(141d) The Effect of Branching on Shear Banding in Wormlike Micelles (WLMs) Under Large Amplitude Oscillatory Shear (LAOS)
By altering WLM solution composition or temperature, a maximum in the zero-shear viscosity, Î·0, is often observed, which corresponds to changes in micellar topology. The increase in viscosity with added surfactant or salt results from micellar growth and entanglement, whereas branching has been shown to lower Î·0  by providing another mechanism for stress relaxation. Micellar branching leads to deviations from Maxwellian behavior in the LVE rheology , and can alter or eliminate steady shear banding [2,3]. Although there are no theoretical predictions of the effects of branching on shear banding, work by Vasquez, Cook and McKinley (VCM model) has made predictions incorporating reversible chain scission that can help interpret nonlinear rheological experiments on shear banding WLMs .
The rheology and shear-induced microstructures of a model series of WLMs is studied to determine the effect of branching on shear flow phenomena. The degree of branching in the mixed cationic/anionic surfactant (CTAT/SDBS) solutions is controlled via the addition of the hydrotropic salt sodium tosylate [2, 6]. The phase behavior has been mapped extensively and we have explored the degree of branching and network formation using SANS, cryo-TEM and rheo-optical methods [2, 6-8]. The shear-induced micellar alignment is spatially and temporally characterized under steady shear, shear startup, and large amplitude oscillatory shear (LAOS) by flow-SANS in the flow-gradient (1-2) and flow-vorticity (1-3) planes. Advanced methods of time-resolved data analysis improve the resolution of the experiments by several-fold .
By employing non-linear rheological techniques with concurrent SANS, we determine rheological and scattering signatures of branching. Segmental orientation and alignment in the 1-3 and 1-2 planes is a complex function of the branching level and deformation type. Shear banding is verified in low and mildly branched solutions (â?¤0.05% NaTos), but is mitigated in highly branched solutions (â?¥0.1% NaTos). In the mildly branched solution, steady shear banding is observed between 2.6<Wi<100. Significant, discontinuous decreases in the scattering anisotropy from the inner to outer wall indicate shear banding (Wi=25, 45, 75). Similar responses at the inner and outer walls indicate shear thinning (Wi=1, 250). An alignment factor (Af) is calculated at each gap position, and when Af>0.2 at all gap positions , the material no longer shear bands. Startup measurements in both planes verify shear banding, where a long transient is observed in the Af response in the low and mildly branched solutions during banding. Differences in this transient suggest different mechanisms of banding between the solutions. No transient is observed in shear thinning conditions and in branched solutions.
Branching also inhibits shear banding under LAOS. In order to experimentally validate the predictions of the VCM model , seven LAOS conditions were examined in the mildly branched solution, of which six exhibited shear banding under steady shear. Only four conditions displayed LAOS shear banding, however. Two distinct forms of dynamic shear banding were identified by focusing on two LAOS conditions: De=0.17, Wi=75 and De=0.58, Wi=75. When De=0.17, the Af(r/H) during LAOS at Wi=75 is similar to Af(r/H) in the steady shear case, indicating a similar form of shear banding. The long oscillation period gives the material several relaxation times near the stress overshoot before reaching Wi=75, resulting in a LAOS stress that is similar to the steady shear stress at Wi=75. At De=0.58, Wi=75 a different form of shear banding is seen, where the material is trapped in a metastable banded state. The material exhibits over-orientation, where the maximum Af under LAOS is larger than in steady shear. The stress and time scales allow little time for relaxation after the stress overshoot, leading to over-orientation and a larger LAOS stress than steady shear stress. Over-orientation is also observed in the non-shear banding conditions at higher De, indicating that shear banding is not a requirement for over-orientation. Further, this over-orientation is magnified by branching.
Novel flow-SANS methods have enabled quantitative differences in branched and linear WLMs to be determined. Branching inhibits flow alignment and shear banding under both steady and dynamic (LAOS) deformations. SANS measurements during startup confirm shear banding, and suggest a different mechanism of shear banding between low and mildly branched solutions. Under LAOS, shear banding has been experimentally verified in Couette flow for the first time, in agreement with VCM model predictions . Distinct shear banding mechanisms are identified, which can be explained by analyzing LAOS time scales. In the first mechanism, the oscillation period is long and the material can relax during the cycle, leading to an alignment similar to steady shear. In the second, the over-orientation is a consequence of the faster period, and thereby incomplete relaxation during the cycle. This multi-technique approach, combining nonlinear rheology and spatially-and temporally-resolved SANS has enabled us to link the micellar microstructure and topology to the macroscopic flow properties of WLM solutions, providing a more complete data set for the development and testing of microstructure-based constitutive equations that explicitly incorporate branching and breakage.
 M. A. Calabrese, et al., J. Rheol., 59, 5 (2015).
 S. A. Rogers, M.A. Calabrese and N. J. Wagner, Curr. Opin. Colloid Interface Sci., 19, 6(2014).
 K. Hyun, et al., Prog. Polym. Sci., 36, 12 (2011).
 A. K. Gurnon, et al., J. Vis. Exp., 84 (2014).
 B. Schubert, N.J. Wagner, and E.W. Kaler, Langmuir 19, 10 (2003).
 M. A. Calabrese, et al., J. Rheol.(under review), (2016).
 M. A. Calabrese, N. J. Wagner, and S. A. Rogers, Soft Matter, (2016).
 S. J. Candau, and R. Oda, Colloid Surface A, 183 (2001).
 F. Snijkers, et al., J. Rheol., 57, 4 (2013).
 L. Zhou, L. P. Cook and G. H. McKinley, J. Non-Newton Fluid, 165, 21 (2010).
 M.E. Helgeson, et al., J. Rheol., 53, 3 (2009).