EUROPEAN POLYMER JOURNAL
European Polymer Journal 40 (2004) 1997–2008
www.elsevier.com/locate/europolj
Complex macromolecular dynamics: I. Estimation technique for time-resolved emission anisotropy ratio of chromophores incorporated into polymer chains Chihiro Hashimoto a, Jaques Rouch b, Jean Lachaise c, Alain Graciaa c, Hideharu Ushiki a,* a
Laboratory of Molecular Dynamics and Complex Chemical Physics, Department of Environmental and Natural Resource Science, Faculty of Agriculture, Tokyo University of Agriculture and Technology, 3-5-8, Saiwai-cho, Fuchu-shi, Tokyo 183-8509, Japan b Centre de Physique Moleculaire Optique et Hertzinne, UMR5798, Universite Bordeaux I, 351, Cours de la Liberation, 33405 Talence, France c Laboratoire de Thermodynamique Etats Metastables et de Physique Moleculaire, U.F.R. Sciences et Techniques, Universite de Pau, avenue de l’universite, 64000 Pau, France Received 23 February 2003; received in revised form 6 April 2004; accepted 7 April 2004 Available online 9 June 2004
Abstract Time-resolved fluorescence emission anisotropy ratios of carbazolyl groups incorporated into polystyrene chains in polyethyleneoxide(PEO)/1,2-dichloroethane mixtures have been measured by the single photon counting method. The fluorescence depolarization method is very excellent to clarify various dynamical modes of polymer chains, and many theoretical and experimental researches have so far been reported in the field of polymer chain dynamics. However there are few reports about the dynamics on the polymer side chain, because the dynamical mechanism of the polymer side chain is very complicated. In this report we tried to analyze the dynamical modes of the polymer side chains by the fluorescence depolarization method. Five dynamical modes of a polymer chain based on the W€ oessner model were estimated by our original analytical technique ‘v2 -map method’. The value of each mode of a polymer side chain was discussed above the overlap concentration (C ) of PEO and the micro-environments were clarified in the vicinity of the chromophore attached to the polymer side chain. 2004 Elsevier Ltd. All rights reserved. Keywords: W€ oessner model; Fluorescence depolarization; C*
1. Introduction In the field of condensed matters, the twisted internal charge transfer (TICT) probe, the fluorescence depolarization, and the excimer formation methods have so far been used in order to analyze the micro-environments, the Brownian movements, and the micro-struc-
*
Corresponding author. Tel./fax: +81-42-367-5616. E-mail address:
[email protected] (H. Ushiki).
tures, respectively [1]. The fluorescence depolarization method is very efficient, especially to clarify the dynamical mechanism of polymer chains. In the field of polymer physics, many researchers found the fact that some dynamical modes of macromolecular chains can be measured directly by the time-resolved fluorescence depolarization method. Various theories for dynamical modes of polymer chains have been reported consequently. Let us explain a history of such development of the fluorescence depolarization method as follows [2].
0014-3057/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.eurpolymj.2004.04.002
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The first period was the establishment of the relationship between the Brownian motion of molecules and the fluorescence depolarization principle (1940–1960). During this period, the approximation of a rigid spherical model was established [3]. The emission anisotropy ratio, r is represented by rðtÞ ¼ r0 expðt=hÞ;
ð1Þ
where r0 and h are the emission anisotropy ratio without the Brownian motion of molecules and the rotational correlation time, respectively. The rotational diffusion coefficient D is represented by D ¼ 1=ð6hÞ. The mean anisotropy ratio r induced by the stationary light is shown by the following equation using 1=h ¼ kT =vg: 1 1 sf 1 kT ¼ : ð2Þ ¼ 1þ 1þ r r0 r0 vg s sf , v, g, T , and k are the fluorescence lifetime of the chromophore, the volume of the spherical rotational body, the solvent viscosity, the absolute temperature and the Boltzmann constant, respectively. Eq. (2) is known as the Perrin–Webber plots. The second period was the establishment of the timeresolved fluorescence depolarization method (1960–1980). During this period, the approximation of a rotational ellipsoid model was established [4], and r is expressed by rðtÞ ¼ A1 expðt=h1 Þ þ A2 expðt=h2 Þ þ A3 expðt=h3 Þ; ð3Þ where 6 3 sin2 a cos2 a; A2 ¼ sin4 a; 5 10 1 1 ¼ DL þ 5DS ; A3 ¼ ð3 cos2 a 1Þ2 ; 10 h1 1 1 ¼ 4DL þ 2DS ; ¼ 6DS : h2 h3
