1
|
Cieśla M, Dybiec B, Krasowska M, Siwy Z, Strzelewicz A. Numerical Modeling of Anisotropic Particle Diffusion through a Cylindrical Channel. Molecules 2024; 29:3795. [PMID: 39202873 PMCID: PMC11356997 DOI: 10.3390/molecules29163795] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2024] [Revised: 07/23/2024] [Accepted: 07/26/2024] [Indexed: 09/03/2024] Open
Abstract
The transport of molecules and particles through single pores is the basis of biological processes, including DNA and protein sequencing. As individual objects pass through a pore, they cause a transient change in the current that can be correlated with the object size, surface charge, and even chemical properties. The majority of experiments and modeling have been performed with spherical objects, while much less is known about the transport characteristics of aspherical particles, which would act as a model system, for example, for proteins and bacteria. The transport kinetics of aspherical objects is an especially important, yet understudied, problem in nanopore analytics. Here, using the Wiener process, we present a simplified model of the diffusion of rod-shaped particles through a cylindrical pore, and apply it to understand the translation and rotation of the particles as they pass through the pore. Specifically, we analyze the influence of the particles' geometrical characteristics on the effective diffusion type, the first passage time distribution, and the particles' orientation in the pore. Our model shows that thicker particles pass through the channel slower than thinner ones, while their lengths do not affect the passage time. We also demonstrate that both spherical and rod-shaped particles undergo normal diffusion, and the first passage time distribution follows an exponential asymptotics. The model provides guidance on how the shape of the particle can be modified to achieve an optimal passage time.
Collapse
Affiliation(s)
- Michał Cieśla
- Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland;
| | - Bartłomiej Dybiec
- Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland;
| | - Monika Krasowska
- Faculty of Chemistry, Silesian University of Technology, Strzody 9, 44-100 Gliwice, Poland; (M.K.); (A.S.)
| | - Zuzanna Siwy
- Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA;
| | - Anna Strzelewicz
- Faculty of Chemistry, Silesian University of Technology, Strzody 9, 44-100 Gliwice, Poland; (M.K.); (A.S.)
| |
Collapse
|
2
|
Ma R, Mu G, Zhang H, Liu J, Gao Y, Zhao X, Zhang L. Percolation analysis of the electrical conductive network in a polymer nanocomposite by nanorod functionalization. RSC Adv 2019; 9:36324-36333. [PMID: 35540620 PMCID: PMC9074929 DOI: 10.1039/c9ra04680a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2019] [Accepted: 10/30/2019] [Indexed: 12/30/2022] Open
Abstract
Chemical functionalization of nanofillers is an effective strategy to benefit the formation of the conductive network in the matrix which can enhance the electrical conductivity of polymer nanocomposites (PNCs). In this work, we adopted a coarse-grained molecular dynamics simulation to investigate the effect of the nanorod (NR) functionalization on the conductive probability of PNCs under the quiescent state or under a shear field. It is found that the direct aggregation structure of NRs is gradually broken down with increasing the NR functionalization degree λA, which improves their dispersion state. Moreover, a local bridging structure of NRs sandwiched via one polymer layer is formed at high λA. Corresponding to it, the percolation threshold of PNCs first quickly decreases, then increases and last slightly decreases again with the increase of λA, which exhibits an anti N-type under the quiescent state. Meanwhile, it shows a non-monotonic dependence on the interaction between polymer and the functionalized beads which reaches the lowest value at the moderate interaction. However, the percolation threshold is nearly independent of λA under the shear field. Compared with in the quiescent state, the decrease or the increase of the percolation threshold can be tuned by λA under the shear field. The significant change in the percolation threshold is attributed to the orientation and the dispersion state of NRs under the shear field, which affects the conductive network. Especially, we found that the dispersion state of NRs is different for different λA under the shear field. However, the percolation threshold is similar which indicates that the dispersion state of NRs is not completely correlated to the conductive network. In summary, this work presents some further understanding of how the NR functionalization affects the electrical conductivity of PNCs. Chemical functionalization of nanofillers is an effective strategy to benefit the formation of the conductive network in the matrix which can enhance the electrical conductivity of polymer nanocomposites (PNCs).![]()
Collapse
Affiliation(s)
- Ruibin Ma
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology 10029 China .,State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology 100029 China
| | - Guangyao Mu
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology 10029 China .,State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology 100029 China
| | - Huan Zhang
- Aerospace Research Institute of Materials and Processing Technology Beijing 100076 China
| | - Jun Liu
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology 10029 China .,State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology 100029 China
| | - Yangyang Gao
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology 10029 China .,State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology 100029 China
| | - Xiuying Zhao
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology 10029 China .,State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology 100029 China
| | - Liqun Zhang
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology 10029 China .,State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology 100029 China
| |
Collapse
|
3
|
Duan X, Zhang H, Liu J, Gao Y, Zhao X, Zhang L. Optimizing the electrical conductivity of polymer nanocomposites under the shear field by hybrid fillers: Insights from molecular dynamics simulation. POLYMER 2019. [DOI: 10.1016/j.polymer.2019.02.028] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
Li F, Duan X, Zhang H, Li B, Liu J, Gao Y, Zhang L. Molecular dynamics simulation of the electrical conductive network formation of polymer nanocomposites with polymer-grafted nanorods. Phys Chem Chem Phys 2018; 20:21822-21831. [DOI: 10.1039/c8cp02809e] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Grafting chains on the surface of a filler is an effective strategy to tune and control the filler conductive network, which can be utilized to fabricate polymer nanocomposites (PNCs) with high electrical conductivity.
