Pyrene Excimer Kinetics in Micellelike Aggregates in a C20-HASE

University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6 ... Union Carbide Corporation, UCAR Emulsion Systems, Research and ...
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Pyrene Excimer Kinetics in Micellelike Aggregates in a C20-HASE Associating Polymer† Elmo Araujo,‡ Yahya Rharbi, Xiaoyu Huang, and Mitchell A. Winnik* Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6

David R. Bassett Union Carbide Corporation, UCAR Emulsion Systems, Research and Development, 410 Gregson Drive, Cary, North Carolina 27511

Richard D. Jenkins Technical Center, Union Carbide Asia Pacific, Inc., 16 Science Park Drive, #04-01/02 The Pasteur, Singapore 118227 Received February 28, 2000. In Final Form: May 23, 2000 We have carried out time-resolved fluorescence quenching experiments, using pyrene derivatives as probes, on aqueous solutions of a hydrophobically modified alkali-soluble emulsion (HASE) polymer 1. This polymer is a 1:1 copolymer of ethyl acrylate and methacrylic acid, containing 1 mol % of a macromonomer with a C20H41 group at the end of an oligo(ethylene oxide) (EO32) spacer. The experiments we describe establish that the polymer 1 at full neutralization in water forms two different types of hydrophobic domains. When various pyrene derivatives are employed as probes, they partition between the two environments and exhibit different fluorescence decay times in the different types of domains. For experiments carried out at elevated probe concentration where excimer formation is important, proper analysis of the data is possible only if the solutions are deaerated. The data are fitted to a series of models invoking the presence of a single hydrophobic domain and two different hydrophobic domains. Only the latter model provides self-consistent results. From this model, we infer that the C20H41 groups form micelles with a mean aggregation number of 55 hydrophobes per micelle.

Introduction The method of choice for characterizing the aggregation number of surfactant micelles in aqueous solution involves fluorescence quenching measurements.1,2 In this approach, one adds a small amount of a fluorescent dye to the solution plus a quencher of its fluorescence. Both are chosen to have a very small but finite solubility in water. In this way, the dye and quencher distribute themselves among the micelles in solution. One measures the fluorescence decay profile of the fluorescent dye in the absence and in the presence of quencher and analyzes the shape of the decay profile in terms of a model that assumes a Poisson distribution of dye and quencher in the system. It is common practice to choose pyrene itself or simple pyrene derivatives as the fluorescent dye. At low pyrene concentrations, i.e., much less than one per micelle, the pyrene † Part of the Special Issue “Colloid Science Matured, Four Colloid Scientists Turn 60 at the Millennium”. This paper is dedicated to the 60th birthdays of Mats Almgren, Josef Holzwarth, Ray MacKay, and Evan Wyn-Jones, in honor of their many excellent scientific contributions to the field of colloid science. ‡ Permanent address: Universidade Federal de Pernambuco, Departamento de Energia Nuclear, Av. Prof. Luiz Freire, 1000, 50740-540 Recife/PE, Brazil.

(1) Zana, R. In Zana, R., Ed.; Surfactant Solutions: New Methods of Investigation; Surfactant Science Series 22; Marcel Dekker: New York, 1987; pp 242-294. (2) (a) Almgren, M. Adv. Colloid Interface Sci. 1992, 41, 9-32. (b) Almgren, M. In Gra¨tzel, M., Kalayanasundaram, K., Eds.; Kinetics and Catalysis in Microheterogeneous Systems; Surfactant Science Series 38; Marcel Dekker: New York, 1991; pp 63-113. (c) Zana, R.; Lang, J. Colloids Surf. 1990, 48, 153-171. (d) Gehlen, M. H.; De Schryver, F. C. Chem. Rev. 1993, 93, 199-221.

decay is exponential, with an “unquenched” lifetime τ0. Under these circumstances, one can add a second species (e.g., dimethylbenzophenone) to the system as a quencher or simply increase the pyrene concentration. At higher pyrene concentrations, the excited pyrene Py* can interact with a ground-state pyrene Py to form an excimer [(Py‚ Py)*]. In this process the pyrene serves both as the fluorophore and the quencher. When pyrene excimer formation is used as the quenching process, data analysis requires the additional assumption that excimer dissociation back to Py* + Py makes a negligible contribution to the fluorescence decay kinetics, a reasonable assumption for most micelles at ordinary temperatures. For both types of experiments, one has to be certain that a negligible fraction of the fluorophore or quencher is in the water phase. When the appropriate assumptions are met, the probe fluorescence decay profile ID(t) should fit the expression derived for Poisson quenching statistics.3

ID(t) ) ID(0) exp[-t/τ0 - n(1 - exp(-kqt))]

(1)

Here ID(0) is the fluorescence intensity at t ) 0 and kq is the pseudo-first-order rate constant for quenching in the micelle. When eq 1 is applied to studies of traditional surfactant micelles, the mean number of quenchers per micelle, n (n ) [Q]/[micelle]), can be related to the aggregation number Nagg through the micelle and quencher concentrations1-3

