Probing the Hydrophobic Interactions of a Series of Pyrene End

Article pubs.acs.org/Langmuir

Probing the Hydrophobic Interactions of a Series of Pyrene EndLabeled Poly(ethylene oxide)s in Aqueous Solution Using TimeResolved Fluorescence Shaohua Chen† and Jean Duhamel* Institute for Polymer Research, Waterloo Institute for Nanotechnology, Department of Chemistry, University of Waterloo, Waterloo, ON N2L 3G1, Canada S Supporting Information *

ABSTRACT: The hydrophobic association of a series of poly(ethylene oxide)s covalently labeled at both ends with pyrene (PEO(X)-Py2 where X represents the number average molecular weight (Mn) of the PEO chains equal to 2, 5, 10, and 16.5 kDa) in aqueous solutions was investigated at different polymer concentrations (CP) using steady-state and time-resolved fluorescence measurements. Phase separation was observed with PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2 samples at high CP. The steady-state fluorescence spectra showed that the ratios of excimer-to-monomer fluorescence intensities (IE/IM) of all PEO samples remained constant when CP was below 4 × 10−5 M and decreased dramatically with increasing PEO chain length due to a decrease in intramolecular pyrene excimer formation. The IE/IM ratio in this regime was found to scale as Mn−2.3±0.2. For CP > 4 × 10−5 M, pyrene excimer is formed by both intra- and intermolecular interactions and the IE/IM ratio increases linearly with increasing CP except for PEO(2 kDa)-Py2 which undergoes phase separation. The decays obtained at various polymer concentrations were fitted according to a “sequential model” (SM) which assumes that the pyrene excimer is formed in a sequential manner. The molar fractions of all excited pyrene species and the rate constants for pyrene excimer formation were determined from the global analysis of the monomer and excimer fluorescence decays. The fraction of pyrenes that formed excimer from ground-state pyrene aggregates ( f E0) was found to increase with CP in the regime where the pyrene excimer is formed both intra- and intermolecularly and decrease with Mn in the regime where the pyrene excimer is formed only intramolecularly. The fraction of pyrene pendants subject to hydrophobic interactions were used to determine the hydrophobic capture radius (Rc) of pyrene in water from the distribution of PEO end-toend distances. Rc was found to equal 2.2 ± 0.2 nm using f E0.

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INTRODUCTION Hydrophobically end-capped monodisperse poly(ethylene oxide)s (PEO) are often used as model polymers to understand the behavior of an important family of commercial associative thickeners, namely, the hydrophobically modified ethoxylated urethane (HEUR) polymers.1 HEUR polymers are composed of short PEO segments linked via urethane interconnecting units and end-terminated by alkyl hydrophobes.2 Numerous reports suggest that HEURs undergo end-to-end hydrophobic association to form “flowerlike” micelles in water at low polymer concentration.3−9 Increasing the HEUR concentration results in a significant increase of the HEUR solution viscosity due to the formation of a polymeric network where the hydrophobes form micelles which are bridged intermolecularly by the polymer chains.5,10,11 Application of a shear to a concentrated HEUR solution results in a dramatic decrease in solution viscosity due to the disruption of the polymeric network.10−14 Thanks to their interesting rheological properties, HEURs have found numerous industrial applications, such as in paint formulation, paper coating, enhanced oil recovery, and antifreeze formulations.15−17 © 2013 American Chemical Society

By replacing the hydrophobes of associative thickeners with the hydrophobic chromophore pyrene, the ability of pyrene to form an excimer can be employed to characterize polymer chain dynamics in solution and the level of association of the hydrophobic pyrene pendants in aqueous solution. In turn, these two parameters can help rationalize the peculiar rheological properties of associative thickeners in aqueous solutions. The fluorescence behavior of many hydrophobically modified water-soluble polymers bearing a pyrene group (PyHMWSP) has been investigated in aqueous solutions, and their studies have been the topic of a number of reviews.18−20 The water-soluble backbones that have been labeled with pyrene and studied by fluorescence include poly(acrylic acid),21−27 poly(maleic acid),28 a terpolymer of methacrylic acid, ethyl acrylate, and a macromonomer terminated at one end with pyrene and at the other end with methyl styrene,29−33 poly(N,N-dimethylacrylamide),34−36 poly(N-isopropylacrylaReceived: November 20, 2012 Revised: January 4, 2013 Published: January 10, 2013 2821

dx.doi.org/10.1021/la304628d | Langmuir 2013, 29, 2821−2834

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To this end, time-resolved fluorescence was used to characterize the kinetics of pyrene excimer formation in water for four monodisperse water-soluble poly(ethylene oxide)s endlabeled with pyrene (PEO(X)-Py2 where X is the molecular weight equal to 2, 5, 10, and 16.5 kDa). In this respect, this study departs from all other studies describing the analysis of the fluorescence decays acquired with aqueous solutions of PEO constructs end-labeled with pyrene, since these earlier studies based on time-resolved fluorescence have focused on polymer samples where the pyrene groups were separated by a single chain length corresponding to a molecular weight typically between 8 and 10 kDa.44,50,54 One exception is the study of Lee and Duhamel which was conducted with different PEO-Py2 constructs where the two pyrene labels were separated by a fixed monodisperse PEO chain of Mn = 3800 g/mol.53 The challenge associated with the kinetic study of a series of PEO(X)-Py2 samples having different molecular weights resides in designing an analysis whose results are not only internally consistent within a chosen theoretical framework but also externally consistent with what is expected from these polymeric constructs. The analysis that was implemented in the present report is based on a proposal made in 1989 by Char et al. where the fluorescence spectra of a series of PEO(X)-Py2 constructs were analyzed according to a sequential model (SM).48 In the SM, the pyrene labels diffuse freely and slowly within the PEO coil until they fall within a capture volume surrounding the pyrenes where hydrophobic forces induce the pyrene groups to form an excimer rapidly. The SM was incorporated a first time in the global analysis of the fluorescence decays acquired for a series of internally labeled PEO(X)-Py2 constructs where two pyrene pendants were separated by a fixed PEO chain length but were flanked by PEO overhangs of different sizes.53 It is used herein to probe the kinetics and levels of pyrene association for a series of pyrene end-labeled PEO(X)-Py2 constructs as a function of polymer chain length and concentration. The range of polymer concentrations was selected to probe intramolecular pyrene excimer formation at low polymer concentration and a combination of intra- and intermolecular pyrene excimer formation at larger polymer concentrations. Not only do the results obtained in this study fit nicely within the bulk of knowledge already available on pyrene end-labeled PEOs, but this study is also the first example in the literature where the steps leading to excimer formation for PEO(X)-Py2 samples are probed in a direct manner by time-resolved fluorescence as a function of both PEO chain length and PEO(X)-Py 2 concentration.

