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Extensional properties of model hydrophobically modified alkali-soluble associative (HASE) polymer solutions
J. Non-Newtonian Fluid Mech. 92 (2000) 167–185
Extensional properties of model hydrophobically modified alkali-soluble associative (HASE) polymer solutions H. Tan a , K.C. Tam a,∗ , V. Tirtaatmadja b , R.D. Jenkins c , D.R. Bassett d a
c
School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore b Department of Chemical Engineering, University of Melbourne, Parkville, Vic. 3052, Australia Union Carbide Asia Pacific Inc., Technical Center, 16 Science Park Drive, The Pasteur, Singapore 118227, Singapore d Union Carbide Corporation, UCAR Emulsions Systems, Research and Development, Cary, NC 27511, USA Received 23 July 1999; received in revised form 13 December 1999
Abstract The relationship between shear and extensional viscosities of a series of model hydrophobically modified alkali-soluble associative (HASE) polymers with varying degree of hydrophobicity was investigated. An opposing jet rheometer (Rheometric RFX) was used to measure the extensional and shear viscosities of 0.3–4.0 wt.% solutions. The deformation rates were varied from 0.1 to 10,000 s−1 . The shear and extensional viscosities increase exponentially with the hydrophobicity and concentration of the polymers. This is attributed to the increase in the strength of the associative junctions. Extensional thickening is observed at moderate extensional rates for the polymer with C12 H25 hydrophobes. This indicates that associative polymer with shorter hydrophobic chain undergoes a conversion from aggregated clusters with predominantly intra-molecular associations at low extension rates to inter-molecular cluster associations at moderate deformation rates. At high extensional rates, the deformation force exceeds the strength of inter-cluster associations, resulting in the destruction of the active junctions, yielding a continuous decrease in the extensional viscosity. The Trouton ratio increases with deformation rates, polymer concentration and the size of the hydrophobes. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Polyelectrolytes; Associative polymer; Opposing jet rheometer; Extensional and shear viscosities
1. Introduction Water-soluble associative polymers are widely used as viscosity modifiers in several industrial applications, such as in paint formulations and paper coatings. They are now replacing the conventional ∗
Corresponding author. Present address: Department of Mechnanical Engineering, MIT, Cambridge, MA, USA. Tel.: +65-790-5590; fax: +65-791-1859. E-mail address: [email protected] (K.C. Tam) 0377-0257/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 0 2 5 7 ( 0 0 ) 0 0 0 9 3 - 8
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non-associative thickeners. Unlike the solvent-based formulations, these water-soluble systems do not contain volatile solvents and hence do not contribute to environmental problems. Higher thickening efficiency is achieved by the self-associating properties of the attached hydrophobic groups, yielding a network structure that enhances the viscosity of the formulation. Associative polymers (APs) are generally of low molecular weights and they produce less spattering in paints during applications by brush rolling. The positive characteristics of APs make them more attractive as the material of choice for use as thickeners in various types of coating formulations. The rheological properties of water-soluble associative polymers depend on factors such as polymer concentrations, molecular weight, degree of hydrophobic modification, characteristics of hydrophobic groups and the flexibility of the polymer backbone. Following the comprehensive study by Jenkins [1], a large number of publications on nonionic associative polymers, particularly the well-defined end-capped hydrophobically-modified ethylene oxide urethane (HEUR) systems have appeared [2–7]. However, only few studies on anionic associative polymers such as the hydrophobically modified alkali-soluble associative (HASE) systems have been reported [8–11]. HASE polymer consists of a backbone of poly(acrylate), with hydrophobic macromonomers distributed along the polymer backbone. At low pH, the polymer exists as insoluble latex dispersed in an aqueous medium. Upon neutralization by raising the pH using a base, the polymer undergoes coil expansion due to electrostatic repulsion of the negative charges on the polymer backbone. The polymer then becomes water-soluble, and its hydrophobic groups associate with those of other polymer chains to form inter-molecular junctions. These junctions produce a polymer network, which enhances the viscosity of the solution. The concentrations of charges along the backbone and the ionic strength of the solutions significantly alter the rheological behavior [12]. Extensional flow studies on transient network systems are scarce. We will summarize some of the recent publications on a few transient network polymer or surfactant systems. The properties of wormlike micelles subjected to extensional flow have been investigated by Walker and co-workers [13] and Prud’homme and Warr [14]. The former authors examined the macroscopic response of wormlike micelles subjected to elongational flow field. They concluded, from scaling analysis that the extensional thickening observed in the semi-dilute solution region was not caused by micellar growth. However, Prud’homme and co-workers concluded from their studies that the increase in extensional viscosity is a result of strong alignment of the micelles in the flow direction. Meadows and co-workers performed extensional studies on non-associative polymer such as hydroxyethylcellulose (HEC) [15]. They examined the extensional properties of different concentrations and molecular weights of HEC in aqueous solutions. The Trouton ratio (Tr) approached a value of 3 at low extension rates regardless of their concentration and molecular weight. However, it increased significantly with extensional strain rates and polymer concentrations. Kennedy and co-workers examined the extensional properties of hydrophobically modified associative polyelectrolytes [9]. They observed extensional thickening of the viscosity at a specific deformation rate when the polymer concentration was increased. On the other hand, Viebke and co-workers reported extensional thinning behavior at all deformation rates when a concentrated latex dispersion was added to the associative polymer [15]. Vlahiotis [16] studied the response of the HEUR polymer subjected to extensional flow field under the direction of Winnik and James at the University of Toronto, but her results have not been published yet. She observed from online fluorescence spectroscopy measurements that the mean aggregation number of the flower micelles remained constant. The behavior of associative polymers under the strong extensional flow field has not been extensively studied, even though, many of the coating processes involve extensional flow fields. In this paper, the
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extensional viscosity of a series of model hydrophobically modified alkali-soluble polymers containing hydrophobes of varying hydrophobicity was examined. The extensional properties are correlated to the polymer concentrations and the strength of the network junction.
2. Experimental 2.1. Materials The associative polymers used are the emulsion co-polymerization products of methacrylic acid (MAA), ethyl acrylate (EA), which form the polymer backbone. Macromonomers capped with a hydrophobic group via a polyethylene-oxide (PEO) chain is then grafted onto the backbone. The general structure of HASE polymer is shown in Fig. 1a. Four model HASE polymers were synthesized and designated as RDJ31-1, RDJ31-3, RDJ31-4 and RDJ31-5. RDJ31-1 is a control polymer without any hydrophobic modification, while RDJ31-3, 31-4 and 31-5 contain C12 , C16 and C20 hydrophobic groups, respectively, attached to the MAA/EA backbone. These polymers are identical to the materials used in our previous publications [8,10,11]. The detailed information on these polymers is summarized in Table 1. In this study, the PEO chains on the hydrophobic macromonomer were kept constant to 31 mol. The synthesis procedure can be found elsewhere [8,17]. Fig. 1b depicts the microstructure of HASE polymer produced by an associative mechanism at its unperturbed state. The hydrophobes can interact with hydrophobes of the same polymer chain (intra-molecular association) or with hydrophobes from different polymer chains (inter-molecular association) to yield clusters consisting of several polymer chains. These clusters are connected to each other through the associative junctions to produce a polymer network [18,19]. In systems with stronger hydrophobic groups, the junctions are stronger and the network is more resistant to deformation. The overall network strength is highly dependent on the active junctions formed by inter-molecular associations. It has been shown by Dai et al. [20] that the ethyl acrylate segments are blocky and they can interact with other EA blocks situated along the polymer backbone. 2.2. Techniques Associative polymer solutions were prepared from a stock solution of 3 wt.% polymer latex dispersion by diluting with 10−4 M potassium chloride (KCl) to the required concentrations. They were then adjusted to pH between 9 and 9.5 by adding 2-amino 2-methyl 1-propanol (AMP). On dissolution, the hydrophobes Table 1 Chemical composition of model HASE polymers Polymer
Hydrophobe type
Precursor Mn
Macro. Mn
GPC Mn /Mw of macro.
