High-frequency Plateau Modulus Research Articles

Increasing valence pushes DNA nanostar networks to the isostatic point

The classic picture of soft material mechanics is that of rubber elasticity, in which material modulus is related to the entropic elasticity of flexible polymeric linkers. The rubber model, however, largely ignores the role of valence (i.e., the number of network chains emanating from a junction). Recent work predicts that valence, and particularly the Maxwell isostatic point, plays a key role in determining the mechanics of semiflexible polymer networks. Here, we report a series of experiments confirming the prominent role of valence in determining the mechanics of a model system. The system is based on DNA nanostars (DNAns): multiarmed, self-assembled nanostructures that form thermoreversible equilibrium gels through base pair-controlled cross-linking. We measure the linear and nonlinear elastic properties of these gels as a function of DNAns arm number, f, and concentration [DNAns]. We find that, as f increases from three to six, the gel's high-frequency plateau modulus strongly increases, and its dependence on [DNAns] transitions from nonlinear to linear. Additionally, higher-valence gels exhibit less strain hardening, indicating that they have less configurational freedom. Minimal strain hardening and linear dependence of shear modulus on concentration at high f are consistent with predictions for isostatic systems. Evident strain hardening and nonlinear concentration dependence of shear modulus suggest that the low-f networks are subisostatic and have a transient, potentially fractal percolated structure. Overall, our observations indicate that network elasticity is sensitive both to entropic elasticity of network chains and to junction valence, with an apparent isostatic point [Formula: see text] in agreement with the Maxwell prediction.

Controlling topological entanglement in engineered protein hydrogels with a variety of thiol coupling chemistries.

Topological entanglements between polymer chains are achieved in associating protein hydrogels through the synthesis of high molecular weight proteins via chain extension using a variety of thiol coupling chemistries, including disulfide formation, thiol-maleimide, thiol-bromomaleimide and thiol-ene. Coupling of cysteines via disulfide formation results in the most pronounced entanglement effect in hydrogels, while other chemistries provide versatile means of changing the extent of entanglement, achieving faster chain extension, and providing a facile method of controlling the network hierarchy and incorporating stimuli responsivities. The addition of trifunctional coupling agents causes incomplete crosslinking and introduces branching architecture to the protein molecules. The high-frequency plateau modulus and the entanglement plateau modulus can be tuned by changing the ratio of difunctional chain extender to the trifunctional branching unit. Therefore, these chain extension reactions show promise in delicately controlling the relaxation and mechanical properties of engineered protein hydrogels in ways that complement their design through genetic engineering.

The instantaneous shear modulus in the shoving model

We point out that the instantaneous shear modulus G(∞) of the shoving model for the non-Arrhenius temperature dependence of viscous liquids' relaxation time is the experimentally accessible high-frequency plateau modulus, not the idealized instantaneous affine shear modulus that cannot be measured. Data for a large selection of metallic glasses are compared to three different versions of the shoving model. The original shear-modulus based version shows a slight correlation to the Poisson ratio, which is eliminated by the energy-landscape formulation of the model in which the bulk modulus plays a minor role.

Transient Network Theory of Wormlike Micelles: Topological Force Accelerates Relaxation

A new transient network theory is developed to study the rheological properties of entangled wormlike micelles. The dynamic mechanical moduli are calculated on the basis of the model network in which local structure of the wormlike micelles is represented by the entangled loops. These loops interact with each other by statistical force due to the topological constraints. They are assumed to pass through each other within a finite time to release the internal stress (phantom chain-crossing model). The high frequency plateau modulus G(infinity) and the relaxation time tau as functions of the micellar concentration are calculated and compared with the experimental data on the aqueous solutions of cetyltrimethylammonium bromide (CTAB) mixed with ionic aromatic compound sodium salicylate (NaSal). It turns out that creation and annihilation of the entanglements are strongly coupled to the topological force. The rheological relaxation time decreases with the concentration of the micelles because the average radius (correlation length xi) of the entangled loops, and their contour length L decrease with the CTAB concentration. Hence, the topological force is amplified by the increase in the concentration and, as a result, accelerates the stress relaxation by chain-crossing.

