Photophysical Studies of Heterogeneous Polymers: The Effect of

9070

J. Phys. Chem. B 1999, 103, 9070-9079

ARTICLES Photophysical Studies of Heterogeneous Polymers: The Effect of Crystallinity on the Distribution and Mobility of Probe Molecules in Partially Crystalline Polyethylene Michael Biscoglio Department of Chemistry and Biochemistry, UniVersity of Notre Dame, Notre Dame, Indiana 46556 ReceiVed: October 8, 1998; In Final Form: March 9, 1999

Photophysical methods are used to study the effect of crystallinity on the distribution and mobility of probe molecules in well-characterized polymer films. A combination of steady-state and time-resolved methods indicate that probe molecules are excluded from lamella-like crystalline zones in the polymer systems. This effect tends to concentrate the probes into the amorphous zones that exist between crystallites. Using the pyrene-perylene donor acceptor pair as a “molecular ruler”, it is shown by Forster analysis that the amorphous zones form a network structure throughout the polymer film. Mobility within this region is greatly reduced from that in solution and is very size selective, as indicated by the quenching rate constants of the pyrene triplet state by oxygen, azulene, and ferrocene. A determination of the oxygen concentration, by comparing the permeability to diffusibility within the film, indicates that crystalline regions are impermeable to gas molecules. The mobility of the guest molecule in the film is orders of magnitude greater at temperatures above the glass transition temperature Tg, compared to the mobility below Tg. Simple calculations using free volume theory can account for the observed rate data.

Introduction The energy and charge transport properties of polymeric solids offer a unique potential for applications in photosynthetic devices, electrophotographic materials, and organic semiconductors.1-4 To support these areas, many photophysical and spectroscopic studies have been carried out to understand the observed chemistry and physics, in the context of what is already established in homogeneous solution.5-11 For the most part, work has been carried out in amorphous polymers, where the extension from homogeneous solution seems to be possible. The objective of this work is to make inroads into the photochemistry and photophysics of partially crystalline materials by means of optical studies in crystalline polymers. The polymer of choice is polyethylene (PE), due to its industrial interest and the availability of several well-characterized samples of varying crystallinity. First, it is pertinent to gain some picture of the nature and importance of the crystallinity in polyethylene. The structure of partially crystalline polyethylene has been described by numerous models, to account for the nature of its crystallinity and lattice imperfections.12-16 Under ideal conditions, large single crystals of polyethylene can be grown from dilute polymer solutions. These crystals show that the polymer chain folds back upon itself to form lamella crystals and the irregularities of folding or reentry of the chain into the crystal gives rise to amorphous material on the crystal surface.12,13 On the other hand, fast crystallization from a polymer melt results in overlap of neighboring chains, which may form crystal lamella, or lattice imperfections by chain entanglement. The * This work was done in conjunction with J. Kerry Thomas to whom correspondence may also be addressed (same address).

latter also gives rise to polymer chains which transverse between crystalline zones creating bulk rigidity, without the material being as brittle as a wax. Diffusion of small molecules occurs via the network of amorphous zones throughout the polymer and thus is highly dependent on the overall degree of crystallinity. The tight packing of the ordered or crystalline region excludes small guest molecules. However, these are generally considered to be located in the more disordered regions. Such a situation will affect radiation induced reactions of the guest molecules, due to the possibility of restricted motion of the guest molecules in the amorphous region. Excitation of the system with highenergy radiation will lead to energy loss in the crystalline and amorphous zones. The question then arises, how efficiently does the radiation induced event in the crystalline zone propagate to the amorphous region? Photophysical and photochemical probe studies where the events occur only in the amorphous regions could give a useful kinetic picture of radiation events in polyethylene. At this point, it is pertinent to draw attention to some of the existing photophysical studies in polymer systems. A variety of experimental methods for the measurement of permeability diffusion and solubility have been established for amorphous polymer systems.8,9,17-19 These include both direct measurements, using time lag20,21 and the measurement of weight increase,22 and indirect methods, using fluorescence9,23 and phosphorescence quenching.8,24,25 Some work reports on the use of photophysical probes to determine the morphology of heterogeneous polymers,10,11 but most information in this area has come from using a combination of microscopy and X-ray diffraction techniques. This work reports on the use of photophysical probes to

10.1021/jp9840228 CCC: $18.00 © 1999 American Chemical Society Published on Web 04/29/1999

Photophysical Studies of Heterogeneous Polymers determine the distribution and mobility of probe molecules in heterogeneous PE polymers and analogous amorphous polymer systems. A comparison of the PE data with corresponding data in amorphous polystyrene is useful, since the latter system is simpler with a homogeneous distribution of guest molecules. Standard methods such as C13 NMR, X-ray diffraction, and calorimetry are used to characterize PE branching of the polymer and its degree of crystallinity. Critical concentrations for excimer formation and singlet energy transfer from pyrene to perylene are used to demonstrate that guest probe molecules are restricted to the amorphous zones of the polymer. The interplay of the crystalline and amorphous regions also comes into play in various quenching studies. In particular, the quenching of excited triplet states by oxygen and other small molecules, such as azulene and ferrocene, is used to comment on the nature of simple reactions induced in the amorphous zones. The data from these studies will be of great use in future photochemical and radiolytic studies.26 Experimental Section Materials. Polyethylene Rx (Rigidex 80 linear, MW ) 80 K), Pn (BPE PN 220 branched, MW ) 100 K)27 were purified by soxolation with cyclohexane and subsequently analyzed for impurities by fluorescence and UV-vis spectroscopy. Amorphous polyethylene (Dow XUR C16) containing nonremovable UV absorbing end groups was washed with cyclohexane to remove plasticizers. Polystyrene (MW ) 280 K), poly(methyl methacrylate) (MW ) 28 K), and docosane (C22H46, 99%) were obtained from Aldrich and used as received. Pyrene (Aldrich, 99%) was purified by three passages down an activated silica gel column using cyclohexane as the eluant. Bromopyrene and perylene were recrystallized three times from methanol before final chromatographic separation. Ferrocene (98%), azulene (99%), cyclohexane (HPLC grade), hexadecane (99%), trichlorobenzene (99+%), and toluene-d8 (99+%) were used as received from Aldrich. Prepurified oxygen was used as received from the Mittler Co. Specific amounts of oxygen were added to the polymers from a reservoir on a vacuum system. The polymer samples were allowed to equilibrate at each oxygen pressure for 15 min before each measurement was taken. Sample Preparation. Probe molecules were incorporated into polymer films using two methods, i.e., by solution casting and by dissolving the probe in the polymer melt. Poly(methyl methacrylate) films were prepared by dissolving both the polymer and probe molecules in toluene followed by casting the system onto a glass slide. The usual method for solvent removal was to allow the system to evaporate for 2 days, followed by heating to 80 °C under vacuum (10-3 Torr) for an additional day. For polyethylene and wax samples known amounts of probe molecules were introduced directly into the melted samples and were then molded into films using a hot press. The films were cooled by quenching them immediately in ice water. The thickness of the film was regulated by the amount of solution cast onto a plate or by pressing the film between two hot plates containing a spacer. For comparison, polystyrene films were prepared by both methods and identical results were found. The concentration of the probe molecules in the film was confirmed by using absorption spectroscopy, and the film thickness was measured with a micrometer. The reproducibility of preparation of the heterogeneous films was confirmed by X-ray and DSC analysis. Instrumentation. Nuclear Magnetic Resonance. A Varian Unity Plus 300 NMR with adjustable temperature probe was used to measure 75 MHz 13C Spectra. Samples consisted of