Collapse
Affiliation(s)
- Fanzhu Li
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
- Beijing University of Chemical Technology
- People's Republic of China
| | - Xiaohui Duan
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
- Beijing University of Chemical Technology
- People's Republic of China
| | - Huan Zhang
- Aerospace Research Institute of Materials and Processing Technology
- Beijing
- People's Republic of China
| | - Bin Li
- CAS Key Laboratory of Nanosystem and Hierarchial Fabrication, CAS Center for Excellence in Nanoscience, National Center for Nanoscience and Technology
- Beijing
- People's Republic of China
| | - Jun Liu
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
- Beijing University of Chemical Technology
- People's Republic of China
| | - Yangyang Gao
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
- Beijing University of Chemical Technology
- People's Republic of China
- State Key Laboratory of Organic–Inorganic Composites, Beijing University of Chemical Technology
- People's Republic of China
| | - Liqun Zhang
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
- Beijing University of Chemical Technology
- People's Republic of China
- State Key Laboratory of Organic–Inorganic Composites, Beijing University of Chemical Technology
- People's Republic of China
| |
Collapse
|
6
|
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.
Collapse
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
| |
Collapse
|
7
|
Vo MD, Shiau B, Harwell JH, Papavassiliou DV. Adsorption of anionic and non-ionic surfactants on carbon nanotubes in water with dissipative particle dynamics simulation. J Chem Phys 2016; 144:204701. [DOI: 10.1063/1.4949364] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
8
|
Gao Y, Cao D, Wu Y, Liu J, Zhang L. Destruction and recovery of a nanorod conductive network in polymer nanocomposites via molecular dynamics simulation. SOFT MATTER 2016; 12:3074-3083. [PMID: 26895557 DOI: 10.1039/c5sm02803e] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
By adopting coarse-grained molecular dynamics simulation, we investigate the effects of end-functionalization and shear flow on the destruction and recovery of a nanorod conductive network in a functionalized polymer matrix. We find that the end-functionalization of polymeric chains can enhance the electrical conductivity of nanorod filled polymer nanocomposites, indicated by the decrease of the percolation threshold. However, there exists an optimal end-functionalization extent to reach the maximum electrical conductivity. In the case of steady shear flow, both homogeneous conductive probability and directional conductive probability perpendicular to the shear direction decrease with the shear rate, while the directional conductive probability parallel to the shear direction increases. Importantly, we develop a semi-empirical equation to describe the change of the homogeneous conductive probability as a function of the shear rate. Meanwhile, we obtain an empirical formula describing the relationship between the anisotropy of the conductive probability and the orientation of the nanorods. In addition, the conductivity stability increases with increasing nanorod volume fraction. During the recovery process of the nanorod conductive network, it can be fitted well by the model combining classical percolation theory and a time-dependent nanorod aggregation kinetic equation. The fitted recovery rate is similar for different nanorod volume fractions. In summary, this work provides some rational rules for fabricating polymer nanocomposites with excellent performance of electrical conductivity.
