Theory of Shear-Thickening in Transient Networks of Associating Polymers

Theory of transient networks with a well-defined junction structure

The present study constructs a theory of physical gels consisting of bifunctional molecules, f-functional molecules, and solvent. This theory considered the formation of loops (i.e., the smallest cycles). First, the association state in the equilibrium state was investigated. Unlike the previous theory proposed by the authors, the present theory was able to describe the effect of functionality on the association state. Second, the dynamics of gelation was studied. As a result, the authors found two regimes: one where the characteristic time of gelation is governed by the association of associative groups and another where it is governed by the dissociation of them. Finally, theoretical results and the existing experimental results were compared in terms of gelation time and the time development of elasticity. With parameters set reasonably, the theory succeeded in the quantitative description of the experimental results.

Oscillatory and Steady Shear Rheology of Model Hydrophobically Modified Ethoxylated Urethane-Thickened Waterborne Paints

Hydrophobically modified ethoxylated urethane (HEUR) thickeners are widely used as rheology modifiers for waterborne paints. Although the rheology of HEUR solutions in water is fairly well-understood, their impact on the rheology of waterborne latex/pigment suspensions (formulated paints) is more complicated. We study the shear rheology of model HEUR/latex/TiO₂ suspensions in water and investigate the dependence of both oscillatory and steady shear behaviors on the strength of the HEUR hydrophobes. We observe that in both oscillatory and steady shear experiments, rheological curves could be shifted onto a single master curve, demonstrating a "time-hydrophobe superposition". We also note that the oscillatory shear behavior exhibits a power-law spectrum of relaxation times, unlike the single-Maxwellian behavior of pure HEUR solutions. On the basis of these results and earlier experimental and theoretical findings, we propose that the rheology of the HEUR-thickened latex/TiO₂ suspensions is mainly determined by the transient network of HEUR-bridged latex particles, with a broad distribution of the characteristic lifetimes of the bridge. The model is found to be in good qualitative and semiquantitative agreement with the experiments for both steady shear and oscillatory shear.

Supramolecular polymeric biomaterials

Polymeric chains crosslinked through supramolecular interactions-directional and reversible non-covalent interactions-compose an emerging class of modular and tunable biomaterials. The choice of chemical moiety utilized in the crosslink affords different thermodynamic and kinetic parameters of association, which in turn illustrate the connectivity and dynamics of the system. These parameters, coupled with the choice of polymeric architecture, can then be engineered to control environmental responsiveness, viscoelasticity, and cargo diffusion profiles, yielding advanced biomaterials which demonstrate rapid shear-thinning, self-healing, and extended release. In this review we examine the relationship between supramolecular crosslink chemistry and biomedically relevant macroscopic properties. We then describe how these properties are currently leveraged in the development of materials for drug delivery, immunology, regenerative medicine, and 3D-bioprinting (253 references).

The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers

Transient polymer networks are ubiquitous in natural and engineered materials and contain cross-links that can reversibly break and re-form. The dynamic nature of these bonds allows for interesting mechanical behavior, some of which include nonlinear rheological phenomena such as shear thickening and shear thinning. Specifically, physically cross-linked networks with reversible bonds are typically observed to have viscosities that depend nonlinearly on shear rate and can be characterized by three flow regimes. In slow shear, they behave like Newtonian fluids with a constant viscosity. With further increase in shear rate, the viscosity increases nonlinearly to subsequently reach a maximum value at the critical shear rate. At this point, network fracture occurs followed by a reduction in viscosity (shear-thinning) with a further increase in shear rate. The underlying mechanism of shear thickening in this process is still unclear with debates between a conversion of intra-chain to inter-chain cross-linking and nonlinear chain stretch under high tension. In this paper, we provide a new framework to describe the nonlinear rheology of transient polymer networks with the so-called chain distribution tensor using recent advances from the transient network theory. This tensor contains quantitatively and statistical information of the chain alignment and possible anisotropy that affect network behavior and mechanics. We investigate shear thickening as a primary result of non-Gaussian chain behavior and derive a relationship for the nonlinear viscosity in terms of the non-dimensional Weissenberg number. We further address the criterion for network fracture at the critical shear rate by introducing a critical chain force when bond dissociation is suddenly accelerated. Finally, we discuss the role of cross-linker density on viscosity using a "sticky" reptation mechanism in the context of previous studies on metallo-supramolecular networks with reversible cross-linkers.