J. Phys. Chem. B, Vol. 103, No. 43, 1999 9071 approximately 75 wt % polymer dissolved in 15% trichlorobenzene with 5% toluene-d8 for reference. X-ray Diffraction. A Scintag X-1 Cu KR X-ray diffractometer was used to measure the diffraction spectra of the polymer samples. Polymer samples of dimensions 2 × 1 cm were glued onto a flat aluminum sample holder. Crystallinity is defined as Xc ) Ic/(Ic + Ia), where I is the area of scattering for the crystalline and amorphous regions, respectively.28 Differential Scanning Calorimetry. A Perkin-Elmer DSC-4 calorimeter with a system 4 microcomputer controller and a intracooler 2 chiller was used to collect calorimetric data, and the data were scanned into computer data files with Adobe Photo Shop. The calorimeter was calibrated using docosane as a standard with an enthalpy of fusion of ∆Hf ) 58 cal/g.29 Crystallinity is defined as Xc ) ∆Hm/∆Hc, where ∆Hm and ∆Hc are the enthalpies of fusion of the polymer melt and purely crystalline samples, respectively.28 Steady-State Absorption Measurements. Steady-state absorption spectra were obtained on a Varian Cary 3 UV-vis spectrophotometer controlled by an IBM-compatible computer using a spectral band-pass of 0.2 nm. Steady-State Fluorescence Spectroscopy. An SLM/Aminco SPF-500C spectrofluorimeter was used to measure fluorescence spectra. Typically, the band-pass for emission spectra was 7.5 nm for the excitation band and 1 nm for the emission band, and vice versus for excitation spectra. The data were collected by an instrument microprocessor and then transferred to an IBMcompatible computer. Time-ResolVed Fluorescence Spectroscopy. Fluorescence studies were carried out using either a Nitromite LN-100 with a 0.2 ns (fwhm) and 70 µJ pulse or a LN-1000 laser having a 1.2 ns fwhm and 1.4 mJ pulse. As in steady-state measurements, the emission of the fluorophore was collected at 90° to the excitation source. A Bausch and Lomb monochromator was used to select the monitoring wavelength, and the emission at this wavelength was detected by a Hamamatsu R1664U microchannel plate photomultiplier. The signal was amplified using a 7A29 amplifier in a Tektronix 7912AD programmable digitizer with a 7B10 time base. The digitized signal was averaged from several traces and stored on an IBM-compatible computer. Steady-State Phosphorescence Spectroscopy. Steady-state phosphorescence was measured on a Perkin-Elmer MPF-44B spectrofluorimeter equipped with a spinning shutter to eliminate fluorescence. A 300-350 nm band-pass filter was used to control the excitation wavelength, and a camera shutter was used to control illumination of the sample and to eliminate photodamage. Time-ResolVed Phosphorescence and Transient Absorption Spectroscopy. A Laser-Photonics model UV-24 with a 10 ns fwhm and 10 mJ pulse and a Hamamatsu IP28 photomultiplier was used for excitation and detection, respectively. For phosphorescence studies a nine-stage IP28 photomultiplier was used to detect the long-lived emission. This system has been previously described.7 Decay times that were longer than 5 ms were collected on a Tektronix TDS210 and then transferred to a computer using the Wavestar program. Faster decays were obtained on the previously described Tektronix 7912AD using a 7A13 differential comparator. Data Analysis. Four types of models were used to simulate the decay kinetics presented in this study. For homogeneous environments, such as solution, the single-exponential function

It ) I0 exp-kt

(1)

is used to describe the decay of species. Heterogeneous systems

9072 J. Phys. Chem. B, Vol. 103, No. 43, 1999

Biscoglio

Figure 1. Integrated proton decoupled 13C NMR spectrum at 75 MHz of docosane at 75 °C (number of transients accumulated, 512).

