Aggregation Number Determination in Aqueous Solutions of a

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Aggregation Number Determination in Aqueous Solutions of a Hydrophobically Modified Poly(ethylene oxide) by Fluorescence Probe Techniques Olga Vorobyova,† Willie Lau,‡ and Mitchell A. Winnik*,† Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6, and Research Laboratories, Rohm and Haas Company, Spring House, Pennsylvania 19477 Received July 31, 2000. In Final Form: November 24, 2000 In this paper, we report the results of fluorescence probe studies of association in aqueous solution of a model polymer ODU, which is a C18H37 end-capped monodisperse poly(ethylene oxide) with a molecular weight of 35 000 and essentially 100% end group substitution. The main parameter of interest is the end group aggregation number NR, which we determine by the time-resolved fluorescence quenching technique using pyrene as a probe. Aiming to extend this technique to situations where the probe is not solubilized completely by the polymer micelles, which happens when the polymer concentration in a solution becomes very low, we modified the standard Poisson quenching model to account for the emission of the probe in the water phase. ODU solutions undergo phase separation at polymer concentrations between 2.1 g/L and 20 g/L. The aggregation number in a 2.1 g/L solution was found to be 23. For high concentration polymer solutions, from 3 to 17 wt %, we found that the aggregation number tends to increase with the polymer concentration, whereas the pyrene quenching constant decreases.

Introduction Associative thickeners (ATs) are members of a class of water-soluble polymers that contain hydrophobic substituents.1 When these polymers are added to water in small amounts, the viscosity increases and the solution “thickens”, giving the name to this class of polymers. The feature of these polymers that makes them interesting from an industrial point of view is their viscosity profile at different shear rates. ATs are used as rheology modifiers in water-borne coatings such as paints and paper coatings, in adhesives and sealants, and in oil recovery applications.2 The field of applications is expanded by the sensitivity of the rheological behavior to the chemical structure of the polymer, the nature of the hydrophobic substituent, and the number of hydrophobes per polymer. As a consequence, there is a deep and growing interest in the underlying science of polymer association in aqueous solution. We now appreciate that these polymers in water associate through local phase separation of the hydrophobic groups into micellelike structures. The polymer backbone forms bridges between micelles, and in this way the polymer self-assembles to form a transient network.3-4 * To whom correspondence should be addressed. E-mail: [email protected]. † University of Toronto. ‡ Rohm and Haas Co. (1) (a) Water-Soluble Polymers: Beauty with Performance; Glass, J. E., Ed.; Advances in Chemistry 213; American Chemical Society: Washington, DC, 1986. (b) Polymers in Aqueous Media: Performance through Association; Glass, J. E., Ed.; Advances in Chemistry 223; American Chemical Society: Washington, DC, 1989. (c) Hydrophilic Polymers; Glass, J. E., Ed.; Advances in Chemistry 248; American Chemical Society: Washington, DC, 1996. (d) Macromolecular Complexes in Chemistry and Biology; Dubin, P., Bock, J., Davis, R., Schulz, D. N., Thies, C., Eds.; Springer-Verlag: Berlin, 1994. (2) Industrial Water Soluble Polymers; Finch, C. A., Ed.; The Royal Society of Chemistry: Cambridge, U.K., 1996. (3) Winnik, M. A.; Yekta, A. Curr. Opin. Colloid Interface Sci. 1997, 2, 424-436. (4) Rubinstein, M.; Dobrynin, A. V. Trends Polym. Sci. 1997, 5, 181186.

To relate rheological properties to structure for these polymers, one of the most important morphological features one needs to characterize is the mean number of hydrophobic substituents NR that associate to form individual micellelike aggregates. NR is an aggregation number analogous to that (Nagg) used to describe the number of surfactant molecules per micelle for simple surfactants in water. For many surfactant micelles, Nagg has values of 60-100 molecules per micelle. For many traditional surfactant systems, these aggregation numbers are relatively easy to determine by scattering methods involving light, X-rays, or neutrons or by fluorescence quenching measurements. For the micellelike structures formed by associating polymers, the values of hydrophobe aggregation numbers are more difficult to determine. As a consequence, they are known with much less confidence. Determination of Aggregation Numbers by Fluorescence Quenching. The fluorescence quenching methodology for determining micelle aggregation numbers was developed in the late 1970s for characterizing micelles formed from low molecular weight surfactants.5-7 In this approach, one introduces a small amount of a fluorophore dye (D) and a larger amount of quencher (Q) into a solution containing micelles. The dye and quencher must be solubilized randomly but completely by the micelles so that a negligible fraction remains in the water phase. The principle of the method is that the dye fluoresces normally in a micelle which contains no quencher, but in micelles containing a dye and one or more quenchers, quenching competes with fluorescence. Data analysis begins with the assumption of a Poisson distribution of Q among micelles. With the assumption that neither the quencher (5) (a)Yekta, A.; Aikawa, M.; Turro, N. J. Chem. Phys. Lett. 1979, 63, 543-548. (b) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289-292. (c) Infelta, P. P.; Gra¨tzel, J.; Thomas, K. J. Phys. Chem. 1974, 78, 190-195. (6) Zana, R. In Surfactant Solutions: New Methods of Investigation; Zana, R., Ed.; Surfactant Science Series, Vol. 22; Marcel Dekker: New York, 1987; pp 242-294. (7) Kalayanasundaram, K. Photochemistry in Microheterogeneous Systems; Academic Press: London, 1987.

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nor the excited probe D* escape the micelle during the lifetime of D*, the expression for time-resolved fluorescence quenching (TRFQ) is given by eq 1.

