1
|
Das P, Dubey AK, Puri S. Pattern dynamics of density and velocity fields in segregation of fluid mixtures. J Chem Phys 2024; 160:154507. [PMID: 38634496 DOI: 10.1063/5.0203489] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2024] [Accepted: 04/02/2024] [Indexed: 04/19/2024] Open
Abstract
We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H.
Collapse
Affiliation(s)
- Prasenjit Das
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, S.A.S. Nagar, 140306 Punjab, India
| | - Awadhesh Kumar Dubey
- Department of Pure and Applied Physics, Guru Ghasidas Vishwavidyalaya, Bilaspur 495009, Chhattisgarh, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| |
Collapse
|
2
|
Gogoi D, Chauhan A, Puri S, Singh A. Segregation of fluids with polymer additives at domain interfaces: a dissipative particle dynamics study. SOFT MATTER 2023; 19:6433-6445. [PMID: 37403605 DOI: 10.1039/d3sm00504f] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/06/2023]
Abstract
This paper investigates the phase separation kinetics of ternary fluid mixtures composed of a polymeric component (C) and two simple fluids (A and B) using dissipative particle dynamics simulations with a system dimensionality of d = 3. We model the affinities between the components to enable the settling of the polymeric component at the interface of fluids A and B. Thus, the system evolves to form polymer coated morphologies, enabling alteration of the fluids' interfacial properties. This manipulation can be utilized across various disciplines, such as the stabilization of emulsions and foams, rheological control, biomimetic design, and surface modification. We probe the effects of various parameters, such as the polymeric concentration, chain stiffness, and length, on the phase separation kinetics of the system. The simulation results show that changes in the concentration of flexible polymers exhibit perfect dynamic scaling for coated morphologies. The growth rate decreases as the polymeric composition is increased due to reduced surface tension and restricted connectivity between A- and B-rich clusters. Variations in the polymer chain rigidity at fixed composition ratios and degrees of polymerization slow the evolution kinetics of AB fluids marginally, although the effect is more pronounced for perfectly rigid chains. Whereas flexible polymer chain lengths at fixed composition ratios slow down the segregation kinetics of AB fluids slightly, varying the chain lengths of perfectly rigid polymers leads to a significant deviation in the length scale and dynamic scaling for the evolved coated morphologies. The characteristic length scale follows a power-law growth with a growth exponent ϕ that shows a crossover from the viscous to the inertial hydrodynamic regime, where the values of ϕ depend on the constraints imposed on the system.
Collapse
Affiliation(s)
- Dorothy Gogoi
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
| | - Avinash Chauhan
- Department of Physics, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh-221005, India.
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
| | - Awaneesh Singh
- Department of Physics, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh-221005, India.
| |
Collapse
|
3
|
Hybrid Time-Dependent Ginzburg–Landau Simulations of Block Copolymer Nanocomposites: Nanoparticle Anisotropy. Polymers (Basel) 2022; 14:polym14091910. [PMID: 35567080 PMCID: PMC9103753 DOI: 10.3390/polym14091910] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 04/27/2022] [Accepted: 05/02/2022] [Indexed: 11/16/2022] Open
Abstract
Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer–particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg–Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg–Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg–Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate nonspherical nanoparticles.
Collapse
|
4
|
König B, Ronsin OJJ, Harting J. Two-dimensional Cahn-Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures. Phys Chem Chem Phys 2021; 23:24823-24833. [PMID: 34714899 DOI: 10.1039/d1cp03229a] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The evolution of the microstructure due to spinodal decomposition in phase separated mixtures has a strong impact on the final material properties. In the late stage of coarsening, the system is characterized by the growth of a single characteristic length scale L ∼ Ctα. To understand the structure-property relationship, the knowledge of the coarsening exponent α and the coarsening rate constant C is mandatory. Since the existing literature is not entirely consistent, we perform phase field simulations based on the Cahn-Hilliard equation. We restrict ourselves to binary mixtures using a symmetric Flory-Huggins free energy and a constant composition-independent mobility term and show that the coarsening for off-critical mixtures is slower than the expected t1/3-growth. Instead, we find α to be dependent on the mixture composition and associate this with the observed morphologies. Finally, we propose a model to describe the complete coarsening kinetics including the rate constant C.
Collapse
Affiliation(s)
- Björn König
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, Fürther Str. 248, 90429 Nürnberg, Germany.
| | - Olivier J J Ronsin
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, Fürther Str. 248, 90429 Nürnberg, Germany.
| | - Jens Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, Fürther Str. 248, 90429 Nürnberg, Germany. .,Department of Chemical and Biological Engineering and Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany
| |
Collapse
|
5
|
Pattanayak S, Mishra S, Puri S. Ordering kinetics in the active model B. Phys Rev E 2021; 104:014606. [PMID: 34412309 DOI: 10.1103/physreve.104.014606] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Accepted: 06/28/2021] [Indexed: 11/07/2022]
Abstract
We undertake a detailed numerical study of the Active Model B proposed by Wittkowski et al., [Nature Commun. 5, 4351 (2014)]2041-172310.1038/ncomms5351. We find that the introduction of activity has a drastic effect on the ordering kinetics. First, the domain growth law shows a crossover from the usual Lifshitz-Slyozov growth law for phase separation (L∼t^{1/3}, where t is the time) to a novel growth law (L∼t^{1/4}) at late times. Second, the equal-time correlation function of the density field exhibits dynamical scaling for a given activity strength λ, but the scaling function depends on λ.