Nagg ) ([S] - cmc)/[micelle] ) n ([S] - cmc)/[Q] (2)

10.1021/la000280w CCC: $19.00 © 2000 American Chemical Society Published on Web 08/09/2000

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where [Q] is the bulk molar quencher concentration, [S] is the total molar concentration of surfactant, and cmc is the critical micelle concentration. Water-soluble polymers with hydrophobic end groups or pendant groups self-associate in water.4 Association occurs through interaction of the hydrophobic substituents to form micellelike structures.5 It would seem natural to try to characterize the size and nature of these aggregates with fluorescence quenching experiments. Under these circumstances, the parameter of interest is NR, the mean number of hydrophobic substituents per micellelike aggregate. In solutions of associating polymers, one expects the probe fluorescence decay profile to fit eq 1, and 〈n〉 maintains its meaning as the mean number of quenchers per micelle. For associative polymers, we prefer to insist upon the angle brackets in 〈n〉 to emphasize that this fitting parameter refers to an average value.

〈n〉 ) [Q]/[micelle] ) [Q]NR/(CpolqR)

(3)

In eq 3, 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. NR values for associative polymers are calculated from the micelle concentration:6,7

NR ) CpolqR/[micelle] ) 〈n〉CpolqR/[Q]

end of an oligo(ethylene oxide) chain with a mean length of 32 units (EO32). This and a number of similar polymers were prepared by Jenkins at Union Carbide,10 and these HASE associating polymers are currently under study by a number of research groups around the world.11,12

(4)

In some cases, particularly poly(ethylene oxide) (PEO) derivatives with long-chain alkyl end groups, this type of analysis has been successful. Even in this relatively simple set of polymers, one can still point to complications or ambiguities in the data.8 While one can calculate from the data the number NR of hydrophobic groups that come together to form the micellelike aggregate, the results are only rarely as clear as they are in the determination of the mean aggregation number Nagg of simple surfactants in aqueous solution. A recent review9 summarizes the complexities found when one attempts to study associating polymers in water with time-resolved fluorescence quenching (TRFQ) measurements. A case in point concerns the hydrophobically modified alkali-soluble emulsion (HASE) polymer 1, whose structure is given below. This model polymer, prepared by emulsion polymerization at low pH, is a 1:1 copolymer of ethyl acrylate and methacrylic acid and contains 1 mol % of a co-macromonomer containing a C20H41-group at the (3) (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. K.; Thomas. J. Phys. Chem. 1974, 78, 190-195. (4) (a) Water-Soluble Polymers: Beauty with Performance; Glass, J. E., Ed.; Advances in Chemistry 213; American Chemical Society: Washington, D.C., 1986. (b) Polymers in Aqueous Media: Performance through Association; Glass, J. E., Ed.; Advances in Chemistry 223; American Chemical Society: Washington, D.C., 1989. (c) Hydrophilic Polymers; Glass, J. E., Ed.; Advances in Chemistry 248; American Chemical Society: Washington, D.C., 1996. (d) Macromolecular Complexes in Chemistry in Biology; Dubin P., Bock J., Davis R., Schulz, D. N., Thies, C., Eds.; Springer-Verlag: Berlin, 1994. (5) Winnik M. A.; Yekta, A. Curr. Opin. Colloid Interface Sci. 1997, 2, 424-436. (6) Yekta, A.; Xu, B.; Duhamel, J.; Adiwidjaja, H.; Winnik, M. A. Macromolecules 1995, 28, 956-966. (7) Vorobyova, O.; Yekta, A.; Winnik, M. A.; Lau, W. Macromolecules 1998, 31, 8998-9007. (8) Alami, E.; Almgren, M.; Brown, W.; Franc¸ ois, J. Macromolecules 1996, 29, 2229-2243. (9) Vorobyova, O.; Winnik, M. A. In Associative Polymers in Aqueous Media; Glass, J. E., Ed.; ACS Books: Washington, D.C., 2000.

