1
|
Taylor MP, Basnet S, Luettmer-Strathmann J. Partition-function-zero analysis of polymer adsorption for a continuum chain model. Phys Rev E 2021; 104:034502. [PMID: 34654113 DOI: 10.1103/physreve.104.034502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 09/13/2021] [Indexed: 11/07/2022]
Abstract
Polymer chains undergoing adsorption are expected to show universal critical behavior which may be investigated using partition function zeros. The focus of this work is the adsorption transition for a continuum chain, allowing for investigation of a continuous range of the attractive interaction and comparison with recent high-precision lattice model studies. The partition function (Fisher) zeros for a tangent-hard-sphere N-mer chain (monomer diameter σ) tethered to a flat wall with an attractive square-well potential (range λσ, depth ε) have been computed for chains up to N=1280 with 0.01≤λ≤2.0. In the complex-Boltzmann-factor plane these zeros are concentrated in an annular region, centered on the origin and open about the real axis. With increasing N, the leading zeros, w_{1}(N), approach the positive real axis as described by the asymptotic scaling law w_{1}(N)-y_{c}∼N^{-ϕ}, where y_{c}=e^{ε/k_{B}T_{c}} is the critical point and T_{c} is the critical temperature. In this work, we study the polymer adsorption transition by analyzing the trajectory of the leading zeros as they approach y_{c} in the complex plane. We use finite-size scaling (including corrections to scaling) to determine the critical point and the scaling exponent ϕ as well as the approach angle θ_{c}, between the real axis and the leading-zero trajectory. Variation of the interaction range λ moves the critical point, such that T_{c} decreases with λ, while the results for ϕ and θ_{c} are approximately independent of λ. Our values of ϕ=0.479(9) and θ_{c}=56.8(1.4)^{∘} are in agreement with the best lattice model results for polymer adsorption, further demonstrating the universality of these constants across both lattice and continuum models.
Collapse
Affiliation(s)
- Mark P Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
| | - Samip Basnet
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
| | | |
Collapse
|
2
|
Foster DP, Majumdar D. Critical behavior of magnetic polymers in two and three dimensions. Phys Rev E 2021; 104:024122. [PMID: 34525598 DOI: 10.1103/physreve.104.024122] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Accepted: 07/28/2021] [Indexed: 01/05/2023]
Abstract
We explore the critical behavior of two- and three-dimensional lattice models of polymers in dilute solution where the monomers carry a magnetic moment which interacts ferromagnetically with near-neighbor monomers. Specifically, the model explored consists of a self-avoiding walk on a square or cubic lattice with Ising spins on the visited sites. In three dimensions we confirm and extend previous numerical work, showing clearly the first-order character of both the magnetic transition and the polymer collapse, which happen together. We present results in two dimensions, where the transition is seen to be continuous. Finite-size scaling is used to extract estimates for the critical exponents and the transition temperature in the absence of an external magnetic field.
Collapse
Affiliation(s)
- Damien Paul Foster
- Centre for Computational Science and Mathematical Modelling, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Debjyoti Majumdar
- Institute of Physics, Bhubaneswar, Odisha 751005, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| |
Collapse
|
3
|
Knežević M, Knežević M. Transverse-size critical exponent of directed percolation from Yang-Lee zeros of survival probability. Phys Rev E 2020; 101:012107. [PMID: 32069588 DOI: 10.1103/physreve.101.012107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Indexed: 06/10/2023]
Abstract
By using transfer-matrix method we compute survival probabilities for the directed percolation problem on strips of a square lattice, and get very precise estimates of their Yang-Lee zeros lying closest to the real axis in the complex plane of occupation probability. This allows us to get accurate values for transverse-size critical exponent and percolation threshold.
