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Cyclodextrins in Hydrophobically Modified Poly(ethylene glycol) Solutions: Inhibition of Polymer-Polymer Associations L. Karlson,*,† K. Thuresson,‡ and B. Lindman‡ Akzo Nobel Surface Chemistry AB, SE-444 85 Stenungsund, Sweden, and Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden Received June 7, 2002. In Final Form: August 27, 2002 In an aqueous solution of a hydrophobically end-modified poly(ethylene glycol) polymer, HM-PEG, the thickening effect is dependent on intermolecular hydrophobic associations and the formation of a network structure. In the present investigation cyclodextrin, CD, has been added to an aqueous HM-PEG solution and a decrease in Newtonian viscosity has been followed. The decreased viscosity refers to polymerpolymer associations becoming less numerous when complexes between polymer hydrophobic tails and CD become more frequent; CD-decorated polymer hydrophobic tails have no possibility of contributing to the network. It was found that deactivation of the first few hydrophobic tails has very large consequences for the viscosity. A termination of a fraction as small as 10% (or below) of the total amount of polymer hydrophobic tails may reduce viscosity to a level almost corresponding to that of the unmodified parent polymer. This can be understood by taking into account that a solution of a HM-PEG polymer is expected to be inhomogeneous with large concentration fluctuations and that the viscosity is likely to be strongly decreased by reducing the probability of hydrophobic associations responsible for connecting different clusters. The effect of CD on rheology is very different for different architectures of hydrophobically modified polymer, in particular between graft copolymers and end-capped ones. This can be understood from the differences in network structure.
Introduction Hydrophobically modified polymers (HM-Ps) or watersoluble associative polymers (WSAPs) are used in a variety of technical formulations that we meet in our daily life. Examples are water-borne paints and shampoos.1,2 A common reason for adding a HM-P to a formulation is that it gives a different rheological behavior as compared to a normal hydrophilic thickener. Another reason to choose a HM-P is that the amphiphilic properties can help to increase stability of dispersions. To be able to predict performance of a hydrophobically modified polymer in an application, it is important to have knowledge about the effect of the hydrophobic modification on macroscopic properties. Such knowledge is also interesting for more fundamental reasons and is often correlated with molecular interactions when HM-Ps are subject to more basic research. One way to obtain information about the effect of a hydrophobic modification is to synthesize both the unmodified and the hydrophobically modified version of the thickener. This is a route that has been employed in several investigations.3-9 In * To whom correspondence should be addressed: fax +46 303 839 21; e-mail
[email protected]. † Akzo Nobel Surface Chemistry. ‡ Lund University. (1) Glass, J. E. Polymers in Aqueous Media; American Chemical Society: Washington, DC, 1989; Vol. 223. (2) Glass, J. E. Hydrophilic Polymers; Performance with Environmental Acceptability; American Chemical Society: Washington, DC, 1996; Vol. 248. (3) Strauss, U. P. Hydrophobic polyelectrolytes. In Polymers in aqueous media; American Chemical Society: Washington, DC, 1989; Vol. 223, pp 317-324. (4) Williams, P. A.; Meadows, J.; Phillips, G. O.; Senan, C. Cellul.: Sources Explor. 1990, 37, 295-302. (5) Landoll, L. M. J. Polym. Sci. 1982, 20, 443-455. (6) Tanaka, R.; Meadows, J.; Phillips, G. O.; Williams, P. A. Carbohydr. Polym. 1990, 12, 443-459.
