, and examine the influence of particle size and shape on the nanorheological information obtained in model polymer solutions based on two related, dynamic-magnetic approaches. The results confirm that as long as the investigated solutions are not entangled, and the particles are much larger than the macromolecular correlation length, a good accordance between macroscopic and nanoscopic results, whereas a strong size-dependent response is observed in cases where the particles are of similar size or smaller than the radius of gyration Rg or the correlation length ξ of the polymer solution.
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Affiliation(s)
- Melissa Hess
- Institute of Physical Chemistry, Chemistry Department, Faculty of Mathematics and Natural Sciences, University of Cologne, Luxemburger Str. 116, D-50939 Köln, Germany.
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6
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Hess M, Roeben E, Rochels P, Zylla M, Webers S, Wende H, Schmidt AM. Size effects on rotational particle diffusion in complex fluids as probed by Magnetic Particle Nanorheology. Phys Chem Chem Phys 2019; 21:26525-26539. [PMID: 31778132 DOI: 10.1039/c9cp04083h] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Rheological approaches based on micro- or nanoscopic probe objects are of interest due to the low volume requirement, the option of spatially resolved probing, and the minimal-invasive nature often connected to such probes. For the study of microstructured systems or biological environments, such methods show potential for investigating the local, size-dependent diffusivity and particle-matrix interactions. For the latter, the relative length scale of the used probes compared to the size of the structural units of the matrix becomes relevant. In this study, a rotational-dynamic approach based on Magnetic Particle Nanorheology (MPN) is used to extract size- and frequency-dependent nanorheological properties by using an otherwise well-established polymer model system. We use magnetically blocked CoFe2O4 nanoparticles as tracers and systematically vary their hydrodynamic size by coating them with a silica shell. On the polymer side, we employ aqueous solutions of poly(ethylene glycol) (PEG) by varying molar mass M and volume fraction φ. The complex Brownian relaxation behavior of the tracer particles in solutions of systematically varied composition is investigated by means of AC susceptometry (ACS), and the results provide access to frequency dependent rheological properties. The size-dependent particle diffusivity is evaluated based on theoretical descriptions and macroscopic measurements. The results allow the classification of the investigated compositions into three regimes, taking into account the probe particle size and the length scales of the polymer solution. While a fuzzy cross-over is indicated between the well-known macroscopic behavior and structurally dominated spectra, where the hydrodynamic radius is equal to the radius of gyration of the polymer (rh ∼ Rg), the frequency-related scaling behavior is dominated by the correlation length ξ respectively by the tube diameter a in entangled solutions for rh < Rg.
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Affiliation(s)
- Melissa Hess
- Institute of Physical Chemistry, Chemistry Department, Faculty of Mathematics and Natural Sciences, University of Cologne, Luxemburger Str. 116, D-50939 Köln, Germany.
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7
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Senanayake KK, Shokeen N, Fakhrabadi EA, Liberatore MW, Mukhopadhyay A. Diffusion of nanoparticles within a semidilute polyelectrolyte solution. SOFT MATTER 2019; 15:7616-7622. [PMID: 31482916 DOI: 10.1039/c9sm01313j] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We studied the diffusion of charged gold nanoparticles within a semidilute solution of weakly charged polyelectrolyte, polyacrylic acid (PAA) of high molecular weight (Mw = 106 g mol-1) by using fluorescence correlation spectroscopy (FCS). Nanoparticle size (d) was varied between 5 nm to 40 nm and PAA volume fraction (φ) in water ranged from about 8φ* to 33φ*, where φ* is the overlap volume fraction. The reduced diffusion coefficient - defined as -D/Do, where D is the diffusion coefficient in PAA solution and Do is that in neat water - has a weak dependence on the particle size. D follows a power law of the form ∼φ-0.5, which can be explained by a mean-field hydrodynamic theory in porous medium. Additional, rheology measurements showed a zero shear rate viscosity and shear thinning, which are typical of high molecular weight polyelectrolytes.
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Affiliation(s)
| | - Namita Shokeen
- Department of Physics, Wayne State University, Detroit, MI 48201, USA.
