RHEOLOGY OF COMPLEX FLUIDS: ASSOCIATIVE POLYMERS

Associative Associative polymerspolymers

They present They present physical physical entanglements and entanglements and electrostatic electrostatic interactionsinteractions

Associative polymersAssociative polymers

Inter-molecularassociation

Intra-molecularassociation

CH3

CH2

OC

NCH2

CH2

ON

CO

CH2

CH3

O

H H

O

n nm

Kásten U., Colloids and surfaces A, 183-185, 805-821, (2001).

Rheological behavior Rheological behavior of associative polymersof associative polymers

Polymer molecules associate with themselves, formation of micelar flowers

Shear viscosity and elasticity depend on polymer concentration and shear rate

Polymermolecule

Micelar flower

Partial aggregation

Network

Comb like structure

Aggregates

Molecular Molecular ArrangementArrangement

Intermolecular association

Intramolecular association

Micellar Flower Petal

Comparison of the Comparison of the shear and complex shear and complex viscosityviscosity

Shear thickening Shear thickening observed at low observed at low concentrations.concentrations.

Newtonian-Newtonian-

shear-thickening-shear-thickening-

Shear-thinning-Shear-thinning-

Slope that tends to -1 at Slope that tends to -1 at high shear rateshigh shear rates

ModellingModelling

Dumbbell model.Dumbbell model. Newtonian—Newtonian—

shear-thickeningshear-thickening

shear-thinningshear-thinning

slope of slope of

-1 at high shear -1 at high shear rates.rates.

Leibler et alLeibler et al

Reptation-kinetic Reptation-kinetic process (breakage-process (breakage-reformation)reformation)

Concentrated SystemsConcentrated Systems

Dumbbell: dilute solutionsDumbbell: dilute solutions Transient network: more concentrated Transient network: more concentrated

solutions and melts.solutions and melts. Models for transient networks should include:Models for transient networks should include: >Coupling between microstructure and flow.>Coupling between microstructure and flow. >>Variable extensibilityVariable extensibility of the segments. of the segments. >Modified spring law and destruction >Modified spring law and destruction

function.function. >>DissipationDissipation in the disentanglement in the disentanglement

process of the network.process of the network. >>Regions of variable entanglement density.Regions of variable entanglement density.

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.

A) 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.

B) 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.

THE TRANSIENT NETWORK MODEL

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.

MICROSTATES PROPERTIES

AVERANGE DISTANCE BETWEEN AVERANGE DISTANCE BETWEEN NODES NODES

)12974(

)4332()(

43210

3 4210

CCCCCV

CCCCCV

L

ll

p

ii

13

1 il

Ll pisegments ofNumber

chains ofNumber )(

The maximum segment length (extensibility) is defined as the critical length above which rupture of nodes occurs.

Definition

Range

Definition for the five microstates

Change in energy Change in energy involvedinvolved

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

The global kinetics can then be expressed as:The global kinetics can then be expressed as:

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

Transition between microstates 0 and 3 gives:Transition between microstates 0 and 3 gives:

Transition between microstates 1 and 3 gives:Transition between microstates 1 and 3 gives:

Steady-state StressSteady-state Stress

J.F. Berret (Associative polymers, 2000)J.F. Berret (Associative polymers, 2000)

Steady-state Viscosity Steady-state Viscosity

Comparison with other Comparison with other modelsmodels

First normal stress First normal stress differencedifference

Stress Relaxation Stress Relaxation

Comparison with Comparison with experimentexperiment

Transient Stress Transient Stress

Comparison with Comparison with experimentexperiment

COMPARISON OF VARIOUS KINETICS AT INCEPTION COMPARISON OF VARIOUS KINETICS AT INCEPTION

OF SHEAR FLOWOF SHEAR FLOW

MAXIMUM SEGMENT LENGTH OR EXTENSIBILITY MAXIMUM SEGMENT LENGTH OR EXTENSIBILITY FOR THE THREE KINETICSFOR THE THREE KINETICS

Microstates(strong Microstates(strong network)network)

Microstates (weak Microstates (weak network)network)

Thixotropy Thixotropy

Comparison with Comparison with experimentexperiment

CONCLUDING REMARKSCONCLUDING 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.