mide),37−40 poly(ethylenimine),41 hydroxyethylcellulose,42,43 and PEO.44−54 The fluorescence properties of these PyHMWSPs in water are quite different from those observed in organic solvents. Pyrene excimer formation takes place primarily via diffusive encounters between pyrene pendants in organic solvents where the pyrene pendants are well-solvated and not preassociated. On the contrary, aggregates of hydrophobic pyrenes form in aqueous solution and pyrene excimer is mostly generated through direct excitation of ground-state pyrene aggregates. These effects are well-known in the field and have been widely communicated.21−54 While the existence of pyrene associations in water is straightforward to demonstrate by a variety of spectroscopic properties, more quantitative information about the dynamics and levels of hydrophobic associations between pyrene pendants is much more challenging to obtain. Of particular interest is the fraction of hydrophobes that are associated and the time scale over which these associations take place. These parameters describe the behavior of the Py-HMWSPs at the molecular level providing knowledge that could be used to rationalize the peculiar viscoelastic properties observed at the macroscopic level for solutions of HMWSPs such as HEURs and HASEs. In theory, such quantitative information can be obtained through careful analysis of the fluorescence decays of the pyrene monomer and excimer.55,56 If the excimer is formed by diffusion between two pyrene groups, excimer formation is delayed and a rise time is observed in the excimer decay that matches the decay time of the pyrene monomer because the kinetics of excimer formation are coupled between the pyrene monomer and excimer. But if the pyrene labels are aggregated, direct excitation of a pyrene aggregate results in the quasiinstantaneous formation of an excimer. Thus, the pyrene monomer and excimer fluorescence decays contain the information relevant to, first, the kinetics of pyrene association in water and, second, the contribution of each pyrene species present in the solution at equilibrium. The former information is retrieved from the decay and rise times found through the analysis of the monomer and excimer fluorescence decays, respectively. The latter information is particularly useful to estimate the level of pyrene association through the molar fraction of aggregated pyrenes which can be inferred from the extent of rise times in the excimer decay. In practice, few analyses of this kind have been carried out due to the complex nature of the fluorescence decays obtained with aqueous solutions of Py-HMWSPs where pyrene aggregates are present. To date, the vast majority of quantitative analyses of the fluorescence decays acquired with aqueous solutions of PyHMWSPs have been conducted by this laboratory with watersoluble polymers that were randomly labeled with pyrene.29−35,53,55,56 The kinetics of pyrene excimer formation in these polymeric constructs are complicated by the distribution of pyrene excimer formation rate constants that results from the distribution of polymer chain lengths spanning every two pyrene labels randomly attached to the polymer. Although this distribution of rate constants can be satisfyingly accounted for with the fluorescence blob model (FBM),35,55 a study of the kinetics of pyrene associations for a Py-HMWSP in aqueous solution would be much simpler to handle if the diffusive encounters between two pyrenyl pendants could be described by a single rate constant. As it turns out, this can be achieved with a water-soluble monodisperse polymer end-labeled with pyrene, since these polymeric constructs are known to form excimer with a single rate constant in organic solvents.57−59

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THEORY The sequential model (SM)53 was introduced in 1998 to provide a dynamic counterpart to the protocol introduced in 1989 by Char et al. to analyze steady-state fluorescence spectra acquired with aqueous solutions of a series of PEO(X)-Py2 samples of different chain lengths.48 According to Char et al., each pyrene pendant is surrounded by a capture volume of radius RC (see Scheme 1B). Outside the capture volume, the pyrene pendants undergo Brownian motion, but if the two pyrene pendants happen to be separated by a distance smaller than 2RC, they are then subject to strong hydrophobic forces that lead to rapid excimer formation. The SM was first applied to a series of PEO(X)-Py2 samples where excimer formation was taking place intramolecularly between two pyrene pendants separated by a single chain length.53 The present study probes 2822


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Scheme 1a

⎛ d[M 2*] 1 ⎞ = −⎜k12 + ⎟[M 2*] dt τM ⎠ ⎝

(2)

⎛ d[Agg*] 1 ⎞ = k11[M1*] + k12[M 2*] − ⎜k 2 + ⎟[Agg*] dt τM ⎠ ⎝ (3)

d[E0*] 1 = k 2[Agg*] − [E0*] dt τE0

(4)

Integration of eqs 1 and 2 is trivial and yields the expressions of [M1*] and [M2*]. These expressions are used in eq 3 to determine [Agg*]. Summing [M1*] + [M2*] + [Agg*] yields the behavior of the pyrene monomer given by eq 5. ⎞ ⎛ k11 k12 [Py*] = ⎜[Agg*]o − [M1*]o − [M 2*]o ⎟ k 2 − k11 k 2 − k12 ⎠ ⎝ ⎡ ⎛ k2 1 ⎞⎤ exp⎢ −⎜k 2 + [M1*]o ⎟t ⎥ + ⎥ ⎢⎣ ⎝ τM ⎠ ⎦ k 2 − k11 ⎡ ⎛ k2 1 ⎞⎤ exp⎢ −⎜k11 + [M 2*]o ⎟t ⎥ + ⎢⎣ ⎝ τM ⎠ ⎦⎥ k 2 − k12 ⎡ ⎛ 1 ⎞⎤ exp⎢ −⎜k12 + ⎟t ⎥ ⎢⎣ ⎝ τM ⎠ ⎥⎦

a

(A) Intra- (top) and inter- (bottom) molecular excimer formation occurring sequentially via the formation of an intermediate pyrene aggregate. (B) Probability distribution function of end-to-end distances for intramolecular pyrene excimer formation.

The expression of [Agg*] is applied to integrate eq 4 which yields the expression of [E0*] given in eq 6. [E0*] = −

the validity of the SM for a series of PEO(X)-Py2 samples having different chain lengths and pushes its applicability to conditions where excimer formation occurs both intra- and intermolecularly. These two pathways for excimer formation are described in Scheme 1 where the pyrene excimer dissociation has been neglected, a reasonable assumption when working at temperatures lower than 35 °C. According to Scheme 1A, the excited pyrene monomers M1* and M2* encounter a ground-state monomer M to form a pyrene aggregate M*···M (Agg*) intra- and intermolecularly with a rate constant k11 and k12, respectively. The two pyrenes forming an aggregate are held together via hydrophobic forces so that each pyrene is assumed to retain its monomer character and emit with its natural lifetime τM. Rapid rearrangement of the two units forming a pyrene aggregate with a rate constant k2 as well as the direct excitation of preassociated ground-state pyrene dimers (MM) result in the formation of an excimer (E0*) that fluoresces with a lifetime τE0. Dynamic encounters between two pyrenes or direct excitation of a pyrene aggregate were assumed to generate the same E0* species emitting with the lifetime τE0 and referred to as excimer. The satisfying results obtained by conducting this analysis suggest that this assumption is reasonable. A more elaborate description of Scheme 1 can be found in the Supporting Information. The differential equations that describe the kinetics involving the species M1*, M2*, Agg*, and E0* introduced in Scheme 1A are listed in eqs 1−4. ⎛ d[M1*] 1 ⎞ * = −⎜k11 + ⎟[M1 ] dt τM ⎠ ⎝

(5)

−

+

+

k2 k2 +

1 τM

1 τE0

−

⎛ k11 [M1*]o ⎜[Agg*]o − k 2 − k11 ⎝

⎡ ⎛ ⎞ k12 1 ⎞⎤ [M 2*]o ⎟ exp⎢ −⎜k 2 + ⎟t ⎥ ⎢⎣ ⎝ τM ⎠ ⎥⎦ k 2 − k12 ⎠ k11[M1*]o

(k

11

+

1 τM

1 τE0

−

)

k12[M 2*]o

(k

12

+

1 τM

−

1 τE0

)

⎡ ⎛ k2 1 ⎞⎤ exp⎢ −⎜k11 + ⎟t ⎥ ⎢⎣ ⎝ τM ⎠ ⎥⎦ (k11 − k 2) ⎡ ⎛ k2 1 ⎞⎤ exp⎢ −⎜k12 + ⎟t ⎥ ⎢⎣ ⎝ τM ⎠ ⎥⎦ (k12 − k 2)