Collapse
Affiliation(s)
- Sudipta Pattanayak
- S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata 700106, India
| | - Shradha Mishra
- Department of Physics, Indian Institute of Technology BHU, Varanasi 221005, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| |
Collapse
|
6
|
Diaz J, Pinna M, Zvelindovsky AV, Pagonabarraga I. Parallel Hybrid Simulations of Block Copolymer Nanocomposites using Coarray Fortran. MACROMOL THEOR SIMUL 2021. [DOI: 10.1002/mats.202100007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Javier Diaz
- CECAM Centre Européen de Calcul Atomique et Moléculaire École Polytechnique Fédérale de Lausanne Batochime ‐ Avenue Forel 2 Lausanne 1015 Switzerland
| | - Marco Pinna
- Centre for Computational Physics University of Lincoln Brayford Pool Lincoln LN6 7TS UK
| | | | - Ignacio Pagonabarraga
- CECAM Centre Européen de Calcul Atomique et Moléculaire École Polytechnique Fédérale de Lausanne Batochime ‐ Avenue Forel 2 Lausanne 1015 Switzerland
- Departament de Física de la Matèria Condensada Universitat de Barcelona Martí i Franquès 1 Barcelona 08028 Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS) Universitat de Barcelona Barcelona 08028 Spain
| |
Collapse
|
7
|
Shen L, Chern GW. Cell dynamics simulations of coupled charge and magnetic phase transformation in correlated oxides. Phys Rev E 2021; 103:032134. [PMID: 33862780 DOI: 10.1103/physreve.103.032134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/26/2020] [Accepted: 03/01/2021] [Indexed: 11/07/2022]
Abstract
We present a comprehensive numerical study on the kinetics of phase transition that is characterized by two nonconserved scalar order parameters coupled by a special linear-quadratic interaction. This particular Ginzburg-Landau theory has been proposed to describe the coupled charge and magnetic transition in nickelates and the collinear stripe phase in cuprates. The inhomogeneous state of such systems at low temperatures consists of magnetic domains separated by quasimetallic domain walls where the charge order is reduced. By performing large-scale cell dynamics simulations, we find a two-stage phase-ordering process in which a short period of independent evolution of the two order parameters is followed by a correlated coarsening process. The long-time growth and coarsening of magnetic domains is shown to follow the Allen-Cahn power law. We further show that the nucleation-and-growth dynamics during phase transformation to the ordered states is well described by the Kolmogorov-Johnson-Mehl-Avrami theory in two dimensions. On the other hand, the presence of quasimetallic magnetic domain walls in the ordered states gives rise to a very different kinetics for transformation to the high-temperature paramagnetic phase. In this scenario, the phase transformation is initiated by the decay of magnetic domain walls into two insulator-metal boundaries, which subsequently move away from each other. Implications of our findings to recent nano-imaging experiments on nickelates are also discussed.
Collapse
Affiliation(s)
- Lingnan Shen
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Gia-Wei Chern
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| |
Collapse
|
8
|
Vats A, Banerjee V, Puri S. Domain growth in ferronematics: slaved coarsening, emergent morphologies and growth laws. SOFT MATTER 2021; 17:2659-2674. [PMID: 33533368 DOI: 10.1039/d0sm01888k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Ferronematics (FNs) are suspensions of magnetic nanoparticles in nematic liquid crystals (NLCs). They have attracted much experimental attention, and are of great interest both scientifically and technologically. There are very few theoretical studies of FNs, even in equilibrium. In this paper, we study the non-equilibrium phenomenon of domain growth after a thermal quench (or coarsening) in this coupled system. Our modeling is based on coupled time-dependent Ginzburg-Landau (TDGL) equations for two order parameters: the LC tensor order parameter Q, and the magnetization M. We consider both shallow and deep quenches from a high-temperature disordered phase. The system coarsens by the collision and annihilation of topological defects. We focus on slaved coarsening, where a disordered Q (or M) field is driven to coarsen by an ordered M (or Q) field. We present detailed results for the morphologies and growth laws, which exhibit unusual features purely due to the magneto-nematic coupling. To the best of our knowledge, this is the first study of non-equilibrium phenomena in FNs.
Collapse
Affiliation(s)
- Aditya Vats
- Department of Physics, Indian Institute of Technology Delhi, New Delhi - 110016, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology Delhi, New Delhi - 110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India.
| |
Collapse
|
9
|
Abstract
In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities.
Collapse
|
10
|
Abate AA, Piqueras CM, Vega DA. Defect-Induced Order–Order Phase Transition in Triblock Copolymer Thin Films. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Anabella A. Abate
- Department of Physics. Instituto de Física del Sur (IFISUR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina
| | - Cristian M. Piqueras
- Department of Chemical Engineering. Planta Piloto de Ingeniería Química (PLAPIQUI), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina
| | - Daniel A. Vega
- Department of Physics. Instituto de Física del Sur (IFISUR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina
| |
Collapse
|
11
|
Das P, Jaiswal PK, Puri S. Surface-directed spinodal decomposition on chemically patterned substrates. Phys Rev E 2020; 102:012803. [PMID: 32794988 DOI: 10.1103/physreve.102.012803] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Accepted: 06/19/2020] [Indexed: 11/07/2022]
Abstract
Surface-directed spinodal decomposition (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical study of SDSD on a chemically patterned substrate. We consider simple surface patterns for our simulations, but most of the results apply for arbitrary patterns. In layers near the surface, we observe a dynamical crossover from a surface-registry regime to a phase-separation regime. We study this crossover using layerwise correlation functions and structure factors and domain length scales.
