Energy Migration in Poly(N-Vinyl Carbazole) and ItsCopolymers with Methyl Methacrylate: FluorescencePolarization, Quenching, and Molecular Dynamics

JAVIER GALLEGO,1 FRANCISCO MENDICUTI,1 WAYNE L. MATTICE2

1Departamento de Quımica Fısica, Universidad de Alcala de Henares, Alcala de Henares, Madrid, Spain

2Institute of Polymer Science, The University of Akron, Akron, Ohio 44325

Received 20 February 2002; revised 1 April 2003; accepted 3 April 2003

ABSTRACT: Fluorescence polarization and quenching measurements were used to ex-amine intramolecular energy migration for poly(N-vinyl carbazole) and copolymers ofN-vinyl carbazole with methyl methacrylate. Quenching measurements of the carba-zole fluorescence by CCl4 were performed in dilute solution in toluene, and fluorescenceanisotropy, r, was measured for the chains dispersed in a solid matrix of poly(methylmethacrylate) (PMMA). The results suggested that the chains with a high carbazolecontent, that is, a high content of excimer trapping sites, do not show the highest valuesof the singlet energy-migration rate. Isotropies, r�1, of the samples in vitrified PMMAcorroborated such conclusions. Molecular dynamics simulations on isotactic and syn-diotactic trichromophoric copolymer fragments were used to obtain parameters relatedto the energy-transfer process as a function of the methyl methacrylate content. Theparameters from the simulations supported the interpretation of the experiments.© 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1615–1626, 2003Keywords: poly(N-vinyl carbazole); energy transfer; energy migration; quenching;fluorescence; molecular dynamics; copolymerization

INTRODUCTION

Singlet energy migration and excimer formationin polymers that contain pendant chromophoreshave been studied extensively.1–3 Intramolecularexcimer formation seems to act as a trap to ter-minate energy migration in these polymers.4–8

Therefore, excimer formation is undesirable, fromthe point of view of photoconduction, because itdecreases the efficiency of carrier generation.9–11

Any change in the parameters that affect excimerformation will alter the singlet energy-migration

rate. The local concentration of chromophores inthe polymer is one of these parameters. Despitethe obvious importance of the photoconductivepolymer in the solid state, the photophysics be-havior of poly(N-vinyl carbazole) (PVCz) is moreoften examined in dilute solution.12–14 Examplesof photophysical studies on polymers having alower local volume fraction of carbazole (Cz) arepoly[2-(9-carbazolyl)ethyl methacrylate];9 poly[2-(9-carbazolyl)ethyl acrylate];15 carbazole-substi-tuted, N-acrylated, linear poly(ethyleneimine) anddehydroaniline main-chain polymers;16 polymerscontaining trans-1,2-biscarbazolylcyclobutane inthe main chain or as pendant substituents;17 andoligoethers such as poly[9-(2,3-epoxypropyl)car-bazole] and poly[1,2-epoxy-6-(9-carbazolyl)-4-oxa-hexane]epoxypropyl)carbazole].8

Correspondence to: F. Mendicuti (E-mail: francisco.mendicuti@uah.es)Journal of Polymer Science: Part B: Polymer Physics, Vol. 41, 1615–1626 (2003)© 2003 Wiley Periodicals, Inc.

1615

We have previously reported energy-transferstudies for polyesters and some bi- or trichro-mophoric model compounds containing differentchromophores. Fluorescence anisotropy in a rigidmedium,18–21 extrapolated to a high-viscosity me-dium,22 or simply the emission spectra at differ-ent viscosities23–25 can provide information aboutthe energy transfer or energy migration in thesesystems. A theoretical treatment18–25 of the ac-cessible conformations, with the equilibrium RISmodel26 or molecular dynamics (MD) simula-tions,27 permits rationalization of the experimen-tal results on the basis of the estimated values ofthe Forster radius (R0).

In this article, which follows another one on in-tramolecular excimer formation,28 we explore theintramolecular energy migration in dilute solutionfor PVCz and copolymers of N-vinyl carbazole (VCz)and methyl methacrylate (MMA). Fluorescence de-polarization and quenching by CCl4 were measuredfor dilute systems of the polymers in a rigid poly-(methyl methacrylate) (PMMA) matrix and in toluenefluid solution, respectively. MD simulations wereperformed on isotactic and syndiotactic trichro-mophoric fragments represented by CH3-A-CH2-Bn-A-CH2-Bn-A-CH3, where A � OCHCzO, B� OC(CH3)COOCH3OCH2O, and n � 0–6, toevaluate the amount of intramolecular energytransfer between Cz groups as a function of theMMA content in the copolymers.

