Polymers as Rheology Modifiers - American Chemical Society

Chapter 13

Steady-Shear and Linear-Viscoelastic Material Properties of Model Associative Polymer Solutions

Downloaded by UNIV OF ARIZONA on August 6, 2012 | http://pubs.acs.org Publication Date: May 13, 1991 | doi: 10.1021/bk-1991-0462.ch013

R. D. Jenkins, C. A. Silebi, and M . S. El-Aasser Department of Chemical Engineering and Emulsion Polymers Institute, Lehigh University, Bethlehem, PA 18015

Model associative polymers, whose structure consists of linear water-soluble poly(oxyethylene) backbones of number average molecular weight 16600-100400 with hydroxyl, dodecyl, or hexadecyl endgroups, are used to investigate the relationships between associative polymer structure and solution rheology. The steady shear viscosity profiles of solutions of model associative polymers with hexadecyl hydrophobic endgroups exhibit shear-thickening and shear-thinning regions that result from the extension and break-up of a dynamic association network under shear. These solutions are linearly viscoelastic with a well defined characteristic relaxationtimeconstant, and exhibit an entanglement plateau in the storage modulus, which is interpreted as the pseudo-equilibrium modulus of the solution. The rheological properties of these solutions scale with a quantity we define as the molar density of association, which is calculated from the pseudo-equilibrium modulus of the solution. Physical interpretation of therheologicaldata yields a qualitative picture of the association mechanism. Until the early 1980's, the predominant commercial rheology modifiers for latex paints were high molecular weight cellulose derivatives. However, undesirable application characteristics, such as roller spatter and the inability of cellulose derivatives to simultaneously produce the proper high shear and low shear viscosities in latex paints, prompted die development of associative polymers. Associative polymers improve the application characteristics of paints over those achieved through the use of cellulose derivatives by providing: better flow and leveling; and superior film build in pad, brush, or roller application; improved spray pattern and bubble release; reduced roller spatter, and the ability to simultaneously achieve these properties through the judicious use of surfactants and cosolvents. The literature contains a compilation of other advantages and comparisons between the performance of associative polymers and cellulose derivatives in paint formulations. (1-2)

0097-6156/91/0462-0222$06.00/0 © 1991 American Chemical Society

In Polymers as Rheology Modifiers; Schulz, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.


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Properties of Model Associative Polymer Solutions223

As a first approach to understanding the association mechanism, researchers examined latex systems containing commercially available associative polymers. Unfortunately, the use of commercial associative polymers obscured the fundamental relationship between polymer structure and rheological properties because the polymers have a distribution of molecular weights and structures and are shipped dispersed in water/cosolvent mixtures. For example, Glass et al. (3-6) studied commercial polymers made by several different manufacturers to determine the effect of the following parameters on the rheological properties of coatings: polymer molecular weight and structure, latex type and size distribution, pigment volume concentration, and surfactant concentration. Their work focused on fully formulated coatings to highlight the numerous interactions possible among formulation components and polymers. Although they presented several complete viscosity profiles, they relied mainly upon changes in the low and high shear viscosities due to changes in dispersion formulation to monitor changes in the association network. In addition, the complexity of the interactions among the various formulation components and polymers hindered quantitative description of the relationship between polymer structure and coatings rheology. Such studies on commercial associative polymers demonstrate the complexity of the technology, and motivate studies on model associative polymers to produce a fundamental understanding of the association phenomenon. In one of the first studies to use model polymers, Thibeault et al. Q) measured the adsorption isotherms and viscosity profiles in monodisperse latex dispersions of the following model polymers: a low molecular weight ethylene oxide based copolymer model associative polymer with large hydrophobe content; an ammonium salt of an anionic acrylic copolymer of high molecular weight with low hydrophobe content; and a (hydroxyethyl)cellulose non-associative polymer. They studied the effect of latex particle size, surfactant concentration, and cosolvent concentration, and observed that the desorption of the model polymer from the latex particle through the addition of surfactants and cosolvents coincided with a decrease in dispersion viscosity. They concluded that the associative polymer interacted with latex particles to physically cross-link the dispersion, and the shear-thinning viscosity profiles of the dispersion resulted from the disruption of the physical cross-links by shear forces. However, since they did not completely disclose the structure of the model polymer, no quantitative structure/property relationships could be drawnfromthe published data. Realizing the need for studies on model polymers, several researchers used model associative polymers to examine the influence of polymer structure on solution properties. Bock et al. (&) synthesized copolymers of alkylacrylamide and acrylamide with weight average molecular weights of 3xl0*\ and probed the effect of hydrophobe structure and electrolyte concentration on intrinsic viscosity and steady shear viscosity. Maerker and Sinton (2) used poly(vinyl alcohol) and polysaccharide with sodium borate at low pH as a model associating polymer system. They measured steady shear viscosity profiles and dynamic mechanical properties to investigate the flow structures induced by shear, and used nuclear magnetic resonance to determine number of association complexes in their solutions. Lundberg et al. (10) studied the viscoelastic properties of solutions that contained one of the following four hydrophobically modified urethane-ethoxylate model associative polymers: a linear polymer of number average molecular weight between 8700 to 24000 with either octyl, dodecyl, or nonylphenol hydrophobic endgroups, or a trimer with a number average molecular weight of 10500 and with nonylphenol hydrophobic endgroups. They concluded that linear polymers with large hydrophobes form an elastic network in solution. Some features seen in the rheological data presented by these studies, such as viscoelasticity and a maximum in the viscosity profile followed


