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J. Phys. Chem. B 2004, 108, 12009-12015
Coil-Globule Transition of Pyrene-Labeled Polystyrene in Cyclohexane: Determination of
Polymer Chain Radii by Fluorescence

Susana Pic¸arra,†,‡ Jean Duhamel,§ A. Fedorov,† and J. M. G. Martinho*,†
Centro de Quı´mica-Fı´sica Molecular, Instituto Superior Te´cnico, AVenida RoVisco Pais 1,1049-001 Lisboa, Portugal, Escola Superior de Tecnologia de Setu´bal, Instituto Polite´cnico de Setu´bal,Campus do IPS, Estefanilha - 2914-508 Setu´bal, Portugal, and Institute for Polymer Research,Department of Chemistry, UniVersity of Waterloo, Waterloo ON N2J 3G1, Canada ReceiVed: March 30, 2004; In Final Form: June 8, 2004 The coil-globule transition of a polystyrene chain (M ) pyrene derivative was studied in cyclohexane under dilute conditions by fluorescence. The coil-globuletransition temperature was found to be around 25 °C from the presence of a break point in the pyrene excimer-to-monomer fluorescence intensity ratio plot with temperature. Analysis of the pyrene monomer fluorescenceintensity decays with the fluorescence blob model modified to consider the presence of ground-state pyrenepairs allowed for the determination of the chain radii at several temperatures between 12 and 50 °C andconfirmed the occurrence of a coil-globule transition. Fluorescence was found to be a reliable technique forstudying the coil-globule transitions in dilute solutions of low-molecular-weight polymers where stable globulesexist without the interference of polymer aggregates in a large temperature interval.
1. Introduction
1.1) in THF allowed us to follow the coil-globule The conformation of a polymer chain in solution varies from transition and to detect isolated globules in a temperature interval an extended random coil in good solvents to a compact globule as large as ∼40 °C.15 Stable globules were also observed in an in poor solvents. In 1960, Stockmayer was the first to predict even larger temperature interval (∼50 °C) with a shorter the collapse of a polymer chain from a coil to a compact globule poly(ethylene oxide) chain (Mn ≈ 4000, Mw/Mn as the quality of the solvent is changed.1 Over the past 40 years, (0.0004 wt %).16 These results were obtained with polymers significant interest in both experimental and theoretical aspects labeled at both ends with pyrene and were feasible because of of this transition has been expressed, not only because of its the high sensitivity of fluorescence. Recently, using randomly importance in biology (used as a simplified model for enzymatic pyrene-labeled poly(dimethyl acrylamide) (PDMA) in methanol, activity, protein folding, or DNA packing)2-4 but also because the chain radii were calculated along the coil-globule transi- of its fundamental role in the understanding of polymer tion17 using the fluorescence blob model (FBM) developed by segment-segment and segment-solvent interactions.5 The initial experimental results were obtained with polystyrene In the present work, the coil-globule transition of a solutions in cyclohexane below the upper critical solution temperature (UCST).6-8 Poly(N-isopropylacrylamide) (PNIPAM) labeled with a pyrene derivative, is studied in dilute cyclohexane in water has also been extensively studied, above its lower solutions (0.0001, 0.001, and 0.01 wt %). The coil-globule critical solution temperature (LCST).9-11 Coil-globule transition transition occurs at 25 °C and was identified from a break in studies are difficult to perform because aggregation occurs the plot of the pyrene excimer-to-monomer fluorescence inten- simultaneously with the formation of globules at the polymer sity ratio with temperature. The pyrene fluorescence decay concentrations required by the limits of detection of the most curves were fitted with the blob model, and the chain radii were common experimental techniques (light scattering, intrinsic calculated from the fitting parameters. A plot of the radius data viscosimetry, etc.). To avoid aggregation, dilute solutions of in terms of a master curve of the scaled contraction factor versus high-molecular-weight polymer chains are frequently used.
