1
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Thwal S, Majumder S. Interplay of phase segregation and chemical reaction: Crossover and effect on growth laws. Phys Rev E 2024; 109:064131. [PMID: 39020944 DOI: 10.1103/physreve.109.064131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 05/23/2024] [Indexed: 07/20/2024]
Abstract
By combining the nonconserved spin-flip dynamics driving ferromagnetic ordering with the conserved Kawasaki-exchange dynamics driving phase segregation, we perform Monte Carlo simulations of the nearest-neighbor Ising model. This kind of mixed dynamics is found in a system consisting of a binary mixture of isomers, simultaneously undergoing a segregation and an interconversion reaction among themselves. Here, we study such a system following a quench from the high-temperature homogeneous phase to a temperature below the demixing transition. We monitor the growth of domains of both the winner; the isomer, which survives as the majority; and the loser, the isomer that perishes. Our results show a strong interplay of the two dynamics at early times, leading to a growth of the average domain size of both the winner and loser as ∼t^{1/7}, slower than a purely phase-segregating system. At later times, eventually the dynamics becomes reaction dominated and the winner exhibits a ∼t^{1/2} growth, expected for a system with purely nonconserved dynamics. On the other hand, the loser at first show a faster growth, albeit, slower than the winner, and then starts to decay before it almost vanishes. Further, we estimate the time τ_{s} marking the crossover from the early-time slow growth to the late-time reaction-dominated faster growth. As a function of the reaction probability p_{r}, we observe a power-law scaling τ_{s}∼p_{r}^{-x}, where x≈1.05, irrespective of the temperature. For a fixed value of p_{r} too, τ_{s} appears to be independent of the temperature.
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2
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Paul T, Vadakkayil N, Das SK. Finite-size scaling in kinetics of phase separation in certain models of aligning active particles. Phys Rev E 2024; 109:064607. [PMID: 39020877 DOI: 10.1103/physreve.109.064607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2023] [Accepted: 05/14/2024] [Indexed: 07/19/2024]
Abstract
To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of interest: one conserves the total momentum of all the constituents and the other does not. We carry out molecular dynamics simulations to obtain results on structural, growth, and aging properties. Results from our studies, with various finite boxes, show that there exist scalings with respect to the system sizes, in both the latter quantities, as in the standard passive cases. We have exploited this scaling picture to accurately estimate the corresponding exponents, in the thermodynamically large system size limit, for power-law time dependences. It is shown that certain analytical functions describe the behavior of these quantities quite accurately, including the finite-size limits. Our results demonstrate that even though the conservation of velocity has at best weak effects on the dynamics of evolution in the thermodynamic limit, the finite-size behavior is strongly influenced by the presence (or the absence) of it.
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3
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Ghosh S, Das SK. Nonuniversal aging during phase separation with long-range interaction. Phys Rev E 2024; 109:L052102. [PMID: 38907470 DOI: 10.1103/physreve.109.l052102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Accepted: 04/11/2024] [Indexed: 06/24/2024]
Abstract
Issues concerning the kinetics of phase transitions are not well established for the cases where the order parameter remains conserved with time, particularly when the interatomic interactions are long-range in nature. Here we present results on structure, growth, and aging from Monte Carlo simulations of the two-dimensional long-range Ising model. In our computer simulations, random initial configurations, for 50:50 compositions of up and down spins, mimicking high-temperature equilibrium states, have been quenched to temperatures inside the coexistence curve. Our analyses of the simulation data, for such a protocol, show interesting dependence of the aging exponent, λ, on σ, the parameter, within the Hamiltonian, that controls the range of interaction. These nonuniversal values of λ are compared with a theoretical result for lower bounds. For this purpose, we extracted information on relevant aspects of structural properties during the evolution. To estimate λ, as is necessary, we also calculated the average domain size and analyzed its time dependence to obtain the growth exponent α which also is nonuniversal. The trends in the values of λ and α, as well as an anomaly in structure, suggest that a crossover from the long-range to the short-range variety occurs at σ≃1. The location of this boundary and the nonuniversality provide a picture that is surprisingly different from that of the corresponding static critical phenomena. Furthermore, our results suggest an important scaling law combining α and λ.