Collapse
Affiliation(s)
- Prasenjit Das
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel.,School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Prabhat K Jaiswal
- Department of Physics, Indian Institute of Technology Jodhpur, Karwar 342037, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| |
Collapse
|
12
|
Grzetic DJ, Wickham RA. Dynamical self-consistent field theory captures multi-scale physics during spinodal decomposition in a symmetric binary homopolymer blend. J Chem Phys 2020; 152:104903. [PMID: 32171199 DOI: 10.1063/1.5142179] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
We study the spinodal decomposition in a symmetric, binary homopolymer blend using our recently developed dynamical self-consistent field theory. By taking the extremal solution of a dynamical functional integral, the theory reduces the interacting, multi-chain dynamics to a Smoluchowski equation describing the statistical dynamics of a single, unentangled chain in a self-consistent, time-dependent, mean force-field. We numerically solve this equation by evaluating averages over a large ensemble of replica chains, each one of which obeys single-chain Langevin dynamics, subject to the mean field. Following a quench from the disordered state, an early time spinodal instability in the blend composition develops, before even one Rouse time elapses. The dominant, unstable, growing wavelength is on the order of the coil size. The blend then enters a late-time, t, scaling regime with a growing domain size that follows the expected Lifshitz-Slyozov-Wagner t1/3 power law, a characteristic of a diffusion-driven coarsening process. These results provide a satisfying test of this new method, which correctly captures both the early and late time physics in the blend. Our simulation spans five orders-of-magnitude in time as the domains coarsen to 20 times the coil size, while remaining faithful to the dynamics of the microscopic chain model.
Collapse
Affiliation(s)
- Douglas J Grzetic
- Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
| | - Robert A Wickham
- Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
| |
Collapse
|
13
|
Zhao W, Li W. Hybrid patterns from directed self-assembly of diblock copolymers by chemical patterns. Phys Chem Chem Phys 2019; 21:18525-18532. [PMID: 31423503 DOI: 10.1039/c9cp02667c] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The surface affinity is a critical factor for controlling the formation of monolayer nanostructures in block copolymer thin films. In general, strong surface affinity tends to induce the formation of domains with low spontaneous curvature. Abiding by this principle, we propose a facile chemoepitaxial scheme for producing large-scale ordered hybrid patterns by the directed self-assembly of diblock copolymers. The guiding chemical pattern is designed as periodic stripes with alternately changing surface affinities. As a consequence, two different geometries of domains are formed on the stripes with different affinities. The self-assembly process of block copolymers guided by the stripe patterns is investigated using cell dynamics simulations based on time-dependent Ginzburg-Landau theory, and the kinetic stability diagram is estimated. Hybrid patterns are successfully achieved with both cylinder-forming and sphere-forming diblock copolymers. In the cylinder-forming system, the major hybrid pattern exhibiting a considerable stability window is composed of parallel cylinders and perforated lamellae, while it is composed of monolayer spheres and parallel cylinders in the other system. Encouragingly, the chemoepitaxial method is valid till the period of the guiding pattern is a large multiple of the domain spacing. The chemoepitaxial scheme demonstrated in this work serves as a nice supplement to the graphoepitaxial one proposed in our previous work.
Collapse
Affiliation(s)
- Wenfeng Zhao
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
| | | |
Collapse
|
14
|
Zhao W, Duan C, Li W. Hybrid line-dot nanopatterns from directed self-assembly of diblock copolymers by trenches. Phys Chem Chem Phys 2019; 21:10011-10021. [PMID: 31041947 DOI: 10.1039/c9cp00949c] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We demonstrate that the directed self-assembly of AB diblock copolymers by periodic trenches can be used to fabricate large-scale ordered hybrid line-dot nanopatterns in addition to a defect-free dot nanopattern. The formation of line or dot nanopatterns in thin films with proper surface affinities is controlled by the film thickness, which is modulated by a topographic pattern consisting of steps and trenches. Two kinds of line-dot nanopatterns are achieved with cylinder-forming and sphere-forming copolymers, respectively. One kind of hybrid nanopatterns is composed of perpendicularly standing cylinders (dots) on the steps and parallel monolayer cylinders (lines) within the trenches, while the dots of the other kind are replaced by monolayer spheres on the steps. The thermodynamic stability region of target hybrid nanopatterns is identified by constructing two-dimensional phase diagrams with respect to two control parameters of step height and film thickness using self-consistent field theory. Furthermore, a process window of the line-dot nanopatterns is estimated using cell dynamics simulations based on time-dependent Ginzburg-Landau theory, confirming their feasibility in kinetics.
Collapse
Affiliation(s)
- Wenfeng Zhao
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
| | | | | |
Collapse
|
15
|
Deng H, Qiang Y, Zhang T, Li W, Yang T. Chiral selection of single helix formed by diblock copolymers confined in nanopores. NANOSCALE 2016; 8:15961-15969. [PMID: 27536966 DOI: 10.1039/c6nr05043c] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Chiral selection has attracted tremendous attention from the scientific communities, especially from biologists, due to the mysterious origin of homochirality in life. The self-assembly of achiral block copolymers confined in nanopores offers a simple but useful model of forming helical structures, where the helical structures possess random chirality selection, i.e. equal probability of left-handedness and right-handedness. Based on this model, we study the stimulus-response of chiral selection to external conditions by introducing a designed chiral pattern onto the inner surface of a nanopore, aiming to obtain a defect-free helix with controllable homochirality. A cell dynamics simulation based on the time-dependent Ginzburg-Landau theory is carried out to demonstrate the tuning effect of the patterned surface on the chiral selection. Our results illustrate that the chirality of the helix can be successfully controlled to be consistent with that of the tailored surface patterns. This work provides a successful example for the stimulus response of the chiral selection of self-assembled morphologies from achiral macromolecules to external conditions, and hence sheds light on the understanding of the mechanism of the stimulus response.
