S1. Materials and Methods

Supporting Information for Formulation-Controlled Positive and Negative First Normal Stress Differences in Waterborne Hydrophobically Modified Ethylene Oxide Urethane (HEUR) - Latex Suspensions Tirtha Chatterjee, * Antony K. Van Dyk, Valeriy V. Ginzburg, Alan I. Nakatani ǁ Materials Science and Engineering, The Dow Chemical Company, Midland, Michigan 48674 Dow Coatings Materials, The Dow Chemical Company, Collegeville, Pennsylvania 19426 ǁ Analytical Sciences, The Dow Chemical Company, Collegeville, Pennsylvania 19426 *tchatterjee@dow.com S1. Materials and Methods Latex synthesis: Binder particles representative of a commercial grade latex were used for all the formulations. The latex was a single stage copolymer of butyl acrylate, methyl methacrylate, and methacrylic acid, which was thermally initiated with ammonium persulfate (APS). 1-2 This material was stabilized with 0.6% sodium lauryl sulfate (SLS, based on monomer) and the batch was neutralized with ammonia. The latex particle size was varied between 83-323 nm nominal diameters (d). The typical size polydispersity was ~ 10-15% as detected using different scattering (light and neutron) techniques and reported previously. 3-4 HEUR RM synthesis: The hydrophobically modified ethylene oxide urethane (HEUR) rheology modifiers (RMs) used in this study were synthesized from the condensation of hexamethylene diisocyanate (HDI) with poly(ethylene oxide) (PEO) diol (weight-averaged molecular weight, M w, about 8,900 g/mol) and a capping alkyl alcohol. Generally, the polymers were synthesized in a two-step process where the PEO diol, excess diisocyanate, and catalyst were first reacted to produce chain extension. After this reaction was completed, the capping alcohol was added. The hydrophobe strength was varied through the selection of the alkyl chain length of the capping alcohol and was varied between C10 and C18. The hydrophobe strength is expressed in terms of Cn which is the effective/equivalent number of methylene groups representative of the combined hydrophobic contributions of the isocyanate linker and alcohol capping agent moieties. 5-6 Sample preparation: Formulations were prepared by combining latex emulsions, HEUR solutions, surfactants (sodium lauryl sulfate) and a neutralizing agent, AMP-95 (CAS number 124-68-5), to 1

maintain a final formulation ph of 9.0 for all samples. The sodium lauryl sulfate surfactant concentration was kept fixed at 0.2% (w/w), below the critical micelle concentration, cmc, but within the range used in commercial coating formulations. The samples were prepared in 25 g batches and mixed on a Hauschild Flacktek SpeedMixer for 2 minutes. ph adjustment was done on the final sample by titrating with AMP- 95, typically around 20 mg. The latex volume fraction (φ) was varied between 0.21-0.40. The HEUR concentration (c in wt%) in the final formulation ranged in between 0.02-2.5 wt%. Table S1 gives the formulation details of the samples corresponding to Figure 2a-b in the main text. The latex surface area/rm molecule or the parameter p was derived in the following way. The available latex surface area per unit formulation mass is 6 / where the latex volume fraction and diameter are and d, respectively, and ρ is the formulation density. The number of HEUR molecules available per unit formulation mass is / where and are Avogadro s number and backbone PEO molecular weight, respectively. Hence, p or the available latex surface area/heur molecule is given as: 6 /. Note that this expression does not consider the presence of admicelles (See section S6 for more details) and assumes all HEURs are attached to the latex surface. The number of HEURs/latex is calculated as πd 2 /p. Table S1: Formulation details of the samples corresponding to Figure 2a-b. Sample code 1-5 was assigned in terms of increasing surface coverage (#1 being the least dense). Sample code VS (φ) Latex nominal diameter (d), nm HEUR Mol. Wt. (M w ), (kg/mol) Hydrophobe strength (#C) HEUR conc. (c), (wt.%) Formulation density (ρ), (g/cc) Gallery spacing (H), nm Area/ HEUR (p), nm 2 #HEURs /latex C12-1 0.21 323 35 12 0.04 1.04 168.6 589 567 - C12-2 0.28 182 20 12 0.16 1.04 69.7 184 576 - C12-3 0.4 120 35 12 1.46 1.05 27.3 76 602 + C12-4 0.28 83 35 12 2.10 1.04 31.8 54 410 + C12-5 0.28 180 35 12 1.00 1.06 68.9 51 1989 - C16-1 0.28 323 35 16 0.05 1.04 123.7 581 575 - C16-2 0.28 182 35 16 0.28 1.04 69.7 184 576 - C16-3 0.28 118 35 16 1.0 1.06 45.2 78 1924 + C16-4 0.21 120 35 16 1.0 1.06 62.6 58 786 + C16-5 0.28 178 35 16 1.0 1.06 68.2 52 560 + N 1 sign at high shear Rotating shaft experiments: For the rotating shaft test, a motor-driven variable speed stirrer (bladeless shaft) was used. The shaft (6 mm diameter) was placed so that the end of the shaft was well immersed into the formulation but well away from the sample holder bottom. The sample holder was secured by a spring-loaded chain during the experiment. This experiment is a qualitative test and still photographs of the shaft-fluid interface were collected to document the experimental outcome. Still images were first collected at rest. The shaft speed was increased in increments (700, 1400, 1800 and, 2100 RPM), and still 2

