RHEOLOGY OF COMPLEX FLUIDS: ASSOCIATIVE POLYMERS

1. RHEOLOGY OF COMPLEX FLUIDS: ASSOCIATIVE POLYMERS

2. Associative polymers • They present physical entanglements and electrostatic interactions

3. Associative polymers Intra-molecular association Inter-molecular association Kásten U., Colloids and surfaces A, 183-185, 805-821, (2001).

4. Rheological behavior of associative polymers Polymer molecules associate with themselves, formation of micelar flowers Shear viscosity and elasticity depend on polymer concentration and shear rate Micelarflower Polymer molecule Network Partialaggregation

5. Micellar Flower Petal Intermolecular association Intramolecular association Molecular Arrangement Comb like structure Aggregates

6. Comparison of the shear and complex viscosity • Shear thickening observed at low concentrations. • Newtonian- shear-thickening- Shear-thinning- Slope that tends to -1 at high shear rates

7. Modelling • Dumbbell model. • Newtonian— shear-thickening shear-thinning slope of -1 at high shear rates.

8. Leibler et al • Reptation-kinetic process (breakage-reformation)

9. Concentrated Systems • Dumbbell: dilute solutions • Transient network: more concentrated solutions and melts. • Models for transient networks should include: • >Coupling between microstructure and flow. • >Variable extensibility of the segments. • >Modified spring law and destruction function. • >Dissipation in the disentanglement process of the network. • >Regions of variable entanglement density.

10. Rincón et al (JNNFM 131, 2005,64) • The dynamics of a transient network are analyzed with two coupled kinetic processes to describe the rheological behavior of complex fluids. • Five microstates are defined, representing the complexity of interactions among the macromolecules suspended in a Newtonian fluid. • The average concentration of microstates at a given time defines the maximum segment length (extensibility) joining the entanglement points in the transient network. • The model predicts shear-banding in steady simple shear and time-dependent non-linear rheological phenomena, such as thixotropy, and stretched exponential relaxation.

11. THE TRANSIENT NETWORK MODEL • This model envisages a polymer solution as a network defined by nodes and segments, where the dynamic of segments joining the entanglement points are described statistically, in such a way that entanglements break and reform due to the deformation imposed by the applied flow. • The nodes, are drawn and joined with straight lines. This composition gives rise to a mesh of triangles, squares or polygons, where the nodes represent the vertex points of these polygons and they are linked by segments of linear molecules.

12. MICROSTATES The microstates can be free chains or pendant chains of the network, on one extreme, or the many-node interactions available in a dense network, on the other extreme.

13. MICROSTATES PROPERTIES

14. AVERANGE DISTANCE BETWEEN NODES The maximum segment length (extensibility) is defined as the critical length above which rupture of nodes occurs. Definition Definition for the five microstates Range

15. Change in energy involved

20. For a more concentrated solution, or when the flow strength is small:

22. The global kinetics can then be expressed as:

23. The forward kinetic constant is a function of temperature, as a thermally activated process. The backward constant is a function of the rate of dissipation.

31. Transition between microstates 0 and 3 gives:

32. Transition between microstates 1 and 3 gives:

34. Steady-state Stress J.F. Berret (Associative polymers, 2000)

35. Steady-state Viscosity

36. Comparison with other models

37. First normal stress difference

38. Stress Relaxation

39. Comparison with experiment

40. Transient Stress

41. Comparison with experiment

42. COMPARISON OF VARIOUS KINETICS AT INCEPTION OF SHEAR FLOW

43. MAXIMUM SEGMENT LENGTH OR EXTENSIBILITY FOR THE THREE KINETICS

44. Microstates(strong network)

45. Microstates (weak network)

46. Thixotropy

47. Comparison with experiment

48. CONCLUDING REMARKS • This model has been developed on the basis of a transient network formulation in which the instantaneous distance between nodes is calculated from the average over all structures presents in a given time. The complex interactions among the molecular chains are represented by a group five microstates, which are functions of temperature and viscous dissipation. • Some of the remarkable predictions of this model include a maximum in flow curve that leads to shear-banding flow under steady state conditions, shear-thickening of the viscosity followed by shear-thinning, stretch exponential behavior in stress relaxation at long times, non-monotonic growth of the stress with time after inception of shear flow, and the variety of hysteretic curves (thixotropic and antithixotropic behavior) under transient deformation histories. • Particular cases of the model include those where the maximum segment length is constant, corresponding to classical transient network models.