1
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Martens CM, Vis M, Tuinier R. Origin of Anomalously Large Depletion Zones in Like-Charged Colloid-Polyelectrolyte Mixtures. PHYSICAL REVIEW LETTERS 2024; 132:158103. [PMID: 38682964 DOI: 10.1103/physrevlett.132.158103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2024] [Accepted: 03/14/2024] [Indexed: 05/01/2024]
Abstract
Depletion zones in polyelectrolyte solutions in contact with like-charged flat surfaces are investigated. Using a coupled self-consistent field and Debye-Hückel approach, an explicit expression for the thickness δ of the depletion layer is derived. It is found that δ∼δ_{n}+cκ^{-1}, where δ_{n} is the depletion thickness at a neutral surface, c is a function of the electrostatic characteristics of the system, and κ^{-1} is the Debye length. It is argued that the theory still holds beyond the mean-field approximation, which is confirmed by quantitative agreement between our theoretical results and experiments.
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Affiliation(s)
- C M Martens
- Department of Chemical Engineering and Chemistry, Laboratory of Physical Chemistry, and Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - M Vis
- Department of Chemical Engineering and Chemistry, Laboratory of Physical Chemistry, and Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - R Tuinier
- Department of Chemical Engineering and Chemistry, Laboratory of Physical Chemistry, and Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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2
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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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3
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Martín-Martín S, Ramos-Tejada MDM, Rubio-Andrés A, Bonhome-Espinosa AB, Delgado ÁV, Jiménez ML. Electro-optical Study of the Anomalous Rotational Diffusion in Polymer Solutions. Macromolecules 2023; 56:518-527. [PMID: 36711111 PMCID: PMC9879198 DOI: 10.1021/acs.macromol.2c01461] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Revised: 12/22/2022] [Indexed: 01/13/2023]
Abstract
Brownian diffusion of spherical nanoparticles is usually exploited to ascertain the rheological properties of complex media. However, the behavior of the tracer particles is affected by a number of phenomena linked to the interplay between the dynamics of the particles and polymer coils. For this reason, the characteristic lengths of the dispersed entities, depletion phenomena, and the presence of sticking conditions have been observed to affect the translational diffusion of the probes. On the other hand, the retardation effect of the host fluid on the rotational diffusion of nonspherical particles is less understood. We explore the possibility of studying this phenomenon by analyzing the electro-orientation of the particles in different scenarios in which we vary the ratio between the particle and polymer characteristic size, and the geometry of the particles, including both elongated and oblate shapes. We find that the Stokes-Einstein relation only applies if the radius of gyration of the polymer is much shorter than the particle size and when some repulsive interaction between both is present.
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Affiliation(s)
- Sergio Martín-Martín
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain
| | | | - Antonio Rubio-Andrés
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain
| | - Ana B. Bonhome-Espinosa
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain
| | - Ángel V. Delgado
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain
| | - María L. Jiménez
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain,
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4
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Kusters GLA, Storm C, van der Schoot P. Controlled gel expansion through colloid oscillation. Phys Rev E 2022; 106:044609. [PMID: 36397475 DOI: 10.1103/physreve.106.044609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
We model the behavior of a single colloid embedded in a cross-linked polymer gel, immersed in a viscous background fluid. External fields actuate the particle into a periodic motion, which deforms the embedding matrix and creates a local microcavity, containing the particle and any free volume created by its motion. This cavity exists only as long as the particle is actuated and, when present, reduces the local density of the material, leading to swelling. We show that the model exhibits rich resonance features, but is overall characterized by clear scaling laws at low and high driving frequencies, and a pronounced resonance at intermediate frequencies. Our model predictions suggest that both the magnitude and position of the resonance can be varied by varying the material's elastic modulus or cross-linking density, whereas the local viscosity primarily has a dampening effect. Our work implies appreciable free-volume generation is possible by dispersing a collection of colloids in the medium, even at the level of a simple superposition approximation.