the scaled reduced temperature is compared with the available However, the phase diagrams of high-molecular-weight polymer solutions show very asymmetric coexistence curves and very The most concentrated polymer solution (0.01 wt %) led to small or even inexistent temperature gaps between the coil- the formation of high-density polymer aggregates below the globule transition temperatures and the binodal lines. For this coil-globule transition temperature. There were also problems reason, many experiments have been carried out with polymer associated with the very dilute solution (0.0001 wt %) since solutions located in the metastable region of the phase diagram, the fluorescence signal was overwhelmed by intense light where polymer globules coexist with aggregates.12-14 scattering. Consequently our discussion focuses mostly on the The use of a very dilute solution (0.002 wt %) of a low- results obtained with the 0.001 wt % solution.
molecular-weight poly( -caprolactone) chain (Mn ≈ 20 000, Mw/ Fluorescence provides an alternative method for calculating * To whom correspondence should be addressed. Fax: 351-21-8464455.
polymer chain dimensions in solution and studying the coil- globule transition of small chains in dilute conditions where † Instituto Superior Te´cnico.
‡ aggregation does not occur and conventional techniques (light Instituto Polite´cnico de Setu´bal.
scattering, intrinsic viscosity) are not sensitive enough.
12010 J. Phys. Chem. B, Vol. 108, No. 32, 2004
2. Experimental Section
Instrumentation. Fluorescence spectra were recorded on a
Figure 1. (A) Fluorescence spectra of PS11Py (0.0001 wt %) and
SPEX Fluorolog F112A fluorometer at several temperatures PS02Py (0.006 wt %) in cyclohexane at 65 °C by excitation at λex330 nm: ( using a cryostat from Oxford Instruments (DN 1704) that allows s) PS11Py, (- - -) PS02Py, (‚‚‚) excimer plus dimer emission obtained by subtraction of the monomer emission (PS02Py spectrum) temperature control to within (0.5 °C. The fluorescence spectra from the PS11Py spectrum. (B) Fluorescence spectra of the PS11Py were recorded between 370 and 600 nm (2.25 nm band- (0.0001 wt % solution) at several temperatures by excitation at λ width) using 330 nm (4.5 nm bandwidth) as excitation wave- 330 nm. The intensities of all spectra are normalized to 1 at λ ) 376 Time-resolved picosecond fluorescence decays were obtained by the single photon timing (SPT) technique using excitation 3. Results and Discussion
laser light at 328 nm. The system consists of a mode-locked Fluorescence Spectra. Figure 1A shows the fluorescence
Coherent Inova 440-10 argon ion laser that synchronously spectra upon excitation at 330 nm of two polystyrene chains pumped a cavity-dumped Coherent 701-2 DCM dye laser, (PS11Py, 0.0001 wt %; PS02Py, 0.006 wt %) in cyclohexane delivering 5-6 ps pulses at a repetition rate of 460 kHz. The fluorescence was selected by a Jobin-Yvon HR320 monochro- The fluorescence spectrum of the PS02Py polymer solution mator with a grating of 100 lines/mm (6 nm bandwidth). Before is mainly composed of several structured bands in the blue entering the emission monochromator, the light beam passes region, characteristic of pyrene monomer emission. 20 The through a cutoff filter to eliminate the excitation scattered light, excimer emission is practically absent because most of the chains as well as a polarizer oriented at the magic angle (54.7°) with have, on average, fewer than two pyrenes and the polymer coils respect to the vertically polarized laser light, to avoid polariza- are far away (low polymer concentration), not allowing for tion effects. The fluorescence was detected by a Hamamatsu diffusive encounters to occur between pyrenes attached to 2809U-01 microchannel plate photomultiplier. All decays were different chains. As the PS11PY chain has a higher degree of fitted using a nonlinear least-squares method based on the labeling, the distances between pyrene groups are shorter, favoring intrachain excimer formation. The spectrum obtained The absorption spectra were recorded with a UV-vis-NIR after subtraction of the monomer emission (see Figure 1A, dotted scanning spectrophotometer (Shimadzu, UV-3101 PC).
