J. Phys. Chem. 1993,97, 13708-13712
13708
A Blob Model To Study Polymer Chain Dynamics in Solution Jean Duhamel, Ahmad Yekta, and Mitchell A. Winnik’ Department of Chemistry and Erindale College, University of Toronto, Toronto, Canada M5S 1 A1
Tze Chi Jao, Munmaya K. Mishra, and Isaac D. Rubm Texaco R&D Department, P.O. Box 509, Beacon, New York 12508 Received: May 25, 1993”
Excimer formation was used as a tool to probe the dynamics in tetrahydrofuran solution of two ethylenepropylene copolymers labeled with pyrene. The excimer kinetics were analyzed by a new model. This model considers that the polymer chain can be divided into equivalent blobs. The fluorescent probe is assumed to be distributed randomly among the blobs. As a consequence, the occupancy probability of chromophores inside a blob follows a Poisson distribution. We can describe the kinetics of the system in terms of the theory of excimer formation in micellar systems. In this way we can obtain the blob size and the magnitude of the first-order rate constant for excimer formation in the blob. The model is applicable to polydisperse polymer systems and provides information by shifting the focus of attention from chain-length-dependent to blob-size-dependent behavior.
SCHEME I
Introduction Fluorescence-quenchingexperiments often provide a useful means of studying aspects of the conformation and dynamics of polymers in dilute solution.Iv2 Theseexperiments take many forms, but all require polymers to which appropriate fluorescentgroups and quencher groups are attached. A specific case of interest to us involves polymers containing pyrene (Py) substituents. Polymers which contain more than one Py group undergo intramolecular excimer formation in dilute solution. When the Py groups are located exclusively at the chain ends, interpretation of the excimer formation kinetics in terms of coil dimensions and endto-end cyclization rate is relatively ~traightforward.~ These experiments can normally be interpreted in terms of the two-stateBirks’ mode14shownin Scheme I. The key to the success of this model is that the excimer formation rate can be described in terms of a singlerate constant, kl . The ‘monomer” and excimer decay with the chain-length-independentrates of 1/ r M and 1 / r ~ , respectively, and the excimer dissociationrate to re-form excited monomer is described by k-1. This step has the highest activation energy, and in many systems, it becomes important only at elevated temperatures. Because of the relative simplicityof the model for dilute solutions of end-labeled polymers, one can obtain values for all the rate constants. One would often like to obtain similar information from polymers randomly labeled with Py groups. Here the fluorescence decay profiles one measures to obtain kinetic information are particularly difficult to analyze. Simple two-state models fail because of the distribution of contour distances separating Py groups along the polymer backbone. The distribution arises both because of positional heterogeneity and because of chain-length polydispersity. Because kl is so sensitive to the chain length separating each pair of chromophores, one consequence of positional heterogeneity is the distribution of kl values in these systems. Here we present a novel method of analyzing fluorescence decay traces obtained in studies of these kinds of polymers. The method is developed in analogy with micelle-quenching kineticssP6 and conceptualizesquenchingoccurring within restricted regions of space which contain portions of the polymer chain. These ‘blobs” are defined in such a way that they contain one or more
’
* Abstract
published in Advance ACS Abstracts, November 1, 1993.