About a year ago, we reported13 detailed TRFQ studies of this polymer using pyrene and 1-ethylpyrene (EtPy) as probes. The polymers, dispersed in water with a particle radius of 75 nm, were neutralized with 1.0 equiv of sodium hydroxide to give solutions whose viscosity depended sensitively on the polymer concentration. We showed that one had to take care to examine the system under conditions where a negligible fraction of the probe was in the water phase. Under these circumstances, individual fluorescence decay curves fit well to eq 1. Treating τ0 as a fitting parameter gave values independent of probe or polymer concentration, for both pyrene and (EtPy) as probes. The most precise way to obtain NR values for associating polymers is to plot n vs [Q]/Cpol (eq 3). This plot should give a straight line passing through the origin, and one can calculate NR from the slope. Unfortunately, the plots obtained for both probes for the polymer 1 were curved and intersected the y-axis at values of n > 0.5. In addition, the kq values varied with [Q]/Cpol. The behavior reported above is clear evidence that the model described in eqs 1-4 does not properly describe the system consisting of either probe solubilized by fully neutralized solutions of 1 in water. In this paper, we look more deeply at the kinetics of excimer formation solutions of 1 at full neutralization. We examine a new probe, 1-(1′pyrenyl)-octanol, and a new method of sample preparation. Experimental Section Materials. The HASE polymer studied in this work, denoted C20EO32, is a copolymer of methacrylic acid (MAA), ethyl acrylate (EA), and C20H41O end-capped macromonomer with molar ratios x:y:z of 49.06:50.04:0.90. A full description of the synthesis and (10) Jenkins, R. D.; Delong, L. M.; Bassett, D. R. In Hydrophobic Polymers; Glass, J. E., Ed.; American Chemical Society: Washington, D.C., 1996; p 425. (11) English, R. J.; Gulati, H. S.; Jenkins, R. D.; Khan, S. A. J. Rheol. 1996, 41, 427. (12) (a) Kumacheva, E.; Rharbi, Y.; Winnik, M. A.; Guo, L.; Tam, K. C.; Jenkins, R. D. Langmuir, 1997, 13, 182. (b) Horiuchi, K.; Rharbi, Y.; Yekta, Y.; Winnik, M. A..; Jenkins, R. D.; Bassett, D. R. Can. J. Chem. 1998, 76, 1779. (c) Tirtaatmadja, V.; Tam, K. C.; Jenkins, R. D. Macromolecules 1997, 30, 1426. (d) Tirtaatmadja, V.; Tam, K. C.; Jenkins, R. D. Macromolecules 1997, 30, 3271. (e) Guo, L.; Tam, K. C.; Jenkins, R. D. Macromol. Chem. Phys. 1998, 199, 1175. (f) Ng, W. K.; Tam, K. C.; Jenkins, R. D. Eur. Polym. J. 1999, 35, 1245. (g) Tirtaatmadja, V.; Tam, K. C.; Jenkins, R. D. AIChE J. 1998, 44, 2756. (13) Horiuchi, K.; Rharbi, Y.; Spiro, J.; Yekta, A.; Winnik, M. A.; Jenkins, R. D.; Bassett, D. R. Langmuir 1999, 15, 1644-1650.

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characterization of this system has been reported by R.D.J.11 In short, a macromonomer was prepared first by ethoxylation to 32 mol of the C20 alcohol, followed by reaction with R,R-dimethyl m-isopropyl benyzlisocyanate. Afterward, this macromonomer was introduced into a conventionally seeded semicontinuous emulsion polymerization under monomer/starved conditions with appropriate amounts of MAA and EA. According to the structure and composition of the polymer, it contains 2.12 × 10-2 g C20H41 groups/g polymer (7.53 × 10-5 mol/g polymer). This and similar polymers in this series were recently characterized by Ou-Yang and co-workers14 using light scattering in the presence of R-cyclodextrin to remove hydrophobic association. The Mw values of the nonassociated polymers were found to be in the range of 200000-250000. 1-Ethylpyrene (EtPy) was purchased from Molecular Probes (Eugene, OR) and used without further purification. The details of the synthesis and characterization of the other probes will be reported elsewhere.15 In brief, 1-octylpyrene (C8Py) and 1-(1′pyrenyl)-octanol (PyC8OH) were synthesized by the reaction of pyrene with octanoyl chloride in the presence of aluminum chloride to yield 1-(1′-pyrenyl)-2-octanone. Reduction with sodium borohydride produced PyC8OH, whereas Wolff-Kishner reduction16 yielded C8Py. 1-Dodecylpyrene was prepared in the same way as 1-octylpyrene using dodecanoyl chloride in the acylation step. NaOH (Aldrich) and NaCl (Aldrich) were used as received. Distilled water was further purified through a MilliQ (Millipore) purification system. Sample Preparation. The latex emulsion (5 wt %) was dialyzed against 3.0 L of deionized water for more than 2 weeks with a cellulose membrane, formulated to cutoff from Mw 12 000 to 14 000 (Fisher Scientific). For further purification, the dialyzed HASE solution was mixed with ca. 30 wt % of a mixture of anionic and cationic resins (Bio-Rad AG-501X8, 20-50 mesh) under stirring for 2 h. The cleaned HASE solution was freeze-dried in Dura-Dry equipment (FTS System Inc.) for 48 h resulting in a HASE powder. For fluorophore solubilization into the HASE sample, a known amount of a solution of dichloromethane containing 0.005 mol/L of probe was deposited on the bottom of a rotary evaporator flask and the solvent was evaporated under a gentle flow of nitrogen. Afterward, some of the HASE powder (25 mg) was added in the same flask in addition to 2 mL of tetrahydrofuran (THF) to promote the dilution of the probe-HASE system. After a few minutes of agitation by a mechanical shaker, complete dissolution of the polymer occurred, and the THF was removed with a rotary evaporator over 1 h (23 °C, 10-15 Torr). A sample of this mixture was then added to NaOH solution in order to produce an aqueous polymeric solution with a concentration ranging from 1 to 8 g/L. The amount of NaOH was chosen to be equal to the number of moles of -COOH groups in the HASE sample, i.e., to yield complete neutralization of -COOH groups in the polymer (R ) 1). To control the ionic strength, salt was added to a concentration of 1.0 mM NaCl. This solution, in a closed small flask, was stirred overnight at room temperature in the dark, to ensure complete polymer dissolution. Afterward, the solution was centrifuged (15 000 rpm, 60 min) in order to remove any excess probe, resulting in a clear solution. The probe-free aqueous HASE solutions were also prepared from the powder in the same manner as described above. UV Absorbance Measurements. The probe concentrations were monitored by UV for solutions in 10 mm quartz cuvettes, using a Perkin-Elmer Lambda 6 dual-beam spectrometer. The concentration was monitored at the strongest absorption peak, 346 nm for EtPy or 344 nm for Py(C8)OH, with a correction for the background absorption (turbidity) of the polymer, taking a probe-free polymer solution with the same polymer concentration as a reference. The concentrations of the micellized probes were calculated from the absorption readings using the following values of the extinction coefficients : EtPy (3.45 × 104 M-1 cm-1, 346 nm) and Py(C8)OH (4.03 × 104 M-1 cm-1, 344 nm). (14) Islam, M. F.; Jenkins, R. D.; Ou-Yang, H. D.; Bassett, D. R. Submitted for publication. (15) Huang, X.; Winnik, M. A. To be submitted for publication. (16) March, J. Advanced Organic Chemistry, 3rd ed.; Wiley: New York, 1985; p 1096.