Figure 2. Proton decoupled 13C NMR spectrum at 75 MHz of polyethylene Rx at 110 °C (number of transients accumulated, 496).

may be described by two or more independently decaying species from multiple environments and require a biexponential of the form

It ) I0[A exp-k1t + (1 - A) exp-k2t]

(2)

or even larger multiple exponential functions. In the latter case, the Gaussian distribution model has been developed to describe such systems, where many different conditions give rise to a distribution (γ) of decay rates (kgaus) related to an average site decay (kav).30 This distribution can be written as

kav ) kgaus exp(γx)

(3)

Integration over the distribution exp(-x2) gives

It

∫exp(-x2) exp[-kavt exp(γx)] dx ) I0 ∫exp(-x2) dx

(4)

which is fitted to the experimentally determined decay profiles. Fitting of the energy transfer data to the Forster type relation (eq 6) and analysis of these data are explained below. Results and Discussion Polymer Characterization by Direct Methods. The photochemistry and photophysics of molecules in polymers, which are presented later, depend on the structural properties of the polymer. Hence, it is essential to have at least a cursory monitoring of the structural properties of the polymers used in the present study. This is provided by several NMR, X-ray diffraction, and differential scanning calorimetry (DSC) studies. The type and degree of branching in polyethylene chains is established using integrated proton decoupled 13C NMR.31 A model alkane system, docosane, shows that differentiation is readily made between the β-CH2, n-CH2, γ-CH2, R-CH2, and CH3 carbons as demonstrated by their chemical shifts at 32.16, 29.99, 29.60, 22.89, and 14.11 ppm (Figure 1). The septuplet seen at 20.4 ppm is from the toluene reference. A long-chain linear polyethylene such as Rx has only one methyl end group per 3000 main chain (n-CH2) carbons and shows only one major peak at 29.9 ppm that corresponds to this (Figure 2). In the branched polyethylene Pn (Figure 3), there is a tertiary carbon peak (37.9 ppm) that is half as intense as its neighboring R (34.3 ppm), β (27.1 ppm), and γ (30.4 ppm) carbons. A comparison of these areas with the n-CH2 carbons gives approximately 15 branches per 1000 backbone carbons (listed

Figure 3. Integrated proton decoupled 13C NMR spectrum at 75 MHz of polyethylene Pn at 100 °C (number of transients accumulated, 720).

as 26 per 1000 backbone carbons). The majority of these branches are butyl and propyl chains as defined by the 2-CH2 (CH2 next to methyl) peaks at 23.3 and 22.8 ppm, respectively. Small peaks for the ethyl branch, i.e., 2-CH2, are found at 26.7 ppm, and CH3 is at 10.9 ppm. β-CH2 for methyl branches can be found at 27.5, and the CH3 connected to it is hidden under the toluene reference. X-ray diffraction spectra (Figure 4-6) of partially crystalline Rx, Pn, and completely amorphous Dow PE confirm that lamellar crystalline packing has taken place in the first two samples, whereas the Dow PE film shows no structure. The figures show the raw scattering data, the underlying amorphous scattering (solid line), and the subtracted spectra of the crystalline phase. A comparison of the areas of scattering for the crystalline and amorphous zones indicate that the crystallinity in Rx (78%) is approximately twice that in PN (44%). The narrower line width of Rx (0.3425 fwhm at 22°) compared to PN (0.5032 fwhm at 22°) suggests that this sample contains larger and more regular crystal sizes. According to the Scherrer relationship the mean dimension of the crystallites (L) can be calculated from the fwhm (βo), wavelength of scattering radiation (λ), and angle of scattering (θ) by

L ) kλ/βo cos θ

(5)

The data indicate that the crystallites in Rx are 50% larger than those in Pn. No single-crystal PE standards were available to calculate (k), so the dimensions of Rx crystals were taken to be

Photophysical Studies of Heterogeneous Polymers

J. Phys. Chem. B, Vol. 103, No. 43, 1999 9073

Figure 4. X-ray diffraction spectra of polyethylene Rx, and spectra with subtracted amorphous scattering (solid line). Figure 7. DSC spectra of polyethylene samples Rx and Pn.

Figure 5. X-ray diffraction spectra of polyethylene Pn and spectra with subtracted amorphous scattering (solid line).

Figure 8. Steady-state fluorescence emission spectra of (a) 30 mM pyrene in cyclohexane and (b) 100 mM, (c) 30 mM, (d) 10 mM, (e) 5 mM, (f) 1 mM, and (g) 0.5 mM pyrene in poly(methyl methacrylate), excitation at 337 nm.

TABLE 1: Crystallinity Obtained From X-ray and DSC

Figure 6. X-ray diffraction spectra of amorphous polyethylene from Dow.

12-15 nm long. This is achieved by comparing our method of preparation and chosen molecular weight with comparable ones previously reported in the literature.12,15 The melting point and heat capacity of the polymer samples were measured by DSC, and typical data are shown in Figure 7. A comparison of the crystallinity data obtained by X-ray analysis to DSC is given in Table 1. There is only one major melting peak in each polyethylene sample (Figure 7) indicating that crystal formation of a regular size has taken place. Multiple peaks would arise from the heterogeneity of mixing different molecular weight or branched polymers as in polymer blends. None of the latter were used in this study, since their additional heterogeneity

% crystalline

polymer

fwhm at 21.5° peak

X-ray

DSC

melting point (°C)

polyethylene Rx polyethylene Pn

0.3425 0.5023

78 44

81 43

136 113

makes characterization more complex. DSC traces of Rx and Pn indicate crystallinities of 81.3% for Rx and 42.5% for Pn, when calculated using an enthalpy of fusion of 69 cal/g.32 These data are consistent with those obtained by X-ray analysis. A lower melting point in Pn (113 °C vs 136 °C in Rx) is consistent with smaller crystallites and is similar to nanocontane alkanes (C94H190, mp ) 113.8 °C).33 This is to be expected since the branching in Pn interferes with chain packing and reduces the folding lengths of the chains and hence the degree of crystallinity. Nanocontane alkane crystals are limited by their chain length to lengths of 11.5 Å. Restriction of Guest Molecules to Amorphous Zones. Photophysical studies have been used widely to comment on solid polymers and polymers in solution.7-11 A popular probe of such systems is pyrene, since it possesses several unique and useful photophysical properties. In fact, pyrene has been used in polyethylene systems of interest to the present work.10,11,34 For the most part only the fluorescence has been studied, and this has been done mainly to comment on the varied environments that the molecule experiences.10,11 This probe molecule


Figure 9. Steady-state fluorescence emission spectra of (a) 30 mM, (b) 10 mM, (c) 5 mM, (d) 1 mM, and (e) 0.5 mM pyrene in polyethylene Rx, excitation at 337 nm.