EXPERIMENTAL

Materials

PVCz, also denoted P0, and nine copolymers, de-noted P1–P9, of VCz with an increasing MMA

content, were prepared by free-radical polymer-ization as described elsewhere.28 Reactivity ratiosof VCz (r1 � 0.13 � 0.09) and MMA (r2 � 1.88� 0.08) reveal a number-average sequence lengthof MMA monomers, �n2�, between 0.49 (P1) and22.6 (P9).28 The molecular weights are largeenough (on the order of 106, with polydispersitiesof 2 or smaller) so that end effects should beabsent. Table 1 collects some of the parametersrelated to the composition of the copolymers. Theethylcarbazole (ECz) model compound (Aldrich,98%) was purified by recrystallization (twice)from methanol. Toluene, p-dioxane, methanol,and CCl4 were of spectrophotometric grade (Al-drich). They were used without additional purifi-cation. MMA (Aldrich), used to prepare dilutesamples of the polymers in glassy PMMA, wasinitially distilled under vacuum to remove theinhibitor. Two sets, A and B, of these sampleswere separately prepared under similar experi-mental conditions. The preparation of the sam-ples can be summarized as follows: Approxi-mately 3 mL of a fresh solution (optical density�0.1–0.3 at 294 nm) of the polymer in distilledMMA were introduced into test tubes of i.d. 22.5mm (set A) or 17.5 mm (set B), used as a mold.Oxygen was removed with an ultrasonic bath(�30 min) and bubbling dry nitrogen throughthe solutions (�12 min). The polymerizationwas carried out in two steps for all samples atthe same time. First, the temperature was in-creased slowly up to 75 °C (�3 h). Second, thetemperature was increased further up to 90 °Cand maintained for �12 h. Vitrified transparentsamples were retrieved by breaking the testtube.

Table 1. Copolymer Composition and Number-Average Sequence Lengthof Monomers for (VCz-co-MMA) Copolymers and PVCz Homopolymer

SampleMole Fraction

MMAVCz Sequence Length,

�n1�MMA Sequence Length,

�n2�

P0 0 � 0P1 0.061 16.0 0.5P2 0.113 8.6 0.5P3 0.644 0.7 3.2P4 0.652 0.9 2.7P5 0.696 0.6 3.6P6 0.707 1.2 2.8P7 0.854 1.1 6.1P8 0.920 1.0 11.8P9 0.957 0.8 22.6

1616 GALLEGO, MENDICUTI, AND MATTICE

Instrumentation

Steady-state fluorescence measurements were re-corded on an SLM 8100 Aminco spectrofluorim-eter equipped with a xenon lamp, a double (sin-gle) concave grating monochromator at the exci-tation (emission) path, and Glan–Thompsonprism polarizers in both paths. The photomulti-plier was cooled by a Peltier system. The excita-tion and emission slit widths were 8 nm.

Fluorescence decay measurements were per-formed on a TCSPC FL900 Edinburgh Instru-ments spectrometer, equipped with a thyratron-gated lamp filled with hydrogen, two concavegratings monochromators at both the excitationand emission paths, and a red-sensitive photo-multiplier immersed in a Peltier cooled housing.Slits were set to18 nm bandwidth. The data ac-quisition was carried out with 1024 channels anda time window width of 125 ns with a total of10,000–15,000 counts in the peak. Instrumentalresponse functions were regularly achieved bymeasuring the scattering of a Ludox solution. De-cay-intensity profiles were fitted to exponentialtrail functions of the type

It � �i�1

n

Aie�t/�i (1)

by the iterative reconvolution method.29

Right-angle geometry, rectangular 10-mmpath cells, and a temperature of 25 °C were usedfor measurements in aerated dilute solutions. Ini-tial absorbances of these samples at the wave-length of excitation of 294 nm were in the 0.1–0.2range. Solvent baselines were measured and sub-tracted from the steady-state fluorescence signal.Front-face illumination, with the incident beamforming a 60° angle with the surface of the solidsamples, was used for fluorescence depolarizationmeasurements at room temperature. The esti-mated polymer concentration in fluid solutionwas very small, around 4–7 � 10�3 g/L, to avoidintermolecular interactions. The concentration inthe PMMA matrix was approximately an order ofmagnitude larger.