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Affiliation(s)
- Guido L A Kusters
- Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Cornelis Storm
- Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Paul van der Schoot
- Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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5
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Cubuk J, Soranno A. Macromolecular crowding and intrinsically disordered proteins: a polymer physics perspective. CHEMSYSTEMSCHEM 2022. [DOI: 10.1002/syst.202100051] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Jasmine Cubuk
- Washington University in St Louis Biochemistry and Molecular Biophysics UNITED STATES
| | - Andrea Soranno
- Washington University in St Louis Biochemistry and Molecular Biophysics 660 St Euclid Ave 63110 St Louis UNITED STATES
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6
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Affiliation(s)
- Konstantin I. Morozov
- Department of Chemical Engineering, Technion − Israel Institute of Technology, Haifa 32000, Israel
| | - Alexander M. Leshansky
- Department of Chemical Engineering, Technion − Israel Institute of Technology, Haifa 32000, Israel
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7
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Wu Z, Chen Y, Mukasa D, Pak OS, Gao W. Medical micro/nanorobots in complex media. Chem Soc Rev 2020; 49:8088-8112. [PMID: 32596700 DOI: 10.1039/d0cs00309c] [Citation(s) in RCA: 117] [Impact Index Per Article: 29.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Medical micro/nanorobots have received tremendous attention over the past decades owing to their potential to be navigated into hard-to-reach tissues for a number of biomedical applications ranging from targeted drug/gene delivery, bio-isolation, detoxification, to nanosurgery. Despite the great promise, the majority of the past demonstrations are primarily under benchtop or in vitro conditions. Many developed micro/nanoscale propulsion mechanisms are based on the assumption of a homogeneous, Newtonian environment, while realistic biological environments are substantially more complex. Moving toward practical medical use, the field of micro/nanorobotics must overcome several major challenges including propulsion through complex media (such as blood, mucus, and vitreous) as well as deep tissue imaging and control in vivo. In this review article, we summarize the recent research efforts on investigating how various complexities in biological environments impact the propulsion of micro/nanoswimmers. We also highlight the emerging technological approaches to enhance the locomotion of micro/nanorobots in complex environments. The recent demonstrations of in vivo imaging, control and therapeutic medical applications of such micro/nanorobots are introduced. We envision that continuing materials and technological innovations through interdisciplinary collaborative efforts can bring us steps closer to the fantasy of "swallowing a surgeon".
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Affiliation(s)
- Zhiguang Wu
- Andrew and Peggy Cherng Department of Medical Engineering, California Institute of Technology, Pasadena, CA, USA.
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8
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Li H, Zheng K, Yang J, Zhao J. Anomalous Diffusion Inside Soft Colloidal Suspensions Investigated by Variable Length Scale Fluorescence Correlation Spectroscopy. ACS OMEGA 2020; 5:11123-11130. [PMID: 32455234 PMCID: PMC7241028 DOI: 10.1021/acsomega.0c01052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/09/2020] [Accepted: 04/24/2020] [Indexed: 06/11/2023]
Abstract
The diffusion of molecules and particles inside the aqueous suspension of soft colloids (polymer microgels) is investigated using variable length scale fluorescence correlation spectroscopy (VLS-FCS). Carbopol 940 is chosen as the model matrix system, and two factors affecting diffusion are investigated: the spatial hindrance and the diffusant-matrix interaction. By studying diffusion of molecules and particles with different sizes inside the suspension, VLS-FCS reveals the restricted motion at a short length scale, that is, in the gaps between the microgels, and normal diffusion at a larger length scale. The information on the gap's length scale is also accessed. On the other hand, by tuning the pH value, the diffusant-matrix electrostatic attraction is adjusted and the results expose a short-time fast diffusion of probe molecules inside the gaps and a long-time restricted diffusion because of trapping inside the microgels. It is proved that VLS-FCS is a powerful method, investigating anomalous diffusion at different length scales and it is a promising approach to investigate diffusion in complex soft matter systems.