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Affiliation(s)
- Soumik Ghosh
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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4
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Dittrich F, Midya J, Virnau P, Das SK. Growth and aging in a few phase-separating active matter systems. Phys Rev E 2023; 108:024609. [PMID: 37723674 DOI: 10.1103/physreve.108.024609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 07/22/2023] [Indexed: 09/20/2023]
Abstract
Via computer simulations we study evolution dynamics in systems of continuously moving active Brownian particles. The obtained results are discussed against those from the passive 2D Ising case. Following sudden quenches of random configurations to state points lying within the miscibility gaps and to the critical points, we investigate the far-from-steady-state dynamics by calculating quantities associated with structure and characteristic length scales. We also study aging for quenches into the miscibility gap and provide a quantitative picture for the scaling behavior of the two-time order-parameter correlation function. The overall structure and dynamics are consistent with expectations from the Ising model. This remains true for certain active lattice models as well, for which we present results for quenches to the critical points.
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Affiliation(s)
- Florian Dittrich
- Institute of Physics, Johannes Gutenberg University Mainz, 55128 Mainz, Germany
| | - Jiarul Midya
- Theoretical Physics of Living Matter, Forschungszentrum Jülich, 52425 Jülich, Germany
- School of Basic Sciences, Indian Institute of Technology, Bhubaneswar 752050, India
| | - Peter Virnau
- Institute of Physics, Johannes Gutenberg University Mainz, 55128 Mainz, Germany
| | - Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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5
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Ragulskaya A, Starostin V, Begam N, Girelli A, Rahmann H, Reiser M, Westermeier F, Sprung M, Zhang F, Gutt C, Schreiber F. Reverse-engineering method for XPCS studies of non-equilibrium dynamics. IUCRJ 2022; 9:439-448. [PMID: 35844477 PMCID: PMC9252156 DOI: 10.1107/s2052252522004560] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Accepted: 04/29/2022] [Indexed: 06/15/2023]
Abstract
X-ray photon correlation spectroscopy (XPCS) is a powerful tool in the investigation of dynamics covering a broad time and length scale. It has been widely used to probe dynamics for systems in both equilibrium and non-equilibrium states; in particular, for systems undergoing a phase transition where the structural growth kinetics and the microscopic dynamics are strongly intertwined. The resulting time-dependent dynamic behavior can be described using the two-time correlation function (TTC), which, however, often contains more interesting features than the component along the diagonal, and cannot be easily interpreted via the classical simulation methods. Here, a reverse engineering (RE) approach is proposed based on particle-based heuristic simulations. This approach is applied to an XPCS measurement on a protein solution undergoing a liquid-liquid phase separation. It is demonstrated that the rich features of experimental TTCs can be well connected with the key control parameters including size distribution, concentration, viscosity and mobility of domains. The dynamic information obtained from this RE analysis goes beyond the existing theory. The RE approach established in this work is applicable for other processes such as film growth, coarsening or evolving systems.
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Affiliation(s)
- Anastasia Ragulskaya
- Institute of Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Vladimir Starostin
- Institute of Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Nafisa Begam
- Institute of Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Anita Girelli
- Institute of Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Hendrik Rahmann
- Department of Physics, University of Siegen, Emmy-Noether-Campus, Walter-Flex-Straße 3, 57076 Siegen, Germany
| | - Mario Reiser
- Department of Physics, University of Siegen, Emmy-Noether-Campus, Walter-Flex-Straße 3, 57076 Siegen, Germany
- European X-ray free-electron laser GmbH, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Fabian Westermeier
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, D-22607 Hamburg, Germany
| | - Michael Sprung
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, D-22607 Hamburg, Germany
| | - Fajun Zhang
- Institute of Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Christian Gutt
- Department of Physics, University of Siegen, Emmy-Noether-Campus, Walter-Flex-Straße 3, 57076 Siegen, Germany
| | - Frank Schreiber
- Institute of Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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6
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Vadakkayil N, Singha SK, Das SK. Influence of roughening transition on magnetic ordering. Phys Rev E 2022; 105:044142. [PMID: 35590609 DOI: 10.1103/physreve.105.044142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 03/31/2022] [Indexed: 06/15/2023]
Abstract
In the literature of magnetic phase transitions, in addition to a critical point, the existence of another special point has been discussed. This is related to the broadening of the interface between two different ordering phases and is referred to as the point of roughening transition. While the equilibrium properties associated with this transition are well understood, the influence of this on nonequilibrium dynamics still needs to be investigated. In this paper we present comprehensive results, from Monte Carlo simulations, on coarsening dynamics in a system, over a wide range of temperature, in space dimension d=3, for which there exists a roughening transition at a nonzero temperature T_{R}. An advanced analysis of the simulation data, on structure, growth, and aging, shows that the onset of unexpected glasslike slow dynamics in this system, that has received attention in recent times, for quenches to zero temperature, actually occurs at this transition point. This implies that the structure and aging depend upon the final temperature, when the latter lies between 0 and T_{R}. This is a very interesting exception to universality in coarsening dynamics. The results also demonstrate an important structure-dynamics connection in the phase-ordering dynamics. We compare the key results with those from d=2, for which there exists no nonzero roughening transition temperature. The absence of the above-mentioned anomalous features in the latter dimension places our conjecture on the role of the roughening transition on a firmer footing.