addition to the fact that this requires extra synthesis work, it is difficult to control the reaction so that the only difference between the two polymers is the hydrophobic modification. Therefore it would be desirable if the effect caused by a hydrophobic modification instead could be studied by inhibition and decoupling of the hydrophobic associations. In a recent paper, we reported on the addition of di(ethylene glycol) monobutyl ether (BDG) to aqueous polymer solutions to obtain such decoupling.9 In other investigations, surfactants have been added at high concentration, which decouples hydrophobic polymerpolymer associations by encapsulating each polymer hydrophobic tail in a micelle.10,11 Another efficient way, which will be employed here, to decouple the hydrophobic associations is offered by addition of cyclodextrin (CD). CD is a cyclic oligomer of glucose with the shape of a truncated cone that has a hydrophilic exterior and a hydrophobic cavity in the center (Figure 1). Three different sizes are available; R-, β-, and γ-cyclodextrin consist of six, seven, and eight glucose units, respectively. In aqueous solutions CD molecules form “nut and bolt” (or inclusion) complexes with substances containing lipophilic groups, e.g., surfactants or HM-Ps, provided that the hydrophobic group has a shape that fits in the cavity. Principles of such complex formation have been studied thoroughly by several groups, and in particular, complexation between CD and surfactants has been a focus of this work.12-18 (7) Picton, L.; Muller, G. Macromol. Symp. 1997, 114, 133-138. (8) Joabsson, F.; Rosen, O.; Thuresson, K.; Piculell, L.; Lindman, B. J. Phys. Chem. 1998, 102, 2954-2959. (9) Karlson, L.; Joabsson, F.; Thuresson, K. Carbohydr. Polym. 2000, 41, 25-35. (10) Nilsson, S.; Thuresson, K.; Hansson, P.; Lindman, B. J. Phys. Chem. 1998, 102, 7099-7105. (11) Piculell, L.; Nilsson, S.; Sjo¨stro¨m, J.; Thuresson, K. Associative polymers in aqueous media; American Chemical Society: Washington, DC, 2000; Vol. 765, pp 317-335.
10.1021/la026040t CCC: $22.00 © 2002 American Chemical Society Published on Web 10/17/2002
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Figure 1. To the left is shown the chemical structure, and to the right, a schematic representation of the geometry of an R-cyclodextrin molecule.
CD has also been used together with HM-P with the purpose of reducing the viscosity of an aqueous solution. This was described for the first time in the early 1990s.19,20 Here the purpose was to reduce viscosity of a highly concentrated aqueous solution of a HM-P thickener to facilitate incorporation of the thickener into technical formulations, e.g., paint. More recently the concept of controlling the self-association of HM-P by addition of CD has been more thoroughly studied in two papers by Zhang et al.21 and Akiyoshi et al.22 A conclusion from these investigations was that CD molecules form complexes with the hydrophobic end groups of the HM-P polymers, which means that polymer hydrophobic tails are hidden within the CD cavities and only the hydrophilic outer shell of the CD molecules is exposed to the aqueous environment. In HM-P solutions the viscosity then decreases, since the three-dimensional polymer network is disrupted when the possibility to form interpolymeric hydrophobic associations is reduced. The concept of encapsulating the hydrophobic tails of HM-P with CD has also been used to avoid disturbing hydrophobic interactions when properties of individual polymer molecules were in focus and investigated with techniques such as gel-permeation chromatography and static light scattering.23 In a recent investigation we focused on how the viscosity in an aqueous solution of a graft copolymer, hydropho(12) Funasaki, N.; Yodo, H.; Hada, S.; Neya, S. Bull. Chem. Soc. Jpn. 1992, 65, 1323-1330. (13) Junquera, E.; Tardajos, G.; Aicart, E. Langmuir 1993, 9, 12131219. (14) Ma, Z.; Glass, J. E. Polym. Mater. Sci. Eng. 1993, 69, 494-495. (15) Mwakibete, H.; Bloor, D. M.; Wyn-Jones, E. Langmuir 1994, 10, 3328-3331. (16) Mwakibete, H.; Bloor, D. M.; Wyn-Jones, E.; Holzwarth, J. F. Langmuir 1995, 11, 57-60. (17) Park, J. W.; Song, H. J. J. Phys. Chem. 1989, 93, 6454-6458. (18) Wan Yunus, W. M. Z.; Taylor, J.; Bloor, D. M.; Wyn-Jones, E. J. Phys. Chem. 1992, 96, 8979-8982. (19) Eisenhart, E. K.; Johnson, E. A., Rohm and Haas Company. Method for improving thickeners for aqueous systems. U.S. Patent 5137571, 1992. (20) Lau, W.; Shah, V. M., Rohm and Haas Company. Method for improving thickeners for aqueous systems. U.S. Patent 5376709, 1994. (21) Zhang, H.; Hogen-Esch, T. E.; Boschet, F.; Margaillan, A. Langmuir 1998, 14, 4972-4977. (22) Akiyoshi, K.; Sasaki, Y.; Kuroda, K.; Sunamoto, J. Chem. Lett. 1998, 93-94. (23) Islam, M. F.; Jenkins, R. D.; Bassett, D. L.; Lau, W.; Ou-Yang, H. D. Macromolecules 2000, 33, 2480-2485.
