Calculation of the Viscosity of Polymer Melts Based on Measurements of the Recovered Rubber-Like Deformation

Elastic Entropic Forces in Polymer Deformation

“…Stretching polymer chains from an equilibrium conformation in flowing polymer melts results in manifestation of the EEF [ 19 , 22 , 23 ] in proportion to the distance, between the ends of a macromolecule (see Appendix A ), viz., where N is the number of monomeric links in the chain, and l is the length of each unit. The emerging entropic force ( 4 ) reduces activation energy allowing for the MKU to jump by a distance proportional to the magnitude of EEF in the direction of flow forces [ 5 , 7 , 14 , 15 , 18 ], viz., where B is a pre-exponential factor, is an activation coefficient having the dimension of energy, a is a coefficient having the dimension of length, and is a dimensionless size of reversible, rubber-like deformations emerging due to chemical bonding between the monomeric links of a macromolecule [ 21 , 23 , 26 ]. The value can be assessed by measuring the volume of recoverable deformation in polymer melts after stopping the rotary plane (cone) in a viscometer [ 14 ].…”

“…The emerging entropic force ( 4 ) reduces activation energy allowing for the MKU to jump by a distance proportional to the magnitude of EEF in the direction of flow forces [ 5 , 7 , 14 , 15 , 18 ], viz., where B is a pre-exponential factor, is an activation coefficient having the dimension of energy, a is a coefficient having the dimension of length, and is a dimensionless size of reversible, rubber-like deformations emerging due to chemical bonding between the monomeric links of a macromolecule [ 21 , 23 , 26 ]. The value can be assessed by measuring the volume of recoverable deformation in polymer melts after stopping the rotary plane (cone) in a viscometer [ 14 ]. Plugging the expression ( 5 ) back into Newton’s formula ( 2 ) and applying the logarithm to the resulting equation, we obtain three linear relationships between the logarithms of viscosity , shear stress , and share rate that might be verified experimentally (see Section 3.1 ), viz., indicating that anomalous viscosity might be considered a manifestation of the EEF reducing jump activation energy in the flow of polymer melts [ 5 , 14 , 15 ].…”

“…The value can be assessed by measuring the volume of recoverable deformation in polymer melts after stopping the rotary plane (cone) in a viscometer [ 14 ]. Plugging the expression ( 5 ) back into Newton’s formula ( 2 ) and applying the logarithm to the resulting equation, we obtain three linear relationships between the logarithms of viscosity , shear stress , and share rate that might be verified experimentally (see Section 3.1 ), viz., indicating that anomalous viscosity might be considered a manifestation of the EEF reducing jump activation energy in the flow of polymer melts [ 5 , 14 , 15 ].…”

“…Many attempts have been made to generalize Eyring’s formula for the different types of molecular kinetic units (MKU) [ 11 ] and in various viscous liquid flows rising the numerous variants of empirical rheological equations in the literature [ 9 , 12 ]. The profound limitation of Eyring’s equation (Equation ( 3 )) in its application to the flows of polymer melts is that it does not account for a possible influence of reversible, rubber-like deformations of MKU stretched along the flow [ 5 , 13 , 14 ].…”

“…In our paper, we review and analyze another explanation for viscosity anomalies in polymer flows, taking into account the entropic nature of elasticity emerging in macromolecules. In our approach, activation energy in Eyring’s equation (Equation ( 3 )) takes into account moving of an entire macromolecule with its valence bonds instead of a jump of a single atom in thermal motion [ 14 , 15 ]. While in the flow of polymer melts, the macromolecule can jump over the potential barrier and take a new equilibrium conformation, maintaining the chemical structure of the kinetic unit.…”