RESULTS AND DISCUSSION

Emission Spectra

Emission spectra for P#, reported previously,28

revealed a broadening to the red of the monomer

band (centered at �350 nm) observed for ECz,attributed to the emission from intramolecularexcimers. The excimer emission intensity, whichstrongly depends on the solvent, monotonicallydecreased from P0 to P9 as the Cz content de-creased. The homopolymer P0 and the first twomembers of the copolymer series, P1 and P2,showed a very high intramolecular excimer con-tent. The last three members P7–P9 exhibitedemission characteristics very similar to that ofunassociated carbazole (ECz).

R0 for the Cz to Cz Transfer

The R0 for a donor–acceptor (D-A) pair or distanceat which the transfer rate D3 A equals the decayrate of D in the absence of A is1–3

R06 � 9000 ln 10�2�DJ/125�5n4NA (2)

where �D denotes the quantum yield for fluores-cence of a donor in the absence of an acceptor, n isthe refractive index of the medium, �2 is an ori-entational factor, NA is Avogadro’s number, and Jis the overlap integral between the normalizedfluorescence intensity I(�) and the extinction co-efficient �(�), defined as

J � � �4I���d� (3)

From eq 2, the ratio of the R0’s for transfer by arandom set of configurations (�2 � 2/3) of twomolecules, D* 3 A and D�* 3 A�, in the sameenvironment is

R0,D–A/R0,D�–A�6 � �DJD–A/�D�JD�–A� (4)

With a reference D�-A� pair for which R0,D�-A� isknown, R0,D-A can be estimated from the experi-mental quantum yields for fluorescence of D andD� and the J values of both systems. We use theaverage value for the naphthalene 3 naphtha-lene (N3N) self-transfer, for which Berlman30,31

reported values of R0,N 3 N � 7.35 and 6.69 A asthe reference. Experimental quantum yields wereobtained by the procedure described previously,32

and J was obtained by graphical integration of eq3. Measurements of � and J for dilute solutions ofN and ECz in methanol (p-dioxane) at room tem-perature gave values of �ECz/�N and JCz3 Cz/JN3 Nof 10.45 (4.17) and 74.0 (82.8). These results gave

ENERGY MIGRATION 1617

values for R0,Cz 3 Cz of 21 � 1.0 A (and 18.6 � 0.9A), that is, an average of R0,Cz 3 Cz �20 � 2 A.TheCz transfers the excitation energy to Cz at dis-tances approximately three times longer thanthose for N to N.

Fluorescence Polarization

The anisotropy of the fluorescence for samples inthe solid state, denoted by r, was measured by thesingle-channel or L-format method, as describedby Lakowicz.33 The anisotropy is

r � IVV GIVH/IVV 2GIVH (5)

where Ixy is the intensity of the emission that ismeasured when the excitation polarizer is in po-sition x (V for vertical, H for horizontal), the emis-sion polarizer is in position y, and the G factor(� IHV/IHH) corrects for any depolarization pro-duced by the optical system.

The left panel of Figure 1 depicts the excitationspectrum for ECz and the excitation anisotropyspectra for ECz and the P# series measured in thesolid matrix of PMMA at room temperature, with

emission at 365 nm. This wavelength was placed15 nm toward the red of the monomer band toavoid interference from scattered exciting light.Excitation spectra of P# are very similar andpresent features matching the absorption spectra,showing bands placed (in the wavelength rangeshown) at approximately 294, 332, and 344 nm.According to Johnson,34 the bands centered at�345 and �295 nm for Cz, designated as 1Lb 41A and 1La4

1A in the Platt notation,35,36 are the(0,0) transitions from the ground to the first andsecond excited singlet states of Cz, respectively.Bands and shoulders around them are vibrationalstructures. For these electronic transitions, theabsorption oscillators are in the plane of the ringsystem and perpendicular to one another. Theyare polarized along the short inplane Z (passingthrough the center of the pyrrole ring and Natom) and the long inplane Y (perpendicular tothe Z axis in the plane of the Cz group) molecularaxis, respectively.