bically modified ethyl (hydroxyethyl) cellulose (HMEHEC), decreased in the transition region where the concentration of CD (cCD) was lower than the total concentration of hydrophobic groups (chydrophobe), and the effect of various cyclodextrins was investigated.24 The complex formation and the concomitant disruption of the polymer network were followed by measuring the viscosity as a function of the CD concentration. The data were rationalized in a simple association model from which the effective binding constant could be extracted together with the concentration of binding sites. We found a reasonable agreement between the model and the data, and in particular the concentration of binding sites equaled the concentration of hydrophobic tails. The interpretation of this was that all hydrophobic tails were important for the network formation in the HM-EHEC system. In the present study we have used methylated R-cyclodextrin (M-R-CD) to decouple associations in aqueous solutions of an associating polymer with a different architecture, a water-soluble polymer hydrophobically end-capped, the choice of polymer being hydrophobically modified poly(ethylene glycol), HM-PEG. The viscosity has been rationalized within the same model as we used for the HM-EHEC/CD system, and it was found that initially the decrease in viscosity is much stronger than what is expected from results in the previous investigation. The observations can be understood by taking into account that the HM-PEG solution is likely to be inhomogeneous with large concentration fluctuations. Experimental Section Materials. Hydrophobically end-modified poly(ethylene glycol) (HM-PEG) with the structure C1618-EO140-IPDU-EO140-C1618 was used in this study. C1618-EO140 denotes an ethoxylate of a mixture of unsaturated alcohols (C16 to C18), and IPDU represents an isophorone diurethane group connecting two ethoxylated alcohol molecules. The synthesis and characterization methods are described elsewhere.25 The weight-average molecular weight (Mw ) 13 500) and the polydispersity index (Mw/Mn ) 1.1) were determined by size-exclusion chromatography (SEC). HM-PEG was purified from low molecular weight impurities (salt origi(24) Karlson, L.; Thuresson, K.; Lindman, B. Carbohydr. Polym. 2002, 50, 219-226. (25) Karlson, L.; Nilsson, S.; Thuresson, K. Colloid Polym. Sci. 1999, 798, 8-804.