Figure 10. Steady-state fluorescence emission spectra of (a) 30 mM, (b) 10 mM, (c) 5 mM, (d) 1 mM, and (e) 0.5 mM pyrene in polyethylene Rx, excitation at 337 nm.

is also used in our studies, and a simple comparison with studies in polyethylene and in cyclohexane is instructive. Figures 8-10 illustrate the dependence of the pyrene fluorescence spectrum on its concentration in cyclohexane, PMMA, Rx, and Pn, respectively. Excimer formation (broad band fluorescence at 470 nm) occurs when there is sufficient mobility and/or concentration for an excited-state pyrene to interact with ground-state pyrene. This occurs readily in cyclohexane but is greatly reduced in PMMA, where diffusion is quite limited. Rx and Pn show similar monomer-to-excimer ratios although their effective concentrations and diffusibilities are different. In both Rx and Pn, the pyrene probe is located in the amorphous regions of the polymer and not in the crystalline zone. Hence, the effective probe concentration is two times greater in Pn and five times greater in Rx than that of the bulk, which promotes pyrene excimer formation. To simulate this condition, docosane wax is used as a highly crystalline model system for polyethylene. The crystalline nature of this system militates against large concentrations of pyrene and other additives. However, small amounts of liquid alkanes, e.g., hexadecane, create liquid or amorphous regions within the crystalline wax that help to solubilize guest molecules. Figure 11 shows that excimer fluorescence is seen at very low concentrations (10-5 M) of pyrene in the completely crystalline docosane sample. Here, the pyrene is forced into local disordered regions of the wax. Excimer formation is reduced with the addition of hexadecane, which creates a greater number

Biscoglio

Figure 11. Steady-state fluorescence emission spectra of (a) 10-5 M pyrene in docosane, with the addition of hexadecane, (b) 3 and (c) 10 mL/g, excitation at 337 nm.

Figure 12. Steady-state fluorescence excitation spectra of 30 mM pyrene in polyethylene Rx, monomer and excimer emissions monitored at 395 (dotted line) and 475 nm (solid line) respectively, with excitation at 337 nm.

of amorphous regions to host the pyrene. Earlier work has shown that in some systems pyrene can be forced to exist as small aggregates and that these aggregates, much like crystalline pyrene, exhibit excimer fluorescence.35 They also exhibit spectral absorption that is red shifted with respect to that of molecular pyrene. In these cases the excimer fluorescence is formed from bimolecular ground states of pyrene. No significant red shifted spectral absorption of pyrene was observed in Rx or Pn below 30 mM or in docosane below 10-5 M. However, Figure 12 shows a red shifted spectral absorption in the excitation spectra of Rx with 30 mM pyrene. This spectrum was obtained by monitoring the excimer emission at 475 nm. No red spectral shift is observed in the spectrum obtained by monitoring the monomer emission at 395 nm. This indicates that aggregates of pyrene are forced to form above 30 mM in this system. Figure 13 shows the time dependence of the fluorescence of pyrene in various systems. At concentrations of 5 mM and less, the decay of pyrene is single-exponential (2.4 × 10-6 to 3.2 × 10-6 s-1) in our systems and agrees with the data obtained by Porter.36 In polyethylene, the onset of excimer formation occurs above 5 mM and is reminiscent of Porter’s work in poly(methyl methacrylate). At 30 mM pyrene, the fluorescence exhibits a growth of the excimer P2* signal in Rx, Pn, docosane, and cyclohexane; the



Figure 13. Time-resolved excimer emission at 475 nm of 30 mM pyrene in polyethylene Rx (thick line), Pn (broken line), cyclohexane (regular line), and 0.5 mM pyrene in cyclohexane (thin line), excitation at 337 nm.

latter is shown for reference. In agreement with the conventional picture of excimer formation, the observed rate of excimer formation in cyclohexane decreases with decreasing pyrene concentration. A similar effect is observed in the Rx and Pn films. As the pyrene is located in the amorphous regions of Rx (22%) and Pn (56%), the effective concentration of pyrene is lower in Pn compared to Rx. This leads to a slower formation of P2* in Pn compared to Rx. These data all point to reactions taking place in the amorphous region of the polyethylene films. Forster type kinetics can throw further light on this unique feature of polyethylene films. “Molecular Ruler” Analysis of Networking of Amorphous Zones in Polymer Films. Transfer of electronic energy between two separated molecules takes place by a dipole-dipole interaction when the donor has a higher excited-state energy level than the acceptor molecule. This Forster type energytransfer process has been used to look at the molecular architecture in many systems.9,37-40 In this work, the pyreneperylene pair was chosen since there is a significant spectral overlap between the pyrene emission and the perylene excitation spectra that gives rise to energy transfer over large distances. An active sphere of interaction is defined as the distance within which quenching takes place, and by using this concept, environmental or spatial comparisons are made between molecules. The size of the active sphere is regulated by changing the quencher concentration. Information of the active sphere is obtained by the Perrin approach, which monitors changes in the emission intensity of the donor, or by the Forster approach, where the lifetime of the excited donor molecule is monitored. The latter has been found to be more precise in highly scattering media such as polymers. The essence of this method is to observe the energy transfer between excited pyrene and perylene as a function of perylene content. As a check of this method, two completely amorphous films, polystyrene and poly(methyl methacrylate), are also used since it is expected that the probe molecules are homogeneously distributed in these polymers. The energy-transfer kinetics should then be directly comparable to literature studies in homogeneous solution. In the case of the polyethylene films Rx and Pn, the local concentration effects created by the crystalline and amorphous zones should be reflected in the measured size of the active sphere. Figure 14A shows the steadystate fluorescence spectra for pyrene with increasing amounts of perylene in polystyrene. It is noted that the pyrene fluorescence, located at λ ∼ 400 nm, decreases with increasing perylene