Araujo et al. Static Fluorescence Measurements. A SPEX Fluorolog 2 Spectrometer with double-grating monochromators was used to determine steady-state fluorescence spectra in a right-angle geometry. Resolution was set at 0.5 nm and integration time at 1 s. The excitation wavelength was 346 nm for EtPy and 344 nm for Py(C8)OH. Dynamic Fluorescence Measurements. Fluorescence decay profiles were measured using the single-photon-timing technique. The wavelengths of the excitation and emission monochromators were fixed, respectively, at 344 and 375 nm for all probes. A long-pass filter was used to prevent scattered excitation light from reaching the detector. To monitor the instrument response function, a solution of p-bis(5-phenyloxazol2-yl)benzene (POPOP) in degassed cyclohexane was used as the reference compound. In these experiments a saturated polymer solution of probe was diluted with a probe-free solution of the same polymer concentration. The lowest probe concentration, corresponding to a dilution ratio of more than 200 times, was used to determine the unquenched lifetime (τ0) under different atmospheres (N2, air, O2). Experiments at higher probe concentrations were carried out under a N2 atmosphere. The solutions were allowed to equilibrate in the different atmospheres for 30 min under agitation prior to each measurement. The quality of fit was judged on the basis of the magnitude of χ2 (χ2 < 1.1), the randomness of the weighted residuals, and the autocorrelation of the residuals. A detailed discussion of the quality of fit and an examination of possible parameter correlation in the fits for this system is described in ref 13. The fluorescence decay from the probe-free sample was used to estimate the contribution of polymer background fluorescence to the signal measured for each probe-containing solution. The measurements were carried out in a 1 cm square cell for a period of time ranging from 60 to 200 min. The decay of each sample was divided by the measurement time. For each decay curve, prior to analysis, we carried out point-by-point subtraction of the time-normalized decay curve of the probe-free sample.

Results and Discussion Preparing Probe-Polymer Solutions. In the fluorescence probe experiments we reported previously for polymer 1, the polymer latex was neutralized with 1 equiv of sodium hydroxide in the presence of 1 mM NaCl. This solution was then exposed to probe crystals, pyrene or EtPy, suspended in water, and the system was allowed to reach “equilibrium”. For low polymer concentrations, the solutions were fluid enough that they could be centrifuged to remove probe crystals still present in the solution. In this way, one could estimate the amount of probe that would “saturate” the polymer. At higher polymer concentrations, the amount of probe added was less than this saturation amount. Here we employ three probes, 1-ethylpyrene (EtPy), 1-dodecylpyrene (C12Py), and 1-(1′-pyrenyl)-octanol (Py C8OH), which have very low solubilities in water. The probe-containing-polymer solutions were prepared by an intermediate step, which involved dissolution of the freezedried polymer plus probe in an organic solvent, tetrahydrofuran (THF). This solution was evaporated while coating it onto the wall of a round-bottom flask. The dry film was then dissolved in water containing 1.0 mM NaCl plus 1 equiv of NaOH. We define R ) (moles of NaOH added)/(moles of -COOH in the sample). Thus complete neutralization of the polymer corresponds to R ) 1.0. For polymer concentrations up to 8 g/L, it was possible to centrifuge the solutions to remove probe that was not solubilized when the polymer was treated with aqueous base. A plot of the amount of probe remaining in solution as a function of polymer concentration is presented in Figure 1. These saturation concentrations were calculated using extinction coefficients at λmax (346(EtPy) ) 3.45 × 104 M-1 cm-1; 344(Py(C8)OH) ) 4.03 × 104 M-1 cm-1) for