Effect of silica colloids on the rheology of viscoelastic gels formed by the surfactant cetyl trimethylammonium tosylate

The effects of the addition of submicrometer-sized colloidal silica spheres on the linear and nonlinear rheology of semidilute solutions of a viscoelastic gel are studied. For a 1.4 wt% solution of the surfactant CTAT, a peak in the zero-shear rate viscosity η 0 is observed at approximately equal weight percents of silica and CTAT. This peak shifts to lower silica concentrations on increasing either the CTAT concentration or the surface charge on silica and disappears when the CTAT concentration is increased to 2.6 wt%. The increases in η 0 and the high frequency plateau modulus G 0 on the introduction of SiO 2 are explained by considering the increasingly entangled wormlike micelles that are formed due to the enhanced screening of the electrostatic interactions. The observed decrease in the values of G 0 and η 0 at higher concentrations of silica particles is explained in terms of the formation of surfactant bilayers due to the adsorption of the positively charged cetyl trimethylammonium to the negatively charged silica.

Hydrophobically Modified Associative Polymer Solutions: Rheology and Microstructure in the Presence of Nonionic Surfactants

We report on the rheology and morphology of a hydrophobically modified alkali-swellable emulsion (HASE) polymer solubilized in alkaline media containing nonionic surfactants. The HASE polymer consists of complex alkylaryl hydrophobes composed of oligomeric nonylphenol condensates attached to a poly(ethyl acrylate-co-methacrylic acid) backbone. The complex linear viscoelastic response of the polymer in alkaline solution suggests an unentangled network with an appreciable fraction of microgel. The concentration and hydrophile−lipophile balance (HLB) of nonionic surfactants profoundly affect the solution rheology. A surfactant of high HLB inhibits the dynamic network connectivity of the HASE polymer, as demonstrated by reductions of both the steady-shear viscosity and the dynamic storage modulus. The shear-induced structuring previously reported for this polymer is also progressively diminished as the surfactant concentration is increased. In contrast, the addition of a low-HLB surfactant promotes system structuring, as evidenced by (i) increases in the shear viscosity and the high-frequency plateau modulus and (ii) retention of the ability to undergo shear-induced structuring. We also employ cryofracture-replication transmission electron microscopy for the first time with regard to HASE associative polymers to examine the morphological characteristics of selected systems. The morphology of the HASE polymer in both latex and solubilized form appears more complex than previously anticipated, and a reasonable interpretation of these new data is provided.

Rheology of poly(methyl methacrylate- co -styrene) particles suspended in water: effects of electrostatic surface layer

Linear and nonlinear viscoelastic properties were examined for aqueous suspensions of monodisperse poly(methyl methacrylate-co-styrene) (MS) particles having the radius a 0 =45 nm and the volume fractions φ=0.428−0.448. These particles had surface charges and the resulting electrostatic surface layer (electric double layer) had a thickness of ts=5.7 nm. At low frequencies in the linear viscoelastic regime, the MS particles behaved approximately as the Brownian hard particles having an effective radius a eff=a 0 + ts, and the dependence of their zero-shear viscosity η0 on an effective volume fraction φeff (={a eff/a 0}3φ) agreed with the φ dependence of η0 of ideal hard-core silica suspensions. In a range of φeff < 0.63, this φeff dependence was well described by the Brady theory. However, the φeff dependence of the high-frequency plateau modulus was weaker and the terminal relaxation mode distribution was narrower for the MS suspensions than for the hard-core suspensions. This result suggested that the electrostatic surface layer of the MS particles was soft and penetrable (at high frequencies). In fact, this “softness” was more clearly observed in the nonlinear regime: the nonlinear damping against step strain was weaker and the thinning under steady shear was less significant for the MS suspension than for the hard-core silica suspensions having the same φeff. These weaker nonlinearities of the concentrated MS particles with φeff∼ 0.63 (maximum volume fraction for random packing) suggested that the surface layers of those particles were mutually penetrating to provide the particles with a rather large mobility.