Collapse
Affiliation(s)
- Hanlin Deng
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
| | | | | | | | | |
Collapse
|
16
|
Krishnan R, Puri S. Molecular dynamics study of phase separation in fluids with chemical reactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052316. [PMID: 26651704 DOI: 10.1103/physreve.92.052316] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2015] [Indexed: 06/05/2023]
Abstract
We present results from the first d=3 molecular dynamics (MD) study of phase-separating fluid mixtures (AB) with simple chemical reactions (A⇌B). We focus on the case where the rates of forward and backward reactions are equal. The chemical reactions compete with segregation, and the coarsening system settles into a steady-state mesoscale morphology. However, hydrodynamic effects destroy the lamellar morphology which characterizes the diffusive case. This has important consequences for the phase-separating structure, which we study in detail. In particular, the equilibrium length scale (ℓ(eq)) in the steady state suggests a power-law dependence on the reaction rate ε:ℓ(eq)∼ε(-θ) with θ≃1.0.
Collapse
Affiliation(s)
- Raishma Krishnan
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| |
Collapse
|
17
|
Ordering Dynamics in Neuron Activity Pattern Model: An Insight to Brain Functionality. PLoS One 2015; 10:e0141463. [PMID: 26506525 PMCID: PMC4623514 DOI: 10.1371/journal.pone.0141463] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2015] [Accepted: 10/08/2015] [Indexed: 11/23/2022] Open
Abstract
We study the domain ordering kinetics in d = 2 ferromagnets which corresponds to populated neuron activities with both long-ranged interactions, V(r) ∼ r−n and short-ranged interactions. We present the results from comprehensive Monte Carlo (MC) simulations for the nonconserved Ising model with n ≥ 2, interaction range considering near and far neighbors. Our model results could represent the long-ranged neuron kinetics (n ≤ 4) in consistent with the same dynamical behaviour of short-ranged case (n ≥ 4) at far below and near criticality. We found that emergence of fast and slow kinetics of long and short ranged case could imitate the formation of connections among near and distant neurons. The calculated characteristic length scale in long-ranged interaction is found to be n independent (L(t) ∼ t1/(n−2)), whereas short-ranged interaction follows L(t) ∼ t1/2 law and approximately preserve universality in domain kinetics. Further, we did the comparative study of phase ordering near the critical temperature which follows different behaviours of domain ordering near and far critical temperature but follows universal scaling law.
Collapse
|
18
|
Deng H, Xie N, Li W, Qiu F, Shi AC. Perfectly Ordered Patterns via Corner-Induced Heterogeneous Nucleation of Self-Assembling Block Copolymers Confined in Hexagonal Potential Wells. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b00681] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Hanlin Deng
- State Key
Laboratory of Molecular Engineering of Polymers, Collaborative Innovation
Center of Polymers and Polymer Composite Materials, Department of
Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Nan Xie
- State Key
Laboratory of Molecular Engineering of Polymers, Collaborative Innovation
Center of Polymers and Polymer Composite Materials, Department of
Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Weihua Li
- State Key
Laboratory of Molecular Engineering of Polymers, Collaborative Innovation
Center of Polymers and Polymer Composite Materials, Department of
Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Feng Qiu
- State Key
Laboratory of Molecular Engineering of Polymers, Collaborative Innovation
Center of Polymers and Polymer Composite Materials, Department of
Macromolecular Science, Fudan University, Shanghai 200433, China
| | - An-Chang Shi
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario Canada L8S 4M1
| |
Collapse
|
19
|
Zhang T, Deng H, Yang T, Li W. Defective morphologies kinetically formed in diblock copolymers under the cylindrical confinement. POLYMER 2015. [DOI: 10.1016/j.polymer.2015.03.059] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
20
|
Sevink GJA. Rigorous embedding of cell dynamics simulations in the Cahn-Hilliard-Cook framework: Imposing stability and isotropy. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:053309. [PMID: 26066281 DOI: 10.1103/physreve.91.053309] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2015] [Indexed: 06/04/2023]
Abstract
We have rigorously analyzed the stability of the efficient cell dynamics simulations (CDS) method by making use of the special properties of the local averaging operator 〈〈*〉〉-* in matrix form. Besides resolving a theoretical issue that has puzzled many over the past three decades, this analysis has considerable practical value: It relates CDS directly to finite-difference approximations of the Cahn-Hilliard-Cook equations and provides a straightforward recipe for replacing the original two- or three-dimensional (2D or 3D) averaging operators in CDS by an equivalent (in terms of stability) discrete Laplacian with superior isotropy and scaling behavior. As such, we open up a route to suppress the unphysical reflection of the computational grid in CDS results (grid artifacts). We found that proper rescaling of discrete Laplacians, needed to employ them in CDS, is equivalent to introducing a well-chosen time step in CDS. In turn, our analysis provides stability conditions for phase-field simulations based on the Cahn-Hilliard-Cook equations. Subsequently, we have quantitatively compared the isotropy and scaling behavior of several discrete 2D or 3D Laplacians, thereby extending the significance of this work to general field-based methodology. We found that all considered discrete Laplacians have equivalent scaling behavior along the Cartesian directions. In addition, and somewhat surprisingly, known "isotropic" discrete Laplacians, i.e., isotropic up to fourth order in |k|, become quite anisotropic for larger wave vectors, whereas "less isotropic" discrete Laplacians (second order) are only slightly anisotropic on the whole |k| range. We identified a hard limit to the accuracy with which the discrete Laplacian can emulate the two important properties of the optimal (continuum) Laplacian, as an improvement of the isotropy, by introducing additional points to the stencil, will negatively affect the scaling behavior. Within this limitation, the discrete compact Laplacians in the DnQm class known from lattice hydrodynamics, D2Q9 in 2D and D3Q19 in 3D, are found to be optimal in terms of isotropy. However, by being only slightly anisotropic on the whole range and enabling larger time steps, the discrete Laplacians that relate to the local averaging operator of Oono and Puri (2D) and Shinozaki and Oono (3D) as well as the less familiar 3D discrete BvV Laplacian developed for dynamic density functional theory are valid alternatives.
