Formulation-Controlled Positive and Negative First Normal Stress

Letter pubs.acs.org/macroletters

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,† and Alan I. Nakatani§ †

Materials Science and Engineering, The Dow Chemical Company, Midland, Michigan 48674, United States Dow Coatings Materials, The Dow Chemical Company, Collegeville, Pennsylvania 19426, United States § Analytical Sciences, The Dow Chemical Company, Collegeville, Pennsylvania 19426, United States ‡

S Supporting Information *

ABSTRACT: Hydrophobically modified ethylene oxide urethane (HEUR) associative thickeners are widely used to modify the rheology of waterborne paints. Understanding the normal stress behavior of the HEUR-based paints under high shear is critical for many applications such as brush drag and spreading. We observed that the first normal stress difference, N1, at high shear (large Weissenberg number) can be positive or negative depending on the HEUR hydrophobe strength and concentration. We propose that the algebraic sign of the N1 is primarily controlled by two factors: (a) adsorption of HEURs on the latex surface and (b) the ability of HEURs to form transient molecular bridges between latex particles. Such transient bridges are favored for dispersions with small interparticle distances and dense surface coverages; in these systems; HEUR-bridged latex microstructures flow-align in high shear and exhibit positive N1. In the absence of transient bridges (large interparticle distances, low surface coverage), the dispersion rheology is similar to that of weakly interacting spheres, exhibiting negative N1. The results are summarized in a simplified phase diagram connecting formulation, microstructure, and the N1 behavior.

C

latex surfaces6 and are not displaced by shear.7 At sufficiently high HEUR loading, the latex-RM combination forms a spherical core−shell microstructure as shown in our previous small-angle neutron scattering study under shear (rheoSANS).7 On the mesoscale level, the scattering study revealed that fractal aggregates are formed where latex particles are connected through transient HEUR bridges.8,9 These aggregates evolve under shear and the energy dissipation from drag on transient latex aggregates is the predominant mechanism of viscosity (η) increase.9 The shear rate (γ̇) dependence of the paint elasticity specifically, the first normal stress difference (N1), is much less understood. Enhanced understanding, however, is important for application properties such as roller texture, paint spreading, roller tracking, and appearance, as suggested by Glass.13,14 In this work, we demonstrate that N1 of HEUR-based paints at high shear can be positive or negative depending on the HEUR hydrophobe strength and concentration. These findings are explained based on the microstructure, specifically by the probability of transient bridge formation and bridge lifetime. Finally, a simplified phase

ommercial paints are complex formulations of polymeric binders, inorganic pigments, colorants, dispersants, surfactants, rheology modifiers (RM), and other additives. Hydrophobically modified ethylene oxide urethane (HEUR) RMs are widely used as thickeners in the coatings industry.1,2 HEURs are generally telechelic nonionic polymers with a poly(ethylene oxide) (PEO) backbone end-capped by alkyl hydrophobes. The strength of the hydrophobe is often expressed as Cn, where n is the equivalent number of methylene groups that represents the combined hydrophobic contributions of the isocyanate linker and alcohol capping agent moieties.3 The n value typically ranges from 8 to 24. A significant volume of work on HEUR-based paint viscosity under simple shear flow is available in the literature4,5 and new understanding6−9 continues to evolve. In a paint formulation, HEUR polymers largely interact with the binder latex particles and their interaction with pigment (TiO2) particles was found to be negligible.10 Even above the HEUR critical micelle concentration (cmc), the HEUR interaction with the latex is energetically favored over inter-HEUR and surfactant-latex interactions, as revealed by pulsed-field gradient nuclear magnetic resonance (PFGNMR) spectroscopy and simulation studies.6,8,11,12 Therefore, for the relevant concentration range, most of the HEUR hydrophobes preferentially adsorb to the © 2017 American Chemical Society

Received: March 7, 2017 Accepted: June 14, 2017 Published: June 21, 2017 716

DOI: 10.1021/acsmacrolett.7b00174 ACS Macro Lett. 2017, 6, 716−720

Letter

ACS Macro Letters

Figure 1. (a) Viscosity and (b) the first normal stress difference (ΔN1) as a function of shear rate and Pe for the samples prepared using HEUR RMs with different hydrophobe strength (C10−C18). The measured N1 data along with the N1(γ̇ → 0) values used to generate Figure 1b are available in the Supporting Information. (c−f) Still photographs of formulations under shear. Vortex formation or shaft-climbing phenomena are marked with arrows. These photographs were taken at a shaft rotational speed of 1800 rpm.