line) has a broad band centered at ∼480 nm attributed to the Polymer Characterization. The synthesis of the polystyrene
excimer and a structured band attributed to the emission of chains and their random chloromethylation and pyrene labeling pyrene dimers. This emission, with vibronic peaks around 380, with a pyrene derivative was described before.18 The molecular 400, and 420 nm, has been observed before in doped silica structure of the final polymer is shown in Chart 1.
glasses,21 sol-gel systems,22,23 and Langmuir-Boldgett films.24 The two polymer chains (PS11Py and PS02Py) were char- Figure 1B shows that, in addition to the monomer, the excimer and dimer emission bands persist for the whole temperature pyrene content established by UV-vis absorption in THF using range studied (between 7 and 65 °C) and that the relative amount of excimer to monomer increases with temperature. All spectra compound. The polystyrene chains differ in the degree of at a given temperature remained invariant with time over several labeling, the average number of pyrenes per chain being 11 and 0.2 for PS11Py and PS02Py, respectively. 18 Figure 2 shows the excitation spectra of the PS11Py solution Sample Preparation. Three solutions of PS11Py were
at 65 °C, recorded at the emission wavelengths of the pyrene prepared in cyclohexane with pyrene concentrations of 10-7, 10-6, and 10-5 M (corresponding to polymer contents of 0.0001, excimers (referred to as E*) cannot be formed by direct 0.001, and 0.01 wt %, respectively). A solution of PS02Py in excitation (their ground state is dissociative), the spectrum cyclohexane at 10-7 M in pyrene (corresponding to 0.006 wt recorded at 500 nm reflects the spectra of all absorbing species % in polymer) was also prepared. Cyclohexane (spectroscopic that produce excimers. The spectra recorded at the excimer (λem distilled under argon. Fluorescence measurements of the polymer overlap, revealing the presence of ground-state species in solutions were performed in quartz cells that were sealed after addition to the pyrene monomer that, once excited, produce being degassed with argon (saturated with the solvent) for 20 excimers. The existence of ground-state species can be estab- min. Samples were maintained in an oven for one night at 42 lished from the broadness of the 0-0 UV-vis absorption peak, °C before measurements to reach equilibrium.
quantified by the ratio between the absorbance at 344 nm and Coil-Globule Transition of Pyrene-Labeled Polystyrene J. Phys. Chem. B, Vol. 108, No. 32, 2004 12011
Figure 2. Excitation spectra of the PS11Py 0.0001 wt % solution in
cyclohexane at 65 °C recorded at λ
Figure 4. Fluorescence decay curves of the PS11Py 0.001 wt %
nm (s). The intensities of both spectra were normalized to 1 at the solution in cyclohexane at 40 °C, by excitation at λ ) 500 nm) were fitted by eqs 1 and 2, respectively, using a global globule transition temperatures of 32 °C (M ) polystyrene chains in cyclohexane7,27 and it is known that thecoil-globule transition temperature increases with molecularweight.28,29 Time-Resolved Fluorescence Decays. Figure 4 shows the
pyrene monomer and excimer fluorescence decay curves of a0.001 wt % PS11Py polymer solution in cyclohexane at 40 °Cupon excitation at λ The decays are complex and cannot be fitted by a sum (monomer) or a difference (excimer) of two exponentials. Thiscomplexity is observed for any type of polymer randomly Figure 3.
Temperature dependence of the excimer-to-monomer labeled with pyrene and has two main causes. The first is the fluorescence intensity ratio IE(500 nm)/IM(376 nm) by excitation at λexc strong dependency of the excimer formation rate constant on 330 nm. The lines are given to guide the eyes.