Mole composition X/Y/Z
RDJ 31-1 RDJ 31-3 RDJ 31-4 RDJ 31-5
None Dodecyl Hexadecyl Eicosanyl
1726 1761 1835
1927 1962 2036
2120/2179 2197/2257 2023/2077
49/51/0 49/50/1 49/50/1 49/50/1
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Fig. 1. (a) Chemical structure of model HASE associative polymer; (b) network structure of HASE associative polymer after neutralization.
associate to form a network junction as shown in Fig. 1b. The samples were kept for 2 days prior to testing to allow the solutions to equilibrate. All experiments were conducted at 25±1◦ C. 2.2.1. Shear viscosity Shear viscosity measurements of HASE polymer solutions were carried out in three different instruments. For shear viscosity measurements, a Contraves LS40 (with a couette geometry of 12 mm diameter cup and 11 mm diameter bob of 8 mm length) and a Carri-med CSL 500 controlledstress (with a cone-and-plate geometry with a cone of 40 mm diameter and 580 angle) was used for
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low and moderate viscosity solutions, respectively. The viscosity at high shear rates was measured using the annular flow geometry of the RFX fluid analyzer with a 5 mm tube with 4.5 mm rod (of 20 mm length). A wide shear rate range of 0.1–10,000 s−1 was achieved using the three instruments. 2.2.2. Extensional viscosity A pictorial representation of the opposing jets extensional rheometer is shown in Fig. 2. The apparatus consists of two opposing nozzles immersed in a fluid sample and separated by an adjustable distance. One of the nozzles is fixed to a mobile arm and the other is a stationary jet connected to a torque rebalance transducer (TRT). The fluid sample is continuously drawn into the syringes through the nozzles at a constant flow rate. The fluid movement creates a hydrodynamic force on the nozzles, causing the movable arm to separate from the fixed distance. The TRT transducer maintains the jet to its preset position and the measured torque give the apparent extensional viscosity of the fluid at the specific deformation rate. Data of apparent extensional viscosity were obtained using six different diameter nozzles ranging from 0.5 to 5 mm. Larger diameter nozzles were used for low extension rates and the smaller nozzles gave data at high extension rates. The optimum jet separation distance, 2 h, was obtained by adjusting the gap to be the same as the internal diameter of the nozzles [21]. The movement of a liquid into the jets creates an exponential flow field with a stagnation point in the center of the plane. This extensional flow field was confirmed by independent light scattering measurement [22]. Thus, the extension rates are not uniform over the cross-section of the flow and an average value is used. The apparent extensional rate is given by ε˙ =
˙ Q , π hR2
(1)
˙ is the total volumetric flow rates, h is one-half the separation distance and R is the jet where Q radius.
Fig. 2. Schematic diagram of Rheometric RFX opposing jets apparatus
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The apparent stress is given by F0 , A where F0 is the force exerted on the stationary jet and A is the area of jet orifice. Hence, the apparent extensional viscosity is given by σ ηe = . ε˙ σ =
(2)
(3)
A function commonly used to compare the shear and extensional viscosities of fluids is the Trouton ratio, defined as the ratio of the extensional to the shear viscosity at the same second invariant √ rate-of-deformation tensor, i.e. when γ˙ = 3˙ε . That is, Tr =
ηe (˙ε) , η(γ˙ )
γ˙ =
√ 3˙ε .
(4)
For Newtonian fluid, Tr is 3. The Reynolds number, NRe , for extensional flow is given by [23] NRe =
ρ ε˙ h2 , η
(5)
where ρ is the sample density and is assumed to be 1000 kg/m3 for all the samples and η is the shear viscosity. The technique of measuring extensional viscosity of low viscosity fluids using opposing jet suffers from several disadvantages. These include the presence of significant shearing components and the lack of homogeneity in the deformation flow field. Hence, measurements of true extensional properties are not possible [24]. Thus, the equipment can only be used for measuring the apparent extensional viscosity. The presence of bubbles in the syringe pumps at high flow rates added to another disadvantage of this instrument. However, loading the syringes manually with polymer solutions can prevent this and any bubbles that are trapped will be purged from the system. All experiments were carried out without bubbles in the syringe. 2.3. Calibrating the RFX with a Newtonian fluid The extensional and shear viscosity data of a Newtonian fluid (mixture of 80 vol.% glycerol and 20 vol.% water) are presented in Fig. 3. The shear viscosity at shear rates less than 100 s−1 was obtained from the Contraves LS40 rheometer and the viscosity at high shear rates was measured using the RFX. The shear viscosity results from the two rheometers are identical, giving an average Newtonian shear viscosity of 0.055 Pa s. For extensional viscosity measurements, the opposing jet rheometer was checked using the Newtonian fluid (mixture of 80 vol.% glycerol and 20 vol.% water). Different diameter nozzles were used to achieve a wide range of extensional rates. Each of the different diameter nozzles covers approximately one decade of extensional rates and the results obtained from them are in concordance with one another, as shown in Fig. 3. The Trouton ratio for the Newtonian test fluid was found to be approximately 3, which confirms that the RFX yields correct extensional viscosity for a Newtonian fluid. The discrepancy observed with the 0.5 mm jet is due to fluids inertia effect, encountered with Newtonian fluids with shear viscosity of
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Fig. 3. Extensional and shear viscosities of 80 vol.% glycerol mixture obtained from the RFX fluid analyzer and the Contraves LS40 rheometer.
less than 100 mPa s [23]. At extension rate of 2000 s−1 (which corresponds to a Reynolds number greater than 5), the viscosity obtained from the 1 mm jet shows a thickening behavior. This effect is attributed to the inertial effects as described by Dontula et al. [23]. However, for extensional rates with Reynolds number less than 5, the opposing jet rheometer yields data that agrees with the expected behavior for Newtonian fluids. 3. Results and discussion 3.1. Shear and extensional viscosities of HASE polymers The shear and apparent extensional viscosities of the HASE polymers are shown in Figs. 4a–d and 5a–d, respectively. The results for the polymer with no hydrophobic group attached to the macromonomer, i.e. RDJ31-1, are shown in Figs. 4a and 5a. The shear viscosity of the polymer remains constant up to very high shear rates, and show only slight shear thinning behavior thereafter. The extensional viscosity also remains constant up to very high deformation rates and starts to show extension thickening at approximately the same deformation rate as when shear thinning is observed. For polymer without hydrophobic association, the shear thinning is due to the orientation and alignment of the polymer clusters and molecules along the shear flow field, reducing the drag force, which contributes to the viscosity. The slight increase in the extensional viscosity may be due to the stretching of the molecules when subjected to extensional flow field. Previous light scattering studies suggested that the ethyl acrylate (EA) on the backbone of RDJ31-1 is blocky [20]. These EA segments are hydrophobic enough to form clusters, which are weak. Under extensional deformation, these aggregates are disrupted, freeing the stiff polymer backbones that become aligned by the flow field. The Trouton ratio is ∼3 at low deformation rates and increases to slightly above 3 at higher rates. Due to its relatively low molecular weight, the extensional viscosity of HASE polymer does not increase to very large values compared to that observed for other polymer solutions such as
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Fig. 4. Shear viscosities vs. shear rates of model HASE polymers at various polymer concentrations: (a) RDJ31-1; (b) RDJ31-3; (c) RDJ31-4; (d) RDJ31-5.
polyacrylamide, which typically possesses molecular weights of the order of 106 . For the same reason, the extension thickening due to entanglement behavior is unlikely for HASE polymer. For the HASE polymer with hydrophobic macromonomers attached to the backbone, the shear and extensional viscosities are predominantly influenced by hydrophobic association, which can lead to aggregation of neighboring molecules into clusters or connected network. The shear and extensional viscosities of RDJ31-3 are shown in Figs. 4b and 5b, respectively. The shear viscosity exhibits a shear-thinning behavior with no zero or low-shear viscosity detected even at relatively low deformation rate of 0.1 s−1 . Although the polymer contains hydrophobic groups, it is believed that they are in the form of clusters with predominantly intra-molecular junctions that are weakly linked to neighboring clusters due to their smaller hydrophobes [8]. Subjected to shear deformation, the polymer clusters rearrange and orientate along the flow field, which results in the reduction in the viscosity. The apparent extensional viscosity of the RDJ31-3 show significant extension thickening for all the concentrations tested. When subjected to extensional flow field, the polymer molecules are stretched, causing the disruption of the intra-molecular junctions. The intra-molecular junctions fragment and hydrophobes released from these junctions reassociate to form inter-molecular associations with neighboring chains. This is thought to be the cause for the increase in the extensional viscosity of the solutions. The onset of thickening behavior occurs at lower extensional rates when the polymer concentration is increased. At higher polymer concentrations, the hydrodynamic volume increases, which decreases the distance separating the polymer chains.
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Fig. 5. Extensional viscosities vs. shear rates of model HASE polymers at various polymer concentrations: (a) RDJ31-1; (b) RDJ31-3; (c) RDJ31-4; (d) RDJ31-5.
