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Liu L, Duan C, Wang R. Theory of polymers in poor solvents: Inter-chain interaction, second virial coefficient, and Θ point. POLYMER 2022. [DOI: 10.1016/j.polymer.2022.125312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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Affiliation(s)
- Pengfei Zhang
- Center for Advanced Low-Dimension Materials, State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, Donghua University, Shanghai 201620, China
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Nayef M. Alsaifi
- Chemical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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Rodrigues NT, Oliveira TJ. Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge. Phys Rev E 2017; 96:062111. [PMID: 29347429 DOI: 10.1103/physreve.96.062111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Indexed: 11/07/2022]
Abstract
We present results from extensive Monte Carlo simulations of polymer models where each lattice site can be visited by up to K monomers and no restriction is imposed on the number of bonds on each lattice edge. These multiple monomer per site (MMS) models are investigated on the square and cubic lattices, for K=2 and 3, by associating Boltzmann weights ω_{0}=1, ω_{1}=e^{β_{1}}, and ω_{2}=e^{β_{2}} to sites visited by 1, 2, and 3 monomers, respectively. Two versions of the MMS models are considered for which immediate reversals of the walks are allowed (RA) or forbidden (RF). In contrast to previous simulations of these models, we find the same thermodynamic behavior for both RA and RF versions. In three dimensions, the phase diagrams, in space β_{2}×β_{1}, are featured by coil and globule phases separated by a line of Θ points, as thoroughly demonstrated by the metric ν_{t}, crossover ϕ_{t}, and entropic γ_{t} exponents. The existence of the Θ lines is also confirmed by the second virial coefficient. This shows that no discontinuous collapse transition exists in these models, in contrast to previous claims based on a weak bimodality observed in some distributions, which indeed exists in a narrow region very close to the Θ line when β_{1}<0. Interestingly, in two dimensions, only a crossover is found between the coil and globule phases.
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Affiliation(s)
- Nathann T Rodrigues
- Departamento de Física, Universidade Federal de Viçosa, 36570-900, Viçosa, MG, Brazil
| | - Tiago J Oliveira
- Departamento de Física, Universidade Federal de Viçosa, 36570-900, Viçosa, MG, Brazil
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Affiliation(s)
- Zhen-Gang Wang
- Division of Chemistry and
Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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Lee JH, Kim SY, Lee J. Exact partition function zeros of a polymer on a simple cubic lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011802. [PMID: 23005443 DOI: 10.1103/physreve.86.011802] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2012] [Indexed: 06/01/2023]
Abstract
We study conformational transitions of a polymer on a simple-cubic lattice by calculating the zeros of the exact partition function, up to chain length 24. In the complex temperature plane, two loci of the partition function zeros are found for longer chains, suggesting the existence of both the coil-globule collapse transition and the melting-freezing transition. The locus corresponding to coil-globule transition clearly approaches the real axis as the chain length increases, and the transition temperature could be estimated by finite-size scaling. The form of the logarithmic correction to the scaling of the partition function zeros could also be obtained. The other locus does not show clear scaling behavior, but a supplementary analysis of the specific heat reveals a first-order-like pseudotransition.
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Affiliation(s)
- Jae Hwan Lee
- School of Systems Biomedical Science and Department of Bioinformatics and Life Science, Soongsil University, Seoul 156-743, Korea
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Fröhlich MG, Vana P, Zifferer G. Shielding Effects in Polymer-Polymer Reactions, 1. MACROMOL THEOR SIMUL 2007. [DOI: 10.1002/mats.200700026] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Sheng YJ, Cheng KL, Ho CC. Effect of solvent quality on the conformations of a model comb polymer. J Chem Phys 2004; 121:1962-8. [PMID: 15260748 DOI: 10.1063/1.1765100] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The effect of solvent quality on the equilibrium structure of a densely branched comb polymer is investigated based on the structure factor analyses by off-lattice Monte Carlo simulations. First, theta temperature (theta(infinity)) must be determined to identify the solvent condition. We locate the characteristic temperature theta(A)(N) at which the second virial coefficient vanishes and the transition temperature theta(R)(N) at which radius of gyration R(g) of the chain varies most rapidly with temperature, i.e., d(2)R(g)/dT(2)|(theta(R)) = 0. N represents the total number of monomers of a comb. As N --> infinity, theta(A) and theta(R) coincide to a point that is identified as the true theta temperature (theta(infinity)). The structure factors of the main chain, the side chain, and the whole polymer are calculated, respectively. It is found that at T = theta(infinity), the structural factors S(qR(g)) for the overall comb polymers match quite well with those of their Gaussian counterparts. When T< theta(infinity), the overall comb polymer assumes collapsed conformations, similar to a homogeneous sphere. However, the structure factor of the side chain indicates that it always remains in an expanded state regardless of the solvent condition. It is attributed to the strong interactions between side chains. The same effect leads to enhanced rigidity of the main chain in comparison to the linear chain, as clearly observed from the rescaled Kratky plot.