the chain length between two pyrenes.30,31 The random attach- the nearest valley.25 A ratio of 3.0 indicates the absence of ment of pyrene moieties along the polymer backbone induces pyrene aggregates, whereas a lower value points to their a distribution of chain lengths between two pyrene labels, existence. The experimental values are around 2.9 and almost leading to a distribution of rate constants of excimer formation.32 independent of temperature, showing that the amount of ground- Consequently, the monomer and excimer decays are expected state species aside from the pyrene monomer is small and does to be represented by an infinite sum of exponentials, instead of not change significantly with temperature. Therefore, the the biexponential behavior predicted by the Birks’ scheme in fluorescence from the dimer in the 380-420 nm spectral region the case of a single rate constant of excimer formation. To (cf. Figure 1A,B) and from the excimer, should result mainly account for the distribution of rate constants for excimer from excited-state processes occurring upon excitation of formation, Duhamel and co-workers developed the blob model.18 Within the framework of this model, a blob is defined as the Figure 3 shows the variation of the excimer-to-monomer volume probed by an excited pyrene during its lifetime. In the fluorescence intensity ratio, IE/IM, as a function of temperature, formulation of the model, the parameters 〈n〉, kdiff, and ke[blob], which refer to the average number of pyrene groups per blob, It is well-known that, at low temperatures, the dissociation the rate constant of excimer formation inside a blob containing rate of the pyrene excimer is negligible when compared to its one excited pyrene and one ground-state pyrene only, and the intrinsic decay and the IE/IM ratio increases with temperature.
rate at which pyrene groups exchange between blobs, respec- In contrast, at high temperatures, when pyrene excimer dis- tively, were defined. The validity and applicability of the blob sociation predominates over the intrinsic deactivation, IE/IM model have been demonstrated for various polymers randomly decreases with temperature. The transition temperature between labeled with pyrene during the past several years.17,18,33,34 the two regions for pyrene is usually around 50 °C.26 Figure 3 The second cause for the complicated behavior of the shows that IE/IM increases with temperature below ∼60 °C, as fluorescence decays of these polymers resides in the randomness predicted for the low-temperature regime. The break in the IE/ of the labeling procedure. Previous studies have shown that four IM plot at 25 °C suggests a change in the conformation of the pyrene species should be considered when dealing with such polystyrene chains that influences the rate of the kinetic processes. A similar transition was detected for PDMA in represent electronically excited pyrenes that form excimers via methanol at 45 °C,17 despite its less clear assignment, because diffusion, that are too isolated to form excimers and fluoresce both the conformation transition and the pyrene kinetic transition with the lifetime τM, that are close to a neighboring pyrene and occur more or less at the same temperature. The break at 25 °C form an excimer instantaneously upon direct excitation (pre- is attributed to the coil-globule transition temperature of formed excimers), and that are close to a neighboring pyrene polystyrene in cyclohexane. This value is reasonable as coil- but do not have the proper geometry to form an excimer and 12012 J. Phys. Chem. B, Vol. 108, No. 32, 2004
form a loose long-lived dimer (preformed dimer) upon absorp- the UV-vis absorption spectra), 〈n tion of a photon, respectively.34-38 The species E0* and D*emit with intrinsic lifetimes of τE and τD, respectively.
This comprehensive approach is unable to handle the monomer decays of PS11Py in cyclohexane, because of the where fdiff is the fraction of pyrenes that form excimers via presence at early times of a short-lived component. The excited pyrene monomer undergoes a rapid quenching (cf. Figure 4A)with a quenching rate constant of about 3 × 108 s-1. Because The monomer decays of the PS11Py solution in cyclohexane no short, 1/(3 × 10-8 s-1), ∼3 ns-rise-time component is found (0.001 wt %) were well fitted by eq 1 over the entire temperature in the excimer decays, the rapid quenching of the pyrene range, after convolution with the instrumental response function monomer does not produce an emissive excimer. Probably, this ( 2 smaller than 1.3). Although the overall features of the process originates from pyrene pairs that do not adopt the proper monomer decays were not altered with temperature (all mono- geometry to form an excimer and form an emissive dimer once mer decays exhibited a strong quenching at the early times a pyrene is electronically excited whose structured emission followed by a smooth multiexponential decay at the longer overlaps the pyrene monomer emission (cf. Figure 1). Neverthe- times), a short decay component did appear in the excimer less, the possibility that this process creates a nonemissive decays for temperatures below 30 °C, i.e., for temperatures excimer (dark species), as was suggested before, cannot be below the coil-globule transition temperature. Such a short discarded.39 To handle this process, a third monomer species, decay component has already been observed in excimer decays Py , was introduced that represents those pyrene monomers for other polymeric systems where pyrene aggregates are that are quenched on a fast time scale with a quenching rate formed.15 This observation supports the assignment of the 25 °C breakpoint of Figure 3 to the coil-globule transition of The monomer and excimer decays were fitted globally with PS11Py in cyclohexane, because the more compact conforma- tion of the polymer globule is expected to increase the localpyrene concentration, which, in turn, favors the formation of pyrene aggregates. Although the presence of pyrene aggregates certainly complicates the analysis of the excimer decays, it should not affect the monomer decays, if one assumes that the aggregates do not dissociate during their short decay time.
