Shear thinning and thixotropy of HMHEC and HEC water solutions

Steady state viscosity and thixotropy of hydrophobically modified hydroxyethyl cellulose ~HMHEC! and nonassociative cellulose water solutions are studied. Although all the samples a shear thinning, only the HMHEC is thixotropic, since the migration of hydrophobes to micelles controlled by diffusion. The Cross model fits steady state curves. The Mewis model, phenomenological model that proposes that the rate of change of viscosity when the shear ra suddenly changed is related to the difference between the steady state and current value viscosity raised to an exponent, fits structure construction experiments when the exponent, n, is estimated to be around 2. The Newtonian assumption used by Mewis cannot be used here, howe This seems to be related to the fact that the thickening is due to bridged micelle formation, whi is a slow process, and also to topological constraints and entanglements, which are rapid proces The kinetic parameter was redefined to kn in order to make it independent of initial conditions. So, kn depends only on how the shear affects the structure. kn reaches a plateau at shear rates too low to produce structure destruction and decreases at higher shear rates. © 2002 The Society of Rheology. @DOI: 10.1122/1.1516789 #


I. INTRODUCTION
Latex paints require the addition of thickeners in order to attain a proper rheology.Thickeners traditionally used were water-soluble derivatives of cellulose, such as hydroxyethyl celluloses of high molecular weight ͑HEC͒ ͓Wetzel et al. ͑1996͔͒.These derivatives thicken the medium because of chain entanglements between the long polymer molecules, which are solvated and extended in an aqueous medium ͓McCormick and Johnson ͑1989͒; Emmons and Travis ͑1978͔͒.Coatings thickened with HECs have high resistance to sagging, but poor leveling ͓Seneker and Glass ͑1996͒; Schwab ͑1986͒; Croll and Kleinlein ͑1986͔͒.To solve this problem, in the last few years these polymers have been substituted in some applications by associative polymers ͑APs͒ ͓Wetzel et al. ͑1996͒; Yekta et al. ͑1993͒; Hoy and Hoy ͑1984͔͒, which consist of a hydrophilic backbone to which hydrophobic groups have been attached so that each molecule has two or more hydrophobes ͓Tarng et al. ͑1996͒; Sau and Landoll ͑1989͔͒ that are randomly distributed along the polymer chain ͓Xu et al. ͑1997͔͒ or are present as terminal groups ͓Tam et al. ͑1998͔͒.In an aqueous medium, these groups form aggregates that are similar to surfactant micelles.Hydrophobes of the same molecule can be joined to the same micelle, forming a loop ͓Yekta et al. ͑1995͔͒.Then flower-like independent micelles form.But these can also aggregate to different micelles.When this happens micelles are bridged by hydrophilic backbones and a three-dimensional network forms that enhances the viscosity of the medium.Under shear conditions, bridges are stretched, hydrophobes are forced to leave their micelles, and a bridge-to-loop transition takes place that weakens the network, resulting in a decrease of viscosity.
Linear viscoelasticity of these polymers has been extensively studied ͓Maestro et al. the thickening mechanism.However, it is not useful for understanding behavior during painting because it takes place out of the linear range, since changes in the structure occur.In fact, the dependence of viscosity on shear ͑steady state curve͒, and the kinetics of the viscosity variation when the shear rate or the shear stress is modified ͑thixotropy͒, are the determinants in the handling of the paint and quality of the final film.Thus, they seem interesting enough to be quantified.
Most associative polymers are found to be shear dependent ͓Zhang ͑2001͒; Besides being shear dependent, a large number of associative polymers are thixotropic ͓Ka ¨stner ͑2001͒; Vittadello and Biggs ͑1998͒; Tarng and Glass ͑1995͒; Ka ¨stner et al. ͑1996͒; Kroon ͑1993͔͒, although their thixotropy has not been studied in a quantitative way, nor has systematic experimentation been developed.Some interesting models have been created that try to predict thixotropic behavior of fluids.They fall into four groups: first, there are those models that use a very general description of microstructure described by a numerical value of a scalar parameter , which can vary between 0 ͑completely destroyed structure͒ and 1 ͑completely formed structure͒.Some authors of this group are None of the models we know of has been used for a description of the thixotropy of the associative polymers used in paints.In the present article, the steady state curves and thixotropy of HMHEC are studied and compared with HECs of several molecular weights.A simple model is developed for an initial quantification of thixotropy.