M
4 Py groups, and the length scale characterizing the blob sizes evolves naturally from the data analysis. This methodology is applied to two samples of ethylenepropylene copolymers (PEP) randomly labeled with Py. The PEP is functionalizedby reaction with maleic anhydride to yield polymers containing a small fraction of succinic anhydride groups.*~9These in turn are reacted with 4 4 1-pyreny1)butanoyl hydrazide to form the corresponding succinimide, as shown in Scheme 11. We have prepared two labeled polymers. Polymer 1 comprises 60 wt % ethylene and 40 wt % propylene and contains 7.79 X mol of Py/g. In polymer 2, the monomer weight ratio is 80:20 and the Py content is 1.51 X 10-4 mol/g. Following the Experimental Section, we develop the theory of the fluorescence-quenchingblob model and then examine its applicability to the case of intramolecular excimer formation in polymers 1 and 2 in dilute solution. Experimental Seetion
Instrumentation. UV spectra were recorded on a HewlettPackard Model 8451A diode array instrument. GPC experiments were carried out on a Varian 5000 liquid chromatograph with two detectors: refractive index (RI), a Waters R401 differential refractometer; fluorescence, a Kratos FS 970 LC fluorometer (bX344 nm, b, >360 nm). Synthesii pad Labeling. The ethylene propylene (EP) copolymer was prepared with a soluble Ziegler-Natta catalyst composed of ethylaluminum sesquichloride and vanadium oxytrichloride. The methods and procedures for characterizing the copolymer have already been de~cribed.~ Maleic anhydride was next grafted onto the EP backbone, yielding a product (EPSA) with about 0.8% (w/w) succinic anhydride groups randomly distributed along the chain. The reaction was carried out in a pressure reactor for 3 h under an inert environment (200 lb of
0022-3654/93/2097-13708$04.00/0 Q 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13709
Polymer Chain Dynamics in Solution
SCHEME 11 0
'
II
CHZ - (CH2)z- C - NH - NHz
+ @
'\
1 .
t
1 -Pyrenebutyrylhydrazine
EPSA
I
xEPI
-~O""""'~""""~'~'"""'~""""~~ 0 10 20
30
40
Rstontion Tins (Mine.)
Figure 1. Size exclusion chromatography trace for polymer 1: flow rate, 0.8 mL/mn, injected volume, 100 pL; fluorescence detector, bX 344 nm, L,,, >360nm; (- -) fluorescencedetector; (-) refractiveindexdetcctor.
-
NH
I c=o I
nitrogen pressure) at 155 'C in hexane or mineral lubricating oil solutioncontaining about 30 wt % of the EP copolymer. Dicumyl peroxide (1 wt % based on polymer) was used as the initiator. The maleic anhydride amount charged to the reactor was about 3% based on polymer. The polymer was purified by repeated precipitations from heptane by methanol or acetone and freed from unreacted maleic anhydride, and the level of grafting was obtained from FTIR by analyzing and comparing the bands at 1785 and 720 cm-I. The fluorescence probe was incorporated by reacting the pendant succinic anhydride groups with [4-(1-pyrenyl)butyryl]hydrazine (Molecular Probes, Inc.; cf. Scheme 11). The reaction was carried out in a resin kettle fitted with a mechanical stirrer, a thermometer, and nitrogen inlet and outlet ports. The required amount of EP copolymer with 0.8 wt % (w/w) succinicanhydride groups was dissolved in solvent neutral oil at 160 OC with mechanical stirring under a nitrogen atmosphere to yield about a 15 wt % polymer solution. After the polymer had dissolved, mixing was continued for an additional 1 h at 160 OC. A slight molar excess of [4-(1-pyrenyl)butyryl]hydrazine, based on the molar amount of pendant succinicanhydride groups, was added, and the system was heated for 3 h at 160 OC. The pyrenefunctionalized polymer was isolated by precipitating the oil solution into methanol. The polymer was then dissolved in heptane. The pyrene-labeledEP (PEP) was purified by repeated precipitations from heptane by methanol or acetone and dried in vacuum at 50 OC for 16 h (overnight). Two EP copolymerswere synthesizedand labeled with pyrene. Polymer 1contains 60 wt % of ethylene and 40 wt % of propylene. Polymer 2 contains 80 wt % of ethylene and 20 wt % of propylene. Sample