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Horkay F, Douglas JF. Influence of solvent quality on the swelling and deswelling and the shear modulus of semi-dilute solution cross-linked poly(vinyl acetate) gels. J Chem Phys 2023; 158:244901. [PMID: 37377156 PMCID: PMC10310356 DOI: 10.1063/5.0156604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Accepted: 06/06/2023] [Indexed: 06/29/2023] Open
Abstract
We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the hydrogel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory-Huggins mean field theory or the Flory-Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized.
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Affiliation(s)
- Ferenc Horkay
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Jack F. Douglas
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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Zheng X, Anisimov MA, Sengers JV, He M. Mesoscopic Diffusion of Poly(ethylene oxide) in Pure and Mixed Solvents. J Phys Chem B 2017; 122:3454-3464. [PMID: 29131952 DOI: 10.1021/acs.jpcb.7b10420] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present results from an experimental dynamic light-scattering study of poly(ethylene oxide) (PEO) in both a pure solvent (water) and a mixed solvent (tert-butanol + water). The concentration dependence of the diffusive relaxation of the PEO molecules is found to be typical of polymers in a good solvent. However, the mesoscopic diffusive behavior of PEO in the mixed solvent is very different, indicating an initial collapse and subsequent reswelling of PEO caused by co-nonsolvency. Furthermore, in the solutions of PEO with very large molecular weights, we found additional hydrodynamic modes indicating the presence of PEO clusters and aggregates similar to those found by some other investigators.
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Affiliation(s)
- Xiong Zheng
- Institute for Physical Science and Technology and Department of Chemical and Biomolecular Engineering , University of Maryland , College Park , Maryland 20742 , United States.,Key Laboratory of Thermo-Fluid Science and Engineering , Ministry of Education, Xi'an Jiaotong University , Xi'an , Shaanxi Province 710049 , People's Republic of China
| | - Mikhail A Anisimov
- Institute for Physical Science and Technology and Department of Chemical and Biomolecular Engineering , University of Maryland , College Park , Maryland 20742 , United States.,Oil and Gas Research Institute of the Russian Academy of Sciences , Moscow 117333 , Russia
| | - Jan V Sengers
- Institute for Physical Science and Technology and Department of Chemical and Biomolecular Engineering , University of Maryland , College Park , Maryland 20742 , United States
| | - Maogang He
- Key Laboratory of Thermo-Fluid Science and Engineering , Ministry of Education, Xi'an Jiaotong University , Xi'an , Shaanxi Province 710049 , People's Republic of China
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3
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Elias HG. Macroconformations. Macromolecules 2014. [DOI: 10.1002/9783527627233.ch4] [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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MAKI Y, DOBASHI T. Light Scattering of Dilute Solutions of Poly(methyl methacrylate) Below the Theta Temperature. KOBUNSHI RONBUNSHU 2012. [DOI: 10.1295/koron.69.373] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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5
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Le Coeur C, Demé B, Longeville S. Compression of random coils due to macromolecular crowding. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:031910. [PMID: 19391974 DOI: 10.1103/physreve.79.031910] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2008] [Indexed: 05/27/2023]
Abstract
The conformation of a linear polymer chain is studied as a function of the concentration of a macromolecular crowding agent by neutron scattering. Excluded volume to random coil due to macromolecular crowding in cells is predicted to exert a compressive force that will tend to reduce its size. It is shown that when reducing free volume due to macromolecular crowding, we observe a compression of the polymer chain with a reduction in its radius of gyration of up to approximately 30% and that the effective chain-chain interactions are strongly modified.
