Macromolecular theory for the rheology of polymer liquids usually proceeds from a scale much larger than chemical bonding. For instance, a bead in a general rigid bead-rod theory can represent a length of the polymer. This is why we sculpt the shape of the macromolecule with a rigid bead-rod model. From the macromolecular hydrodynamics that follow, we then discover that the rheology of polymeric liquids depends on the macromolecular moments of inertia. In this paper, we use this discovery to arrive at a way of proceeding directly from the chemical bonding diagram to dimensionless complex viscosity curves. From the equilibrium conformation of the macromolecule, its atomic masses and positions, we first arrive at the macromolecular principal moments of inertia. From these, we then get the shapes of the complex viscosity curves from first principles thusly. We call this the macromolecular moment method. The zero-shear viscosity and relaxation time must still be fit to measurement. Using space-filling equilibrium structures, we explore the roles of (i) end group type, (ii) degree of polymerization, and (iii) pendant group type. We compare our results with complex viscosity measurements of molten atactic polystyrene.
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Macromolecular complex viscosity from space-filling equilibrium structure
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September 2022
Research Article|
September 20 2022
Macromolecular complex viscosity from space-filling equilibrium structure
Special Collection:
Rheology Testing and Analysis of Polymers
R. Chakraborty
;
R. Chakraborty
(Conceptualization, Formal analysis, Investigation, Methodology, Software)
1
Chemical Engineering Department, Jadavpur University
, Kolkata 700032, India
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D. Singhal
;
D. Singhal
(Methodology)
2
Chemical Engineering Department, Indian Institute of Technology Kanpur
, Kanpur 208016, India
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M. A. Kanso
;
M. A. Kanso
(Writing – original draft, Writing – review & editing)
3
Chemical Engineering Department, Polymers Research Group, Queen's University
, Kingston, Ontario K7L 3N6, Canada
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A. J. Giacomin
A. J. Giacomin
a)
(Supervision)
3
Chemical Engineering Department, Polymers Research Group, Queen's University
, Kingston, Ontario K7L 3N6, Canada
4
Mechanical and Materials Engineering Department, Queen's University
, Kingston, Ontario K7L 3N6, Canada
5
Physics, Engineering Physics and Astronomy Department, Queen's University
, Kingston, Ontario K7L 3N6, Canada
a)Author to whom correspondence should be addressed: giacomin@queensu.ca
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a)Author to whom correspondence should be addressed: giacomin@queensu.ca
Note: This paper is part of the special topic, Rheology Testing and Analysis of Polymers.
Physics of Fluids 34, 093109 (2022)
Article history
Received:
July 29 2022
Accepted:
August 17 2022
Citation
R. Chakraborty, D. Singhal, M. A. Kanso, A. J. Giacomin; Macromolecular complex viscosity from space-filling equilibrium structure. Physics of Fluids 1 September 2022; 34 (9): 093109. https://doi.org/10.1063/5.0116558
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