ID(t) ) ID(0) exp[-t/τD - n(1 - exp(-kqt))]

(1)

Here, ID(t) is the fluorescence intensity of the dye at time t. ID(0) is its initial intensity; τD is the unquenched lifetime, and kq is the pseudo-first-order rate constant for quenching in the micelle. In experiments in which one uses excimer formation as the quenching process, ID(t) refers to the “monomer” fluorescence decay profile. In this case, the dye is commonly excited pyrene, Py*, and groundstate Py serves as the quencher. One has to be careful to ensure that excimer formation is essentially irreversible on the time scale of the Py* lifetime. The mean number of quenchers per micelle, n, is related to the aggregation number through the micelle concentration: n ) [Q]/[micelle] ) [Q]/(C - cmc)Nagg, where [Q] is the bulk molar quencher concentration, C is the total concentration of surfactant, and cmc is the critical micelle concentration. For traditional surfactants, one determines the aggregation number Nagg. For associative polymers, the parameter n is related to the aggregation number of hydrophobic substituents NR by the equation

n ) [Q]/[micelle] ) [Q] NR/(CpolqR)

(2)

where qR is the alkyl chain content of the polymer (in moles of alkyl groups per gram of polymer) and Cpol is the polymer concentration in g/L. In this equation, the critical micelle concentration (or critical association concentration, cac) is assumed to be negligible compared to Cpol. The cac is not always small, particularly in telechelic polymers with a long water-soluble backbone and relatively weak hydrophobic end groups. Aggregation Numbers in Telechelic Polymers: Recent Results. Of the various associative polymers that have been studied, we have the deepest understanding of the telechelic associating polymers. These are linear watersoluble polymers, normally based upon poly(ethylene oxide) (PEO), with hydrophobic end groups. In 1995, Yekta et al.8 reported NR values for a set of HEUR polymers (hydrophobically modified ethoxylated urethane polymers) with C16H33O- end groups. These model polymers were prepared by reacting oligomeric PEO chains with isophorone diisocyanate to elongate the chain and to permit attachment of the end groups. In this system, C16H33Ogroups are attached to the chain ends via isophorone diurethane (IPDU) moieties, which serve as part of the total hydrophobic end group. In these experiments, quenching occurs through pyrene excimer formation: excited pyrene serves as the fluorophore, and groundstate pyrene serves as the quencher. The experiments were carried out over a range of pyrene concentrations for each polymer concentration and at three different polymer concentrations. At the lowest of the polymer concentrations, the solution was characterized primarily by flower micelles, whereas at the highest concentration the onset of network formation was indicated by the 100-fold increase in the solution viscosity. For this particular sample (Mn ) 34 000), they found a value of NR ) 18 ( 1 independent of the polymer concentration. From this result, it was concluded that the primary association to form the flower micelles was a closed association process and that the core size of the micellelike aggregate was (8) Yekta, A.; Xu, B.; Duhamel, J.; Adiwidjaja, H.; Winnik, M. A. Macromolecules 1995, 28, 956-966.

conserved during the secondary association into the network. Because the highest concentration examined was only about 2 wt % polymer, this conclusion applies specifically to solutions containing up to this amount of polymer. These experiments were extended to other HEUR polymers differing in chain length (Mn from 34 000 to 51 000) but all containing C16H33O- as the hydrophobic end group. For these polymers, the NR values ranged from 18 to 28, but for any one polymer the value of NR did not change over a limited range of concentrations that spanned flower micelles to well-formed networks. This result leads one to conclude that the system follows a closed association model for micelle core formation over this concentration range. In each of the various experiments described above, the end group aggregation number determined was on the order of 20-30. These numbers are significantly smaller than those commonly found for nonionic micelles formed from surfactants with shorter EOx chains. Nevertheless, these numbers are significantly larger than the values of 3-6 inferred indirectly from rheology measurements through calculations that did not take full account of looping chains.9 Persson et al.10 used a method based upon electron paramagnetic resonance (EPR) spectroscopy to determine the NR value for a PEO polymer of M ) 9300 with C12H25 groups attached to the chain ends by an ether linkage. Like the fluorescence quenching technique, the EPR approach assumes a Poisson distribution of hydrophobic spin probes among micelles. In this way, the authors determined that NR ) 31 ( 6 at a polymer concentration of 2.5 wt %. In an earlier paper,11 they reported NR ) 28 determined by fluorescence quenching and an onset of aggregation (the cac) of 1.5 × 10-5 M. By comparison, the nonionic surfactant C12H25-EO23 has a critical micelle concentration (cmc) of 1.8 × 10-4 M and Nagg ) 40. The longer EO chain length of the associating polymer leads to a lower end group aggregation number. Similar polymers were examined by SAXS and SANS by the group of J. Franç ois in France.12-14 They carried out small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) measurements on C12 endcapped poly(ethylene oxides) with various chain lengths. In SANS experiments performed on polymers with deuterated hydrophobes, a mixture of H2O and D2O matching the PEO chain contrast was used as a solvent, thus allowing the researchers to characterize the hydrophobic clusters. At a low polymer concentration, the scattering curve shows the presence of only one peak, and when the concentration increases a second peak appears. The authors interpreted their data in terms of a disorderorder transition taking place with increasing polymer concentration, which they visualized as the organization of spherical micelles into a cubic lattice. Using the model of monodisperse spheres, they were able to calculate the mean radius of hydrophobic clusters from their scattering curves. From these results, they inferred an increase in (9) Annable, T.; Buscall, R.; Ettelaie, R.; Whittlestone, D. J. Rheol. 1993, 37, 695-726. (10) Persson, K.; Bales, B. L. J. Chem. Soc., Faraday Trans. 1995, 91 (17), 2863-2870. (11) Persson, K.; Wang, G.; Oloffson, J. J. Chem. Soc., Faraday Trans. 1994, 90, 3555. (12) Alami, E.; Rawiso, M.; Isel, F.; Beinert, G.; Binana-Limbele, W.; Franç ois, J. Hydrophilic Polymers; Advances in Chemistry Series 248; American Chemical Society: Washington, DC, 1995; pp 344-362. (13) Franç ois, J.; Maitre, S.; Rawiso, M.; Sarazin, D.; Beinert, G.; Isel, F. Colloids Surf., A 1996, 112, 251-265. (14) Abrahmseń-Alami, S.; Alami, E.; Franç ois, J. J. Colloid Interface Sci. 1996, 179, 20-33.