photographs were taken at each speed. The maximum shaft speed applied in this experiment was 2200 RPM. S2: The Measured N 1 Data and Shift Factors [ ] Used to Generate Figure 1b (main text) In Figure 1b, main text, the N 1 data are presented as a function of shear rate. As elucidated in the main text, the N 1 data were calculated using the following expression: Δ = 0, where is the rheometer measured first normal stress difference (after inertia correction) and 0 is a vertical shift factor. The rheometer measured data without any vertical shift [i.e. ] are presented in Figure S1a. Figure 1b, main text, is also reproduced here as Figure S1b for quick comparison. To generate Figure 1b (or S1b) the following shift factors, [ 0 ], were used: C10 based formulation: 26.1, C12 based formulation: 14.5, C14 based formulation: 9.3, C16 based formulation: -11.9, and C18 based formulation: 0.8. All values correspond to the N 1 measured at the stress, σ = 0.1 Pa except for the C10 HEUR based formulation for which N 1 value at σ = 0.5 Pa was used. (a) 200 100 Pe 10-7 10-5 10-3 10-1 10 1 φ: 0.28 c: 1.0 wt% (b) 200 100 Pe 10-7 10-5 10-3 10-1 10 1 φ: 0.28 c: 1.0 wt% N 1 (Pa) 0-100 -200 Hydrophobe (Cn) C18 C16 C14 C12 C10 N 1 (Pa) 0-100 -200 Hydrophobe (Cn) C18 C16 C14 C12 C10-300 10-4 10-2 10 0 10 2 10 4-300 10-4 10-2 10 0 10 2 10 4 Figure S1: The shear rate dependent (a) N 1 and (b) N 1 responses for the samples prepared using HEUR RMs with different hydrophobe strength (C10-C18). S3: HEUR RM Solution and Binder Latex Dispersion Rheology HEUR RM solutions and binder latex dispersions were studied to understand their normal stress behavior under high shear as limiting cases. The viscosity and N 1 behavior as a function of applied shear rate for a 1.5 wt% C16 hydrophobe HEUR RM aqueous solution is presented in Figure S2a-b. At low shear rate, a 3

Newtonian viscosity plateau was observed followed by a weak shear thickening effect and finally strong shear thinning at high shear rate. The linear viscoelasticity of the HEUR RM solution is characterized by a single-maxwellian time constant behavior where the characteristic time (τ) is ascribed to association/dissociation of a single hydrophobe to/from the associating transient network (flower micelles). 7-8 For shear rates below the characteristic time <1/, a viscosity plateau was observed. At ~1/ moderate shear-thickening was observed which is often attributed to either the finite extensible nonlinear elasticity effect 9-10 of HEUR strands, or shear-induced structural orientation (an increase in effective strand density) 11 or their combination. Finally, at very high shear rate, strong shear thinning arises from the breaking of the network into smaller fragments and individual HEUR chains. These findings are consistent with HEUR RM solution rheology previously reported. 11-14 (a) (b) 1 RM concentration 1.5 wt% 1400 1200 RM concentration 1.5 wt% 1000 η (Pa-s) N 1 (Pa) 800 600 400 200 0 0.1 1 10 100 1000 1 10 100 1000 Figure S2: (a) Steady-shear viscosity and (b) the first normal stress difference as a function of shear rate for a 1.5% C16 hydrophobe HEUR RM aqueous solution. The first normal stress difference, N 1, for the HEUR solution was ~ 0 at low shear and showed a positive value at high shear. Similar to semi-dilute polymer solution rheology, the HEUR strand/transient network alignment/stretching along the flow direction gives rise to a positive N 1. 11-13 The HEUR solution also demonstrated the shaft-climbing phenomenon in a rotating-shaft experiment (not shown). For low hydrophobe strength (C10 or C12) HEUR solutions, the algebraic sign of the N 1 could not be detected unambiguously at low concentration (c 10.0 wt%) as the longest network relaxation time is much shorter than the shear time scale <1. 13 4

