1548
Langmuir 1998, 14, 1548-1553
Effect of Soluble Polymers on the Shear and Extensional Viscosity Characteristics of a Concentrated Latex Dispersion C. Viebke, J. Meadows,* J. C. Kennedy,† and P. A. Williams North East Wales Institute, Centre for Water Soluble Polymers, Mold Road, Wrexham L11 2AW, United Kingdom Received September 8, 1997. In Final Form: November 19, 1997 The extensional viscosity characteristics of concentrated (45% w/w) latex dispersions containing various soluble polymers have been determined by using an opposing jet rheometer. In all cases, the latex dispersions were found to exhibit strain thinning behavior. Quantitative comparison with shear flow data, through calculation of the Trouton ratio, indicated the extensional viscosities of the dispersions to be 1-2 orders of magnitude greater than their shear flow viscosity at a comparable deformation rate. For a given added polymer concentration, the latex dispersions containing cellulose ether type thickeners exhibited more pronounced shear and strain thinning characteristics and higher Trouton ratios than those dispersions thickened with associative polyelectrolytes. Mathematical modeling of the shear and extensional viscosities of the dispersions as a function of deformation rate has been undertaken by modification of the recent model of Barnes and Roberts.1 The modified model was found to give an excellent fit of the shear viscosity data and a reasonably good fit of the extensional flow data over several decades of deformation rate.
Introduction In recent years, environmental and market driven pressures have seen an increasing demand for aqueous based formulations across a broad spectrum of industries. Due to the inherently low viscosity of the aqueous carrier fluid, such formulations usually require the use of water soluble polymers to impart the desired rheology. The shear flow characteristics of polymer thickened systems have been studied in great detail and many mathematical models have been developed to describe shear flow behavior as a function of deformation rate.2 In sharp contrast, primarily due to the scarcity of available experimental techniques, the extensional flow properties of aqueous based systems have not been studied to any great extent and, consequently, are still poorly understood. However, the development of new instrumentation such as the filament stretching device of Tirtaatmadja and Sridah3 and the commercially available opposing jet rheometer (RFX; Rheometrics Inc., NJ) now provide an opportunity to study the extensional flow behavior of relatively low viscosity systems in more detail.4-12 While † Present address; Kilfrost (Ltd.), Albion Works, Haltwhistle, Northumberland, U.K.
(1) Barnes, H. A.; Roberts, G. P. J. Non-Newtonian Fluid Mech. 1992, 44, 113. (2) Barnes, H. A.; Hutton, J. F.; Walters, K. An Introduction to Rheology; Elsevier: Amsterdam, 1989. (3) Tirtaatmadja, V.; Sridhar, T. J. Rheol. 1995, 39, 1133. (4) Anklam, M. R.; Warr, G. G.; Prud’homme, R. K. J. Rheol. 1994, 38, 797. (5) Hu, Y.; Wang, S. Q.; Jamieson, A. M. J. Phys. Chem. 1994, 98, 8, 8555. (6) Prud’homme, R. K.; Warr, G. G. Langmuir 1994, 10, 3419. (7) Hermansky, C. G.; Boger, D. V. J. Non-Newtonian Fluid Mech. 1995, 56, 1. (8) Meadows, J.; Williams, P. A.; Kennedy, J. C. Macromolecules 1995, 28, 2683. (9) Kennedy, J. C.; Meadows, J.; Williams, P. A. J. Chem. Soc., Faraday Trans. 1995, 91, 911. (10) Al-Assaf, S.; Meadows, J.; Phillips, G. O.; Williams, P. A. Biorheology 1996, 33, 319. (11) Ng, S. L.; Mun, R. P.; Boger, D. V.; James, D. F. J. Non-Newtonian Fluid Mech. 1996, 65, 291. (12) Clark, R. Food Technology 1997, 51, 49.