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the size of the hydrophobic domains when polymer concentration is increased from 5 to 54 wt %. The degree of polydispersity Rw/Rn was found to be in the range of 1.2-1.4, with the lower values obtained at the higher polymer concentrations. Another report by the same group13 shows a similar picture for C18H37 end-capped polymers. Some information is available on aggregation numbers in flower micelles from diffusion coefficient measurements. For example, if dynamic light scattering (DLS) or pulsedgradient spin-echo NMR measurements indicate a narrow distribution of diffusing species in solution at concentrations above the cmc, the size of these species can be inferred by comparison with intrinsic viscosity data. Assuming hard-sphere behavior for these objects, one can combine the intrinsic viscosity with the diffusion coefficient determined to calculate the mean number of polymer molecules per flower micelle. From the diffusion coefficient, one first calculates the hydrodynamic radius RH of the flower micelle using the Stokes-Einstein equation:

RH )

kT 6πηD

(3)

In this equation, k is the Boltzmann constant, T is the temperature, η is the solvent viscosity, and D is the diffusion coefficient. The following equation relates the intrinsic viscosity and the hydrodynamic radius to yield the aggregation number:

p)

10πRH3NA 3M[η]

(4)

where NA is Avogadro’s number, M is the molecular weight of the polymer, and p is the aggregation number expressed as the number of polymer molecules in the micelle. Determined from fluorescence measurements, NR describes the number of hydrophobes, or polymer chain ends, per micelle. If each polymer contains two hydrophobic end groups, then NR ) 2p. In this way, an NR value of 30 was estimated from pulsed-gradient spin-echo NMR measurements carried out on a PEO polymer of M ) 35 000 with C8F17CH2CH2Oend groups, each coupled to the chain end via an IPDU group.15 For the same polymer, TRFQ measurements using a pyrene derivative with a short fluorocarbon chain as a probe resulted in smaller aggregation numbers on the order of 15-20 chain ends per micelle. Pham et al.16 have performed extensive rheological and dynamic light scattering experiments on C16H33- (HDU) and C18H37- (ODU) end-capped monodisperse PEOs with a molecular weight of 35 000 and the degree of substitution close to unity. The TRFQ measurements on HDU that we described previously17 and on ODU that we report here were carried out on the same polymer samples investigated by Pham et al. These authors report that at low concentrations where the polymers exist as flower micelles the hydrodynamic radius RH for the ODU polymer is equal to 21.2 ( 1.3 nm, and for HDU RH ) 17.3 ( 0.4 nm. The value of intrinsic viscosity for ODU is (51 ( 0.5) × 10-3 L/g, and for HDU it is (47 ( 3) × 10-3 L/g. For ODU, the mean aggregation number NR is estimated as 66 ( 18 (15) Xu, B.; Li, L.; Yekta, A.; Masoumi, Z.; Kanagalingam, S.; Winnik, M. A.; Zhang, K.; Macdonald, P. M. Langmuir 1997, 13, 2447-2456. (16) (a) Pham, Q. T.; Russel, W. B.; Thibeault, J. C.; Lau, W. Macromolecules 1999, 32, 2996-3005. (b) Pham, Q. T.; Russel, W. B.; Thibeault, J. C.; Lau, W. Macromolecules 1999, 32, 5139-5146. (17) Vorobyova, O.; Yekta, A.; Winnik, M. A.; Lau, W. Macromolecules 1998, 31, 8998-9007.

using eq 4; for HDU, a lower value of NR is obtained, 40 ( 4. These results were obtained for polymer concentrations between 0.2 and 1.5 g/L. Reviewing the available literature data on aggregation numbers of similar telechelic PEO polymers, the authors draw attention to the gross discrepancy often found between the NR values obtained by TRFQ and those inferred from a combination of DLS or NMR and viscometry measurements. The aggregation numbers obtained with fluorescence techniques are about 50% lower than those calculated via eq 4 at lower concentrations. For the samples described by Yekta et al.,8 the two approaches give similar values of NR. In the other cases, however, this discrepancy is not yet adequately explained. In light of this discussion, it is instructive to review the difficulties one faces when using TRFQ as the method of determination of the aggregation numbers in associative polymer solutions. In a recent publication, Alami et al.18 reported fluorescence quenching measurements to determine NR values for a C12H25 end-capped PEO of M ) 20 000 using two different quenchers. Using pyrene as a probe and dimethylbenzophenone as a quencher, they found an aggregation number of 28 ( 3 for polymer concentrations ranging from 2 to 7 wt %. When the experiment was repeated at a higher pyrene concentration, quenching by pyrene excimer formation led to a different aggregation number (16) for a 6 wt % polymer solution. To explain this difference, the authors expressed their concern about the validity of the Poisson distribution of fluorophores and quenchers in the micellelike structures formed by their polymer. The most important aspect of this work is that it emphasizes the difficulties in applying fluorescence quenching methods to associative polymer solutions. In our previous paper,17 we reported the results of our studies of hydrophobically modified monodisperse poly(ethylene oxide) polymer end-capped with C16H33 groups. Using TRFQ with two probes, pyrene and ethylpyrene, we determined aggregation numbers of this polymer HDU over a range of polymer and probe concentrations (0.4 wt % < Cpol < 17 wt %). We found that the aggregation number increased with polymer concentration in solution; in solutions with Cpol < 10 wt %, the aggregation number NR was 21 ( 1, and the pyrene quenching constant kq was 8.7 ( 0.6 µs-1. When Cpol > 10 wt %, NR ) 35 ( 6, and kq ) 6 ( 1 µs-1. In this paper, we describe the results obtained with a similar polymer, ODU, using pyrene as a probe. The only difference in chemical structure between ODU and HDU is the length of the hydrophobic substituent: ODU has C18H37 alkyl groups whereas HDU has C16H33 groups.

When the polymer concentration is less than 2 wt %, ODU solutions quickly undergo phase separation, as reported by Pham et al.16 The dilute upper phase of phaseseparated solutions has a low polymer concentration. When micelles are present at low concentrations, probes (18) Alami, E.; Almgren, M.; Brown, W.; Franç ois, J. Macromolecules 1996, 29, 2229-2243.