Preparation and Molecular Weight Estimation. Polymers 1 and 2 were examined by GPC (solvent: tetrahydrofuran (THF)) using lo3-and 1@-AUltrastyragelcolumns in conjunction with tandem refractive index and fluorescencedetectors. In the low molecular weight range, the GPC trace exhibits, for both polymers 1 and 2, a small peak in the fluorescence signal, characteristic of the presence of pyrene derivatives not bound to the polymer (cf. Figure 1). We estimate that about 5% of the pyrene emission arises from free pyrene derivatives. In order to circumvent this problem, solutions of polymers 1 and 2 in THF were injected into the GPC; the main peak was collected, while
the low molecular weight portion was discarded. This ensured that all pyrene emission was from pyrene bound to the polymer chains. The molecular weights and polydispersities of polymers 1and 2 were estimated to be 40 000 and 2.6 and 95 000 and 2.3, respectively,from comparison with polystyrene standards in THF. Fluorescence Measurements. Polymer solutions were prepared in Spectrograde THF (Caledon) so that the absorbance at 344 nm was less than 0.06 to ensure only intramolecular excimer formation. UV spectra were recorded for each sample. Fluorescencespectra were recorded on a SPEX Fluorolog 2 12 spectrometer. Decay curves were obtained by the timecorrelated single-photon-counting(SPC) technique. The excitation source was a coaxial flash lamp (Edinburgh Instruments, Model 199F). The excitation wavelength was selected by a Jobin-Yvon Model H-20 monochromator, and that of the fluorescence, by a SPEX Minimate Model 1760 monochromator. The analysis of the excited monomer decay curves was performed with the mimic technique. Reference decay curveswere obtained from degassed solutionsof 2,5-diphenyloxazole (PPO) in cyclohexane( 7 = 1.33 ns) and were used for analysis of monomer decay curves. Each polymer solution was degassed by nitrogen bubbling. First, fluorescence decay profiles were measured by following the pyrene monomer fluorescenceat 375 nm (Lx344 nm). Then, steady-state fluorescence spectra were recorded using Lx344 nm. "ry
Excimer formation kinetics are analyzed here in terms of a compartmentalization model.1° In this model we arbitrarily subdividethe polymer chain into a sequenceof blobs of identical size. Each blob contains the same volume vb and the same mass of polymer mb. The fundamental assumptionof this data analysis is that excimer formation occurs only between pairs of Py within the same blob. This is the feature of the model which is similar to that used in analyzing excimer formation kinetics for pyrenes solubilized by aqueous surfactant micelles.5v6 To accommodate the assumption that processes within each blob are independent of neighboring blobs, the model is developed in such a way that the blob size becomes smalleras the number of Py groups attached to the polymer increases. A picture of this blob model, with a particular Py distribution, is shown in Figure 2. By analogy with the blob model of de Gennes? where the blobs represent domains in which excluded-volume effects are prominent, the blob volume is related to the mass of polymer contained
Duhamel et al.
13710 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
on a time scale sufficiently short that the condition of the blobs being independent holds. In practical terms, this means that if a blob contains one M* plus i = 1 ground-state chromophores at measurement timer, it contained i chromophoresat the instant of excitation and will continue to contain i chromophores until the excitation energy has been dissipated. We note here that these considerations are identical to those which describe the kinetics of excimer formation in micellar s y ~ t e m s . ~This . ~ type of fluorescence-quenching in these systems is well documented. For pyrene excimer formation in micellar systems, one commonly assumes that k-1 in Scheme I is negligible. One can then derive eq 8 from the above mechanism to describe
mb
W Depictionoftheblobmodelemployedtodescribe thedistribution of pyrcne groups along the polymer chain. -2.