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Figure 1. Probe solubility at saturation in the HASE polymer 1 in water at R ) 1.0, as determined by UV absorption measurements on samples in which the probe was codissolved with the polymer in an organic solvent, taken to dryness, redispersed in water, and then centrifuged to remove excess probe.

the micellized probe determined at subsaturation amounts of probe at Cpol ) 8 g/L. From the data in Figure 1, we find that at saturation, there is a slightly larger amount of EtPy solubilized than Py(C8)OH. We calculate ratios of C20H41/EtPy ) 7.4 and C20H41/Py(C8)OH ) 10. From these values we can see that by introducing the probe in this way we solubilize more probe than by the previous method. In those experiments, we appeared to obtain saturation at a ratio of C20H41/EtPy ) 30. Fluorescence spectra for the solutions shown in Figure 1, saturated in solubilized probe, are shown in Figure 2. The spectra are normalized at the (0,0) band of the pyrene monomer emission, and the monomer emission has a similar shape for both probes. The major difference between the probes is the smaller extent of excimer emission for Py(C8)OH shown in Figure 2b. Decay Profiles at Low Probe Concentration. In Figure 3, we show the fluorescence decay profiles measured for ca. 0.5 µM EtPy in 4 g/L polymer solution. These solutions exhibit no detectable excimer emission. One sees that under nitrogen, in the presence of air, and in solutions saturated with oxygen, the decay profiles are not exponential. One reason for this shape is that the HASE solution itself is characterized by a weak fluorescence with a short-lived component. By carefully matching the measurement times of the various samples, the weak impurity fluorescence from the HASE solution lacking the probe can be subtracted from the emission of the other solutions. These corrected decay profiles are not exponential but can be fitted to a sum of two exponential terms.

ID(t) ) Ashort exp(- t/τ0short) + Along exp (- t/τ0long) (5) Our first major insight into the nature of the hydrophobic domains in solutions of polymer 1 is that for all three probes, we obtain linear plots of 1/τ vs external oxygen partial pressure pO2 for both the short and long components of the decay. These plots are shown in Figure 4.

1 1 ) + ki,O2 Si,O2pO2 (i ) short, long) 0 τ τi i

(6)

The implication of the linear plots is that there are two

Figure 2. Fluorescence spectra of (a) 1-ethylpyrene (EtPy) and (b) 1-(1′-pyrenyl)octanol (Py(C8)OH) at saturation in the HASE polymer 1 in water at R ) 1.0. The spectra correspond to solutions with the polymer concentrations shown in Figure 1.

Figure 3. Fluorescence decay profiles of a low concentration solution of EtPy (ca. 0.5 µM) in a 4 g/L solution of the HASE polymer 1 in water at R ) 1.0. Top curve (N2), degassed with nitrogen; second curve (air), aerated; third curve (O2), equilibrated with oxygen gas. Bottom curve, a probe-free HASE solution, 4 g/L, degassed with nitrogen. The sharply decaying peak at the left (lamp profile) is the profile of the excitation source.

distinct probe environments in the polymer solution. One is characterized by a relatively long probe lifetime (τ0long), and the other, by a shorter probe lifetime (τ0short). When the solutions are exposed to oxygen, oxygen partitions into both environments. In eq 6, ki,O2 is the pseudo-firstorder rate constant for quenching by oxygen in each environment (i ) short, long), and Si,O2 is the proportionality constant between external oxygen partial pressure and local oxygen concentration in each environment.

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Figure 4. Stern-Volmer plots (1/τ vs external partial pressure of oxygen, pO2) for quenching by oxygen for the fluorescence decay of three different pyrene probes solubilized in the HASE polymer 1 in water at 4 g/L and R ) 1.0: (a) EtPy; (b) Py(C8)OH; (c) 1-dodecylpyrene (PyC12). The two lifetimes (τlong and τshort) were calculated from fits to the decay curves after correction for the contribution to the signal of emission from the polymer itself.

Decay Profiles at Higher Probe Concentration. In Figures 5 we show pyrene monomer decay profiles for three different probe concentrations in water containing 1 at 4 g/L and R ) 1. The data for EtPy are in Figure 5a, whereas the data for Py(C8)OH are presented in Figure 5b. For similar concentrations of probe, the decays are more rapid and there is a greater extent of fluorescence quenching in the solutions containing EtPy. For these degassed solutions and elevated probe concentrations, background fluorescence from the polymer itself makes a negligible contribution to the measured intensity. One-Domain Model: One Micelle Environment. As a point of departure, we analyze the decay profiles with eq 1, fitting all four parameters: I(0), n, kq, and τ. This approach is similar to what we reported in our previous publication. What is different here, for the case of EtPy, is that the solutions are deaerated, and we used a different method of sample preparation. The dependence of the fitting parameters on [EtPy]/Cpoly is shown in Figure 6. As in our previous set of results, the fitted lifetime is independent of probe and polymer concentration. Unlike our previous results, however, the kq values are also independent of the [EtPy]/Cpoly ratio. In addition, 〈n〉 depends linearly upon the [EtPy]/Cpoly ratio, and from the slope, we calculate a value of NR ) 53. When this type of data analysis is carried out on the data from the experiments, which employ Py(C8)OH, we obtain similar plots, Figure 7. The fitted lifetime of the probe is longer (203 ns) than that fitted for EtPy (170 ns), but the value of NR

Araujo et al.

