A dissipative particle dynamics (DPD) model is developed and demonstrated for studying dynamics in colloidal rod suspensions. The solvent is modeled as conventional DPD particles, while individual rods are represented by a rigid linear chain consisting of overlapping solid spheres, which interact with solvent particles through a hard repulsive potential. The boundary condition on the rod surface is controlled using a surface friction between the solid spheres and the solvent particles. In this work, this model is employed to study the diffusion of a single colloid in the DPD solvent and compared with theoretical predictions. Both the translational and rotational diffusion coefficients obtained at a proper surface friction show good agreement with calculations based on the rod size defined by the hard repulsive potential. In addition, the system-size dependence of the diffusion coefficients shows that the Navier–Stokes hydrodynamic interactions are correctly included in this DPD model. Comparing our results with experimental measurements of the diffusion coefficients of gold nanorods, we discuss the ability of the model to correctly describe dynamics in real nanorod suspensions. Our results provide a clear reference point from which the model could be extended to enable the study of colloid dynamics in more complex situations or for other types of particles.
REFERENCES
1.
V. J.
Anderson
and H. N. W.
Lekkerkerker
, “Insights into phase transition kinetics from colloid science
,” Nature
416
, 811
–815
(2002
).2.
Y.
Wang
, Y.
Wang
, D. R.
Breed
, V. N.
Manoharan
, L.
Feng
, A. D.
Hollingsworth
, M.
Weck
, and D. J.
Pine
, “Colloids with valence and specific directional bonding
,” Nature
491
, 51
–55
(2012
).3.
S.
Whitelam
and R. L.
Jack
, “The statistical mechanics of dynamic pathways to self-assembly
,” Annu. Rev. Phys. Chem.
66
, 143
–163
(2015
).4.
M. A.
Boles
, M.
Engel
, and D. V.
Talapin
, “Self-assembly of colloidal nanocrystals: From intricate structures to functional materials
,” Chem. Rev.
116
, 11220
–11289
(2016
).5.
B. M. I.
Van Der Zande
, J. K. G.
Dhont
, M. R.
Böhmer
, and A. P.
Philipse
, “Colloidal dispersions of gold rods characterized by dynamic light scattering and electrophoresis
,” Langmuir
16
, 459
–464
(2000
).6.
W.
Ahmed
, E. S.
Kooij
, A.
Van Silfhout
, and B.
Poelsema
, “Quantitative analysis of gold nanorod alignment after electric field-assisted deposition
,” Nano Lett.
9
, 3786
–3794
(2009
).7.
A.
Singh
, N. J.
English
, and K. M.
Ryan
, “Highly ordered nanorod assemblies extending over device scale areas and in controlled multilayers by electrophoretic deposition
,” J. Phys. Chem. B
117
, 1608
–1615
(2013
).8.
Z.
Tan
, M.
Yang
, and M.
Ripoll
, “Anisotropic thermophoresis
,” Soft Matter
13
, 7283
–7291
(2017
).9.
Z.
Wang
, D.
Niether
, J.
Buitenhuis
, Y.
Liu
, P. R.
Lang
, J. K. G.
Dhont
, and S.
Wiegand
, “Thermophoresis of a colloidal rod: Contributions of charge and grafted polymers
,” Langmuir
35
, 1000
–1007
(2019
).10.
H.
Zhang
, Y.
Liu
, M. F. S.
Shahidan
, C.
Kinnear
, F.
Maasoumi
, J.
Cadusch
, E. M.
Akinoglu
, T. D.
James
, A.
Widmer-Cooper
, A.
Roberts
, and P.
Mulvaney
, “Direct assembly of vertically oriented, gold nanorod arrays
,” Adv. Funct. Mater.
31
, 2006753
(2020
).11.
B. J.
Berne
and R.
Pecora
, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics
(Courier Corporation
, 2000
).12.
D.
Lehner
, H.
Lindner
, and O.
Glatter
, “Determination of the translational and rotational diffusion coefficients of rodlike particles using depolarized dynamic light scattering
,” Langmuir
16
, 1689
–1695
(2000
).13.
R.
Cerbino
and V.