Collapse
Affiliation(s)
- G J A Sevink
- Leiden Institute of Chemistry, Leiden University, P. O. Box 9502, 2300 RA Leiden, The Netherlands
| |
Collapse
|
21
|
Singh A, Puri S. Phase separation in ternary fluid mixtures: a molecular dynamics study. SOFT MATTER 2015; 11:2213-2219. [PMID: 25643209 DOI: 10.1039/c4sm02726d] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present detailed results from molecular dynamics (MD) simulations of phase separation in ternary (ABC) fluid mixtures for d = 2 and d = 3 systems. Our MD simulations naturally incorporate hydrodynamic effects. The domain growth law is l(t) ∼ t(ϕ) with dynamic growth exponent ϕ. Our data clearly indicate that a ternary fluid mixture reaches a dynamical scaling regime at late times with a gradual crossover from ϕ = 1/3 → 1/2 → 2/3 in d = 2 and ϕ = 1/3 → 1 in d = 3 resulting from the hydrodynamic effect in the system. These MD simulations do not yet access the inertial hydrodynamic regime (with l(t) ∼ t(2/3)) of phase separation in ternary fluid mixtures in d = 3.
Collapse
Affiliation(s)
- Awaneesh Singh
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India.
| | | |
Collapse
|
22
|
Instability-induced pattern formation of photoactivated functional polymers. Proc Natl Acad Sci U S A 2014; 111:17017-22. [PMID: 25404346 DOI: 10.1073/pnas.1409718111] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Since the pioneering work of Turing on the formation principles of animal coat patterns [Turing AM (1952) Phil Trans R Soc Lond B 237(641):37-72], such as the stripes of a tiger, great effort has been made to understand and explain various phenomena of self-assembly and pattern formation. Prominent examples are the spontaneous demixing in emulsions, such as mixtures of water and oil [Herzig EM, et al. (2007) Nat Mater 6:966-971]; the distribution of matter in the universe [Kibble TWB (1976) J Phys A: Math Gen 9(8):1387]; surface reconstruction in ionic crystals [Clark KW, et al. (2012) Nanotechnol 23(18):185306]; and the pattern formation caused by phase transitions in metal alloys, polymer mixtures and binary Bose-Einstein condensates [Sabbatini J, et al. (2011) Phys Rev Lett 107:230402]. Photoactivated pattern formation in functional polymers has attracted major interest due to its potential applications in molecular electronics and photoresponsive systems. Here we demonstrate that photoactivated pattern formation on azobenzene-containing polymer films can be entirely explained by the physical concept of phase separation. Using experiments and simulations, we show that phase separation is caused by an instability created by the photoactivated transitions between two immiscible states of the polymer. In addition, we have shown in accordance with theory, that polarized light has a striking effect on pattern formation indicated by enhanced phase separation.
Collapse
|
23
|
Singh A, Puri S, Dasgupta C. Kinetics of phase separation in polymer mixtures: A molecular dynamics study. J Chem Phys 2014; 140:244906. [DOI: 10.1063/1.4884824] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Awaneesh Singh
- Department of Physics, Indian Institute of Science, Bangalore – 560012, India
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi – 110067, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi – 110067, India
| | - Chandan Dasgupta
- Department of Physics, Indian Institute of Science, Bangalore – 560012, India
| |
Collapse
|
24
|
Xie N, Li W, Zhang H, Qiu F, Shi AC. Kinetics of lamellar formation on sparsely stripped patterns. J Chem Phys 2013; 139:194903. [PMID: 24320351 DOI: 10.1063/1.4830396] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Chemical epitaxy based on the self-assembly of block copolymers is viewed as a promising technique to achieve ordered patterns on a large scale. Herein, we study the kinetics of lamellar formation of block copolymers under the direction of sparsely stripped patterns using cell dynamics simulations of the time-dependent Ginzburg-Landau theory. First, a scaling law is unveiled with the ordering time of lamellae, tp, with respect to the multiples between the periods of lamellae and stripe patterns, which is consistent with the power law evolution of the correlation length existing in the bulk phase of lamellae. Second, the tolerative windows of perfect order, with deviation from integer multiples, are also estimated from the aspect of kinetics. The results of the ordering time and tolerative windows are of great interest for relevant experiments or applications. Finally, a two-stage evolution is explored during the pattern formation of chemical epitaxy by probing into the evolution of defects, which is of fundamental interest for us to understand the coarsening kinetics of block copolymers under the direction of chemical patterns.
Collapse
Affiliation(s)
- Nan Xie
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | | | | | | | | |
Collapse
|
25
|
Krishnan R, Jaiswal PK, Puri S. Phase separation in antisymmetric films: a molecular dynamics study. J Chem Phys 2013; 139:174705. [PMID: 24206320 DOI: 10.1063/1.4827882] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have used molecular dynamics (MD) simulations to study phase-separation kinetics in a binary fluid mixture (AB) confined in an antisymmetric thin film. One surface of the film (located at z = 0) attracts the A-atoms, and the other surface (located at z = D) attracts the B-atoms. We study the kinetic processes which lead to the formation of equilibrium morphologies subsequent to a deep quench below the miscibility gap. In the initial stages, one observes the formation of a layered structure, consisting of an A-rich layer followed by a B-rich layer at z = 0; and an analogous structure at z = D. This multi-layered morphology is time-dependent and propagates into the bulk, though it may break up into a laterally inhomogeneous structure at a later stage. We characterize the evolution morphologies via laterally averaged order parameter profiles; the growth laws for wetting-layer kinetics and layer-wise length scales; and the scaling properties of layer-wise correlation functions.