⎛ ⎜ + ⎜[E0*]o + ⎜ ⎝

(k

+

k 2k12[M 2*]o

(k

12

+

1 τM

k 2k11[M1*]o

−

11

1 τE0

+

1 τM

)(k

2

−

+

1 τE0

)(k

1 τM

−

⎞ k 2[Agg*]o ⎟ + exp( −t /τE0) 1 1 ⎟ k2 + τ − τ ⎟ M E0 ⎠

2

+

1 τE0

)

1 τM

−

1 τE0

)

(6)

Beside the species M1*, M2*, and Agg* observed in the monomer decay, the small number of PEO chains labeled with only one pyrene that cannot form excimer intermolecularly at low polymer concentration needs to be accounted for. This is accomplished by introducing the species Pyfree* which behaves as if these pyrenes were free in solution. The molar fractions of

(1) 2823


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those pyrenes that form excimer by diffusion (M1* and M2*), through aggregation (Agg*), and those that do not (Pyfree*) can be determined from the analysis of the monomer fluorescence decays and are referred to as f M1diff, f M2diff, f Magg, and f Mfree, respectively. In a similar fashion, the molar fractions f E1diff, f E2diff, f Eagg, and f EE0 are introduced to describe the molar fractions of the pyrene species M1*, M2*, Agg*, and E0* recovered from the analysis of the excimer fluorescence decays. Global analysis of the monomer and excimer fluorescence decays using eqs 5 and 6 allows the determination of the fractions f M1diff, f M2diff, f Mfree, f Magg, f E1diff, f E2diff, f EE0, and f Eagg, which are given in eqs 7−14.

fdiff1 =

−1 ⎛ fMagg f f ⎞ = ⎜⎜1 + + Mfree + EE0 ⎟⎟ fM1diff fM1diff fE1diff ⎠ ⎝

fdiff2 =

[PyM1diff *](t = 0) + [PyM2diff

Magg

*](t = 0) + [Py *](t = 0) Mfree

ffree =


Magg

*](t = 0) + [Py *](t = 0) Mfree

fagg =

(8) fMagg =

[Pydiff1*](t = 0) + [Pyfree*](t = 0) + [Pyagg*](t = 0) + [PyE0*](t = 0)

[PyM1diff *](t = 0) + [PyM2diff *](t = 0) + [PyMagg*](t = 0) + [PyMfree*](t = 0)

fE =

(9)


[PyMfree*](t = 0) *](t = 0) + [Py

(10) fE1diff = [PyE1diff *](t = 0) * [PyE1diff ](t = 0) + [PyE2diff *](t = 0) + [PyEagg*](t = 0) + [PyEE0*](t = 0)

(11) fE2ddiff =

Eagg

fMagg fMdiff1

= fdiff1 ×

fEagg fEdiff1

(18)

[PyE0*](t = 0) * * [Pydiff1 ](t = 0) + [Pyfree ](t = 0) + [Pyagg*](t = 0) + [PyE0*](t = 0) fEE0 fEdiff1

(19)

SM The overall contributions of the aggregated pyrene, fagg , SM SM diffusional pyrene, fdiff , and isolated pyrene, f free, of PEO(X)Py2 in water can be obtained according to eqs 20−22. The superscript “SM” indicates that the fractions were obtained using the sequential model.

*] + [PyMfree*](t = 0) Magg (t = 0)

[PyE2diff *](t = 0) *](t = 0) + [Py

(17)


= fdiff1 ×

fMfree =

fMfree fMdiff1 [Pyagg*](t = 0)

= fdiff1 ×

[PyMagg*](t = 0)

(16)

[Pyfree*](t = 0)

= fdiff1 ×

fM2diff = [PyM2diff *](t = 0) *](t = 0) + [Py

[Pydiff2*](t = 0) + [Pydiff2*](t = 0) + [Pyagg*](t = 0) + [PyE0*](t = 0)

−1 ⎛f fEagg fE1diff fEE0 ⎞ E2diff ⎜ ⎟ =⎜ + + + = fE2diff fE2diff fE2diff fE2diff ⎟⎠ ⎝ fE2diff

(7)

[PyE1diff *](t = 0) + [PyE2diff

[Pydiff1*](t = 0)

(15)

−1 ⎛ fMagg fM1diff fEE0 ⎞ ⎜ ⎟ = ⎜1 + + + fM2diff fM2diff fE2diff ⎟⎠ ⎝

fM1diff = [PyM1diff *](t = 0) *](t = 0) + [Py

[Pydiff1*](t = 0)


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*](t = 0) + [Py *](t = 0) EE0

SM f agg = fagg + fE0

(20)

SM f diff = fdiff1 + fdiff2

(21)

SM f free = ffree

(22)

EXPERIMENTAL SECTION

Materials. The synthesis of the PEO(X)-Py2 samples was described elsewhere.60 The general chemical structure of the polymers is shown in Figure 1. UV−vis measurements carried out elsewhere suggest that all PEO chains were fully end-capped with a pyrene group.60 Milli-Q water which was deionized from Millipore Milli-RO 10 Plus and MilliQ UF Plus (Bedford, MA) was used to prepare all aqueous solutions.

(12) fEagg = [PyEagg*](t = 0) [PyE1diff *](t = 0) + [PyE2diff *](t = 0) + [PyEagg*](t = 0) + [PyEE0*](t = 0)

(13) fEE = [PyEE0*](t = 0) [PyE1diff *](t = 0) + [PyE2diff *](t = 0) + [PyEagg*](t = 0) + [PyEE0*](t = 0)

(14)

The fractions obtained from eqs 7−14 can be used to calculate the contributions of fdiff1, fdiff2, f free, fagg, and f E0 according to eqs 15−19.

Figure 1. Chemical structure of the PEO(X)-Py2 samples. n = 45, 113, 227, and 375 for PEO(X)-Py2 with X = 2, 5, 10, and 16.5 kDa, respectively. 2824