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Figure 2. Complex viscosity, η* (9), from oscillatory shear measurements and viscosity, η (O), obtained from continuous shear measurements for a solution containing 10% HM-PEG (14.8 mmolal hydrophobes) and 0.005% (w/w) CD (0.047 mmolal). nating from the catalyst, low molecular weight PEG, etc.) by dialysis; a 3% (w/w) solution of HM-PEG was dialyzed against an excess of Millipore water for several days with repeated exchange of the dialysis water. The dialysis was performed by using Spectra/Por molecular porous membrane tubing with a molecular weight cutoff of 6000-8000. After dialysis, the polymer material was recovered by freeze-drying. Methylated R-cyclodextrin (M-R-CD) was supplied by WackerChemie (under the trade name Cyclodextrin Alpha W6 M1.8). The degree of methylation per glucose unit was 1.6-1.9, as given by the supplier. The M-R-CD was of pharmaceutical quality and was used without further purification. For all samples, water of Millipore quality was used. Methods. Aqueous HM-PEG solutions of three concentrations, 3%, 5%, or 10% (w/w), were prepared, without and with 0.5% (w/w) M-R-CD. These six stock solutions were prepared by weighing the components in test tubes that were sealed with Teflon tightened caps. Before proceeding, the stock solutions were left to equilibrate for at least 24 h. Furthermore, to facilitate preparation of test solutions with a CD concentration below 0.1% (w/w), a dilution with respect to CD of the more concentrated stock solutions was made. From these, in all nine stock solutions, samples with desired compositions were prepared by weight. The M-R-CD concentration was varied in the range 0.002-0.5% (w/w) (corresponding to 0.018-4.5 mmolal). Before any rheological measurements were started, the final samples were left to equilibrate at room temperature for at least 12 h. The rheological measurements were performed with a StressTech rheometer from Rheologica, Sweden. A 4 cm, 1° cone and plate geometry was used, and the temperature of the sample was controlled to within (0.1 °C by an external water bath. Measurements were performed at 20 °C, both as continuous and as oscillatory shear measurements. The viscosity, η or η*, was determined as a function of the shear rate, γ˘ or 2π f, where f denotes the frequency. Within a range of shear rates the viscosity data from the two methods coincide and are independent of γ˘ or 2π f (Figure 2). Values from this Newtonian plateau are reported in the following figures. Model Considerations. Our results were interpreted in a simple model where CD molecules are regarded to bind to the hydrophobic tails of the polymer chains with a complex formation constant K. It is assumed that 1:1 “nut and bolt” complexes are formed, and we represent this complex formation within a Langmuir adsorption model. The concentration of “adsorption sites”, B, in the model is restricted by the concentration of polymer hydrophobic tails and cannot exceed this value. To obtain the K and B values from our rheological data we have assumed that η ∝ G∞τ ∝ nkbTτ.26,27 kb is the Boltzmann constant, and T is the (26) Green, M. S.; Tobolsky, A. V. J. Chem. Phys. 1946, 14, 80-89.
Karlson et al.
Figure 3. Viscosity as a function of the CD concentration as calculated from eq 1. Complex constants, K, 3 or 44 mmolal-1, and concentrations of adsorption sites, B, 4.4 or 14.8 mmolal, respectively, have been used. These B-values equal the concentration of HM-PEG hydrophobic tails at HM-PEG concentrations of 3% or 10% (w/w), respectively. The dashed line is a linear extrapolation of the trend in the region 0 e cCD e 0.5B for K ) 44 mmolal-1 and B ) 4.4 mmolal. absolute temperature. Furthermore, we have assumed that the characteristic time, τ, of the relaxation process, that is important for the viscosity at the Newtonian plateau, is independent of the CD concentration, cCD. By this latter assumption the main contribution to the viscosity in the HM-PEG solutions is regarded to stem from associations of the polymer hydrophobic tails, and the effect from entanglements of the PEG backbone is regarded as insignificant; i.e., a change in viscosity at the Newtonian plateau is only dependent on the concentration of rheologically active chains, n (η ∝ n). In fact, an earlier study of HM-PEG has shown that disruption of hydrophobic associations is likely to be the main contributor to the relaxation time,27 and since the coil size of an unperturbed PEG chain with similar molecular weight suggests an overlap concentration far above the concentrations used in this study, the effect from chain entanglements is likely to be negligible.28 From this follows that:24
η - η∞ )1-Θ) η0 - η∞
1-
B + cCD + 1/K 2
x
(B + cCD + 1/K)2 - BcCD 4 (1) B
Here η0 and η∞ are the viscosities that are obtained without CD and at excess CD, respectively, and Θ is the fraction of occupied binding sites in the Langmuir model. In a previous paper we have studied the complex formation between a graft hydrophobically modified polymer, HM-EHEC, and CD.24 In this work we fitted eq 1 to our experimental data points [(η - η∞)/(η0 - η∞) vs cCD] with K and B as fitting parameters. In that way we could determine K for several combinations of different hydrophobic groups and CDs. We also found a very good correlation between the number of adsorption sites, B, and the total amount of hydrophobic groups in the solution, chydrophobe. This observation was not too surprising and this was taken as an indication of all hydrophobic groups being equally important and contributing in a similar way to the network formation and to the viscosity. Figure 3 is obtained by use of eq 1 and illustrates how the viscosity (η) as a function of cCD is influenced by a variation in B and K. From this figure it appears that the initial behavior at low cCD is largely determined by B, and provided K has a sufficiently high value (>10 mmolal-1) B strongly influences the (27) Annable, T.; Buscall, R.; Ettelaie, R.; Whittlestone, D. J. Rheol. 1993, 37, 695-726. (28) Gregory, P.; Huglin, M. B. Makromol. Chem. 1986, 187, 17451755.