Trappe
, “Differential dynamic microscopy: Probing wave vector dependent dynamics with a microscope
,” Phys. Rev. Lett.
100
, 188102
(2008
).14.
Y.
Liu
and A.
Widmer-Cooper
, “A versatile simulation method for studying phase behavior and dynamics in colloidal rod and rod-polymer suspensions
,” J. Chem. Phys.
150
, 244508
(2019
).15.
S.
Broersma
, “Rotational diffusion constant of a cylindrical particle
,” J. Chem. Phys.
32
, 1626
–1631
(1960
).16.
S.
Broersma
, “Viscous force constant for a closed cylinder
,” J. Chem. Phys.
32
, 1632
–1635
(1960
).17.
M. M.
Tirado
and J. G.
de la Torre
, “Translational friction coefficients of rigid, symmetric top macromolecules. Application to circular cylinders
,” J. Chem. Phys.
71
, 2581
–2587
(1979
).18.
M. M.
Tirado
and J. G.
de la Torre
, “Rotational dynamics of rigid, symmetric top macromolecules. Application to circular cylinders
,” J. Chem. Phys.
73
, 1986
–1993
(1980
).19.
H.
Löwen
, “Brownian dynamics of hard spherocylinders
,” Phys. Rev. E
50
, 1232
–1242
(1994
).20.
A.
Patti
and A.
Cuetos
, “Brownian dynamics and dynamic Monte Carlo simulations of isotropic and liquid crystal phases of anisotropic colloidal particles: A comparative study
,” Phys. Rev. E
86
, 011403
(2012
).21.
A.
Cuetos
and A.
Patti
, “Equivalence of Brownian dynamics and dynamic Monte Carlo simulations in multicomponent colloidal suspensions
,” Phys. Rev. E
92
, 022302
(2015
).22.
J. T.
Padding
and A. A.
Louis
, “Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length scales
,” Phys. Rev. E
74
, 031402
(2006
).23.
I.
Pagonabarraga
, B.
Rotenberg
, and D.
Frenkel
, “Recent advances in the modelling and simulation of electrokinetic effects: Bridging the gap between atomistic and macroscopic descriptions
,” Phys. Chem. Chem. Phys.
12
, 9566
(2010
).24.
D. S.
Bolintineanu
, G. S.
Grest
, J. B.
Lechman
, F.
Pierce
, S. J.
Plimpton
, and P. R.
Schunk
, “Particle dynamics modeling methods for colloid suspensions
,” Comput. Part. Mech.
1
, 321
–356
(2014
).25.
U. D.
Schiller
, T.
Krüger
, and O.
Henrich
, “Mesoscopic modelling and simulation of soft matter
,” Soft Matter
14
, 9
–26
(2018
).26.
R. D.
Groot
and P. B.
Warren
, “Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation
,” J. Chem. Phys.
107
, 4423
–4435
(1997
).27.
P.
Español
and P. B.
Warren
, “Perspective: Dissipative particle dynamics
,” J. Chem. Phys.
146
, 150901
(2017
).28.
P. J.
Hoogerbrugge
and J. M. V. A.
Koelman
, “Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics
,” Europhys. Lett.
19
, 155
–160
(1992
).29.
M.
Whittle
and K. P.
Travis
, “Dynamic simulations of colloids by core-modified dissipative particle dynamics
,” J. Chem. Phys.
132
, 124906
(2010
).30.
H.
Maeda
and Y.
Maeda
, “Direct observation of Brownian dynamics of hard colloidal nanorods
,” Nano Lett.
7
, 3329
–3335
(2007
).31.
J.
Rodríguez-Fernández
, J.
Pérez-Juste
, L. M.
Liz-Marzán
, and P. R.
Lang
, “Dynamic light scattering of short Au rods with low aspect ratios
,” J. Phys. Chem. C
111
, 5020
–5025
(2007
).32.
S. L.
Eichmann
, B.
Smith
, G.
Meric
, D. H.
Fairbrother
, and M. A.
Bevan
, “Imaging carbon nanotube interactions, diffusion, and stability in nanopores
,” ACS Nano
5
, 5909
–5919
(2011
).33.
A.
Günther
, P.
Bender
, A.