the former instrument requires the sample to be able to sustain a continuous filament over periods of several seconds, the RFX performs in situ measurements, thereby avoiding the need for such “spinnability”. In previous papers, we have reported on the use of the RFX to characterize the extensional flow behavior of aqueous solutions of two different types of polymeric thickener, i.e., cellulose ethers8 and hydrophobically associating polyelectrolytes.9 In a progression from these studies, we now report on the effect of these thickeners on the shear and extensional flow behavior of a concentrated aqueous based latex dispersion. The ability of a recent mathematical model1 to simultaneously describe the shear and extensional viscosity of these systems as a function of deformation rate has also been evaluated. Experimental Section Materials. A series of hydrophobically associating polyelectrolytes consisting of copolymers of methacrylic acid and ethyl acrylate (1:1 mole ratio) with 0, 1, and 2 mol % incorporation of an octadecyl (C18) hydrophobe were kindly synthesized by Allied Colloids Ltd., UK,13 and supplied in the form of low viscosity aqueous emulsions (30% w/w active polymer content). The weight average molecular masses of the polymers were determined to be (6 ( 1) × 105 using multiangle laser light scattering.9 In the following text, the adopted nomenclature for this series of polymers is, for example, that CP-1 represents a hydrophobically modified copolymer derivative containing 1 mol % of the pendant C18 side chains. Commercial samples of hydroxyethylcellulose of two different molecular masses (HEC-med and HEC-high) and a hydrophobically modified hydroxyethylcellulose (HMHEC) were kindly supplied by Aqualon (U.K.) Ltd under the trade names Natrosol 250 GR, Natrosol 250 MR, and Natrosol 330 Plus grade, respectively. The viscosity average molecular masses of the HEC samples were determined to be 1.9 × 105 and 4.5 × 105 for HECmed and HEC-high, respectively.8 The sample of HMHEC is of comparable molecular mass to HEC-med. The cellulose ethers are water soluble at room temperature with the quoted molar substitution of ethylene oxide units being 2.5 for both HEC (13) Allied Colloids Ltd., U.K., U.S. Patent 4,892,916, 1990; European Patent 216479B, 1991.
S0743-7463(97)01009-3 CCC: $15.00 © 1998 American Chemical Society Published on Web 02/19/1998
Effect of Soluble Polymers on Viscosity
Figure 1. Shear viscosity-shear rate profiles of a 45% (w/w) latex dispersions containing varying concentrations of CP-1: ([) 0%; (0) 0.375%; (b) 0.5%; (O) 0.75%. samples and 3.3 for HMHEC. HMHEC also contains approximately 1% w/w of chemically grafted C12-C18 alkyl side chains. The polymer latex used in these studies was a commercially available sample (Vinamul 3459; Vinamul Ltd., Surrey, U.K.), which is a vinyl acetate/vinyl chloride/ethylene terpolymer latex with a cellulose ether stabilizing layer. The average hydrodynamic particle diameter of the latex was determined to be 374 ( 8 nm by photon correlation spectroscopy. Methods. Preparation of Latex Dispersions with Associative Polyelectrolytes. Latex (as supplied; 52% w/w solids), 199 g, was adjusted to pH 8-9 by careful addition of aqueous sodium hydroxide solution (4 mol dm-3). The appropriate amount of the supplied polymer emulsion was diluted to a total mass of 31 g with distilled water and then added to the latex to give the desired concentration of polymer in a 45% w/w latex dispersion. The dispersion was tumbled for approximately 30 min to mix in the polymer, after which the system was readjusted to pH 8-9 and tumbled for approximately 1 h prior to performing any rheological measurements. Preparation of Latex Dispersions with Cellulose Ethers. The appropriate cellulose ether, 1.15 g, was dissolved in 31 g of distilled water by tumbling for several hours. The latex, 199 g, was added to this solution to give a polymer concentration of 0.5% w/w in a 45% w/w latex dispersion. The sample was tumbled for approximately 1 h and then mixed for a further 2-3 h by using an overhead stirrer. The resultant mixture was then tumbled overnight prior to any rheological measurements. Shear Flow Measurements. The shear viscosity-shear rate profiles of the various dispersions were recorded over the shear rate range 0-1000 s-1 at 25 °C by using the Carrimed CS 100 controlled stress rheometer (TA Instruments, Surrey, U.K.) fitted with a cone and plate measurement geometry. Extensional Flow Measurements. The extensional viscositystrain rate profiles of the various dispersions were recorded over the strain rate range 0-1000 s-1 at 25 °C by using the RFX fluids analyzer (Rheometrics Inc, NJ), which has been described in detail previously.6-9 A series of opposing jets of 4-, 2-, and 1-mm diameter were used during this study with, in all instances, the chosen jet separation being equivalent to their diameter.14 Each presented result is an average of at least two independent measurements. Comparison of the shear and extensional viscosity characteristics of the various dispersions was achieved through calculation of the Trouton ratio, Tr, which is the ratio of the extensional viscosity of a system (at a given strain rate, ˘ ) to its shear viscosity (at the corresponding shear rate, γ˘ ). The latter parameter was identified by using the convention γ˘ ) 31/2˘ , as proposed by Jones et al.15 Polymer-Particle Interaction. Investigations using spinlabeled polymers in conjunction with electron spin resonance (14) Schunk, P. R.; de Santos, J. M.; Scriven, L. E. J. Rheol. 1990, 34, 387. (15) Jones, D. M.; Walters, K.; Williams, P. R. Rheol. Acta. 1987, 26, 20.