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Steady-State Fluorescence Measurements. The steady-state fluorescence measurements were performed using a Photon Technology International (PTI) fluorometer with a continuous Ushio UXL-75Xe xenon arc lamp as the light source and a PTI 814 photomultiplier detection system. To avoid the inner filter effect61 when acquiring the fluorescence spectra, a triangular cell purchased from Hellma was used for front-face geometry measurements when the absorbance of the solution was greater than 0.1 OD. Below this concentration, a square cell was used to acquire the fluorescence spectra with the right-angle geometry. All PEO(X)-Py2 samples were excited at a wavelength of 344 nm. The fluorescence intensity of the monomer (IM) was determined by integrating the fluorescence spectra from 372 to 378 nm. To avoid the residual monomer fluorescence that might have leaked into the excimer emission and would contribute to the IE/IM ratio, the fluorescence intensity of the excimer (IE) was determined by normalizing the fluorescence spectrum acquired with a dilute (2.5 × 10−6 M) aqueous solution of a pyrene monolabeled PEO sample having a molecular weight of 2000 g/mol (PEO(2 kDa)-Py1) to that of PEO(X)-Py2 at the first monomer peak (∼375 nm), subtracting the normalized spectrum of PEO(2 kDa)-Py1 from that of PEO(X)-Py2 and integrating the resulting spectrum from 500 to 530 nm. Details about the synthesis and characterization of PEO(2 kDa)Py1 have been published elsewhere.60 Time-Resolved Fluorescence Measurements. The fluorescence decays were acquired with the time-correlated single-photon counting technique (TC-SPC) on an IBH time-resolved fluorometer using a front-face or a right-angle geometry depending on the sample absorption. The excitation source was an IBH 340 nm LED used with a 500 kHz repetition rate. All fluorescence decays were acquired over 1024 channels ensuring a minimum of 20 000 counts at their maximum. All solutions were excited at 344 nm, and the emission wavelength of the pyrene monomer and excimer was set at 375 and 510 nm, respectively. To reduce potential scattered light, cutoff filters of 370 and 495 nm were used to obtain the fluorescence decays of the pyrene monomer and excimer, respectively. A time per channel of 2.04 ns/ch was used for the acquisition of the monomer and excimer decays of all solutions. For the analyses of the decays, reference decays of degassed solutions of PPO [2,5-diphenyloxazole] in cyclohexane (τ = 1.42 ns) for the pyrene monomer and BBOT [2,5-bis(5-tert-butyl-2benzoxazolyl)thiophene] in ethanol (τ = 1.47 ns) for the pyrene excimer were used to obtain the instrument response function (IRF) via the MIMIC method.62 Analysis of the Fluorescence Decays. To determine τM, the fluorescence decay of a dilute (2.5 × 10−6 M) aqueous solution of PEO(2 kDa)-Py1 was fitted biexponentially. The largest decay time obtained with a pre-exponential weight of 92% was attributed to τM. It was found to equal 154 ns and was fixed in the analysis of all fluorescence decays. The small contribution of the shorter decay time was attributed to pyrene−PEO interactions, and it was neglected in the analysis. This procedure was expected to affect mostly the contribution of the pyrenes that do not form excimer, namely, f free. But since f free was found to be no larger than 0.15, small variations in the already small contribution from the monolabeled PEO chains are not expected to affect the conclusions of this study. The global analysis of the decays with eqs 5 and 6 was carried out with the Marquardt−Levenberg algorithm63 to obtain the optimized pre-exponential factors and decay times. The fits were considered good with χ2 being smaller than 1.30, and residuals and autocorrelation of the residuals randomly distributed around zero.

Figure 2. IE/IM ratio of PEO(2 kDa)-Py2 (□), PEO(5 kDa)-Py2 (◇), PEO(10 kDa)-Py2 (△), and PEO(16.5 kDa)-Py2 (○) as a function of polymer concentration, λex = 344 nm. Solid lines are provided to guide the eye; vertical dashed line indicates CF = 4 × 10−5 M.

remains constant for CP below 4 × 10−5 M, and increases linearly with polymer concentration for PEO(5 kDa)-Py2, PEO(10 kDa)-Py2, and PEO(16.5 kDa)-Py2 for CP above 4 × 10−5 M. Char et al.46 reported a similar behavior using pyrene end-labeled monodisperse PEOs having weight-average molecular weights of 4800, 9200, and 11 200 g/mol. The onset concentration indicating the transition between the two regimes for the PEO(X)-Py2 samples is shown by the dashed line in Figure 2 at CP = 4 × 10−5 M, the same concentration obtained by Char et al.46 Here we will refer to this critical concentration obtained by fluorescence as CF. The plateau regime where the IE/IM ratio is constant reflects intramolecular pyrene excimer formation, while the regime of increasing IE/IM ratio observed above CF for the PEO(X)-Py2 samples other than PEO(2 kDa)-Py2 results from a mixture of intra- and intermolecular excimer formation.46 Interestingly, the IE/IM ratio obtained with PEO(2 kDa)-Py2 does not show any break point and remains constant over the entire range of CP values presented in Figure 2. Furthermore, IE/IM obtained with PEO(5 kDa)-Py2 plateaus when CP is greater than 5 × 10−4 M. The effects observed at high Cp in Figure 2 are due to phase separation of the PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2 samples in water as has been reported earlier.46 At high CP, phase separation can be visually observed. When a 1 g/L solution of PEO(2 kDa)-Py2 (∼0.4 mM) was prepared, the sample was not soluble in water and underwent phaseseparation forming a yellow insoluble liquid at the bottom of the solution vial. Similarly, the solution in the upper layer of the fluorescence cell probed by the steady-state fluorometer was saturated and resulted in a constant IE/IM ratio in Figure 2 regardless of the actual amount of PEO(2 kDa)-Py2 sample used to prepare the solution. Since the steady-state and timeresolved fluorescence measurements took about 0.5 h to perform, the stability of the PEO(X)-Py2 solutions needed to be checked over time to ensure that they would remain homogeneous during acquisition of the fluorescence spectra and decays. This was done by monitoring the absorption and fluorescence intensity of PEO(X)-Py2 solutions using the UV− vis spectrophotometer and steady-state fluorometer, respectively. The absorption and fluorescence spectra overlapped

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RESULTS AND DISCUSSION Steady-State Fluorescence Spectra. The fluorescence spectra of PEO(X)-Py2 in water were acquired at different PEO(X)-Py2 concentrations. The ratio of the fluorescence intensities of the pyrene excimer over that of the monomer, the IE/IM ratio, was plotted in Figure 2 as a function of PEO(X)Py2 concentration (CP) expressed in mol/L using a log−log scale. The data shown in Figure 2 can be divided into two regimes where the IE/IM ratio of all PEO(X)-Py2 samples 2825


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scaling relationship is no longer valid for PEO(X)-Py2 in aqueous solution where pyrene aggregates. For CP larger than CF, the IE/IM ratio of PEO(X)-Py2 increased linearly with increasing polymer concentration as pyrene excimer formation occurs intra- and intermolecularly in this concentration regime. The slopes of the straight lines equaled 0.97 ± 0.01, 0.99 ± 0.03, and 1.00 ± 0.03 for PEO(5 kDa)-Py 2, PEO(10 kDa)-Py 2, and PEO(16.5 kDa)-Py 2, respectively. The data obtained with PEO(5 kDa)-Py2 at concentrations larger than 2 × 10−4 M were not used to obtain the slopes due to the phase separation that occurs with some of the samples. The linear increase of IE/IM with CP is usually attributed to intermolecular pyrene excimer formation via diffusional encounters.64,65 Another interesting result of Figure 2 also observed by Char et al.46 is that the break point occurs at CF = 4 × 10−5 M for all PEO(X)-Py2 samples regardless of their molecular weight. At concentrations beyond the break point, the polymer chains interact with other polymer chains, resulting in intermolecular excimer formation. CF would thus be expected to mark the boundary between the dilute and the semidilute regime, typically described by C*, the overlap concentration. C* is taken as the inverse of the intrinsic viscosity ([η]).66,67 [η] for unmodified PEO in water can be estimated from the Mark− Houwink−Sakurada parameters K = 49.9 × 10−3 mL·g−1 and a = 0.67.68 Therefore, C* is determined to equal 1.33 × 10−2, 4.19 × 10−3, and 1.81 × 10−3 M for PEO(5 kDa), PEO(10 kDa), and PEO(16.5 kDa), respectively. Not only does C* change more than 7-fold between PEO(5 kDa) and PEO(16.5 kDa), but it is also 45−330 times larger than CF = 4 × 10−5 M. That CF is so much smaller than C* can be easily understood by noting that C* and CF represent a static and dynamic description of the polymer solution, respectively. Indeed, the fact that two polymer coils are not overlapping at concentrations CP < C* does not imply that the polymer coils are completely isolated from one another. Brownian motions allow them to diffuse in solution and encounter one another, leading to intermolecular excimer formation for concentrations CP > CF. The independence of CF with respect to polymer molecular weight indicates that CF depends on pyrene concentration rather than chain length. CF is simply the pyrene concentration describing the boundary between two regimes, whether CP is smaller or larger than CF corresponding to regimes where pyrene excimer formation occurs intra- or intermolecularly. Analysis of the Fluorescence Decays. The pyrene monomer and excimer fluorescence decays of PEO(X)-Py2 in water at various polymer concentrations were acquired and globally fitted according to the sequential model (SM)53 described in the Theory section. The programs used to fit the decays obtained under various conditions are slightly different due to the complicated kinetics of pyrene excimer formation encountered in this study. When CP is smaller than CF, the pyrene excimer is formed intramolecularly via hydrophobic interactions between two pyrene pendants with a rate constant k2, diffusional encounters with a rate constant k11, and direct excitation of ground-state pyrene dimers. At CP larger than CF, intermolecular pyrene excimer formation is accounted for with the rate constant k12. However, it should be noted that the two different rate constants of excimer formation k11 and k12 can be considered only if k12 is smaller than k11. Yet this condition was not always obeyed in our experiments, since k11 decreases with increasing chain length while k12 increases with polymer