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Affiliation(s)
- Nalina Vadakkayil
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Sanat K Singha
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
- Assam Energy Institute, Centre of Rajiv Gandhi Institute of Petroleum Technology, Sivasagar 785697, India
| | - Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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7
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Midya J, Das SK. Kinetics of domain growth and aging in a two-dimensional off-lattice system. Phys Rev E 2021; 102:062119. [PMID: 33465989 DOI: 10.1103/physreve.102.062119] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 11/18/2020] [Indexed: 11/07/2022]
Abstract
We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single-component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth, and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-"liquid" as well as vapor-"solid" coexistence. For the vapor-liquid phase separation we observe that ℓ, the average domain length, grows with time (t) as t^{1/2}, a behavior that has connection with hydrodynamics. At low-enough temperature, a sharp crossover of this time dependence to a much slower, temperature-dependent, growth is identified within the timescale of our simulations, implying "solid"-like final state of the high-density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data collapse with respect to ℓ/ℓ_{w}, ℓ, and ℓ_{w} being the average domain lengths at times t and t_{w} (≤t), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: ∼(ℓ/ℓ_{w})^{-λ} for t≫t_{w}. The decay exponent λ, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.
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Affiliation(s)
- Jiarul Midya
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany.,Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India.,School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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8
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Chakraborty S, Das SK. Relaxation in a phase-separating two-dimensional active matter system with alignment interaction. J Chem Phys 2020; 153:044905. [PMID: 32752724 DOI: 10.1063/5.0010043] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Via computer simulations, we study kinetics of pattern formation in a two-dimensional active matter system. Self-propulsion in our model is incorporated via the Vicsek-like activity, i.e., particles have the tendency of aligning their velocities with the average directions of motion of their neighbors. In addition to this dynamic or active interaction, there exists passive inter-particle interaction in the model for which we have chosen the standard Lennard-Jones form. Following quenches of homogeneous configurations to a point deep inside the region of coexistence between high and low density phases, as the systems exhibit formation and evolution of particle-rich clusters, we investigate properties related to the morphology, growth, and aging. A focus of our study is on the understanding of the effects of structure on growth and aging. To quantify the latter, we use the two-time order-parameter autocorrelation function. This correlation, as well as the growth, is observed to follow power-law time dependence, qualitatively similar to the scaling behavior reported for passive systems. The values of the exponents have been estimated and discussed by comparing with the previously obtained numbers for other dimensions as well as with the new results for the passive limit of the considered model. We have also presented results on the effects of temperature on the activity mediated phase separation.
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Affiliation(s)
- Saikat Chakraborty
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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9
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Das K, Vadakkayil N, Das SK. Aging exponents for nonequilibrium dynamics following quenches from critical points. Phys Rev E 2020; 101:062112. [PMID: 32688577 DOI: 10.1103/physreve.101.062112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2020] [Accepted: 05/20/2020] [Indexed: 06/11/2023]
Abstract
Via Monte Carlo simulations we study nonequilibrium dynamics in the nearest-neighbor Ising model, following quenches to points inside the ordered region of the phase diagram. With the broad objective of quantifying the nonequilibrium universality classes corresponding to spatially correlated and uncorrelated initial configurations, in this paper we present results for the decay of the order-parameter autocorrelation function for quenches from the critical point. This autocorrelation is an important probe for the aging dynamics in far-from-equilibrium systems and typically exhibits power-law scaling. From the state-of-the-art analysis of the simulation results, we quantify the corresponding exponents (λ) for both conserved and nonconserved (order-parameter) dynamics of the model in space dimension d=3. Via structural analysis we demonstrate that the exponents satisfy a bound. We also revisit the d=2 case to obtain more accurate results. It appears that irrespective of the dimension, λ is approximately the same for both conserved and nonconserved dynamics.