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Affiliation(s)
- Hengyi Li
- Beijing
National Laboratory for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- The
University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kaikai Zheng
- Beijing
National Laboratory for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- The
University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jingfa Yang
- Beijing
National Laboratory for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- The
University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jiang Zhao
- Beijing
National Laboratory for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- The
University of Chinese Academy of Sciences, Beijing 100049, China
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9
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Sorichetti V, Hugouvieux V, Kob W. Determining the Mesh Size of Polymer Solutions via the Pore Size Distribution. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02166] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Valerio Sorichetti
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, F-34095, Montpellier, France
- IATE, INRAE, CIRAD, Montpellier SupAgro, Université Montpellier, F-34060, Montpellier, France
| | - Virginie Hugouvieux
- IATE, INRAE, CIRAD, Montpellier SupAgro, Université Montpellier, F-34060, Montpellier, France
| | - Walter Kob
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, F-34095, Montpellier, France
- Institut Universitaire de France
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10
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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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11
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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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12
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Diffusion Mode Transition between Gaussian and Non-Gaussian of Nanoparticles in Polymer Solutions. CHINESE JOURNAL OF POLYMER SCIENCE 2019. [DOI: 10.1007/s10118-019-2237-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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13
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Nath P, Mangal R, Kohle F, Choudhury S, Narayanan S, Wiesner U, Archer LA. Dynamics of Nanoparticles in Entangled Polymer Solutions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:241-249. [PMID: 29192503 DOI: 10.1021/acs.langmuir.7b03418] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The mean square displacement ⟨r2⟩ of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (Rg), are investigated. In simple fluids and for polymer solutions in which d ≫ Rg, long-time particle dynamics obey random-walk statistics ⟨r2⟩:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < Rg, polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes-Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. We analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.
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Affiliation(s)
| | - Rahul Mangal
- Department of Chemical Engineering, Indian Institute of Technology Kanpur , Kanpur, Uttar Pradesh 208016, India
| | | | | | - Suresh Narayanan
- Advanced Photon Source, Argonne National Laboratory , Argonne, Illinois 60349, United States
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14
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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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15
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Park N, Conrad JC. Phase behavior of colloid-polymer depletion mixtures with unary or binary depletants. SOFT MATTER 2017; 13:2781-2792. [PMID: 28345105 DOI: 10.1039/c6sm02891h] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Adding depletants to a colloidal suspension induces an attractive interparticle interaction that can be tuned to obtain desired structures or to probe phase behavior. When the depletant is not uniform in size, however, both the range and strength of the attraction become difficult to predict and hence control. We investigated the effects of depletant bidispersity on the non-equilibrium phase behavior of colloid-polymer mixtures. We added unary or binary mixtures of polystyrene as the depletant to suspensions of charged poly(methyl methacrylate) particles. The structure and dynamics of the particles were compared over three sets of samples with various mixtures of two different polystyrenes whose size varied by an order of magnitude. The structure and dynamics were nearly independent of depletant dispersity if the polymer concentration was represented as a sum of normalized concentrations of each species. Near the transition region between a fluid of clusters and an interconnected gel at intermediate volume fractions, partitioning of polymers in a binary mixture into colloid-rich and polymer-rich phase leads to a slightly different gelation pathway.
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Affiliation(s)
- Nayoung Park
- Department of Chemical and Biomolecular Engineering, University of Houston, Houston, TX 77204-4004, USA.
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16
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Qing J, Chen A, Zhao N. A new scaling for the rotational diffusion of molecular probes in polymer solutions. Phys Chem Chem Phys 2017; 19:32687-32697. [DOI: 10.1039/c7cp07047k] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In the present work, we propose a new scaling form for the rotational diffusion coefficient of molecular probes in semi-dilute polymer solutions, based on a theoretical study.