Transient Network at Large Deformations: Elastic⁻Plastic Transition and Necking Instability

We theoretically investigate the mechanical response of a transient network, which is characterised by dynamically breaking and re-forming crosslinks, and accounts for the finite chain extensibility (thus permitting the large deformations to be described). We build the general theory that incorporates the widely accepted empirical model of hyper-elasticity at large deformations (the Gent model) and naturally includes the microscopic behavior of transient crosslinks under the local tension applied to them. The full analytical expression for the elastic energy, or equivalently, the constitutive relation for arbitrary deformation is derived, and then the example of uniaxial tensile strain is focused on. In this case, we show that the mechanical response depends on the ratio of the imposed strain rate and the breakage rate of the crosslink: the system flows plastically (over a yield point) when the strain rate is much smaller than the breakage rate, while it remains elastic when the strain rate is much larger than the breakage rate. There is a broad range of this transition when the elastic and plastic regions of the sample coexist, and a resulting necking instability occurs. As a generalisation, we also consider a dual transient network, with two components penetrating each other, each having its own microscopic crosslink dynamics. The two networks add their local forces and share the deformation; we find that the network with a lower breakage rate determines the global deformation of the system.

Concentration dependence of rheological properties of telechelic associative polymer solutions

We consider concentration dependence of rheological properties of associative telechelic polymer solutions. Experimental results for model telechelic polymer solutions show rather strong concentration dependence of rheological properties. For solutions with relatively high concentrations, linear viscoelasticity deviates from the single Maxwell behavior. The concentration dependence of characteristic relaxation time and moduli is different in high- and low-concentration cases. These results suggest that there are two different concentration regimes. We expect that densely connected (well percolated) networks are formed in high-concentration solutions, whereas sparsely connected (weakly percolated) networks are formed in low-concentration solutions. We propose single chain type transient network models to explain experimental results. Our models incorporate the spatial correlation effect of micellar cores and average number of elastically active chains per micellar core (the network functionality). Our models can reproduce nonsingle Maxwellian relaxation and nonlinear rheological behavior such as the shear thickening and thinning. They are qualitatively consistent with experimental results. In our models, the linear rheological behavior is mainly attributable to the difference of network structures (functionalities). The nonlinear rheological behavior is attributable to the nonlinear flow rate dependence of the spatial correlation of micellar core positions.

Multiple Dynamic Processes Contribute to the Complex Steady Shear Behavior of Cross-Linked Supramolecular Networks of Semidilute Entangled Polymer Solutions

Molecular theories of shear thickening and shear thinning in associative polymer networks are typically united in that they involve a single kinetic parameter that describes the network -- a relaxation time that is related to the lifetime of the associative bonds. Here we report the steady-shear behavior of two structurally identical metallo-supramolecular polymer networks, for which single-relaxation parameter models break down in dramatic fashion. The networks are formed by the addition of reversible cross-linkers to semidilute entangled solutions of PVP in DMSO, and they differ only in the lifetime of the reversible cross-links. Shear thickening is observed for cross-linkers that have a slower dissociation rate (17 s(-1)), while shear thinning is observed for samples that have a faster dissociation rate (ca. 1400 s(-1)). The difference in the steady shear behavior of the unentangled vs. entangled regime reveals an unexpected, additional competing relaxation, ascribed to topological disentanglement in the semidilute entangled regime that contributes to the rheological properties.