Collapse
Affiliation(s)
- Raishma Krishnan
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | | | | |
Collapse
|
26
|
Liu Y, Kuksenok O, Balazs AC. Using light to guide the motion of nanorods in photoresponsive binary blends: designing hierarchically structured nanocomposites. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2013; 29:12785-12795. [PMID: 23848191 DOI: 10.1021/la401775p] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
One of the challenges in creating high-performance polymer nanocomposites is establishing effective routes for tailoring the morphology of both the polymer mixture and the dispersed nanoparticles, which contribute desirable optical, electrical, and mechanical properties. Using computational modeling, we devise an effective method for simultaneously controlling the spatial regularity of the polymer phases and the distribution of the rods within this matrix. We focus on mixtures of photosensitive AB binary blends and A-coated nanorods; in the presence of light, the binary blends undergo a reversible chemical reaction and phase separation to yield a morphology resembling that of microphase-separated diblock copolymers. We simulate the effects of illuminating this sample with a uniform background light and a higher intensity, spatially localized light, which is rastered over the sample with a velocity v. The resulting material displays a periodically ordered, essentially defect-free morphology, with the A-like nanoparticles localized in lamellar A domains. The dynamic behavior of the rods within this system can be controlled by varying the velocity v and Γ2, the reaction rate coefficient produced by the higher intensity light. Specifically, the rastering light can drive the rods to be "pushed" along the lamellar domains or oriented perpendicular to these stripes. Given these attributes, we isolate scenarios where the system encompasses a complex hierarchical structure, with rods that are simultaneously ordered along two distinct directions within the periodic matrix. Namely, the rods form long nanowires that span the length of the sample and lie perpendicular to these wires in regularly spaced A lamellae. Hence, our approach points to new routes for producing self-organized rectangular grids, which can impart remarkable optoelectronic or mechanical properties to the materials.
Collapse
Affiliation(s)
- Ya Liu
- Chemical Engineering Department, University of Pittsburgh , Pittsburgh, Pennsylvania 15261, United States
| | | | | |
Collapse
|
27
|
Xu Y, Xie N, Li W, Qiu F, Shi AC. Phase behaviors and ordering dynamics of diblock copolymer self-assembly directed by lateral hexagonal confinement. J Chem Phys 2012. [DOI: 10.1063/1.4765098] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuci Xu
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Nan Xie
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Weihua Li
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Feng Qiu
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
- Key Laboratory of Computational Physical Sciences, Ministry of Education of China, Shanghai 200433, China
| | - An-Chang Shi
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| |
Collapse
|
28
|
Singh A, Puri S, Dasgupta C. Growth Kinetics of Nanoclusters in Solution. J Phys Chem B 2012; 116:4519-23. [DOI: 10.1021/jp211380j] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Awaneesh Singh
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India
- Department of Physics, Indian Institute of Science, Bangalore - 560012, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India
| | - Chandan Dasgupta
- Department of Physics, Indian Institute of Science, Bangalore - 560012, India
| |
Collapse
|
29
|
Jaiswal PK, Vashishtha M, Puri S, Khanna R. Morphological phase separation in unstable thin films: pattern formation and growth. Phys Chem Chem Phys 2011; 13:13598-603. [PMID: 21701762 DOI: 10.1039/c0cp03013a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present results from a comprehensive numerical study of morphological phase separation (MPS) in unstable thin liquid films on a 2-dimensional substrate. We study the quantitative properties of the evolution morphology via several experimentally relevant markers, e.g., correlation function, structure factor, domain-size and defect-size probability distributions, and growth laws. Our results suggest that the late-stage morphologies exhibit dynamical scaling, and their evolution is self-similar in time. We emphasize the analogies and differences between MPS in films and segregation kinetics in unstable binary mixtures.
Collapse
Affiliation(s)
- Prabhat K Jaiswal
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | | | | | | |
Collapse
|
30
|
Majumder S, Das SK. Diffusive domain coarsening: early time dynamics and finite-size effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021110. [PMID: 21928952 DOI: 10.1103/physreve.84.021110] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2011] [Revised: 03/21/2011] [Indexed: 05/31/2023]
Abstract
We study the diffusive dynamics of phase separation in a symmetric binary (A + B) mixture with a 50:50 composition of A and B particles, following a quench below the demixing critical temperature, both in spatial dimensions d=2 and d=3. The particular focus of this work is to obtain information about the effects of system size and correction to the growth law via the appropriate application of the finite-size scaling method to the results obtained from the Kawasaki exchange Monte Carlo simulation of the Ising model. Observations of only weak size effects and a very small correction to scaling in the growth law are significant. The methods used in this work and information thus gathered will be useful in the study of the kinetics of phase separation in fluids and other problems of growing length scale. We also provide a detailed discussion of the standard methods of understanding simulation results which may lead to inappropriate conclusions.
Collapse
Affiliation(s)
- Suman Majumder
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | | |
Collapse
|
31
|
Sun M, Zhang JJ, Wang B, Wu HS, Pan J. Domain patterns in a diblock copolymer-diblock copolymer mixture with oscillatory particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011802. [PMID: 21867200 DOI: 10.1103/physreve.84.011802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2010] [Revised: 05/04/2011] [Indexed: 05/31/2023]
Abstract
We investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-diblock copolymer mixtures in the presence of periodic oscillatory particles. Under certain conditions, although the macrophase separation of a system is almost isotropic, microphase separation of one diblock copolymer takes place and becomes anisotropic gradually. By changing the oscillatory frequency and amplitude, the orientational order transition of a striped microphase structure from the state parallel to the oscillatory direction to the state perpendicular to the oscillatory direction is observed. We also find that the order transition occurs when we change the initial composition ratio. Furthermore, we examine the domain size and the orientational order parameter of microstructure in the process of orientational order transition. The results may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition of soft materials by changing the oscillatory field.