The ECz monomer emission (0,0) band occursfrom the 1Lb state, that is, it corresponds to the1Lb 3

1A transition. From Figure 1(a), a value ofthe angle between excitation- and emission-tran-sition moments for ECz of 25.6 � 4.1°33 (r � 0.288� 0.028) is achieved when exciting into some vi-brational levels of the 1Lb 4

1A transition (344� 5 nm). This result indicates that excitation- andemission-transition moments are nearly parallel.The anisotropy decreases as the excitation pro-ceeds toward lower wavelengths, from 1Lb4

1A tothe 1La4

1A absorption band. A negative value ofr � �0.071 � 0.002, which corresponds approxi-mately to the (0,0) 1La4

1A transition, is reachedaround 294 nm (�5 nm) of excitation. This valueof r corresponds to an angle between excitation-and emission-transition moments of 62.4 � 0.3°,signifying a transition along a molecular axisnearly perpendicular to the emitting axis. Thefact that the emission wavelength is fixed a littlebit farther away from the (0,0) 1Lb 3

1A transi-tion, along with some intrinsic causes of depolar-ization, is responsible for the values of �25° awayfrom 0 and 90°, respectively. When emission isfixed at 350 nm, the angles between excitationand emission dipole moments when exciting at294 (�5 nm) become closer to 90° (78.8 � 1.0°).

Polymers exhibit absolute values of r at thewavelength of such transitions that are consider-ably smaller than those for the ECz model com-pound. The details depend on the Cz content ofthe copolymer. Figure 1(b) depicts the emissionspectra for ECz and P0 and the emission anisot-

Figure 1. (a) Fluorescence excitation anisotropyspectra for ECz and the P# series in the PMMA solidmatrix at room temperature, detected with emission at365 nm. The dashed line depicts the excitation spec-trum for the ECz sample at the same experimentalconditions. (b) Fluorescence emission anisotropy spec-tra upon excitation at 332 nm for ECz and the P# seriesand emission spectrum (dashed lines) for ECz and P0 inthe PMMA solid matrix at room temperature. Symbolsfor r are ECz (■), P0 (F), P1 (Œ), P2 (�), P3 (�), P4 ( ),P5 (�), P6 (�), P7 (E), P8 (‚), and P9 (ƒ).

1618 GALLEGO, MENDICUTI, AND MATTICE

ropy spectra for the ECz and P# upon excitationat 332 nm. This wavelength was taken approxi-mately 10 nm to the blue from the (0,0) 1Lb4

1Aabsorption band to avoid interference at themonomer emission band (350 nm) from scatteredlight. The largest r value is again obtained forECz (r � 0.24 � 0.01 for 350 � 5 nm), whichdenotes excitation and emission dipole momentsforming an angle of �30°. Polymers nearly alwayshave values of r that are smaller than 0.1, asshown in Table 2. Because energy migration be-tween a set of chromophores attached to the poly-mer chain serves to depolarize the radiation emit-ted by the system, in a rigid medium the degree ofdepolarization depends on the extent of migra-tion. Because the MD simulations provide no ev-idence for a strong preference for preferred orien-tations of pairs of chromophores, the isotropy r�1

(reciprocal of anisotropy) is proportional to theextent of energy migration.

Table 2 lists values of r for ECz and the poly-mer series at different pairs of excitation–emis-sion wavelengths (where the transitions 1Lb4

1Aand 1Lb 3

1A are involved). Such data were ob-tained from the emission and excitation anisot-ropy spectra of two different sets of samples invitrified PMMA. The largest anisotropy valueswere obtained for the ECz model, for which en-ergy is not allowed to transfer at this concentra-tion of chromophores.

Figure 2 portrays the average of the values ofthe isotropies relative to the one for the ECzmodel compound, rP#

�1/rECz�1, which is a mea-

sure of the amount of energy migration betweenCz groups in P#. These averages were obtainedfor the two sets of samples from all anisotropydata collected in Table 2. Although the resultswere accompanied by large uncertainties, the firstthree members (P0, P1, and P2) of the series witha higher Cz content (lower �n2� values) do notshow the highest values rP#

�1/rECz�1. The largest

values of rP#�1/rECz

�1 were obtained for copoly-mers of intermediate values of �n2�. The rP#

�1/rECz

�1 decrease monotonically for the three lastmembers of the series.