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Affiliation(s)
- C Le Coeur
- Laboratoire Léon Brillouin, CEA-CNRS, CEA Saclay, 91191 Gif-sur-Yvette, France
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Horkay F, Basser PJ. Ionic and pH effects on the osmotic properties and structure of polyelectrolyte gels. ACTA ACUST UNITED AC 2008; 46:2803-2810. [PMID: 20016687 DOI: 10.1002/polb.21590] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
We investigate the effects of salt concentration and pH on neutralized poly(acrylic acid) (PAA) gels in near physiological salt solutions. Either adding calcium ions or decreasing the pH are found to induce reversible volume transitions but the nature of these transitions seems to be different. For example, the osmotic pressure exhibits a simple power law dependence on the concentration as the transition is approached in both systems, but the power law exponent n is substantially different in the two cases. On decreasing the pH the value of n gradually increases from 2.1 (at pH = 7) to 3.2 (at pH = 1). By contrast, n decreases with increasing calcium ion concentration from 2.1 (in 100 mM NaCl solution) to 1.6 (0.8 mM CaCl(2) in 100 mM NaCl solution). In both systems, a strong increase of the small-angle neutron scattering intensity (SANS) is observed near the volume transition. The SANS results reveal that calcium ions favor the formation of linearly aligned regions in PAA gels.
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Affiliation(s)
- Ferenc Horkay
- Section on Tissue Biophysics and Biomimetics, Laboratory of Integrative and Medical Biophysics, NICHD, National Institutes of Health, 13 South Drive, Bethesda, MD 20892, USA
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7
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Zhao Y, Dar YL, Caneba GT. Modeling Copolymerization of Styrene and Acrylic Acid via the Free-Radical Retrograde-Precipitation Polymerization (FRRPP) Process. Ind Eng Chem Res 2008. [DOI: 10.1021/ie0712176] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Yi Zhao
- Department of Chemical Engineering, Michigan Technological University, Houghton, Michigan 49931
| | - Yadunandan L. Dar
- Department of Chemical Engineering, Michigan Technological University, Houghton, Michigan 49931
| | - Gerard T. Caneba
- Department of Chemical Engineering, Michigan Technological University, Houghton, Michigan 49931
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On Mechanism of Intermediate-Sized Circular DNA Compaction Mediated by Spermine: Contribution of Fluorescence Lifetime Correlation Spectroscopy. J Fluoresc 2008; 18:679-84. [DOI: 10.1007/s10895-008-0345-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2007] [Accepted: 01/30/2008] [Indexed: 10/22/2022]
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Kaiser A, Schmidt AM. Phase Behavior of Polystyrene-Brush-Coated Nanoparticles in Cyclohexane. J Phys Chem B 2008; 112:1894-8. [DOI: 10.1021/jp076218q] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andreas Kaiser
- Institut für Organische Chemie und Makromolekulare Chemie, Heinrich-Heine-Universität, Universitätsstr. 1, D-40225 Düsseldorf, Germany
| | - Annette M. Schmidt
- Institut für Organische Chemie und Makromolekulare Chemie, Heinrich-Heine-Universität, Universitätsstr. 1, D-40225 Düsseldorf, Germany
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Tirumala VR, Caneba GT, Mancini DC, Wang HH. Microfabrication by X-ray-induced polymerization above the lower critical solution temperature. J Appl Polym Sci 2006. [DOI: 10.1002/app.24073] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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11
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DAR YADUNANDAN, CANEBA GERARDT. FREE-RADICAL RETROGRADE-PRECIPITATION POLYMERIZATION: A MATHEMATICAL MODELING STUDY OF POLYMERIZATION OF STYRENE IN DIETHYL ETHER. CHEM ENG COMMUN 2004. [DOI: 10.1080/00986440490472733] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Caneba GT, Zhao Y, Dar Y. Amphiphilic styrene-acrylic acid copolymers from the free-radical retrograde-precipitation polymerization (FRRPP) process. J Appl Polym Sci 2003. [DOI: 10.1002/app.12154] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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14
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Villani V. Complexity of polypeptide dynamics: chaos, Brownian motion and elasticity in aqueous solution. ACTA ACUST UNITED AC 2003. [DOI: 10.1016/s0166-1280(02)00541-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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15
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Demir MM, Erman B. Dimensions of Polystyrene Particles Deposited on Mica from Dilute Cyclohexane Solution at Different Temperatures. Macromolecules 2002. [DOI: 10.1021/ma020676+] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mustafa M. Demir
- Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli, 81474 Tuzla, Istanbul, Turkey, and Departments of Chemistry and Mechanical Engineering, Koc University, Rumelifeneri Yolu, Sariyer 80910, Istanbul, Turkey
| | - Burak Erman
- Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli, 81474 Tuzla, Istanbul, Turkey, and Departments of Chemistry and Mechanical Engineering, Koc University, Rumelifeneri Yolu, Sariyer 80910, Istanbul, Turkey
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Abstract
We study the transition of polymers in the dilute regime from a swollen shape at high temperatures to their low-temperature structures. The polymers are modeled by a single self-avoiding walk (SAW) on a lattice for which l of the monomers (the H monomers) are self-attracting, i.e., if two nonbonded H monomers become nearest neighbors on the lattice they gain energy of interaction (epsilon = -/epsilon/); the second type of monomers, denoted P, are neutral. This HP model was suggested by Lau and Dill (Macromolecules 1989, 22, 3986-3997) to study protein folding, where H and P are the hydrophobic and polar amino acid residues, respectively. The model is simulated on the square and simple cubic (SC) lattices using the scanning method. We show that the ground state and the sharpness of the transition depend on the lattice, the fraction g of the H monomers, as well as on their arrangement along the chain. In particular, if the H monomers are distributed at random and g is larger than the site percolation threshold of the lattice, a collapsed transition is very likely to occur. This conclusion, drawn for the lattice models, is also applicable to proteins where an effective lattice with coordination number between that of the SC lattice and the body centered cubic lattice is defined. Thus, the average fraction of hydrophobic amino acid residues in globular proteins is found to be close to the percolation threshold of the effective lattice.
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Affiliation(s)
- Hagai Meirovitch
- University of Pittsburgh, School of Medicine, Center for Computational Biology and Bioinformatics (CCBB), Pennsylvania 15213, USA.
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17
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Nakamura Y, Sasaki N, Nakata M. Kinetics of the Coil−Globule Transition of Poly(methyl methacrylate) in a Mixed Solvent. Macromolecules 2001. [DOI: 10.1021/ma010063h] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yoshiki Nakamura
- Department of Polymer Science, Faculty of Science, Hokkaido University, Kita-ku, Sapporo 060-0810, Japan
| | - Naoki Sasaki
- Department of Polymer Science, Faculty of Science, Hokkaido University, Kita-ku, Sapporo 060-0810, Japan
| | - Mitsuo Nakata
- Department of Polymer Science, Faculty of Science, Hokkaido University, Kita-ku, Sapporo 060-0810, Japan
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18
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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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19
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20
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21
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Raos G, Allegra G. Chain Interactions in Poor-Solvent Polymer Solutions: Equilibrium and Nonequilibrium Aspects. Macromolecules 1996. [DOI: 10.1021/ma960503i] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Guido Raos
- Dipartimento di Chimica, Politecnico di Milano, Via L. Mancinelli 7, 20131 Milano, Italy
| | - Giuseppe Allegra
- Dipartimento di Chimica, Politecnico di Milano, Via L. Mancinelli 7, 20131 Milano, Italy
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22
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Nakata M. Coil-globule transition of poly(methyl methacrylate) in a mixed solvent. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:5770-5775. [PMID: 9963313 DOI: 10.1103/physreve.51.5770] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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23
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Abstract
The conformation of linear polymer chains trapped in a matrix of cross-linked polymer has been measured by neutron scattering. Three regimes were found depending on the length of the linear chain, Nl, with respect to the mesh size of the network, N(c). When N(c) > Nl, the radius of gyration, R(g), of the linear chain is the same as that observed in the uncrosslinked melt. When N(c) < Nl, R(g) shrinks according to the scaling relation R(g)(-1) approximately N(c)(-1) that has been predicted for isolated polymer chains trapped in a field of random obstacles. When N(c) << Nl the linear chains are observed to segregate.