224

POLYMERS AS R H E O L O G Y MODIFIERS


by shear thinning and elasticity, are qualitatively similar to features in our rheological data, which we discuss more fully later in this paper. A review of the cited literature shows that a thorough investigation of the solution properties of model associative polymers of known structure, which vary systematically in hydrophobe length and molecular weight, should give considerable insight into the association mechanism. Our work studies the self-association mechanism, and the relationship between network dynamics and solution rheology, by measuring viscosity profiles and linear viscoelastic properties over a broad range of shear rates and frequencies. Once we understand the behavior of the model associative polymers in pure water, we can more easily understand the effect of surfactants, cosolvent, latex particles, and their complex interactions, on dispersion rheology. Experimental Detail To elucidate the self-association mechanism, we studied the rheological properties of aqueous solutions of model associative polymers, kindly supplied by Union Carbide Corporation (Π). As shown in Table I, die model polymers' structure consists of linear water-soluble poly(oxyethylene) backbones of Table I: Structure and Nomenclature of Model number average molecular Associative Polymers weight 16600-100400 with hydroxyl, dodecyl, or hexadecyl Calculatedt Structure§ endgroups. The hydroxyl Reference Mole. Wt. R Y Cf|_fn terminated polymers serve as a 17,400 2 C12H25 control group by which we can Cl2-17 4 34,200 C12H25 Cl2-34 measure the influence of the 6 50,700 C12H25 presence of linear alkyl C12-51 8 67,700 C12H25 hydrophobic endgroups on C12-68 10 84,500 C12H25 Cl2-85 solution rheology. Intrinsic 12 99,900 C12H25 viscosity measurements of the C12-IOO model associative polymers 17,500 2 C16H33 corroborate the number average C16-I8 4 34,200 C16H33 molecular weights listed in Table Cl6-34 6 51,000 C16H33 I, as we will report elsewhere. Cl6-51 8 67,600 C16H33 The notation C -m> where η C16-68 10 84,300 C16H33 Cl6-84 represents the number of carbon 12 100,400 C16H33 atoms in the alkyl endgroup and C16-IOO m represents the polymer number 16,600 2 H average molecular weight in Co-17 4 33,400 H Co-33 thousand Daltons, describes the H 6 50,200 structure of the polymer Co-50 8 67,000 H Co-67 molecule. Stock solutions of 5% H 10 84,000 associative polymer by weight Co-84 12 100,400 H Co-100 were prepared by adding a weighed amount of solid § Structure is : R - 0 - ( D I - P E O ) Y - D I O - R , where polymer to double distilled D I is a diisocyanate, and P E O is C A R B O W A X deionized (DDI) water which 8000 with a nominal number average molecular contained 5 ppm of weight of 8200 hydroquinone inhibitor. The tNumber average molecular weight calculated steady shear and oscillatory shear from reaction stoichiometry responses of solutions of n


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Properties of Model Associative Polymer Solutions225

1% to 5% model polymer by weight were measured with a Bohlin VOR rheometer equipped with a set of Mooney-Couette concentric cylinders and a 1 degree angle cone and plate. Comparison of model solutions' rheological properties will help to elucidate die self-association mechanism.