Langmuir, Vol. 14, No. 7, 1998 1549
Figure 2. Extensional viscosity-strain rate profiles of a 45% (w/w) latex dispersion containing varying concentrations of CP1: ([) 0%; (0) 0.375%; (b) 0.5%; (O) 0.75%.
Figure 3. Trouton ratio-strain rate profiles of a 45% w/w latex dispersion in the presence of varying concentrations of CP-1: ([) 0%; (0) 0.375%; (b) 0.5%; (O) 0.75%. spectroscopy indicated that none of the polymers used in this study adsorbed onto the latex from water. This can be attributed to the presence of the cellulose ether stabilizing layer. It can, therefore, be assumed that, for each system, all of the added polymer remains in the continuous phase of the latex dispersions. Thus, the aqueous phase concentration of the polymer in the various dispersions is approximately a factor of 1.8 times greater than the percent weight/weight values quoted in the text. Mathematical Modeling. Tirtaatmadja and Sridah16 recently evaluated the ability of several constitutive equations to predict the extensional flow behavior of both ideal elastic and shear thinning fluids. They concluded the White-Metzner model17 to be the most appropriate model for describing the extensional flow of shear thinning systems. Barnes and Roberts1 adapted the White-Metzner model to allow finite values of extensional viscosity to be obtained at all deformation rates and found that their model was able to simultaneously describe the shear and extensional viscosity characteristics of a variety of polymer melts over a wide range of deformation rates. However, from our initial use of this model in this study, it was evident that unsatisfactory fits were being obtained for the shear viscosity data of the polymer thickened latex dispersions at (i) low deformation rates, due to the lack of experimental data relating to the attainment of a low shear apparent Newtonian plateau, and (ii) high deformation rates, due to the inability of the WhiteMetzner model to account for deviation away from power law behavior in the approach to any high shear apparent Newtonian plateau. We have, therefore, modified the approach of Barnes and Roberts by use of the Sisko model to fit the shear viscosity data but have retained the equations of Barnes and Roberts1 to fit our extensional viscosity data. The principal features of the chosen model are that the deformation rate dependent shear (16) Tirtaatmadja, V.; Sridhar, T. J. Rheol. 1995, 39, 1133. (17) White, J. L.; Metzner, A. B. J. Appl. Polym. Sci. 1963, 7, 1867.
1550 Langmuir, Vol. 14, No. 7, 1998
Viebke et al.
Figure 4. Shear viscosity-shear rate profiles of a 45% w/w latex dispersion in the absence, and presence, of 0.5% w/w of various associative polyelectrolytes: ([) no added polymer; (b) CP-0; (0) CP-1; (O) CP-2.
Figure 6. Trouton ratio-strain rate profiles of a 45% w/w latex dispersion in the absence, and presence, of 0.5% w/w of various associative polyelectrolytes: ([) no added polymer; (b) CP-0; (0) CP-1; (O) CP-2.