Mechanism of Shear Thickening in Reversibly Cross-linked Supramolecular Polymer Networks

We report here the nonlinear rheological properties of metallo-supramolecular networks formed by the reversible cross-linking of semi-dilute unentangled solutions of poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO). The reversible cross-linkers are bis-Pd(II) or bis-Pt(II) complexes that coordinate to the pyridine functional groups on the PVP. Under steady shear, shear thickening is observed above a critical shear rate, and that critical shear rate is experimentally correlated with the lifetime of the metal-ligand bond. The onset and magnitude of the shear thickening depend on the amount of cross-linkers added. In contrast to the behavior observed in most transient networks, the time scale of network relaxation is found to increase during shear thickening. The primary mechanism of shear thickening is ascribed to the shear-induced transformation of intrachain cross-linking to interchain cross-linking, rather than nonlinear high tension along polymer chains that are stretched beyond the Gaussian range.

Stress buildup under start-up shear flows in self-assembled transient networks of telechelic associating polymers

The nonaffine transient network theory is used to study the time development of the shear and normal stresses under start-up shear flows in networks formed by self-assembled telechelic, hydrophobically modified water-soluble polymers. The initial slope, strain hardening, and overshoot of the shear stress are studied in detail in relation to the nonlinear tension-elongation curve of the elastically active chains in the network. The condition for the occurrence of strain hardening (upward deviation of the stress from the reference curve defined by the linear moduli) is found to be gamma > gammac(A), where gamma is the shear rate, gamma(c) is its critical value for strain hardening, and A is the amplitude of the nonlinear term in the tension of a chain. The critical shear rate gamma(c) is calculated as a function of A. It is approximately 6.3 (in the time unit of the reciprocal thermal dissociation rate) for a nonlinear chain with A = 10. The overshoot time t(max) when the stress reaches a maximum and the total deformation gamma(max) = gamma(t max) accumulated before the peak time are obtained in terms of the molecular parameters of the polymer chain. The maximum deformation gamma(max) turns out to depend weakly upon the shear rate gamma. The first and second normal stress differences are also studied on the basis of the exact numerical integration of the theoretical model by paying special attention to their overshoot, undershoot, and sign change as a function of the shear rate. These theoretical results are compared with recent rheological experiments of the solutions of telechelic hydrophobically modified poly(ethylene oxide)s carrying short branched alkyl chains (2-decyl-tetradecyl) at both ends.

Nonlinear rheology of surfactant wormlike micelles bridged by telechelic polymers

We have investigated the nonlinear rheology of a soft composite transient network made of a solution of surfactant wormlike micelles (WM) in the semidilute regime that are reversibly bridged by telechelic polymers. The samples are well described, in the linear regime, as two Maxwell fluids components blends, characterized by two markedly different characteristic times. The slow mode is mainly related to the transient network of entangled WM, and the fast mode to the network of telechelic chains. In this paper we investigate the nonlinear viscoelasticity and show that the nonlinear behavior reflects as well the behavior of two coupled networks. On one hand, stress relaxation experiments and time-resolved stress response following the application of a constant shear rate show that, in the weakly nonlinear regime, these novel composite networks stiffen. A fourfold increase of the elastic modulus with respect to the linear value is reached for strain amplitude of about 200%. This strain hardening is due to the nonlinear stretching of the telechelic polymer chains. On the other hand, the samples exhibit shear banding in the highly nonlinear regime, similarly to pure semidilute solutions of WM.

Nonlinear rheology of aqueous solutions of hydrophobically modified hydroxyethyl cellulose with nonionic surfactant

Shear thickening and strain hardening behavior of hydrophobically modified hydroxyethyl cellulose (HMHEC) aqueous solutions was experimentally examined. We focused on the effects of polymer concentration, temperature, and addition of nonionic surfactant. It is found that HMHEC shows stronger shear thickening at intermediate shear rates in a certain concentration range. In this range, the zero-shear viscosity scales with polymer concentration as eta(0) approximately c(5.7), showing a stronger concentration dependence than for more concentrated solutions. The critical shear stress for complete disruption of the transient network follows tau(c) approximately c(1.62) in the concentrated regime. Dynamic tests of the transient network on addition of surfactants show that the enhanced zero-shear viscosity is due to an increase in network junction strength, rather than their number, which in fact decreases. The reduction in the junction number could partly explain the weak variation of strain hardening extent for low surfactant concentrations, because of longer and looser bridging chain segments, and hence lesser nonlinear chain stretching.