Figure 5. Fluorescence decay profiles for two different pyrene probes at the concentrations indicated on the plots for probes solubilized in the HASE polymer1 in water at 4 g/L and R ) 1.0: (a) EtPy; (b) Py(C8)OH.

calculated from the slope of the 〈n〉 vs [EtPy]/Cpoly plot is similar, 57. Two features of this data analysis remain troubling. First, the data are interpreted in the context of a model that presumes a single type of hydrophobic environment, whereas the data in the previous section were interpreted to mean that there are two types of different hydrophobic environments in the solution. Second, the plots of 〈n〉 vs [probe]/Cpoly, while straight, have substantial intercepts on the y-axis. Two-Domain Models. If the polymer solution contains two types of hydrophobic domains, both of which solubilize pyrene derivatives, then the fluorescence decay curves should properly be described by eq 7 with two independent Poisson quenching terms. Equation 7 has seven parameters, the fraction of probe in each environment (Al, As ) 1 - Al), the unquenched lifetime in each domain (τ0long, τ0short), the [Py]/[micelle] ratio in each domain (〈n〉l, 〈n〉s), and the two quenching rate constants (kq,l, kq,s) for the two domains. Even though, in terms of this model, the fraction of probe in each environment can be inferred from the experiments at low probe concentration, and the two unquenched lifetimes are known independently, there are still too many fitting parameters to obtain a unique fit to the data. We must simplify this type of model to reduce the number of fitting parameters, and at the same time maintain the essential physics of the quenching process.

IM(t) ) Al exp[-t/τ0long - 〈n〉l(1 - exp(-kq,lt))] + As exp[- t/τ0short - 〈n〉s (1 - exp(-kq,st))] (7)

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Figure 8. Plot of the fitting parameters kq and 〈n〉 vs probe concentration for solutions of Py(C8)OH in polymer 1 in terms of the two-domain model, in which the probe lifetime in both the “short-lifetime” and “long-lifetime” domains are fixed. To fit the decay curves, we set τshort ) 92 ns and τ0long ) 217 ns, and Al ) 49%, As ) 51%.

Figure 6. Plot of the fitting parameters for the one-domain model, as a function of the ratio of the probe concentration [EtPy] to the polymer concentration, for solutions of the probe solubilized in the HASE polymer 1 in water at 4 g/L and R ) 1.0. The decay curves, corrected for background emission from the polymer, were fitted to eq 1.

Figure 7. Plot of the fitting parameters for the one-domain model, as a function of the ratio of the probe concentration [Py(C8)OH] to the polymer concentration, for solutions of the probe solubilized in the HASE polymer 1 in water at 4 g/L and R ) 1.0. The decay curves, corrected for background emission from the polymer, were fitted to eq 1.

IM(t) ) A1 exp[-t/τ0long- 〈n〉(1 - exp(-kqt))] + As exp(- t/τ0short) (8) Model 2H1Q: Two Hydrophobic Environments, One without Quenching. We first consider a two-domain model in which we set kq,s ) 0 in eq 7. Thus the additional term

reduces to a second exponential with lifetime τ0short, as shown in eq 8. This model is based upon the (incorrect) idea that the fraction of the probe confined to “shortlifetime” domain is so much less susceptible to quenching that we can treat the probe lifetime in this domain as constant. This model is physically unrealistic but pedagogically useful. By examining the way in which the software forces the data to fit this model, we develop a strategy for constructing a more realistic model. An example is shown in Figure 8 for Py(C8)OH in the HASE polymer at a concentration of 4 g/L. To fit the data to eq 8, we set τ0short ) 92 ns and τ0long ) 217 ns, and Al ) 49%, As ) 51%. There are two fitting parameters, kq and 〈n〉 . Each individual fit to the monomer decay curve IM(t) was reasonable. The interesting feature of the data analysis is that 〈n〉 is proportional to [Py(C8)OH]/Cpoly, and the intercept on the y-axis is much reduced. We infer from this behavior that the much larger intercept seen in Figure 4 is a result of the software treating a short-lived component of the decay at low [Py] as quenching within a micelle. It is curious that the magnitude of NR calculated from the slope of the plot in Figure 8 is 57, very similar to that obtained from the one-domain model. On the other hand, fitting data to eq 8 gives values of kq that are no longer constant. If we arbitrarily vary the fixed value of τ0short and reanalyze the data, we find similar results: 〈n〉 remains proportional to [Py(C8)OH]/Cpoly, NR remains close to 55, and the fitted value of kq varies. We find, however, that the fitted value of kq is strongly correlated to the assumed value of τshort. Model 2H2Q: Two Hydrophobic Environments, Variable τshort. We next relax the constraint that τshort remains constant. To minimize the number of fitting parameters in the analysis of each decay curve, we proceed as follows: for each decay curve, τshort is fixed sequentially to a series of different values ranging from 52 to 92 ns. Values of 〈n〉 and kq are obtained for each fit. The data in Figure 9 suggest that allowing τshort to vary has little influence on the “best fit” value of 〈n〉. In the previous analysis, we saw that values of τshort and kq appear to be correlated. We examine their interdependence in Figure 10: There is a range of τshort values (here up to 70 ns) for which kq is relatively constant, and for higher values of τshort, there is a strong variation in the kq values obtained. The message we take from this analysis is that there is a range of τshort values over which kq depends very weakly upon τshort. In