Figure 14. (A, top) steady-state fluorescence emission spectra of (a) 10 mM pyrene in polystyrene, with the addition of (b) 1, (c) 5, (d) 10, (e) 20, and (f) 40 mM perylene, excitation at 337 nm. (B, bottom) Time-resolved fluorescence emission at 395 nm of (a) 10 mM pyrene in polystyrene, with the addition of (b) 1, (c) 5, (d) 10, (e) 20, and (f) 40 mM perylene, excitation at 337 nm. Smooth traces are the best calculated fits to the Forster relation (eq 6) given in the text. Pyrene alone has a single-exponential decay of 3.16 × 10-6 s-1.

and that a new emission grows in at λ ∼ 450-500 nm, which is due to excited perylene. The Forster relation

I ) I0[-kdt - 2γ(kdt)D/6]

(6)

γ ) CA/CA°

(7)

relates the intensity of fluorescence (I) to the is the initial pyrene fluorescence intensity at time zero (I0) and the decay rate constant of the donor in the absence of quencher (kd). Fitting of the data using eq 6 gave values of D (the dimensionality of interaction) as 3 in all cases. Small deviations in D have a large effect on the other parameters calculated, so it was set at 3 in all cases of γ determination. The threedimensional interaction indicates that the amorphous zones are quite large with respect to the interaction radius; otherwise a lower dimensional interaction would have been observed. Figure 14B shows the time-resolved decays of pyrene and the best fits using the Forster relation. Figure 15 shows the linear dependence obtained for the γ values versus pyrene concentration. The slope of this curve was used to calculate the critical acceptor concentration (CA° in moles/liter) using eq 7 above and to determine the critical transfer distance (R0) by eq 8, where N is Avogadro’s number. This treatment assumes a completely random distribution of the probe molecules in the amorphous zone.


Biscoglio TABLE 2: Calculated and Measured Energy-Transfer Distances in Several Polymers polymer

% crystalline

polyethylene Rx polyethylene Pn polystyrene PMMA waxes

80 43 0 0 >99

R0 (Å)

concentrating effecta

calcd

measd

5 1.8 1 1

62 43 36 36

41.7 38.2 35.5 36.2 >100b

a Factor by which the concentration in amorphous zones is greater than bulk. b From ref 41.

Figure 15. Plot and linear fit of γ values determined by the Forster relation versus perylene concentration.

R0 ) [1500/π3/2NCA°)]1/3 × 108 Å

(8)

The measured values of R0 given in Table 2 illustrate that the critical radii for PS and PMMA are close to 36 Å as found in homogeneous systems. However, the R0 for the PE samples are significantly larger than those obtained in homogeneous systems. An R0 calculated with the assumption of a homogeneous distribution of guest molecules in PS and PMMA, and with the molecules confined to the amorphous zones in PE, is also included. Agreement is excellent for PS and PMMA, but for PE the measured R0, although larger than that for a homogeneous system, is nevertheless smaller than that calculated. This indicates a significant sequestering of the probe molecules between the crystallites, but that significant photophysical communication still occurs between the amorphous regions. Earlier authors41 have suggested that the large radii obtained in wax systems are due to efficient singlet energy transfer across crystalline zones. The concentration effect, however, indicates that the increase in R0 with increasing crystallinity is a result of restriction of the solutes to amorphous zones, thereby creating local concentrations that are larger than those in bulk. It is noted that more isolation is observed with the increased crystal structure in Rx compared to Pn. Molecular motions of all solutes are restricted in polymer films, with the restriction increasing markedly with molecular size. Polyethylene films containing perylene can be prepared in a metastable condition with respect to the dispersion of the solute. In a film prepared from a melt of PE and perylene, which is supersaturated, an “aging” of the perylene distribution can be found as the solutes crystallize. Figure 16 shows the reduced quenching of pyrene by 15 mM perylene in the polyethylene film Pn as a function of time. With time the perylene crystallizes and is no longer an effective quencher of the pyrene fluorescence. Days later, the crystals have grown large enough to be observed by the naked eye, a process that takes much longer in Rx films. The effect is reversible as remelting of the film redisperses the probe molecules. Over the time period of the energy-transfer experiments, no crystallization of the probes occurs. Diffusion studies involving quenching of the pyrene triplet by oxygen, azulene, and ferrocene presented below give further insight into the nature of molecular motion in polymer films. Oxygen Quenching of the Pyrene Triplet. An understanding of the mobility of small molecules in polymer films is obtained by phosphorescence quenching of the excited triplet state of bromopyrene (br-py) by oxygen.25 Figure 17A shows the phosphorescence decay traces and best Gaussian fits of 1 mM

Figure 16. Time-resolved fluorescence emission at 395 nm of polyethylene Pn with 0.5 mM pyrene and 15 mM perylene (a) after initial preparation of the film and times of (b) 1 h, (c) 5 h, and (d) 2 days thereafter. Decay can no longer be fit to the Forster relation due to heterogeneous distributions of crystallized perylene.

br-py in polystyrene with successive amounts of oxygen equilibrated with the film. The non-single-exponential quenching has been addressed by several authors.8 This is attributed to the varied environments experienced by the probe molecules and oxygen. Figure 17B shows decay rates (k) versus equilibrated pressures of oxygen for Rx, Pn, polystyrene, and PMMA films. A solubility dependent quenching (kqS) rate is determined by the dependence of the quenching rate on the pressure of oxygen. Solubilities of oxygen at 1 atm are found in the literature and are proportional to pressure according to Henry’s law. These are used to determine the quenching rate (kq) given in Table 3. The diffusion rate constant of oxygen (DO2) in a polymer film is obtained by steady-state quenching in which the decrease in phosphorescence intensity of an evacuated film is monitored as oxygen is allowed to diffuse into it. Figure 18 shows the steady-state phosphorescence of the bromopyrene triplet in polystyrene as the evacuated film is equilibrated with 1atm of air. For a film of thickness L, diffusion is defined by eq 942

[(Ie0/Iet) - 1]/[(Ie0/Ies) - 1] ) (4/L)(DO2t/π)1/2

(9)

where Ie0 is the intensity of phosphorescence in the absence of oxygen and Iet and Ies are the intensities after time t of diffusion and saturation of the polymer with oxygen, respectively. Figure 19 shows a plot of

[(Ie0/Iet) - 1]/[(Ie0/Ies) - 1]

versus

t1/2

(10)

for the data given above. The induction period before the linear portion of the curve has been related to nontypical polymer structure in the surface layers,19 so it is reasonable to use the



Figure 18. Steady-state quenching of phosphorescence at 590 nm as 1 atm of air is equilibrated with an evacuated film of 1 mM bromopyrene in polystyrene.