such a fluid would show a shaft-climbing phenomenon known as the Weissenberg effect.15 A negative N1 pulls the fixtures together and exhibits vortex formation in the rotating-shaft experiment.15 The η and N1 responses on a series of formulations differing only in their hydrophobe strength (C10−C18) are reported in Figure 1a,b. All the other formulation variables were kept constant (d = 120 nm, ϕ = 0.28, HEUR Mw = 35 kg/mol, and c = 1.0 wt %). All the formulations demonstrated similar shearthinning viscosity profiles (Figure 1a) largely differing in absolute values and an earlier onset of shear thinning as hydrophobe strength increases. In Figure 1b, the N1 values at high shear (large Weissenberg number, Wi = γ̇τ ≫ 1, where τ is a characteristic viscoelastic relaxation time) were found to be positive for the samples formulated with C16−C18 hydrophobes and negative for the samples formulated with C10−C12 hydrophobes HEURs. For the sample formulated with the C14 hydrophobe, the N1 changed sign, going from negative (intermediate γ̇) to positive (high γ̇). For the C12 hydrophobe formulated system, excellent agreement was found between the parallel plate and cone-and-plate measurements (both η and N1) ruling out the possibility of a negative N1 arising from measurement artifacts (Supporting Information). Further, the sign of the N1 was visually verified through rotating-shaft experiments as presented in Figure 1c−f. Consistent with rheological measurements, formulations with a positive N1 demonstrated the shaft-climbing phenomenon, and formulations with a negative N1 exhibited the formation of a vortex around the rotating shaft. The hydrophobe-strength dependent viscosity profiles (Figure 1a) can be explained by latex-HEUR interactions. The latex-RM binding energy increases by roughly 1 kBT per CH2 group,16 and hence, the transient bridge lifetime becomes longer as hydrophobe strength increases. In addition, the cmc of the HEUR polymers decreases as Cn increases, which increases the probability of indirect bridge formation through admi-

diagram is presented connecting the algebraic sign of the N1 at high shear and formulation compositions. The waterborne formulations used in this study were primarily made of binder particles, HEUR RMs and surfactants. For simplicity, pigment (TiO2) particles were not used in this study. The major compositional variables were the nominal diameter of the latex (d), the volume fraction of latex (ϕ), the HEUR concentration (c), hydrophobe strength (Cn), and the backbone PEO weight-average molecular weight (Mw; see the Supporting Information for more details). All rheological measurements were performed on a stress controlled AR-G2 rheometer (TA Instruments) primarily using a 40 mm diameter, parallel plate fixture. For selected cases, 25 mm parallel plate and cone-and-plate (cone angle 2°) fixtures were also used. The lower plate was a temperature controlled Peltier plate and the test temperature was maintained at 298 K. Both η and N1 were monitored as a function of applied stress, σ (varied between 0.1 and 1000 Pa), and reported as a function of shear rate (γ̇) calculated using the following expression: η = σγ̇. For the parallel plate geometry, N1 − N2 is measured, whereas for the cone-and-plate geometry, N1 is measured directly, where N1 = σ11 − σ22 and N2 = σ22 − σ33, and the σiis are the diagonal components of the stress tensor. The coordinates 1, 2, and 3 represent the direction of shear (flow), direction transverse to the flow in the shear plane (velocity gradient), and direction perpendicular to flow but parallel to shear plane (vorticity), respectively. Throughout this work we assumed that for parallel plate measurements |N1| ≫ |N2| and reported data in the form of ΔN1(γ̇), where ΔN1(γ̇) = N1(γ̇) − N1 (γ̇ → 0) and N1(γ̇ → 0) was the N1 measured at the γ̇ for which σ = 0.1 Pa. Further, selected formulations were subjected to rotating-shaft tests, details of which are provided in the Supporting Information. According to the sign convention used here, a positive N1 indicates that the thrust of fluids exerted on the transducer under steady shear is acting to separate the fixtures from each other (i.e., a tensile force).15 In a rotating-shaft experiment, 717

