Polymers Research Group Technical Report Series
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This series includes technical reports prepared by faculty, students and staff who are affiliated with the Polymers Research Group in the Department of Chemical Engineering at Queen’s University. These reports are intended to furnish rapid communication to persons who have an active interest in the subject matter and to stimulate comment, including corrections of possible errors.
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Item Complex Viscosity of Star-Branched Macromolecules from Analytical General Rigid Bead-Rod Theory(2021-07) Coombs, Steacy J.; Kanso, Mona A.; Haddad, Karl E.; Giacomin, A. JeffreyThe complex viscosity of planar star-branched polymers has been derived from general rigid bead-rod theory, but only for singly-beaded arms. Here, we explore the respective roles of branch functionality, arm length and non-planar arrangements, analytically from general rigid bead-rod theory. For non-planar arrangements, we include polyhedral, both regular and irregular. Further, for all structures, we compare with and without the central bead. We fit the theory to complex viscosity measurements on polybutadiene solutions, one quadrafunctional star-branched, the other unbranched, of the same molecular weight (!! = 200,000 g/gmol). We learn that when general rigid bead-rod theory is applied to quadrafunctional polybutadiene, a slightly irregular center-beaded tetrahedron of interior angle 134º is required (with 1,360,000 g/gmol per bead) to describe its complex viscosity behaviour.Item Confinement and Complex Viscosity: Experiments(2021-03) Coombs, Steacy J.; Giacomin, A. Jeffrey; Pasquino, R.Whereas much is known about the complex viscosity of polymeric liquids, far less is understood about the behaviour of this material function when macromolecules are confined. By confined, we mean that the gap along the velocity gradient is small enough to reorient the polymers. We examine classical analytical solutions [Park and Fuller, JNNFM, 18, 111 (1985)] for a confined rigid dumbbell suspension in small-amplitude oscillatory shear flow. We test these analytical solutions against the measured effects of confinement on both parts of the complex viscosity of a carbopol suspension and three polystyrene solutions.Item Cole-Cole Relation for Long-Chain Branching From General Rigid Bead-Rod Theory(2020-08) Coombs, Steacy J.; Kanso, Mona A.; Giacomin, A. JeffreyEmpirically, we find that parametric plots of the imaginary versus real parts of the complex viscosity may depend neither on temperature, nor on average molecular weight. Moreover, for fixed polydispersity, these Cole-Cole curves amplify both rightward and upward with long-chain branching content. In this paper, we find that general rigid bead-rod theory [O. Hassager, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. II. Linear unsteady flow properties,” J. Chem. Phys. 60(10), 4001–4008 (1974)] can explain these rightward and upward amplifications. We explore the effects of branching along a straight chain in small-amplitude oscillatory shear flow. Specifically, we explore the number of branches, branch length, branch position and branch distribution.Item Large-Amplitude Oscillatory Shear Flow Loops for Long-Chain Branching From General Rigid Bead-Rod Theory(2020-04) Kanso, Mona A.; Giacomin, A. Jeffrey; Saengow, ChaimongkolGeneral rigid bead-rod theory [Hassager, J Chem Phys, 60, 4001 (1974)] explains polymer viscoelasticity from macromolecular orientation. By means of this theory, we relate the complex viscosity of polymeric liquids to the architecture of axisymmetric branched macromolecules. In this work, we explore how adding long-chain branching to polymers affects the shapes of largeamplitude oscillatory shear flow (LAOS) loops. By loops, we mean plots of the alternant part of the shear stress response versus the cosinusoidal shear rate. When non-dimensionalized with the product of the zero-shear viscosity and the shear rate amplitude, the loop shapes depend upon the sole dimensionless architectural parameter, the macromolecular lopsidedness of the long-chain branched macromolecule. In this work, in this way, we compare and contrast the loop shapes of macromolecular chains that are straight, with those branched. Specifically, we explore symmetric branch multiplicity, branch functionality, branch length, branch position, branch distribution and multiple branch asymmetry. We find that adding branching collapses and distorts the loops. We then find that, so long as branch length, branch position and branch distribution are held constant, and so long as the branching is symmetric about the center of mass, the peak shear stress increases with branch multiplicity. We also find that branch functionality hardly affects the loops.Item Van Gurp-Palmen Relations for Long-Chain Branching From General Rigid Bead-Rod Theory(2020-02) Kanso, Mona A.; Giacomin, A. JeffreyEmpirically, we find that parametric plots of mechanical loss angle versus complex shear modulus may depend neither on temperature [van Gurp and Palmen, Rheol Bull (SoR), 67, 5 (1998)], nor on average molecular weight [Hatzikiriakos (2000), Pol Eng Sci, 40, 2279 (2000)]. Moreover, Hatzikiriakos (2000) discovered that, for fixed polydispersity, these van Gurp-Palmen curves descend with long-chain branching content. In this paper, we find that general rigid beadrod theory [Hassager, J Chem Phys, 60, 4001 (1974)] can explain these descents. We explore the effects of branching along a straight chain in small-amplitude oscillatory shear flow. Specifically, we explore the number of branches, branch length, branch position and branch distribution.