Figure 5. Extensional viscosity-strain rate profile of a 45% w/w latex dispersion in the absence, and presence, of 0.5% w/w of various associative polyelectrolytes: ([) no added polymer; (b) CP-0; (0) CP-1; (O) CP-2.
Figure 7. Shear viscosity-shear rate profiles of a 45% w/w latex dispersion in the absence, and presence, of 0.5% w/w of various cellulose ethers: ([) no added polymer; (b) HMHEC; (0) HEC-med; (O) HEC-high.
viscosity, ηs, and relaxation time, λs, are represented by
ηs(ΠD) ) η∞ + k1ΠD
n-1
(1)
λs(ΠD) ) λ0/[1 + k2ΠD]
(2)
where ΠD is the deformation rate, η∞ is the high shear apparent Newtonian plateau viscosity, k1 is the consistency index, and n is the power law index. λ0 is the relaxation time at zero deformation rate and k2 is a time constant which characterizes the deformation rate dependence of the relaxation time. The extensional viscosity data were modeled using the equation
ηe )
2ηs(ΠD) 1/2
[1 - (2/3 )λs(ΠD)ΠD]
+
ηs(ΠD) [1 + (1/31/2)λs(ΠD)ΠD]
(3)
The adopted experimental procedure was to use eq 1 to fit the shear flow viscosity data to determine the values of k1, n, and η∞, and then to use these parameters in addition to the two further variables λ0 and k2 to fit the extensional flow behavior according to eq 3.
Results and Discussion Double logarithmic scale plots of the shear viscosityshear rate and extensional viscosity-strain rate profiles of the latex dispersion in the presence of various amounts of CP-1 are given in Figures 1 and 2, respectively. In the absence of added polymer, the latex dispersion exhibits shear thinning characteristics in shear flow and strain thinning characteristics in extensional flow. This is indicative of the presence of significant interparticle
interactions within the system, which can be attributed to the relatively high volume fraction. The Trouton ratio data (Figure 3) illustrates the extensional viscosity of the latex dispersion to be approximately 20-30 times its comparable shear viscosity over the entire range of deformation rates studied. From Figures 1 and 2, it can be seen that the addition of increasing amounts of CP-1 causes a gradual increase in both the shear and extensional viscosity of the latex dispersion. This can be attributed to the progressive viscosification of the aqueous phase by the nonadsorbing polymer. While the overall shear thinning characteristics of the dispersion are maintained at all levels of polymer addition, it is interesting to note the presence of regions of reduced shear thinning, commencing at relatively high shear rates (102 - 103 s-1), in the profiles of the polymer thickened latex dispersions. This phenomenon appears to become more prominent with increasing polymer addition. Similar effects have been reported, but not explained, by other workers investigating the rheological properties of polymer thickened particulate dispersions.18,19 The extensional viscosity profiles (Figure 2) of the latex dispersions containing CP-1 illustrate the systems to be strain thinning over the entire range of strain rates (18) Rokowski, J. M.; Schaller, E. J.; Aviles, R. G. In Advances in Organic Coatings Science and Technology Series; Patsis, A. V., Ed.; Technomic Publishing AG: Lancaster, PA, 1990; Vol. 12. (19) Fernando, R. H.; Glass, J. E. J. Oil Colour Chem. Assoc. 1984, 67, 279.
Effect of Soluble Polymers on Viscosity
Figure 8. Extensional viscosity-strain rate profiles of a 45% w/w latex dispersion in the absence, and presence, of 0.5% w/w of various cellulose ethers: ([) no added polymer; (b) HMHEC; (0) HEC-med; (O) HEC-high.
Langmuir, Vol. 14, No. 7, 1998 1551
Figure 10. Mathematical modeling of the (b) shear and ([) extensional viscosity characteristics of 45% w/w latex dispersion.