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such as pyrene are often incompletely partitioned into the micelle phase. Under these conditions, analysis of fluorescence decay profiles in terms of the traditional Poisson quenching model (eq 1) produces poor results because of the competing emission of the probe outside the micelles. We show that better results can be obtained if one uses a modified Poisson quenching model, which accounts for probe emission from the water phase. Finally, we describe the effect of the polymer concentration on the aggregation number. Experimental Section Materials. The ODU and HDU associative polymers were prepared at Rohm and Haas. Their synthesis and characterization have been reported previously.16,17 These polymers have a molecular weight of 35 000, with Mw/Mn ) 1.10. Reversed phase HPLC measurements showed that more than 99% of the polymers contained two end groups. The ODU polymer contains a white water-insoluble impurity that could have a strong undesirable effect on all spectroscopic measurements. For low polymer concentrations, this impurity can be filtered out directly from water solution of polymer using a 0.8 µm filter, whereas for higher polymer concentrations the very high viscosity of the solutions makes filtering very difficult. To overcome this problem, the polymer was dissolved in methanol (10-15 wt %). The resulting solutions were opaque but could be easily filtered through a 0.65 µm cellulose acetate filter. The filtrates were clear. After filtration, methanol was removed on the rotary evaporator under vacuum. Pyrene (Aldrich) was recrystallized from ethanol and twice sublimed. Distilled water was further purified through a Millipore Milli Q purification system. Sample Preparation. ODU solutions of 0.8 and 1.2 wt % were prepared by adding the required quantity of deionized water to the purified polymer. After the mixture of the dry polymer and water was stirred for 2 days, the solutions were cloudy, and very quickly (within hours) phase separation occurred. The relative amounts of the two phases were approximately the same as those reported by the Princeton group.19 The diluted phase (upper phase) was a clear, nonviscous solution of ca. 0.1 wt % of polymer. The concentrated phase (lower phase) had a much higher viscosity and was slightly opalescent. Before pyrene saturation experiments were performed, the phases were separated. UV Absorption Measurements. A Hewlett-Packard 8452A diode-array spectrophotometer was used. In all measurements, a background correction was made by taking a probe-free polymer solution with the same polymer concentration as a reference. The probe partitions between polymer domains and water. For most of the solutions we examined, the contribution to the optical density by the probe in the water phase was negligible because of its much lower concentration and lower extinction coefficient at the excitation wavelength in comparison to the probe solubilized by the polymer. The concentrations of the micellized probes were calculated from the absorption readings using the following value of the pyrene extinction coefficient: ) 3.70 × 104 M-1 cm-1at 338 nm, determined from the UV absorption measurements at high concentrations of HDU, where virtually all of the dye is incorporated into a micellar phase.17 This value is very close to the value determined by Yekta et al. for pyrene solubilized in a similar telechelic associating polymer.8, 20 Static Fluorescence Measurements. A SPEX Fluorolog 2 spectrometer with double grating monochromators was used for measurements of pyrene fluorescence (resolution 0.5 nm, integration time 1 s). The excitation wavelength for pyrene (λex) was 338 nm. All measurements were carried out on aerated solutions. From pyrene emission spectra, two intensity ratios were calculated: the ratio of the first vibrational band (at 371.5 nm) to the third band (at 383 nm) (I1/I3) and the ratio of the maximum of the excimer emission (480 nm) to the maximum of the monomer emission (371.5 nm) (IE/IM). (19) Pham, Q. T.; Russel, W. B.; Lau, W. J. Rheol. 1998, 42, 159176. (20) Yekta, A.; Duhamel, J.; Brochard, P.; Adiwidjaja, H.; Winnik, M. A. Macromolecules 1993, 26, 1829-1836.

Vorobyova et al. Dynamic Fluorescence Measurements. Fluorescence decay profiles of the probe monomer emission were measured using the single-photon-timing technique.21 Data were collected to a maximum of 20 000 counts in the most intense channel. In this technique, the measured decay profile is a convolution of the true decay and the instrument response function. To determine the instrument response function, the mimic technique22 was employed, using p-bis[2-(5-phenyloxazyl)] benzene in degassed cyclohexane as the reference compound with a lifetime of 1.1 ns. For each polymer concentration, a series of “dilution” experiments was made. The probe concentration was changed in the following way, while keeping the polymer concentration constant. Initially, the decay profiles were taken for the probe-saturated polymer solutions. Then, an aliquot of solution was removed from the fluorescence cell, and the same amount of probe-free polymer solution was added. The contents of the cell were stirred for at least 2 h before each experiment to ensure the complete redistribution of the probe between micelles. Probe Saturation Experiments. An excess amount of a probe (0.25 mL of 0.005 M solution in acetone) was deposited on the wall of a centrifuge tube. Acetone was evaporated under a stream of nitrogen, and a polymer solution (2.5-3 mL) was introduced into the tube. The solutions were stirred for 4 days. Then, the excess probe was removed by centrifugation for 40 min at 15 000 rpm, and UV absorption spectra were taken. To make sure that saturation had been reached, the solutions were returned to the centrifuge tubes and stirred for one more day, and the centrifugation and UV measurements were repeated. The absorption did not change, indicating that the solutions were saturated with the probe. For each solution, excitation spectra were recorded at the monomer emission wavelength (371.5 nm) and at the excimer emission wavelength (480 nm). If the two excitation spectra show no difference when compared, one can infer the lack of ground-state preassociation of the probe and a complete removal of all the excess probe crystals.23 For a 2.1 g/L ODU solution (upper phase), the comparison of the excitation spectra revealed that all excess probe crystals were removed successfully. For the more viscous 20 g/L ODU solution (lower phase), it was much more difficult to get rid of the excess pyrene. Here, the monomer and excimer excitation spectra look completely different.24 However, the excess pyrene microcrystals could still be removed by prolonged centrifugation. The excitation spectra of the supernatant solutions show only slight differences at about 350-360 nm, and there are no strange features in the emission spectrum. These results clearly demonstrate that the solubilization procedure described above is problematic when applied to concentrated solutions. To avoid these problems, we developed the following procedure for probe solubilization for solutions with high viscosity. The required amount of 1 × 10-3 M probe solution in CH2Cl2 (less than the saturation limit) was added to the dry purified polymer. Then, additional dichloromethane (spectro grade) was added to the mixture to make a 15-20 wt % solution. This solution was stirred overnight, and then the CH2Cl2 was removed on a rotary evaporator. The resulting mixture is a homogeneous “solid solution” of probe in the polymer, with a fixed probe-to-polymer ratio. Different portions of this mixture were put in small test tubes, and deionized water was added to obtain the desired concentration of polymer. The test tubes were sealed with Parafilm and a plastic cap, and the mixtures were allowed to swell overnight. To ensure full mixing, the test tube was placed into the centrifuge with the empty end down and then centrifuged for 15 min at 5000 rpm. When the centrifuge stopped spinning, the test tube was turned over and the operation was repeated four times. Next, the solutions, which were clear and slightly opalescent, were allowed to sit for at least 1 week before measurements were carried out. All solutions were stored in the dark at room temperature. (21) O’Connor, D. V.; Phillips, D. Time-Correlated Single Photon Counting; Academic Press: New York, 1984. (22) James, D. R.; Demmer, D. R. M.; Verrall, R. E.; Steer, R. P. Rev. Sci. Instrum. 1983, 54, 1121. (23) Winnik, F. M. Chem. Rev. 1993, 93, 587-614. (24) Vorobyova, O. Ph.D. Thesis, University of Toronto, 2000.