A1 ¼
ð3aÞ
DL and DS are the rotational diffusion coefficients of the long- and short-axes of an ellipsoid, respectively. a is the angle between the long-axis and the emission transition moment of the chromophore. Various emission anisotropy ratio decay curves were measured by the timeresolved fluorescence depolarization technique, and some researchers had begun to notice the existence of the non-exponential decay phenomena in nature. The third period was the establishment of the analytical method based on the restricted rotational motions of macromolecules (1970–1980). During this period, the researchers discussed the theme that the non-exponential decay curves of the fluorescence emission anisotropy ratio were caused by various motional modes of macromolecules. The complex biomolecular dynamics were further extended by a number of investigators using ESR and NMR techniques at that time, and the measured
emission anisotropy ratio decay curve of chromophores in condensed biomolecules actually showed various non-exponential functions [5]. Researchers picked up some important information of intramolecular motions of biomolecules by the time-resolved fluorescence depolarization technique, that is, the restricted rotational motions of macromolecules in membrane (Wobbling– Cone model) and the twisted motions of supermacromolecules (DNA) as shown in Eqs. (4) and (5), respectively: rðtÞ Dw t ¼ A1 þ ð1 A1 Þ exp ; ð4Þ rð0Þ hri where A1 ¼ rð1Þ rð0Þ ¼ fð1=2Þ cos að1 þ cos aÞg2 ; X Aj rj =ð1 A1 Þ hri ¼
ð4aÞ
j6¼1
and pffi pffi rðtÞ ¼ A1 expðr t=4Þ þ A2 expðr tÞ þ A3 ;
ð5Þ
where r¼
2kT pffiffiffiffiffiffi : pR gY
ð5aÞ
Y is a molecular elasticity. The fourth period was the establishment of the analytical method based on the local motions of polymer chain segments (1970–now). During this period, the micro-environmental modes of polymer main chains were discussed in details using the time-resolved fluorescence depolarization technique [6], and various model functions of the local motions of polymer chain segments have been proposed [7]. However, the theoretical dynamical models of the polymer side chains are little reported except for the W€ oessner model [8]. In this model, the internal anisotropic rotations in the vicinity of a polymer side chain are separated into five dynamical modes. The discussion about the relationship between the W€ oessner model and the experimental data based on the time-resolved fluorescence depolarization technique would be very complicated. So few researchers tried to estimate the dynamical modes of polymer chains based on the fluorescence emission anisotropy decay curves of the chromophores attached to the polymer main chains. In this report, we estimate the appropriateness of the W€ oessner model in our experiments using our original analytical method. Our original estimation technique based on the W€ oessner model is very excellent to clarify various dynamical modes of a flexible polymer in the region of semi-concentrated polymer concentration.
C. Hashimoto et al. / European Polymer Journal 40 (2004) 1997–2008