when acquired at different times if the solution did not precipitate over time. It was found that no precipitation occurred when CP was smaller than 2 × 10−5 and 2 × 10−4 M for PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2, respectively. Above these concentrations, the fluorescence intensity of PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2 decreased over time. Therefore, the IE/IM ratios and fluorescence decays obtained with PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2 for polymer concentrations larger than 2 × 10−5 and 2 × 10−4 M were not considered in the analysis of the results. No phase separation was detected for PEO(10 kDa)-Py2 and PEO(16.5 kDa)-Py2 in Figure 2 over the whole range of CP considered. Phase separation being a result of hydrophobic interaction between the pyrene groups,46 this attraction is stronger for the shorter PEO chains and at larger CP. When CP was less than CF, IE/IM remained constant for all PEO(X)-Py2 samples, suggesting that pyrene excimer formation occurred intramolecularly independently of the overall pyrene concentration in the solution.64 To investigate how the IE/IM ratio varied with the chain length of the PEO(X)-Py2 samples, the values taken by the IE/IM ratio in the plateau regime were averaged over all polymer concentrations smaller than CF and graphed in Figure 3 as a function of the number average

Figure 3. Natural log−log plot of IE/IM ratios at CP < CF versus PEO molecular weights. Data obtained in this study (□) and by Char et al.46 (◇).

molecular weight (Mn) of the samples as a log−log plot. A straight line was obtained with a slope of −2.3 ± 0.1. A log−log plot of the IE/IM ratios versus the molecular weight of the samples studied by Char et al.46 yielded a straight line with a similar slope of −2.3 ± 0.2. Differences in the absolute IE/IM ratios between this study and Char’s result from differences in the analysis of the fluorescence spectra. The trends shown in Figure 3 indicate that the IE/IM ratio scales as Mn−2.3±0.2 for PEO(X)-Py2 in water. This scaling law, however, disagrees with that obtained for the PEO(X)-Py2 samples in organic solvents where pyrene and PEO are soluble and pyrene excimer is formed by diffusive encounters between the two pyrene end groups.60 In organic solvents, the IE/IM ratio was found to scale as η−1Nn−1.6, where Nn is the number-average degree of polymerization which is proportional to the molecular weight of PEO.60 This latter scaling relationship agrees with theoretical work conducted by Wilemski and Fixman.58,59 However, this 2826


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Figure 4. Excimer fluorescence decays obtained with (A) PEO(5 kDa)-Py2 at 5 × 10−4 M (□) and 1.25 × 10−6 M (◇) and (B) PEO(2 kDa)-Py2 (□), PEO(5 kDa)-Py2 (◇), PEO(10 kDa)-Py2 (△), and PEO(16.5 kDa)-Py2 (○) at 1.25 × 10−6 M. The solid lines are drawn for those decays where no rise time was detected at the beginning of the decays. λex = 344 nm, λem = 510 nm.

Figure 5. SM analysis of the fluorescence decays of the pyrene monomer (left; λex = 344 nm, λem = 375 nm) and excimer (right; λex = 344 nm, λem = 510 nm) of PEO(5 kDa)-Py2 in water at [Py] = 2.5 × 10−6 M with a time per channel of 2.04 ns/ch. χ2 = 1.18.

decay of PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2 showed no rise time at concentrations larger than 4 × 10−5 and 5 × 10−4 M, respectively. These concentrations lay in the regime where the solutions undergo phase separation and where strong pyrene aggregation leads to predominant excimer formation via direct excitation of pyrene aggregates. The excimer decays obtained for the two largest concentrations of PEO(5 kDa)-Py2 in Figure 2 do not show a rise time at the early times of the excimer decays, suggesting that the kinetics between the excited monomer and excimer are no longer coupled, a consequence of the strong pyrene aggregation. Figure 4A shows the excimer decays of PEO(5 kDa)-Py2 acquired at concentrations of 5 × 10−4 and 1.25 × 10−6 M. No rise time was observed with the solution at the higher polymer concentration. The plateau observed for the IE/IM ratios at CP > 5 × 10−4 M for PEO(5 kDa)-Py2 in Figure 2 and the lack of rise time in the excimer decays is certainly a consequence of the phase separation undergone by these solutions at higher CP. Second, PEO(16.5

concentration. In the case of PEO(10 kDa)-Py2 and PEO(16.5 kDa)-Py2, k11 was too small and was rapidly overtaken by k12. Therefore, only one rate constant (kdiff) was used to represent the pyrenes forming excimer via diffusion for PEO(10 kDa)-Py2 and PEO(16.5 kDa)-Py2 solutions at CP > CF. Below CF, the fraction of pyrenes that cannot form excimer, f free, is not equal to zero due to the presence of PEO chains monolabeled with pyrene that act as fluorescent impurities for the shorter chains69 and pyrene groups which are too far from each other to form an excimer for the longer chains,60 or a combination of both effects. Above CF, f free for PEO(5 kDa)-Py2 was set to equal zero and f free obtained for PEO(10 kDa)-Py2 and PEO(16.5 kDa)-Py2 took small values close to zero as expected in this polymer concentration regime where excimer is formed intermolecularly. The fluorescence decays could not be fitted globally when the excimer decays showed no rise time. The absence of a rise time was observed under two conditions. First, the excimer 2827


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SM SM SM SM SM Figure 6. Fractions fSM agg (◆), fdiff (■), and f free (▲) as well as the fractions fagg (□), f E0 (◇), fdiff1 (○), and fdiff2 (△) used to calculate fagg , fdiff and f free as a function of CP obtained with (A) PEO(2 kDa)-Py2, (B) PEO(5 kDa)-Py2, (C) PEO(10 kDa)-Py2, and (D) PEO(16.5 kDa)-Py2. The vertical dashed lines represent the position of CF.

