1
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Gessert D, Christiansen H, Janke W. Superdiffusion-like behavior in zero-temperature coarsening of the [Formula: see text] Ising model. Sci Rep 2023; 13:13270. [PMID: 37582791 PMCID: PMC10427613 DOI: 10.1038/s41598-023-39328-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2023] [Accepted: 07/24/2023] [Indexed: 08/17/2023] Open
Abstract
One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent [Formula: see text] is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with [Formula: see text] was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations on simple-cubic lattices with linear lattice sizes up to [Formula: see text] employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law-but surprisingly, at still later times domains even grow superdiffusively, i.e., with [Formula: see text]. We argue that this new problem is possibly caused by sponge-like structures emerging at early times.
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Affiliation(s)
- Denis Gessert
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
- Centre for Fluid and Complex Systems, Coventry University, Coventry, CV1 5FB UK
| | - Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
- Present Address: NEC Laboratories Europe GmbH, Kurfürsten-Anlage 36, 69115 Heidelberg, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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2
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Paul S, Majumder S, Janke W. Activity mediated globule to coil transition of a flexible polymer in a poor solvent. SOFT MATTER 2022; 18:6392-6403. [PMID: 35979819 DOI: 10.1039/d2sm00354f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Understanding the role of self-propulsion on the conformational properties of active filamentous objects has relevance in biology. In this work, we consider a flexible bead-spring model for active polymers with both attractive and repulsive interactions among the non-bonded monomers. The activity for each monomer works along its intrinsic direction of self-propulsion which changes diffusively with time. We study its kinetics in the overdamped limit, following quenching from good to poor solvent conditions. We observe that with low activities, though the kinetic pathways remain similar, the scaling exponent for the relaxation time of globule formation becomes smaller than that for the case with no activity. Interestingly, for higher activities when self-propulsion dominates over interaction energy, the polymer conformation becomes extended coil-like. There, in the steady state, the variation of the spatial extension of the polymer, measured via its gyration radius, shows two completely different scaling regimes: the corresponding Flory exponent ν changes from 1/3 to 3/5 similar to a transition of the polymer from a globular state to a self-avoiding walk. This can be explained by an interplay among the three energy scales present in the system, viz., the "ballistic", thermal, and interaction energy.
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Affiliation(s)
- Subhajit Paul
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
- International Center for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore-560089, India
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
- Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida 201313, India
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
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3
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Paul S, Majumder S, Das SK, Janke W. Effects of alignment activity on the collapse kinetics of a flexible polymer. SOFT MATTER 2022; 18:1978-1990. [PMID: 35023525 DOI: 10.1039/d1sm01055g] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following quenching from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. The results from our MD simulations reveal that though the globular state is also the typical final state in the active case, the nonequilibrium pathways to arrive at such a state differ from the picture for the passive case due to the alignment interaction among the beads. We notice that deviations from the intermediate "pearl-necklace"-like arrangement, which is observed in the passive case, and the formation of more elongated dumbbell-like structures increase with increasing activity. Furthermore, it appears that while a small active force on the beads certainly makes the coarsening process much faster, there exists a nonmonotonic dependence of the collapse time on the strength of active interaction. We quantify these observations by comparing the scaling laws for the collapse time and growth of pearls with the passive case.
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Affiliation(s)
- Subhajit Paul
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, 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.
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
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4
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Christiansen H, Majumder S, Janke W. Zero-temperature coarsening in the two-dimensional long-range Ising model. Phys Rev E 2021; 103:052122. [PMID: 34134321 DOI: 10.1103/physreve.103.052122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 04/20/2021] [Indexed: 11/07/2022]
Abstract
We investigate the nonequilibrium dynamics following a quench to zero temperature of the nonconserved Ising model with power-law decaying long-range interactions ∝1/r^{d+σ} in d=2 spatial dimensions. The zero-temperature coarsening is always of special interest among nonequilibrium processes, because often peculiar behavior is observed. We provide estimates of the nonequilibrium exponents, viz., the growth exponent α, the persistence exponent θ, and the fractal dimension d_{f}. It is found that the growth exponent α≈3/4 is independent of σ and different from α=1/2, as expected for nearest-neighbor models. In the large σ regime of the tunable interactions only the fractal dimension d_{f} of the nearest-neighbor Ising model is recovered, while the other exponents differ significantly. For the persistence exponents θ this is a direct consequence of the different growth exponents α as can be understood from the relation d-d_{f}=θ/α; they just differ by the ratio of the growth exponents ≈3/2. This relation has been proposed for annihilation processes and later numerically tested for the d=2 nearest-neighbor Ising model. We confirm this relation for all σ studied, reinforcing its general validity.