2. Experimental 2.1. Materials N -(2-Naphthylmethyl)carbazole (NMC) was synthesized by a reaction of potassium carbazolide with 2-chloromethylnaphthalene as shown in Fig. 1 [9]. Copoly(styrene-vinylcarbazole) (P(St–Cz)) was prepared using an usual radical polymerization of styrene and vinylcarbazole as shown in Fig. 1. The number-average molecular weight and the molecular-weight distribution of P(St–Cz) were Mn ¼ 2.5 · 104 and Mw =Mn ¼ 1.84, respectively. The content of carbazolyl group in P(St– Cz) was about 7.0% unit/polymer. Poly(ethylene oxide) with Mn ¼ 300 (PEO300) and 1,2-dichloroethane were purchased from Wako Chemical Co., and used as received. 2.2. Measurements NMC and P(St–Cz) were respectively dissolved in a mixture solvent of PEO300 and 1,2-dichloroethane at a carbazolyl group concentration of 1.0 · 107 mol dm3 . The solvent viscosity changed by the fraction volume of PEO300 from 50% to 80% was in the range from 0.006 to 0.033 N s m2 . The viscosities of the mixed solvent were measured using an Ubbelohde viscometer at 30 C. The samples were deaerated by several freeze-pump-thaw cycles under a high vacuum system, and sealed in a cylindrical cell of 1 cm diameter. The fluorescence depolarization spectroscopy measurement of NMC or P(St–Cz) in a PEO300/1,2-dichloromethane mixture at 25 C was carried out as a part of perfective laboratory automation system for macromolecular analysis (PLASMA) which is a new measurement system that consists of various spectro-
1999
scopic apparatus supported by a personal computer network with many original electric circuits and analytical programs [2,10]. The flowchart of the fluorescence depolarization measurement of PLASMA is shown in Fig. 2 [2,11]. The stationary fluorescence depolarization spectroscopy measurements were carried out by the fluorescence spectrophotometer (Hitachi: 650-60). The excited wavelength for the fluorescence depolarization spectroscopy was selected at 340 nm according to the absorption, excitation and emission spectra and the nano-second time-resolved and consequently the data were analyzed by our programs. Then the fluorescence decay curve and the polarized fluorescence decay curve of NMC or P(St–Cz) excited at 340 nm were measured by a nano-second time-resolved fluorescence spectroscopy using a time-correlated single-photon counting method (Horiba: NAES-1100). Observed fluorescence decay curve Iobs ðtÞ and emission anisotropy ratio decay curve robs ðtÞ were calculated by Iobs ðtÞ ¼ IVV ðtÞ þ 2GIVH ðtÞ
ð6Þ
and robs ðtÞ ¼
IVV ðtÞ GIVH ðtÞ ; IVV ðtÞ þ 2GIVH ðtÞ
ð7Þ
respectively. G is the compensating factor for anisotropic sensitivity of the photomultiplier of NAES-1100 and defined by Z Z G ¼ IHV ðtÞ dt IHH ðtÞ dt: ð8Þ IVV ðtÞ, IVH ðtÞ, IHH ðtÞ and IHV ðtÞ indicate the decay curves of the polarized fluorescence intensities measured through a sharp cut filter (Toshiba: UV35). Subscripts
Fig. 1. Chemical structures of NMC and P(St–Cz).
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Fig. 2. Flow chart of fluorescence depolarization measurement of PLASMA. The stationary anisotropy spectra are measured by the fluorescence spectrophotometer (Hitachi: 650-60) and analyzed together with the absorption, excitation and emission spectra. On the other hand, nano-second time-resolved fluorescence depolarization spectroscopy measurements were carried out by a time-correlated single-photon counting method (Horiba: NAES-1100). Nano-second time-resolved fluorescence depolarization spectroscopy measurements were carried out and consequently the data were analyzed by our programs. Integral transformation method is a new analytical approach for the fluorescence decay curve (16). In this report we applied a v2 -map method to the emission anisotropy ratio analysis.
‘V’ and ‘H’ represent the parallel and the perpendicular directions to the vertical line. The first suffix indicates
the direction of an incident light and the second to an emitted light.
C. Hashimoto et al. / European Polymer Journal 40 (2004) 1997–2008
2.3. Calculations
v2 ¼
In general, the fluorescence decay curve Ical ðtÞ and the emission anisotropy ratio decay curve rcal ðtÞ are represented by Ical ðtÞ /
Z
P ðT ÞSðt T Þ dT
ð9Þ
and Rt 0
P ðT ÞDðt T ÞSðt T Þ dT ; Rt P ðT ÞSðt T Þ dT 0
ð10Þ
respectively. P ðtÞ, SðtÞ and DðtÞ represent a response function of the apparatus, a fluorescence decay curve corresponding to an infinitely short excitation, and an orientational auto-correlation function, respectively. P ðtÞ was assumed as an exciting light pulse. SðtÞ is usually a sum of exponential fluorescence decay curves and was used in this report as a double exponential function SðtÞ ¼ a1 expðt=s1 Þ þ a2 expðt=s2 Þ;
ð11Þ
