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Lopez CG, Horkay F, Mussel M, Jones RL, Richtering W. Screening lengths and osmotic compressibility of flexible polyelectrolytes in excess salt solutions. SOFT MATTER 2020; 16:7289-7298. [PMID: 32667374 PMCID: PMC8281568 DOI: 10.1039/d0sm00464b] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
We report results of small angle neutron scattering measurements made on sodium polystyrene sulfonate in aqueous salt solutions. The correlation length (ξ) and osmotic compressibility are measured as a function of polymer (c) and added salt (cS) concentrations, and the results are compared with scaling predictions and the random-phase approximation (RPA). In Dobrynin et al.'s scaling model the osmotic pressure consists of a counter-ion contribution and a polymer contribution. The polymer contribution is found to be two orders of magnitude smaller than expected from the scaling model, in agreement with earlier observations made on neutral polymers in good solvent condition. RPA allows the determination of single-chain dimensions in semidilute solutions at high polymer and added salt concentrations, but fails for cS≤ 2 M. The χ parameter can be modelled as the sum of an intrinsic contribution (χ0) and an electrostatic term: χ∼χ0 + K'/√cS, where χ0 > 0.5 is consistent with the hydrophobic nature of the backbone of NaPSS. The dependence of χelec∼ 1/√cS disagrees with the random-phase approximation (χelec∼ 1/cs), but agrees with the light scattering results in dilute solution and Dobrynin et al.'s scaling treatment of electrostatic excluded volume.
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Affiliation(s)
- Carlos G Lopez
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52056 Aachen, Germany.
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2
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Nallet F. Scattering studies in self-organised diblock copolymer systems. Colloid Polym Sci 2017. [DOI: 10.1007/s00396-017-4082-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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3
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Elias HG. Thermodynamics of Polymer Solutions. Macromolecules 2014. [DOI: 10.1002/9783527627233.ch10] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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4
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Heo Y, Larson RG. Universal Scaling of Linear and Nonlinear Rheological Properties of Semidilute and Concentrated Polymer Solutions. Macromolecules 2008. [DOI: 10.1021/ma800521g] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Youngsuk Heo
- Macromolecular Science and Engineering Program, and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136
| | - Ronald G. Larson
- Macromolecular Science and Engineering Program, and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136
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Mishima E, Matsumiya Y, Yamago S, Watanabe H. Kinetics of Living Anionic Polymerization of Polystyrenyl Lithium in Cyclohexane. Polym J 2008. [DOI: 10.1295/polymj.pj2008047] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Wieczorek SA, Freyssingeas E, Hołyst R. Relaxation Processes in Semidilute Solutions of Polymers in Liquid Crystal Solvents. J Phys Chem B 2005; 109:16252-62. [PMID: 16853066 DOI: 10.1021/jp0510950] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We investigate the relaxation phenomena in a polymer (polystyrene)/liquid crystal (4-cyano-4'-n-octyl-biphenyl) system, in its homogeneous isotropic phase near the isotropic-isotropic, isotropic-nematic, and isotropic-smectic coexistence curve, using both polarized and depolarized photon correlation spectroscopy (PCS). We study this system for different polystyrene molecular weights (4750, 12 500, and 65 000 g/mol), different compositions (50, 40, 30, and 10% polystyrene (PS) by weight), and different temperatures close to phase boundaries. First of all, we determine the phase diagrams of this system for the different molecular weights. The shape of the phase diagrams strongly depends on the molecular weight. However, in all cases, at low temperatures, these systems separate into an almost pure liquid crystalline (LC) phase and polystyrene-rich phase. PCS measurements show that the relaxation processes in the homogeneous phase are not affected by the proximity of the nematic, or smectic, boundaries (even at a temperature of 0.1 degrees C above the phase separation in two phases). In polarized PCS experiments, we always see three relaxation processes well separated in time: one, very fast, with a relaxation time of the order of 10(-5) s; a second one with a relaxation time within the range 10(-2)-10(-3) s; and a last one, very slow, with a relaxation time of the order of 1 s. Both the fast and slow modes are independent of the wave vector magnitude, while the intermediate relaxation process is diffusive. In depolarized PCS experiments, the intermediate mode disappears and only the fast and slow relaxation processes remain, and they are independent of the magnitude of the wave vector. The diffusive mode is the classical diffusive mode, which is associated with the diffusion of polymer chains in all polymer solutions. The fast mode is due to the rotational diffusion of 4-cyano-4'-n-octyl-biphenyl (8CB) molecules close to polystyrene chains (transient network). Finally, we assign the slowest mode to reorientational processes of small aggregates of PS chains that are not dissolved in 8CB.