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8
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Gratz M, Tschöpe A. Size Effects in the Oscillatory Rotation Dynamics of Ni Nanorods in Poly(ethylene oxide) Solutions. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b00788] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- Micha Gratz
- Experimentalphysik, Universität des Saarlandes, Campus D2 2, 66123 Saarbrücken, Germany
| | - Andreas Tschöpe
- Experimentalphysik, Universität des Saarlandes, Campus D2 2, 66123 Saarbrücken, Germany
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9
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Senanayake KK, Mukhopadhyay A. Nanoparticle Diffusion within Dilute and Semidilute Xanthan Solutions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:7978-7984. [PMID: 31117734 DOI: 10.1021/acs.langmuir.9b01029] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We measured the translation diffusion coefficient ( D) of nanoparticles within dilute and semidilute solutions of a semiflexible polymer, xanthan. Our results showed that for particle diameters ( d) of 5 and 10 nm, the obstruction theory can explain the concentration ( c) dependence of D in the dilute regime. Diffusion in semidilute solutions is better explained by additionally considering the modified Darcy flow with the hydrodynamic screening length varying according to κ ≈ c-0.76. The depletion effect is operative for larger particles ( d = 30 nm) within semidilute solutions. We used a scaling relation for the depletion layer thickness δ ≈ ξν, where ξ is the static correlation length and the exponent ν ≈ 0.42 that can explain our data. This is in contrast with a flat surface, where the exponent is expected to be 1. Our results showed that in the situation, when the polymer network relaxation is much slower compared to the diffusive time-scale of particles, no single theory is capable to describe the concentration and size dependence of particle mobility.
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Affiliation(s)
- Kavindya K Senanayake
- Department of Physics , Wayne State University , Detroit , Michigan 48201 , United States
| | - Ashis Mukhopadhyay
- Department of Physics , Wayne State University , Detroit , Michigan 48201 , United States
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10
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Zöttl A, Yeomans JM. Driven spheres, ellipsoids and rods in explicitly modeled polymer solutions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:234001. [PMID: 30836331 DOI: 10.1088/1361-648x/ab0cf8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Understanding the transport of driven nano- and micro-particles in complex fluids is of relevance for many biological and technological applications. Here we perform hydrodynamic multiparticle collision dynamics simulations of spherical and elongated particles driven through polymeric fluids containing different concentrations of polymers. We determine the mean particle velocities which are larger than expected from Stokes law for all particle shapes and polymer densities. Furthermore we measure the fluid flow fields and local polymer density and polymer conformation around the particles. We find that polymer-depleted regions close to the particles are responsible for an apparent tangential slip velocity which accounts for the measured flow fields and transport velocities. A simple two-layer fluid model gives a good match to the simulation results.
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Affiliation(s)
- Andreas Zöttl
- The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Lab., Parks Rd., Oxford, OX1 3PU, United Kingdom. Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria. Erwin Schrödinger Int. Institute for Mathematics and Physics, University of Vienna, Boltzmanngasse 9, A-1090 Wien, Austria
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11
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Du Y, Jiang H, Hou Z. Study of active Brownian particle diffusion in polymer solutions. SOFT MATTER 2019; 15:2020-2031. [PMID: 30724318 DOI: 10.1039/c8sm02292e] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The diffusion behavior of an active Brownian particle (ABP) in polymer solutions is studied using Langevin dynamics simulations. We find that the long time diffusion coefficient D can show a non-monotonic dependence on the particle size R if the active force Fa is large enough, wherein a bigger particle would diffuse faster than a smaller one which is quite counterintuitive. By analyzing the short time dynamics in comparison to the passive one, we find that such non-trivial dependence results from the competition between persistent motion of the ABP and the length-scale dependent effective viscosity that the particle experiences in the polymer solution. We have also introduced an effective viscosity ηeff experienced by the ABP phenomenologically. Such an active ηeff is found to be larger than a passive one and strongly depends on R and Fa. In addition, we find that the dependence of D on propelling force Fa presents a good power-law scaling at a fixed R and the scaling factor changes non-monotonically with R. Such results demonstrate that the active process plays rather subtle roles in the diffusion of nano-particles in complex solutions.
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Affiliation(s)
- Yunfei Du
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China.
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12
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Gutiérrez-Sosa C, Merino-González A, Sánchez R, Kozina A, Díaz-Leyva P. Microscopic Viscoelasticity of Polymer Solutions and Gels Observed from Translation and Rotation of Anisotropic Colloid Probes. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01005] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Carlos Gutiérrez-Sosa
- Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, 09340 Mexico City, Mexico
| | - Arturo Merino-González
- Instituto de Química, Universidad Nacional Autónoma de México, P.O.
Box 70-213, 04510 Mexico City, Mexico
| | - Rodrigo Sánchez
- Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, 09340 Mexico City, Mexico
| | - Anna Kozina
- Instituto de Química, Universidad Nacional Autónoma de México, P.O.