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The ODU solutions with high polymer concentrations and/or a high pyrene concentration have a very high optical density even when a 1 mm cell is used. To measure UV and fluorescence spectra of these solutions, a special cell was constructed. It consists of two round quartz plates (25 mm in diameter, 2 mm in thickness) separated by a 120 µm thick Mylar (PET) spacer. After a small drop of solution was placed between the plates to form a spot about 1 cm in diameter, the plates were put in a special holder and sealed to prevent water evaporation. After each measurement, the sample was discarded.

Results and Discussion Determination of the Critical Association Concentration (cac). Pyrene is a hydrophobic molecule with a relatively low water solubility (0.7 µM).7,25,26 In the associative polymer solutions, however, its solubility increases considerably, owing to the transfer of the probe to the hydrophobic core of polymer micelles. The change in the probe environment is reflected in its absorption and fluorescence spectra. By an examination of a series of solutions with different polymer concentrations but a constant probe concentration, the onset of aggregation (the cac) of the polymer in water can be determined. The challenge is to analyze the data in a way that can distinguish the onset of aggregation of the polymer from a shift in the partition equilibrium of the probe. This problem was addressed in detail in the paper of Wilhelm et al.26 and was further examined by Kabanov et al.27 and by Zhao et al.28 The procedure suggested by Wilhelm et al.26 is used in the present study. A number of HDU and ODU solutions were prepared with concentrations ranging from 0.001 to 2 g/L. The concentration of pyrene in these solutions was kept constant at 6 × 10-7 M, just below the water solubility limit (7 × 10-7 M). Both excitation and emission spectra were recorded. The excitation spectra monitored at 371 nm show a shift in the maximum corresponding to the (0,0) band in the S2 r S0 transition, from 335.5 nm for the lowest polymer concentration used to 339 nm. This change is brought on by the transfer of pyrene from water to the hydrophobic core of the polymer micelles. In Figure 1, the wavelength of the maximum in the excitation spectra is plotted versus polymer concentration for HDU and ODU solutions. The data can be described by a sigmoidal curve, with two plateaus at 335.5 and 339 nm, corresponding to low and high polymer concentrations, connected by a rather steep line at intermediate concentrations. In the approach of Wilhelm et al.,26 one defines F ) I339/I335.5. This ratio has a constant value, both at a low polymer concentration (Fmin), where pyrene is entirely in the water phase, and at a high polymer concentration (Fmax), where almost all of the pyrene molecules are solubilized by the micelles. A plot of (F - Fmin)/(Fmax - F) versus Cpol is predicted to be linear at elevated polymer concentrations and to intersect the x-axis at Cpol ) cac. This ratio for HDU and ODU solutions is plotted against polymer concentration in Figure 2. At a low polymer concentration, this ratio is close to zero, and then it increases linearly with polymer concentration. In Figure 2, one finds the cac at the intersection of the best-fit line drawn through the data points and the x-axis. For HDU, (25) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977, 99, 2039-2044. (26) Wilhelm, M.; Zhao, C. L.; Wang, Y.; Xu, R.; Winnik, M. A. Macromolecules 1991, 24, 1033-1040. (27) Kabanov, A. V.; Nazarova, I. R.; Astafieva, I. V.; Batrakova, E. V.; Alakhov, V. Yu.; Yaroslavov, A. A.; Kabanov, V. A. Macromolecules 1995, 28, 2303-2314. (28) Zhao, J.; Allen, C.; Eisenberg, A. Macromolecules 1997, 30, 71437150.

Figure 1. Shift in the wavelength of the (0,0) band of the S2 r S0 transition of pyrene (circles) and the ratio I339/I335.5 calculated from the excitation spectra (squares) with the polymer concentration: (A) HDU solutions and (B) ODU solutions.

Figure 2. Dependence of the (F - Fmin)/(Fmax - F) ratio with the polymer concentration: (top) HDU solutions and (bottom) ODU solutions.

we find cac ) 0.06 g/L (1.6 × 10-6 M), and for ODU cac ) 0.04 g/L (1.1 × 10-6 M). The lower value for ODU is explained by the increased hydrophobicity of the polymer containing C18 hydrophobes, in comparison with HDU containing C16 hydrophobes.

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Some authors estimate the cac or cmc by examining the change in the intensity ratio I1/I3 for the first and third bands in the pyrene fluorescence spectrum as a function of polymer concentration. For HDU and ODU solutions, this ratio is constant at low polymer concentrations where the pyrene is almost entirely in the water phase. It decreases sharply over a range of increasing polymer concentrations, to level off at values of I1/I3 ) 1.22 for HDU and 1.21 for ODU. The strategy for estimating the cac is to draw a line through the tangent to the curve at its inflection point and to see where this line intersects the horizontal line drawn through the values at low polymer concentration. This approach does not distinguish between a shift in the partition of pyrene and the onset of hydrophobe association. When we carry out this analysis (for details, see ref 24), we obtain estimated “cac” values of 0.1 g/L (2.8 × 10-6 M) for HDU and 0.08 g/L (2.2 × 10-6 M) for ODU, higher than those obtained by analyzing the data from the excitation spectra using the method of Wilhelm et al.26 This difference emphasizes that the I1/I3 analysis can provide only an upper bound to the cac. Determination of the Probe Partition Coefficient. The process of probe partitioning between water and micellar phases can be described by the following equation:

K ) [P]msat/([P]wsatCpol)