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Figure 9. Plot of the fitting parameter 〈n〉 vs the concentration of the probe Py(C8)OH for a series of solutions of 1 at 4 g/L. For each concentration of Py(C8)OH, each decay curve was fitted to eq 8 with eight different fixed values of τshort ranging from 55 to 92 ns. The parameters τ0long ) 217 ns, Al ) 49%, As ) 51% were fixed in each analysis. Only 〈n〉 and kq were allowed to vary. The error bars represent the extreme values of 〈n〉 for the different fits.

Araujo et al.

Figure 11. For the same solution described in Figure 10, a plot of 〈n〉 and the goodness-of-fit parameter χ2 vs the value of τshort employed in fitting the decay curve. In this analysis, the following parameters were fixed: kq ) 5 µs-1, τ0long ) 217 ns, and Al ) 49%, As ) 51%.

Figure 12. Plot 〈n〉 vs the concentration of the probe Py(C8)OH for a series of solutions of 1 at 4 g/L. In fitting the data, τ0long ) 217 ns, and Al ) 49%, As ) 51% were fixed. Values of 〈n〉 were obtained as shown in Figure 11 with the τshort values at the minimum of the τshort vs χ2 plots. Figure 10. Plot of the fitting parameter kq vs the preset value of τshort employed in fitting the decay curve for Py(C8)OH (5.38 mM in HASE polymer 1 at 4.0 g/L) to eq 8. To fit the IM(t) decay curve, we set τ0long ) 217 ns, and Al ) 49%, As ) 51%, and fixed τ0short to each of the values plotted on the x-axis.

our search for a global minimum in the data analysis, we can then fix the value of kq while we optimize values of 〈n〉. We now examine the results of this analysis for a solution containing 5.38 µM Py(C8)OH and 4 g/L 1. The measured monomer fluorescence decay profile is analyzed by fitting it repeatedly with 〈n〉 as the only fitting parameter. In these analyses, values of four of the parameters in eq 8 (kq ) 5 × 106 s-1, τ0long ) 217 ns, and Al ) 49%, As ) 51%) were fixed over the entire analysis, and a series of different values of τshort, ranging from 35 to 70 ns, were fixed in each individual analysis. For each assumed value of τshort, we plot the fitted value of 〈n〉 and the χ2 of the fit in Figure 11. We see that 〈n〉 is not very sensitive to the assumed value of τshort, and that there is a pronounced minimum in χ2 at τshort ) 55 ns. We now repeat this procedure for each of the four different concentrations of probe, obtaining for each the value of τshort for which χ2is a minimum. From the analysis described above, we have learned that in terms of the model described by eq 8, values of τshort decrease with increasing probe concentration. We

now return to the measured decay curves and refit each decay curve with eq 8. In this analysis, we seek two fitting parameters, 〈n〉 and kq; we fix the values of τ0long ) 217 ns, and Al ) 49%, As ) 51%, and use the optimized value of τshort obtained for each concentration of Py(C8)OH. We plot the corresponding 〈n〉 values against [Py(C8)OH]/ Cpoly in Figure 12. There is now a remarkable improvement in the behavior of the data. The data fit a straight line that passes through the origin. These micelles have a mean hydrophobe aggregation number NR ) 55. Equally interesting is that the kq values are constant for each probe concentration, with a value of 5 × 106 s-1. If the data analysis strategy described above is appropriate, the changes in τshort should reflect quenching associated with the probability of finding multiple probes in the short-lifetime domain. If the extent of quenching is modest, we may anticipate that within these domains, quenching can be described by Stern-Volmer kinetics.

1 1 ) τshort τ0

+ kq,s[Py]s

(9)

short

This expectation is indeed fulfilled, as shown in Figure 13. The plot of (1/τshort) is linear, and the intercept has a value close to that measured at low probe concentration. The slope of this line is the product of the second-order rate constant kq,s for quenching (excimer formation) in

Pyrene Excimer Kinetics of a HASE Polymer

Figure 13. Plot of 1/τshort vs [Py(C8)OH] for the τshort values obtained at the minimum of the τshort vs χ2 plots.