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Affiliation(s)
- Yu-Jane Sheng
- Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan, Republic of China
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Sheng YJ, Liao CS. The effect of topological constraint on the theta temperature of a knotted polymer. J Chem Phys 2003. [DOI: 10.1063/1.1543939] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zifferer G, Neubauer B, Olaj OF. Monte Carlo investigations of dense copolymer systems II, Properties of ABA triblocks. J Chem Phys 2000. [DOI: 10.1063/1.480655] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Schillén K, Yekta A, Ni S, Farinha JPS, Winnik MA. Characterization of Polyisoprene-b-Poly(methyl methacrylate) Diblock Copolymer Micelles in Acetonitrile. J Phys Chem B 1999. [DOI: 10.1021/jp990251y] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Karin Schillén
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
| | - Ahmad Yekta
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
| | - Shaoru Ni
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
| | - J. P. S. Farinha
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
| | - Mitchell A. Winnik
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
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Kremer K, Baumgartner A, Binder K. Collapse transition and crossover scaling for self-avoiding walks on the diamond lattice. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/15/9/036] [Citation(s) in RCA: 159] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Ishinabe T, Douglas JF, Nemirovsky AM, Freed KF. Examination of the 1/d expansion method from exact enumeration for a self-interacting self-avoiding walk. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/27/4/006] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Shew CY, Yethiraj A. Conformational properties of isolated polyelectrolytes in poor solvents. J Chem Phys 1999. [DOI: 10.1063/1.478138] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Olaj OF, Neubauer B, Zifferer G. Dilute Solutions of Block Copolymers. 2. Triblock Copolymers. Macromolecules 1998. [DOI: 10.1021/ma971088c] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- O. F. Olaj
- Institut für Physikalische Chemie, Universität Wien, Währinger Strasse 42, A-1090 Wien, Austria
| | - B. Neubauer
- Institut für Physikalische Chemie, Universität Wien, Währinger Strasse 42, A-1090 Wien, Austria
| | - G. Zifferer
- Institut für Physikalische Chemie, Universität Wien, Währinger Strasse 42, A-1090 Wien, Austria
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Olaj OF, Neubauer B, Zifferer G. Dilute Solutions of Block Copolymers. 1. Diblock Copolymers. Macromolecules 1998. [DOI: 10.1021/ma971087k] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- O. F. Olaj
- Institut für Physikalische Chemie, Universität Wien, Währinger Strasse 42, A-1090 Wien, Austria
| | - B. Neubauer
- Institut für Physikalische Chemie, Universität Wien, Währinger Strasse 42, A-1090 Wien, Austria
| | - G. Zifferer
- Institut für Physikalische Chemie, Universität Wien, Währinger Strasse 42, A-1090 Wien, Austria
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Beaucage G, Rane S, Sukumaran S, Satkowski MM, Schechtman LA, Doi Y. Persistence Length of Isotactic Poly(hydroxy butyrate). Macromolecules 1997. [DOI: 10.1021/ma970373t] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | | | | | | | | | - Y. Doi
- The Institute of Physics and Chemistry Research (RIKEN), 2-1 Hirosawa, Wakoshi, Saitama 351-01, Japan
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Rubio AM, Freire JJ. Tricritical behavior of an off-lattice flexible polymer model: Monte Carlo calculation of second virial coefficients. J Chem Phys 1997. [DOI: 10.1063/1.473584] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Rubio AM, Freire JJ. Monte Carlo Calculation of Second Virial Coefficients for Linear and Star Chains in a Good Solvent. Macromolecules 1996. [DOI: 10.1021/ma960346n] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ana M. Rubio
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense, 28040 Madrid, Spain
| | - Juan J. Freire
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense, 28040 Madrid, Spain
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Douglas JF, Ishinabe T. Self-avoiding-walk contacts and random-walk self-intersections in variable dimensionality. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:1791-1817. [PMID: 9962837 DOI: 10.1103/physreve.51.1791] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Boothroyd AT, Rennie AR, Boothroyd CB, Fetters LJ. Direct measurement of the three-body interaction parameter in a dilute polymer solution. PHYSICAL REVIEW LETTERS 1992; 69:426-429. [PMID: 10046936 DOI: 10.1103/physrevlett.69.426] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Higgs PG, Orland H. Scaling behavior of polyelectrolytes and polyampholytes: Simulation by an ensemble growth method. J Chem Phys 1991. [DOI: 10.1063/1.461774] [Citation(s) in RCA: 60] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Meirovitch H, Lim HA. Computer simulation study of the θ‐point in three dimensions. I. Self‐avoiding walks on a simple cubic lattice. J Chem Phys 1990. [DOI: 10.1063/1.458548] [Citation(s) in RCA: 57] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Meirovitch H, Lim HA. The collapse transition of self‐avoiding walks on a square lattice: A computer simulation study. J Chem Phys 1989. [DOI: 10.1063/1.457014] [Citation(s) in RCA: 66] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Okamoto H. A study of the applicability of the renormalization group idea to multichain lattice systems by numerical experiments. J Chem Phys 1988. [DOI: 10.1063/1.454663] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kolinski A, Skolnick J, Yaris R. The collapse transition of semiflexible polymers. A Monte Carlo simulation of a model system. J Chem Phys 1986. [DOI: 10.1063/1.450930] [Citation(s) in RCA: 80] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Okamoto H, Ohde Y. A first order transition of a lattice polymer under stretching force. J Chem Phys 1986. [DOI: 10.1063/1.450626] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Orientational effects and ordering of flexible-chain polymers in concentrated solutions and in bulk. POLYMER 1982. [DOI: 10.1016/0032-3861(82)90249-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Baumgärtner A. Statics and dynamics of the freely jointed polymer chain with Lennard‐Jones interaction. J Chem Phys 1980. [DOI: 10.1063/1.439242] [Citation(s) in RCA: 96] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Olaj OF, Pelinka KH. The concentration dependence of the chain dimensions of cubic lattice model chains under Θ-conditions. ACTA ACUST UNITED AC 1976. [DOI: 10.1002/macp.1976.021771127] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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