(5)

where [P]sat is the saturated probe concentration in the micellar (m) and the water (w) phases, Cpol is the polymer concentration in g/L, and K is an equilibrium constant in L/g. The concentration of the probe in the micellar phase can be calculated from the absorption values using Beer’s law. The concentration of the probe in the water phase upon saturation is equal to the probe solubility and can be determined independently. In eq 5, the critical association concentration cac is neglected, because the polymer concentration used is much greater than the cac. The partitioning can also be described by a partition coefficient that takes into account the quantities of pyrene in the micellar and water phases relative to the phase volumes:

Kv ) ([Py]m/Vm)/([Py]w/Vw) ) K/qRν

(6a)

where Vm and Vw are the volumes of the micellar phase and the water phase, qR is the number of moles of hydrophobe per gram of polymer, and ν is the molar volume of the hydrophobe. If the molecular weight of the polymer is known accurately, one can write

Kv ) KMn/Nν

(6b)

where Mn is the number average molecular weight of the polymer (36 000) and N is the number of moles of the hydrophobe per mole of polymer (N ) 2 for ODU). Equation 6b is based on the “liquid drop” model, in which the micelle cores are treated as though they consist of droplets containing molecules of the corresponding alkane. For C18H37 groups, we use the molar volume of octadecane (ν ) 0.327 L/mol). From the partitioning data, we can calculate the fraction of probe remaining in the water phase, fw:

fw ) [Py]w/([Py]w +[Py]m) ) 1/(1 + KCpol)

(7)

To determine the partition coefficient of pyrene in ODU solutions, four solutions (0.2, 0.4, 0.6, and 1 g/L) were

Figure 3. Concentration of pyrene solubilized by ODU micelles versus polymer concentration. The pyrene concentration is calculated from the measured absorbance of the solutions using the molar extinction coefficient for pyrene in ODU determined at a high polymer concentration, where a negligible fraction of pyrene is in the water phase.

prepared and saturated with pyrene. The plot of the pyrene concentration versus polymer concentration is given in Figure 3. The data show some scatter with R2 ) 0.96. The calculated value of the equilibrium constant K is 8.4 L/g. The value determined for the HDU polymer (4.8 L/g) is less than that for ODU, which is not surprising, considering the difference in the hydrophobe size. The partition coefficient for ODU calculated with eq 6b is Kv ) 4.6 × 105. The corresponding value for HDU is of the same order of magnitude but smaller (Kv ) 2.9 × 105), indicating that ODU solubilizes pyrene more efficiently, a result which is not entirely consistent with the liquid drop model, which would predict nearly identical values of Kv. Using eq 5, it is possible to calculate the polymer concentration in the phase-separated ODU solutions, knowing the saturated pyrene concentration from UV absorption measurements and assuming that the same K is valid for the whole range of polymer concentrations. For the upper phase, [Py]msat ) 13 µM, from which we calculate Cpol ) 2.1 g/L; for the lower phase, [Py]msat ) 118 µM, and Cpol ) 20 g/L. These values are close to those obtained gravimetrically by Pham and Russel at Princeton19 (upper phase, less than 2 g/L; lower phase, 18 g/L). In a 2.1 g/L ODU solution, we calculated that 5.4% of the pyrene is in the water phase. Determination of the Aggregation Number in ODU Micelles for Cpol ) 2 g/L. Aggregation Number in the Upper Phase. At concentrations less than 2 wt %, the ODU polymer undergoes phase separation in aqueous solution, where the upper phase of low viscosity is a dilute solution of the flowerlike micelles and the lower gel-like phase is a network formed by interconnecting micelles. We will limit our discussion here to the results obtained for the upper phase of a phase-separated solution, where we estimate the polymer concentration to be 2.1 g/L. In the following experiments, the polymer concentration was kept constant. The pyrene concentration was systematically decreased from the saturation point to less than 5% of saturation by consecutive dilutions with a polymer solution of the same concentration but without pyrene. Each series consisted of 5-6 dilutions; the measurements were repeated three times, each time starting from a freshly prepared saturated solution. Following each dilution, fluorescence emission spectra and decay profiles were measured. Steady-state fluorescence measurements provide us with I1/I3 and IE/IM ratios; both sets of data are plotted in Figure 4 versus pyrene concentration. The I1/I3 values are


Langmuir, Vol. 17, No. 5, 2001 1363

Figure 4. Dependence of I1/I3 and IE/IM ratios with pyrene concentration in 2.1 g/L ODU solutions (upper phase). Figure 6. Fitting parameters versus pyrene concentration for 2.1 g/L ODU solutions (upper phase): lifetime τ (squares) and quenching constant kq (diamonds).

Figure 5. Fluorescence decay profiles of pyrene in 2.1 g/L ODU solution (upper phase). The pyrene concentration from top to bottom in µM is 1.3, 4.7, 7.8, and 12.6.

randomly scattered with an average of 1.21, whereas the excimer-to-monomer ratio varies linearly with pyrene concentration. Examples of pyrene decay profiles are presented in Figure 5 for different pyrene concentrations in 2.1 g/L ODU solutions. At high pyrene concentrations, the semilogarithmic decay profiles are strongly nonexponential, indicating quenching of the probe fluorescence through pyrene excimer formation. As the concentration of pyrene decreases, so does the probability of the excimer formation, and the decay profiles begin to straighten. However, even for the smallest pyrene concentration used, the decay profile is still noticeably nonexponential. The decay profiles were fitted to the Poisson quenching model, eq 1. All parameters were kept free during the fitting, which always produced statistically good fits. The fitting parameters τ and kq are plotted against pyrene concentration in Figure 6. The data do not show a good agreement with the model. The parameters τ and kq should be constant, yet the values appear to be correlated. The quenching constant kq does not change when the pyrene concentration is low (1-6 µM); for higher pyrene concentrations, kq increases noticeably (by 20%). The lifetime τ shows the reverse pattern; it decreases from 233 ns at low pyrene concentrations to 190 ns at higher pyrene concentrations. The fitting parameter n also behaves in a peculiar fashion. For very low pyrene concentrations (less than 5 µM), the plot of n versus [Py] (see Figure 7) is linear with an intercept of about 0.5. At higher pyrene concentrations, the data fit a straight line with a smaller slope.

