Changes of Activation Energy during Deformation of Rubber

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 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 ].…”

“…This process is described macroscopically by Hooke’s law, relating elastic stresses to strains , viz., where E is the Young’s modulus describing the relative stiffness of a material, which is measured by the slope of elastic of a stress and strain graph, and by Newton’s flow law, stating that the application of shear stress on a liquid leads to the share rate in direct proportion to the amount of stress applied, with the coefficient of (apparent) viscosity . Eyring’s absolute rate theory [ 3 ], used in chemical kinetics to describe changes in the rate of chemical reactions against absolute temperature , predicts the following dependence of dynamic viscosity on shear stress [ 3 , 4 , 5 , 6 , 7 ], viz., where is the activation energy required for a molecule to jump, B is a pre-exponential factor, b is Eyring’s coefficient of viscous volume [ 3 ], and is Boltzmann’s constant. Although most low molecular weight liquids do obey simple Newton’s law ( 2 ), the anomalous behavior of viscosity following from Eyring’s equation (Equation ( 3 )) was observed experimentally in the studies of deformation process [ 8 ] where shear stress transferred through a system of elastic interatomic bonds may act directly on atoms during their thermal motion.…”

“…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 ].…”

Rheological Behavior of Raw Natural Rubber Coagulated by Microorganisms

“…The activation energy (E) of viscous flow is the lowest energy, which overcomes the potential barrier for jumping of molecular-kinetic units of a polymer network into vacancies during flow processing; it is based on the entropy elasticity of a macromolecular network that causes an increase of the material's flow resistance in the course of deformation [26] . E values of NR-a and NR-m at different shear rates are plotted in Figures 8 and 9, respectively.…”