Box 70-213, 04510 Mexico City, Mexico
| | - Pedro Díaz-Leyva
- Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, 09340 Mexico City, Mexico
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13
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Nakamura Y, Yoshimori A, Akiyama R, Yamaguchi T. Stick boundary condition at large hard sphere arising from effective attraction in binary hard-sphere mixtures. J Chem Phys 2018; 148:124502. [DOI: 10.1063/1.5025202] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuka Nakamura
- Department of Physics, Kyushu University, Fukuoka 812-0395, Japan
| | - Akira Yoshimori
- Department of Physics, Niigata University, Niigata 950-2181, Japan
| | - Ryo Akiyama
- Department of Chemistry, Kyushu University, Fukuoka 812-0395, Japan
| | - Tsuyoshi Yamaguchi
- Department of Materials Process Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
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14
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Leitmann S, Höfling F, Franosch T. Dynamically crowded solutions of infinitely thin Brownian needles. Phys Rev E 2018; 96:012118. [PMID: 29347251 DOI: 10.1103/physreve.96.012118] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 11/07/2022]
Abstract
We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly non-Gaussian; rather, it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.
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Affiliation(s)
- Sebastian Leitmann
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Felix Höfling
- Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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15
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Chen A, Zhao N, Hou Z. The effect of hydrodynamic interactions on nanoparticle diffusion in polymer solutions: a multiparticle collision dynamics study. SOFT MATTER 2017; 13:8625-8635. [PMID: 29115361 DOI: 10.1039/c7sm01854a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The diffusion of nanoparticles (NPs) in polymer solutions is studied by a combination of a mesoscale simulation method, multiparticle collision dynamics (MPCD), and molecular dynamics (MD) simulations. We investigate the long-time diffusion coefficient D as well as the subdiffusive behavior in the intermediate time region. The dependencies of both D and subdiffusion factor α on NP size and polymer concentration, respectively, are explicitly calculated. Particular attention is paid to the role of hydrodynamic interaction (HI) in the NP diffusion dynamics. Our simulation results show that the long-time diffusion coefficients satisfy perfectly the scaling relation found by experimental observations. Meanwhile, the subdiffusive factor decreases with the increase in polymer concentration but is of little relevance to the NP size. By parallel simulations with and without HI, we reveal that HI will generally enhance D, while the enhancement effect is non-monotonous with increasing polymer concentration, and it becomes most pronounced at semidilute concentrations. With the aid of a scaling law based on the diffusive activation energy model, we understand that HI affects diffusion through decreasing the diffusive activation energy on the one hand while increasing the effective diffusion size on the other. In addition, HI will certainly influence the subdiffusive behavior of the NP, leading to a larger subdiffusion exponent.
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Affiliation(s)
- Anpu Chen
- College of Chemistry, Sichuan University, Chengdu 610064, China.
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16
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Maldonado-Camargo L, Yang C, Rinaldi C. Scale-dependent rotational diffusion of nanoparticles in polymer solutions. NANOSCALE 2017; 9:12039-12050. [PMID: 28795729 DOI: 10.1039/c7nr01603d] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
It is shown that the rotational diffusivity of nanoparticles in polymer solutions spanning the dilute to semi-dilute regimes deviates from the predictions of the Stokes-Einstein (SE) relationship, and that this deviation can be explained by the existence of a polymer depletion layer with the viscosity of the bath solvent. The measurements of the rotational diffusion coefficient of poly(ethylene glycol) (PEG) grafted magnetic nanoparticles in PEG solutions spanning the dilute to semi-dilute regimes and a wide range of polymer molecular weights were obtained from the dynamic magnetic response of the nanoparticles to alternating magnetic fields. Experimental rotational diffusion coefficient values were compared with those predicted by the SE relation using the macroscopic viscosity of the polymer solutions and the hydrodynamic radius of the nanoparticles. Deviations between experimental and SE rotational diffusivity values were observed for nanoparticles in polymer solutions where the radius of gyration of the polymer exceeded the hydrodynamic radius of the particles. A simple model for the rotational hydrodynamic drag on a particle surrounded by a polymer depletion layer was found to describe the experimental rotational diffusivities well, suggesting that the observed phenomenon arises due to the formation of a polymer depletion layer around the nanoparticles.
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Affiliation(s)
- Lorena Maldonado-Camargo
- Department of Chemical Engineering, University of Florida, P.O. Box 116005, Gainesville, FL 32603, USA.