Figure 9. Trouton ratio-strain rate profiles of a 45% w/w latex dispersion in the absence, and presence, of 0.5% w/w of various cellulose ethers: ([) no added polymer; (b) HMHEC; (0) HEC-med; (O) HEC-high.
studied. Interestingly, aqueous solutions of CP-1 have been shown to exhibit maxima in their extensional viscosity-strain rate profiles.9 The contrast between this observation and the data given in Figure 2 suggests that the presence of the latex particles has a substantial influence on the overall rheological properties of the dispersions. The Trouton ratio-strain rate profiles of the latex dispersions containing varying amounts of CP-1 are displayed in Figure 3. Allowing for experimental scatter, the value of Tr seems to exhibit little dependence on the level of polymer addition over the range studied. This observation again emphasizes the dominant influence of the latex particles in controlling the overall rheology of the system. For all systems, there appears to be a slight increase in Tr with increasing strain rate. Cohu and Magnin,20 using the RFX instrument, found the values of Tr for three fully formulated paints to decrease with increasing strain rate and to exhibit their defined “Newtonian” value for Tr of 3-7 at high strain rates (>102 s-1). Cohu and Magnin attributed this surprising observation, considering the non-Newtonian nature of the paints, to a decrease of the influence of the apparent yield stress behavior of the paints on the measurement of extensional stresses and, hence, extensional viscosities as the strain rates were increased. The marked differences in general extensional behavior of the latex dispersions investigated in this study and the reported findings of Cohu and Magnin may be a consequence of the relative complexity of the (20) Cohu, O.; Magnin, A. J. Rheol. 1995, 39, 767.
Figure 11. Mathematical modeling of the (b) shear and ([) extensional viscosity characteristics of 45% w/w latex dispersion containing various concentrations of CP-1: (a) 0.375%; (b) 0.5%; (c) 0.75%.
latter systems. Although the two sets of dispersions are of comparable solids content (∼45% w/w), the formulated paints presumably contained a mixture of irregularly shaped particulate constituents, while the latex dispersions used in this study contained solely spherical particles
1552 Langmuir, Vol. 14, No. 7, 1998
Viebke et al.
Figure 12. Mathematical modeling of the (b) shear and ([) extensional viscosity characteristics of 45% w/w latex dispersion containing 0.5% w/w of various associative polyelectrolytes with different levels of incorporation of pendant hydrophobe: (a) CP0; (b) CP-2.
and were found not to exhibit any apparent yield stress behavior. Figures 4 and 5 give the shear viscosity-shear rate and extensional viscosity-strain rate profiles, respectively, for the latex dispersion in the absence, and presence, of 0.5% w/w of various copolymers. In both flow modes, the viscosity of the dispersions decreases with increasing deformation rate and increases with increasing hydrophobe content of the added polymer. This latter observation can be attributed to the consequent increase in the number of intermolecular hydrophobic associations between the polymer molecules in the continuous phase. The corresponding Trouton ratios are displayed in Figure 6. All systems generally exhibited a slight increase in Tr with increasing strain rate. In simple solution, the Tr values of the various associative polyelectrolytes increased with increasing hydrophobe content,9 but a similar correlation is not apparent for the various polymer thickened dispersions (Figure 6), for which there is no apparent trend. Double logarithmic scale plots of the shear viscosityshear rate and extensional viscosity-strain rate profiles for the latex dispersion in the absence, and presence, of 0.5% w/w of various cellulose ethers are displayed in Figures 7 and 8, respectively. As might be expected, the dispersion viscosity, in both flow modes, increases with increasing molecular weight of the added HEC. The rheological properties of the HMHEC thickened dispersion are very similar to those thickened with the higher molecular mass HEC-high. The viscosity of the dispersions decreases with increasing deformation rate in both flow modes. The Trouton ratio-strain rate curves for dispersions thickened with the various cellulose ethers are displayed in Figure 9 together with, for comparison purposes, the corresponding data for the dispersion thickened with 0.5%
Figure 13. Mathematical modeling of the (b) shear and ([) extensional viscosity characteristics of 45% w/w latex dispersion containing 0.5% w/w of various cellulose ethers: (a) HEC-med; (b) HEC-high; (c) HMHEC.