Figure 17. (A, top) time-resolved phosphorescence emission at 590 nm of 1 mM bromopyrene in polystyrene under (a) vacuum and equilibrated pressures of (b) 4 and (c) 10 mbar oxygen. Smooth traces are the best calculated Gaussian fits. (B, bottom) Stern-Volmer plot and fits of decay rates versus equilibrated pressures of oxygen in various polymer films (where 1.40E+05, for example, represents 1.40 × 105).

TABLE 3: Triplet Quenching Rates by Oxygen in Different Polymers polymer

kqSa (mbar-1 s-1)

kqb (M-1 s-1)

Doxygenc (cm2 s-1)

kq(calc)d (M-1 s-1)

polyethylene Rx polyethylene Pn polystyrene PMMA

591 841 286 60

1.74 × 108 2.48 × 108 1.16 × 108 6.90 × 106

4.49 × 107 6.30 × 107 2.38 × 107 2.31 × 108

2.04 × 108 2.86 × 108 1.08 × 108 1.05 × 107

a From time-resolved laser experiment. b Using solubility of oxygen data from literature for completely amorphous films. c Diffusion coefficient obtained from steady-state experimental data. d Calculated quenching rate using Smoluchowski relation.

slope of the linear portion to represent bulk diffusion.25 Table 3 gives the diffusion coefficients obtained by this method and the diffusional quenching rates (kq(calc)) calculated by use of the Smoluchowski relation43

kD ) 4πNDRAB

(11)

where D is the diffusion rate and RAB (6 Å)44 is the interaction radius between donor and quencher. There is a good agreement between the quenching rates determined by time-resolved and steady-state methods. Time-resolved quenching rates indicate the permeation rate (P) through the film, which is directly proportional the product of the diffusion (D) rate and the solubility (S) in the film,17,45

Figure 19. Plot of [(Ie0/Iet) - 1]/[(Ie0/Ies) - 1] versus t1/2 in polystyrene under 1 atm of air. Line with best fit after t1/2 ) 6 is shown.

TABLE 4: Calculated Oxygen Solubilities versus Literature Values [O2] × 10-3 polymer

calcda

lit.

polyethylene Rx polyethylene Pn polystyrene PMMA

2.90 2.95 2.65 5.73

2.1-2.9 b 2.1-2.9 b 2.46 8.70

a Calculated from measured values using P ) S*D, indicating concentration in amorphous zones only. b Dependent on sample crystallinity.

P ) DS

(12)

In Table 3 quenching rates were calculated using literature values of solubility; however, knowledge of both the permeation and diffusion rates can also be used to calculate the solubility. Table 4 shows literature values17 of oxygen solubility versus those calculated from the present study and eq 12. Since this method only probes the amorphous regions where the dopants are present, it is expected that the solubility of the oxygen measured would reflect values found in completely amorphous films.45 This method is useful in determining the solubility of oxygen in polymer films where it is not known. Determination of the triplet quenching using azulene and ferrocene will demonstrate the effect of increasing molecular size in decreasing the quenching rate. Quenching of Triplet Pyrene by Larger Molecules. Several studies have investigated the motion of large molecules in polymer films.9,10,46,47 We have studied the quenching of the pyrene triplet by azulene and ferrocene in polymer films to


Biscoglio

TABLE 5: Comparison of Triplet Quenching Rates with the Size of the Quencher polymer polyethylene Rx polyethylene Pn polystyrene (20 °C) polystyrene (54 °C) polystyrene (81 °C) polystyrene (96 °C) polystyrene (110 °C) PMMA a

oxygen kq (M-1 s-1)

azulene kq (M-1 s-1) {kq (M-1 s-1)}a

ferrocene kq (M-1 s-1) {kq (M-1 s-1)}a

1.74 × 108 2.48 × 108 1.16 × 108

8.07 × 105 {1.53 × 105} 4.26 × 106 {2.43 × 106} 64

1.96 × 105 {3.72 × 104} 9.96 × 105 {5.68 × 105} 46 642 1.13 × 104 4.30 × 105 2.77 × 106

6.90 × 106

Corrected for concentrating effect of crystallinity.

room temperature. These diffusion constants are in the same range 10-10 to 10-16 cm2 s-1 as those measured for several molecules in other polymer films.8-10,21,42,46,47 In other studies Weiss10 has measured much larger diffusion coefficients for DMA in polyethylene. This discrepancy may be due to the fact that he used solvent swollen PE films for his measurement or solvent in contact with the polymer films. It is instructive to view the polystyrene data from the point of view of free volume Vg. In this concept48-50 the molecules are constrained to move in the free volume of the matrix, which is polystyrene. A diffusion constant D can be calculated with the formulation in the work of Cohen and Turnbull48

D ) ga*u exp[-γV*/Vf] Figure 20. Time-resolved decay rates of 1 mM bromopyrene in polystyrene (diamonds) alone and quenched by 1 mM ferrocene (triangles) versus temperature.