Tschöpe
, and R.
Birringer
, “Rotational diffusion of magnetic nickel nanorods in colloidal dispersions
,” J. Phys.: Condens. Matter
23
, 325103
(2011
).34.
M.
Glidden
and M.
Muschol
, “Characterizing gold nanorods in solution using depolarized dynamic light scattering
,” J. Phys. Chem. C
116
, 8128
–8137
(2012
).35.
P.
Zijlstra
, M.
Van Stee
, N.
Verhart
, Z.
Gu
, and M.
Orrit
, “Rotational diffusion and alignment of short gold nanorods in an external electric field
,” Phys. Chem. Chem. Phys.
14
, 4584
–4588
(2012
).36.
B.-Y.
Cao
and R.-Y.
Dong
, “Molecular dynamics calculation of rotational diffusion coefficient of a carbon nanotube in fluid
,” J. Chem. Phys.
140
, 034703
(2014
).37.
A.
Kharazmi
and N. V.
Priezjev
, “Molecular dynamics simulations of the rotational and translational diffusion of a Janus rod-shaped nanoparticle
,” J. Phys. Chem. B
121
, 7133
–7139
(2017
).38.
R.
Nixon-Luke
and G.
Bryant
, “A depolarized dynamic light scattering method to calculate translational and rotational diffusion coefficients of nanorods
,” Part. Part. Syst. Charact.
36
, 1800388
(2019
).39.
R.
Nixon-Luke
and G.
Bryant
, “Differential dynamic microscopy to measure the translational diffusion coefficient of nanorods
,” J. Phys.: Condens. Matter
32
, 115102
(2020
).40.
M. M.
Tirado
, C. L.
Martínez
, and J. G.
de la Torre
, “Comparison of theories for the translational and rotational diffusion coefficients of rod-like macromolecules. Application to short DNA fragments
,” J. Chem. Phys.
81
, 2047
–2052
(1984
).41.
H.
Hasimoto
, “On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres
,” J. Fluid Mech.
5
, 317
(1959
).42.
I.-C.
Yeh
and G.
Hummer
, “System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions
,” J. Phys. Chem. B
108
, 15873
–15879
(2004
).43.
K.
Ichiki
, A. E.
Kobryn
, and A.
Kovalenko
, “Targeting transport properties in nanofluidics: Hydrodynamic interaction among slip surface nanoparticles in solution
,” J. Comput. Theor. Nanosci.
5
, 2004
–2021
(2008
).44.
W.
Sutherland
, “LXXV. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin
,” London, Edinburgh Dublin Philos. Mag. J. Sci.
9
, 781
–785
(1905
).45.
J. C. M.
Li
and P.
Chang
, “Self-diffusion coefficient and viscosity in liquids
,” J. Chem. Phys.
23
, 518
–520
(1955
).46.
M.
Linke
, J.
Köfinger
, and G.
Hummer
, “Rotational diffusion depends on box size in molecular dynamics simulations
,” J. Phys. Chem. Lett.
9
, 2874
–2878
(2018
).47.
G. H.
Koenderink
, H.
Zhang
, D. G. A. L.
Aarts
, M. P.
Lettinga
, A. P.
Philipse
, and G.
Nägele
, “On the validity of Stokes–Einstein–Debye relations for rotational diffusion in colloidal suspensions
,” Faraday Discuss.
123
, 335
–354
(2003
).48.
J.
Zhou
, J.
Smiatek
, E. S.
Asmolov
, O. I.
Vinogradova
, and F.
Schmid
, “Application of tunable-slip boundary conditions in particle-based simulations
,” in High Performance Computing in Science and Engineering ’14
, edited by W. E.
Nagel
, D. H.
Kröner
, and M. M.
Resch
(Springer International Publishing
, 2015
), pp. 19
–30
.49.
P.
Español
, “Fluid particle dynamics: A synthesis of dissipative particle dynamics and smoothed particle dynamics
,” Europhys. Lett.
39
, 605
–610
(1997
).50.
P.
Español
, “Fluid particle model
,” Phys. Rev. E
57
, 2930
–2948
(1998
).51.
S.
Plimpton
, “Fast parallel algorithms for short-range molecular dynamics
,” J. Comput. Phys.