However, the presence of the short decay component in the excimer decays prevented the use of eq 2 to fits the excimer decay acquired at temperature below 30 °C. Nevertheless, the fluorescence decays of the monomer and excimer were very well fitted from 30 to 50 °C using the global analysis with eqs 1 and 2, respectively. The parameters 〈n〉, kdiff, and ke[blob] were kept common to eqs 1 and 2 while the global analysis wasperformed. The lifetime of the isolated pyrenes (τM) was fixed + A + iA )t]+([E0*] + to the value obtained from the decay of a dilute solution of PS02Py in cyclohexane at the same temperature. The qualityof the fits was good ( 2 < 1.3) and was judged by visualinspections of the distributions of the residuals and the auto- correlation of the residuals. The fractions were obtained from the fit of the monomer decay, whereas thefractions Because a substantial fraction of the pyrene monomers form pairs or aggregates, the distribution of pyrenes inside the polymer coil is not random. As a result, the parameter 〈n〉 must Pydiff in eqs 3a and 3b, where 〈nPydiff represents the average number of quencher species that undergo dynamic excimer formation with the rate constant k the amount of ground-state dimers is negligible (according to Coil-Globule Transition of Pyrene-Labeled Polystyrene J. Phys. Chem. B, Vol. 108, No. 32, 2004 12013
were obtained from the fit of the excimer decays.
The parameters obtained from the fits are listed in Table 1.
Above 30 °C, where the global analysis was carried out,excellent fits were obtained. The results indicate that there isvirtually no difference whether the fits are performed on themonomer decay alone or by the global analysis of the monomerand excimer decays. This can be visualized more easily in Figure5.
The fractions fMQ, fMdiff, fMfree, fEdiff, fEE, and fED obtained by the global analysis can be combined to determine the fractionsof ground-state pyrenes fQ, fdiff, ffree, fE, and fD present under Figure 5. Parameters recovered from the fit of the pyrene monomer
and excimer decays (eqs 1 and 2) with the FBM analysis as a function electronic excitation. Within experimental error, the fractions of temperature for the PS11Py 0.001 wt % solution in cyclohexane: fQ, fdiff, ffree, fE, and fD are constant and equal 0.42 ( 0.02, 0.45 (A) rate constant for excimer formation (k 0.02, 0.04 ( 0.01, 0.09 ( 0.01, and 0.01 ( 0.01, respectively.