Consequently, some of the free hydrophobes that are detached from intra-molecular junctions have a higher probability to re-associate with hydrophobes from other polymer chains to produce a larger number of inter-molecular associative junctions. As the extension rate is increased further, the apparent extensional viscosity exhibits a decline, possibly due to the disruption of the inter-molecular junctions and the subsequent alignment of polymer backbones. The deformation rates for the maxima in extensional viscosities are very similar for all the concentrations, and indicate that the rate of junction disruption is faster than the rate at which they can be reformed. However, the maxima in the extensional viscosity, and the level of the viscosity in general, increase with polymer concentrations. It is evident from Fig. 6a that the maxima of the extensional viscosities shift to higher extensional stresses with increasing polymer concentrations. This suggests that the strength of the inter-molecular junctions (proportional to the extensional stress) is concentration dependent since more active junctions are formed at higher concentrations. It also indicates that the contribution from the extension of polyelectrolyte backbones to the thickening effect as observed in RDJ 31-1 sample is not as significant when compared to hydrophobic associations. In other words, the viscosity profile is dominated by hydrophobic aggregations through the creation of active junctions, rather than from the stiff polyelectrolytes backbones. This finding also strongly supports the argument that the viscosity behavior is predominantly influenced by the characteristics of the associative junctions. The maximum extensional viscosity indicates that most of the intra-molecular junctions are converted to inter-molecular associations.
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Fig. 6. (a) Extensional viscosities vs. extensional stress of 0.5–2.0 wt.% RDJ31-3; (b) shear viscosities vs. stress of 1 wt.% RDJ31-4 and 31-5.
The shear viscosities of the HASE polymer with larger hydrophobic groups, i.e. RDJ31-4 (C16 hydrophobe) and 31-5 (C20 hydrophobe) are shown in Figs. 4c and d, respectively. For these polymers, the viscosity exhibits shear-thinning characteristics and, again, no constant low-shear viscosity region is discernable even at relatively low shear rate of 0.1 s−1 . The level of shear viscosity of the RDJ31-4 is higher than RDJ31-3 at comparable concentrations due to the stronger hydrophobic associations. Closer inspection of the viscosity profiles of the RDJ31-4 and 31-5 polymers reveals that the shear-thinning behavior does not yield a power-law region with constant slope. This behavior is especially evident above the overlap concentration of approximately 0.3–0.5 wt.%. This thinning behavior with different slopes is especially discernable when the viscosity is plotted as a function of shear stress, as shown in Fig. 6b for the 1 wt.% solutions of RDJ31-4 and 31-5. Due to their larger hydrophobic groups and hence higher hydrophobic strength, these hydrophobic groups form intermolecular associations with those of neighboring molecules to produce clusters, whose size increases with increasing polymer concentration and may span the whole volume at sufficiently high concentrations. However, the aggregation number
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in each associative junction is highly heterogeneous at low salt concentrations as observed from relaxation spectra of these systems [25]. Subjected to shear deformation, the clusters are broken into smaller units, lowering the viscosity [8,25]. For the RDJ31-5, the shear viscosity appears to approach a plateau of 700–800 Pa s at an applied stress of less than 0.5 Pa. Below 0.5 Pa, the associative network of the HASE polymer containing C20 hydrophobe is sufficiently strong to resist the deformation stress. Above 0.5 Pa, the network structure of the polymer is broken into smaller clusters, yielding a rapid decrease in viscosity (a reduction from 800 to 10 Pa s is observed when the shear stress is increased from 0.5 to 10 Pa). Further increase in the stress beyond approximately 10 Pa results in an increase in the resistance to flow, which manifests as a decrease in the slope of the shear-thinning curve. This may be due to the fact that an equilibrium cluster size is reached, which undergoes orientation along the flow field without further breakdown of the structure. At applied stress in excess of 60 Pa, another region of rapid viscosity decrease is encountered, and this is due to further destruction of clusters at higher deformation stresses. Similar multi-shear thinning behavior can be seen for the RDJ31-4 with C16 hydrophobe. The extensional viscosities of both RDJ31-4 and 31-5 decreases with increasing deformation, with the level of the viscosity being higher for the polymer with higher hydrophobic strength. For these two polymers with sufficiently strong hydrophobic groups, inter-molecular associations are dominant. The decrease in the extensional viscosity with extensional rates is due to the disruption of these inter-molecular junctions in the polymer network. However, when plotted as Trouton ratio against extensional rate as in Fig. 9b for 1 wt.% HASE polymer, the values for all three HASE polymers containing hydrophobic groups show an increase with increasing extensional rates. The increase in Trouton ratio is proportional to the hydrophobicity of HASE polymer. The shear and extensional viscosity profiles of 1 wt.% associative polymers with different hydrophobe sizes are compared in Figs. 7a and b, respectively. By increasing the hydrophobe chain length, the viscosity increases proportionally. This is attributed to the fact that longer hydrophobic chain produces junctions with larger aggregation number, which are stronger. The difference in the shear and extensional viscosities at low deformation rates of 1 wt.% RDJ31-4 and RDJ31-5 is ∼10. The differential gap is even more pronounced when comparing RDJ31-3 and RDJ31-4 system. When the hydrophobic group is increased from C12 to C16 , the extension-thickening phenomenon at moderate extensional rates disappears. This seems to suggest that in the vicinity of between C12 and C16 hydrocarbon chain, a critical hydrophobic carbon content exists, where the conversion of predominantly intra-molecular junctions to inter-molecular junctions is not significant enough to cause the thickening behavior. The nature of the polymer network, which is a strong function of the hydrophobicity of the macromonomer, controls the magnitude of the viscosity and its profile. At high deformation rates, the shear viscosity of all the model polymers approaches that of RDJ31-1. This is brought about by the disruption of the hydrophobic junctions, which produces individual or isolated polymer chains or small micellar clusters. 3.2. Elastic behavior of HASE polymers Fig. 8 shows the storage modulus, G0 profiles of three model HASE polymers (RDJ31-3, 31-4 and 31-5). The elasticity of RDJ31-1 is so low that it could not be measured by the existing rheometer. Associative polymer with the longest hydrophobe exhibits the largest G0 . The results demonstrate that there are more mechanically active junctions in the solution of larger hydrophobic macromonomer than in the smaller ones.
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Fig. 7. (a) Comparison of the steady shear viscosities of 1 wt.% model HASE polymers with C0 , C12 , C16 and C20 hydrophobes; (b) comparison of the extensional viscosities of 1 wt.% model HASE polymers with C0 , C12 , C16 and C20 hydrophobes.
The meaning of the mechanically active junctions can be analyzed based on the transient network theory proposed in 1946 by Green and Tobolsky [26]. The theory is based on the extension of classical rubber elasticity theories for transient networks, which was first introduced to account for entanglements or reversible physical bonds. The theory predicts a constant steady-shear viscosity of η(γ˙ ) = η0 = τ G∞ ,
(6)
where the relaxation time τ is the reciprocal of the bond breaking and re-formation rate, and G∞ is the high-frequency or plateau modulus given by G∞ = veff RT,
(7)
where veff is the number density of effective or elastic chains, R is the universal gas constant and T the absolute temperature. Thus, from the knowledge of the plateau modulus, the mechanically active
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Fig. 8. Comparison of the storage moduli of 1 wt.% model HASE polymers with C12 , C16 and C20 hydrophobes.
junctions in the system may be estimated. The magnitude of the storage modulus at a fixed frequency can be correlated to the plateau modulus as given in Eq. (7). Hence, from the results in Fig. 8, it is evident that the plateau modulus of RDJ31-3 (C12 hydrophobe) is lower than that of the C16 and C20 hydrophobic system. This suggests that the number of mechanically active junctions of the RDJ31-3 system is lower than RDJ31-4 and 31-5 at the same polymer concentration. 3.3. Comparison of the Trouton ratio of model HASE polymers The relative significance of the extensional and shear properties can be better discussed by comparing the magnitude of the ratio of the extensional to the shear viscosity as given by the Trouton ratio. Figs. 9a and b show Tr as a function of extensional rates for various concentrations of RDJ31-5 system and 1 wt.% model HASE polymers, respectively. At low extensional rates, the Tr of 0.3, 0.5, 0.8 and 1 wt.% RDJ31-5 solutions is approximately 3. It is interesting to note that Tr of the 0.3 wt.% RDJ31-5 remains unchanged at ∼3 over a wide range of extensional rates (5–5000 s−1 ). This means that the structure of the individual polymer clusters is isolated and is not perturbed to any significant extent by the extensional flow field. This correlates well with the overlap concentration of these model polymers estimated to be approximately 0.3 wt.%. When the concentration is increased to 0.5 wt.%, Tr increases with extensional rates. However, the increase becomes steeper at higher polymer concentration of 0.8 and 1 wt.%. A Tr of about 50 is observed at extensional rate of 1000 s−1 . Fig. 9b shows a comparison between 1 wt.% model HASE polymer with different hydrophobic modification. The Tr for the polymers containing hydrophobic groups depart from 3 at higher extensional rates, while that for the control polymer RDJ31-1 (without hydrophobe) remained roughly constant at about 3 at low extensional rates. It increases slightly and then decreases at high extensional rates. The increase in Tr with extensional rates is proportional to the hydrophobicity of the macromonomer, where RDJ31-5 shows the highest Tr. Another interesting feature is that of RDJ31-3, where the Tr reaches a maximum at extension rate 1000 s−1 , and beyond this limit, Tr decreases. The magnitude and the dependence of Tr on hydrophobicity and extensional rates are indicative of the strength of the transient polymer network. For RDJ31-5, the aggregation number is larger, yielding stronger network, which can be deformed to
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Fig. 9. (a) The relationship between Trouton ratio and extensional rates of 0.3, 0.5, 0.8 and 1 wt.% RDJ 31-5 model polymer solutions; (b) comparison of the Trouton ratio at different extensional rates of 1 wt.% RDJ 31 model polymer series with C0 , C12 , C16 and C20 hydrophobes.
a greater extent before they fragment into smaller isolated micellar clusters. Similar behavior was also reported for associative polyelectrolyte systems [9] and hydroxyethylcellulose solutions [27]. The dependence of both the extensional and shear viscosities at a fixed deformation rate of 50 s−1 on polymer concentrations is depicted on a double logarithmic plot in Figs. 10a and b. A power law relationship is observed which can be represented by the expression given below: ηE = Acα ,
(8a)
η = Bcβ .