Fluorescence Quenching

Fluorescence quenching has been used to mea-sure intramolecular transfer and energy-migra-tion processes in polymer systems dispersed indilute fluid solutions,1–3 including Cz containingpolymers.8,16,37,38 If an individual excited speciesis quenched by a collision with a quencher Q, the T

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ENERGY MIGRATION 1619

steady-state Stern–Volmer quenching constant,KSV, provides a measure of the efficiency ofquenching by

F0/F � 1 KSV�Q� � 1 kQ�0�Q� (6)

where F0 and F are the values of a relevant fluo-rescence parameter (fluorescence quantum yield,�, intensity, I, or lifetime, �) in the absence andpresence of a given concentration of quencher [Q],kQ is the second-order quenching constant, and �0is the excited-state lifetime in the absence of aquencher.

Because our polymer excited states do not de-cay as a single exponential, � was taken to be aweighted average of the individual components ofthe decay. Then, the average lifetime of a multi-ple-exponential decay function can be defined as

��� � � tItdt/� Itdt � �Ai�i2/�Ai�i (7)

and the relative quantum yield of the ith compo-nent is

�i � � Aie�t/�idt/� Itdt � Ai�i/�Ai�i (8)

Equations 7 and 8 assume that each lifetime com-ponent of the fluorescence for the polymers acts asa kinetically independent species. They do notconsider the presence of the excimer formation–dissociation equilibrium of monomer species orother more complicated mechanisms. The Stern–Volmer equation is strictly applicable to thequenching of an individual species. If we alsoassume that each component is independentlyquenched by Q with the same kQ value, then as anapproximation F0/F can be treated as the sum ofindividual quenching relations, weighted by therelative quantum yield of each component:

F0/F � ��i1 kQ�i,0�Q� � 1

kQ�Ai�i,02 /�Ai�i,0�Q� � 1 kQ��0��Q� (9)

The modified Smoluchoswki–Einstein39 equa-tion can be used to interpret kQ

Figure 2. Average of the isotropes relative to the one for ECz, rP#�1/rECz

�1, obtainedfrom the data in Table 2 for sample series A and B versus the number-average sequencelength of MMA monomer, �n2�.

1620 GALLEGO, MENDICUTI, AND MATTICE

kQ � 4�NARDc DQ �sP (10)

where Dc and DQ are the diffusion constants ofthe excited chromophore species and quencher,respectively (DCCl4 � 1.5 � 10�5 cm2 s�1);40 R isthe sum of radii for the excited species and Q; �sis the singlet energy-migration coefficient; and Pis an efficiency factor or quenching probability percollision. We assume that P and R are the same inall polymer samples, Dc � 0 for Cz groups at-tached to the polymer chains, and �s � 0 for themodel polymer P9 whose Cz groups are presum-ably rather isolated along the chain.

From the last equation we obtain

�s

DCCl4�

kQP# kQ

P9

kQP9 (11)

On the basis of a one-dimensional random walk,the excitation diffusion length Ls can be evalu-ated from

Ls � 2�s��0�1/2 (12)

The fluorescence decays for ECz when emission ismonitored at either 350 or 375 nm in the presenceof a quencher or not can be adequately describedby a single exponential decay (and � � ���). How-ever, the fluorescence decays for P0 and P1–P9were more complicated, and most of them requirea three-component exponential decay function tofit the emission satisfactorily at both emissionwavelengths 350 and 375 nm. The set of Ai and �iparameters of eq 1, not reported individuallyhere, depend on P#, the emission wavelengthmonitored, and the quencher concentration.Thus, the homopolymer P0, when [Q] � 0, showsthree lifetimes of 14.1 ns (14.3 ns), 4.4 ns (4.8 ns),and �0.8 ns (1.2 ns) at the emission of 350 nm(375 nm). In other copolymers with smaller Czcontents, several effects are observed: First, the �for the intermediate component increases from P0to P9 up to a value of 8.5 ns, which is similar tothe value obtained for the model compound. Itsrelative proportion also increases from approxi-mately 30 up to 96% when going from P0 to P9.Some researchers41 attribute the decrease in �with increasing Cz content to an enhancedquenching through energy transfer into the con-tiguous sequences containing Cz groups. This in-termediate component is characteristic of isolatedCz chromophores in the chain. Second, becausethe component with the longest lifetime makes a

larger contribution to the total emission as theanalysis wavelength increases, this component isascribed to the emission from an excimer. Thiscomponent disappears for the last three membersP7–P9, and their decays can be perfectly fitted bythe sum of two exponentials. Third, the fast compo-nent, which was detected in all samples, does nothave any special trend with # or the wavelength ofemission. The same researchers41 attribute thiscomponent to the monomers that are quenched byexcimer formation, existing in the adjacent se-quences of Cz units. However, the last three mem-bers P7–P9, which hardly have any excimer emis-sion, exhibit this component. The values of the com-ponents, except for the fastest one that apparentlydoes not have any special trend, decrease withquencher concentration. In any case, the purpose ofthis work is not to discuss and analyze the compo-nents of the decay but instead to use the fitting ofthe decay curves as a device by which we obtain theaverage decay time, ���.