An example of pure binder latex dispersion rheology is presented in Figure S3a-b. The pure latex dispersion rheology can be characterized by two dimensionless parameters: the volume fraction (φ ) signifying particle number density, and the Pèclet number =6 / signifying the competition between the Brownian and hydrodynamic forces under flow. Here η f is the fluid/matrix viscosity (0.001 Pa-s), k B is the Boltzmann constant and T is the absolute temperature. Results are shown for φ = 0.44 and 0.28 with a nominal particle diameter, d, of 120 nm and a size polydispersity 3 of ~ 13.6%. At low shear rate, viscosity appears to be diverging as the shear rate approaches zero, indicating a possible yield-stress behavior. As the shear rate is increased, one observes a strong shear thinning arising from breakup of latex particle clusters under steady shear. The flow curve data were collected only on ascending steady stress and flow hysteresis was not probed. This yield-like behavior and subsequent shear thinning were found to be much more pronounced for the denser suspension ( = 0.44). At the high shear limit, a Newtonian plateau is expected (where particles are dispersed individually), but it is beyond the highest shear rate studied here. For the suspension with = 0.28, the shear rate dependence of the viscosity was much weaker and nearly Newtonian, consistent with reported literature. 15 Note that these suspensions did not show any shear thickening (dilatancy) as the latex volume fractions were low ( < 0.5), the particles were polydisperse, and the upper stress limit studied here was presumably below the critical stress for strain-hardening. 15-17 At low shear rate (or low Pe), the latex suspensions exhibited a N 1 ~ 0 which became negative at higher shear rate or ~ 1. This behavior is similar to that predicted by Brady and coworkers 18-19 in their Stokesian Dynamics simulation of colloidal hard spheres. At low shear rate, flow causes a deviation in the position of the particles from a random distribution and the latex particles must thermally diffuse to regain positional equilibrium giving rise to a Brownian stress. The hydrodynamic stress remains low or negligible if the system maintains an overall well-dispersed state. At higher shear rate or high Pe, the hydrodynamic force brings the particles closer and hydroclusters are formed with a higher particle density along the compressional axis. As the particles get closer, the lubrication force tends to increase (scale as ~ 1/distance). Physically, the particles need to be pulled apart along the extensional axis to overcome the hydrodynamic lubrication forces (restoring effect) which results in the rheometer fixtures being pulled towards each other, or a negative N 1. In passing, we mention that recently Mari and coworkers have proposed an alternative explanation, where negative N 1 values are attributed to a transition from the flow of lubricated non-contacting particles to the flow of a frictionally contacting network of particles. 20-21 5