(8b)
Using regression to fit the data, the values of the exponents α and β and the constants A and B were determined and tabulated in Table 2. It can be seen that α and β increase with increasing hydrophobe chain length with α being always larger than β. Hence, the extensional viscosity exhibits a stronger dependence on the polymer concentration than shear viscosity. This is indicative of the
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Fig. 10. (a) Concentration dependence of extensional viscosities of model HASE polymers with C12 , C16 and C20 hydrophobes at ε˙ of 50 s−1 ; (b) concentration dependence of shear viscosities of model HASE polymers with C12 , C16 and C20 hydrophobes at γ˙ of 50 s−1 .
sensitivity of the network structure to the stronger deformation experienced in extensional flows. The values of the exponents are plotted against the activation energy at γ˙ =50 s−1 in Fig. 11a. The activation energy was obtained by conducting shear viscosity tests at different temperatures. Based on the Arrhenius equation, the slope of the viscosity versus 1/T curves gives the magnitude of the activation Table 2 Fitted parameters for Eqs. (8a) and (8b) of 1 wt.% model HASE polymers at ε˙ and γ˙ =50 s−1 HASE polymer
α
A
β
B
RDJ 31-1 RDJ 31-3 RDJ 31-4 RDJ 31-5
0.92 1.54 3.15 4.33
0.068 0.464 2.710 17.839
0.82 1.06 2.68 3.21
0.025 0.048 0.261 1.216
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Fig. 11. (a) Dependence of exponent α and β on the activation energy of 1 wt.% model HASE polymers at ε˙ and γ˙ of 50 s−1 ; (b) Effect of hydrophobic content on the shear and extensional viscosity of 1 wt.% model HASE polymer at ε˙ and γ˙ of 50 s−1 .
energy: η(γ˙ ) = Ae−Ea /RT ,
(9)
where, η(γ˙ ) is the shear viscosity at given shear rate, Ea is the activation energy (J/mol), A is the Arrhenius constant, R is the gas constant, and T is the temperature. The plot (Fig. 11a) and the numerical values tabulated in Table 2 indicate that there is a correlation between the exponents with the strength of the polymer network. The dependence of extensional and shear viscosities of 1 wt.% polymer solutions at a fixed deformation rate of 50 s−1 on the size of the hydrophobic group is depicted in Fig. 11b. The figure shows that both viscosities display similar dependence with a slope of 0.43, however the magnitude of the extensional viscosity is ∼10 times larger than the shear viscosity. The significance of this result is that the ratio at the fixed deformation rate is independent of the hydrophobicity of the macromonomer. Significant enhancement
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in the shear and extensional viscosity is observed when the carbon content of the hydrophobes exceeds 8 to 10. 3.4. Mechanism of HASE polymers under extensional flow From the present study on HASE polymers in extensional flow, the hydrophobicity of the macromonomer has a strong bearing on the extensional viscosity profiles. Based on our understanding of the microstructure of HASE polymers in solutions, the evolution of the network structure during deformation is proposed. The pictorial representation of the network structure in the extensional flow field is summarized in Fig. 12. 3.4.1. HASE polymer with weak hydrophobic interactions The polymer chains at the quiescent state consist of very weak associations at the backbone brought about by the blocky ethyl acrylate segments. When extensional stress is applied, the polymer clusters dissociate into individual polymer chain, which are aligned in the direction of the extensional stress. Due to the stiff polyelectrolyte backbone, the polymer chains offer some resistance to deformation. The consequence of this is a mild shear-thickening behavior at moderate extensional rates.
Fig. 12. Microstructure of HASE polymers under extensional flow fields (a) weak association; (b) moderate association and (c) strong association.
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3.4.2. HASE polymer with moderate hydrophobic interactions Polymer with shorter hydrophobes, such as RDJ31-3 system form clusters with predominantly intramolecular junctions and a loose connection with other clusters as depicted in Fig. 12b. When the stress is applied, some of the intra-molecular junctions are detached and the free hydrophobes re-associate to form inter-molecular junctions. This induces the formation of a network with larger proportion of inter-molecular junctions. Hence, the polymer network is more resistant to deformations and is responsible for the extensional-thickening behavior. However, when a critical shear stress is exceeded, the inter-associations breakdown, yielding a lower viscosity solution. 3.4.3. HASE polymer with strong hydrophobic interactions HASE polymer with stronger hydrophobes such as RDJ 31-4 and RDJ31-5, exhibits extensive network structure through inter-molecular associations (Fig. 12c). Since the hydrophobicity is stronger, the aggregation number is larger, resulting in stronger junctions. When sufficient extensional stress is applied, the network deforms and progressively degenerates to several individual clusters. This yields a continuous decrease in the extensional viscosity. 4. Conclusions The associative polymers form a transient network through association of hydrophobes grafted onto the polymer backbone. The strength of the network junction is proportional to the hydrophobic chain length of the macromonomer. However, the network formed by shorter hydrophobic chain (C12 ) is predominantly intra-molecular. The intra-molecular junctions are converted to inter-molecular associations at moderate deformation rates giving rise to the observed extensional thickening behavior. The Trouton ratio at low concentration (<0.3 wt.%) and unmodified polymer (RDJ31-1) remains at ∼3 over 5 decades of extensional rates. However, the Trouton ratio of polymers with C12 , C16 and C20 hydrophobes increases with polymer concentrations and extensional rates. Such dependence is directly related to the strength of the network junction. Acknowledgements One of the authors (HT) would like to acknowledge the financial support provided by the university. We would also like to acknowledge the financial support provided by the National Science and Technology Board of Singapore, the Ministry of Education and the Singapore-Ontario collaborative research program. References [1] R.D. Jenkins, The Fundamental Thickening Mechanism of Associative Polymers in Latex Systems: a Rheological Approach, Ph.D. Thesis, Lehigh University, Bethlehem 1991. [2] T. Annable, R. Buscall, R. Ettelaie, D. Whittlestone, J. Rheol. 37 (1993) 695. [3] K. Zhang, B. Xu, M.A. Winnik, P.M. Macdonald, J. Phys. Chem. 100 (1996) 9834. [4] E. Alami, M. Almgren, W. Brown, J. Francois, Macromolecules 29 (1996) 2229. [5] Y. Uemura, P.M. Macdonald, Macromolecules 29 (1996) 63. [6] A. Yekta, B. Xu, J. Duhamel, H. Adiwidjaya, M.A. Winnik, Macromolecules 28 (1995) 956.
