Supporting Information for. Extensional flow behavior of methylcellulose solutions containing fibrils

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1 Supporting Information for Extensional flow behavior of methylcellulose solutions containing fibrils Svetlana Morozova, 1* Peter W. Schmidt, 2* Athena Metaxas, 2* Frank S. Bates, 2 Timothy P. Lodge, 1,2 Cari S. Dutcher 3 1 Department of Chemistry, University of Minnesota, Minneapolis, MN Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, MN Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN * These authors contributed equally to this work

2 MC (DS = 1.8, M w = 530 kg/mol, Ð = 4.1) was first dried at 50 C under vacuum (~100 mtorr) for 24 hours. To prepare salt-free aqueous solutions, 0.75 or 1 g of MC were dissolved in 50 ml Milli-Q de-ionized 60 C water and stirred for 10 minutes in a 100 ml jar. The remaining quantity of the room-temperature water was then added such that the total solution weight was 100 g. The solutions were stirred at room temperature for 10 min, and then on ice for 10 min and stored at 20 C for at least 24 h. To prepare MC solutions in 8 wt% NaCl, 8 g of NaCl was dissolved along with MC in 50 ml Milli-Q de-ionized 60 C water and stirred for 10 min in a 100 ml jar. The rest of the procedure was equivalent to the salt-free solution protocol. MC solutions in 8 wt% NaCl were annealed at room temperature for 24 h prior to rheological studies. Shear and oscillatory rheology were measured on an TA Instruments AR-G2 rheometer using a 2 steel 40 mm cone and a peltier plate geometry for steady state shear flows and a DIN bob and cup geometry for oscillatory measurements. For steady state shear, the viscosity was measured after torque values reached an equilibrium for each shear rate from Hz. Two oscillatory tests were done: a temperature ramp at 1 C/min at 3% strain from 0 C to 80 C at 1 rads/s, and a rads/s frequency sweep at 3% strain every 2 h for 24 h. For capillary break-up experiments the HAAKE CaBER was used. For all experiments, 4 mm diameter plates were used at a ms strike time. The sample is first loaded between the plate at an initial separation distance of 2 mm. The plates are then rapidly separated to a final height of 8 to 9 mm with an exponentially increasing rate over 30 to 50 ms to impart a step strain on the fluid. Other conditions (e.g., longer strike times, linear strike profiles, and varied final separations) were found to result in filaments that broke up immediately after the power law decay or instabilities such as the formation of the beads on a string. After the plates come to a stop, the fluid bridge flows due to a resulting force balance between surface tension and capillary-thinning forces. The midpoint of the liquid filament diameter is recorded over time as the raw data. 1 The capillary thinning and breakup profile depend on the fluid type, and a constitutive model can be used to extract relevant extensional parameters. 2

3 For 1 wt% solutions without salt, R crit is expected to be at 0.1 mm, based on the viscosity of the solution, and the estimated Zimm time, λ " ~ $.& ' ' () * ~ 0.03 s, where η is the intrinsic +, -. / viscosity, k B is Boltzmann s constant, and N A is Avogadro s number. 2 For MC solutions in water, [η] is equal to 1100 ml/g for M w = 530 kg/mol, 3 and η s is Pa s. For lower concentrations, R crit is higher due to a decrease in viscosity. a) b) η (Pa s) wt% MC, 8 wt% NaCl wt% MC, 8 wt% NaCl 0.75 wt% MC, 8 wt% NaCl wt% MC, 8 wt% NaCl 0.5 wt% MC, 8 wt% NaCl 1 wt% MC, 0 wt% NaCl dg/ dt (1/s) 1 wt% MC, 8 wt% NaCl 1 wt% MC, 0 wt% NaCl 0.75 wt% MC, 8 wt% NaCl 0.75 wt% MC, 0 wt% NaCl Figure S1. Both shear and extensional solution properties of MC solutions change drastically with the presence of fibers formed due to the addition of 8 wt% NaCl at 25 C. a) Viscosity in a cone and plate (40 mm) geometery as a function of shear rate. For solutions with no salt (black points), only MC coils contribute to the viscosity, which exhibits shear thinning behavior at larger shear rates. With the addition of salt (hollow points), two shear thinning regions are present, one at high frequency due to shear thinning effects of MC coils, and the other at long time scales due to shear thinning effects of MC fibers. b) CaBER results for 1 wt% and 0.75 wt% with and without salt. With the addition of salt, elastic fluid properties are observed at long times. D/D t (s) 3