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Figure 4. Relative viscosity, η/η0, as a function of the CD concentration in a solution with 3% (w/w) HM-PEG. (b) Experimental data. (s) Theoretical viscosity calculated from eq 1 with K ) 44 mmolal-1 and B ) 4.4 mmolal, or with B ) 0.4 mmolal-1 (---). curve in a large viscosity range. In such a situation the initial behavior (at low cCD) is well represented by a straight line with the slope of -1/B (see eq 2). The viscosity at excess CD (η∞) is expected to be virtually independent of cCD and to be the same as that found in a solution containing an unmodified polymer with a corresponding molecular weight. K influences the curve in the intermediate region where a transformation from the slope -1/B to the plateau value at high cCD (slope 0) appears. High values of K cause a very abrupt transition, while a low value leads to a more extended transition. In our previous work we determined K for the complexation between M-R-CD and C14alkyl hydrophobes of HM-C14-EHEC to K ) 44 mmolal-1,24 and since similar hydrophobes (C16-18) are used also in the present polymer, we have no reasons to believe that K is lower here. The value of B can therefore be obtained from the initial behavior via a simplified equation:
cCD η - η∞ η ≈ ∝1η0 - η∞ η0 B
(2)
Results and Discussion The solid line in Figure 4 is obtained from eq 1 with values of B ) 4.4 mmolal [the concentration of polymer hydrophobic tails in a 3% (w/w) HM-PEG solution], and K ) 44 mmolal-1 (the binding constant that was obtained for a C14 aliphatic chain in combination with M-R-CD in our previous investigation).24 However, the experimental data are very different and it is obvious that initially CD influences the viscosity much more strongly than expected from these values of B and K. At low cCD only a small fraction of the hydrophobic tails can be deactivated (from stoichiometrical considerations), but the effect on the viscosity is dramatic. Obviously deactivation of the first few hydrophobic associations has a much stronger influence on the viscosity than what could at first be expected. Actually, by changing the value of B from 4.4 to 0.4 mmolal, a value that is suggested by the initial slope, and by keeping K ) 44 mmolal-1 constant, a much better representation of the experimental data is obtained (dashed line). This is a quite surprising result since this means that it is enough to eliminate only about 10% of the hydrophobic tails to reduce the viscosity to a level virtually corresponding to that at excess CD. As was explained in the Experimental Section, this is based on the assumption that 1:1 complexes are formed. Since the hydrophobic tails are relatively long, we note that there is a possibility that higher complexes may form. Olson et al.29 have shown by NMR measurements that two or even more R-CD mol(29) Olson, K.; Chen, Y.; Baker, G. L. J. Polym. Sci. Part A: Polym. Chem. 2001, 39, 2731-2739.