kDa)-Py2 solutions at CP below 6 × 10−5 M form little excimer. The excimer decays obtained with all PEO(X)-Py2 samples with a pyrene concentration of 2.5 × 10−6 M are shown in Figure 4B. Compared with the other three samples, the excimer decay obtained with PEO(16.5 kDa)-Py2 shows no rise time on the time scale used for these experiments. Global analysis of the monomer and excimer decays implies that any decay of the pyrene monomer shorter than the monomer decay induced by its natural lifetime τM results in an excimer rise time. The absence of a rise time in the excimer decay of PEO(16.5 kDa)Py2 indicates that the monomer and excimer decays acquired with this solution cannot be fitted globally. In the case of PEO(16.5 kDa)-Py2, the pyrene labels are so far apart that excimer formation by diffusion is weak and the majority of pyrenes that form excimer are preassociated. All the other decays were successfully fitted by the SM yielding χ2 smaller than 1.30, and residuals and autocorrelation of the residuals randomly distributed around zero. An example of the fits is shown in Figure 5. It was obtained by analyzing the pyrene monomer and excimer fluorescence decays of PEO(5 kDa)-Py2 at [Py] = 2.5 × 10−6 M. The small excimer rise time suggests that excimer formation occurs on a fast time scale, as was observed by Lee and Duhamel for another series of pyrene-

labeled PEOs whose fluorescence decays were analyzed with the SM.53 The differences in rise times obtained for the excimer decays acquired in water53 and those acquired in organic solvents52,60 reflect differences in the kinetics of excimer formation.48,53 The parameters retrieved from the SM analysis of the fluorescence decays are listed in Table SI.1 of the Supporting Information. The excimer lifetime τE0 of PEO(5 kDa)-Py2, PEO(10 kDa)-Py2, and PEO(16.5 kDa)-Py2 was found to be independent of PEO chain length and equaled 47 ± 3 ns, a reasonable value for τE0.60,65 The independence of τE0 with PEO chain length is expected as τE0 represents an intrinsic property of the pyrene excimer. For PEO(2 kDa)-Py2, τE0 took a substantially shorter value of 39 ns, a consequence of the strong aggregation experienced by the pyrene pendants in this sample. Using eqs 15−22, the molar fractions of pyrenes that aggragate via hydrophobic interactions (fSM agg ), form excimer by SM diffusion ( fSM diff ), and are isolated and do not form excimer ( f free) were determined and they are listed in Table SI.2 in the Supporting Information. These fractions were plotted as a function of CP for each PEO(X)-Py2 samples in Figure 6. The SM fractions f E0, fagg, fdiff1, and fdiff2 used to calculate fSM agg , fdiff , and SM f free were also plotted in Figure 6. For PEO(2 kDa)-Py2, Figure 2828


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Figure 7. Rate constants as a function of Cp: k11 (■) and k12 (◆) obtained with (A) PEO(2 kDa)-Py2 and (B) PEO(5 kDa)-Py2; kdiff (■) obtained with (C) PEO(10 kDa)-Py2 and (D) PEO(16.5 kDa)-Py2. The dashed lines represent the position of CF.

6A shows that most pyrene groups are aggregated (fSM agg = 0.97) at low CP. All fractions remained constant in the dilute regime where excimer is formed intramolecularly. Figure 6B shows that fSM agg for PEO(5 kDa)-Py2 in the dilute for PEO(2 kDa)-Py2 and more pyrene regime is lower than fSM agg excimer is formed by intramolecular diffusion. When CP is SM increased above CF, fSM agg increases and fdiff decreases, indicating that as more PEO(5 kDa)-Py2 sample is being added to the solution, the pyrene groups form more intermolecular hydrophobic aggregates, and consequently more excimer is formed by direct excitation of pyrene aggregates rather than by diffusive encounters. Excimer formation occurs mostly intramolecularly as fdiff1 represents the main contribution to fSM diff . fdiff2 remains small and constant as a function of CP. For PEO(10 kDa)-Py2, Figure 6C shows that fSM agg is very small in the dilute regime with about 10% of the pyrene groups being associated. In fact, 90% of the pyrene pendants are not associated. Furthermore, around 70% of the excited pyrenes form excimer by diffusive encounter with a ground-state pyrene located at the opposite PEO chain end. At first glance, this result is a little surprising since it seems to disagree with the hydrophobic nature of pyrene. However it agrees with an earlier study by the Winnik group in Toronto which showed that only 7% of the pyrene end-groups were preassociated in water for pyrene end-labeled monodisperse PEO having a molecular weight of 8,000 g·mol−1.50 The rather

weak associative character of this PEO(X)-Py2 constructs is unexpected when it is compared to the strong associative behavior of commercial HEURs bearing alkyl hydrophobes which are known to form rosette micelles in water at very low polymer concentration.5 The weak associative character of the PEO(X)-Py2 samples leads to two conclusions. First, the small fraction fSM agg is probably due to interactions taking place between the pyrene groups and the PEO chain which reduces the drive of the pyrene groups to associate in water. Second, the hydrophobicity of pyrene is dramatically decreased after its covalent attachment onto the hydrophilic long PEO chains. When CP > CF, fSM agg increases and fSM diff decreases for PEO(10 kDa)-Py2 and PEO(16.5 kDa)-Py2 due to the formation of intermolecular pyrene aggregates. This behavior is similar to that observed with PEO(5 kDa)-Py2. At the largest CP, f SM free decreases to around zero as all pyrene species are contributing to excimer formation. PEO(16.5 kDa)Py2 shows a trend similar to that of PEO(10 kDa)-Py2 at higher CP in Figure 6D. As mentioned earlier, the absence of a rise time for the excimer decays acquired in the dilute regime (i.e., with CP < 4 × 10−5 M) prevents the global analysis of the decays of PEO(16.5 kDa)-Py2 (see Figure 4B). The rate constants obtained for intramolecular (k11) and intermolecular (k12) excimer formation by diffusion for PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2, and for diffusive excimer 2829


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one rate constant representing pyrene excimer formation by diffusion (kdiff) was applied to PEO(10 kDa)-Py2 and PEO(16.5 kDa)-Py2 because their k11 has been shown to be much smaller than the samples with shorter PEO chain length.60 Figure 7C and D shows that kdiff of PEO(10 kDa)-Py2 and PEO(16.5 kDa)-Py2 increases with CP for CP > CF as expected when intermolecular excimer formation takes place. The rate constant describing pyrene excimer formation through hydrophobic interactions, k2, was found to be independent of PEO chain length and CP, as shown in Figure 8. This result is expected from the definition of k2 which represents an intrinsic property of pyrene in water reflecting the rapid rearrangement of two pyrene groups within their capture volume. After averaging, k2 was found to equal 7.3(±0.5) × 107 s−1, which is three times smaller than the k2 value of 2.3(±0.5) × 108 s−1 found by Lee and Duhamel53 probably because the hydrophobic attraction induced by the pyrene butyric linker used in that latter study is stronger than that of the pyrene methyl linker used in the present study. SM SM The fractions fSM agg , fdiff , and f free obtained with PEO(2 kDa)Py2, PEO(5 kDa)-Py2, and PEO(10 kDa)-Py2 for CP < CF were averaged and plotted as a function of PEO molecular weights in Figure 9A. fSM agg decreases dramatically with increasing PEO chain length reflecting the stronger hydrophobic interaction experienced by the shorter polymers. The rate constants k11 and k2 averaged for CP < CF were also plotted as a function of PEO molecular weights in Figure 9B. k11 decreases significantly with increasing molecular weight as also observed with the PEO(X)Py2 samples in organic solvents60 and with linear chains in organic solvents without the rapid capture process.57,71−78 k2 remained constant and significantly larger than k11 for the three samples because k2 characterizes the behavior of pyrene inside the capture volume which is a characteristic feature of pyrene and does not change with chain length, while k11 represents the pyrene’s motion inside the volume of the polymer coil (Vcoil) that is outside the capture volume and this volume increases with pyrene chain length. Another important observation is that, according to the fractions obtained for PEO(10 kDa)-Py2 for CP < CF, this sample should behave in water in a manner similar as in organic solvents since most of the excimer is formed by diffusion. However, the eximer decay in water (see Figure 4B) does not exhibit the pronounced rise