TABLE 6: Comparison of Diffusion Rates with Size of Quencher polymer polyethylene Rx polyethylene Pn polystyrene (20 °C) polystyrene (54 °C) polystyrene (81 °C) polystyrene (96 °C) polystyrene (110 °C) PMMA

Doxygen (cm2/s)

Dazulene (cm2/s

Dferrocene (cm2/s)

4.49 × 10-7 6.30 × 10-7 2.38 × 10-7

3.38 × 10-10 5.36 × 10-9 1.42 × 10-13

8.22 × 10-11 1.25 × 10-9 1.02 × 10-13 1.42 × 10-12 2.51 × 10-11 9.53 × 10-10 6.14 × 10-9

2.31 × 10-8

demonstrate the effect of size on the mobility of these molecules. Table 5 gives quenching rates of these molecules as well as corrected values for the effect of crystallinity in each polymer film. The diffusion rates calculated by eq 11 are given in Table 6 and show that they become significantly slower as the size increases from oxygen to azulene and ferrocene. A striking feature of Table 5 is the marked decreased (∼2000-fold) for azulene and ferrocene quenching of triplet pyrene in polystyrene compared to both polyethylene samples. This is attributed to the fact that at room temperature both PE samples are well above their glass transition (Tg ) 195 K), while PS is well below its Tg (Tg ) 373 K).17 This is clearly illustrated by the increased quenching rate in polystyrene of the triplet by ferrocene over a wide temperature range. Figure 20 shows the decay rate of millimolar bromopyrene in polystyrene and its quenching by a millimole of ferrocene versus temperature. The natural decay rate of bromopyrene significantly increases above the glass transition temperature of polystyrene (Tg ) 100 °C)17 and is accompanied by an increase in the quenching rate of ferrocene. As indicated in Table 5, the quenching rate of ferrocene above 100 °C in polystyrene becomes comparable to that in polyethylene (Tg ) 195 K) at

(13)

where g is a geometric factor of 1/6, a* is the diameter of the diffusing molecule, u is the root-mean-square velocity given by

u ) (3kT/m)1/2

(14)

and γV* is the volume of the guest molecule. The difficulty with using the above equation for D lies in calculating the free volume Vf. This is taken as the volume that the host molecule occupies less its van der Waals volume. However, if the system is rigid, i.e., well below the Tg, then all of this free volume cannot be used. To calculate Dferrocene from the above equation, it is necessary to have a free volume that varies from 13 Å3/ (styrene unit) at 22 °C to 24 Å3 at 110 °C. This simple calculation demonstrates the marked effect of Vf on D and hence the rate constant. The values of Vf given above are the free volume available for diffusion. A literature value17 for the volume at 25 °C is given as 60 3 Å /(styrene unit), while the calculation shows that only 13 Å3 of this volume can be used for diffusion. The density of polystyrene changes from 1.050 to 1.016 g/cm3 from 20 to 110 °C.51 The corresponding increase in volume is 0.033 cm3/g or 5.5 Å3/(styrene unit). The calculation shows that at 110 °C an added 11 Å3 increase in Vf is needed to explain the observed increase in D, i.e., Vf ) 24 Å3. The conclusion is that, at 110 °C, some (5.5 Å3) of the original Vf at 20 °C that was unavailable for diffusion of guest molecules now becomes available. Although the calculation using Vf leaves much to be desired, nevertheless this approach provides a good initial explanation of the marked increase in diffusion (increase in rate of reaction) of large guest molecules in a polymer on varying the temperature across the glass transition. It is pertinent to note that in two completely different sets of studies of diffusion constants of small molecules in polymer films, Torkelson5 and Hedenqvist21 also found they were able to satisfactorily explain their data by a free volume theory.

Photophysical Studies of Heterogeneous Polymers Conclusions Energy-transfer studies show that, in polyethylene, probe molecules are concentrated into the amorphous zones of partially crystalline polyethylene films. This is effectively described by a lamella crystalline structure, where entangled chains interconnecting crystalline zones make up a network of amorphous zones. Triplet quenching studies show that diffusion is highly size selective in polymer films. The rapidity of motion is dependent on the available free volume for diffusion, which is significantly reduced below the glass transition temperature. Heating of a polystyrene film to above its glass transition temperature shows a correlation between increased diffusion with decreased density of the polymer. These studies show that the conventional model for polyethylene and simple diffusion theory can be used to satisfactorily explain photoinduced events in partially crystalline polymer films. Acknowledgment. The authors wish to thank the National Science Foundation (Grant CHE96-10187-002) for support of this work and the Department of Chemical Engineering for use of their X-ray and DSC (CTS96-01780). The authors would also like to thank Dr. G. Zhang for much help in the earlier part of this work and for many stimulating discussions. We are also grateful to Professor L. Mandelkern of Florida State University, Tallahassee, and Dr. P. Barham from Bristol University, U.K., for generous gifts of several polyethylene samples. M.B. would like to thank the Bayer foundation for support of his research. References and Notes (1) Mort, J.; Pfister, G. Electronic Properties of Polymers; John Wiley & Sons: New York, 1982. (2) Guillet, J. Polymer Photophysics and Photochemistry; Cambridge University Press: Cambridge, U.K., 1985. (3) Webber, S. E. Chem. ReV. 1990, 90, 1469. (4) Mirkin, C. A.; Ratner, M. A. Annu. ReV. Phys. Chem. 1990, 43, 719. (5) Hoyle, C. E., Torkelson, J. M., Eds. Photophysics of Polymers; ACS Symposium Series 358; American Chemical Society: Washington, D.C., 1987. (6) Rabek, J. F. Mechanisms of Photophysical Processes and Photochemical Reactions in Polymers; John Wiley & Sons: New York, 1991. (7) Zhang, G.; Thomas, J. K. J. Phys. Chem. 1995, 99, 11203. Zhang, G.; Thomas, J. K. J. Phys. Chem. 1996, 100, 11438. Zhang, G.; Thomas, J. K. J. Phys. Chem. 1998, 102, 5465. (8) Masoumi, Z.; Stoeva, V.; Yekta, A.; Pang, Z.; Manners, I.; Winnik, M. Chem. Phys. Lett. 1996, 261, 551. Yekta, A.; Masoumi, Z.; Winnik, M. Can. J. Chem. 1995, 73, 2021. (9) Deppe, D.; Dhinojwala, A.; Torkelson, J. Macromolecules 1997, 30, 4871. (10) Zimerman, O.; Cui, C.; Wang, X.; Atvars, T.; Weiss, R. Polymer 1998, 39, 1177. He, Z.; Hammond, G.; Weiss, R. Macromolecules 1992, 25, 1568. Jenkins, R.; Hammond, G.; Weiss, R. J. Phys. Chem. 1992, 96, 496. (11) Vigil, M.; Bravo, J.; Atvars, T.; Basegla, J. Macromolecules 1997, 30, 4871.