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Affiliation(s)
- Jing Qing
- College of Chemistry
- Sichuan University
- Chengdu 610064
- China
| | - Anpu Chen
- College of Chemistry
- Sichuan University
- Chengdu 610064
- China
| | - Nanrong Zhao
- College of Chemistry
- Sichuan University
- Chengdu 610064
- China
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17
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Feng X, Chen A, Wang J, Zhao N, Hou Z. Understanding Protein Diffusion in Polymer Solutions: A Hydration with Depletion Model. J Phys Chem B 2016; 120:10114-10123. [DOI: 10.1021/acs.jpcb.6b06248] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Xiaoqing Feng
- College
of Chemistry, Sichuan University, Chengdu 610064, China
| | - Anpu Chen
- College
of Chemistry, Sichuan University, Chengdu 610064, China
| | - Juan Wang
- College
of Chemistry, Sichuan University, Chengdu 610064, China
| | - Nanrong Zhao
- College
of Chemistry, Sichuan University, Chengdu 610064, China
| | - Zhonghuai Hou
- Hefei National Laboratory for Physical Sciences at the Microscale & Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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18
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Pryamitsyn V, Ganesan V. Noncontinuum effects on the mobility of nanoparticles in unentangled polymer solutions. ACTA ACUST UNITED AC 2016. [DOI: 10.1002/polb.24138] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Victor Pryamitsyn
- Department of Chemical Engineering; University of Texas at Austin; Austin Texas 78712
| | - Venkat Ganesan
- Department of Chemical Engineering; University of Texas at Austin; Austin Texas 78712
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19
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Ishii Y, Ohtori N. Molecular insights into the boundary conditions in the Stokes-Einstein relation. Phys Rev E 2016; 93:050104. [PMID: 27300813 DOI: 10.1103/physreve.93.050104] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2016] [Indexed: 06/06/2023]
Abstract
In order to mimic the Brownian particle in liquid, molecular dynamics calculations of dilute solutions of spherical fullerene molecules with various sizes in liquid Ar were performed. To establish the scaling equation for self-diffusion coefficient, D, of the fullerenes, the dependence of D was examined on the mass ratio of solute to solvent and on the energy-parameter ratio used in the Lennard-Jones potentials. The dependence on the energy-parameter ratio remains up to C_{540}, whereas D rapidly becomes independent of the mass ratio with increasing mass of the solute. The product of the scaling equations obtained for the D of the solute and for shear viscosity, η_{sv}, for the solvent gives a relation which replaces the Stokes-Einstein relation based on the hydrodynamics. The present expression does not need both the boundary conditions and the hydrodynamic particle size, but instead the energy-parameter ratio, packing fraction of solvent, and bare size of solute. From the viewpoint of the tackiness at the boundary, the cage correlation function around the diffusing particle was examined; it was found that the decay time of the function depends mainly on the the energy-parameter ratio. Therefore, the energy-parameter ratio accounts for the main part of both the boundary conditions and the hydrodynamic particle size in the Stokes equation, which have so far been ill-defined in any molecular theories.
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Affiliation(s)
- Yoshiki Ishii
- Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no cho, Nishi-ku, Niigata 950-2181, Japan
| | - Norikazu Ohtori
- Faculty of Science, Niigata University, 8050 Ikarashi 2-no cho, Nishi-ku, Niigata 950-2181, Japan
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20
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Kalwarczyk T, Sozanski K, Ochab-Marcinek A, Szymanski J, Tabaka M, Hou S, Holyst R. Motion of nanoprobes in complex liquids within the framework of the length-scale dependent viscosity model. Adv Colloid Interface Sci 2015; 223:55-63. [PMID: 26189602 DOI: 10.1016/j.cis.2015.06.007] [Citation(s) in RCA: 56] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2015] [Revised: 06/27/2015] [Accepted: 06/27/2015] [Indexed: 01/12/2023]
Abstract
This paper deals with the recent phenomenological model of the motion of nanoscopic objects (colloidal particles, proteins, nanoparticles, molecules) in complex liquids. We analysed motion in polymer, micellar, colloidal and protein solutions and the cytoplasm of living cells using the length-scale dependent viscosity model. Viscosity monotonically approaches macroscopic viscosity as the size of the object increases and thus gives a single, coherent picture of motion at the nano and macro scale. The model includes interparticle interactions (solvent-solute), temperature and the internal structure of a complex liquid. The depletion layer ubiquitously occurring in complex liquids is also incorporated into the model. We also discuss the biological aspects of crowding in terms of the length-scale dependent viscosity model.
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Affiliation(s)
- Tomasz Kalwarczyk
- Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
| | - Krzysztof Sozanski
- Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Anna Ochab-Marcinek
- Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Jedrzej Szymanski
- Nencki Institute of Experimental Biology of the Polish Academy of Sciences, 3 Pasteur Street, 02-093 Warsaw, Poland
| | - Marcin Tabaka
- Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Sen Hou
- Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland; State Key Laboratory of Medicinal Chemical Biology, Nankai University, China
| | - Robert Holyst
- Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
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Kuhnhold A, Paul W. Active one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042601. [PMID: 25974519 DOI: 10.1103/physreve.91.042601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Indexed: 06/04/2023]
Abstract
We present molecular dynamics simulations for active one-particle microrheology of an unentangled polymer melt. The tracer particle is forced to oscillate by an oscillating harmonic potential, which models an experiment using optical tweezers. The amplitude and phase shift of this oscillation are related to the complex shear modulus of the polymer melt. In the linear response regime at low frequencies, the active microrheology gives the same result as the passive microrheology, where the thermal motion of a tracer particle is related to the complex modulus. We expand the analysis to include full hydrodynamic effects instead of stationary Stokes friction only, and show that different approaches suggested in the literature lead to completely different results, and that none of them improves on the description using the stationary Stokes friction.