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17
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Bharadwaj NAK, Kang JG, Hatzell MC, Schweizer KS, Braun PV, Ewoldt RH. Integration of colloids into a semi-flexible network of fibrin. SOFT MATTER 2017; 13:1430-1443. [PMID: 28124056 DOI: 10.1039/c6sm02141g] [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
Typical colloid-polymer composites have particle diameters much larger than the polymer mesh size, but successful integration of smaller colloids into a large-mesh network could allow for the realization of new colloidal states of spatial organization and faster colloid motion which can allow the possibility of switchable re-configuration of colloids or more dramatic stimuli-responsive property changes. Experimental realization of such composites requires solving non-trivial materials selection and fabrication challenges; key questions include composition regime maps of successful composites, the resulting structure and colloidal contact network, and the mechanical properties, in particular the ability to form a network and retain strain stiffening in the presence of colloids. Here, we study these fundamental questions by formulating composites with fluorescent (though not stimuli-responsive) carboxylate modified polystyrene/latex (CML) colloidal particles (diameters 200 nm and 1000 nm) in bovine fibrin networks (a semi-flexible biopolymer network with mesh size 1-5 μm). We describe and characterize two methods of composite preparation: adding colloids before fibrinogen polymerization (Method I), and electrophoretically driving colloids into a network already formed by fibrinogen polymerization (Method II). We directly image the morphology of colloidal and fibrous components with two-color fluorescent confocal microscopy under wet conditions and SEM of fixed dry samples. Mechanical properties are studied with shear and extensional rheology. Both fabrication methods are successful, though with trade-offs. Method I retains the nonlinear strain-stiffening and extensibility of the native fibrin network, but some colloid clustering is observed and fibrin network integrity is lost above a critical colloid concentration that depends on fibrinogen and thrombin concentration. Larger colloids can be included at higher volume fractions before massive aggregation occurs, indicating surface interactions as a limiting factor. Method II results in a loss of measurable strain-stiffening, but colloids are well dispersed and template along the fibrous scaffold. The results here, with insight into both structure and rheology, form a foundational understanding for the integration of other colloids, e.g. with stimuli-responsive functionalities, into semi-flexible networks.
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Affiliation(s)
- N Ashwin K Bharadwaj
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Jin Gu Kang
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Marta C Hatzell
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Kenneth S Schweizer
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Paul V Braun
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Randy H Ewoldt
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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18
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Leitmann S, Höfling F, Franosch T. Tube Concept for Entangled Stiff Fibers Predicts Their Dynamics in Space and Time. PHYSICAL REVIEW LETTERS 2016; 117:097801. [PMID: 27610885 DOI: 10.1103/physrevlett.117.097801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2016] [Indexed: 06/06/2023]
Abstract
We study dynamically crowded solutions of stiff fibers deep in the semidilute regime, where the motion of a single constituent becomes increasingly confined to a narrow tube. The spatiotemporal dynamics for wave numbers resolving the motion in the confining tube becomes accessible in Brownian dynamics simulations upon employing a geometry-adapted neighbor list. We demonstrate that in such crowded environments the intermediate scattering function, characterizing the motion in space and time, can be predicted quantitatively by simulating a single freely diffusing phantom needle only, yet with very unusual diffusion coefficients.
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Affiliation(s)
- Sebastian Leitmann
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Felix Höfling
- Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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19
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Appel J, Fölker B, Sprakel J. Mechanics at the glass-to-gel transition of thermoresponsive microgel suspensions. SOFT MATTER 2016; 12:2515-2522. [PMID: 26843322 DOI: 10.1039/c5sm02940f] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We study the rheology of systems of thermoresponsive microgels which can transition between a repulsive glass and an attractive gel state. We find marked differences between these two colloidal solids, within the same experimental system, due to the different origins for their dynamic arrest. While the rigidity of the repulsive systems depends solely on particle volume fraction, we find that the change in linear elasticity upon introducing attractive bonds in the system scales linearly with the adhesive bond strength which can be tuned with the temperature in our experiments. And while the glasses yield reversibly and with a rate-dependent energy dissipation, bond-reorganisation in the gels is suppressed so that their rupture is irreversible and accompanied by a high, but rate-independent, dissipation. These results highlight how colloids with responsive interactions can be employed to shed new light onto solid-solid transitions.
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Affiliation(s)
- Jeroen Appel
- Physical Chemistry and Soft Matter, Wageningen University, Dreijenplein 6, 6703 HB, Wageningen, The Netherlands.
| | - Bart Fölker
- Physical Chemistry and Soft Matter, Wageningen University, Dreijenplein 6, 6703 HB, Wageningen, The Netherlands.
| | - Joris Sprakel
- Physical Chemistry and Soft Matter, Wageningen University, Dreijenplein 6, 6703 HB, Wageningen, The Netherlands.