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24
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Gan HH, Eu BC. Integral equation theory of polymers: Translational invariance approximation and properties of an isolated linear polymer in solution. J Chem Phys 1994. [DOI: 10.1063/1.467105] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Szleifer I, O’Toole EM, Panagiotopoulos AZ. Monte Carlo simulation of the collapse‐coil transition in homopolymers. J Chem Phys 1992. [DOI: 10.1063/1.463633] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Brender C. Coil to rod transitions in Monte Carlo simulations of a short polyelectrolyte. III. Contact as a new type of bond. J Chem Phys 1991. [DOI: 10.1063/1.459790] [Citation(s) in RCA: 13] [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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27
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Matsuyama A, Tanaka F. Theory of solvation‐induced reentrant coil–globule transition of an isolated polymer chain. J Chem Phys 1991. [DOI: 10.1063/1.460296] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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28
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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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31
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Novotny VJ, Hussla I, Turlet J, Philpott MR. Liquid polymer conformation on solid surfaces. J Chem Phys 1989. [DOI: 10.1063/1.456392] [Citation(s) in RCA: 53] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Janeczek H, Turska E. Investigation of conformational transitions in bisphenol A poly(carbonate) macromolecules in mixtures of 1,1,2,2-tetrachloroethane and n-propyl alcohol. POLYMER 1987. [DOI: 10.1016/0032-3861(87)90239-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Tanaka F, Ushiki H. Internal condensation of a polymer molecule induced by saturating bonds. J Chem Phys 1986. [DOI: 10.1063/1.450777] [Citation(s) in RCA: 10] [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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35
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Nose T. Chain dimension of a guest polymer in the semidilute solution of compatible and incompatible polymers. ACTA ACUST UNITED AC 1986. [DOI: 10.1051/jphys:01986004703051700] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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36
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Tanaka F. Theory of the second virial coefficients in polymeric solutions below the theta temperature. J Chem Phys 1985. [DOI: 10.1063/1.448680] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Oyama TO, Shiokawa K, Baba K. A Semi-Theoretical Equation for the Chain Dimension in Dilute Solutions and Its Experimental Verification, and the Coil-Globule Transition. Polym J 1985. [DOI: 10.1295/polymj.17.713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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38
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Keller A, Odell JA. The extensibility of macromolecules in solution; A new focus for macromolecular science. Colloid Polym Sci 1985. [DOI: 10.1007/bf01415506] [Citation(s) in RCA: 300] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Perzynski R, Delsanti M, Adam M. Intrinsic viscosity of flexible macromolecules : transition from theta to collapsed state. ACTA ACUST UNITED AC 1984. [DOI: 10.1051/jphys:0198400450110176500] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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42
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43
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Janeczek H, Turska E. Investigation of conformational transitions in polyamide-6 macromolecules in mixtures of m-cresol and methanol. POLYMER 1983. [DOI: 10.1016/0032-3861(83)90176-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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44
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45
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Déjardin P. Variation with temperature of the thickness of an adsorbed polymer layer in the collapsed state. ACTA ACUST UNITED AC 1983. [DOI: 10.1051/jphys:01983004404053700] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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46
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47
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Novotny VJ. Temperature dependence of hydrodynamic dimensions of polystyrenes in cyclohexane by quasielastic light scattering. J Chem Phys 1983. [DOI: 10.1063/1.444539] [Citation(s) in RCA: 16] [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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48
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Post CB, Zimm BH. Light-scattering study of DNA condensation: competition between collapse and aggregation. Biopolymers 1982; 21:2139-60. [PMID: 7171730 DOI: 10.1002/bip.360211105] [Citation(s) in RCA: 67] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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49
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Perzynski R, Adam M, Delsanti M. Dynamic measurements on polymer chain dimensions below the θ-temperature. ACTA ACUST UNITED AC 1982. [DOI: 10.1051/jphys:01982004301012900] [Citation(s) in RCA: 36] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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50
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Baumgärtner A. Collapse of a polymer : evidence for tricritical behaviour in two dimensions. ACTA ACUST UNITED AC 1982. [DOI: 10.1051/jphys:019820043090140700] [Citation(s) in RCA: 76] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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