DOI: 10.1021/acsmacrolett.7b00174 ACS Macro Lett. 2017, 6, 716−720

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ACS Macro Letters celles.8 Therefore, for formulations with the same ϕ, d, Mw, and c values, increasing the hydrophobe strength leads to higher values of the low-shear viscosity and a decrease of the shear rate for the onset of shear thinning (longer characteristic time). The change in sign of high-shear N1 was further investigated by formulating a series of samples using either a C12 or C16 hydrophobe HEUR (formulations details are provided in Table S1 in the Supporting Information). The formulations can be described in terms of two derived parameters−the average distance between the particle surfaces or gallery spacing, H (nm), and the latex surface area per HEUR molecule, p (nm2). Assuming a uniform distribution of unimodal spherical particles ⎡ π 1/3 ⎤ − 1⎥, and and uniform surface coverage, H = d⎢ 3 2 ϕ ⎣ ⎦

(p values were 76 and 51 nm2 for the C12−3 and −5, respectively). This is presumably due to a shorter gallery spacing in the C12−3 (27.3 nm) compared to C12−5 (68.9 nm). For the second pair (C16−2 and −5), the H values were nearly similar (69.7 nm for the C16−2 and 68.2 nm for the C16−5). However, the surface coverage was much denser for the C16−5 (52 nm2) compared to the C16−2 (184 nm2). In this case, the C16−2 sample exhibited a negative N1 compared to C16−5, which showed a positive N1 at high shear. To the best of our knowledge, a change in the N1 sign as a function of HEUR hydrophobe strength, molecular weight or concentration is unusual and has not been reported. Previously, a transition from a positive to a negative N1 as a function of formulation change was reported when noncolloidal microspheres were introduced to poly(dimethylsiloxane).17 The formulations studied here can broadly be classified as associative polymer mediated colloidal suspensions. Therefore, it is relevant to discuss two limiting cases: (a) pure HEUR RM solutions and (b) pure latex suspensions. A C16 hydrophobe HEUR aqueous solution (1.5 wt %) demonstrated a positive N1 at high shear (Supporting Information), consistent with literature reports.18,19 The HEUR solution rheology can be characterized by a single time constant Maxwellian behavior20 and a positive N1 arises from alignment/stretching of the HEUR network along the flow direction that does not relax on the shear time scale. It is hard to determine the sign of the N1 for a low concentration (c < 10 wt %) C10 or C12 hydrophobe HEUR solution as the characteristic network relaxation time is much shorter than shear time scale.18 Latex suspension rheology can be characterized by two dimensionless parameters: volume fraction, ϕ, and Pèclet ⎡ ⎤ d 3 number ⎢Pe = 6πηf γ ̇ 2 /(kBT )⎥, which signifies the com⎣ ⎦

( )

p=

6ϕM w , NAcdρ

where NA is Avogadro’s number and ρ is the

formulation density. Note that a smaller p corresponds to a denser surface coverage. The shear-rate dependent N1 data are presented in Figure 2a,b. It was found that for the two different Cn studied (C12 or C16), the sign of N1 at high shear rate could be positive or negative, depending on H and p. Comparisons of two pairs of samples, C12−3 and −5 and C16−2 and −5, are particularly instructive. In the first case, C12−3 showed a positive N1, while C12−5 showed a negative N1, even when the surface coverage was denser for the C12−5

()

petition between the Brownian and hydrodynamic forces under flow. Here ηf is the fluid/matrix viscosity (=0.001 Pa·s), kB is Boltzmann’s constant, and T is the absolute temperature. The pure latex suspensions demonstrated N1 ∼ 0 at Pe ≪ 1.0, which becomes negative at Pe ∼ 1.0 (Supporting Information). These findings are consistent with the reported experimental21 and computational22,23 results. At high shear, an anisotropic microstructure is formed where neighboring particles concentrate along the compressional axis in the shear plane.23 As a consequence, the hydrodynamic contribution to the stress increases when the lubrication force diverges as the particle surfaces come into contact. At Pe ∼ 6(1) the negative N1 contribution from the hydrodynamic force overcomes the positive N1 contribution from the Brownian forces and an overall negative N1 is realized.21,24 In the light of these limiting conditions, it appears that depending on the hydrophobe strength, Mw, and the overall formulation composition, the HEUR-latex dispersion elasticity at high shear can either be colloidal suspension (hard sphere)like (negative N1) or HEUR solution-like (positive N1). In our case, such a transition was observed by either varying the hydrophobe strength while keeping the H and p parameters the same (Figure 1b) or by varying the H and p parameters for the same hydrophobe strength (Figure 2a,b). Note that when N1 was plotted as a function of Pe (calculated using the latex diameter only and neglecting the adsorbed HEUR shell contributions), the transition (from zero to positive or negative N1) was observed at Pe < 1.0 (Figure 1b). This suggests that the