A. Materials and preparation
All compounds were obtained from Aldrich.Molecular weight M w , molar substitution MS, and degree of substitution DS of cellulose derivatives are summarized in Table I.
The celluloses were received as a solid powder and were used as supplied.De-ionized water further purified through a Millipore MilliQ purification system was used to prepare solutions.Water was stirred and heated to 40 °C, and polymer was gradually added.Stirring was maintained for 2 h and solutions were stored for at least 24 h before use to assure complete hydration.When butoxy ethanol was used, a 20% butoxy ethanol-80% water solution was prepared before the addition of the thickener.Solutions were used during a 7-day period in order to avoid undesirable effects produced by enzymatic degradation.

B. Rheological measurements
All rheological measurements were performed with a Haake RS150 rheometer.This rheometer can work either as a controlled shear rate or a controlled shear stress rheometer.The controlled shear rate mode was chosen.Two different sensors were used, depending on the range of viscosity of the solutions, so as to ensure adequate sensitivity.A 60 mm diam double cone and 1°cone angle was used for solutions with small viscosity, and a cone-and-plate sensor with a 60 mm diameter and 4°cone angle was used for the other solutions.Some measurements were carried out with both sensors, and results were compared to assure they did not influence the experimental data.The temperature was controlled, with a deviation less than Ϯ0.2 °C.
Steady state curves were obtained for a range of shear rates between 0.07 and 500 s Ϫ1 .Evolution of the viscosity over time when the shear rate changes suddenly from one value to another was measured.The initial shear rate was maintained until the steady state was reached, and then it was changed to the final shear rate, which was maintained for 15 min.Data of viscosity versus time were taken throughout the experiment.

A. Viscosity as a function of shear rate "steady state curve…
Figure 1 shows the steady state viscosity as a function of shear rate for HEC and HMHEC solutions.For comparative purposes, we present the concentrations where similar low shear viscosities 0 were obtained.For a 0 around 1.3 Pa s, 10% HEC9 is needed, but only 0.75% HEC130 or 0.5% HMHEC.As expected, the thickening efficiency of HEC increases with the molecular weight due to the presence of more interactions and entanglements.Hydrophobic modification of HEC increases efficiency because of the formation of a three-dimensional micellar network.HMHEC solution has the higher shear thinning behavior because of the shear-induced transitions from inter-to intramolecular association.The influence of temperature and concentration on the steady state curve of HMHEC was studied.Figure 2 shows curves at different concentrations, and Fig. 3 at different temperatures.The concentration increases viscosity over all the shear rate range because of the presence of a large number of micelle-like aggregates, which favors the formation of bridges and enhances the network.Shear thinning behavior is observed for all concentrations studied.Only at the lower concentration is a previous shear thickening region observed.Tam et al. ͑1998͒ attributed the shear thickening behavior observed in HEUR solutions to shear-induced loop-to-bridge transitions that increase the fraction of micelles included in the mechanically active network and increase the number of bridges.At higher concentrations of HMHEC, this shear thickening region is not observed, probably because when the fraction of micelles is high enough micelles are close together and the ͑1͔͒, where 0 and ϱ are the low and high shear viscosities, respectively.The exponent m is found to be around 0.9.As shown, the fitting is quite good, except at 0.5%, because the shear thickening behavior cannot be described by the Cross model, The high shear viscosity cannot be known accurately because of limitations of the measuring range and possible hydrodynamic instabilities at very high shear rates, although the results were very reproducible and no oscillation or evidence of instability was observed for these shear rates.Figure 3 shows that the low shear viscosity 0 decreases with temperature T, but viscosity tends to be independent of T at high shear rates.An Arrhenius dependence on the temperature was found for 0 , in agreement with other authors ͓Annable and Buscall ͑1993͔͒.The potential barrier to disengagement of a chain end from a junction point, E m , which may be equated to the binding energy of the hydrophobe to its micelle ͓Tam et al. ͑1998͔͒, is determined to have a value of E m ϭ 72 kJ/mol, similar to that found by Annable for HEUR polymers.At higher shear rates the Arrhenius dependence is lost.While at low shear, in the Newtonian range, the associated structure and, as a consequence, the viscosity, depend on thermal motion, at higher shear rates thermal dependence is negligible because it is masked by shear effects.Thus, viscosity tends to be independent of the temperature.