J. Phys. Chem. B, Vol. 103, No. 43, 1999 9079 (12) Keller, A. Philos. Mag. 1957, 2, 1171. Barham, P.; Chivers, R.; Jarvis, D.; Martinez-Salazar, J.; Keller, A. J. Polym. Sci., Polym. Lett. Ed. 1981, 19, 539. Chivers, R.; Barham, P.; Martinez-Salazar, J.; Keller, A. J. Polym Sci., Polym. Phys. Ed. 1982, 20, 1717. Barham, P.; Keller, A. J. Polym. Sci., Polym. Phys. Ed. 1989, 27, 1029. (13) Till, P. J. Polym. Sci. 1957, 106, 301. (14) Aitken, D.; Cutler, D.; Glotin, M.; Handra, P.; Cudby, M.; Willis, H. Polymer 1979, 20, 1465. (15) Mandelkern, L. Crystallization of Polymers; NATO ASI Series; Kluwer Academic: Dordrecht, The Netherlands, 1993. Mandelkern, L. Acc. Chem. Res. 1990, 23, 380. Stribeck, N.; Alamo, R.; Mandelkern, L.; Zachman, H. Macromolecules 1995, 28, 5029. (16) Sperling, L. Introduction to Physcial Polymer Science, 2nd ed.; John Wiley & Sons: New York, 1992. (17) Van Krevelen, D. W. Properties of Polymers: Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction from AdditiVe Group Contributions; Elsevier: Amsterdam, 1990. (18) Meares, P. Polymers; Structure and Bulk Properties; Van Nostrand: London, 1965. (19) Comyn, J. Polymer Permeability; Elsevier: New York, 1985. (20) Michaels, A. S.; Bixler, H. J.; Fein, H. L. J. Appl. Phys. 1964, 35, 3165. (21) Hedenqvist, M.; Angelstok, L.; Edsberg, L.; Larsson, P.; Gedde, U. Polymer 1996, 37, 3887. (22) Lowell, P. N.; MacCrum, N. G. J. Polym. Sci. 1971, 1935. (23) MaCallum, J. R.; Rudkin, A. L. Eur. Polym. J. 1978, 14, 655. (24) Oster, G.; Geacintov, N.; Khan, A. U. Nature (London) 1962, 196, 1089. (25) Chu, D. Y.; Thomas, J. K. Macromolecules 1988, 21, 2094. (26) Biscoglio, M. B.; Thomas, J. K. Manuscript in preparation. (27) These samples were kindly provided by P. Barham, Bristol University, U.K. (28) Kavesh, S.; Schults, J. M. Polym. Eng. Sci. 1969, 9, 5. (29) Warth, A. H. The Chemistry and Technology of Waxes; Reinhold: New York, 1956. (30) Krasnansky, R.; Koike, K.; Thomas, J. K. J. Phys. Chem. 1990, 94, 4521. (31) Carman, C. ACS Symp. Ser. 1980, 142, 81. (32) Flory, P. J.; Vrij, A. J. J. Am. Chem. Soc. 1963, 85, 3548. (33) Broadhurst, M. G. J. Res. Natl. Bur. Stand., Sect. A 1962, 66, 241. (34) Stevens, B.; Algar, B. E. J. Phys. Chem. 1968, 72, 3794. (35) Hara, K.; De Mayo, P.; Ware, W. R.; Weedon, A. C.; Wong, G. S.; Wu, K. C. Chem. Phys. Lett. 1980, 69, 105. (36) Avis, P.; Porter, G. J. Chem. Soc., Faraday Trans. 2 1974, 70, 1057. (37) Iu, K.; Liu, X.; Thomak, J. K. Mater. Res. Symp. Proc. 1991, 233, 119. (38) Mataga, N.; Obashi, H.; Okada, T. J. Phys. Chem. 1969, 73, 370. (39) Even, U.; Rademann, K.; Jortner, J. Phys. ReV. Lett. 1984, 52, 2164. (40) Blumen, A.; Klafter, J.; Zumofen, G. J. Chem. Phys. 1986, 84, 1397. Blumen, A.; Bilbey, R. J. Chem. Phys. 1979, 70, 3707. (41) Zwick, M.; Kuhn, H. Z. Naturforsch. 1962, 17a, 411. (42) MacCallum, J. R.; Rudkin, A. L. Eur. Polym. J. 1978, 14, 655. (43) Smoluchowski, M. Z. Phys. Chem. 1917, 92, 129. (44) Ware, W. R. J. Phys. Chem. 1962, 66, 455. (45) Michaels, A. S.; Parker, R. B. J. Polym. Sci. 1961, 50, 413. Michaels, A. S.; Parker, R. B. J. Polym. Sci. 1959, 41, 53. (46) Jenkins, R. M.; Hammond, G. S.; Weiss, R. G. J. Phys. Chem. 1992, 96, 496. (47) Zhang, G.; Thomas, J. K. ACS Symp. Ser. 1996, 620, 55; J. Phys. Chem. 1998, 102, 5465. (48) Cohen, M. H.; Turnbull, D. J. Chem. Phys. 1959, 31, 1164. (49) Vrentas, J. S.; Duda, J. L. Macromolecules 1976, 9, 785. (50) Chu, D. Y.; Thomas, J. K. J. Phys. Chem. 1989, 93, 6250. (51) Patnode, W.; Scheiber, W. J. J. Am. Chem. Soc. 1939, 61, 3449.

Photophysical Studies of Heterogeneous Polymers: The Effect of

Recommend Documents