Figure 2. First normal stress difference as a function of shear rate for the samples formulated using (a) C12 and (b) C16 hydrophobe HEUR RMs. For sample details, see Table S1 (Supporting Information). Sample codes 1−5 were assigned in terms of increasing surface coverage (#1 being the least dense). 718

DOI: 10.1021/acsmacrolett.7b00174 ACS Macro Lett. 2017, 6, 716−720

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ACS Macro Letters N1 behavior is governed by shear-induced changes within the large-scale HEUR-latex microstructure. To explain these findings, we focus on the influence of hydrophobe strength and the H and p parameters on the formulation microstructure as it deforms under shear in terms of two dimensionless parameters, H/2Ree and psat/p. Here, Ree is the root-mean-square end-to-end distance of HEUR chain calculated as Ree = √(Nb2), N and b are the number and length of the Kuhn unit, respectively (for PEO, N = Mw/137 and b = 1.1 nm).25 The value of psat is the estimated area per adsorbed HEUR chain at maximum surface saturation (see the Supporting Information for more details). The dimensionless variable, H/2Ree, is thus related to the formation of conformationally relaxed HEUR bridges between latex particles (H/2Ree < 1.0 for the relaxed conformation). The physical interpretation of the psat/p parameter is the morphology of the adsorbed layer (isolated “mushroom” structures for psat/p ≪1, and a thick brush with some hydrophobes unable to attach to the surface for psat/p ∼ 1). A phase diagram is constructed which summarizes our experimental results in Figure 3 by plotting

particles and HEURs jointly forming a transient network. In cases where psat/p is sufficiently large, as shown in numerical simulation,8 there are many hydrophobes available to form transient bridges, and the associated conformational penalty is relatively small. This, in our view, promotes multiple-strand large-scale bridge formation. The lifetimes of these bridges, τ, are orders of magnitude higher than the typical HEUR−HEUR interaction time scale, as shown in simulation11 studies and linear viscoelastic measurements presented in Supporting Information. In high shear (i.e., Wi = γ̇τ ≫ 1.0), these bridges stretch, forming anisotropic clusters aligned along the flow direction. Interestingly, in certain cases, the normal stress difference was found to change sign, going from negative (at intermediate γ̇) to positive (at high γ̇), indicating a rearrangement of transient networks as a function of shear (for example, see C14 HEUR rheology in Figure 1b). This behavior is referred to as N1-inversion (N1-inv) in Figure 3. It should be taken into account that HEUR-latex systems usually demonstrate multiple relaxations (Figure S6, Supporting Information) and that these relaxation modes are quite broad in nature. Therefore, continuous evolution of structure (loop to bridge ratio as a function of applied shear) is likely to contribute to the N1-inversion behavior. At high shear, as particles come closer, it is easier to form transient bridges that may lead to the N1 signinversion. The above analysis does not fully capture the influence of the hydrophobe strength since H/2Ree and psat/p do not depend on it explicitly. As seen in Figure 1b, increasing Cn from 12 to 14 can produce a transition from negative to positive N1. The systems described in Figure 1 all happen to lie on the phase boundary (red line in Figure 3). We therefore hypothesize that while bridges are formed for all systems considered in Figure 1, they are easily broken under shear in the case of smaller hydrophobes (C10 and C12) yet are able to withstand the shear for the case of larger hydrophobes (C14−C18). In other words, for smaller hydrophobes, bridges relax faster compared to the stretching time scale, while for larger hydrophobes, they stretch prior to relaxation. In conclusion, this phase diagram suggests that HEUR-based formulation nonlinear elasticity (N1) is controlled by two factors: (a) adsorption of HEURs onto particles and (b) ability of HEURs (directly adsorbed and admicelles) to form transient bridges between latex particles with HEUR shells. By controlling these two factors through formulation composition, one can design paints with targeted N1 behavior.