where the si s are the fluorescence decay constants. DðtÞ was assumed as an exponential function for NMC, while two-type trial functions of DðtÞ were applied for P(St– Cz), that is, a double exponential function (Eq. (12)) or a function based on the W€ oessner model (Eq. (16)): DðtÞ ¼ A1 expðt=h1 Þ þ A2 expðt=h2 Þ:
ð12Þ
We made a deconvolution and a curve fitting programs on the basis of the Wahl’s method [12] and the quasiMarquardt algorithm [13], respectively. The goodness of the fitting calculation was evaluated by a value of the residual sum of squares v2 . The program computed adequate values of variable parameters of a fitting function until the variation of v2 become less than 1 · 106 . On determining the value of parameters ai and si in SðtÞ for the curve fitting of Ical ðtÞ, v2 was calculated by Z t2 1 v2 ¼ wðtÞfIobs ðtÞ Ical ðtÞg2 dt; ð13Þ t2 t1 4 t1 where wðtÞ, t1 and t2 indicate the weighting function at time t, the lower and upper cut-off times for the fitting calculation, respectively. The weighting function adopted for Ical ðtÞ [12] is wðtÞ ¼
Z
t2
wðtÞfrobs ðtÞ rcal ðtÞg2 dt;
ð15Þ
t1
where m is the number of variable parameters of DðtÞ and equals to 6 in case of the W€ oessner model. The weighting function was replaced by [12]
t
0
rcal ðtÞ /
1 t2 t1 m
2001
1 : IVV ðtÞ þ 4G2 IVH ðtÞ
ð14Þ
In contrast, on estimating the value of parameters in DðtÞ for the curve fitting of rcal ðtÞ, Eq. (13) is substituted by
wðtÞ ¼
3Iobs ðtÞ
: 1 þ G þ 3Grobs ðtÞ 3robs ðtÞ2 2ð2G 1Þrobs ðtÞ3 ð16Þ
2.4. v2 -map method In order to estimate the validity of various models, we proposed a novel method called ‘v2 -map method’ [2,14]. Select two parameters and calculate the value of v2 as the value of the parameters is changed independently. We consider an orthogonal coordinate system, O–XYZ, and the two parameters of the fitting function are selected as X and Y coordinate axes and the calculated 1=v2 are plotted on the Z coordinate one. The value of 1=v2 approaches 1 when a function fits well to the measured data. We named such three-dimension graph a ‘v2 -map’. This method enables us to estimate the fitting properties in the vicinity of a stable point in a trial function. Fig. 3 shows a v2 -map together with various quantitative estimation techniques of the v2 -map. A unique peak in a v2 -map means a unique fitting result for variable parameters in a trial function. The full width at half maximum of the peak represents the sensibility of the parameter. The more narrow the value of the full width at half maximum become, the more sensible the parameter will. If selected parameters are dependent each other, the shape of v2 -map is to be a distorted shape like a horseshoe.
3. Results and discussion 3.1. Fluorescence and emission anisotropy ratio decay curves of carbazolyl groups incorporated into polystyrene Fluorescence decay curves of NMC and P(St–Cz) were fitted well by Eq. (9) and the fitting parameters were listed in Table 1. In case of NMC, a1 =a2 is almost 1 at any PEO300 concentration and SðtÞ of NMC seems like a single exponential decay. On the other hand, it is clear that a double exponential has a good agreement with SðtÞ of P(St–Cz) as shown in Fig. 4. SðtÞ with these parameter values was used in Eq. (10) for the fitting of the emission anisotropy ratio decay curve, rðtÞ. As listed in Table 1, rðtÞ of NMC was fitted well by Eq. (10) with DðtÞ as a single exponential function. But rðtÞ of P(St– Cz) was not fitted well using DðtÞ as a single exponential function. This is because the decay curve of P(St–Cz)
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Fig. 3. Analytical image of v2 -map. Obtained v2 -map contains the information of the fitting condition and the condition can be numerized by the following images via various procedures: (a) contour graph, (b) v2 value along Y -axis of maximum, (c) maximum value plot of X - and Y -axis, (d) maximum v2 value of Y -axis, (e) v2 value along X -axis of maximum, (f) area over half width, (g) maximum v2 value of X -axis, (h) area over half width along X - and Y -axis, (i) distribution of v2 value within 46–255, (j) 3D graphics of v2 -map.