within it through the expression
where a is the size of a monomer, mmonis its molecular mass, and Y takes the values 0.5 in a @-solventand 0.6 in a good solvent for the polymer.7J1 The strength of a polymer study based upon the blob concept is that the object of interest is shifted from the polymer chain to the polymer blob. In this way, at least for fluorescence-quenching processes, the influence of molecular weight polydispersity is removed from the problem. In a randomly labeled polymer, the chromophores are distributed randomly among the blobs. Under these circumstances, chromophore occupancy inside a blob follows a Poisson distribution. If (n) is the average number of chromophores per blob, the probability Pr(i) of having i chromophores in a blob is described by ( )
Pr(i) = i! Upon exposure to a weak pulse of light, a minute fraction of the chromophores M are excited. The probability of forming two or more M *chromophores within a single blob is negligible. If one or several ground-state chromophores are present in a blob containing an M*, then a number of reaction pathways are possible. The reaction mechanism is shown in eqs 3-7. The rate
the fluorescence decay fM(t) of the excited chromophore? In micelles, (n) describes the average number of pyrenes per micelle. Here, by analogy, ( n ) describes the mean number of pyrenes per blob. Fits of monomer fluorescence decays of the excited monomer give ( n ) and kl, which is the average excimer formation rate constant in a blob containing M * and one ground-state M. A common description of the first-order rate constant for intramolecular reaction of two species attached to a polymer, or otherwise constrained to a restricted volume, is given in terms of the product of a hypothetical second-order rate constant times the local concentration of M groups. In a polymer, coil expansion leads to a dilution of M groups, and coil contraction, to an increase in local concentration. In terms of our blob model, kl is inversely proportional to the blob volume. This blob volume, in turn, is related to the mass of polymer within the blob by eq 1. Knowing ( n ) , we can calculate values useful for describing properties of the polymer in solution. We begin by defining the following parameters:
Ni number of blobs in chain i xi fraction of chain i in the sample mb mass of polymer within each blob M, number-average molecular weight of the polymer We first need to know the chromophore content of the polymer. This can be obtained from UV-vis measurements on solutions of carefully weighed samples of polymer, coupled with knowledge of the molar extinction coefficient of the chromophore. In this way we obtain A, the concentration of chromophores per gram of polymer. From the definition of X A=
--
CxiNj(n) CxjNj(n) Mn
(3)
M+hv,,-M*
M*
+ (i - l ) M
-
(i- I ) k l
E* + (i - 2)M
-. k-t
E*
M*
+M
i = 2, 3,
... ( 5 )
cXiNimb
(n) =-
(9)
mb
The numerator ( n ) on the far right-hand side of eq 9 is obtained from fluorescence decay measurements. Thus mb can be calculated from A. From the definition of mb,we see that 1/X represents the average polymer mass between two pyrene molecules. At this stage of the discussion, we obtain a relationshipbetween the excimer formation rate constant and the polymer mass within a blob
(6)
of excimer formation is taken to be linearly dependent on the number of unexcited M chromophores in each blob. This is written explicitly in eq 5 . We assume that the processes of eqs 3-7 occur
An expression equivalentto eq 10 holds for end-to-end cyclization of polymers. In such systems, m bis replaced by M,,and kl is the end-teendcyclization ratecon~tant.~ Note that thisapproach is independent of polymer chain polydispersity and that the polymer mass of interest, mb,is determined in a very straightforward manner.
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13711
Polymer Chain Dynamics in Solution
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1 m e (ns) Fipare3. Fluorescence decay profile of 4-( 1-pyreny1)butanoyl hydrazide in THF (Lx344 nm, Lm375 nm). 8.3140+067
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Figure 5. Fluorescence decay profile of polymer 1 in THF (Lx 344 nm, Lm375 nm).
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Figure 4. Fluorescence spectrum of polymer 1 in dilute solution in THF
Figure 6. Fluorescence decay profile of polymer 2 in THF (Lx 344 nm, bm 375 nm).
Results and Discussion
TABLE I: Lifetimes and Preexponential Factors Recovered from a Three-Exponential Fit of the Fluorescence Decays of the Monomer and Excimer for Polymers 1 and 2 in THF
(LX344 nm).
