A two-species model for the rheology of associative polymer networks from nonequilibrium thermodynamics

Pavlos S. Stephanou,1 Ioanna Ch. Tsimouri,2 and Vlasis G. Mavrantzas3,4

1 Department of Chemical Engineering, Cyprus University of Technology, 30 Archbishop Kyprianou Str., 3036, Limassol, Cyprus, This email address is being protected from spambots. You need JavaScript enabled to view it.
2 Department of Materials, Polymer Physics, ETH Zurich, Leopold-Ruzicka-Weg 4, HCP F 45.2, CH-8093 Zurich, Switzerland, This email address is being protected from spambots. You need JavaScript enabled to view it.
3 Department of Chemical Engineering, University of Patras, Patras, GR 26504, Greece, This email address is being protected from spambots. You need JavaScript enabled to view it.
4 Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zurich, Sonneggstrasse 3, Zurich 8092, Switzerland, This email address is being protected from spambots. You need JavaScript enabled to view it.

Correspondence: This email address is being protected from spambots. You need JavaScript enabled to view it.

We employ the generalized bracket formalism of nonequilibrium thermodynamics [1] to derive a constitutive model for reversibly crosslinked networks of associative polymers, fluids that find extensive usages as rheology modifiers in a variety of commercial products today (health and personal care, enhanced oil recovery, paints and paper coatings, and many others) [2]. For these fluids, several important rheological models have been proposed over the years, mostly on the basis of separate contributions from bridges and (temporary) dangling chains [3-4].

A novel feature of the work presented here is that the expressions for the attachment and detachment rates as functions of applied flow and chain conformation arise naturally from the formalism. This is achieved by assuming a kinetic model [5, 6] for the formation/dissociation of chains from the network through, and is a big advantage compared to other efforts wherein these expressions are typically specified externally. The final set of evolution equations obtained from our approach [7] are very similar to those of earlier models based on network kinetic theory, which is very nice given the totally different approaches followed (thermodynamics compared to polymer kinetic theory). A detailed analysis demonstrates the capability of the new model to describe various sets of rheological data for solutions of associative polymers [7].

A drawback of our new model is that it cannot predict the weak shear thickening observed experimentally prior to shear thinning in steady shear [8], despite the self-consistent incorporation of non-Gaussian effects in the attachment/detachment rates. According to Tripathi et al. [4], shear-thickening arises by allowing the detachment rate to be a function of the conformation of both bridges and dangling chains, leading to a shear-induced enhancement of bridges, but this cannot be accommodated in the current version of our model. We are currently working on this [9].

[1] Beris A. N., Edwards B. J. (1994). Thermodynamics of Flowing Systems with Internal Microstructure, Oxford University Press: New York.
[2] C. Chassenieux, T. Nicolai, and L. Benyahia, Curr. Opin. Colloid Interface Sci. 16, 18–26 (2011).
[3] F. Tanaka and S.F. Edwards, Macromolecules 25, 1516 (1992).
[4] A. Tripathi, K.C. Tam, and G.H. McKinley, Macromolecules 39, 1981 (2006).
[5] N. Germann, L.P. Cook, and A.N. Beris, J. Non-Newton. Fluid Mech. 196, 51 (2013).
[6] I.C. Tsimouri, P.S. Stephanou, and V. G. Mavrantzas, Phys. Fluids 30, 030710 (2018).
[7] P.S. Stephanou, I.Ch. Tsimouri, and V.G. Mavrantzas, J. Rheology 64, 1003-1016 (2020).
[8] T. Annable, R. Buscall, R. Ettelaie, and D. Whittlestone, J. Rheol. 37, 695–726 (1993).
[9] P.S. Stephanou, Phys. Fluids 33, 063107 (2021).

Dr. Pavlos S. Stephanou graduated from the Department of Chemical Engineering, University of Patras, Patras, Greece in 2006. He then pursued postgraduate studies at the same department under the guidance of Prof. Vlasis Mavrantzas. His PhD thesis is entitled “Development of scale-bridging methodologies and algorithms founded on the outcome of detailed atomistic simulations for the reliable prediction of the viscoelastic properties of polymer melts”. During his postgraduate career he has worked at the University of Cyprus (Cyprus), the ETH Zürich (Switzerland), the Cyprus University of Technology (Cyprus), and Novamechanics Ltd (Cyprus) having received numerous grants and awards.

He received the «Cyprus Research Award – Young Researcher 2015» (Thematic area: Physical Sciences and Engineering), for his research work entitled «Modelling the viscoelasticity of polymer-based nanocomposites guided by principles of non-equilibrium thermodynamics» which was undertaken at the University of Cyprus (Department of Mathematics and Statistics) between 2011-2014 by the Research Promotion Foundation (RPF) of Cyprus on November 23rd 2015. The "Cyprus Research Award - Young Researcher" ("Young Researcher" being one who has a maximum of seven years of research experience from his/her doctoral title until the date of the announcement of the competition) is awarded to young researchers who have carried out specific research work of high quality, which has been completed within the last three years before the competition is announced.

Since September 2019 he is an Assistant Professor at the Department of Chemical Engineering of the Cyprus University of Technology.