Steady Shear Viscosity Profiles Figure 1 displays viscosity profiles that are typical of aqueous solutions of model polymers with hexadecyl endgroups. In contrast to solutions of the polymers without hydrophobic endgroups, which have viscosities which are independent of shear rate for the polymer concentrations and molecular weights used in this study, the solutions of the model associative polymers with hexadecyl hydrophobic endgroups are Newtonian at low concentrations and become non-Newtonian as polymer concentration increases. The non-Newtonian viscosity profiles consist of a limiting low shear viscosity, a shear-thickening region at moderate shear rates, and a shearthinning region at high shear rates, which is similar to the data of Bock et al. and of Maerker and Sinton for their model associating systems. Shear-thinning begins at the shear rate at which shear forces disrupt the association network. At die highest shear rates observed in this study, the high shear viscosities of solutions of model polymers with hydrophobic endgroups are still greater than those of solutions of the model polymers without hydrophobic endgroups, which indicates that the shear forces have yet to completely disrupt the hydrophobic intermolecular associations.

y (1/sec) Figure 1: Steady shear viscosity profiles of C16-100 model associative polymer in water at 24.5°C, which are representative of all solutions of model associative polymers with hexadecyl hydrophobic endgroups. Polymer concentrations are by weight.



226


i (1/sec) Figure 2: Shear-thickening steady shear viscosity profiles of 1% solutions of model associative polymers with hexadecyl hydrophobic endgroups, normalized against the low shear viscosity. Data taken at 24.5°C. The lack of an apparent yield stress, which would cause the viscosity to become infinite as shear rate is decreased to zero, indicates that either the network is of finite extent or that the hydrophobic junctions which make up the network are constantly forming, breaking, and reforming by Brownian motion, or both. Otherwise, if the network junctions were permanent, and if the network was large enough to consider it a single cluster in solution, the solution would exhibit a yield stress. As in Witten and Cohen's theory on the shear-thickening behavior of ionomers, (12) a dynamic network can support stress and appear to have properties similar to those of permanent networks when the lifetime of an association junction is nearly as long as the hydrodynamic relaxation time of the association unit The shear-thickening region that occurs at a shear rate of nearly 10 sec~l in the 2.5% and 5% curves of Figure 2 is not surprising, because shear-thickening occurs at nearly the same shear rate as in the data for model associating systems presented by Bock et al. and by Maerker and Sinton. The molecular network theory used by Vrahopoulou and McHugh (13) qualitatively predicts such a shear thickening region in the steady shear viscosity profile, and also predicts that the magnitude of viscosity enhancement in the shear-thickening region increases as the polymer molecular weight decreases, as seen in Figure 2. According to this theory, the shear-thickening region of the viscosity curve results from the extension of network chains under shear, which provides an additional energy dissipation mechanism. Since smaller chains reach the limit of their extensibility before longer chains, networks with smaller chains should exhibit larger increases in viscosity by this mechanism. The magnitude of the absolute increase in viscosity in the shearthickening region shown in Figure 1 decreases with increasing polymer concentration, and, as Maerker and Sinton have also observed in their solutions, the



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JENKINS E T A L .