Collapse
Affiliation(s)
- Yangyang Gao
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, People's Republic of China.
| | - Dapeng Cao
- State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, 100029 Beijing, People's Republic of China
| | - Youping Wu
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, People's Republic of China. and Beijing Engineering Research Center of Advanced Elastomers, People's Republic of China and Engineering Research Center of Elastomer Materials on Energy Conservation and Resources, Ministry of Education, People's Republic of China
| | - Jun Liu
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, People's Republic of China. and Beijing Engineering Research Center of Advanced Elastomers, People's Republic of China and Engineering Research Center of Elastomer Materials on Energy Conservation and Resources, Ministry of Education, People's Republic of China
| | - Liqun Zhang
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, People's Republic of China. and State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, 100029 Beijing, People's Republic of China and Beijing Engineering Research Center of Advanced Elastomers, People's Republic of China and Engineering Research Center of Elastomer Materials on Energy Conservation and Resources, Ministry of Education, People's Republic of China
| |
Collapse
|
9
|
Kim MJ, Cho HW, Kim J, Kim H, Sung BJ. Translational and rotational diffusion of a single nanorod in unentangled polymer melts. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042601. [PMID: 26565264 DOI: 10.1103/physreve.92.042601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2015] [Indexed: 06/05/2023]
Abstract
Polymer nanocomposites have been an issue of both academic and industrial interest due to promising electrical, mechanical, optical, and magnetic properties. The dynamics of nanoparticles in polymer nanocomposites is a key to understanding those properties of polymer nanocomposites and is important for applications such as self-healing nanocomposites. In this article we investigate the translational and the rotational dynamics of a single nanorod in unentangled polymer melts by employing extensive molecular dynamics simulations. A nanorod and polymers are modeled as semiflexible tangent chains of spherical beads. The stiffness of a nanorod is tuned by changing the bending potential between chemical bonds. When polymers are sufficiently long and the nanorod is stiff, the nanorod translates in an anisotropic fashion along the nanorod axis within time scales of translational relaxation times even in unentangled polymer melts. The rotational diffusion is suppressed more significantly than the translational diffusion as the polymer chain length is increased, thus the translational and rotational diffusion of the nanorod are decoupled. We also estimate the winding numbers of polymers, i.e., how many times a polymer winds the nanorod. The winding number increases with longer polymers but is relatively insensitive to the nanorod stiffness.
Collapse
Affiliation(s)
- Min Jung Kim
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
| | - Hyun Woo Cho
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
| | - Jeongmin Kim
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
| | - Heesuk Kim
- Photo-electronic Hybrids Research Center, Korea Institute of Science and Technology (KIST), Seoul 136-791, South Korea
| | - Bong June Sung
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
| |
Collapse
|
10
|
Xiao S, Chen HY, Sheng YJ, Tsao HK. Induced polar order in sedimentation equilibrium of rod-like nanoswimmers. SOFT MATTER 2015; 11:2416-2422. [PMID: 25662710 DOI: 10.1039/c4sm02701a] [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 active diffusion and sedimentation equilibrium of rod-like nanoswimmers with length L are investigated by dissipative particle dynamics. In the absence of propulsion, the nanorod has the rotational correlation time τθ and mobility μ0, which vary with L. On the basis of the mean squared displacement, the diffusive behavior of rod-like nanoswimmers subject to active force Fa is found to follow (D - D0) ∝ (μ0Fa)(2)τθ, where D0 depicts the Brownian diffusivity. When the nanoswimmer suspension is under the external force Fe, the balance between the downward migration and upward active diffusion yields the sedimentation length δ = D/(μ0Fe), which no longer obeys δ0 = kBT/Fe obtained from the Einstein-Smoluchowski relationship, D0 = μ0kBT. Different from the suspension of passive rods, the polar order is clearly seen for active rods. The local polar order is essentially constant within the distance of about 2δ from the bottom wall but decays as the distance is further increased. In this work, the active Peclet number is small compared to unity and the maximum polar order grows linearly with Fe/Fa. The polar order arises because it is easier for the nanoswimmer with the swimming direction opposite to the external force to escape from the bottom wall.
Collapse
Affiliation(s)
- Song Xiao
- Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650500, China
| | | | | | | |
Collapse
|
11
|
|
12
|
Zhao T, Wang X. Distortion and flow of nematics simulated by dissipative particle dynamics. J Chem Phys 2014; 140:184902. [DOI: 10.1063/1.4873699] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
|
13
|
Gao Y, Liu J, Shen J, Zhang L, Cao D. Molecular dynamics simulation of dispersion and aggregation kinetics of nanorods in polymer nanocomposites. POLYMER 2014. [DOI: 10.1016/j.polymer.2014.01.042] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
|
14
|
Zhao T, Wang X. Dissipative particle dynamics study of translational diffusion of rigid-chain rodlike polymer in nematic phase. J Chem Phys 2013; 139:104902. [DOI: 10.1063/1.4820134] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
|