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Affiliation(s)
- A Kuhnhold
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
| | - W Paul
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
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Grabowski CA, Mukhopadhyay A. Size Effect of Nanoparticle Diffusion in a Polymer Melt. Macromolecules 2014. [DOI: 10.1021/ma501670u] [Citation(s) in RCA: 91] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
- Christopher A. Grabowski
- Department of Physics & Astronomy, Wayne State University, Detroit, Michigan 48201, United States
| | - Ashis Mukhopadhyay
- Department of Physics & Astronomy, Wayne State University, Detroit, Michigan 48201, United States
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Kuhnhold A, Paul W. Passive one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022602. [PMID: 25215751 DOI: 10.1103/physreve.90.022602] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2014] [Indexed: 06/03/2023]
Abstract
We present a molecular dynamics simulation study of the possibility of performing a microrheological analysis of a polymer melt by following the Brownian motion of a dispersed nanoparticle. We study the influence of the size of the nanoparticle, taken to be comparable to the radius of gyration of the chains, and of the strength of the interaction between the nanoparticle and the repeat units of the polymer chains. The influence of the presence of the nanoparticle on the melt mechanical behavior is analyzed, and the importance of effects of different levels of hydrodynamic analysis on the frequency-dependent dynamic shear modulus derived from the particle motion is worked out.
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Affiliation(s)
- A Kuhnhold
- Institut für Physik, Martin-Luther-Universität, Halle-Wittenberg, 06099 Halle (Saale), Germany
| | - W Paul
- Institut für Physik, Martin-Luther-Universität, Halle-Wittenberg, 06099 Halle (Saale), Germany
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Karzar-Jeddi M, Tuinier R, Taniguchi T, Fan TH. Stochastic interactions of two Brownian hard spheres in the presence of depletants. J Chem Phys 2014; 140:214906. [DOI: 10.1063/1.4880199] [Citation(s) in RCA: 2] [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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Gerasin VA, Antipov EM, Karbushev VV, Kulichikhin VG, Karpacheva GP, Talroze RV, Kudryavtsev YV. New approaches to the development of hybrid nanocomposites: from structural materials to high-tech applications. RUSSIAN CHEMICAL REVIEWS 2013. [DOI: 10.1070/rc2013v082n04abeh004322] [Citation(s) in RCA: 82] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Kumar AVA. Binary colloidal mixtures in a potential barrier: Demixing due to depletion. J Chem Phys 2013; 138:154903. [DOI: 10.1063/1.4801333] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Berli CLA. The apparent hydrodynamic slip of polymer solutions and its implications in electrokinetics. Electrophoresis 2013; 34:622-30. [DOI: 10.1002/elps.201200476] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2012] [Revised: 12/05/2012] [Accepted: 12/06/2012] [Indexed: 11/06/2022]
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Eom HS, Park IH. Measurement of Polymer Chain Depletion Layer in the Poly(vinyl alcohol)/Dimethyl Sulfoxide/Polystyrene Latex System by Dynamic Light Scattering. POLYMER-KOREA 2012. [DOI: 10.7317/pk.2012.36.5.628] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
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Taniguchi T, Arai Y, Tuinier R, Fan TH. How flow changes polymer depletion in a slit. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2012; 35:88. [PMID: 23015262 DOI: 10.1140/epje/i2012-12088-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2012] [Revised: 06/12/2012] [Accepted: 08/09/2012] [Indexed: 06/01/2023]
Abstract
A theoretical model is developed for predicting dynamic polymer depletion under the influence of fluid flow. The results are established by combining the two-fluid model and the self-consistent field theory. We consider a uniform fluid flow across a slit containing a solution with polymer chains. The two parallel and infinitely long walls are permeable to solvent only and the polymers do not adsorb to these walls. For a weak flow and a narrow slit, an analytic expression is derived to describe the steady-state polymer concentration profiles in a Θ-solvent. In both Θ- and good-solvents, we compute the time evolution of the concentration profiles for various flow rates characterized by the Peclet number. The model reveals the interplay of depletion, solvent condition, slit width, and the relative strength of the fluid flow.