Properties of Model Associative Polymer Solutions

shear rate at which shear-thickening begins decreases with increasing polymer concentration. Witten and Cohen attributed the shear-thickening viscosity, and the decrease in the shear rate required to induce it as polymer concentration increases, to a change from intramolecular to intermolecular association as molecules elongate under shear. According to this theory, many of die association junctions in a network at rest are intramolecular. During flow, shear forces stretch the polymer chains and break some of the intramolecular associations, allowing intermolecular junctions to form at the expense of intramolecular junctions, and enhancing viscosity without increasing the total number of association junctions. Since the shear rate required to produce a given degree of elongation decreases as solution viscosity increases, the shear rate at which shear thickening begins decreases as solution viscosity increases. Likewise, the magnitude of shear thickening decreases as solution viscosity increases because the relative number of intermolecular to intramolecular associations increases. Figures 3 and 4 illustrate how the low shear viscosities of the model polymer solutions depend on polymer concentration, molecular weight, and the length of the alkyl endgroups. The low shear viscosities, obtained by using least squares regression to extrapolate the viscosity profiles to zero shear rate, depend upon the amount of network structure in the solution at rest. The inverse viscosity-molecular weight relationship shown by solutions of the model polymers with hydrophobic endgroups in Figures 3 and 4 becomes more pronounced as polymer concentration increases: the low shear viscosity depends upon polymer concentration as cP, where β is greater than 1 and increases with increasing ratio of alkyl chain length to polymer molecular weight. Although the diisocyanates that connect the poly(oxyethylene) units in the model polymers' backbone are slightly hydrophobic, the primary hydrophobicity of the model polymer comes from its alkane endgroups. Thus, the viscosity behavior depicted in Figures 3 and 4 indicates that the driving force for intermolecular association increases with increasing length of the alkane endgroup relative to the hydrophilic polymer backbone, and that interaction between the hydrophobic endgroups of the polymer molecules increases the apparent molecular weight of the polymer in solution.

Yisçrelastiç Material Properties Figure 5 presents storage G'(co) and loss G"(co) moduli typical of concentrated solutions of our model polymers with hexadecyl hydrophobes. All of the solutions were tested in the region of linear viscoelasticity, where the measured properties did not depend upon the amplitude of the oscillating shear strain. Hence, the measurements did not significantly perturb the networkfromits equilibrium rest state, and did not change the number of effective physical crosslinks in the association network. At lowfrequencies,G'(cu) has a slope of 2 and G"(co) has a slope of 1 on a doubly logarithmic plot, which indicates that the response is viscous since the complex viscosity tends toward the zero shear limiting viscosity in this region. At higherfrequencies,G'((o) crosses G"(cu) to reach an entanglement plateau, and G"(co) passes through a maximum. Maerker and Sinton observed a similar plateau in G'(co) between 6 and 300 rad/s for their solutions due to entanglement coupling. Thus, the range of frequencies used in our experiments encompasses the longest relaxationtimesin the relaxation spectrum of our solutions. This viscoelasticity resultsfromthe association between the hydrophobes, since solutions of model


111



228

Figure 4: Low shear limiting viscosities of 5% solutions (by weight) of model associative polymers with alkyl endgroups (CI6 or CI2). The control polymers do not have alkyl endgroups.


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ΠΠ Β Β Β

ου (rad/sec) Figure 5: Comparison of the corotational Maxwell fluid model to the complex shear moduli of 2.5% solutions of the C16-34 model associative polymer in water at 24.5°C. polymers without hydrophobic endgroups of the similar molecular weight and concentrations lack viscoelasticity. As indicated by the theory of Witten and Cohen, the hydrodynamic relaxationtimemeasured by this method is characteristic of the lifetime of the association junction because the association network acts as a single rheological unit. Since, as a first approximation the relaxation spectrum Η(τ) equals 2 ^G"(cu)Ix=I/q), the maximum in G"(œ) results from the longest relaxation times of the relaxation spectrum associated with the network, which we can use to calculate v, the average molar density of network junctions by association. (14) In analogy to rubber elasticity, the pseudo-equilibrium modulus ( G ° ) is: N

a (1) —00

where R is the gas constant, Τ is the temperature in Kelvin, and a', the frequency at the upper limit of integration, is chosen to include the maximum in longesttimesof the relaxation spectrum within the range of integration. To determine the pseudo-equilibrium modulus, we can integrate Equation 1 graphically from the data, or analytically by either fitting the data with a empirical


229


230

function or a constitutive equation. In this work, we use the corotational Maxwell constitutive equation (15), which appro- nates the relaxation spectrum by a relaxation time constant λ, so that we can physically interpret the result of the integration, viz.:

ο e n

2ηο f j ^ . ^ ^ λπ Jl+(Xœ)2 λπ

i

^

» '

0

λπ

λ

() 2

J

ο In Equation 2, a'=ln(a), η is the low shear limiting viscosity, and the relaxation time constant λ is the frequency at which G'((u) equals G"(co). As shown in Figure 5, the corotational Maxwell fluid model describes the oscillatory shear response well. The last simplification in Equation 2 results because the upper limit of the frequency range that encompasses the maximum in G"(œ) in the data is so large that the inverse tangent is always within 6% of τς/2. The physical interpretation of this result is that the plateau value of the storage modulus equals the pseudo-equilibrium modulus for these solutions. In general, both the zero shear limiting viscosity and the relaxation


0

time constant depend upon v. Discussion The viscoelastic response and the enhanced viscosity of solutions of polymers with hydrophobic endgroups, as compared to solutions of polymers without hydrophobic endgroups, suggest that the contribution to network junctions by chain entanglement is small relative to that by association. Hence, the pseudo-equilibrium modulus of an associative polymer solution essentially measures the molar density of network junctions formed by association. As shown in Figure 6, when the viscosities presented in Figure 3 for all six model polymers with hexadecyl hydrophobes at various concentrations are plotted against the molar density of association junctions, a single line with a slope of 4/3 results. This correlation between rheological parameters and the molar association density indicates that the morphology, size, and strength of the association junctions, rather than traditional volume exclusion mechanisms, determine the rheological properties of associative polymer solutions. The pseudo-equilibrium modulus is usually interpreted in terms of an apparent molecular weight between entanglement points: ν = G ^ / R Τ = c/Me, where M is the apparent molecular weight between entanglement points and c is the e

associative polymer mass concentration. (16) Hence, the ratio c/v , where c is the molar concentration of model associative polymer, is the dimensionless ratio of the apparent molecular weight between junctions to the polymer molecular weight, Me/M . Thus Me/M is 1 or greater for an association network. As shown in the Figure 7 for solutions of model polymers with hexadecyl hydrophobes, Me/M is greater than one and decreases as concentration increases. This implies that several associative polymers must cooperate to span the distance between hydrophobic junctions. n

n

n


JENKINS ET AL.


ο


ο

L "Ρ

10 γ3

10"

ν

z

10^

10

(milliMolar)

Figure 6: Correlation between low shear limiting viscosities (taken from Figure 3) for solutions of model associative polymer with hexadecyl hydrophobic endgroups and the molar density of association.

80000

100000

Figure 7: Number of model associative polymers between network junctions for solutions of model associative polymers with hexadecyl hydrophobic endgroups.



232

The rheological data of many polymers often exhibit a power law dependence on concentration and molecular weight, as predicated by the de Gennes c* theorem: 01)

η ~[C/C*]X , λ ~ [ δ / 0 * ] Υ

(3)

where c* is the overlap concentration. Experimental evidence demonstrates that the exponent X can be as high as 4, but is usually near 3.4 for most polymers. Following Equation 3, we regressed the rheological properties of the concentrated polymer solutions to an equation of the form: η,ν,λ = c M*\ where c is in wt%. Selecting the results with best regression statistics yielded: η = C3-36/m1.67 = (c/VM)3-36 v=c /M^ = ( C / V M ) - ; and λ= 0.88/m0.44 = ( / V M ) - , which are selfconsistent because they satisfy η = ν ^ j η=νλ. de Gennes showed that in a dense system of chains, such as found in a concentrated solution, the polymer chains follow a random walk where c* ~ M ~ * / , so that [c / C * ] ~ (c/VM). Hence, the scaling of the rheological properties of the model associative polymer solutions with (c/VM) is not surprising. In Figure 7, the ratio Mq/M scales as (c/VM)--6, hich indicates that the correlation length ξ (i.e., mesh size of the network), decreases rapidly with increasing concentration. This is comparable to de Gennes's prediction that the correlation length ξ ~ [c / C * Therefore, the strength and completeness of the network decreases as molecular weight increases. A


;