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20
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Dong Y, Feng X, Zhao N, Hou Z. Diffusion of nanoparticles in semidilute polymer solutions: A mode-coupling theory study. J Chem Phys 2015; 143:024903. [DOI: 10.1063/1.4926412] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yunhong Dong
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Xiaoqing Feng
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Zhonghuai Hou
- Department of Chemical Physics, Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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21
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Piedrahita M, Cuetos A, Martínez-Haya B. Transport of spherical colloids in layered phases of binary mixtures with rod-like particles. SOFT MATTER 2015; 11:3432-3440. [PMID: 25797280 DOI: 10.1039/c4sm02865a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The transport properties of colloids in anisotropic media constitute a general problem of fundamental interest in experimental sciences, with a broad range of technological applications. This work investigates the transport of soft spherical colloids in binary mixtures with rod-like particles by means of Monte Carlo and Brownian Dynamics simulations. Layered phases are considered, that range from smectic phases to lamellar phases, depending on the molar fraction of the spherical particles. The investigation serves to characterize the distinct features of transport within layers versus those of transport across neighboring layers, both of which are neatly differentiated. The insertion of particles into layers and the diffusion across them occur at a smaller rate than the intralayer diffusion modulated by the formation of transitory cages in its initial stages. Collective events, in which two or more colloids diffuse across layers in a concerted way, are described as a non-negligible process in these fluids.
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Affiliation(s)
- Mauricio Piedrahita
- Department of Physical, Chemical and Natural Systems, Universidad Pablo de Olavide, 41013 Seville, Spain.
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22
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Klein MK, Klinkenberg N, Schuetter S, Saenger N, Pfleiderer P, Zumbusch A. PMMA/PMMA core-shell particles with ellipsoidal, fluorescent cores: accessing rotational dynamics. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:2655-2661. [PMID: 25654438 DOI: 10.1021/la5045046] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
For several decades, nonaqueous dispersions of PMMA particles have played an important role in colloid research. They have found application as colloidal model systems, which are used to probe glassy dynamics or to explore crystal nucleation. To date, most research has focused on spherical particles, in which only translational motion can be investigated. Recently, however, there has been a surge of interest in analyzing also rotational dynamics. In this contribution, we introduce a new class of core-shell particles, which can be used as rotational probes. The colloids described herein are composed of shape anisotropic, fluorescent cores covered with nonfluorescent PMMA shells. The core-shell particles are built up in four steps. In a first step, we produce fluorescent and photo-cross-linkable PMMA colloids. In the second step, these particles are thermomechanically elongated and fixed in defined ellipsoidal shapes by photo-cross-linking. Subsequently, we cover the cross-linked, fluorescent core with a nonfluorescent PMMA shell. The shape of the resulting core-shell colloids is tunable between the initial anisotropic and perfect spherical shape. For shaping, we apply a simple solvent swelling procedure. As one option, this method yields perfect PMMA spheres with ellipsoidal, fluorescent centers. We also report morphological particle characterization using various fluorescence microscopy techniques. Finally, we demonstrate that the rotational dynamics of individual colloids can be tracked and analyzed.
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Affiliation(s)
- Matthias K Klein
- Department of Chemistry and ‡Department of Physics, University of Konstanz , Universitätsstraße 10, 78457 Konstanz, Germany
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23
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24
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Nakamura Y, Yoshimori A, Akiyama R. Effects of the solvation structure on diffusion of a large particle in a binary mixture studied by perturbation theory. J Mol Liq 2014. [DOI: 10.1016/j.molliq.2014.06.021] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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25
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Kohli I, Mukhopadhyay A. Diffusion of Nanoparticles in Semidilute Polymer Solutions: Effect of Different Length Scales. Macromolecules 2012. [DOI: 10.1021/ma301237r] [Citation(s) in RCA: 106] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Indermeet Kohli
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, United States
| | - Ashis Mukhopadhyay
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, United States
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26
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Martchenko I, Dietsch H, Moitzi C, Schurtenberger P. Hydrodynamic Properties of Magnetic Nanoparticles with Tunable Shape Anisotropy: Prediction and Experimental Verification. J Phys Chem B 2011; 115:14838-45. [DOI: 10.1021/jp2078264] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ilya Martchenko
- Adolphe Merkle Institute and Fribourg Center for Nanomaterials, Route de l’Ancienne Papeterie, CP 209, 1723 Marly 1, Switzerland
- Division of Physical Chemistry, Department of Chemistry, Lund University, Box 124, 22100 Lund, Sweden
| | - Hervé Dietsch
- Adolphe Merkle Institute and Fribourg Center for Nanomaterials, Route de l’Ancienne Papeterie, CP 209, 1723 Marly 1, Switzerland
| | | | - Peter Schurtenberger
- Division of Physical Chemistry, Department of Chemistry, Lund University, Box 124, 22100 Lund, Sweden
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Abstract
Many of the chapters in this volume are concerned with processes or structures inside the nucleus, and it is relevant to consider the properties of their environment, or rather of the multiple different and specific environments that must exist in local regions of the highly heterogeneous intranuclear space. Relatively little is known about the fundamental physical properties of these environments, and theoretical treatments of phenomena in such concentrated mixtures of charged macromolecules are complex and as yet poorly developed. Some of the phenomena that occur at the molecular level are unexpected and counterintuitive for biologists, although well known to colloid and polymer scientists; for example, the existence of short-range attractive forces between macromolecules or structures with like charges. As a background for the chapters that follow, we consider here some of the particular features of intranuclear environments, how they may influence processes and structures in the nucleus, and their implications for working with nuclei.