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Affiliation(s)
- Koyel Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | - Nalina Vadakkayil
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
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10
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Das SK, Das K, Vadakkayil N, Chakraborty S, Paul S. Initial correlation dependence of aging in phase separating solid binary mixtures and ordering ferromagnets. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:184005. [PMID: 31952063 DOI: 10.1088/1361-648x/ab6d10] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Following quenches of initial configurations having long range spatial correlations, prepared at the demixing critical point, to points inside the miscibility gap, we study aging phenomena in solid binary mixtures. Results on the decay of the two-time order-parameter autocorrelation functions, obtained from Monte Carlo simulations of the two-dimensional Ising model, with Kawasaki exchange kinetics, are analyzed via state-of-the art methods. The outcome is compared with that obtained for the ordering in uniaxial ferromagnets. For the latter, we have performed Monte Carlo simulations of the same model using the Glauber mechanism. For both types of systems we provide comparative discussion of our results with reference to those concerning quenches with configurations having no spatial correlation. We also discuss the role of structure on the decay of these correlations.
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Affiliation(s)
- Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, India
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11
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Paciolla M, Arismendi-Arrieta DJ, Moreno AJ. Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent. Polymers (Basel) 2020; 12:E531. [PMID: 32121665 PMCID: PMC7182883 DOI: 10.3390/polym12030531] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2019] [Revised: 02/04/2020] [Accepted: 02/20/2020] [Indexed: 11/16/2022] Open
Abstract
This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provides a consistent characterization of the domain growth. Our results indicate that the coarsening kinetics presents a scaling behaviour that is independent of the solvent quality parameter, in analogy to the time-temperature superposition principle. Interestingly, the domain growth in time follows a power-law behaviour that is approximately independent of the architecture for all the flexible systems; while it is steeper for the semiflexible chains. Nevertheless, the fractal nature of the dense regions emerging during the collapse exhibits the same scaling behaviour for all the macromolecules. This suggests that the faster growing length scale in the semiflexible chains originates just from a faster mass diffusion along the chain contour, induced by the local stiffness. The decay of the dynamic correlations displays scaling behavior with the growing length scale of the system, which is a characteristic signature in coarsening phenomena.
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Affiliation(s)
- Mariarita Paciolla
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain;
| | | | - Angel J. Moreno
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain;
- Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018 San Sebastián, Spain;
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12
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Roy S, Bera A, Majumder S, Das SK. Aging phenomena during phase separation in fluids: decay of autocorrelation for vapor-liquid transitions. SOFT MATTER 2019; 15:4743-4750. [PMID: 31149698 DOI: 10.1039/c9sm00366e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We performed molecular dynamics simulations to study relaxation phenomena during vapor-liquid transitions in a single component Lennard-Jones system. Results from two different overall densities are presented: one in the neighborhood of the vapor branch of the coexistence curve and the other being close to the critical density. The nonequilibrium morphologies, growth mechanisms and growth laws in the two cases are vastly different. In the low density case growth occurs via diffusive coalescence of droplets in a disconnected morphology. On the other hand, the elongated structure in the higher density case grows via advective transport of particles inside the tube-like liquid domains. The objective in this work has been to identify how the decay of the order-parameter autocorrelation, an important quantity to understand aging dynamics, differs in the two cases. In the case of the disconnected morphology, we observe a very robust power-law decay, as a function of the ratio of the characteristic lengths at the observation time and at the age of the system, whereas the results for the percolating structure appear rather complex. To quantify the decay in the latter case, unlike the standard method followed in a previous study, here we have performed a finite-size scaling analysis. The outcome of this analysis shows the presence of a strong preasymptotic correction, while revealing that in this case also, albeit in the asymptotic limit, the decay follows a power-law. Even though the corresponding exponents in the two cases differ drastically, this study, combined with a few recent ones, suggests that power-law behavior of this correlation function is rather universal in coarsening dynamics.
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Affiliation(s)
- Sutapa Roy
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany.