2A1

u

2

4 7

8 8

c

c

4

9 a n (

2

w

Conclusions Physical interpretation of the rheological properties of aqueous model associative polymer solutions suggests the following qualitative association mechanism At rest, Brownian processes build up a highly entangled association network, where the primary source of entanglement comes from associations among the model polymers' hydrophobic endgroups. Nevertheless, intramolecular associations between hydrophobic endgroups that belong to the same polymer molecule, which do not contribute to the overall strength of the network, can exist. Because the association junctions are dynamic (i.e., continuously building and rupturing through Brownian processes), the network is not an infinite cluster that spans the entire solution, but is instead a finitely sized hydrodynamic unit whose lifetime is longer than the relaxation time of the solution. Since the association junctions are relatively strong and longlived, small to moderate small amounts of shear stress can extend the network structure before rupturing it. This extension promotes intermolecular associations to form at the expense of intramolecular associations, and also decreases the configurational entropy of the polymer chains that construct the network system. Both effects provide an additional resistance to flow, as manifested in the solutions' shear-thickening viscosity profiles. Larger levels of shear stress break down the network system to lower solution viscosity. The number density and functionality of the association junctions primarily determine the strength of the overall network, and hence, the rheological properties of the solutions.


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233 Properties of Model Associative Polymer Solutions


Literature Cited 1. Schwab,F.G., In Water Soluble Polymer: Beauty withPerformance;Glass, J.E., Ed.; Advances in Chemistry Series No. 213; American Chemical Society: Washington, DC, 1986; p. 369. 2. Croll,S.G.; Kleinlein,R.L., In Water Soluble Polymer:Beauty with Performance: Glass, J.E., Ed.; Advances in Chemistry Series No. 213; American Chemical Society: Washington, DC, 1986; p. 333. 3. Glass,J.E., In Water Soluble Polymer:Beauty with Performance: Glass, J.E., Ed; Advances in Chemistry Series No. 213; American Chemical Society: Washington, DC, 1986; p. 391. 4. GlassJ.E.; Fernando,R.H.; Egland-Jongewaard,S.K.; Brown,R.G., J. Oil Colour Chem. Assoc. 1984,67No. 10, p.256. 5. Fernando,R.H.; Glass,J.E.J. Oil Colour Chem. Assoc. 1984,67No. 11, p.279 6. Fernando,R.H.; McDonald,W.F.; Glass,J.E.,J. Oil Colour Chem. Assoc. 1986, 69 No. 10, p.263. 7. Thibeault,J.C.; Sperry,P.R.; and Schaller,E.J., In Water Soluble Polymer: Beauty with Performance: Glass, J.E., Ed.; Advances in Chemistry Series No. 213; American Chemical Society: Washington, DC, 1986; p. 375. 8. Bock,J.; Siano,D.B.; Valint,P.L.; Pace,S.J., Proc. of the ACS Div. of Polymeric Mater: Sci. and Eng., 1987, 57, p.487. 9. MaerkerJ.M.; Sinton,S.W., J. Rheol. 1986, 30(1), p.77. 10. Lundberg, D.J.,Glass,J.E.,Eley,R.R., Proc. of the ACS Div. of Polymeric Mater: Sci. and Eng., 1989,61,p.533. 11. D. Bassett, Union Carbide Corp., private communication 12. Witten,T.A.; Cohen,M.H., Macromol., 1985, 18,p. 1915. 13. Vrahopoulou,E.P., and McHugh,AJ., J. Rheol., 1987, 31(5),p. 371. 14. FerryJ.D., Viscoelastic Properties of Polymers ; Wiley: New York, 1970; p.404. 15. Bird,R.B.; Armstrong,R.C.; Hassager,O., Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics: Wiley and Sons: New York, 1977; p.355. 16. Graessley, W.W.,The Entanglement Concept in PolymerRheology;SpringerVerlag: Berlin, 1974; p.58. 17. de Gennes, P.G., Scaling Concepts in Polymer Physics. Cornell University Press: Ithaca, 1979; p.54. RECEIVED August 22, 1990


Polymers as Rheology Modifiers - American Chemical Society

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