Polyelectrolyte complexes are a fascinating class of soft materials that can span the full spectrum of mechanical properties from low-viscosity fluids to glassy solids. This spectrum can be accessed by modulating the extent of electrostatic association in these complexes. However, to realize the full potential of polyelectrolyte complexes as functional materials, their molecular level details need to be clearly correlated with their mechanical response. The present work demonstrates that by making simple amendments to the chain architecture, it is possible to affect the salt responsiveness of polyelectrolyte complexes in a systematic manner. This is achieved by quaternizing poly­(4-vinylpyridine) (QVP) with methyl, ethyl, and propyl substituentsthereby increasing the hydrophobicity with increasing side chain lengthand complexing them with a common anionic polyelectrolyte, poly­(styrene­sulfonate). The mechanical behavior of these complexes is compared to the more hydrophilic system of poly­(styrene­sulfonate) and poly­(diallyldimethyl­ammonium) by quantifying the swelling behavior in response to salt stimuli. More hydrophobic complexes are found to be more resistant to doping by salt, yet the mechanical properties of the complex remain contingent on the overall swelling ratio of the complex itself, following near universal swelling–modulus master curves that are quantified in this work. The rheological behaviors of QVP complex coacervates are found to be approximately the same, only requiring higher salt concentrations to overcome strong hydrophobic interactions, demonstrating that hydrophobicity can be used as an important parameter for tuning the stability of polyelectrolyte complexes in general, while still preserving the ability to be processed “saloplastically”.

Cellulose derivatives containing associating hydrophobic groups along their hydrophilic backbone are used as rheology modifiers in the formulation of water-based spray paints, medicinal sprays, cosmetics and printable inks. Jetting and spraying applications of these materials involve progressive thinning and break-up of a fluid column or sheet into drops. Strong extensional kinematics develop in the thinning fluid neck. In viscous Newtonian fluids, inertial and viscous stresses oppose the surface tension-driven instability. In aqueous solutions of polymers such as Ethyl Hydroxy-Ethyl Cellulose (EHEC), chain elongation provides additional elastic stresses that can delay the capillary-driven pinch-off, influencing the sprayability or jettability of the complex fluid. In this study, we quantify the transient response of thinning filaments of cellulose ether solutions to extensional flows in a Capillary Break-up Extensional Rheometer (CaBER) and in a forced jet undergoing break-up using Rayleigh Ohnesorge Jetting Extensional Rheometry (ROJER). We also characterize the steady state molecular deformations using measurements of the flow-induced birefringence and excess pressure drop in an extensional stagnation point flow using a Cross-Slot Extensional Rheometer (CSER). We show that under the high extension rates encountered in jetting and spraying, the semi-dilute solutions of hydrophobically modified ethyl hydroxy-ethyl cellulose (hmEHEC) exhibit extensional thinning, while the unmodified bare chains of EHEC display an increase in extensional viscosity, up to a plateau value. For both EHEC and hmEHEC dispersions, the low extensibility of the cellulose derivatives limits the Trouton ratio observed at the highest extension rates attained (close to 10(5) s(-1)) to around 10-20. The reduction in extensional viscosity with increasing extension rate for the hydrophobically modified cellulose ether is primarily caused by the disruption of a transient elastic network that is initially formed by intermolecular association of hydrophobic stickers. This extensional thinning behavior, in conjunction with the low extensibility of the hydrophobically modified cellulose ether additives, makes these rheology modifiers ideal for controlling the extensional rheology in formulations that require jetting or spraying, with minimal residual stringiness or stranding.