ecules can bind to a C12 hydrophobic group attached to a PEG chain. This tendency is likely to be more important at high cCD. However, this cannot explain the behavior that was observed since formation of higher complexes would actually mean that the 10% is an overestimation. To be able to rationalize this observation, a general discussion about structure in a HM-PEG solution, and its concentration dependency, is needed.30 Micellelike structures may appear already at concentrations of about 10-3% (w/w).31,30 Since the triblock structure of the HM-PEG chains results in an attraction between micelles,32 clusters that contain many micelles are likely to form. While micelles probably have fairly well-defined aggregation numbers, the clusters may appear in a wide range of sizes, and it seems reasonable that the average cluster size increases with concentration.33-35 Below the concentration where clusters start to interact and connect to each other, the viscosity of the solution is likely to be low, while above this concentration the viscosity increases rapidly. At this stage the solution is often referred to as containing a threedimensional network that extends over macroscopic distances. The structure as a function of the concentration that follows from the above discussion is schematically illustrated in Figure 5. Regions with higher concentrations of polymer correspond to clusters of micelles, and within these clusters intermicellar links are likely to be numerous, while polymers that connect micelles located in different clusters have to span polymer-depleted regions and are more rare. One indication of that the solution is inhomogeneous is given by the phase behavior (Figure 6). A solution of the “corresponding diblock polymer”, which has a chemical structure corresponding to half the triblock polymer, has a phase behavior very much resembling that of an unmodified PEG polymer with a phase separation at high temperatures. This is expected since the hydrophobic tails are hidden in the core of micelles and it is only the PEG part that is exposed toward the aqueous solution. Despite the fact that similar micellar structures are expected to form with the triblock polymer, a solution based on HM-PEG has a much more pronounced tendency to phase-separate, and a phase concentrated in polymer is obtained in equilibrium with a phase depleted in polymer. This situation appears already at slightly elevated temperatures, and only a small change of the PEG/solvent interaction is needed to induce phase separation. The very pronounced difference in phase behavior between the di- and triblock polymers can be traced to the attraction between micelles.36 The molecular picture that emerges is that the solution is likely to be inhomogeneous with large concentration fluctuations, and at intermediate concentrations a percolated network forms via relatively few bridges between different clusters. This picture is valid in the concentration range that has been investigated. With this in mind, we are now in a position to explain the fact that the viscosity was affected much more strongly (30) Winnik, M. A.; Yekta, A. Curr. Opin. Colloid Interface Sci. 1997, 2, 424-436. (31) Yaminsky, V. V.; Thuresson, K.; Ninham, B. W. Langmuir 1999, 15, 3683-3688. (32) Semenov, A. N.; Joanny, J.-F.; Khokhlov, A. R. Macromolecules 1995, 28, 1066-1075. (33) Alami, E.; Rawiso, M.; Isel, F.; Beinert, G.; Binana-Limbele, W.; Francois, J. Hydrophilic polymers. Performance with environmental acceptance; American Chemical Society: Washington, DC, 1993; Vol. 248, pp 343-362. (34) Alami, E.; Almgren, M.; Brown, W. Macromolecules 1996, 29, 2229-2243. (35) Xu, B.; Li, L.; Yekta, A.; Masoumi, Z.; Kanagalingam, S.; Winnik, M. A.; Zhang, K.; Macdonald, P. M.; Menchen, S. Langmuir 1997, 13, 2447-2456. (36) Thuresson, K.; Nilsson, S.; Kjoniksen, A.-L.; Walderhaug, H.; Lindman, B.; Nystro¨m, B. J. Phys. Chem. 1999, 103, 1425-1436.
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Figure 5. Schematic representation of the self-aggregation of HM-PEG as function of increasing cHM-PEG.