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[7] B. Xu, L. Li, K. Zhang, P.M. Macdonald, M.A. Winnik, R.D. Jenkins, D.R. Bassett, D. Wolf, O. Nuyken, Langmuir 13 (1997) 6896. [8] V. Tirtaatmadja, K.C. Tam, R.D. Jenkins, Macromolecules 30 (1997) 3271. [9] J.C. Kennedy, J. Meadows, P.A. Williams, J. Chem. Soc. Faraday Trans. 91 (5) (1995) 911. [10] V. Tirtaatmadja, K.C. Tam, R.D. Jenkins, Macromolecules 30 (1997) 1426. [11] L. Guo, K.C. Tam, R.D. Jenkins, Macromol. Chem. Phys. 199 (1998) 1175. [12] E.J. Schaller, P.R. Sperry, Handbook of Coatings Additives, Vol. 2, Marcel Dekker, New York, 1992 (Chapter 4). [13] L.M. Walker, P. Moldenaers, J. Berret, Langmuir 12 (1996) 6309. [14] R.K. Prud’homme, G.G. Warr, Langmuir 10 (1994) 3419. [15] C. Viebke, J. Meadows, J.C. Kennedy, P.A. Williams, Langmuir 14 (1998) 1548. [16] T.D.S. Vlahiotis, Extensional Flow Behaviour of Associative Polymer Solutions, Ph.D. Thesis, University of Toronto, 1992. [17] R.D. Jenkins, L.M. Delong, D.R. Bassett, Hydrophilic polymers: performance with environmental acceptability, in: J.E. Glass (Ed.), Advances in Chemical Series 248, American Chemical Society, Washington DC, 1996, p. 425. [18] S. Dai, K.C. Tam, R.D. Jenkins, Macromol. Chem. Phys., in Press. [19] S. Dai, K.C. Tam, R.D. Jenkins, Macromolecules 33 (2000) 404. [20] S. Dai, K.C. Tam, R.D. Jenkins, European Polym. J. (2000), in press. [21] K.J. Mikkelsen, C.W. Macosko, G.G. Fuller, Proc. Xth Int. Congr. on Rheology, Sydney, Australia, Vol. 2, 1989, p. 125. [22] A.J. Muller, J.A. Odell, J.P. Tatham, J. Non-Newtonian Fluid Mech. 35 (1990) 231. [23] P. Dontula, M. Pasquali, L.E. Scriven, C.W. Macosko, Rheol. Acta 36 (1997) 429. [24] V. Tirtaatmadja, T. Sridhar, J. Rheol. 37 (6) (1993) 1081. [25] H. Tan, Extensional and Viscoelastic Properties of Associative Polymer Solution, Master Thesis, NTU, Singapore, 1999. [26] M.S. Green, A.V. Tobolsky, J. Chem. Phys. 14 (1946) 80. [27] J. Meadows, P.A. Williams, J.C. Kennedy, Macromolecules 28 (1995) 2683.
Extensional properties of model hydrophobically modified alkali-soluble associative (HASE) polymer solutions H. Tan a , K.C. Tam a,∗ , V. Tirtaatmadja b , R.D. Jenkins c , D.R. Bassett d a
c
School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore b Department of Chemical Engineering, University of Melbourne, Parkville, Vic. 3052, Australia Union Carbide Asia Pacific Inc., Technical Center, 16 Science Park Drive, The Pasteur, Singapore 118227, Singapore d Union Carbide Corporation, UCAR Emulsions Systems, Research and Development, Cary, NC 27511, USA Received 23 July 1999; received in revised form 13 December 1999
Abstract The relationship between shear and extensional viscosities of a series of model hydrophobically modified alkali-soluble associative (HASE) polymers with varying degree of hydrophobicity was investigated. An opposing jet rheometer (Rheometric RFX) was used to measure the extensional and shear viscosities of 0.3–4.0 wt.% solutions. The deformation rates were varied from 0.1 to 10,000 s−1 . The shear and extensional viscosities increase exponentially with the hydrophobicity and concentration of the polymers. This is attributed to the increase in the strength of the associative junctions. Extensional thickening is observed at moderate extensional rates for the polymer with C12 H25 hydrophobes. This indicates that associative polymer with shorter hydrophobic chain undergoes a conversion from aggregated clusters with predominantly intra-molecular associations at low extension rates to inter-molecular cluster associations at moderate deformation rates. At high extensional rates, the deformation force exceeds the strength of inter-cluster associations, resulting in the destruction of the active junctions, yielding a continuous decrease in the extensional viscosity. The Trouton ratio increases with deformation rates, polymer concentration and the size of the hydrophobes. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Polyelectrolytes; Associative polymer; Opposing jet rheometer; Extensional and shear viscosities
1. Introduction Water-soluble associative polymers are widely used as viscosity modifiers in several industrial applications, such as in paint formulations and paper coatings. They are now replacing the conventional ∗
Corresponding author. Present address: Department of Mechnanical Engineering, MIT, Cambridge, MA, USA. Tel.: +65-790-5590; fax: +65-791-1859. E-mail address: [email protected] (K.C. Tam) 0377-0257/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 0 2 5 7 ( 0 0 ) 0 0 0 9 3 - 8
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non-associative thickeners. Unlike the solvent-based formulations, these water-soluble systems do not contain volatile solvents and hence do not contribute to environmental problems. Higher thickening efficiency is achieved by the self-associating properties of the attached hydrophobic groups, yielding a network structure that enhances the viscosity of the formulation. Associative polymers (APs) are generally of low molecular weights and they produce less spattering in paints during applications by brush rolling. The positive characteristics of APs make them more attractive as the material of choice for use as thickeners in various types of coating formulations. The rheological properties of water-soluble associative polymers depend on factors such as polymer concentrations, molecular weight, degree of hydrophobic modification, characteristics of hydrophobic groups and the flexibility of the polymer backbone. Following the comprehensive study by Jenkins [1], a large number of publications on nonionic associative polymers, particularly the well-defined end-capped hydrophobically-modified ethylene oxide urethane (HEUR) systems have appeared [2–7]. However, only few studies on anionic associative polymers such as the hydrophobically modified alkali-soluble associative (HASE) systems have been reported [8–11]. HASE polymer consists of a backbone of poly(acrylate), with hydrophobic macromonomers distributed along the polymer backbone. At low pH, the polymer exists as insoluble latex dispersed in an aqueous medium. Upon neutralization by raising the pH using a base, the polymer undergoes coil expansion due to electrostatic repulsion of the negative charges on the polymer backbone. The polymer then becomes water-soluble, and its hydrophobic groups associate with those of other polymer chains to form inter-molecular junctions. These junctions produce a polymer network, which enhances the viscosity of the solution. The concentrations of charges along the backbone and the ionic strength of the solutions significantly alter the rheological behavior [12]. Extensional flow studies on transient network systems are scarce. We will summarize some of the recent publications on a few transient network polymer or surfactant systems. The properties of wormlike micelles subjected to extensional flow have been investigated by Walker and co-workers [13] and Prud’homme and Warr [14]. The former authors examined the macroscopic response of wormlike micelles subjected to elongational flow field. They concluded, from scaling analysis that the extensional thickening observed in the semi-dilute solution region was not caused by micellar growth. However, Prud’homme and co-workers concluded from their studies that the increase in extensional viscosity is a result of strong alignment of the micelles in the flow direction. Meadows and co-workers performed extensional studies on non-associative polymer such as hydroxyethylcellulose (HEC) [15]. They examined the extensional properties of different concentrations and molecular weights of HEC in aqueous solutions. The Trouton ratio (Tr) approached a value of 3 at low extension rates regardless of their concentration and molecular weight. However, it increased significantly with extensional strain rates and polymer concentrations. Kennedy and co-workers examined the extensional properties of hydrophobically modified associative polyelectrolytes [9]. They observed extensional thickening of the viscosity at a specific deformation rate when the polymer concentration was increased. On the other hand, Viebke and co-workers reported extensional thinning behavior at all deformation rates when a concentrated latex dispersion was added to the associative polymer [15]. Vlahiotis [16] studied the response of the HEUR polymer subjected to extensional flow field under the direction of Winnik and James at the University of Toronto, but her results have not been published yet. She observed from online fluorescence spectroscopy measurements that the mean aggregation number of the flower micelles remained constant. The behavior of associative polymers under the strong extensional flow field has not been extensively studied, even though, many of the coating processes involve extensional flow fields. In this paper, the
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extensional viscosity of a series of model hydrophobically modified alkali-soluble polymers containing hydrophobes of varying hydrophobicity was examined. The extensional properties are correlated to the polymer concentrations and the strength of the network junction.
2. Experimental 2.1. Materials The associative polymers used are the emulsion co-polymerization products of methacrylic acid (MAA), ethyl acrylate (EA), which form the polymer backbone. Macromonomers capped with a hydrophobic group via a polyethylene-oxide (PEO) chain is then grafted onto the backbone. The general structure of HASE polymer is shown in Fig. 1a. Four model HASE polymers were synthesized and designated as RDJ31-1, RDJ31-3, RDJ31-4 and RDJ31-5. RDJ31-1 is a control polymer without any hydrophobic modification, while RDJ31-3, 31-4 and 31-5 contain C12 , C16 and C20 hydrophobic groups, respectively, attached to the MAA/EA backbone. These polymers are identical to the materials used in our previous publications [8,10,11]. The detailed information on these polymers is summarized in Table 1. In this study, the PEO chains on the hydrophobic macromonomer were kept constant to 31 mol. The synthesis procedure can be found elsewhere [8,17]. Fig. 1b depicts the microstructure of HASE polymer produced by an associative mechanism at its unperturbed state. The hydrophobes can interact with hydrophobes of the same polymer chain (intra-molecular association) or with hydrophobes from different polymer chains (inter-molecular association) to yield clusters consisting of several polymer chains. These clusters are connected to each other through the associative junctions to produce a polymer network [18,19]. In systems with stronger hydrophobic groups, the junctions are stronger and the network is more resistant to deformation. The overall network strength is highly dependent on the active junctions formed by inter-molecular associations. It has been shown by Dai et al. [20] that the ethyl acrylate segments are blocky and they can interact with other EA blocks situated along the polymer backbone. 2.2. Techniques Associative polymer solutions were prepared from a stock solution of 3 wt.% polymer latex dispersion by diluting with 10−4 M potassium chloride (KCl) to the required concentrations. They were then adjusted to pH between 9 and 9.5 by adding 2-amino 2-methyl 1-propanol (AMP). On dissolution, the hydrophobes Table 1 Chemical composition of model HASE polymers Polymer
Hydrophobe type
Precursor Mn
Macro. Mn
GPC Mn /Mw of macro.