Representative Stern–Volmer plots of �0/� and��0�/��� of ECz and P# in toluene at 25 °C aredepicted in Figure 3. Linear behaviors of lifetimerepresentations for all members of the series wereobtained. However, some of the plots of quantumyield show a slight deviation from linearity in therange of the quencher concentrations measured.This deviation, which was also observed for ECz,decreases as the VCz content in P# decreases,that is, as the intramolecular excimer decreases.This kind of dependence was also observed byothers when analyzing the quenching of excimerstates or in the case of strong overlapping of ex-cimer and monomer fluorescence bands in severalpolymers including PVCz.8,37 In these situations,the Stern–Volmer KSV of eq 6 is wavelength de-pendent. Our results for KSV obtained fromStern–Volmer plots of fluorescence intensities re-corded at 350 nm (mainly monomer band) and375 nm (mainly excimer component) show similardeviation of linearity but KSV (at 375 nm) � KSV(at 350 nm), especially for the first members ofthe P# series with a larger excimer component.However, the fact that a similar curvature is ob-served in the monomeric ECz model and the lin-ear behavior of lifetime Stern–Volmer plots sug-gests that perhaps there are other contributionsto the deviations from linearity. The presence of astatic quencher could be one of these reasons.However, the quenching deviation that is ob-tained for ECz and P# does not follow the typicalquadratic relationship that assumes that ground-state complexes of CCl4 and Cz species exist in

ENERGY MIGRATION 1621

equilibrium with a free quencher, enhancing theeffect of collisional quenching. We could also tryto explain the results that pertain to the CCl4molecules adjacent to the Cz chromophore at themoment of excitation, which should have an in-fluence on � but not on �. The effect on Stern–Volmer plots should be larger as [CCl4] increases.The fact that the curvature decreases as the Czcontent decreases and the linear behavior of life-time Stern–Volmer plots should confirm this.

Table 3, columns 2–6, lists values of KSV ob-tained from Stern–Volmer plots of �/�0, �/�0 (at 350and 375 nm), and I/I0 (at 350 and 375 nm), respec-tively, versus [CCl4]. The next two columns collectaverage lifetimes in the absence of a quencher, ob-tained with eq 7 at the two emission wavelengths,350 and 375 nm, where the monomer and the exci-mer components are, respectively, dominant.

Figure 4 depicts average values of the singletenergy migration rate ��s� (eq 11) and the excita-

Figure 3. Stern–Volmer plots of �0/� and ��0�/��� for ECz (�) and polymers P0 (E), P4(‚), and P7 (ƒ) at 25 °C in toluene, with CCl4 as the quencher.

Table 3. Stern–Volmer Constants (M�1) and Average Lifetime (ns) in the Absence of Guencher

Sample KSVa KSV

b KSVc KSV

d KSVe ��0�f ��0�g

ECz 108 � 5 77 � 2 74 � 1 114 � 7 118 � 8 7.2 7.2P0 127 � 3 65 � 1 66 � 2 97 � 3 123 � 5 12.4 12.9P1 115 � 4 62 � 1 69 � 2 87 � 3 108 � 5 9.5 12.3P2 109 � 2 59 � 2 70 � 3 83 � 2 106 � 4 9.0 11.8P3 83 � 1 54 � 2 50 � 2 80 � 3 93 � 2 7.9 8.3P4 77 � 1 55 � 1 52 � 2 74 � 2 80 � 0 7.9 8.3P5 89 � 2 50 � 0 45 � 1 91 � 3 100 � 2 7.7 8.2P6 76 � 1 49 � 0 51 � 0 80 � 2 86 � 3 7.8 8.2P7 54 � 1 40 � 1 37 � 1 57 � 1 57 � 2 7.9 8.1P8 56 � 3 37 � 0 36 � 1 64 � 5 58 � 4 8.2 8.4P9 55 � 5 33 � 0 34 � 0 62 � 4 56 � 5 8.4 8.6

a From �0/� Stern–Volmer plots.b From �0/� at 350 nm.c From �0/� at 375 nm.d From I0/I at 350 nm.e From I0/I at 375 nm.f At 350 nm.g At 375 nm.