Figure 6. Partial phase diagram for HM-PEG: (b) triblock, (O) diblock. Reproduced from ref 36.
than what was first expected from eq 1. To reduce viscosity strongly it is only necessary to decouple associations between different clusters, and since these are only expected to involve a small fraction of the total number of HM-PEG chains, a strong initial decrease in viscosity on addition of CD can be understood. This could be the explanation for the fact that a CD concentration corresponding to only about 10% of the hydrophobic groups has to be added to the 3 wt % HM-PEG solution to give a viscosity that is virtually the same as in a solution containing the unmodified PEG. One reason for this behavior could be that bridges between clusters correspond to HM-PEG chains that are more stretched than links between micelles within the clusters. This means that the former break and re-form more frequently and are more likely to be presented to CD molecules. Furthermore, the fact that the solution is depleted in polymer between clusters may result in a relatively high CD concentration here, and termination of HM-PEG chains located in this region increases also for this reason. A cartoon picture of a HM-PEG solution containing a low CD concentration could then, as illustrated in Figure 7, be viewed as discrete clusters covered on the surface by CD. It should, however, be noted that we do not believe that this is a static situation but rather that Figure 7 should be seen as a snapshot. For the sake of completeness we have to mention the possibility that
the phenomenon (with a rapidly decreasing viscosity) possibly could be shear-induced, and the network is being broken down into fragments that orient in the flow. However, we find this unlikely since identical results have been obtained with many different measuring geometries of the rheometer (cone and plate of different diameters, plate-plate, and double gap), and special care was paid to perform control measurements also at very low shear rates. The results were not affected by whether the samples had been subject to preshear or not, and identical results also were obtained with the rheometer in the oscillatory shear mode. Measurements have also been performed at other polymer concentrations [5% and 10% (w/w) polymer]. As a matter of fact, a similar result but even more pronounced deviation from the expected value of B was found at the two other investigated concentrations (Table 1 and Figure 8). The value of B obtained from the experimental data is virtually unaffected by an increased HM-PEG concentration (in the investigated range). This means that the fraction B/chydrophobe decreases with increasing HM-PEG concentration, and at the highest HM-PEG concentration this ratio is as low as 4%. This may mean that the number of polymer chains that participate within one cluster grows with increasing polymer concentration (increasing cluster size), which also has been suggested before.34 An increasing size of the “decoupled” clusters would be likely to give a contribution to the viscosity of the solution. Indeed, in a closer look it can be seen that the experimental curves can be divided into three different regions instead of two (Figure 8). This behavior becomes more pronounced with increasing HM-PEG concentration, and in the second region, located at intermediate CD concentrations, the change in viscosity is less dramatic than the initial steep decrease. We refer the decrease in this intermediate region to disengagement of individual clusters and micelles by CD. While B was obtained by extrapolation to η/η0 ) 0 at low CD concentration, a similar extrapolation can be made in this intermediate region to obtain B2. B2 would then be connected to the actual HM-PEG concentration in the solution. Indeed, B2 is, in contrast to B, dependent on the HM-PEG concentration (Table 1). In the structural picture that evolved above, clusters are connected with a rather small number of bridges, and by adding CD these bridges are deactivated. This is related to the situation for which the percolation theory has been
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Figure 7. Schematic representation of the binding of CD to HM-PEG hydrophobic tails. Already at rather low concentrations of CD the percolated network structure is eliminated because hydrophobic associations between clusters are inhibited. At higher CD concentrations, clusters and individual micelles also are expected to be disengaged by CD. Table 1. Data from Three Different HM-PEG Concentrationsa concn of HM-PEG (% w/w)
concn of hydrophobic tails, chydrophobe (mmolal)
B (mmolal)
B/ chydrophobe
B2 (mmolal)
3 5 10
4.4 7.4 14.8
0.45 0.42 0.53
10% 6% 4%
2.42 3.30 4.39
a B and B were obtained by extrapolation to η/η ) 0 in the low 2 0 cCD and intermediate cCD regions, respectively.