Spectroscopy. Pyrenylbutanoyl hydrazide, from which the labeled polymer is prepared, exhibits a typical pyrene emission spectrum (not shown) in dilute solution in THF and has as an exponential decay time of 205 ns; cf. Figure 3. This lifetime is somewhat longer than the unquenched lifetime of pyrene groups attached to polymers 1and 2 (1 85 ns; see below). The difference may be due to the succinimide group through which the Py is attached to the polymers or by some weak intrinsic quenching by the polymer itself. The fluorescence spectrum of polymer 1 in THF is shown in Figure 4. One sees a classic monomer-plus-excimer spectrum from a pyrene-labeled polymer. The amount of excimer emission is substantial, but significantly less than we observe for the polymer in hydrocarbonsolvents such as methylcyclohexane(MCH). One complicating feature of the spectroscopyof polymers 1 and 2 is the evidence for 'preformed"excimer.I2 In MCH, the excitation spectrum of the excimer is red-shifted relative to that of the monomer by ca. 2 nm, clear evidence for preassociation of Py groups prior to excitation. Proximity of the pyrenes may be promoted by hydrogen bonding between the hydrazide groups through which the chromophores are attached to the polymer. In THF, the excitation spectra are very similar, but there is still some indicationof a small amount of preassociatedor rapidly associating pyrenes. Careful analysis of the growth and decay profile of the excimer suggeststhat some excimer is formed faster than we can resolve (1 ns) with our instrumentation; cf. Table I. The excimer shows a rapid rise, followed by a much slower decay with a lifetime (60 ns) typical of pyrene excimers. In addition, we observe a very weak component with a lifetime (185
71 (ns) ~~~~
~
polymer 1 monomer polymer 1 excimer polymer 2 monomer polymer 2 excimer
AI 15.0 41.0% 15.0 -0.830 12.0 46.9% 12.0 -0.766
(ns) A2 73.1 29.9% 72.1 1 .ooo 61.1 28.3% 68.1 1 .ooo
72
TM
(ns) AM 191 29.196 190 0.023 181 24.8% 190 0.019
ns) identical to that of the long-time tail of the monomer emission, which we attribute to monomer emission detected at X >SO0 nm. There is no indicationof excimer dissociation making a significant contribution to our decay profiles. In analyzing monomer decay profiles in terms of the theory developed above, we will assume that kl= 0. The monomer decays for polymers 1 and 2 (cf. Figures 5 and 6) are nonexponential. When we fit these decays to sums of exponentials, the only consistent feature for their degassed solutions in THF is the presence of a long component with a lifetime of 185 ns and a weighting factor of about 25% (cf. Table I). Becauseof the way in which we purify and analyzeour samples, this long-lived pyrene emission must originate from parts of the polymer chain with a low pyrene content. During their lifetime, these excited pyrenes cannot diffuse sufficiently far to encounter another ground-state pyrene. They represent a subset of the population of pyrene groups that decay with their unquenched lifetime. This is the type of behavior that characterizes pyrene
Duhamel et al.
13712 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
TABLE II: Values of ( n ) , % kl, and k and 2 wlvmer
(n)
mb
polymer 1
0.86
polymer 2
0.99
1 1 000 256 units 6700 169 units
kl (ns-l) 0.0128 0.0134
l for~Polymers ~ 1 klmb.”
(ns-1)
278 137
in surfactant micelles,5?6where a long-lived emission arises from singly occupied micelles. Kinetic Analysis. It was the presence of a significant unquenched pyrene contribution to our measured decay profiles that suggested to us the possibility of developing a micelle-type kinetic model for this system. Therefore we fit our decay profiles toeq 8. For polymer 1, we recovered a x* of 1.71;and for polymer 2, a x* of 1.47. While these values seem high, we note that the weighted residuals and the autocorrelation function of the residuals in each analysis are reasonable. Examples are presented in Figures 3 and 4. The fitting procedure recovers three parameters: T M , the unquenched lifetime of pyrene groups located inside singly occupied blobs, (n),the average number of pyrene mulecules per blob, and kl, the average excimer formation rate inside a blob containing one excited pyrene and one ground-state pyrene only. Using eq 8, we recover T M values of ca. 180ns. This value is close to those obtained when the decays are fitted with a sum of three exponentials. Values for (n) and kl are listed in Table 11. We haveshown ineq9 that the blob size (mb)can beobtained through combining the fluorescence decay analysis with knowledge of the pyrene content of the polymer. UV absorption measurements indicate pyrene contents of 7.79 X 10-5 and 1.51 X 10-4 mol/g, respectively, for polymers 1 and 2. The calculated mb values are presented in Table 11. Inside a blob of mass mb occupied by two pyrenes, the excimer formation rate constant is kl. Qualitatively, the chain portion within a blob can be regarded as similar to a polymer chain of length mb/mmonlabeled a t both ends with pyrene. Under these circumstances, our recovered kl values should be similar in magnitude to the end-to-end cyclization rate constants for similar polymer chains of similar length in similar solvents. Only limited data are available,2JJ3J4 and none for PEP. We do know from previous work that polystyrene of M , = 4500 has an end-to-end cyclization rate constant of 0.015 ns-1 in acetone.15 Most of the data available in the literature show values for k l around 0.01 ns-I for polymer chains with degrees of polymerization of ca. 70-90. We take this to indicate that the magnitudes of our k , values are reasonable. In the context of our model, we expect the product klmb3Yto be a measure of the dynamic flexibility of the polymers. If the proportionality constants of eq 10 are similar for polymers 1 and 2, we would conclude that polymer 1 is significantly more flexible than polymer 2.