Thixotropy of HEC and HMHEC
The evolution of viscosity over time when the shear rate changes suddenly was studied for solutions of HECs and HMHEC.An example of the results is shown in Fig. 4, where it can be seen that the viscosity of the HECs studied increases and quickly reaches the steady state viscosity corresponding to the new shear rate.The same happens at all temperatures and concentrations tested.So, thixotropy of these HECs is so fast that the kinetics cannot be quantified.In contrast, the increase of viscosity for the HMHEC solution is gradual enough to be measured, so that a significant thixotropic behavior is observed.These differences between HEC and HMHEC are in agreement with Ka ¨stner studies ͑1996, 2001͒.We attribute them to the fact that the thickening mechanism of HECs is due to topological constraints and entanglements between the long chains of polymer, which are fast processes.On the other hand, although topological constraints and entanglements also exist for the HMHEC water solutions, the main thickening mechanism is due to hydrophobic interactions.So, the recovery of viscosity requires the migration of hydrophobes through the medium towards the micelles, which is a slow diffusion-controlled process.It can be concluded that the HEC water solutions studied do not have significant thixotropy at the concentrations and temperatures tested.The thixotropic behavior of HMHEC water solutions is studied in Sec.III B2.

Model used for HMHEC
Experiments were carried out in which the shear rate was suddenly changed from a low value to higher ones ͑structure destruction experiments͒, and from a high value to lower ones ͑structure construction experiments͒.Figure 5 shows the results obtained when the shear rate was changed from 0.1 s Ϫ1 to several higher values.Viscosity is seen to decrease over time and tends to move toward the new equilibrium viscosity because of the structure destruction produced by shear.An overshoot is observed at short times; this indicates the presence of elasticity ͓Bautista et al. ͑1999͒; Barnes ͑1997͔͒.This is supported by the fact that HMHEC solutions were found to be viscoelastic in publications where linear viscoelasticity was studied ͓Maestro et al. ͑2002͒; Karlson et al. ͑2000͒;Svanholm et al. ͑1997͒;Brown ͑1994͒;Sau and Landoll ͑1989͒;Goodwin et al. ͑1989͒;Landoll ͑1982͔͒.Although this overshoot is not so evident at 5 s Ϫ1 , and cannot be observed at 50 s Ϫ1 or higher shear rates, it is only due to partial masking of the effect produced by the shear.As a result, if some model were to be found for the description of thixotropic behavior, elasticity should be included.␥ ˙1 .Although, of course, these curves are also influenced by elasticity, their shape seems to indicate that a single kinetic constant could be used that would include pure thixotropy and elasticity.This seems interesting for initial quantification of the thixotropy of an associative polymer.
A phenomenological model devised by Mewis and Schryvers ͓Barnes ͑1997͔͒ was used to fit results.It proposes that the rate of change of viscosity when the shear rate is suddenly changed from an initial shear rate ␥ ˙0 ͑at the steady state͒ to a new one ␥ ˙1 is related to the difference between the steady state and current values of viscosity: This integrates as