Figure 7. Variation of fitting parameter n with pyrene concentration in 2.1 g/L ODU solution obtained using two different models: the extended Poisson model (eq 8, squares) and the standard Poisson model (eq 1, diamonds).

A likely source of these problems in the data analysis is competing emission from pyrene molecules present in the water phase. Over this range of polymer concentrations, the fraction of pyrene in the water phase is low but not negligible. In the aqueous environment, the lifetime of pyrene is 150 ns,8 which differs considerably from that (233 ns) of pyrene in the micellar phase. One could try to account for pyrene emission from the water phase by adding a corresponding term to the Poisson quenching model:

I(t) ) I(0) {B exp[-t/τm - n(1 - exp(-kqt))] + (1 - B) exp(-t/τw)} (8) In this equation, τm and τw are the lifetimes of the unquenched pyrene in the micellar and water phases; B is a parameter associated with the fraction of pyrene dispersed in the micelles. At the excitation wavelength, pyrene in water has a lower value of the extinction coefficient and a lower fluorescence intensity than pyrene solubilized by the polymer micelles. Therefore, the fraction of pyrene in the water phase fw should be greater than (1 - B). The data can be fitted to this extended model that

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Vorobyova et al.

Table 1. Results of Fitting Fluorescence Decay Profiles to the Poisson Quenching Model and to the Extended Poisson Quenching Modela [Py], µM

nb

kqb

τb

nc

kqc

rc

nd

kqd

12.6 9.74 7.78 5.53 4.65 2.45 1.31 0.61

2.03 1.74 1.64 1.51 1.39 1.00 0.79 0.61

7.23 6.9 6.86 6.16 6.01 6.3 6.22 8.03

193 204 211 223 227 229 233 234

2.97 2.34 2.06 1.67 1.47 1.02 0.76 0.59

6.17 6.72 7.03 6.67 6.52 7.27 7.23 9.24

0.9 0.87 0.88 0.9 0.91 0.9 0.93 0.96

2.94 2.27 2.02 1.67 1.48 1.03 0.75 0.57

6.14 6.35 6.65 6.66 6.73 7.23 7.77 11.12

a The ODU concentration is 2.1 g/L. b Data were fitted to the Poisson quenching model. The values of τ are given in ns, and the values of kq are in µs-1. The χ2 values were less than 1.3 in all fits. c Data were fitted to the extended Poisson quenching model with the parameters τm ) 233 ns and τw ) 150 ns. The mean value of kq is 6.80 µs-1, neglecting the value at the lowest [Py]. d Data were fitted to the extended Poisson quenching model with the parameters τm ) 233 ns, τw ) 150 ns, and r ) 0.9.

estimates four parameters: I(0), B, n, and kq; the lifetimes τm and τw are determined independently. The quality of fits of individual decay curves to eq 8 was very good as judged by the χ2 values and the autocorrelation and residual plots. One set of data is given in Table 1. The following results were obtained for CODU ) 2.1 g/L. The kq values scatter about 7 µs-1; the B values are very close to 0.9, indicating that 10% of the emission signal comes from pyrene molecules in the water phase. This value is high but not an unreasonable estimate. The extended micelle model has its strongest impact on the n values. At high pyrene concentrations, the n values increase dramatically, so that the new plot of n versus pyrene concentration (Figure 7) is close to linear. At low pyrene concentrations, the results are close to the ones obtained when the same decay curves were fitted to eq 1. An estimate of the aggregation number in the upper phase can be obtained from the slope in Figure 7. We calculate an aggregation number NR ) 23 for the 2.1 g/L solution of ODU. The disturbing feature of the plot in Figure 7 is the nonzero intercept. This behavior is similar to the result we obtained in the study of HDU (with C16H33 end groups),17 where phase separation was not a serious problem. We were able to carry out those experiments under conditions in which the fraction of the pyrene probe in the aqueous phase was negligible, and the decay curves could be analyzed with eq 1. Nevertheless, the data for both pyrene and ethylpyrene as probes gave positive intercepts in the plots of n versus [pyrene probe]. We developed a model that showed that if the polymer itself contained a trace of a fluorescence quencher as an impurity and this impurity had a Poisson distribution in the micelles formed by the end groups, data analysis by eq 1 would yield the correct value of NR but a finite intercept in the plot of n versus [pyrene probe]/Cpol. The data analysis here for ODU is complicated by the emission of excited pyrene in the aqueous phase. We suggest that the finite intercept seen in Figure 7 is a reflection of the same phenomenon found for HDU in water. Influence of the Pyrene Partitioning on the Decay Parameters. The following experiments were designed to test the limits of the extended Poisson quenching model (eq 8) by examining solutions with an increasing fraction of the probe present in the water phase. A series of solutions were prepared which had the same probe-topolymer ratio, [Py]/Cpol ) 4 µmol/g. The polymer concentration was varied from 2.1 to 0.28 g/L (the corresponding bulk pyrene concentration changed from 8.00 to 1.06 µM).

Figure 8. Two ways of fitting a common set of data for pyrene in ODU solutions with different concentrations (pyrene-topolymer ratio [Py]/Cpol ) 4.00 µmol/g): (A, B) plots of the quenching constant kq and (C, D) plots of the parameter n versus polymer concentration.

In these solutions, the fraction of pyrene in the water phase, fw, increased with decreasing polymer concentration, from 0.05 to 0.30. In the steady-state fluorescence spectra, both the I1/I3 and IE/IM ratios show changes supporting this trend: the solutions with the lowest polymer concentration (and the highest fraction of pyrene in the water phase) have the highest values of the I1/I3 ratio and the lowest values of the excimer-to-monomer ratio. When the decay profiles for these solutions are fitted to eq 1, the fitted τ values increase with polymer concentration, and the parameters kq and n behave as shown in Figure 8A,B. For the same probe-to-polymer ratio, one would expect similar values of these parameters, yet all of them show systematic changes. With decreasing polymer concentration, there is a larger fraction of pyrene in water. These pyrenes are characterized by a lower lifetime than the pyrene in the micellar phase. The computer program tries to respond to this situation by decreasing the values of the parameters kq and n. When the same decay profiles were fitted to the extended Poisson quenching model (eq 8), the results are more consistent. The parameter n plotted in Figure 8D behaves as expected; the data are scattered around a constant value. The values of the parameter kq, however, show some variation, especially at low polymer concentrations (Figure 8C). The extended quenching model can also be used to estimate the fraction of the probe in the water phase. With the decreasing polymer concentration, the values of fw obtained in the model increase as expected. These values are listed in Table 2 together with the fw values obtained from the partitioning data. The agreement between the two sets of data is not perfect, and the values estimated in the extended quenching model tend to be higher. Effect of Polymer Concentration on Aggregation Number. A number of ODU solutions with polymer concentrations ranging from 3 to 17 wt % were prepared with pyrene-to-polymer ratios [Py]/Cpol equal to 2.00 and 0.43 µmol/g. The steady-state fluorescence spectra looked