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Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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5
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Christiansen H, Majumder S, Henkel M, Janke W. Aging in the Long-Range Ising Model. PHYSICAL REVIEW LETTERS 2020; 125:180601. [PMID: 33196262 DOI: 10.1103/physrevlett.125.180601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Revised: 08/01/2020] [Accepted: 09/10/2020] [Indexed: 06/11/2023]
Abstract
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with λ=1.25 in the effectively short-range regime, while for stronger long-range interactions the data are consistent with λ=d/2=1. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as subaging.
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Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Malte Henkel
- Laboratoire de Physique et Chimie Théoriques (CNRS UMR 7019), Université de Lorraine Nancy, 54506 Vandœuvre-lès-Nancy Cedex, France
- Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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Schneider J, Meinel MK, Dittmar H, Müller-Plathe F. Different Stages of Polymer-Chain Collapse Following Solvent Quenching–Scaling Relations from Dissipative Particle Dynamics Simulations. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01315] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jurek Schneider
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Melissa K. Meinel
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Han Dittmar
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
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7
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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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Majumder S, Hansmann UHE, Janke W. Pearl-Necklace-Like Local Ordering Drives Polypeptide Collapse. Macromolecules 2019; 52:5491-5498. [PMID: 31631912 PMCID: PMC6795215 DOI: 10.1021/acs.macromol.9b00562] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2019] [Revised: 05/31/2019] [Indexed: 11/30/2022]
Abstract
![]()
The
collapse of the polypeptide backbone is an integral part of
protein folding. Using polyglycine as a probe, we explore the nonequilibrium
pathways of protein collapse in water. We find that the collapse depends
on the competition between hydration effects and intrapeptide interactions.
Once intrapeptide van der Waal interactions dominate, the chain collapses
along a nonequilibrium pathway characterized by formation of pearl-necklace-like
local clusters as intermediates that eventually coagulate into a single
globule. By describing this coarsening through the contact probability
as a function of distance along the chain, we extract a time-dependent
length scale that grows in a linear fashion. The collapse dynamics
is characterized by a dynamical critical exponent z ≈ 0.5 that is much smaller than the values of z = 1–2 reported for nonbiological polymers. This difference
in the exponents is explained by the instantaneous formation of intrachain
hydrogen bonds and local ordering that may be correlated with the
observed fast folding times of proteins.
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Affiliation(s)
- Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Ulrich H E Hansmann
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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9
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Christiansen H, Majumder S, Janke W. Phase ordering kinetics of the long-range Ising model. Phys Rev E 2019; 99:011301. [PMID: 30780293 DOI: 10.1103/physreve.99.011301] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Indexed: 11/07/2022]
Abstract
We use an efficient method that eases the daunting task of simulating dynamics in spin systems with long-range interaction. Our Monte Carlo simulations of the long-range Ising model for the nonequilibrium phase ordering dynamics in two spatial dimensions perform significantly faster than the standard Metropolis approach and considerably more efficiently than the kinetic Monte Carlo method. Importantly, this enables us to establish agreement with the theoretical prediction for the time dependence of domain growth, in contrast to previous numerical studies. This method can easily be generalized to applications in other systems.
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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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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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Wu J, Cheng C, Liu G, Zhang P, Chen T. The folding pathways and thermodynamics of semiflexible polymers. J Chem Phys 2018; 148:184901. [PMID: 29764123 DOI: 10.1063/1.5018114] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.
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Affiliation(s)
- Jing Wu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Chenqian Cheng
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Gaoyuan Liu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Ping Zhang
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Tao Chen
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
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