of temperature and viscosity, (B) product of the rate constant for pyrenes The strongest contributions to the decays appear to be that of exchange between blobs by the concentration of blobs (ke[blob]), (C) the pyrenes being quenched with a rate constant k sum of the reciprocal pyrene intrinsic lifetime with the quasi-static (3.1 ( 0.3) × 108 s-1 and that of pyrene monomers forming quenching rate constant of pyrene in pairs (1/τM number of pyrenes per blob that can form excimers by diffusion excimers via diffusion. One can also note that fdiff (0.45 ( 0.02) 〉).The filled symbols refer to values obtained from the analysis obtained from the global analysis of the pyrene monomer and of the pyrene monomer decay (eq 1), and the open symbols are for the excimer between 30 and 50 °C is very close to fMdiff (0.50 ( global analysis of the pyrene monomer and excimer decays (eqs 1 and 0.02) obtained from the analysis of the monomer decays with eq 1 over the same temperature range. This is because thefractions fE and fD of the preformed excimer and dimer species τE, was found to increase smoothly from 54 to 68 ns with represent a small fraction of all other pyrene species (f ) decreasing temperature. The values and range of these excimer 0.01 ( 0.01). Consequently, fMdiff will be used lifetimes are reasonable for pyrene20 and have been found for as a substitute for fdiff for temperatures at which the global Figure 5 shows the variation of the kinetic parameters kdiff, The good fits obtained from the global analysis of the pyrene Pydiff , ke[blob], and 1/τM monomer and excimer decays with eqs 1 and 2 confirm that with eqs 3 using the parameters of the fit. Both rate constants the rapid quenching of pyrene does not give emissive excimers for pyrene exchange between blobs, ke[blob], and the sum 1/τM because the fast decay component with reciprocal lifetime 1/τ kQS are practically invariant with temperature (cf. Figure + kQ used in eq 1 for the monomer decay analysis has no 5B,C). The mean number of quencher species per blob, 〈n equivalent in eq 2 for the excimer. The fractions fMQ, fMdiff, and decreases with decreasing temperature (see Figure 5D), with a fMfree shown in Table 1, where the subscript M indicates that diffuse break at the coil-globule transition temperature that these fractions were derived from the analysis of the monomer reflects a decrease of the number of blobs. The diffusion rate decays, remained constant over the entire temperature range and constant corrected for changes in temperature and solvent equal 0.46 ( 0.02, 0.47 ( 0.04, and 0.07 ( 0.03.
viscosity (kdiffη/T) is partially constant from 50 to 30 °C, The recovered fraction of the loose long-lived dimers (f ) increasing rapidly until 12 °C. The increase observed below 0.01 ( 0.01) is too small to support their presence in the current 30 °C reflects, according to eq 8, a reduction of the blob system. This long decay can be simply caused by the fitting procedure or by a very small contamination of the excimer Lee and Duhamel40 suggested that the diffusion rate constant, decays by the monomer emission. The lifetime of the excimer, kdiff, for two pyrenes attached to the backbone of a short polymer TABLE 1: Parameters retrieved from the FBM Analysis of the Fluorescence Decays of the PS11Py 0.001 wt % Solution in

a Results in parentheses indicate that they were obtained by using eq 1 to fit the monomer decay only. Results not in parentheses were obtained by fitting the monomer and excimer decays globally with eqs 1 and 2 12014 J. Phys. Chem. B, Vol. 108, No. 32, 2004
where kB is the Boltzman constant, T is the temperature, η isthe viscosity, Vcoil is the volume of the polymer coil, Rc is theencounter radius between the two pyrenes, and σ is the reactionradius. The expression for kdiff would be more complex if chaindynamics was considered.41 Assuming that the diffusion insidethe blob can be described by the same equation with R ) Vblob, an expression for the volume of the blob can Figure 6. Plot of the contraction factors determined by fluorescence
versus temperature: (A) PS11Py, 0.001 wt % solution; (B) PS11Py,0.01 wt % solution, where aggregation occurs simultaneously with The volume of the polymer coil is given by V globule formation. The contraction factors were obtained from the h , where Nh represents the average number of blobs per chain.
analysis of the pyrene monomer (filled symbols) and the global analysis This parameter is given by the ratio of the number of pyrenes of the monomer and excimer decays (open symbols). The lines areprovided to guide the eyes.
j) to the average number of pyrenes in a blob (〈n〉).
The chain radius can then be determined by17 using the values found in Table 1 and 〈n〉 calculated by eq 4.