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Vadakkayil N, Chakraborty S, Das SK. Finite-size scaling study of aging during coarsening in non-conserved Ising model: The case of zero temperature quench. J Chem Phys 2019; 150:054702. [DOI: 10.1063/1.5052418] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nalina Vadakkayil
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Saikat Chakraborty
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K. Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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14
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Moreno AJ, Lo Verso F. Computational investigation of microgels: synthesis and effect of the microstructure on the deswelling behavior. SOFT MATTER 2018; 14:7083-7096. [PMID: 30118116 DOI: 10.1039/c8sm01407h] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We present computer simulations of a realistic model of microgels. Unlike the regular network frameworks usually assumed in the simulation literature, we model and simulate a realistic and efficient synthesis route, mimicking cross-linking of functionalized chains inside a cavity. This model is inspired, e.g., by microfluidic fabrication of microgels from macromolecular precursors and is different from standard polymerization routes. The assembly of the chains is mediated by a low fraction of interchain crosslinks. The microgels are polydisperse in size and shape but globally spherical objects. In order to deeply understand the microgel structure and eventually improve the synthesis protocol we characterize their conformational properties and deswelling kinetics, and compare them with the results found for microgels obtained via underlying regular (diamond-like) structures. For the same molecular weight, monomer concentration and effective degree of cross-linking, the specific microstructure of the microgel has no significant effect on the locus of the volume phase transition (VPT). However, it strongly affects the deswelling kinetics, as revealed by a consistent analysis of the domain growth during the microgel collapse. Though both the disordered and the regular networks exhibit a similar early growth of the domains, an acceleration is observed in the regular network at the late stage of the collapse. Similar trends are found for the dynamic correlations coupled to the domain growth. As a consequence, the fast late processes for the domain growth and the dynamic correlations in the regular network are compensated, and the dynamic correlations follow a power-law dependence on the growing length scale that is independent of the microgel microstructure.
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Affiliation(s)
- Angel J Moreno
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain.
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15
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Das SK. Pattern, growth, and aging in aggregation kinetics of a Vicsek-like active matter model. J Chem Phys 2018; 146:044902. [PMID: 28147512 DOI: 10.1063/1.4974256] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Via molecular dynamics simulations, we study kinetics in a Vicsek-like phase-separating active matter model. Quantitative results, for isotropic bicontinuous pattern, are presented on the structure, growth, and aging. These are obtained via the two-point equal-time density-density correlation function, the average domain length, and the two-time density autocorrelation function. Both the correlation functions exhibit basic scaling properties, implying self-similarity in the pattern dynamics, for which the average domain size exhibits a power-law growth in time. The equal-time correlation has a short distance behavior that provides reasonable agreement between the corresponding structure factor tail and the Porod law. The autocorrelation decay is a power-law in the average domain size. Apart from these basic similarities, the overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation. The functional forms of these have been quantified. An exceptionally rapid growth in the active system occurs due to fast coherent motion of the particles, mean-squared-displacements of which exhibit multiple scaling regimes, including a long time ballistic one.
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Affiliation(s)
- Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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16
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Paul S, Das SK. Ballistic aggregation in systems of inelastic particles: Cluster growth, structure, and aging. Phys Rev E 2018; 96:012105. [PMID: 29347235 DOI: 10.1103/physreve.96.012105] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2016] [Indexed: 11/07/2022]
Abstract
We study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.
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Affiliation(s)
- Subhajit Paul
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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Christiansen H, Majumder S, Janke W. Coarsening and aging of lattice polymers: Influence of bond fluctuations. J Chem Phys 2017; 147:094902. [DOI: 10.1063/1.4991667] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
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18
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Majumder S, Zierenberg J, Janke W. Kinetics of polymer collapse: effect of temperature on cluster growth and aging. SOFT MATTER 2017; 13:1276-1290. [PMID: 28106216 DOI: 10.1039/c6sm02197b] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using state of the art Monte Carlo simulations of a bead-spring model we investigate both the equilibrium and the nonequilibrium behavior of the homopolymer collapse. The equilibrium properties obtained via multicanonical sampling recover the well-known finite-size scaling behavior of collapse for our model polymer. For the nonequilibrium dynamics we study the collapse by quenching the homopolymer from an expanded coiled state into the globular phase. The sequence of events observed during the collapse is independent of the quench depth. In particular, we focus on finding out universal scaling behaviors related to the growth or coarsening of clusters of monomers, by drawing phenomenological analogies with ordering kinetics. We distinguish the cluster coarsening stage from the initial stage of primary cluster formation. By successful application of a nonequilibrium finite-size scaling analysis we show that at all quench temperatures, during the coarsening stage, the cluster growth is roughly linear and can be characterised by a universal finite-size scaling function. In addition, we provide evidence of aging by constructing a suitable autocorrelation function and its corresponding dynamical power-law scaling with respect to the growing cluster sizes. The predicted theoretical bound for the exponent governing such scaling is strictly obeyed by the numerical data irrespective of the quench temperature. The results and methods presented here in general should find application in similar phenomena such as the collapse of a protein molecule preceding its folding.
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Affiliation(s)
- Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany.
| | - Johannes Zierenberg
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany.
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany.
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