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28
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Cichocki B, Ekiel-Jeżewska ML. Self-diffusion of a sphere in an effective medium of rods. J Chem Phys 2009; 130:214902. [DOI: 10.1063/1.3146786] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Hoffmann M, Lu Y, Schrinner M, Ballauff M, Harnau L. Dumbbell-Shaped Polyelectrolyte Brushes Studied by Depolarized Dynamic Light Scattering. J Phys Chem B 2008; 112:14843-50. [DOI: 10.1021/jp806765y] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Martin Hoffmann
- Physikalische Chemie I, University of Bayreuth, 95440 Bayreuth, Germany
| | - Yan Lu
- Physikalische Chemie I, University of Bayreuth, 95440 Bayreuth, Germany
| | - Marc Schrinner
- Physikalische Chemie I, University of Bayreuth, 95440 Bayreuth, Germany
| | - Matthias Ballauff
- Physikalische Chemie I, University of Bayreuth, 95440 Bayreuth, Germany
| | - Ludger Harnau
- Max-Planck-Institut für Metallforschung, Heisenbergstraβe 3, D-70569 Stuttgart (Germany) and Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart (Germany)
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30
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Höfling F, Munk T, Frey E, Franosch T. Entangled dynamics of a stiff polymer. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:060904. [PMID: 18643210 DOI: 10.1103/physreve.77.060904] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2008] [Indexed: 05/26/2023]
Abstract
Entangled networks of stiff biopolymers exhibit complex dynamic response, emerging from the topological constraints that neighboring filaments impose upon each other. We propose a class of reference models for entanglement dynamics of stiff polymers and provide a quantitative foundation of the tube concept for stiff polymers. For an infinitely thin needle exploring a planar course of point obstacles, we have performed large-scale computer simulations proving the conjectured scaling relations from the fast transverse equilibration to the slowest process of orientational relaxation. We determine the rotational diffusion coefficient of the tracer, its angular confinement, the tube diameter, and the orientational correlation functions.
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Affiliation(s)
- Felix Höfling
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Fakultät für Physik, Ludwig-Maximilians-Universität München, Theresienstrasse 37, München, Germany
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31
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Michailidou VN, Loppinet B, Vo CD, Rühe J, Tauer K, Fytas G. Observation of slow down of polystyrene nanogels diffusivities in contact with swollen polystyrene brushes. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2008; 26:35-41. [PMID: 18473116 DOI: 10.1140/epje/i2007-10322-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2007] [Accepted: 04/09/2008] [Indexed: 05/26/2023]
Abstract
The diffusion of dilute colloids in contact with swollen polymer brushes has been studied by evanescent wave dynamic light scattering. Two polystyrene nanogels with 16 nm and 42 nm radius were put into contact with three polystyrene brushes with varying grafting densities. Partial penetration of the nanogels within the brushes was revealed by the evanescent wave penetration depth-dependent scattering intensities. The experimental short-time diffusion coefficients of the penetrating particles were measured and found to strongly slow down as the nanoparticles get deeper into the brushes. The slow down is much more marked for the smaller (16 nm) nanogels, suggesting a size exclusion type of mechanism and the existence of a characteristic length scale present in the outer part of the brush.
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Affiliation(s)
- V N Michailidou
- FORTH, Institute of Electronic Structure and Laser, Heraklion, Greece
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32
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33
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Pryamitsyn V, Ganesan V. Dynamics of probe diffusion in rod solutions. PHYSICAL REVIEW LETTERS 2008; 100:128302. [PMID: 18517916 DOI: 10.1103/physrevlett.100.128302] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2007] [Indexed: 05/26/2023]
Abstract
Applications of probe diffusion in polymer matrices typically envision that for particles sizes (R) larger than the correlation length of the polymer solution (xi), the probe (at long times) diffuses as in a continuum polymer solution. We present simulation results for probe diffusion in rod solutions which challenge this conventional wisdom and indicate a new mechanism of a probe diffusion operative for R>xi. Our simulation results are rationalized by scaling arguments invoking a novel mechanism of the constraint release motion of the rods, and suggest that the dynamical characteristics of the polymer matrix also proves important in developing a complete description of the probe motion.