Mole composition X/Y/Z
RDJ 31-1 RDJ 31-3 RDJ 31-4 RDJ 31-5
None Dodecyl Hexadecyl Eicosanyl
1726 1761 1835
1927 1962 2036
2120/2179 2197/2257 2023/2077
49/51/0 49/50/1 49/50/1 49/50/1
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Fig. 1. (a) Chemical structure of model HASE associative polymer; (b) network structure of HASE associative polymer after neutralization.
associate to form a network junction as shown in Fig. 1b. The samples were kept for 2 days prior to testing to allow the solutions to equilibrate. All experiments were conducted at 25±1◦ C. 2.2.1. Shear viscosity Shear viscosity measurements of HASE polymer solutions were carried out in three different instruments. For shear viscosity measurements, a Contraves LS40 (with a couette geometry of 12 mm diameter cup and 11 mm diameter bob of 8 mm length) and a Carri-med CSL 500 controlledstress (with a cone-and-plate geometry with a cone of 40 mm diameter and 580 angle) was used for
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low and moderate viscosity solutions, respectively. The viscosity at high shear rates was measured using the annular flow geometry of the RFX fluid analyzer with a 5 mm tube with 4.5 mm rod (of 20 mm length). A wide shear rate range of 0.1–10,000 s−1 was achieved using the three instruments. 2.2.2. Extensional viscosity A pictorial representation of the opposing jets extensional rheometer is shown in Fig. 2. The apparatus consists of two opposing nozzles immersed in a fluid sample and separated by an adjustable distance. One of the nozzles is fixed to a mobile arm and the other is a stationary jet connected to a torque rebalance transducer (TRT). The fluid sample is continuously drawn into the syringes through the nozzles at a constant flow rate. The fluid movement creates a hydrodynamic force on the nozzles, causing the movable arm to separate from the fixed distance. The TRT transducer maintains the jet to its preset position and the measured torque give the apparent extensional viscosity of the fluid at the specific deformation rate. Data of apparent extensional viscosity were obtained using six different diameter nozzles ranging from 0.5 to 5 mm. Larger diameter nozzles were used for low extension rates and the smaller nozzles gave data at high extension rates. The optimum jet separation distance, 2 h, was obtained by adjusting the gap to be the same as the internal diameter of the nozzles [21]. The movement of a liquid into the jets creates an exponential flow field with a stagnation point in the center of the plane. This extensional flow field was confirmed by independent light scattering measurement [22]. Thus, the extension rates are not uniform over the cross-section of the flow and an average value is used. The apparent extensional rate is given by ε˙ =
˙ Q , π hR2
(1)
˙ is the total volumetric flow rates, h is one-half the separation distance and R is the jet where Q radius.
Fig. 2. Schematic diagram of Rheometric RFX opposing jets apparatus
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The apparent stress is given by F0 , A where F0 is the force exerted on the stationary jet and A is the area of jet orifice. Hence, the apparent extensional viscosity is given by σ ηe = . ε˙ σ =
(2)
(3)
A function commonly used to compare the shear and extensional viscosities of fluids is the Trouton ratio, defined as the ratio of the extensional to the shear viscosity at the same second invariant √ rate-of-deformation tensor, i.e. when γ˙ = 3˙ε . That is, Tr =
ηe (˙ε) , η(γ˙ )
γ˙ =
√ 3˙ε .
(4)
For Newtonian fluid, Tr is 3. The Reynolds number, NRe , for extensional flow is given by [23] NRe =
ρ ε˙ h2 , η
(5)
where ρ is the sample density and is assumed to be 1000 kg/m3 for all the samples and η is the shear viscosity. The technique of measuring extensional viscosity of low viscosity fluids using opposing jet suffers from several disadvantages. These include the presence of significant shearing components and the lack of homogeneity in the deformation flow field. Hence, measurements of true extensional properties are not possible [24]. Thus, the equipment can only be used for measuring the apparent extensional viscosity. The presence of bubbles in the syringe pumps at high flow rates added to another disadvantage of this instrument. However, loading the syringes manually with polymer solutions can prevent this and any bubbles that are trapped will be purged from the system. All experiments were carried out without bubbles in the syringe. 2.3. Calibrating the RFX with a Newtonian fluid The extensional and shear viscosity data of a Newtonian fluid (mixture of 80 vol.% glycerol and 20 vol.% water) are presented in Fig. 3. The shear viscosity at shear rates less than 100 s−1 was obtained from the Contraves LS40 rheometer and the viscosity at high shear rates was measured using the RFX. The shear viscosity results from the two rheometers are identical, giving an average Newtonian shear viscosity of 0.055 Pa s. For extensional viscosity measurements, the opposing jet rheometer was checked using the Newtonian fluid (mixture of 80 vol.% glycerol and 20 vol.% water). Different diameter nozzles were used to achieve a wide range of extensional rates. Each of the different diameter nozzles covers approximately one decade of extensional rates and the results obtained from them are in concordance with one another, as shown in Fig. 3. The Trouton ratio for the Newtonian test fluid was found to be approximately 3, which confirms that the RFX yields correct extensional viscosity for a Newtonian fluid. The discrepancy observed with the 0.5 mm jet is due to fluids inertia effect, encountered with Newtonian fluids with shear viscosity of
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Fig. 3. Extensional and shear viscosities of 80 vol.% glycerol mixture obtained from the RFX fluid analyzer and the Contraves LS40 rheometer.
less than 100 mPa s [23]. At extension rate of 2000 s−1 (which corresponds to a Reynolds number greater than 5), the viscosity obtained from the 1 mm jet shows a thickening behavior. This effect is attributed to the inertial effects as described by Dontula et al. [23]. However, for extensional rates with Reynolds number less than 5, the opposing jet rheometer yields data that agrees with the expected behavior for Newtonian fluids. 3. Results and discussion 3.1. Shear and extensional viscosities of HASE polymers The shear and apparent extensional viscosities of the HASE polymers are shown in Figs. 4a–d and 5a–d, respectively. The results for the polymer with no hydrophobic group attached to the macromonomer, i.e. RDJ31-1, are shown in Figs. 4a and 5a. The shear viscosity of the polymer remains constant up to very high shear rates, and show only slight shear thinning behavior thereafter. The extensional viscosity also remains constant up to very high deformation rates and starts to show extension thickening at approximately the same deformation rate as when shear thinning is observed. For polymer without hydrophobic association, the shear thinning is due to the orientation and alignment of the polymer clusters and molecules along the shear flow field, reducing the drag force, which contributes to the viscosity. The slight increase in the extensional viscosity may be due to the stretching of the molecules when subjected to extensional flow field. Previous light scattering studies suggested that the ethyl acrylate (EA) on the backbone of RDJ31-1 is blocky [20]. These EA segments are hydrophobic enough to form clusters, which are weak. Under extensional deformation, these aggregates are disrupted, freeing the stiff polymer backbones that become aligned by the flow field. The Trouton ratio is ∼3 at low deformation rates and increases to slightly above 3 at higher rates. Due to its relatively low molecular weight, the extensional viscosity of HASE polymer does not increase to very large values compared to that observed for other polymer solutions such as
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Fig. 4. Shear viscosities vs. shear rates of model HASE polymers at various polymer concentrations: (a) RDJ31-1; (b) RDJ31-3; (c) RDJ31-4; (d) RDJ31-5.
polyacrylamide, which typically possesses molecular weights of the order of 106 . For the same reason, the extension thickening due to entanglement behavior is unlikely for HASE polymer. For the HASE polymer with hydrophobic macromonomers attached to the backbone, the shear and extensional viscosities are predominantly influenced by hydrophobic association, which can lead to aggregation of neighboring molecules into clusters or connected network. The shear and extensional viscosities of RDJ31-3 are shown in Figs. 4b and 5b, respectively. The shear viscosity exhibits a shear-thinning behavior with no zero or low-shear viscosity detected even at relatively low deformation rate of 0.1 s−1 . Although the polymer contains hydrophobic groups, it is believed that they are in the form of clusters with predominantly intra-molecular junctions that are weakly linked to neighboring clusters due to their smaller hydrophobes [8]. Subjected to shear deformation, the polymer clusters rearrange and orientate along the flow field, which results in the reduction in the viscosity. The apparent extensional viscosity of the RDJ31-3 show significant extension thickening for all the concentrations tested. When subjected to extensional flow field, the polymer molecules are stretched, causing the disruption of the intra-molecular junctions. The intra-molecular junctions fragment and hydrophobes released from these junctions reassociate to form inter-molecular associations with neighboring chains. This is thought to be the cause for the increase in the extensional viscosity of the solutions. The onset of thickening behavior occurs at lower extensional rates when the polymer concentration is increased. At higher polymer concentrations, the hydrodynamic volume increases, which decreases the distance separating the polymer chains.