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Affiliation(s)
- T Taniguchi
- Graduate School of Engineering, Kyoto University Katsura Campus, Nishikyo-ku, Kyoto, Japan.
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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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Klann M, Koeppl H. Spatial simulations in systems biology: from molecules to cells. Int J Mol Sci 2012; 13:7798-7827. [PMID: 22837728 PMCID: PMC3397560 DOI: 10.3390/ijms13067798] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2012] [Revised: 06/08/2012] [Accepted: 06/12/2012] [Indexed: 12/23/2022] Open
Abstract
Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This review gives an overview of methods which can be used to simulate the complete cell at least with molecular detail, especially Brownian dynamics simulations. Such simulations require correct implementation of the diffusion-controlled reaction scheme occurring on this level. Implementations and applications of spatial simulations are presented, and finally it is discussed how the atomic level can be included for instance in multi-scale simulation methods.
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Affiliation(s)
- Michael Klann
- Authors to whom correspondence should be addressed; E-Mails: (M.K.); (H.K.); Tel.: +41-44-632-4274 (M.K.); +41-44-632-7288 (H.K.); Fax: +41-44-632-1211 (M.K.; H.K.)
| | - Heinz Koeppl
- Authors to whom correspondence should be addressed; E-Mails: (M.K.); (H.K.); Tel.: +41-44-632-4274 (M.K.); +41-44-632-7288 (H.K.); Fax: +41-44-632-1211 (M.K.; H.K.)
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Cai LH, Panyukov S, Rubinstein M. Mobility of Nonsticky Nanoparticles in Polymer Liquids. Macromolecules 2011; 44:7853-7863. [PMID: 22058573 PMCID: PMC3205984 DOI: 10.1021/ma201583q] [Citation(s) in RCA: 251] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We use scaling theory to derive the time dependence of the mean-square displacement 〈Δr2〉 of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (〈Δr2 (t)〉 ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (〈Δr2 (t)〉 ~ t1/2) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τ e of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τ e ) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τrep. At longer times t > τrep, the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.
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Affiliation(s)
- Li-Heng Cai
- Curriculum in Applied Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 27599-3287
| | - Sergey Panyukov
- P. N. Lebedev Physics Institute, Russian Academy of Sciences, Moscow 117924, Russia
| | - Michael Rubinstein
- Curriculum in Applied Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 27599-3287
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290
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Holyst R, Bielejewska A, Szymański J, Wilk A, Patkowski A, Gapiński J, Żywociński A, Kalwarczyk T, Kalwarczyk E, Tabaka M, Ziębacz N, Wieczorek SA. Scaling form of viscosity at all length-scales in poly(ethylene glycol) solutions studied by fluorescence correlation spectroscopy and capillary electrophoresis. Phys Chem Chem Phys 2009; 11:9025-32. [DOI: 10.1039/b908386c] [Citation(s) in RCA: 152] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Sprakel J, van der Gucht J, Cohen Stuart MA, Besseling NAM. Brownian particles in transient polymer networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:061502. [PMID: 18643267 DOI: 10.1103/physreve.77.061502] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2007] [Indexed: 05/26/2023]
Abstract
We discuss the thermal motion of colloidal particles in transient polymer networks. For particles that are physically bound to the surrounding chains, light-scattering experiments reveal that the submillisecond dynamics changes from diffusive to Rouse-like upon crossing the network formation threshold. Particles that are not bound do not show such a transition. At longer time scales the mean-square displacement (MSD) exhibits a caging plateau and, ultimately, a slow diffusive motion. The slow diffusion at longer time scales can be related to the macroscopic viscosity of the polymer solutions. Expressions that relate the caging plateau to the macroscopic network elasticity are found to fail for the cases presented here. The typical Rouse scaling of the MSD with the square root of time, as found in experiments at short time scales, is explained by developing a bead-spring model of a large colloidal particle connected to several polymer chains. The resulting analytical expressions for the MSD of the colloidal particle are shown to be consistent with experimental findings.
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Affiliation(s)
- Joris Sprakel
- Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, HB Wageningen, The Netherlands.
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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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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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