formation (kdiff) for PEO(10 kDa)-Py2 and PEO(16.5 kDa)Py2, as well as for excimer formation between two pyrenes inside the capture volume (k2) were obtained from the global analysis of the fluorescence decays with eqs 5 and 6. They are plotted as a function of CP in Figures 7 and 8. For PEO(2

Figure 8. Plot of k2 obtained for PEO(2 kDa)-Py2 (□), PEO(5 kDa)Py2 (◇), PEO(10 kDa)-Py2 (△), and PEO(16.5 kDa)-Py2 (○) as a function of CP. The dashed line represents the position of CF, and the horizontal solid line represents the average value of k2.

kDa)-Py2 and PEO(5 kDa)-Py2, k12 was set to equal zero for CP < CF because no excimer can be formed by intermolecular diffusion at low concentration. As more polymer was added to the solution, the fits required a nonzero k12 and the recovered k12 increased with increasing concentration for PEO(5 kDa)Py2. The k11 values obtained for PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2 are larger than the rate constant of cyclization (kcy) obtained for these samples in N,N-dimethylformamide (DMF)60 which has a viscosity (0.79 mPa.s at 25 °C) similar to that of water (0.89 mPa.s at 25 °C).70 If pyrene in water interacts with a section of the PEO chain, a smaller part of the chain would remain free to constitute the polymer coil, reducing its overall dimension, thus increasing the local pyrene concentration and k11. Since the rate constant of intermolecular pyrene excimer formation k12 cannot be larger than k11, only

SM SM Figure 9. (A) Molar fractions of fSM agg (◇), fdiff (□), and f free (△) and (B) rate constants of k11 (◆) and k2 (■) as a function of PEO molecular weight.

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time observed in organic solvents.60 This behavior is due to the large k2 which is at least 60 times larger than kdiff. Although fSM agg is much smaller than fSM diff , the rapid excimer formation within the capture distance results in a less apparent rise time in the excimer decay. Determination of the Capture Radius (RC). Using PEO(X)-Py2 samples with X = 4.8 kDa, 9.2 kDa, and 11.2 kDa, Char et al. proposed that the steep drop in IE/IM as a function of Mn observed in Figure 3 was due to a change in the local pyrene concentration of isolated ground-state pyrene [Py]loc in the polymer coil.48 As illustrated in Scheme 1B, the existence of a capture volume inside the polymer coil where excimer is formed quasi-instantaneously reduces the volume available to the pyrene labels that undergo Brownian motion thereby increasing [Py]loc. Assuming a Gaussian chain for PEO, Char et al. derived an expression for the fraction of aggregated chain ends, obtained as f E0 from the SM analysis of the fluorescence decays, which they used to renormalize the distribution of end-to-end distances and derive the average endto-end distance ⟨R2⟩. The expression of f E0 and ⟨R2⟩ derived by Char et al. is given in eqs 24 and 25, respectively.48 fE0

the process yielded inconsistent results, probably because the chain ends of PEO(2 kDa)-Py2 have a probability of 63% of being within 2RC; that is, the majority of chain ends are preassociated and form very little excimer by diffusion. Indeed, f E0 equals 0.76 ± 0.01 in Figure 6 for PEO(2 kDa)-Py2. In such a case, the fraction of end-to-end distances (63%) that cannot be included in the renormalization procedure conducted by Char et al. to obtain eqs 24 and 25 is too large and the procedure fails. Considering the three samples PEO(5 kDa)Py2 , PEO(10 kDa)-Py2 , and PEO(16.5 kDa)-Py 2, this procedure could be refined further by substituting lEO by lK in eqs 24 and 25. The parameters lK and N for PEO have been determined to equal 0.707 nm and 0.0141Mn, respectively.81 This adjustment led to a small change in RC which was found to equal 2.1 ± 0.2 nm. Within experimental error and regardless of the unit length employed, all RC values determined from the analysis of the fluorescence spectra of PEO(X)-Py2 samples with X > 4.8 kDa agree with the original value obtained by Char et al.48 The capture radius could also be determined by applying eq 24 to the f E0 values obtained in Figure 9A by time-resolved fluorescence. In this case, the PEO(X)-Py2 samples with X = 5 kDa and 10 kDa were used as PEO(16.5 kDa)-Py2 did not form enough excimer by diffusion for Cp < CF to apply the SM analysis (see Figure 4B). Using lK as the unit length, an RC value of 2.2 ± 0.2 nm was retrieved, again in very good agreement with the RC value obtained by steady-state fluorescence.

π ⎡ ⎛ m ⎞3/2 ⎢ R c m 2 exp( −4mR c ) + = 4π ⎜ ⎟ ⎢ − ⎝π⎠ m 4m ⎣

erf(2R c

⎤ ⎥ m )⎥ ⎦

⎡ 2 ⎛ m ⎞3/2 ⎢ R c 4R c + 2 ⎜ ⎟ ⟨R ⟩ = (1 − fE0 )4π ⎝π⎠ ⎢ m ⎣

(

exp( − 4mR c 2) +

■

(24)

3

π m 2

8m

⎤ ⎥ erfc(2R c m )⎥ ⎦

3 2m

CONCLUSIONS The hydrophobic interactions of a series of PEO(X)-Py2 samples have been investigated in aqueous solution using pyrene fluorescence spectra and decays. The samples with shorter PEO chain length exhibited strong hydrophobic interactions which resulted in phase separation of PEO(2 kDa)-Py2 and PEO(5 kDa)-Py2 at high polymer concentration. In the dilute regime where polymer concentration was below 4 × 10−5 M, no change in the fluorescence behavior was observed for all polymer samples regardless of polymer concentration since excimer formation occurs intramolecularly. When the polymer concentration was larger than 4 × 10−5 M, the excimer formed both intra- and intermolecularly. The concentration when intermolecular excimer formation occurred was the same for all PEO(X)-Py2 constructs regardless of PEO chain length. The complex fluorescence decays were globally fitted according to the SM which assumes that the excimer is formed according to two sequential steps. Two pyrenes located outside a capture volume diffuse randomly, but once they both enter the capture volume, they become subject to hydrophobic interactions and encounter rapidly to form an excimer. Consequently, three rate constants were used to describe the kinetics of excimer formation. The rate constant of intermolecular diffusion in the dilute regime equals zero and increases with increasing CP for CP > CF. The rate constant representing intramolecular diffusion is independent of polymer concentration and decreases significantly with increasing polymer chain length. Inside the capture volume, excimers are formed with a rate constant of 7.3(±0.5) × 107 s−1 that is larger than k11 or k12, as expected from the strong hydrophobic attraction experienced by the two pyrene pendants. This rate constant is independent of PEO chain length and polymer concentration. According to the concept of capture volume initially introduced by Char et al.,48 the capture radius of pyrene in water was determined