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Fig. 5. Extensional viscosities vs. shear rates of model HASE polymers at various polymer concentrations: (a) RDJ31-1; (b) RDJ31-3; (c) RDJ31-4; (d) RDJ31-5.
Consequently, some of the free hydrophobes that are detached from intra-molecular junctions have a higher probability to re-associate with hydrophobes from other polymer chains to produce a larger number of inter-molecular associative junctions. As the extension rate is increased further, the apparent extensional viscosity exhibits a decline, possibly due to the disruption of the inter-molecular junctions and the subsequent alignment of polymer backbones. The deformation rates for the maxima in extensional viscosities are very similar for all the concentrations, and indicate that the rate of junction disruption is faster than the rate at which they can be reformed. However, the maxima in the extensional viscosity, and the level of the viscosity in general, increase with polymer concentrations. It is evident from Fig. 6a that the maxima of the extensional viscosities shift to higher extensional stresses with increasing polymer concentrations. This suggests that the strength of the inter-molecular junctions (proportional to the extensional stress) is concentration dependent since more active junctions are formed at higher concentrations. It also indicates that the contribution from the extension of polyelectrolyte backbones to the thickening effect as observed in RDJ 31-1 sample is not as significant when compared to hydrophobic associations. In other words, the viscosity profile is dominated by hydrophobic aggregations through the creation of active junctions, rather than from the stiff polyelectrolytes backbones. This finding also strongly supports the argument that the viscosity behavior is predominantly influenced by the characteristics of the associative junctions. The maximum extensional viscosity indicates that most of the intra-molecular junctions are converted to inter-molecular associations.
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Fig. 6. (a) Extensional viscosities vs. extensional stress of 0.5–2.0 wt.% RDJ31-3; (b) shear viscosities vs. stress of 1 wt.% RDJ31-4 and 31-5.
The shear viscosities of the HASE polymer with larger hydrophobic groups, i.e. RDJ31-4 (C16 hydrophobe) and 31-5 (C20 hydrophobe) are shown in Figs. 4c and d, respectively. For these polymers, the viscosity exhibits shear-thinning characteristics and, again, no constant low-shear viscosity region is discernable even at relatively low shear rate of 0.1 s−1 . The level of shear viscosity of the RDJ31-4 is higher than RDJ31-3 at comparable concentrations due to the stronger hydrophobic associations. Closer inspection of the viscosity profiles of the RDJ31-4 and 31-5 polymers reveals that the shear-thinning behavior does not yield a power-law region with constant slope. This behavior is especially evident above the overlap concentration of approximately 0.3–0.5 wt.%. This thinning behavior with different slopes is especially discernable when the viscosity is plotted as a function of shear stress, as shown in Fig. 6b for the 1 wt.% solutions of RDJ31-4 and 31-5. Due to their larger hydrophobic groups and hence higher hydrophobic strength, these hydrophobic groups form intermolecular associations with those of neighboring molecules to produce clusters, whose size increases with increasing polymer concentration and may span the whole volume at sufficiently high concentrations. However, the aggregation number
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in each associative junction is highly heterogeneous at low salt concentrations as observed from relaxation spectra of these systems [25]. Subjected to shear deformation, the clusters are broken into smaller units, lowering the viscosity [8,25]. For the RDJ31-5, the shear viscosity appears to approach a plateau of 700–800 Pa s at an applied stress of less than 0.5 Pa. Below 0.5 Pa, the associative network of the HASE polymer containing C20 hydrophobe is sufficiently strong to resist the deformation stress. Above 0.5 Pa, the network structure of the polymer is broken into smaller clusters, yielding a rapid decrease in viscosity (a reduction from 800 to 10 Pa s is observed when the shear stress is increased from 0.5 to 10 Pa). Further increase in the stress beyond approximately 10 Pa results in an increase in the resistance to flow, which manifests as a decrease in the slope of the shear-thinning curve. This may be due to the fact that an equilibrium cluster size is reached, which undergoes orientation along the flow field without further breakdown of the structure. At applied stress in excess of 60 Pa, another region of rapid viscosity decrease is encountered, and this is due to further destruction of clusters at higher deformation stresses. Similar multi-shear thinning behavior can be seen for the RDJ31-4 with C16 hydrophobe. The extensional viscosities of both RDJ31-4 and 31-5 decreases with increasing deformation, with the level of the viscosity being higher for the polymer with higher hydrophobic strength. For these two polymers with sufficiently strong hydrophobic groups, inter-molecular associations are dominant. The decrease in the extensional viscosity with extensional rates is due to the disruption of these inter-molecular junctions in the polymer network. However, when plotted as Trouton ratio against extensional rate as in Fig. 9b for 1 wt.% HASE polymer, the values for all three HASE polymers containing hydrophobic groups show an increase with increasing extensional rates. The increase in Trouton ratio is proportional to the hydrophobicity of HASE polymer. The shear and extensional viscosity profiles of 1 wt.% associative polymers with different hydrophobe sizes are compared in Figs. 7a and b, respectively. By increasing the hydrophobe chain length, the viscosity increases proportionally. This is attributed to the fact that longer hydrophobic chain produces junctions with larger aggregation number, which are stronger. The difference in the shear and extensional viscosities at low deformation rates of 1 wt.% RDJ31-4 and RDJ31-5 is ∼10. The differential gap is even more pronounced when comparing RDJ31-3 and RDJ31-4 system. When the hydrophobic group is increased from C12 to C16 , the extension-thickening phenomenon at moderate extensional rates disappears. This seems to suggest that in the vicinity of between C12 and C16 hydrocarbon chain, a critical hydrophobic carbon content exists, where the conversion of predominantly intra-molecular junctions to inter-molecular junctions is not significant enough to cause the thickening behavior. The nature of the polymer network, which is a strong function of the hydrophobicity of the macromonomer, controls the magnitude of the viscosity and its profile. At high deformation rates, the shear viscosity of all the model polymers approaches that of RDJ31-1. This is brought about by the disruption of the hydrophobic junctions, which produces individual or isolated polymer chains or small micellar clusters. 3.2. Elastic behavior of HASE polymers Fig. 8 shows the storage modulus, G0 profiles of three model HASE polymers (RDJ31-3, 31-4 and 31-5). The elasticity of RDJ31-1 is so low that it could not be measured by the existing rheometer. Associative polymer with the longest hydrophobe exhibits the largest G0 . The results demonstrate that there are more mechanically active junctions in the solution of larger hydrophobic macromonomer than in the smaller ones.
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Fig. 7. (a) Comparison of the steady shear viscosities of 1 wt.% model HASE polymers with C0 , C12 , C16 and C20 hydrophobes; (b) comparison of the extensional viscosities of 1 wt.% model HASE polymers with C0 , C12 , C16 and C20 hydrophobes.
The meaning of the mechanically active junctions can be analyzed based on the transient network theory proposed in 1946 by Green and Tobolsky [26]. The theory is based on the extension of classical rubber elasticity theories for transient networks, which was first introduced to account for entanglements or reversible physical bonds. The theory predicts a constant steady-shear viscosity of η(γ˙ ) = η0 = τ G∞ ,
(6)
where the relaxation time τ is the reciprocal of the bond breaking and re-formation rate, and G∞ is the high-frequency or plateau modulus given by G∞ = veff RT,
(7)
where veff is the number density of effective or elastic chains, R is the universal gas constant and T the absolute temperature. Thus, from the knowledge of the plateau modulus, the mechanically active
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Fig. 8. Comparison of the storage moduli of 1 wt.% model HASE polymers with C12 , C16 and C20 hydrophobes.