Collapse
Affiliation(s)
- Minna Sun
- School of Chemistry and Materials Science, Shanxi Normal University, Linfen 041004, China
| | | | | | | | | |
Collapse
|
32
|
Xue F, Wang ZX, Zhang GD, Qu BP, Shi HJ, Shu GG, Liu W. Numerical simulations of the phase separation properties for the thermal aged CDSS with Phase Field Model. NUCLEAR ENGINEERING AND DESIGN 2011. [DOI: 10.1016/j.nucengdes.2011.04.010] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
33
|
Pezzutti AD, Vega DA, Villar MA. Dynamics of dislocations in a two-dimensional block copolymer system with hexagonal symmetry. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2011; 369:335-350. [PMID: 21149375 DOI: 10.1098/rsta.2010.0269] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Block copolymer thin films have attracted considerable attention for their ability to self-assemble into nanometre-scale architectures. Recent advances in the use of block copolymer thin films as nano-lithographic masks have driven research efforts in order to have better control of long-range ordering in the plane of the film. Irrespective of the method of sample preparation, different quasi-two-dimensional systems with hexagonal symmetry unavoidably contain translational defects, called dislocations. Dislocations control the process of coarsening in the nano/meso-scales and provide one of the most important mechanisms of length-scale selection in hexagonal patterns. Although in the last decade the nonlinear dynamics of topological defects in quasi-two-dimensional systems has witnessed significant progress, still little is known about the role of external fields on the creation and annihilation mechanisms involved in the relaxation process towards equilibrium states. In this paper, the dynamics of dislocations in non-optimal hexagonal patterns is studied in the framework of the Ohta-Kawasaki model for a diblock copolymer. Measurements of the climb and glide velocities as a function of the wave vector deformation reveal the main mechanisms of relaxation associated with the motion of dislocations.
Collapse
Affiliation(s)
- Aldo D Pezzutti
- Instituto de Física del Sur, Department of Physics, Universidad Nacional del Sur-CONICET, Avenida L.N. Alem 1253, (8000) Bahía Blanca, Argentina
| | | | | |
Collapse
|
34
|
Singh A, Mukherjee A, Vermeulen HM, Barkema GT, Puri S. Control of structure formation in phase-separating systems. J Chem Phys 2011; 134:044910. [DOI: 10.1063/1.3530784] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
35
|
Yan LT, Balazs AC. Self-assembly of nanorods in ternary mixtures: promoting the percolation of the rods and creating interfacially jammed gels. ACTA ACUST UNITED AC 2011. [DOI: 10.1039/c1jm10397k] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
36
|
Bosse AW. Phase-Field Simulation of Long-Wavelength Line Edge Roughness in Diblock Copolymer Resists. MACROMOL THEOR SIMUL 2010. [DOI: 10.1002/mats.201000018] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
37
|
Li W, Qiu F, Yang Y, Shi AC. Ordering Dynamics of Directed Self-Assembly of Block Copolymers in Periodic Two-Dimensional Fields. Macromolecules 2010. [DOI: 10.1021/ma9023203] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Weihua Li
- The Key Laboratory of Molecular Engineering of Polymers, Ministry of Education, China
- Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Feng Qiu
- The Key Laboratory of Molecular Engineering of Polymers, Ministry of Education, China
- Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Yuliang Yang
- The Key Laboratory of Molecular Engineering of Polymers, Ministry of Education, China
- Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - An-Chang Shi
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada, L8S 4M1
| |
Collapse
|
38
|
Nagamine Y. ELECTROCHEMISTRY 2010; 78:769-773. [DOI: 10.5796/electrochemistry.78.769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
|
39
|
Iwamatsu M. Minimum free-energy path of homogenous nucleation from the phase-field equation. J Chem Phys 2009; 130:244507. [DOI: 10.1063/1.3158471] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
40
|
Li JL, Yan LT, Xie XM. Phase dynamics and wetting layer formation mechanisms of pattern-directed phase separation in binary polymer mixture films with asymmetry compositions. POLYMER 2009. [DOI: 10.1016/j.polymer.2009.03.014] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
|
41
|
Hayase Y, Kobayashi M, Vollmer D, Pleiner H, Auernhammer GK. Asymmetric oscillations during phase separation under continuous cooling: A simple model. J Chem Phys 2008; 129:184109. [PMID: 19045388 DOI: 10.1063/1.3009867] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the phase separation of binary mixtures under continuous cooling using the Cahn-Hilliard equation including the effect of gravity. In our simple model, sedimentation is accounted for by instantaneously "removing" droplets from the supersaturated mixture into the coexisting phase once the droplets have reached a defined maximum size. Our model predicts an oscillatory variation of turbidity. Depending on the composition, either both phases oscillate (symmetric oscillations) or only one of the phases oscillates (asymmetric oscillations). In the asymmetric case, droplet sedimentation from the majority phase into the minority phase reduces supersaturation in the minority phase. This inhibits droplet formation in the minority phase. The cooling rate dependence of the period agrees with experimental results.