)

(25)

The capture radius RC in eqs 24 and 25 is unitless and is expressed as a number of unit lengths used to model the PEO chain, either lEO = 0.439 nm for an ethylene oxide repeating segment as done by Char et al.48 or lK for a Kuhn segment. The parameter m equals 3/(2N) where N is such that the contour length L of the polymer equals NlEO or NlK depending on whether an ethylene oxide unit or a Kuhn segment was used to describe the chain, respectively. As a first approximation, the IE/IM ratio can be viewed as a representation of [Py]loc since a larger [Py]loc results in a larger IE/IM ratio. Since the pyrene end-labeled polymers probed by fluorescence exhibit one excited pyrene at one end of the chain and one ground-state pyrene at the other end, [Py] loc represents the concentration equivalent to one ground-state pyrene in the volume defined by the polymer coil, namely 1/ Vcoil.79,80 Assuming that Vcoil is proportional to ⟨R2⟩1.5, Char et al. used lEO = 0.439 nm to compare the three IE/IM ratios that they obtained with PEO(4.8 kDa)-Py2, PEO(9.8 kDa)-Py2, and PEO(11.2 kDa)-Py2 with their corresponding ⟨R2⟩1.5 calculated as a function of RC. The best match between the IE/IM ratios and ⟨R2⟩1.5 values was obtained for an RC value of 2.0 nm. The same protocol was applied to the PEO(5 kDa)-Py2, PEO(10 kDa)-Py2, and PEO(16.5 kDa)-Py2 samples resulting in an RC value of 1.9 ± 0.2 nm in very good agreement with the RC value of 2.0 nm retrieved by Char et al. Including PEO(2 kDa)-Py2 in 2831


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using the fraction f E0. RC was found to equal 2.2 ± 0.2 nm in agreement with Char et al.’s earlier study that used steady-state fluorescence only.

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Comb Associative Polymers Based On Poly(ethylene oxide). Langmuir 1997, 13, 6903−6911. (13) Xu, B.; Li, L.; Yekta, A.; Masoumi, Z.; Kanagalingam, S.; Winnik, M. A.; Zhang, K. W.; Macdonald, P. M.; Menchen, S. Synthesis, Characterization, and Rheological Behavior of Polyethylene Glycols End-Capped with Fluorocarbon Hydrophobes. Langmuir 1997, 13, 2447−2456. (14) Tripathi, A.; Tam, K. C.; McKinley, G. H. Rheology and Dynamics of Associative Polymers in Shear and Extension: Theory and Experiments. Macromolecules 2006, 39, 1981−1999. (15) Anwari, F. M.; Schwab, F. G. In Polymers in Aqueous Media. Performance Through Association; Glass, J. E., Ed.; Advances in Chemistry series 223; American Chemical Society: Washington, DC, 1989; pp 527−542. (16) François, J. Association in Water of Model Hydrophobically End-Capped Poly(ethylene oxide). Prog. Org. Coat. 1994, 24, 67−79. (17) Maechling-Strasser, C.; Clouet, F.; François, J. Hydrophobically End-Capped Polyethylene-oxide Urethanes: 2. Modelling their Association in Water. Polymer 1992, 33, 1021−1025. (18) Winnik, F. M. Photophysics of Pre-associated Pyrenes in Aqueous Polymer Solutions and in Other Organized Media. Chem. Rev. 1993, 93, 587−614. (19) Winnik, F. M. Fluorescence Methods in the Study of the Interactions of Surfactants with Polymers. Colloids Surf., A 1996, 118, 1−39. (20) Duhamel, J. In Molecular Interfacial Phenomena of Polymers and Biopolymers; Chen, P., Ed.; Woodhead Publishing Company: 2005; pp 214−248. (21) Chandar, P.; Somasundaran, P.; Turro, N. J. Fluorescence probe investigation of anionic polymer-cationic surfactant interactions. Macromolecules 1988, 21, 950−953. (22) Anghel, D. F.; Alderson, V.; Winnik, F. M.; Mizusaki, M.; Morishima, Y. Fluorescent Dyes as Model “Hydrophobic Modifiers” of Polyelectrolytes: A Study of Poly(Acrylic Acid)s Labelled with Pyrenyl and Naphthyl Groups. Polymer 1998, 39, 3035−3044. (23) Pokhrel, M. R.; Bossmann, S. H. J. Phys. Chem. B 2000, 104, 2215−2223. (24) Seixas de Melo, J.; Costa, T.; Miguel, M. D.; Lindman, B.; Schillén, K. Time-Resolved and Steady-State Fluorescence Studies of Hydrophobically Modified Water-Soluble Polymers. J. Phys. Chem. B 2003, 107, 12605−12621. (25) Seixas de Melo, J.; Costa, T.; Francisco, A.; Maçanita, A. L.; Gago, S.; Gonçalves, I. S. Dynamics of Short as Compared with Long Poly(Acrylic Acid) Chains Hydrophobically Modified with Pyrene, as Followed by Fluorescence Techniques. Phys. Chem. Chem. Phys. 2007, 9, 1370−1385. (26) Costa, T.; Schillén, K.; Miguel, M.; da, G.; Lindman, B.; Seixas de Melo, J. Association of a Hydrophobically Modified Polyelectrolyte and a Block Copolymer Followed by Fluorescence Techniques. J. Phys. Chem. B 2009, 113, 6194−6204. (27) Costa, T.; Seixas de Melo, J.; Castro, C. S.; Gago, S.; Pillinger, M.; Gonçalves, I. S. Picosecond Dynamics of Dimer Formation in a Pyrene Labeled Polymer. J. Phys. Chem. B 2010, 114, 12439−12447. (28) Deo, P.; Deo, N.; Somasundaran, P.; Jockusch, S.; Turro, N. J. Conformational Changes of Pyrene-Labeled Polyelectrolytes with pH: Effect of Hydrophobic Modifications. J. Phys. Chem. B 2005, 109, 20714−20718. (29) Prazeres, T. J. V.; Beingessner, R.; Duhamel, J.; Olesen, K.; Shay, G.; Bassett, D. R. Characterization of the Association Level of PyreneLabeled HASEs by Fluorescence. Macromolecules 2001, 34, 7876− 7884. (30) Siu, H.; Duhamel, J. Comparison of the Association Level of a Pyrene-Labeled Associative Polymer Obtained from an Analysis Based on Two Different Models. J. Phys. Chem. B 2005, 109, 1770−1780. (31) Prazeres, T. J. V.; Duhamel, J.; Olesen, K.; Shay, G. Correlations between the Viscoelastic Behavior of Pyrene-Labeled Associative Polymers and the Associations of Their Fluorescent Hydrophobes. J. Phys. Chem. B 2005, 109, 17406−17416.

ASSOCIATED CONTENT

S Supporting Information *

Description of the reaction scheme for pyrene excimer formation, tables listing the parameters retrieved from the analysis of the fluorescence decays of the pyrene monomer and excimer. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Present Address †

S.C.: EOR Research Department, Petroleum Exploration & Production Research Institute, Sinopec, Beijing 10083, China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors want to thank NSERC and the Petroleum Research Fund for supporting this research.

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REFERENCES

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