Figure 3. Phase diagram showing the algebraic sign of the N1 as a function of formulation composition expressed in terms of normalized parameters. Markers represent the sign of N1 at high shear observed in rheological experiments. Schematics of microstructures associated with different N1 behavior are presented as insets. The region colored red and labeled “Un” corresponds to formulation space that is generally unstable and prone to phase separation.

the algebraic sign of the N1 in terms of H/2Ree and psat/p. At small psat/p (low HEUR concentration) and low H/2Ree (high latex volume fraction), dispersions are known to be unstable.26 Going to larger psat/p and/or H/2Ree, we see a clear demarcation between the regions with negative N1 (above the red line) and positive N1 (below the red line). Below, we outline our hypothesis describing this phase behavior in terms of microstructure. The demarcation corresponds to the point presumably where the adsorbed HEURs begin to form brushes on the surfaces, and there are sufficient “dangling” hydrophobes present to form transient bridges between HEUR-covered latex particles. The negative N1 behavior corresponds to the case where the lack of “free” or “dangling” HEUR chains and large interparticle distances prevents formation of dynamic transient bridges between latex particles. In this case, latex surfaces are “patchy” (nonuniformly covered by adsorbed HEURs) and often can flocculate into large aggregates. At high shear, these aggregates break and the hydrodynamic contribution (arising from large lubrication stress) dominates, giving rise to an overall negative N1. The positive N1 behavior, on the other hand, is indicative of

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.7b00174. Additional experimental details, selected linear and nonlinear rheology data, inertia correction of N1 data, and psat calculation (PDF).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Tirtha Chatterjee: 0000-0003-2104-5235 Valeriy V. Ginzburg: 0000-0002-2775-5492 719

DOI: 10.1021/acsmacrolett.7b00174 ACS Macro Lett. 2017, 6, 716−720

Letter

ACS Macro Letters Notes

(19) Suzuki, S.; Uneyama, T.; Inoue, T.; Watanabe, H. Nonlinear Rheology of Telechelic Associative Polymer Networks: Shear Thickening and Thinning Behavior of Hydrophobically Modified Ethoxylated Urethane (HEUR) in Aqueous Solution. Macromolecules 2012, 45 (2), 888−898. (20) Annable, T.; Buscall, R.; Ettelaie, R.; Whittlestone, D. The Rheology of Solutions of Associating Polymers - Comparison of Experimental Behavior with Transient Network Theory. J. Rheol. 1993, 37 (4), 695−726. (21) Stickel, J. J.; Powell, R. L. Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 2005, 37, 129−149. (22) Bergenholtz, J.; Brady, J. F.; Vicic, M. The non-Newtonian rheology of dilute colloidal suspensions. J. Fluid Mech. 2002, 456, 239−275. (23) Foss, D. R.; Brady, J. F. Structure, diffusion and rheology of Brownian suspensions by Stokesian Dynamics simulation. J. Fluid Mech. 2000, 407, 167−200. (24) Cwalina, C. D.; Wagner, N. J. Material properties of the shearthickened state in concentrated near hard-sphere colloidal dispersions. J. Rheol. 2014, 58 (4), 949−967. (25) Rubinstein, M.; Colby, R. H. Polymer Physics, 1st ed.; Oxford University Press, 2003. (26) Kostansek, E. Using dispersion/flocculation phase diagrams to visualize interactions of associative polymers, latexes, and surfactants. J. Coat. Technol. 2003, 75 (940), 27−34.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Drs. James Bohling and John Rabasco for latex and HEUR synthesis, respectively. We acknowledge many Dow colleagues and Prof. Ronald G. Larson for insightful discussions. Dow Coatings Materials, a business unit of The Dow Chemical Company, supported this research.

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REFERENCES

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DOI: 10.1021/acsmacrolett.7b00174 ACS Macro Lett. 2017, 6, 716−720