The extensional rheological properties of dilute polymer solutions play a dominant role in many commercial processes such as air-assisted atomization. This is a high deformation rate process important in application of diverse materials such as paints, fertilizer sprays and delivery of airborne drugs. Dilute polymeric solutions which have identical values of high shear-rate viscosity (HSV) often exhibit different values of Sauter Mean Diameter (SMD) in their spray size distributions as a result of differing extensional rheological properties. We explore the atomization of a series of model Poly(ethylene oxide) (PEO) solutions dissolved in water/glycerol mixtures. Each solution is sprayed with an air-assisted spray gun under similar conditions and imaged with a commercial spray measurement system. The values of HSV for PEO solutions are close to the solvent viscosity and matched to those of typical ink or paint samples. The surface tensions of the fluids are also tuned to be very similar, however both the SMD and the droplet size distribution change considerably. For the highest molecular weight PEO systems, interconnected beads-on-string structures are observed at different positions of the spray fan. Capillary Break-up Extensional Rheometry (CaBER) can be used to measure the extensional properties of the more viscous solutions, but the well-known limitations of this approach include inertially-induced asymmetries, gravitational sagging and the very short filament lifetimes of low viscosity samples all of which constrain the range of relaxation times that can be probed. Consequently we also explore the use of Rayleigh Ohnesorge Jet Elongational Rheometry (ROJER) to probe the extensional response of these viscoelastic solutions at realistic timescales and deformation rates. A cylindrical liquid jet is excited by a piezo-actuator at a known frequency as it exits a micromachined nozzle, and stroboscopic imaging provides high temporal and spatial resolution in the break-up process. Analyzing the evolution in the jet diameter before break-up enables meaningful measurement of relaxation times down to values as small as 60 microsecond, and these values can be directly correlated with the differences in the final spray size distributions and the mean diameters. We outline a simple model for the fluid dynamics of the thinning filaments close to breakup that accurately describes the variation of the average droplet diameter as a function of the elongational relaxation time measured for each fluid. in their spray size distributions as a result of di↵ering extensional rheological properties. Studying the E↵ects of Elongational Properties onWe explore the atomization of a series of model Poly (

Polymer gels behave as soft viscoelastic solids and exhibit a generic nonlinear mechanical response characterized by pronounced stiffening prior to irreversible failure, most often through macroscopic fractures. Here, we aim at capturing the latter scenario for a protein gel using a nonlinear integral constitutive equation built upon (i) the linear viscoelastic response of the gel, here well described by a power-law relaxation modulus, and (ii) the nonlinear viscoelastic properties of the gel, encoded into a "damping function". Such formalism predicts quantitatively the gel mechanical response to a shear start-up experiment, up to the onset of macroscopic failure. Moreover, as the gel failure involves the irreversible growth of macroscopic cracks, we couple the latter stress response with Bailey's durability criterion for brittle solids in order to predict the critical values of the stress σc and strain γc at the failure point, and how they scale with the applied shear rate. The excellent agreement between theory and experiments suggests that the crack growth in this soft viscoelastic gel is a Markovian process, and that Baileys' criterion extends well beyond hard materials such as metals, glasses, or minerals.

The breakup and atomization of complex fluids can be markedly different than the analogous processes in a simple Newtonian fluid. Atomization of paint, combustion of fuels containing antimisting agents, as well as physiological processes such as sneezing are common examples in which the atomized liquid contains synthetic or biological macromolecules that result in viscoelastic fluid characteristics. Here, we investigate the ligament-mediated fragmentation dynamics of viscoelastic fluids in three different canonical flows. The size distributions measured in each viscoelastic fragmentation process show a systematic broadening from the Newtonian solvent. In each case, the droplet sizes are well described by Gamma distributions which correspond to a fragmentation-coalescence scenario. We use a prototypical axial step strain experiment together with high-speed video imaging to show that this broadening results from the pronounced change in the corrugated shape of viscoelastic ligaments as they separate from the liquid core. These corrugations saturate in amplitude and the measured distributions for viscoelastic liquids in each process are given by a universal probability density function, corresponding to a Gamma distribution with n min ¼ 4. The breadth of this size distribution for viscoelastic filaments is shown to be constrained by a geometrical limit which can not be exceeded in ligament-mediated fragmentation phenomena.