͑3͒
where e is the equilibrium viscosity at a given shear rate ␥ ˙1 , i is the initial viscosity for this new shear rate ␥ ˙1 , and n is the kinetics order.Mewis and Schryvers then made the Newtonian assumption i (␥ ˙1) ϭ e (␥ ˙0), which makes use of the equation simpler because it is easier to measure the viscosity of the initial steady state condition.This assumes that the viscosity at the end of the initial steady state period is the same as that at the beginning of the new shear rate test, i.e., the system is Newtonian between these conditions and viscosity is only a function of the quantity of structure formed and not a function of both the structure and shear rate.However, as Mewis points out, this is only true for high shear rates.
Figure 6 shows some examples of fitting experimental data using the Mewis and Schryvers model, but with some modifications.First of all, the kinetics order n was found to be n Х 2. Second, the model was unable to fit results if the Newtonian assumption used by Mewis was made.So, i was used as a free parameter.Then, the equation used to fit experimental data was Three parameters are used: the equilibrium viscosity at the new shear rate, e ; the initial viscosity at the new shear rate, i ; and the kinetic constant, k.

Shear rate dependence of the fitting parameters
Experiments at several initial and final shear rates were performed.The dependence of the initial viscosity i on the initial (␥ ˙0) and the final (␥ ˙1) shear rate is shown in Fig. 7.
As expected, i decreases with ␥ ˙0 , since the transient network is destroyed under shear and, at time t ϭ 0, when shear rate has just been changed, the intramolecular to intermolecular balance corresponding to the initial state still remains.However, i also decreases with ␥ ˙1 for the same ␥ ˙0 , indicating that the Newtonian assumption proposed by Mewis cannot be used here.This is attributed to the fact that topological constraints and chain entanglements, which are rapid processes, are one of the factors that determine the viscosity of HMHEC solutions, besides bridged micelle formation.Figure 8͑a͒ shows the steady state viscosity of HMHEC solutions when 20% of butoxy ethanol was added in order to prevent micelle formation.It can be seen that this solution is also shear thinning, although, of course, to a much smaller extent than HMHEC, indicating that chain interactions or entanglements contribute to the thickening besides hydrophobic interactions.
For the same solution, Fig. 8͑b͒ shows time curves when the shear rate changes from an initial shear rate ␥ ˙0 ϭ 2000 s Ϫ1 to several smaller shear rates ␥ ˙1 .It can be seen that equilibrium viscosity is quickly reached and no significant thixotropy is observed.So, besides the slow process of micelle formation, the HMHEC solutions are characterized by a rapid relaxation process that is very likely responsible for the invalidity of the Mewis Newtonian assumption.
The equilibrium viscosity e , as expected, is independent of ␥ ˙0 and shows shear thinning behavior with ␥ ˙1 .The results coincide with the steady state curves found through shear rate sweeps and shown in Fig. 2.This indicates that e is correctly estimated by the model proposed.
Figure 9 shows that the kinetic constant k depends on ␥ ˙1 , and also on ␥ ˙0 , i.e., it depends on the initial conditions.This constant was substituted for a new kinetic constant k n defined as ͑5͒ Equations ͑2͒ and ͑4͒ can be rewritten as follows: Figure 10 shows the dependence of k n on ␥ ˙1 for several ␥ ˙0 .It can be observed that k n is independent of ␥ ˙0 .On the other hand, k n decreases with ␥ ˙1 for high shear rates, but takes a constant value at lower ones.So, this curve qualitatively has the same shape as the steady state curve ͑Fig.2͒.In the range of high shear rates, the shear rate greatly influences the structure.Here, k n increases when the shear rate is decreased.On the other hand, in the range of low shear rates, where the shear does not affect the structure and, as a consequence, a plateau is observed for the equilibrium viscosity, k n becomes independent of the shear rate.It now appears that k n only depends on how the shear rate affects the structure.