reflects a great amount of relaxation modes of chromophores attached to a backbone polymer chain. As a general method for the time-resolved fluorescence depolarization, such a non-exponential decay is fitted by a double exponential function. But, there is a problem that the physical meaning of a trial double exponential function is not clear. As the fitting results are listed in
Table 1, the PEO300 concentration dependence on two characteristic times was not obvious. On the other hand, the W€ oessner model has a clear dynamical image of polymer side chain as shown in the left-side of Fig. 6. The orientational auto-correlation function, DðtÞ of the W€ oessner model is given by
C. Hashimoto et al. / European Polymer Journal 40 (2004) 1997–2008
2003
Table 1 Values of various parameters of fluorescence and emission anisotropy ratio decay curves of NMC and P(St–Cz) fitted to single and double exponential functions, and the Woessner model NMC / (PEO)
0.5
0.6
P(St–Cz) 0.8
0.5
0.6
0.7
0.923 1.50 7.23
0.555 3.14 11.7
0.681 2.11 11.1
1.26 1.45 10.2
Emission anisotropy decay curves (single and double exponential functions) 0.182 0.260 0.154 0.268 A1 A1 =A2 3.66 h1 (ns) 0.487 0.368 2.46 1.12 0.775 15.3 h2 (ns) v2 1.63 1.55 1.20 1.85 0.903
4.96 0.450 12.3 1.18
Emission anisotropy decay curves (W€oessner model) A0 a (ns) h1 (ns) h2 (ns) h3 (ns) h4 (ns) v2
0.0298 89.8 4.77 14.5 0.444 1.11 · 107 1.79
Emission decay curves (double exponential a1 =a2 1.11 0.922 s1 (ns) 2.74 2.64 7.33 7.32 s2 (ns)
0.7 function) 0.891 1.92 7.16
0.0175 85.5 6.78 12.4 0.433 2.22 · 109 1.01
2.56 0.660 9.38 0.880 0.0415 90.6 6.78 36.2 0.530 1.00 · 104 1.04
0.8 1.52 3.66 9.82
4.17 0.520 89.9 0.801 0.0416 90.8 12.3 43.0 0.627 3.32 · 108 1.43
Fluorescence decay curves of NMC and P(St–Cz): SðtÞ ¼ a1 expðt=s1 Þ þ a2 expðt=s2 Þ. Fluorescence anisotropy decay curves of NMC: DðtÞ ¼ A1 expðt=h1 Þ. Fluorescence anisotropy decay curves of P(St–Cz): DðtÞ ¼ A1 expðt=h1 Þ þ A2 expðt=h2 Þ. W€ oessner model: DðtÞ ¼ A0 ðA1 þ A2 expðt=h1 Þ þ A3 expðt=h1 ÞÞexpðt=h2 Þð0:578expðt=h3 Þ0:422expðt=h4 ÞÞ A1 ¼ ð1=4Þð3cos2 a 1Þ2 , A2 ¼ ð3=4Þsin2 ð2aÞ, A3 ¼ ð3=4Þsin4 a.
t t þ A3 exp DðtÞ ¼ A0 A1 þ A2 exp h1 h1
t t 0:578 exp exp h2 h3 t ; ð17Þ þ 0:422 exp h4 where 1 A1 ¼ ð3 cos2 a 1Þ2 ; 4 3 A3 ¼ sin4 a: 4
A2 ¼
3 sin2 ð2aÞ; 4
were fitted well by Eq. (10) with DðtÞ as Eq. (16) as shown in Fig. 4 and the fitting parameters are listed in Table 1. In the previous paper [15], it was shown that the rotational mode of NMC was varied from the whole to the carbazolyl group by the addition of PEO300 molecules. The crossover point of the rotational motion of NMC were estimated by the stationary and the nanosecond fluorescence depolarization methods, and they coincided with the overlap polymer concentration C of PEO300. The overlap concentration C was evaluated by
ð17aÞ C ¼
A0 is pre-factor and the other fitting parameters are dynamical modes of carbazolyl groups attached to polymer chain, that is, a is the angle between excited transition dipole moment and rotation axis of chromophore attached to a polymer chain, h1 is the rotational relaxation time of a polymer side chain, h2 is the rotational relaxation time of a polymer main chain, h3 is the relaxation time of three-bond crankshaft and tetrahedral lattice motions of a polymer main chain, and h4 is the relaxation time of the fluctuation of a whole polymer. The emission anisotropy ratio decay curves of P(St–Cz)
Mw NA hs2 i3=2
;
ð18Þ
where Mw , NA and s are the molecular weight, Avogadro’s constant and the end-to-end distance, respectively, and calculated at C ¼ ab 53%. PEO300 molecules are isolated from each other in the solvent at C < C . However PEO300 molecules begin to be packed closely near to the overlap threshold C , and they entangle with each other over C . In this report, all the fluorescence and the emission anisotropy ratio decay curves were measured over C . Therefore, it can be considered that only
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Fig. 4. Dependence of PEO300 concentration on the fluorescence and emission anisotropy decay curves of carbazolyl groups incorporated into polystyrene. Data are fitted by Eq. (9) (left side) and Eq. (10) (right side) with SðtÞ and DðtÞ as a double exponential and Eq. (16). The profile of an exciting light pulse, P ðtÞ is also shown.
the carbazolyl group rotates in both cases of NMC and P(St–Cz), and that there is no need to consider the polymer itself in this report. The W€ oessner model is
appropriate to describe such dynamical mode in the vicinity of carbazolyl group. But the discussion about the adequacies of the W€ oessner model to the experimental
C. Hashimoto et al. / European Polymer Journal 40 (2004) 1997–2008
2005
Fig. 5. v2 -maps between each parameters of the W€ oessner model (Eq. (16)) applied to the emission anisotropy ratio decay curve of P(St–Cz) in PEO300/1,2-dichloroethane ¼ 7/3 mixtures.