(a) (b) Pe Pe 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.1 0-100 η (Pa-s) 0.01 φ = 0.44 φ = 0.28 N 1 (Pa) -200-300 φ =0.44 φ = 0.28 0.001 10 0 10 1 10 2 10 3 10 4-400 -500 10 0 10 1 10 2 10 3 10 4 Figure S3: (a) Steady-shear viscosity and (b) the first normal stress difference as a function of shear rate for the latex aqueous suspensions. S4: C12 Hydrophobe HEUR-latex Formulation Rheology Measured Using Parallel Plate and Cone-and-Plate Fixtures In commercial rheometers, pressure transducers are used where the total thrust on the transducer or normal force (after area correction), F N, is recorded. For parallel plate geometry, after the inertia correction, the relation between the normal force and normal stress is given as: =.22-23 The fluids. 22-23 underlying assumption is that the F N is proportional to which is valid for second order For cone-and-plate geometry, N 1 is readily available from the measured, inertia corrected F N given as: =. 22-23 Throughout this work we assumed that for the parallel plate geometry >> or =. However, for the parallel plate measurements, it is possible that an overall negative F N may arise from a large positive N 2 contribution. In order to demonstrate the sign of F N obtained by parallel plate measurements was correct, rheological measurements using a coneand-plate fixture (25-mm plate diameter, cone angle 2 o ) were performed. The results comparing the geometry dependence of the steady shear viscosity and shear rate dependence of the normal force for the C12 HEUR-latex formulation (HEUR M w = 35 kg/mol and concentration = 1 wt%, latex volume fraction = 0.28 and nominal diameter =120 nm) are presented in Figure S4a-b. Excellent agreement in both the viscosity and F N data were found between the measurements performed using different fixtures. Similar good agreement was observed for the C10 HEUR based formulation, which is not reported here. These 6

measurements confirmed that for these samples, (a) N 2 was small or negligible; (b) for the parallel plate geometry; and (c) the observed negative F N was real and did not arise from any measurement artifacts. (a) 10 Pe 10-5 10-4 10-3 10-2 10-1 10 0 (b) 50 Pe 10-5 10-4 10-3 10-2 10-1 10 0 0 η (Pa-s) 1 0.1 φ: 0.28 c: 1.0 wt% C12 hydrophobe Fixture (dimension) parallel plate (40 mm) parallel plate (25 mm) cone & plate (25 mm) 0.01 0.1 1 10 100 1000 N 1 (Pa) -50-100 -150-200 -250 φ: 0.28 c: 1.0 wt% C12 hydrophobe Fixture (dimension) parallel plate (40 mm) parallel plate (25 mm) cone & plate (25 mm) 0.01 0.1 1 10 100 1000 Figure S4: (a) Steady-shear viscosity and (b) the first normal stress difference as a function of shear rate for a C12 HEUR-latex formulation. Another source of a negative N 1 response may arise from inertia and secondary flow contributions that arise at high Reynolds number (i.e. at high shear rate and/or for a low viscosity fluid). The Reynolds number is given as = where ρ and η are the formulation density and viscosity, respectively. Here is the shear rate at the edge of the plate where R and h are the plate diameter and gap between the plates, respectively. For rotational rheometers, secondary flows are significant when the Reynolds number, Re, is >>1.0. The largest Re achieved at the highest shear rate in our experiments was on the order of << 10.0 and therefore the secondary flow can be neglected. Further, the particle Reynolds number, = / /, ranged between 1x10-9 to 3 x 10-4 and hence Stokes flow can be assumed for the shear rate window studied here. This ensures that the inertial forces experienced by the latex particles due to advection are negligible compared to the viscous forces. All the first normal stress difference data (both the N 1 and N 1 ) reported here were corrected for inertia contribution. For two specific cases, the C10 and C12 HEUR RM based formulations, N 1 data with and without inertia correction are shown in Figure S5. Note that the inertia corrected data (solid lines with solid symbols in Figure S5) are the same that are reported in Figure S1a. The N 1 data without inertia 7

correction (dashed lines with open symbols in Figure S5) were generated using the following expression 24 : ] = ] 0.15, where, is the angular velocity calculated as =. The underlying assumptions were: (a) 2nd order fluids and (b) for parallel plate fixtures the relation between the first normal stress difference and the inertiacorrected total thrust imparted on pressure transducer is given as: =. The N 1 response was found to be enhanced when inertia correction was not applied. This was expected, as centrifugal force tends to push fluids away from the rotation axis that gives rise to a negative pressure. The shift between the data with and without inertia correction was relatively small below the shear rate ~ 1000 s -1. Beyond that inertia contribution was significant for these fluids as shown in Figure S5, but the sign of the N 1 remains unchanged. 100 0 N 1 (Pa) -100-200 -300-400 φ: 0.28 c: 1.0 wt.% C10 C10 after inertia correction without inertia correction -500 C12 C12 after inertia correction without inertia correction 10-1 10 0 10 1 10 2 10 3 10 4 Figure S5: The N 1 data as a function of shear rate for the C10 and C12 hydrophobe HEUR RM compatibilized formulations before (solid lines with solid symbols) and after (dashed lines with open symbols) inertia correction. The vertical line is drawn at shear rate 1000 s -1. S5: Linear Rheology of Selected HEUR-based Latex Suspensions: End- Hydrophobe Strength Effect The linear viscoelasticity of HEUR in pure aqueous solution has been extensively studied and reported in the literature. 7-8, 25 The dynamic viscoelasticity of the HEUR RM solution can be described using a single viscoelastic Maxwell element, where the characteristic relaxation time (τ) is ascribed to 8