117
, 1
–19
(1995
).52.
D.
Einzel
, P.
Panzer
, and M.
Liu
, “Boundary condition for fluid flow: Curved or rough surfaces
,” Phys. Rev. Lett.
64
, 2269
–2272
(1990
).53.
K.
Falk
, F.
Sedlmeier
, L.
Joly
, R. R.
Netz
, and L.
Bocquet
, “Molecular origin of fast water transport in carbon nanotube membranes: Superlubricity versus curvature dependent friction
,” Nano Lett.
10
, 4067
–4073
(2010
).54.
L.
Guo
, S.
Chen
, and M. O.
Robbins
, “Slip boundary conditions over curved surfaces
,” Phys. Rev. E
93
, 013105
(2016
).55.
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation: From Algorithms to Applications
, 2nd ed. (Elsevier
, 2010
), pp. 518
–519
.56.
B.
Dünweg
and K.
Kremer
, “Molecular dynamics simulation of a polymer chain in solution
,” J. Chem. Phys.
99
, 6983
–6997
(1993
).57.
S.
Kämmerer
, W.
Kob
, and R.
Schilling
, “Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules
,” Phys. Rev. E
56
, 5450
–5461
(1997
).58.
M. G.
Mazza
, N.
Giovambattista
, H. E.
Stanley
, and F. W.
Starr
, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes–Einstein and Stokes–Einstein–Debye relations in water
,” Phys. Rev. E
76
, 031203
(2007
).59.
A. A.
Zick
and G. M.
Homsy
, “Stokes flow through periodic arrays of spheres
,” J. Fluid Mech.
115
, 13
–26
(1982
).60.
A. J. C.
Ladd
, “Hydrodynamic interactions in a suspension of spherical particles
,” J. Chem. Phys.
88
, 5051
–5063
(1988
).61.
A. J. C.
Ladd
, “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part I. Theoretical foundation
,” J. Fluid Mech.
271
, 285
–309
(1994
).62.
A. J. C.
Ladd
, “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part II. Numerical results
,” J. Fluid Mech.
271
, 311
–339
(1994
).63.
H.
Hoang
and G.
Galliero
, “Local viscosity of a fluid confined in a narrow pore
,” Phys. Rev. E
86
, 021202
(2012
).64.
S.
Gómez-Graña
, F.
Hubert
, F.
Testard
, A.
Guerrero-Martínez
, I.
Grillo
, L. M.
Liz-Marzán
, and O.
Spalla
, “Surfactant (Bi) layers on gold nanorods
,” Langmuir
28
, 1453
–1459
(2012
).65.
J. L.
Anderson
, “Colloid transport by interfacial forces
,” Annu. Rev. Fluid Mech.
21
, 61
–99
(1989
).66.
R. P.
Sear
and P. B.
Warren
, “Diffusiophoresis in nonadsorbing polymer solutions: The Asakura-Oosawa model and stratification in drying films
,” Phys. Rev. E
96
, 46
–48
(2017
).67.
A. J. C.
Ladd
, “Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation
,” Phys. Rev. Lett.
70
, 1339
–1342
(1993
).68.
A.
Furukawa
, M.
Tateno
, and H.
Tanaka
, “Physical foundation of the fluid particle dynamics method for colloid dynamics simulation
,” Soft Matter
14
, 3738
–3747
(2018
).69.
G.
Cinacchi
, A. M.
Pintus
, and A.
Tani
, “Diffusion of helical particles in the screw-like nematic phase
,” J. Chem. Phys.
145
, 134903
(2016
).70.
D. M.
Heyes
, “Translational and rotational diffusion of rod shaped molecules by molecular dynamics simulations
,” J. Chem. Phys.
150
, 184503
(2019
).71.
X.
Yang
, Q.
Zhu
, C.
Liu
, W.
Wang
, Y.
Li
, F.
Marchesoni
, P.
Hänggi
, and H. P.
Zhang
, “Diffusion of colloidal rods in corrugated channels
,” Phys. Rev. E
99
, 020601
(2019
).© 2021 Author(s).
2021
Author(s)
You do not currently have access to this content.