Collapse
Affiliation(s)
- Milan Knežević
- Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade, Serbia
| | - Miloš Knežević
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany
| |
Collapse
|
4
|
Bradly CJ, Owczarek AL, Prellberg T. Phase transitions in solvent-dependent polymer adsorption in three dimensions. Phys Rev E 2019; 99:062113. [PMID: 31330636 DOI: 10.1103/physreve.99.062113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2019] [Indexed: 06/10/2023]
Abstract
We consider the phase diagram of self-avoiding walks (SAWs) on the simple cubic lattice subject to surface and bulk interactions, modeling an adsorbing surface and variable solvent quality for a polymer in dilute solution, respectively. We simulate SAWs at specific interaction strengths to focus on locating certain transitions and their critical behavior. By collating these new results with previous results we sketch the complete phase diagram and show how the adsorption transition is affected by changing the bulk interaction strength. This expands on recent work considering how adsorption is affected by solvent quality. We demonstrate that changes in the adsorption crossover exponent coincide with phase boundaries.
Collapse
Affiliation(s)
- C J Bradly
- School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
| | - A L Owczarek
- School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
| | - T Prellberg
- School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| |
Collapse
|
5
|
Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model. ENTROPY 2019; 21:e21020153. [PMID: 33266869 PMCID: PMC7514635 DOI: 10.3390/e21020153] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/20/2018] [Revised: 01/28/2019] [Accepted: 01/31/2019] [Indexed: 11/17/2022]
Abstract
The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.
Collapse
|
6
|
Martins PHL, Plascak JA, Bachmann M. Adsorption of flexible polymer chains on a surface: Effects of different solvent conditions. J Chem Phys 2018; 148:204901. [DOI: 10.1063/1.5027270] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- P. H. L. Martins
- Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, MT, Brazil
| | - J. A. Plascak
- Departamento de Física, Centro de Ciências Exatas e da Natureza, CCEN, Universidade Federal da Paraíba, Cidade Universitária, 58051-970 João Pessoa, PB, Brazil
- Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
| | - M. Bachmann
- Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, MT, Brazil
- Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
| |
Collapse
|
7
|
Abstract
The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data over a wide range of sphere radius and temperature, we have constructed entire phase diagrams both for nongrafted and end-grafted polymers. For the identification of the conformational phases, we have calculated several energetic and structural observables such as gyration tensor based shape parameters and their fluctuations by canonical statistical analysis. Despite the simplicity of our model, it qualitatively represents in the considered parameter range real systems that are studied in experiments. The work discussed here could have experimental implications from protein-ligand interactions to designing nanosmart materials.
Collapse
Affiliation(s)
- Handan Arkin
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
- Department of Physics Engineering, Faculty of Engineering, Ankara University, Tandogan, 06100 Ankara, Turkey
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| |
Collapse
|
8
|
Williams MJ, Bachmann M. The effect of surface adsorption on tertiary structure formation in helical polymers. J Chem Phys 2017; 147:024902. [DOI: 10.1063/1.4991564] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthew J. Williams
- Institute of Engineering, Murray State University, Murray, Kentucky 42071, USA
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| |
Collapse
|
9
|
Plascak JA, Martins PHL, Bachmann M. Solvent-dependent critical properties of polymer adsorption. Phys Rev E 2017; 95:050501. [PMID: 28618616 DOI: 10.1103/physreve.95.050501] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Indexed: 11/07/2022]
Abstract
Advanced chain-growth computer simulation methodologies have been employed for a systematic statistical analysis of the critical behavior of a polymer adsorbing at a substrate. We use finite-size scaling techniques to investigate the solvent-quality dependence of critical exponents, critical temperature, and the structure of the phase diagram. Our study covers all solvent effects from the limit of super-self-avoiding walks, characterized by effective monomer-monomer repulsion, to poor solvent conditions that enable the formation of compact polymer structures. The results significantly benefit from taking into account corrections to scaling.