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Affiliation(s)
- Stefan A Wieczorek
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
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Andreozzi L, Faetti M, Giordano M, Zulli F. Molecular-Weight Dependence of Enthalpy Relaxation of PMMA. Macromolecules 2005. [DOI: 10.1021/ma0507037] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Laura Andreozzi
- Physics Department of the University of Pisa and I.N.F.M U.d.R. Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Massimo Faetti
- Physics Department of the University of Pisa and I.N.F.M U.d.R. Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Marco Giordano
- Physics Department of the University of Pisa and I.N.F.M U.d.R. Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Fabio Zulli
- Physics Department of the University of Pisa and I.N.F.M U.d.R. Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy
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Ngai T, Wu C. Effect of Cross-Linking on Dynamics of Semidilute Copolymer Solutions: Poly(methyl methacrylate-co-7-acryloyloxy-4-methylcoumarin) in Chloroform. Macromolecules 2003. [DOI: 10.1021/ma021580i] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- To Ngai
- Department of Chemistry, The Chinese University of Hong Kong, Shatin. N. T., Hong Kong, and The Open Laboratory of Bond Selective Chemistry, Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, China
| | - Chi Wu
- Department of Chemistry, The Chinese University of Hong Kong, Shatin. N. T., Hong Kong, and The Open Laboratory of Bond Selective Chemistry, Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, China
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9
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Huang JR, Witten TA. Universal Ratios of Characteristic Lengths in Semidilute Polymer Solutions. Macromolecules 2002. [DOI: 10.1021/ma020792c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jung-Ren Huang
- James Franck Institute and Department of Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637
| | - Thomas A. Witten
- James Franck Institute and Department of Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637
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Tan H, Watanabe H. Effect of Solvent Quality on Stability of Diblock Copolymer Micellar Lattice. Polym J 2002. [DOI: 10.1295/polymj.34.775] [Citation(s) in RCA: 3] [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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11
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Kilbey SM, Watanabe H, Tirrell M. Structure and Scaling of Polymer Brushes near the ϑ Condition. Macromolecules 2001. [DOI: 10.1021/ma001343k] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- S. Michael Kilbey
- Department of Chemical Engineering, Clemson University, Clemson, South Carolina 29634
| | - Hiroshi Watanabe
- Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Matthew Tirrell
- Departments of Chemical Engineering and of Materials, Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, California 93106
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Saito S, Hashimoto T. Critical conditions for structure formation in semidilute polymer solutions induced under continuous shear flow. J Chem Phys 2001. [DOI: 10.1063/1.1372330] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Adam M, Farago B, Schleger P, Raspaud E, Lairez D. Binary Contacts in Semidilute Solution: Good and ϑ Solvents. Macromolecules 1998. [DOI: 10.1021/ma980936g] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Adam
- Institut Laue-Langevin, BP 156, 38042 Grenoble, France
| | - B. Farago
- Institut Laue-Langevin, BP 156, 38042 Grenoble, France
| | - P. Schleger
- Institut Laue-Langevin, BP 156, 38042 Grenoble, France
| | - E. Raspaud
- Laboratoire de Physique des Solides, CNRS URA D 002, Universite Paris Sud, 91405 Orsay Cedex, France
| | - D. Lairez
- Laboratoire Léon Brillouin (CEA-CNRS), CE-Saclay, 91191 Gif-sur-Yvette Cedex, France
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Adam M, Lairez D, Raspaud E, Farago B. Dynamic Properties of Semidilute Solutions at the Theta Point. PHYSICAL REVIEW LETTERS 1996; 77:3673-3676. [PMID: 10062279 DOI: 10.1103/physrevlett.77.3673] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Nicolai T, Brown W. Cooperative Diffusion of Concentrated Polymer Solutions: A Static and Dynamic Light Scattering Study of Polystyrene in DOP. Macromolecules 1996. [DOI: 10.1021/ma946430p] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Taco Nicolai
- Laboratoire de Physico Chemie Macromoleculaire, URA CNRS, Université du Maine, 72017 Le Mans, France
| | - Wyn Brown
- Department of Physical Chemistry, University of Uppsala, Box 532, 751 21 Uppsala, Sweden
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Brown W, Nicolai T. Static and dynamic behavior of semidilute polymer solutions. Colloid Polym Sci 1990. [DOI: 10.1007/bf01410586] [Citation(s) in RCA: 98] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Chen SJ, Berry G. Moderately concentrated solutions of polystyrene: 4. Elastic and quasi-elastic light scattering at the Flory theta temperature. POLYMER 1990. [DOI: 10.1016/0032-3861(90)90037-y] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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18
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Cherayil BJ, Kholodenko AL, Freed KF. Semidilute polymer solutions in the theta domain: A renormalization group study. J Chem Phys 1987. [DOI: 10.1063/1.452322] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Perzynski R, Delsanti M, Adam M. Experimental study of polymer interactions in a bad solvent. ACTA ACUST UNITED AC 1987. [DOI: 10.1051/jphys:01987004801011500] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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Duplantier B, Jannink G. Tricritical effect of attractive and repulsive forces on a single polymer coil in a poor solvent. PHYSICAL REVIEW LETTERS 1986; 56:2080-2083. [PMID: 10032852 DOI: 10.1103/physrevlett.56.2080] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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