association/dissociation of a single hydrophobe to/from the associating transient network (flower micelles). Annable and coworkers have shown that the relaxation time varies exponentially with endhydrophobe strength (Cn) with an activation energy increment of ~ 0.9 k B T/CH 2 group where k B is the Boltzmann constant and T is the absolute temperature. 8 Assuming that the association and dissociation rates are independent of the backbone chain length, the high frequency elastic modulus (G ) can be calculated as per the transient network theory. 26-29 In aqueous mixtures of HEURs with surfactants, these responses become more complex due to competitive micellization that impacts the HEUR bridge to loop ratio. 25 In a HEUR thickened waterborne latex suspension, the linear viscoelastic response is more complex and less understood. Multiple interactions are possible including HEUR-HEUR, HEUR-latex, HEURsurfactant and surfactant-latex interactions. Using pulsed-field gradient NMR spectroscopy, Beshah and coworkers have shown that the HEUR-latex interaction is dominant for HEUR concentrations below about 3 wt% (for a latex volume fraction 0.28 with nominal diameter 120 nm). 30 These experimental data were also supported by a simulation study reported by Ginzburg and coworkers. 31 Chatterjee and coworkers have shown that for a sufficiently high HEUR loading (above critical micelle concentration, cmc), the latex-rm combination under quiescent condition forms a spherical core-shell microstructure as revealed in small-angle neutron scattering studies. 3 On the mesoscale level, fractal aggregates are formed, where latex particles are connected through transient HEUR bridges as demonstrated by Van Dyk and coworkers through USANS. 4 These aggregates evolve under shear and the structural evolution can be reaction or diffusion limited based on latex surface chemistry and HEUR hydrophobe strength. 4 Here we briefly discuss the oscillatory shear rheology of two selected HEUR-based latex formulations (HEUR hydrophobe strength C10 and C18) under oscillatory shear. Additional linear viscoelastic data for a C12- HEUR formulated latex suspension has already been reported by Chatterjee and coworkers in an earlier publication. 3 These samples were formulated with latex volume fraction = 0.28, nominal diameter = 120 nm and a C10 or C18 hydrophobe HEUR (Mw 35 kg/mol). The HEUR concentration was the same in both samples, 0.44 wt%, slightly lower than the HEUR amount used in the sample series for which steady-shear viscosity and the first normal stress difference data are presented in Figure 1a-b (main text). A small amount of TiO 2 pigment (volume fraction 0.07) was also present in these samples. Note that Van Dyk and coworkers have previously shown that TiO 2 particles do not have any specific interaction with the HEUR molecules. 4 All measurements were performed in a stress-controlled AR-G2 rheometer (TA Instruments) at 25 o C using a 40-mm parallel plate fixture. The measurement frequency window was 100-0.1 rad/s. The oscillatory shear measurements (G, G and η* as a function of oscillation frequency (ω) are 9