4 The shear behavior of MC solutions is modified by the presence of fibrils. In Figure S1, we overlay the viscosity as a function of shear rate for MC solutions at 1 wt% without added salt and 0.5 1wt % MC solutions in 8 wt% NaCl. Although highly viscous, the solutions still flow at 25 C. The 1 wt% solution without added salt shows the expected shear thinning behavior previously observed for MC solutions. At low shear rates, the viscosity asymptotes to the zero shear viscosity value of 1.6 Pa s. At high shear rates, the viscosity starts to decrease as the sample shear thins. To determine the flow behavior index, n, we fit a power law to thigher shear rate values: n-1 h = Kg! (S1) where K is the flow consistency index. Without salt, the power law index is n = For the MC solutions in 8 wt% NaCl, the flow behavior is modified. Instead of observing a constant, zero shear viscosity regime at low shear rates, we observe a second shear thinning regime for all concentrations of MC in 8 wt% NaCl. At higher shear rates, the samples shear thin in a similar way to the control (salt-free MC). The two shear thinning regimes are indicative of a mixture of high molecular weight aggregates, which are responsible for the low shear rate behavior, and free MC chains, which dictate the shear thinning at high shear rates. This behavior corroborates the oscillatory behavior from Figure 1 in the main Letter. The addition of 8 wt% salt leads to partial aggregation of free MC chains into fibrils after annealing at room temperature for 24 h. Fitting eqn S1 to both shear thinning regimes, we find that for all concentrations, the low shear rate behavior is consistent with the highest possible shear thinning, where n approaches zero. At the highest shear rates, n = 0.33, 0.36, 0.48, 0.33, and 0.55, for wt%, respectively. Overall, the presence of fibrils increases the low shear rate (0.1 s 1 ) viscosity in a dramatic way, from 1.6 Pa s to approximately 100 Pa s for the 1 wt% solution, consistent with large molecular weight anisotropic aggregates. 4

5 For 530 kg/mol MC, the overlap concentration is estimated as: c 3M w = ~ 0.1 wt% (S2) 4pN R * 3 A g where R g is the radius of gyration that depends on the number of monomers in the polymer chains (N) and the length of each polymer (b), R 6 bn :. In a CaBER experiment, as the fluid thins, the polymer chains extend, effectively lowering c*. Even for dilute and ultra-dilute concentrations, this effect leads to Rouse dynamics at the end of the flow. The polymers entangle, and beyond a dynamic correlation length, ξ, hydrodynamic interactions are screened out. Within the correlation volume, ξ 3, the chains relax as single strands. Clasen et al. 4 have hypothesized that as the concentration increases, the correlation length decreases proportionally, increasing the relaxation time: 5 -n 3n -1 x ~ bc (S3) Above c*, as the liquid bridge thins, the chains are even more concentrated, and Rouse dynamics no longer apply. Instead, Liu et al. 6 have hypothesized that the polymer chain reptate past each other. As the solution concentration increases, the reptation model dynamics are slowed considerably more than Rouse model dynamics. The chain relaxation time is: 3 æ N ö l ç (S4) ~ E l0ç è N 0 ø where λ 0 is the relaxation time of the strand within the correlation blob and N 0 is the number of monomers that makes up that strand. In this case, by noting that c*~n 1 υ and combining eqn. S3 v with the assumed molecular weight dependence of the correlation length, x ~ bn 0, we arrive at: æ c ö l ~ l0 ç è c * ø which has been previously modified to take into account contour length fluctuations: 7 æ c ö l ~ l0 ç è c * ø 3-3n 3n n 3n -1 (S5) (S6) 5

6 (1) Anna, S. L.; McKinley, G. H. Elasto-Capillary Thinning and Breakup of Model Elastic Liquids. J. Rheol. 2001, 45, (2) Rodd, L. E.; Scott, T. P.; Cooper-White, J. J.; McKinley, G. H. Capillary Break-up Rheometry of Low-Viscosity Elastic Fluids. Appl. Rheol. 2005, 15, (3) Chatterjee, T.; Nakatani, A. I.; Adden, R.; Brackhagen, M.; Redwine, D.; Shen, H.; Li, Y.; Wilson, T.; Sammler, R. L. Structure and Properties of Aqueous Methylcellulose Gels by Small-Angle Neutron Scattering. Biomacromolecules 2012, 13, (4) Clasen, C.; Plog, J. P.; Kulicke, W.-M.; Owens, M.; Macosko, C.; Scriven, L. E.; Verani, M.; McKinley, G. H. How Dilute Are Dilute Solutions in Extensional Flows? J. Rheol. 2006, 50, (5) De Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, (6) Liu, Y.; Jun, Y.; Steinberg, V. Concentration Dependence of the Longest Relaxation Times of Dilute and Semi-Dilute Polymer Solutions. J. Rheol. 2009, 53, (7) Lodge, T. Reconciliation of the Molecular Weight Dependence of Diffusion and Viscosity in Entangled Polymers. Phys. Rev. Lett. 1999, 83,