the hydrophobic domain responsible for the short-lived pyrene decay. It would be very interesting if one could estimate a magnitude for kq,s. One could the use the magnitude of the slope of the plot in Figure 13 to estimate the volume in the solution that contains the 51% of the pyrene probe molecules in the short-lifetime environment. In a recent paper, Dai et al.17 report the results of dynamic light scattering experiments on a polymer analogous to 1 containing a C16H33 group attached to the end of the oligo(ethylene oxide) (here EO35) spacer chains. These authors find that the fully neutralized polymers in dilute aqueous solution (e.g., 0.05 g/L) are characterized by a fast- and a slow-moving component. The fast component is assigned to the unimer, with intrapolymeric association, and the slow component is assigned to an aggregate containing five macromolecules. A polymer of Mn ≈ 200 000 would have on the order of 20 hydrophobic groups. In dilute solution, the unimer could not form micelles with 55 hydrophobes per micelle. Our experiments with the polymer 1, which has C20H41 groups attached to the end of the oligo(ethylene oxide) (here EO32) spacer chains, were carried out at a higher polymer concentration (e.g., 4 g/L), conditions that Dai et al. show are dominated by polymer aggregates for their polymer. Even though the two polymers differ in the length of their hydrophobic substituents, the results are not inconsistent. Aggregates containing ca. 5 polymer molecules could form two micelles with an aggregation number of 55 hydrophobes per micelle. More recently, Dai et al.18 carried out similar studies of a methacrylic acid/ethyl acetate copolymer with the same MAA/EA composition as the HASE polymers described above. Here too, at full neutralization (R ) 1), aqueous solutions of the polymer exhibit fast and slow modes in dynamic light scattering experiments. In contrast, only a single diffusive mode is found in solutions of the polymer in tetrahydrofuran. These experiments establish the fact that even without the hydrocarbon substituent, the polymers have a tendency to associate in dilute aqueous solution. The authors suggest that during the synthesis of the polymer by emulsion polymerization at low pH, blocky EA sequences form. They suggest that these sequences form the hydrophobic domains that promote polymer association in water. From our perspective, we believe that these experiments provide independent evidence for the existence of a second type of hydrophobic domain in the HASE polymers. (17) Dai, S.; Tam, K. C.; Jenkins, R. D. Macromolecules 2000, 33, 404. (18) Dai, S.; Tam, K. C.; Jenkins, R. D. Eur. Polym. J., in press.

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Nature of the Hydrophobic Domains. In the discussion above, we imply but do not explicitly state that the hydrophobic domains in which the pyrene derivatives have the longer decay time are micellelike structures consisting of the C20H41 hydrocarbon chains. If this is the case, then the second hydrophobic domain is formed by ethyl acrylate groups from the polymer backbone as suggested by Dai et al.17,18 There is good evidence that domains formed by these groups will solubilize pyrene and its derivatives. Several years ago12b we reported that pyrene itself was easily solubilized into latex particles of the HASE polymer 1 at low pH. Under these conditions, the latex polymer is insoluble in water. It becomes soluble in water only after more than 60-70% of the methacrylic acid groups are neutralized. The particles at low pH were able to solubilize much more pyrene than the fully neutralized polymer at R ) 1.0. We inferred that the pyrene was solubilized by the latex polymer itself. As the latex polymer is neutralized with base, the pyrene becomes concentrated in domains containing the C20H41 alkyl chains. We also found that the mean decay time of pyrene in the latex polymer at low pH is shorter than that of pyrene after neutralization of the methacrylic acid groups. These results all support the idea that the domains characterized by τlong are micellelike domains formed from the C20H41 alkyl chains, and the domains characterized by τshort are formed primarily from ethyl-acetate-rich regions of the polymer. We have no evidence, however, to establish that the short-lifetime domains are free of C20H41 chains. When we deduce an aggregation number value of 55 for the longlifetime domain, we compare n-values from our fluorescence decay analysis with the known concentration of C20H41 alkyl chains in the solution. If a fraction of these chains is associated with the short-lifetime environment, then the mean NR value of the long-lifetime domains will be correspondingly smaller. Conclusions We have established that the HASE polymer 1 at full neutralization in water forms two different types of hydrophobic domains. When various pyrene derivatives are employed as probes, they partition between the two environments and exhibit different fluorescence decay times in the different types of domains. For experiments carried out at elevated probe concentration where excimer formation is important, proper analysis of the data is possible only if the solutions are deaerated. We are able to attribute the long-decay-time environment with micellelike structures formed by the C20H41substituents of the polymer. These micelles have a mean hydrophobe aggregation number NR ) 55 and a pseudofirst-order quenching rate constant of 5 × 106 s-1. The number 55 presumes that all of the C20H41 alkyl chains are associated with the long-decay-time environment. If some of these chains are associated with the short-decaytime environment, then NR will be correspondingly smaller than 55. In the short-lifetime environment, the pyrene decay time decreases with increasing probe concentration, and the changes follow the Stern-Volmer equation. Attributing a structure to the short lifetime hydrophobic domains is difficult. We speculate that these domains are made up of ethyl-acrylate-rich sequences along the polymer backbone. Acknowledgment. The authors thank NSERC Canada for their support of this research. E.S.A. thanks the Brazilian Government for a fellowship that helped to support his stay in Toronto. LA000280W