The average number of pyrenes per chain, n determined by UV-vis absorption measurements. The viscosi-ties of cyclohexane (mPa s) at different temperatures werecalculated from an extrapolation performed with the viscosityvalues provided in the CRC handbook [η ) exp(1439/T -4.94)].42 The value of the fluorescence radius at the θ tem-perature (34.5 °C),43 R the gyration radius, ) 10.0 ( 0.1 nm (R Figure 7. Variation of the scaled expansion factor determined from
1/2, with the scaled reduced temperature, )44,45 and the hydrodynamic radius, R , for the PS11Py 0.001 wt % solution in cyclohexane (b). Plots 0.07 nm, calculated by ) 3/8π1/2.46 of gyration (9) and hydrodynamic (0) radii for other polystyrene- The reasonable agreement between radii is surprising owing to both the empirical derivation of eq 7 and the complication of having a nonrandom distribution of pyrenes inside the C, caused by the beginning of excimer dissociation, not considered in the decay curve analysis.
expected to be more accurate because they can benefit from a Figure 7 shows the universal plot of the scaled expansion cancellation of errors during the division of radii. Figure 6A factor (R3|τ|Mw ) as a function of the scaled reduced temper- ature (|τ|Mw ), where τ ) T/θ - 1. The data obtained from the fluorescence contraction factors (for the PS11Py 0.001 wt The trend shown in Figure 6A for the PS11Py 0.001 wt % % solution) fall on a straight line with unitary slope for |τ|Mw solution indicates that the globules contract no more than 20% 10 in the vicinity of the θ temperature. The figure shows with respect to the radius of the polymer coil under θ conditions.
also other values collected by B. Chu and co-workers12 for This contraction is much smaller than most of the published polystyrene-cyclohexane systems in the absence of aggregation.
values for polystyrene chains of similar molecular weight in values point toward distinct plateau values for the same solvent.7,8,47 Some authors have, however, reported each average radius as found before for the hydrodynamic and contraction factors similar to ours,12-14 with even longer chains.
They suggested that the higher degrees of contraction were 4. Conclusions
caused by the presence of small aggregates of higher densities,as theoretically predicted by Raos and Allegra.48 The results The blob model, modified to consider the presence of pyrene shown in Figure 6B are in agreement with these predictions pairs, was successfully applied to fit the pyrene monomer and because a contraction of ∼40% was observed for the most excimer decays of a polystyrene chain (M concentrated solution, PS11Py 0.01 wt %, where aggregates randomly labeled with pyrene in cyclohexane. The radii of the were formed (detected by the time variation of the fluorescence polystyrene coil at temperatures below and above the θ spectra at the lowest temperatures).
temperature were calculated from the fitted parameters of the Above the θ temperature, R seems to be constant or to pyrene monomer decays. The contraction coefficients follow decrease slightly. The unexpected decrease is caused by the the master curve of R3|τ|M 1/2 uncertainty in the radius evaluations for temperatures above 45 aggregation, which seems to tend to a plateau with a lower value Coil-Globule Transition of Pyrene-Labeled Polystyrene J. Phys. Chem. B, Vol. 108, No. 32, 2004 12015
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Acknowledgment. This work was supported by the “Fun-
(28) Ivanov, V. A.; Paul, W.; Binder, K. J. Chem. Phys. 1998, 13, 109.
dac¸a˜o para a Cieˆncia e a Tecnologia” (FCT) under Project (29) Doye, J. P. K.; Sear, R.; Frenkel, D. J. Chem. Phys. 1998, 108,
POCTI/QUI/33866/2000. S.P. acknowledges FCT for the Ph.D.
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I am but a story, unfinished, I go on as long as there are storytellers, but some parts are finished, some parts of greater tales need to be set down. But know this: any tale can be amended so take from this only that it is part of a greater story, one that can never be finished and so never be told in its entirety. In the hour of darkest need, when even the Unconquered Sun was made ineffective

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Kardiologie, UniversitätsSpital Zürich Publikationen 2004 Published Original Reviews Nitric oxide gene transfer inhibits biological features of bypass graft disease in the Tanner F.C., Largiadèr T., Greutert H., Yang Z., Lüscher T.F. J. Thorac. Cardiovasc. Surg. 127, 20-26, 2004. Oxidative stress-associated vascular aging is independent of the protein kinase Bachschmid M., v

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