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Affiliation(s)
- Victor Pryamitsyn
- Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
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34
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Tuinier R, Fan TH. Scaling of nanoparticle retardation in semi-dilute polymer solutions. SOFT MATTER 2008; 4:254-257. [PMID: 32907237 DOI: 10.1039/b711902j] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We analyze the scaling law for the polymer-induced retardation a nanoparticle experiences as it moves through a semi-dilute polymer solution. The translational friction is calculated from a modified Stokes flow using a local viscosity near the nanosphere. The results rationalize a general retardation factor, R = exp(Kaµcν) [T. Odijk, Biophys. J., 2000, 79, 2314], revealing scaling exponents µ = 0.77 and ν = 1, which are in agreement with experiment. We find that rotational motion also has a self-similar behavior and R can be described too by a stretched exponential with slightly different exponents.
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Affiliation(s)
- Remco Tuinier
- Helmholtz Zentrum Jülich, Institut für Festkörperforschung, 52425, Jülich, Germany.
| | - Tai-Hsi Fan
- Department of Mechanical Engineering, University of Connecticut, Storrs, CT 06269-3139, USA
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35
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Fan TH, Xie B, Tuinier R. Asymptotic analysis of tracer diffusivity in nonadsorbing polymer solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:051405. [PMID: 18233657 DOI: 10.1103/physreve.76.051405] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2007] [Revised: 10/18/2007] [Indexed: 05/25/2023]
Abstract
We present an asymptotic and scaling analysis of the long-time self-diffusivity of a Brownian spherical particle in dilute polymer solutions with nonadsorbing chains. The polymer depletion zone near the particle surface is described by a continuous polymer density profile. Hydrodynamics formulated by the modified Stokes equation with nonuniform viscosity is solved by a regular perturbation approximation using the Green function method. The asymptotes predict how polymer depletion alters the friction a spherical particle experiences during translational and rotational motion within a quiescent fluid. The analysis agrees very well with full numerical computation, which enables us to investigate the scaling law for the polymer-mediated retardation effect using a stretched exponential form that is commonly applied by experimentalists. The scaling exponents revealed are consistent with the nominal values from collected experiment observations.
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Affiliation(s)
- Tai-Hsi Fan
- Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139, USA
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36
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Kang K, Wilk A, Patkowski A, Dhont JKG. Diffusion of spheres in isotropic and nematic networks of rods: electrostatic interactions and hydrodynamic screening. J Chem Phys 2007; 126:214501. [PMID: 17567202 DOI: 10.1063/1.2737446] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Translational diffusion of a small charged tracer sphere in isotropic and nematic suspensions of long and thin charged rods is investigated as a function of ionic strength and rod concentration. A theory for the diffusive properties of a small sphere is developed, where both (screened) hydrodynamic interactions and charge interactions between the tracer sphere and the rod network are analyzed. Hydrodynamic interactions are formulated in terms of the hydrodynamic screening length. As yet, there are no independent theoretical predictions for the hydrodynamic screening length for rod networks. Experimental tracer-diffusion data are presented for various ionic strengths as a function of the rod concentration, both in the isotropic and nematic states. Orientational order parameters are measured for the same ionic strengths as a function of the rod concentration. The hydrodynamic screening length is determined from these experimental data and scaling relations obtained from the above mentioned theory. For the isotropic networks, a master curve is found for the hydrodynamic screening length as a function of the rod concentration. For the nematic networks the screening length turns out to be a very sensitive function of the orientational order parameter.
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Affiliation(s)
- Kyongok Kang
- Forschungszentrum Jülich, Institute für Festkörper Forschung (IFF), Weiche Materie, D-52425 Jülich, Germany
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37
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Sattler R, Kityk A, Wagner C. Molecular configurations in the droplet detachment process of a complex liquid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051805. [PMID: 17677091 DOI: 10.1103/physreve.75.051805] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2006] [Indexed: 05/16/2023]
Abstract
We studied the microscopic polymer conformations in the droplet detachment process of an elastic semidilute polyelectrolytic xanthan solution by measuring the instantaneous birefringence. As in earlier studies, we observe the suppression of the finite time singularity of the pinch-off process and the occurrence of an elastic filament. Our microscopic measurements reveal that the relatively stiff xanthan molecules are already significantly prestretched to about 90% of their final extension at the moment the filament appears. At later stages of the detachment process, we find evidence of a concentration enhancement due to the elongational flow.