IV. CONCLUSIONS
The HEC and the HMHEC water solutions tested present shear thinning behavior.Only the HMHEC presents thixotropy, since transitions from intra-to intermolecular associations are limited by diffusion.
Steady state curves obtained with HMHEC can be fitted through the Cross model for concentrations higher than 0.75%.For lower concentrations, shear thickening behavior is observed at intermediate shear rates, due to shear-induced transitions from intra-to intermolecular associations.
As HMHEC is a viscoelastic fluid, elastic effects are observed coupled to thixotropy.The Mewis and Schryvers model, with some modifications, properly fits structure construction experiments.However, the Newtonian assumption i (␥ ˙1) ϭ e (␥ ˙0) used by Mewis cannot be made for this case since, although the main thickening mechanism is due to hydrophobic interactions, viscosity is also influenced by rapid chain interactions and entanglements.The kinetic parameter k can be redefined to k n ϭ k( e Ϫ i ) 2 .This parameter is independent of the initial conditions and only depends on how the shear rate affects the structure.Then, k n decreases with shear at the higher shear rates and takes a constant value at shear rates too low to affect the structure.
͑2002͒; Tam et al. ͑1998͒; Svanholm et al. ͑1997͒; Xu et al. ͑1996͒; Groot and Agterof ͑1995͒; Annable and Buscall ͑1993͒; Yekta et al. ͑1993͒; Kaczmarski and Glass ͑1993͒; Tanaka et al. ͑1992͒; Glass et al. ͑1991͒; Karunasena et al. ͑1989͔͒ because it gives information about Reuvers ͑1999͒; Svanholm et al. ͑1997͒; Xu et al. ͑1996͒; Ka ¨stner ͑2001͒; Sau and Landoll ͑1989͒; Goodwin et al. ͑1989͔͒.A plateau region followed by shear thickening and shear thinning regions at higher shear rates is observed for HEUR solutions ͓Jenkins et al. ͑1996͒; Tarng et al. ͑1996͒; Svanholm et al. ͑1997͒; Annable and Buscall ͑1993͒; Xu et al. ͑1996͔͒.The shear thickening behavior at intermediate shear rates is attributed to a change from intramolecular to intermolecular association as molecules become elongated under shear ͓Jenkins et al. ͑1991͒; Witten and Cohen ͑1985͔͒.Shear thinning is also observed with HMHEC solutions ͓Svanholm et al. ͑1997͒; Sau and Landoll ͑1989͒; Goodwin et al. ͑1989͔͒.Goodwin and Hughes ͑1997͒ proposed the Cross model ͓Cross ͑1965͔͒ or the Papir model ͓Papir and Krieger ͑1970͔͒ for the fitting of viscosity curves.These models do not fit shear thickening behavior.
Tiu and Boger ͑1974͒, Alessandrini et al. ͑1982͒, De Kee et al. ͑1983͒, and Baravian et al. ͑1996͒.Second are those authors who attempt some direct description of the temporal change of the microstructure such as, for example, the number of bonds or the size of the aggregates, for instance, Denny and Brodkey ͑1962͒ or Lapasin et al. ͑1996͒.Third, there are authors that use the viscosity-time data itself on which to base a theory, such as Fredrickson ͑1970͒ or Mewis and Schryvers ͑1996͒ reported by Barnes ͑1997͒.Finally, a number of authors use viscoelastic models, termed ''thixoelastic'' by some.They introduce some modifications in the linear viscoelasticity expressions in order to describe structural changes and obtain nonlinear viscoelasticity expressions.Some of the authors in this last group are Acierno et al. ͑1976͒, Soong and Shen ͑1979͒, Bautista et al. ͑1999͒, and Quemada ͑1999͒.

TABLE I .
Thickeners used in the experiments.