junctions in the system may be estimated. The magnitude of the storage modulus at a fixed frequency can be correlated to the plateau modulus as given in Eq. (7). Hence, from the results in Fig. 8, it is evident that the plateau modulus of RDJ31-3 (C12 hydrophobe) is lower than that of the C16 and C20 hydrophobic system. This suggests that the number of mechanically active junctions of the RDJ31-3 system is lower than RDJ31-4 and 31-5 at the same polymer concentration. 3.3. Comparison of the Trouton ratio of model HASE polymers The relative significance of the extensional and shear properties can be better discussed by comparing the magnitude of the ratio of the extensional to the shear viscosity as given by the Trouton ratio. Figs. 9a and b show Tr as a function of extensional rates for various concentrations of RDJ31-5 system and 1 wt.% model HASE polymers, respectively. At low extensional rates, the Tr of 0.3, 0.5, 0.8 and 1 wt.% RDJ31-5 solutions is approximately 3. It is interesting to note that Tr of the 0.3 wt.% RDJ31-5 remains unchanged at ∼3 over a wide range of extensional rates (5–5000 s−1 ). This means that the structure of the individual polymer clusters is isolated and is not perturbed to any significant extent by the extensional flow field. This correlates well with the overlap concentration of these model polymers estimated to be approximately 0.3 wt.%. When the concentration is increased to 0.5 wt.%, Tr increases with extensional rates. However, the increase becomes steeper at higher polymer concentration of 0.8 and 1 wt.%. A Tr of about 50 is observed at extensional rate of 1000 s−1 . Fig. 9b shows a comparison between 1 wt.% model HASE polymer with different hydrophobic modification. The Tr for the polymers containing hydrophobic groups depart from 3 at higher extensional rates, while that for the control polymer RDJ31-1 (without hydrophobe) remained roughly constant at about 3 at low extensional rates. It increases slightly and then decreases at high extensional rates. The increase in Tr with extensional rates is proportional to the hydrophobicity of the macromonomer, where RDJ31-5 shows the highest Tr. Another interesting feature is that of RDJ31-3, where the Tr reaches a maximum at extension rate 1000 s−1 , and beyond this limit, Tr decreases. The magnitude and the dependence of Tr on hydrophobicity and extensional rates are indicative of the strength of the transient polymer network. For RDJ31-5, the aggregation number is larger, yielding stronger network, which can be deformed to
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Fig. 9. (a) The relationship between Trouton ratio and extensional rates of 0.3, 0.5, 0.8 and 1 wt.% RDJ 31-5 model polymer solutions; (b) comparison of the Trouton ratio at different extensional rates of 1 wt.% RDJ 31 model polymer series with C0 , C12 , C16 and C20 hydrophobes.
a greater extent before they fragment into smaller isolated micellar clusters. Similar behavior was also reported for associative polyelectrolyte systems [9] and hydroxyethylcellulose solutions [27]. The dependence of both the extensional and shear viscosities at a fixed deformation rate of 50 s−1 on polymer concentrations is depicted on a double logarithmic plot in Figs. 10a and b. A power law relationship is observed which can be represented by the expression given below: ηE = Acα ,
(8a)
η = Bcβ .
(8b)
Using regression to fit the data, the values of the exponents α and β and the constants A and B were determined and tabulated in Table 2. It can be seen that α and β increase with increasing hydrophobe chain length with α being always larger than β. Hence, the extensional viscosity exhibits a stronger dependence on the polymer concentration than shear viscosity. This is indicative of the
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Fig. 10. (a) Concentration dependence of extensional viscosities of model HASE polymers with C12 , C16 and C20 hydrophobes at ε˙ of 50 s−1 ; (b) concentration dependence of shear viscosities of model HASE polymers with C12 , C16 and C20 hydrophobes at γ˙ of 50 s−1 .
sensitivity of the network structure to the stronger deformation experienced in extensional flows. The values of the exponents are plotted against the activation energy at γ˙ =50 s−1 in Fig. 11a. The activation energy was obtained by conducting shear viscosity tests at different temperatures. Based on the Arrhenius equation, the slope of the viscosity versus 1/T curves gives the magnitude of the activation Table 2 Fitted parameters for Eqs. (8a) and (8b) of 1 wt.% model HASE polymers at ε˙ and γ˙ =50 s−1 HASE polymer
α
A
β
B
RDJ 31-1 RDJ 31-3 RDJ 31-4 RDJ 31-5
0.92 1.54 3.15 4.33
0.068 0.464 2.710 17.839
0.82 1.06 2.68 3.21
0.025 0.048 0.261 1.216
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Fig. 11. (a) Dependence of exponent α and β on the activation energy of 1 wt.% model HASE polymers at ε˙ and γ˙ of 50 s−1 ; (b) Effect of hydrophobic content on the shear and extensional viscosity of 1 wt.% model HASE polymer at ε˙ and γ˙ of 50 s−1 .
energy: η(γ˙ ) = Ae−Ea /RT ,
(9)
where, η(γ˙ ) is the shear viscosity at given shear rate, Ea is the activation energy (J/mol), A is the Arrhenius constant, R is the gas constant, and T is the temperature. The plot (Fig. 11a) and the numerical values tabulated in Table 2 indicate that there is a correlation between the exponents with the strength of the polymer network. The dependence of extensional and shear viscosities of 1 wt.% polymer solutions at a fixed deformation rate of 50 s−1 on the size of the hydrophobic group is depicted in Fig. 11b. The figure shows that both viscosities display similar dependence with a slope of 0.43, however the magnitude of the extensional viscosity is ∼10 times larger than the shear viscosity. The significance of this result is that the ratio at the fixed deformation rate is independent of the hydrophobicity of the macromonomer. Significant enhancement
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in the shear and extensional viscosity is observed when the carbon content of the hydrophobes exceeds 8 to 10. 3.4. Mechanism of HASE polymers under extensional flow From the present study on HASE polymers in extensional flow, the hydrophobicity of the macromonomer has a strong bearing on the extensional viscosity profiles. Based on our understanding of the microstructure of HASE polymers in solutions, the evolution of the network structure during deformation is proposed. The pictorial representation of the network structure in the extensional flow field is summarized in Fig. 12. 3.4.1. HASE polymer with weak hydrophobic interactions The polymer chains at the quiescent state consist of very weak associations at the backbone brought about by the blocky ethyl acrylate segments. When extensional stress is applied, the polymer clusters dissociate into individual polymer chain, which are aligned in the direction of the extensional stress. Due to the stiff polyelectrolyte backbone, the polymer chains offer some resistance to deformation. The consequence of this is a mild shear-thickening behavior at moderate extensional rates.
Fig. 12. Microstructure of HASE polymers under extensional flow fields (a) weak association; (b) moderate association and (c) strong association.
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3.4.2. HASE polymer with moderate hydrophobic interactions Polymer with shorter hydrophobes, such as RDJ31-3 system form clusters with predominantly intramolecular junctions and a loose connection with other clusters as depicted in Fig. 12b. When the stress is applied, some of the intra-molecular junctions are detached and the free hydrophobes re-associate to form inter-molecular junctions. This induces the formation of a network with larger proportion of inter-molecular junctions. Hence, the polymer network is more resistant to deformations and is responsible for the extensional-thickening behavior. However, when a critical shear stress is exceeded, the inter-associations breakdown, yielding a lower viscosity solution. 3.4.3. HASE polymer with strong hydrophobic interactions HASE polymer with stronger hydrophobes such as RDJ 31-4 and RDJ31-5, exhibits extensive network structure through inter-molecular associations (Fig. 12c). Since the hydrophobicity is stronger, the aggregation number is larger, resulting in stronger junctions. When sufficient extensional stress is applied, the network deforms and progressively degenerates to several individual clusters. This yields a continuous decrease in the extensional viscosity. 4. Conclusions The associative polymers form a transient network through association of hydrophobes grafted onto the polymer backbone. The strength of the network junction is proportional to the hydrophobic chain length of the macromonomer. However, the network formed by shorter hydrophobic chain (C12 ) is predominantly intra-molecular. The intra-molecular junctions are converted to inter-molecular associations at moderate deformation rates giving rise to the observed extensional thickening behavior. The Trouton ratio at low concentration (<0.3 wt.%) and unmodified polymer (RDJ31-1) remains at ∼3 over 5 decades of extensional rates. However, the Trouton ratio of polymers with C12 , C16 and C20 hydrophobes increases with polymer concentrations and extensional rates. Such dependence is directly related to the strength of the network junction. Acknowledgements One of the authors (HT) would like to acknowledge the financial support provided by the university. We would also like to acknowledge the financial support provided by the National Science and Technology Board of Singapore, the Ministry of Education and the Singapore-Ontario collaborative research program. References [1] R.D. Jenkins, The Fundamental Thickening Mechanism of Associative Polymers in Latex Systems: a Rheological Approach, Ph.D. Thesis, Lehigh University, Bethlehem 1991. [2] T. Annable, R. Buscall, R. Ettelaie, D. Whittlestone, J. Rheol. 37 (1993) 695. [3] K. Zhang, B. Xu, M.A. Winnik, P.M. Macdonald, J. Phys. Chem. 100 (1996) 9834. [4] E. Alami, M. Almgren, W. Brown, J. Francois, Macromolecules 29 (1996) 2229. [5] Y. Uemura, P.M. Macdonald, Macromolecules 29 (1996) 63. [6] A. Yekta, B. Xu, J. Duhamel, H. Adiwidjaya, M.A. Winnik, Macromolecules 28 (1995) 956.
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