Collapse
Affiliation(s)
- João A Plascak
- Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Paraíba, Brazil.,Departamento de Física, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, Minas Gerais, Brazil.,Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Paulo H L Martins
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA.,Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, Mato Grosso, Brazil
| | - Michael Bachmann
- Departamento de Física, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, Minas Gerais, Brazil.,Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA.,Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, Mato Grosso, Brazil
| |
Collapse
|
10
|
Koci T, Bachmann M. Subphase transitions in first-order aggregation processes. Phys Rev E 2017; 95:032502. [PMID: 28415362 DOI: 10.1103/physreve.95.032502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2016] [Indexed: 11/07/2022]
Abstract
In this paper, we investigate the properties of aggregation transitions in the context of generic coarse-grained homopolymer systems. By means of parallel replica-exchange Monte Carlo methods, we perform extensive simulations of systems consisting of up to 20 individual oligomer chains with five monomers each. Using the tools of the versatile microcanonical inflection-point analysis, we show that the aggregation transition is a first-order process consisting of a sequence of subtransitions between intermediate structural phases. We unravel the properties of these intermediate phases by collecting and analyzing their individual contributions towards the density of states of the system. The central theme of this systematic study revolves around translational entropy and its role in the striking phenomena of missing intermediate phases. We conclude with a brief discussion of the scaling properties of the transition temperature and the latent heat.
Collapse
Affiliation(s)
- Tomas Koci
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA.,Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá (MT), Brazil.,Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte (MG), Brazil
| |
Collapse
|
11
|
Martins PHL, Bachmann M. Interlocking order parameter fluctuations in structural transitions between adsorbed polymer phases. Phys Chem Chem Phys 2016; 18:2143-51. [PMID: 26690091 DOI: 10.1039/c5cp05038c] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
By means of contact-density chain-growth simulations of a simple coarse-grained lattice model for a polymer grafted at a solid homogeneous substrate, we investigate the complementary behavior of the numbers of surface-monomer and monomer-monomer contacts under various solvent and thermal conditions. This pair of contact numbers represents an appropriate set of order parameters that enables the distinct discrimination of significantly different compact phases of polymer adsorption. Depending on the transition scenario, these order parameters can interlock in perfect cooperation. The analysis helps understand the transitions from compact filmlike adsorbed polymer conformations into layered morphologies and dissolved adsorbed structures, respectively, in more detail.
Collapse
Affiliation(s)
- Paulo H L Martins
- Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, MT, Brazil.
| | | |
Collapse
|
12
|
Janke W, Paul W. Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations. SOFT MATTER 2016; 12:642-657. [PMID: 26574738 DOI: 10.1039/c5sm01919b] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.
Collapse
Affiliation(s)
- Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, 04009 Leipzig, Germany.
| | | |
Collapse
|
13
|
Koci T, Bachmann M. Confinement effects upon the separation of structural transitions in linear systems with restricted bond fluctuation ranges. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042142. [PMID: 26565203 DOI: 10.1103/physreve.92.042142] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2015] [Indexed: 06/05/2023]
Abstract
By means of advanced parallel replica-exchange Monte Carlo methods we examine the influence of elasticity and confinement on the structural transitions of linear systems with restricted bonded interaction. For this purpose, we adopt a model for coarse-grained flexible polymers of finite length in the dilute regime. Hyperphase diagrams are constructed using energy-dependent canonical quantities to demonstrate the effects of the changes in the range of the confined interaction on the liquid and solid structural phases. With increasing bonded interaction range we observe the disappearance of the liquid phase and the fusion of the gas-liquid (or Θ) and the liquid-solid transitions. One of the most remarkable features, the liquid-gas transition, changes from second to first order if the confined interaction range exceeds a threshold that separates polymeric from nonpolymeric systems. The notoriously difficult sampling of the entropically suppressed conformations in the region of very strong first-order transitions is improved by using multiple Gaussian modified ensembles.
Collapse
Affiliation(s)
- Tomas Koci
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
- Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá (MT), Brazil
- Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte (MG), Brazil
| |
Collapse
|