1622 GALLEGO, MENDICUTI, AND MATTICE

tion diffusion length �Ls� (eq 12) from the sixbimolecular quenching constants derived fromdifferent Stern–Volmer plots. All polymer sam-ples (with the exception of P9 that was taken as amodel) show values of ��s� and �Ls� that are non-zero. This result indicates migration of energyalong the polymer chain for all copolymers exam-ined. The value of �Ls� for P0 is similar to thatfound by Webber et al.37 (�40 A). Both parame-ters seem to increase as �n2� increases for the firstmembers of the series up to �n2� � 3.5. However,above this value for the last three members P7–P9, both parameters decrease with �n2�. As beforewith the anisotropy measurement, compoundswith the highest number of Cz–Cz sequences,with the highest excimer formation, do not showthe highest migration rate. However, after a cer-tain Cz composition, when chromophores are faraway in the chain, the migration rate decreases.

MD

The MD trajectories of trichromophoric frag-ments were computed in vacuo with Sybyl 6.4.42

Fragments were isotactic and syndiotactic formsof CH3-A-CH2-Bn-A-CH2-Bn-A-CH3 where A� OCHCzO, B � OC(CH3)COOCH3OCH2O,and n � 0–6. In the remainder of this article,

they are named In or Sn for isotactic and syndio-tactic forms, respectively. The default Tripos forcefield designed for the electronic ground state wasused.43 The duration of each trajectory was 1 ns,computed with a time step of 1.0 fs. Conforma-tions were saved at intervals of 200 fs for subse-quent analysis, yielding N � 5000 conformations.Because the purpose of the trajectory is to providea representative sample of the conformationalspace accessible to the molecule within reason-able computer time, it was performed at a tem-perature high enough (600 K) to avoid entrap-ment in an energy minimum. More details aboutthe simulations have been reported.28

Three parameters related to the rate of energytransfer pR, the normalized �2pR, and the effi-ciency in the energy transfer were calculated. pRis the probability of finding the center of mass ofa Cz group within a distance R of the center ofmass of another Cz group. This value can be ob-tained as

pR � �0

R

wRdR (15)

where wR is the distribution function of the dis-tance between Cz neighbors. �2 is the orienta-

Figure 4. Average values of the singlet energy migration rate ��s� and the excitationdiffusion length �Ls� versus the number-average sequence length of MMA monomer,�n2�. Averages are obtained from the data in Table 3.

ENERGY MIGRATION 1623

tional factor for fixed dipole transition momentsof absorption and emission in the direction of theshort inplane Z axis of each Cz chromophore. Theefficiency in the energy transfer �teo is obtainedas

�teo �1

2N �i�1

N �1 2/3R6

�2R06 ��1

(16)

which considers the two possible interactions be-tween adjacent Cz chromophores in the frag-ments. R0 is assigned the experimental value of20 A. Figure 5 portrays the distribution functionfor the average of the two adjacent Cz–Cz dis-tances along the trajectory for In and Sn. Even forI6 and S6 fragments, almost all conformationshave a Cz chromophore within a sphere of radiusR0 from its nearest neighbor Cz. The averagedistances between adjacent Cz obviously decreasewith n. The averages are 4.3 (5.0), 6.2 (6.6), 8.7(8.3), 9.9 (10.0), 13.2 (10.7), 13.5 (12.8), and 15.9 A(and 13.3 A) for n � 0–6 for In (Sn). The averageorientational factors ��2� between adjacent Czgroups are 1.00 (0.94), 0.47 (0.71), 0.77 (0.49),0.62 (0.65), 0.67 (0.48), 0.71 (0.80), and 0.56 (0.73)in the same sequence.

Figure 6 depicts the dependence of pR and �2pR

on n for different assumed values of R includingthe experimental value of 20 A for In and Sn. Theplotted values of pR and �2pR were the normalizedsum of two possible interactions, those betweenpairs of adjacent Cz chromophores in the trichro-mophoric model compounds. When R has the ex-perimental value of 20 A, pR � 1 for all fragmentswith the exception of some conformations for I6and S6. This indicates that the distance betweentwo adjacent chromophores is always smallerthan the experimental R0, even for the most ex-tended conformations. Thus, energy transfershould be possible for all members of the series.There are no quantitative differences betweenisotactic and syndiotactic fragments.