Conclusions We propose a new model for studying the kinetics of excimer formation in polymers labeled with excimer-forming chromophores. The basic assumptions of this blob model are that the labeling occurs randomly on the polymer backbone and that excimer dissociation to re-form excited monomer can be.neglected. The major advantage of this model is that it allows one to analyze nonexponential monomer decay profiles to obtain quantitative information about the polymer conformation and dynamics in dilute solution. One obtains three parameters from this analysis, the blob size (Mb),the mean number of chromophores per blob ((n )), and the first-order rate constant ( k l )for excimer formation in a blob containing M * and one M. Like all blob models, it shifts the focus of attention from chain length to blob size. In this way, molecular weight polydispersity no longer poses a problem in the data analysis. This blob model was applied to the study of excimer formation kinetics for two EP copolymers labeled with pyrene. Fits of the fluorescence decays with eq 8 are reasonable. We observe that a change in the ethylene content from 60 wt % (polymer 1) to 80 wt % (polymer 2) decreases the flexibility of the EPcopolymer as reflected in the magnitude of kl. Acknowledgment. The authors thank the NSERC of Canada and the Ontario Centre for Materials Research for financial support. References and Notes (1) (a) Guillet, J. E., Polymer Photochemistry and Photophysics; Cambridge University Press: Cambridge, U.K., 1985. (b) Winnik, M. A., Ed. Phorophysical and Photochemical Tools in Polymer Science; NATO AS1 C182; Reidel: Dordrecht, Holland, 1986. (2) (a) Winnik, M. A. Acc. Chem. Res. 1985, 18, 73. (b) Perico, A.; Cuniberti, C. J . Polym.Sci., Polym. Phys. Ed. 1977,15, 1435. (c) Cuniberti, C.; Perico, A. Prog. Polym. Sci. 1984, 10, 271. (3) Winnik, M. A.; Redpath, A. E. C.; Paton, K.; Danhelka, J. Polymer 1984, 25, 91. (4) Birks, J. B. Phorophysics ofAromaric Molecules; Wiley: New York, 1971. (5) Infelta, P. P.; Gratzel, M. J . Chem. Phys. 1979, 70, 179. (6) Yekta,A.;Aikawa, M.;Turro,N. J. Chem. Phys.Lett. 1979,63,543. (7) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, and London, 1979. (8) Jao, T. C.; Mishra, M. K.; Rubin, I. D. Macro. Rep. 1992,A29,283. (9) Sen,A.; Rubin, I. D. Macromolecules 1989, 23, 2519. (10) Klafter, J.; Drake, J . M. Molecular Dynamics in Restricted Geometries; Wiley: New York, 1989. (1 1) Flory, P. J. Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (12) Winnik, F. M. Chem. Reu. 1993, 93, 587. (13) (a) Horie, K.; Schnabel, W.; Mita, I.; Ushiki, M. Macromolecules 1981, 14, 1422. (b) Ushiki, H.; Horie, K.; Okamoto, A.; Mita, I. Polym. J . 1980, 12, 35. (c) Duhamel, J.; Khaykin, Y.; Hu, Y. 2.;Winnik, M. A.; Boileau, S.; Mhhin, F., Eur. Polym. J., in press. (14) Winnik, M. A,, In Cyclic Polymers; Semlyen, A. J., Ed.; Elsevier Applied Sciences: London, 1986. (15) Martinho, J. M. G.; Winnik, M. A. Macromolecules 1986, 19, 2281.