Collapse
Affiliation(s)
- Yumino Hayase
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany.
| | | | | | | | | |
Collapse
|
42
|
Chen XB, Niu LS, Shi HJ. Modeling the phase separation in binary lipid membrane under externally imposed oscillatory shear flow. Colloids Surf B Biointerfaces 2008; 65:203-12. [PMID: 18502621 DOI: 10.1016/j.colsurfb.2008.04.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2008] [Revised: 04/09/2008] [Accepted: 04/09/2008] [Indexed: 11/18/2022]
Abstract
By adding external velocity terms, the two-dimensional time-dependent Ginzburg-Landau (TDGL) equations are modified. Based on this, the phase separation in binary lipid membrane under externally imposed oscillatory shear flow is numerically modeled employing the Cell Dynamical System (CDS) approach. Considering shear flows with different frequencies and amplitudes, several aspects of such a phase evolving process are studied. Firstly, visualized results are shown via snapshot figures of the membrane shape. And then, the simulated scattering patterns at typical moments are presented. Furthermore, in order to more quantitatively discuss this phase-separation process, the time growth laws of the characteristic domain sizes in both directions parallel and perpendicular to the flow are investigated for each case. Finally, the peculiar rheological properties of such binary lipid membrane system have been discussed, mainly the normal stress difference and the viscoelastic complex shear moduli.
Collapse
Affiliation(s)
- Xiao-Bo Chen
- Key Laboratory of Failure Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
| | | | | |
Collapse
|
43
|
Fiałkowski M, Hołyst R. Dynamics of Phase Separation in Polymer Blends Revisited: Morphology, Spinodal, Noise, and Nucleation. MACROMOL THEOR SIMUL 2008. [DOI: 10.1002/mats.200800020] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
|
44
|
Yan LT, Li J, Zhang F, Xie XM. Surface-Directed Phase Separation via a Two-Step Quench Process in Binary Polymer Mixture Films with Asymmetry Compositions. J Phys Chem B 2008; 112:8499-506. [DOI: 10.1021/jp801648t] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Li-Tang Yan
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Jialin Li
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Fengbo Zhang
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Xu-Ming Xie
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
| |
Collapse
|
45
|
Yan LT, Li J, Xie XM. Three-dimensional numerical simulations of lamellar structure via two-step surface-directed phase separation in polymer blend films. J Chem Phys 2008; 128:224906. [DOI: 10.1063/1.2938370] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
46
|
Xu H, Wang T, Huang Y, Hu Y. Microphase Separation and Morphology of the Real Polymer System by Dynamic Density Functional Theory, Based on the Equation of State. Ind Eng Chem Res 2008. [DOI: 10.1021/ie701776r] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hui Xu
- State Key Laboratory of Chemical Engineering and Department of Chemistry East China University of Science and Technology, Shanghai 200237, China
| | - Tengfang Wang
- State Key Laboratory of Chemical Engineering and Department of Chemistry East China University of Science and Technology, Shanghai 200237, China
| | - Yongmin Huang
- State Key Laboratory of Chemical Engineering and Department of Chemistry East China University of Science and Technology, Shanghai 200237, China
| | - Ying Hu
- State Key Laboratory of Chemical Engineering and Department of Chemistry East China University of Science and Technology, Shanghai 200237, China
| |
Collapse
|
47
|
Yan LT, Li J, Li Y, Xie XM. Kinetic Pathway of Pattern-Directed Phase Separation in Binary Polymer Mixture Films. Macromolecules 2008. [DOI: 10.1021/ma702616s] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Li-Tang Yan
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Jialin Li
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Yao Li
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Xu-Ming Xie
- Advanced Materials Laboratory, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| |
Collapse
|
48
|
Yan LT, Xie XM. The phase dynamics and wetting layer formation mechanisms in two-step surface-directed spinodal decomposition. J Chem Phys 2008; 128:154702. [DOI: 10.1063/1.2897974] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
49
|
Wu XF, Dzenis YA. Phase-field modeling of the formation of lamellar nanostructures in diblock copolymer thin films under inplanar electric fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031807. [PMID: 18517414 DOI: 10.1103/physreve.77.031807] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2007] [Revised: 02/04/2008] [Indexed: 05/26/2023]
Abstract
Recent experiments show that external inplanar electric field can be employed to guide the molecular self-assembly in diblock copolymer (BCP) thin films to form lamellar nanostructures with potential applications in nanotechnology. We study this self-assembly process through a detailed coarse-grained phase-separation modeling. During the process, the free energy of the BCP films is modeled as the Ginzburg-Landau free energy with nonlocal interaction and electrostatic coupling. The resulting Cahn-Hilliard (CH) equation is solved using an efficient semi-implicit Fourier-spectral algorithm. Numerical results show that the morphology of order parameter formed in either symmetric or asymmetric BCP thin films is strongly influenced by the electric field. For symmetrical BCPs, highly ordered lamellar nanostructures evolved along the direction of the electric field. Phase nucleation and dislocation climbing in the BCP films predicted by the numerical simulation are in a good agreement with those observed in recent BCP electronanolithography. For asymmetrical BCPs, numerical simulation shows that nanodots are guided to align to the electric field. Furthermore, in the case of high electric field, nanodots formed in asymmetrical BCPs may further convert into highly ordered lamellar nanostructures (sphere-to-cylinder transition) parallel to the electric field. Effects of the magnitude of electric field, BCP asymmetry, and molecular interaction of BCPs on the self-assembly process are examined in detail using the numerical scheme developed in this study. The present study can be used for the prediction of the formation of nanostructures in BCP thin films and the quality control of BCP-based nanomanufacturing through optimizing the external electric fields.
Collapse
Affiliation(s)
- Xiang-Fa Wu
- Department of Engineering Mechanics, Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0526, USA.
| | | |
Collapse
|
50
|
Iwamatsu M. Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method. J Chem Phys 2008; 128:084504. [DOI: 10.1063/1.2883652] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|