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Shi G, Schweizer KS. Theory of the center-of-mass diffusion and viscosity of microstructured and variable sequence copolymer liquids. SOFT MATTER 2023; 19:8893-8910. [PMID: 37955602 DOI: 10.1039/d3sm01193c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/14/2023]
Abstract
Biomolecular condensates formed through the phase separation of proteins and nucleic acids are widely observed, offering a fundamental means of organizing intracellular materials in a membrane-less fashion. Traditionally, these condensates have been regarded as homogeneous isotropic liquids. However, in analogy with some synthetic copolymer systems, our recent theoretical research has demonstrated that model biomolecular condensates can exhibit a microemulsion-like internal structure, contingent upon the specific sequence, inter-chain site-site interactions, and concentrated phase polymer density. Motivated by these considerations, here we present a microscopic dynamical theory for the self-diffusion constant and viscosity of a simpler class of model systems - concentrated unentangled A/B regular multiblock copolymer solutions. Our approach integrates static equilibrium local and microdomain scale structural information obtained from PRISM integral equation theory and the time evolution of the autocorrelation function of monomer scale forces at the center-of-mass level to determine the polymer diffusion constant and viscosity in a weak caging regime far from a glass or gel transition. We focus on regular multi-block systems both for simplicity and for its relevance to synthetic macromolecular science. The impact of sequence and inter-chain attraction strength on the slowing down of copolymer mass transport and flow due to local clustering enhanced collisional friction and emergent microdomain scale ordering are established. Analytic analysis and metrics employed in the study of biomolecular condensates are employed to identify key order parameters that quantity how attractive forces, packing structure, multiblock sequence, and copolymer density determine dynamical slowing down above and below the crossover to a fluctuating polymeric microemulsion state.
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Affiliation(s)
- Guang Shi
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA.
| | - Kenneth S Schweizer
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA.
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana, Illinois 61801, USA
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
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Martin TB, Gartner TE, Jones RL, Snyder CR, Jayaraman A. pyPRISM: A Computational Tool for Liquid-State Theory Calculations of Macromolecular Materials. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b00011] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Tyler B. Martin
- National Institute
of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | | | - Ronald L. Jones
- National Institute
of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Chad R. Snyder
- National Institute
of Standards and Technology, Gaithersburg, Maryland 20899, United States
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Lyubimov I, Beltran-Villegas DJ, Jayaraman A. PRISM Theory Study of Amphiphilic Block Copolymer Solutions with Varying Copolymer Sequence and Composition. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b01419] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Ivan Lyubimov
- Department of Chemical & Biomolecular Engineering, Colburn Laboratory, University of Delaware, 150 Academy Street, Newark, Delaware 19716, United States
| | - Daniel J. Beltran-Villegas
- Department of Chemical & Biomolecular Engineering, Colburn Laboratory, University of Delaware, 150 Academy Street, Newark, Delaware 19716, United States
| | - Arthi Jayaraman
- Department of Chemical & Biomolecular Engineering, Colburn Laboratory, University of Delaware, 150 Academy Street, Newark, Delaware 19716, United States
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Zherenkova LV, Komarov PV. Study of the phase behavior of a diblock copolymer in an ionic liquid: Outlook for use of the integral-equation theory. POLYMER SCIENCE SERIES A 2014. [DOI: 10.1134/s0965545x14030201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Hall LM, Schweizer KS. Impact of Monomer Sequence, Composition and Chemical Heterogeneity on Copolymer-Mediated Effective Interactions between Nanoparticles in Melts. Macromolecules 2011. [DOI: 10.1021/ma200079z] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Lisa M. Hall
- Department of Chemical and Biomolecular Engineering and ‡Department of Materials Science and Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Kenneth S. Schweizer
- Department of Chemical and Biomolecular Engineering and ‡Department of Materials Science and Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
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Mansour AS, Johnson LF, Lodge TP, Bates FS. Thermodynamic characteristics of poly(cyclohexylethylene-b
-ethylene-co-
ethylethylene) block copolymers. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/polb.21923] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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Jayaraman A, Schweizer KS. Liquid state theory of the structure and phase behaviour of polymer-tethered nanoparticles in dense suspensions, melts and nanocomposites. MOLECULAR SIMULATION 2009. [DOI: 10.1080/08927020902744680] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Jayaraman A, Schweizer KS. Effective Interactions, Structure, and Phase Behavior of Lightly Tethered Nanoparticles in Polymer Melts. Macromolecules 2008. [DOI: 10.1021/ma801722m] [Citation(s) in RCA: 77] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Arthi Jayaraman
- Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801
| | - Kenneth S. Schweizer
- Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801
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Jayaraman A, Schweizer KS. Effect of the number and placement of polymer tethers on the structure of concentrated solutions and melts of hybrid nanoparticles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2008; 24:11119-11130. [PMID: 18729491 DOI: 10.1021/la801432b] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We have generalized and applied the microscopic polymer reference interaction site model theory to study intermolecular pair correlation functions and collective structure factors of concentrated solutions and melts of spherical nanoparticles carrying one, two, or four tethered polymer chains. A complex interplay of entropy (translational, conformational, and packing) and enthalpy (particle-particle attraction) leads to different structural arrangements with distinctive small- and wide-angle scattering signatures. Strong concentration fluctuations indicative of aggregate formation and/or a tendency for microphase separation occur as the total packing fraction and/or particle-particle attraction strength increase. In analogy with block copolymers, the microphase spinodal curve is estimated by extrapolation of the inverse of the amplitude of the small-angle scattering peak. As the number of tethered chains on nanoparticles increases, the microphase separation boundary spinodal occurs at higher particle-particle attraction strength or lower temperature. For nanoparticles with two tethers, increasing the angle between the attached chains shifts the microphase spinodal to lower temperatures. For nanoparticles with four tethers, the structural correlations are insensitive to various symmetric placements. The tendency for microphase transition is enhanced upon asymmetrically placing all four tethers on one side of the particle due to the high anisotropy of steric hindrance.
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Affiliation(s)
- Arthi Jayaraman
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA
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Jayaraman A, Schweizer KS. Structure and assembly of dense solutions and melts of single tethered nanoparticles. J Chem Phys 2008; 128:164904. [DOI: 10.1063/1.2907717] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Maheshwari S, Tsapatsis M, Bates FS. Synthesis and Thermodynamic Properties of Poly(cyclohexylethylene-b-dimethylsiloxane-b-cyclohexylethylene). Macromolecules 2007. [DOI: 10.1021/ma071132g] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Affiliation(s)
- Bong June Sung
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706
| | - Arun Yethiraj
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706
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Zherenkova LV, Khalatur PG, Khokhlov AR. Solution properties of charged quasi-random copolymers: Integral equation theory. J Chem Phys 2003. [DOI: 10.1063/1.1604383] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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Almdal K, Hillmyer MA, Bates FS. Influence of Conformational Asymmetry on Polymer−Polymer Interactions: An Entropic or Enthalpic Effect? Macromolecules 2002. [DOI: 10.1021/ma020148y] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Kristoffer Almdal
- The Danish Polymer Centre, Risø National Laboratory, P.O. Box 49, DK-4000 Roskilde, Denmark
| | - Marc A. Hillmyer
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455-0431
| | - Frank S. Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55405-0132
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Khalatur PG, Khokhlov AR. Phase behavior of comblike copolymers: The integral equation theory. J Chem Phys 2000. [DOI: 10.1063/1.481038] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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