developed.37 This was quite recently used to rationalize rheological data in a related system, where microemulsion droplets were connected into a network with HM-PEG.38 At a certain concentration of bridges (here between clusters) a percolated network is anticipated, and at this point the viscosity is expected to increase rapidly (diverge) since an infinite network that extends over macroscopic distances forms. Below the percolation threshold, the viscosity can be seen as a summation of contributions from all different cluster sizes and is given by37
η0 ∝ [(cHM-PEG - cCD)c - (cHM-PEG - cCD)]-0.7
(3)
In eq 3 we have used the concentration variable (cHM-PEG - cCD) since a HM-PEG molecule that is terminated with CD at one end is expected to be incapable of forming a bridge between clusters. At all three investigated HM-PEG concentrations (3%, 5%, and 10%) we expect a percolated network at cCD ) 0. Following the discussion above, in the initial stages addition of CD terminates hydrophobic tails of HM-PEG polymers that are important for the percolated network (between clusters), leaving the clusters almost unaffected. Thus, in the present view the percolation threshold, (cHM-PEG - cCD)c, becomes dependent on the HM-PEG concentration, and the specificity of CD to preferentially deactivate bridges between clusters implies that a pure HM-PEG solution should always have a higher viscosity than a CD containing sample with the same effective concentration (cHM-PEG - cCD) (Figure 9). In the figure it can be seen that the percolation theory provides a good representation of CD-containing solutions. (37) Stauffer, D.; Coniglio, A.; Adam, M. Adv. Polym. Sci. 1982, 44, 103-158. (38) Bagger-Jo¨rgensen, H.; Coppola, L.; Thuresson, K.; Olsson, U.; Mortensen, K. Langmuir 1997, 13, 4204-4218.
Figure 8. Relative viscosity, η/η0, as a function of CD concentration in solutions with 3%, 5%, or 10% (all w/w) HMPEG, respectively. B-values were obtained by extrapolation to η/η0 ) 0 from the behavior at low CD concentration (data represented as b have been used in the extrapolation). The B2 values were obtained by extrapolation to η/η0 ) 0 from the behavior at intermediate CD concentrations (O). Data represented by 0 have not been used in the extrapolations.
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tigated concentration range). This may be taken as evidence that the structure and its dependency on the concentration variable in solutions of HM-PEG is different if the solution also contains CD. Conclusions
Figure 9. Viscosity as a function of the effective concentration variable (cHM-PEG - cCD); see text. Three sets of data with varying cHM-PEG [3% (4), 5% (O), and 10% (0) (all w/w)] are shown. The solid lines are best fits to eq 3 for each HM-PEG concentration, and dotted vertical lines represent the corresponding percolation thresholds (cHM-PEG - cCD)c. The viscosity as a function of cHM-PEG without CD is represented by 9.
It is interesting to see that the viscosity as a function of HM-PEG concentration (without CD) has a rather different behavior, with a different functional form. Obviously eq 3 cannot be used to represent the decrease in viscosity upon dilution of a pure HM-PEG solution (in the inves-
The most surprising observation in the present investigation is that it is enough to terminate a rather small fraction (about 10% in a 3% HM-PEG solution) of the HMPEG hydrophobic tails with CD molecules to reduce the viscosity to a level virtually corresponding to that at excess CD. To rationalize this observation, advantage was taken of the fact that concentration fluctuations are likely to be substantial in a HM-PEG solution of this concentration and that viscosity, in this view, becomes strongly dependent on HM-PEG chains that connect different clusters of micelles. By deactivating these latter associations, the viscosity decreases rapidly. Another interesting observation is that the fraction of HM-PEG chains that are active in interconnecting different clusters seems to decrease with an increasing polymer concentration (in the investigated range). This may be taken as an indication that sizes of the clusters increase with increasing HM-PEG concentration. Acknowledgment. This investigation was sponsored by the Center for Amphiphilic Polymers (CAP). LA026040T