presented in Figure S6a-b. Here G and G are the dynamic storage and loss moduli, respectively and η*, the magnitude component of the complex viscosity was calculated as: = ". (a) 1000 100 T=25 o C d=120 nm φ=0.28 c=0.44 wt.% (b) 100 T=25 o C d=120 nm φ=0.28 c=0.44 wt.% G' or G" (Pa) 10 η* (Pa-s) 10 1 1 0.1 C10 G' G" C18 G' G" 0.1 Hydrophobe (Cn) C10 C18 0.1 1 10 100 frequency (ω, rad/s) 0.1 1 10 100 frequency (ω, rad/s) Figure S6: (a) Dynamic storage (G ) and loss (G ) modulus as a function of oscillation frequency (ω) for two selected samples prepared using HEUR RMs with different hydrophobe strengths (C10 and C18). (b) Magnitude component of the complex viscosity as a function of oscillation frequency. Close inspection reveals that at least two major relaxation time scales are associated with these systems. The shorter of these two timescales is attributed to characteristic time scale of HEUR loop/bridge relaxation from the latex surface. Note that for these formulations predominantly HEUR loops or direct bridges between the latex particles (with very few micelles or free HEUR in solution) are expected as per the PFGNMR 30 and simulation 31 study. The bridge/loop relaxation was only observed for the C18 hydrophobe formulated system (at ω ~ 20 rad/s, shown by a blue vertical line in Figure S6a) while for the C10 hydrophobe it is expected to occur at much higher frequency. The second, longer timescale is attributed to HEUR-mediated latex cluster relaxation that was only found for the C10 formulated system within the measurement frequency window (at ω ~ 0.15 rad/s, shown by a black vertical line in Figure S6a). For other HEUR based formulations, this relaxation is expected to occur at a longer timescale or lower frequency, well below the lower bound of the measured frequency. None of these formulations demonstrated the standard single Maxwell element relaxation at low frequency (i.e. G ~ ω 2 and G ~ω as ω 0). Using these two selected samples, we show that the linear viscoelastic response of the HEURthickened latex suspension is determined by both the relaxation of HEUR molecules attached to the latex surface and (HEUR-mediated) latex cluster relaxations. Further experimental studies on linear viscoelasticity and theoretical model development are currently ongoing in our laboratory. 10

S6: HEUR Adsorption onto Latex Surfaces Adsorption of HEUR molecules onto latex surfaces depends on a number of factors, such as the HEUR molecular weight, hydrophobe type, and the surfactant coverage of the latex surface. 31-33 These factors dictate the maximum (saturation) surface coverage on the latex, often expressed as an adsorbed amount (in mg/m 2 ) or the density of adsorbed chains (chains/nm 2 ). As shown in our recent paper, 31 for HEURs with C8, C12, and C16 hydrophobes, most HEURs tend to adsorb directly onto the surface until saturation is reached; after that, adsorption takes place indirectly, in the form of adsorbed micelles ( admicelles ) that promote indirect bridging between neighboring latex particles. The ratio of all available HEURs (per unit latex surface) to the maximum direct adsorption coverage can be estimated as: =, the latex surface area per adsorbed HEUR molecule is given by, =6, and saturation coverage, =, with the maximum adsorbed amount, MAA 1.0 2.0 mg/m2. 31-32 For the formulations in this study, we assume a value for MAA = 1.5 mg/m 2. For systems with X < 1, almost all the HEURs should be able to adsorb directly onto the latex surfaces. Thus, the overall systems should behave as dispersions of soft or fuzzy spheres with little or no bridging or viscoelasticity. Note that if X<<1 and steric/electrostatic stabilization is insufficient, the binder particles would form large aggregates. In these cases, the overall behavior would be that of a particle dispersion in water, and thus, N 1 is expected to be negative. For larger X, a large fraction of HEURs would not adsorb directly to the latex and would form admicelles instead. Those admicelles would be weakly adsorbing to the particles and would promote formation of transient bridges between particles. In that case, the overall rheological behavior would be more similar to that of a transient network solution, leading to positive N 1. References 1. Even, R. C.; Slone, R. V. Coating Method. US Patent 6524656 B2, 2003. 2. Li, Z. F.; Van Dyk, A. K.; Fitzwater, S. J.; Fichthorn, K. A.; Milner, S. T., Atomistic Molecular Dynamics Simulations of Charged Latex Particle Surfaces in Aqueous Solution. Langmuir 2016, 32 (2), 428-441. 3. Chatterjee, T.; Nakatani, A. I.; Van Dyk, A. K., Shear-Dependent Interactions in Hydrophobically Modified Ethylene Oxide Urethane (HEUR) Based Rheology Modifier-Latex Suspensions: Part 1. Molecular Microstructure. Macromolecules 2014, 47 (3), 1155-1174. 4. Van Dyk, A. K.; Chatterjee, T.; Ginzburg, V. V.; Nakatani, A. I., Shear-Dependent Interactions in Hydrophobically Modified Ethylene Oxide Urethane (HEUR) Based Coatings: Mesoscale Structure and Viscosity. Macromolecules 2015, 48 (6), 1866-1882. 11

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