w/w CP-1. While there is little apparent difference between the plots for the various cellulose ether thickened dispersions, with Tr again increasing slightly with increasing strain rate, the values of Tr for all of these former systems are significantly higher over the entire strain rate range studied than those of both the latex dispersion and the dispersion containing CP-1. Such differences are not apparent between aqueous solutions of CP-1 and HEChigh which, at comparable concentrations to those present in the aqueous phase of the dispersions, display similar Trouton ratio-strain rate characteristics to each other.8,9 This observation suggests that the differences in Trouton ratio characteristics evident in Figure 9 may arise from differences in polymer-latex interactions. For example, it has been reported that cellulose ethers can induce depletion flocculation of latex particles,21 although no visible flocculation was observed in any of the dispersions. The mathematical fits of the shear viscosity-shear rate and extensional viscosity-strain data for (i) the latex (21) Sperry, P. R. J. Colloid Interface Sci. 1984, 99, 97.
Effect of Soluble Polymers on Viscosity
Langmuir, Vol. 14, No. 7, 1998 1553
Table 1. Various Parameters from the Mathematical Modeling of the Shear and Extensional Viscosity Characteristics of 45% w/w Latex Dispersions Containing Various Added Polymers added polymer latex CP-1 CP-1 CP-1 CP-0 CP-2 HEC-med HEC-high HMHEC
concn,n % w/w k1, Pa s 0 0.375 0.5 0.75 0.5 0.5 0.5 0.5 0.5
1.6 3.1 3.9 10.0 2.2 13.5 8.5 16.9 15.0
n
η∞, Pa s
0.33 0.44 0.49 0.45 0.40 0.34 0.26 0.25 0.24
0.06 0.2 0.3 0.8 0.1 0.3 0.3 0.2 0.2
k2, s
λo, s
228 180 71 54 30 23 6860 9190 405 542 860 681 1430 1175 9 7 1540 1270
dispersion, (ii) the latex dispersion containing varying concentrations of CP-1, (iii) the latex dispersion containing 0.5% w/w of various associative polyelectrolytes, and (iv) the latex dispersion containing 0.5% w/w of various cellulose ethers are given in Figures 10-13, respectively. It can be seen that there is excellent agreement between the Sisko model and the shear flow data and also that a reasonably good fit was obtained by using the equations of Barnes and Roberts1 to model the extensional flow data. The values of the various parameters obtained from the simultaneous modeling of the shear and extensional flow data of the polymer thickened latex dispersions are given in Table 1. From the power law indices, it is evident that the dispersions containing any of the various cellulose ethers exhibit a greater degree of shear thinning than those containing the various associative polyelectrolytes. The values of the fitting parameters λ0 and k2 used to fit the extensional flow data differ by up to 2 or 3 orders of magnitude for the various dispersions. Barnes and
Roberts1 reported a similarly broad range of values for λ0 and k2 in their modeling of the extensional flow characteristics of various polymer melts. There are no evident correlations between the values of λ0 and k2 and polymer variables such as concentration, molecular mass, and the level of hydrophobe incorporation. This may be a reflection of the relative complexity of the dispersions which, consequently, are likely to exhibit a broad spectrum of relaxation phenomena. Conclusions Concentrated, polymer thickened latex dispersions were found to exhibit strain thinning extensional flow behavior, with the absolute values of their extensional viscosities being 1-2 orders of magnitude greater than their corresponding shear flow viscosity. For a given added polymer concentration, the latex dispersions containing cellulose ether type thickeners exhibited more pronounced shear and strain thinning characteristics and higher Trouton ratios than those dispersions thickened with associative polyelectrolytes. A modified version of the recent model of Barnes and Roberts1 was found to give an excellent fit of the shear viscosity data and a reasonably good fit of the extensional flow data over several decades of deformation rate. Acknowledgment. We express our gratitude to EPSRC (Process Engineering Committee) for the provision of a Cooperative Research Grant (GR/H79648) in conjunction with Allied Colloids Ltd., which enabled this work to be undertaken. We also thank the EU for a supporting grant for C.V. through the Human Capital and Mobility program (Contract No. CHRX-CT94-0655). LA971009Q