Langmuir, Vol. 17, No. 5, 2001 1365

Table 2. Summary of Results Obtained for Py-Containing ODU Solutions of Different Concentrationsa extended model (τw )150, τm )233)

Poisson quenching model [Py], µM

CODU, g/L

I1/I3

IE/IM

n

kq

τ

fw

n

kq

B

fw estimated

8.00 5.34 3.54 2.33 1.06

2.10 1.40 0.93 0.61 0.28

1.23 1.24 1.32 1.32 1.36

0.96 0.84 0.77 0.63 0.38

1.72 1.59 1.46 1.35 1.15

6.13 6.31 5.83 5.41 4.48

212 205 199 196 186

0.05 0.08 0.11 0.16 0.30

2.15 2.15 2.19 2.09 2.19

6.39 6.42 6.11 5.61 4.91

0.87 0.84 0.78 0.74 0.62

0.13 0.16 0.22 0.26 0.38

a

[Py]/CODU ) 4.00 µmol/g. Table 3. Results for Concentrated ODU Solutionsa

[Py]/Cpol, µmol/g

[Py], µM

Cpol, wt %

I1/I3

IE/IM

n

kq, µs-1

τ, ns

n (τ ) 233 ns)

kq, µs-1 (τ ) 233 ns)

2.00 2.00 2.00 2.00 0.43 0.43 0.43

0.67 1.13 1.89 2.87 0.15 0.18 0.71

3.4 5.7 9.4 14.3 3.6 4.1 16.4

1.07 1.06 1.15 1.10 1.05 1.09 1.11

0.46 0.55 0.29 0.47 0.21 0.21 0.15

1.06 1.31 1.21 1.39 0.60 0.56 0.71

6.44 6.43 4.99 5.18 7.02 7.41 6.81

233 212 220 227 229 225 209

1.06 1.61 1.42 1.47 0.64 0.65 1.08

6.44 4.9 4.15 4.81 6.12 5.86 3.48

a

3-17 wt %.

normal. The I1/I3 ratio in these solutions was close to 1.1, which is lower than that found in the 2.1 g/L solutions. This result is expected, because at high polymer concentrations the probe is almost completely localized in the polymer micelles. The fluorescence decays were fitted to the Poisson quenching model, and the results are listed in Table 3. There is a considerable scatter in the data. The n values tend to increase with the polymer concentration, whereas the kq values show the opposite trend: they decrease as the polymer concentration increases. The τ values show random scatter with polymer concentration. The n values for the solutions with the higher probe-topolymer ratio are higher. This is expected, as n is proportional to the probe concentration and is indeed a function of the probe-to-polymer ratio. In an attempt to decrease the scatter in the data, we refit the data assuming a constant and fixed value of τ ) 233 ns. This reanalysis of the data did not reduce the scatter; in contrast, the correlation between the parameters became clearer. We are obliged to consider that the increasing values of n with an increase in the polymer concentration mean an increase in the aggregation number. In this way, the behavior of the quenching constant kq can be rationalized: at a low polymer concentration, kq has higher values of about 6 µs-1. This value is close to that obtained for Cpol ) 2.1 g/L. When the ODU concentration increases, the kq values decrease. If we assume that the size of the micelles changes with polymer concentration, the trend in the kq values corroborates that assumption: in the smaller micelles, the kq values are higher, and in the larger micelles the kq values are smaller. In Figure 9, the data for high concentration solutions are plotted together with the data for the 2.1 g/L solution. We observe that some of the data points agree well with the data for the 2.1 g/L solution if the polymer concentration is not very high. For the highest polymer concentration used, 14 and 16 wt %, the n values are higher than the ones we obtain at lower polymer concentrations. The main conclusion is that the data for the ODU polymer closely resemble the data for the HDU polymer.17 The unusual behavior at high polymer concentrations is seen in both systems, which differ only in the size of the hydrophobe. At this stage, it is difficult to explain the behavior we observed at high polymer concentrations, particularly the variability in the n and kq values. We need further

Figure 9. Variation of the parameter n in ODU solution plotted against pyrene-to-polymer ratio. The lifetime τ ) 233 ns.

experiments and independent evidence to know whether we are observing a peculiarity of the fluorescence quenching experiment or a real change in the micellar structure. Our results are particularly interesting in light of scattering experiments by Franç ois et al.,12-14 that suggest an increase in the hydrophobic core size and in the mean aggregation number with increasing polymer concentration. Conclusions Fluorescent probe experiments were used to study aqueous solutions of the associative polymer ODU, a poly(ethylene oxide) of M ) 35 000 with C18H37 end groups. This polymer is monodisperse with a degree of end group substitution equal to unity. The hydrophobic end groups of these polymers associate in water to form micellelike structures that serve as solubilization sites for the pyrene molecules. The parameter of interest is NR, the mean number of end groups per micelle. ODU solutions undergo phase separation when Cpol is between 2.1 and 20 g/L. Using pyrene as a probe, the aggregation number in a 2.1 g/L solution was found to be 23. At low polymer concentrations, the probe is not completely solubilized by the polymer micelles. We studied this effect in low concentration ODU solutions and showed that the extended Poisson quenching model that accounts

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for the emission of the probe in the water phase provides a significant improvement to the standard Poisson quenching model. We found that aggregation numbers in ODU solutions are not constant with the polymer concentration. Although the data at high concentrations show some scatter, we

Vorobyova et al.

observe that the aggregation number tends to increase as polymer concentration increases. Acknowledgment. The authors thank NSERC Canada for the support of this research. LA0011026

Aggregation Number Determination in Aqueous Solutions of a

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