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Affiliation(s)
- R Sattler
- Experimentalphysik, Universität des Saarlandes, Postfach 151150, Saarbrücken, Germany
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38
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Fan TH, Dhont JKG, Tuinier R. Motion of a sphere through a polymer solution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:011803. [PMID: 17358176 DOI: 10.1103/physreve.75.011803] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2006] [Indexed: 05/14/2023]
Abstract
We present analytical solutions of the hydrodynamic resistance force a spherical particle experiences when it moves through a polymer solution containing nonadsorbing chains. Polymer depletion results in a reduced polymer concentration and fluid viscosity near the particle surface. The nonuniform physical properties in the fluid phase affect the transport behavior of a translating and rotating sphere as compared with the case of uniform properties. Based on Stokes' stream function theory, we develop a simplified two-layer approximation by using a step function to represent the viscosity profile. The presence of the polymer solution is formulated in terms of correction functions to the translational and rotational friction of a sphere in a pure solvent. The results are in fair agreement with systematic measurements of the friction of a colloidal sphere when it moves through a polymer solution [Koenderink, Phys. Rev. E 69, 021804 (2004)]. The analysis also predicts an apparent slip length in terms of the viscosity ratio and thickness of the depletion layer.
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Affiliation(s)
- Tai-Hsi Fan
- Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139, USA
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39
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Huh JY, Furst EM. Colloid dynamics in semiflexible polymer solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031802. [PMID: 17025658 DOI: 10.1103/physreve.74.031802] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2006] [Indexed: 05/07/2023]
Abstract
We investigate the dynamics of monodisperse colloidal polystyrene particles suspended in solutions of the semiflexible polymer filamentous actin, over a range of filament lengths that either exceed or are substantially less than the particle radius. The filament length is controlled by the capping protein gelsolin, and particle surface chemistries that minimize the adsorption of filaments are used. The particle dynamics are measured on short time scales using diffusing wave spectroscopy. A sharp transition in the initial particle diffusivity marks the expected shift from a dilute to a tightly entangled polymer network as the filament average length increases. In both the dilute and entangled regimes, the measured particle dynamics are compared with the theories of rodlike and semiflexible polymer solution rheology using the generalized Stokes-Einstein relationship. In the dilute limit, the particle dynamics are in good agreement with theory. However, in the tightly entangled regime, the particle response is consistent with polymer depleted near the surfaces of the particles. The magnitude of the depletion layer thickness depends strongly on particle size and weakly on filament length. This behavior is in agreement with nonlocal entropic repulsions and the loss of conformational entropy associated with rodlike molecules near impenetrable particles. These results illustrate the use of microrheology as a method to investigate local structure and dynamics in colloid-polymer solutions.
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Affiliation(s)
- Ji Yeon Huh
- Department of Chemical Engineering, Colburn Laboratory, University of Delaware, 150 Academy Street, Newark, Delaware 19716, USA
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40
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Kang K, Wilk A, Buitenhuis J, Patkowski A, Dhont JKG. Diffusion of spheres in isotropic and nematic suspensions of rods. J Chem Phys 2006; 124:044907. [PMID: 16460212 DOI: 10.1063/1.2161204] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Diffusion of a small tracer sphere (apoferritin) in isotropic and nematic networks [of fd virus] is discussed. For a tracer sphere that is smaller than the mesh size of the network, screened hydrodynamic interactions between the sphere and the network determine its diffusion coefficient. A theory is developed for such interactions as well as their relation to the long-time self-diffusion coefficient. Fluorescence correlation spectroscopy measurements on mixtures of apoferritin and fd virus are presented. The long-time self-diffusion coefficient of apoferritin is measured as a function of the fd-virus concentration, both in the isotropic and nematic state, in directions parallel and perpendicular to the nematic director. The hydrodynamic screening length of the fd-virus network as a function of fd concentration is obtained by combining these experimental data with the theory. Surprisingly, the screening length increases with increasing concentration in nematic networks. This is due to the increase in the degree of alignment, which apparently leads to a strong increase of the screening length. Hydrodynamic screening is thus strongly diminished by alignment. A self-consistent calculation of the screening length does not work at higher concentrations, probably due to the strong variation of the typical incident flow fields over the contour of a rod.
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Affiliation(s)
- Kyongok Kang
- Forschungszentrum Jülich, Institute für Festkörper Forschung, Weiche Materie, D-52425 Julich, Germany
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Kang K, Gapinski J, Lettinga MP, Buitenhuis J, Meier G, Ratajczyk M, Dhont JKG, Patkowski A. Diffusion of spheres in crowded suspensions of rods. J Chem Phys 2005; 122:44905. [PMID: 15740296 DOI: 10.1063/1.1834895] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.
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Affiliation(s)
- Kyongok Kang
- Forschungszentrum Jülich, Institute für Festkörper Forschung (IFF), Weiche Materie, D-52425 Jülich, Germany
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