The incorporation of the orientational factor,by depicting �2pR, does not substantially changethe previous results. As with pR, the product �2pRmust approach 1 as R becomes higher than the

Figure 6. pR and �2pR for different assumptions of Rfor the interaction between adjacent Cz groups for Inand Sn as a function of n. Dotted lines denote calcula-tions performed for R with the experimental Forsterradius (R0 � 20 A). Symbols are values of R � 4 (F), 8(�), 12 ( ), 16 (*), R0 (V), and 24 A (E).

Figure 5. Distribution of the distances between thecenters of neighboring Cz groups for (a) In and (b) Snfragments obtained from the analysis of MD simula-tions at 600 K. Symbols are n � 0 (�), 1 (E), 2 (‚), 3 (ƒ),4 (�), 5 ( ), and 6 (�).

1624 GALLEGO, MENDICUTI, AND MATTICE

maximum distance between the centers of theadjacent Cz groups. Trends of pR and �2pR arevery similar, and In and Sn behave in a similarway. For a distance R � R0, with the exception ofI6 and S6, the normalized product �2pR is nearlyone.

Figure 7 presents the efficiency of the Forstertransfer �teo obtained from eq 14 as a function ofn. �teo is high for all In and Sn members, and itobviously decreases as n increases. Figure 7 alsodepicts the probability of the conformations thatcan adopt a sandwich geometry (or excimer) as afunction of n for same compounds.28 The largestcontribution to these values comes from interac-tion between adjacent Cz chromophores. The con-tribution due to interaction between Cz of bothends is always smaller than 10% and is usuallysmaller than 1%. These results indicate that theamount of intramolecular excimer decreasesmonotonically as n increases and is almost zerofor n � 2. The highest probability for n � 0 indi-cates the highest amount of excimer for P0, whichis the experimental result, but also that most ofthe excimers in the copolymers should be due to

an interaction between Cz groups in Cz–Cz se-quences. The values of probability are almost zerowhen more than two MMA units are between Czgroups. If it is true that excimers can trap theenergy migration, decreasing the efficiency ofsuch a process, then our results for probability ofexcimer imply that for the fragments with n � 2,the efficiency of energy transfer should be smallerthan the one predicted by ignoring the presence oftraps.

Our experimental results suggest that theamount of intramolecular excimers continuouslydecreases as the MMA content, �n2�, increases.28

Furthermore, on the basis of the behavior of pa-rameters such as r�1, ��s�, and �Ls�, the efficiencyfor energy migration passes through a maximumat �n2� � 3.5. For the polymers with a high con-tent of Cz–Cz sequences (P0–P2), the largeamount of intramolecular excimer28 substantiallyinhibits the process of energy transfer. Intramo-lecular excimer formation acts by trapping theexcitation energy.

CONCLUSIONS

Quenching measurements performed in dilute so-lutions of toluene with CCl4 as a quencher andfluorescence anisotropy measured in a solid ma-trix of PMMA provide evidence for the presence ofsinglet energy migration in VCz/MMA copoly-mers. The experiments showed a double behaviorwith the number-average sequence length ofMMA monomer �n2�. From the homopolymer up tocopolymers with a relatively high Cz content, �n2�� 3.5, the energy migration increased because ofa decrease in the presence of excimer traps. Itthen decreased for samples with a higher value of�n2� because the Cz groups were remote from oneanother.

Therefore, a decreasing density of excimer-forming sites could serve to increase the energy-migration rate and then the photoconductingproperties of PVCz. Theoretical MD analysis ofseveral parameters for isotactic and syndiotacticforms of fragments examined supports this inter-pretation of the experiments.

This research was supported by DGESIC grantBQU2001-1158 (F. Mendicuti) and National ScienceFoundation grant DMR 9844069 (W. L. Mattice). F.Mendicuti expresses thanks to M. L. Heijnen for assis-tance with the preparation of this article.

Figure 7. Efficiency of Cz to Cz Forster transfer �teo

for the experimental values of R0 of 20 A in In (�) andSn (E) fragments as a function of n and values ofprobability of intramolecular excimers (from ref. 28) forIn (■) and Sn (F) obtained from analysis of the MDtrajectories.

ENERGY MIGRATION 1625

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1626 GALLEGO, MENDICUTI, AND MATTICE