data based on the time-resolved fluorescence depolarization technique would be very complicated. Because
the internal anisotropic rotations in the vicinity of a polymer side chain are separated into five dynamical
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modes according to the W€ oessner model,. Therefore, we estimate the appropriateness of the W€ oessner model using our original analytical method as follows. 3.2. v2 -Maps for relationship between the W€oessner model and the emission anisotropy ratio decay curves of carbazolyl groups incorporated into polystyrene The v2 -map method was applied to the curve fitting of the anisotropy ratio decay curves by the W€ oessner model. As mentioned above, the v2 -map method enables us to estimate the fitting properties in the vicinity of a stable point in a fitting function. All v2 -maps for each fitting parameter of Eq. (17) applied to rðtÞ of the sample 70% PEO300 are shown in Fig. 5. In the v2 map for a vs. h2 , for example, the large values of Z-axis exist within a very narrow width along a. It indicates the fact that there is no stable solution of a, while h2 is identically determined in the relationship between a and h2 . In other words, h2 is independent on a. On the other hand, the v2 -map for h1 vs. h2 represents a horseshoe form in Fig. 5. It can be presumed that there is a strong correlation between h1 and h2 . It may be difficult to separate h1 and/or h2 in Eq. (17) to fit the experimental data. All estimated results of such relationship between fitting parameters in Eq. (17) are shown in Fig. 6. ‘Narrow’, ‘wide’, and ‘horseshoe form’ in this figure mean the relationships of ‘independent’,
‘meaningless’, and ‘dependent’ between the parameters, respectively. 3.3. Estimation technique for emission anisotropy ratio of chromophores incorporated into polymer chain The relationships between each parameter of Eq. (17) as showed in Table 2 are summarized as a correlation map in the right side of Fig. 6. When an arrow directs from X to Y , X is a meaningless parameter and Y is an independently defined one. Solid line is the horseshoe form type and it means the dependency between these parameters. In this schematic diagram, we find an interesting fact that all arrows gather around a, h1 and h3 . It indicates the validity of these three dynamical parameters, a, h1 and h3 , while the discussion about parameters remaining h2 and h4 are attended by many risks in the relationship between our experimental data and Eq. (17) (the W€ oessner model). Therefore, we cannot discuss about the rotational relaxation time of a polymer main chain, h2 and the relaxation time of fluctuation of a whole polymer, h4 in this report. Note that the above estimation result as showed in Fig. 6 was also obtained over all PEO300 concentrations. The angle a between the excited transition dipole moment and the rotation axis of a chromophore attached to a polymer side chain is almost constant at 85.5–90.8 and not dependent on the PEO300 concen-
Fig. 6. Dynamical modes of a carbazolyl group attached to polymer chain in the W€ oessner model and a correlation map of the effectiveness of parameters of these six dynamical modes when the emission anisotropy ratio decay curves of P(St–Cz) are fitted by Eq. (16).
Table 2 Estimation for v2 -maps between each fitting parameter of the W€ oessner model (Eq. (17)) applied to the emission anisotropy ratio decay curves of P(St–Cz) in PEO300/1,2-dichloroethane ¼ 7/3 mixtures a h1 h2 h3 h4
a
h1
h2
h3
h4
– Narrow Wide Narrow Very wide
Very narrow – Horseshoe form Narrow Very wide
Very narrow Horseshoe form – Very narrow Very wide
Very narrow Narrow Wide – Very wide
Very narrow Narrow Wide Very narrow –
C. Hashimoto et al. / European Polymer Journal 40 (2004) 1997–2008
2007
Fig. 7. Dynamical modes for a carbazolyl group attached to polymer side chain in PEO/1,2-dichloroethane mixtures.
tration as listed in Table 1. The rotational relaxation time of a polymer side chain, h1 is about nano-second order and about 10 fold of that of NMC as a monomer model compound. The relaxation time of three-bond crankshaft, h3 is about 100 ps order and about 1/10 fold of rotational relaxation times of a polymer side chain. These values for dynamical parameters of a polymer chain are reasonable [6,7]. Characteristic times of P(St– Cz), h1 and h3 increase with increasing PEO300 concentration as well as the rotational correlation time of NMC. A slight increase in the rotational correlation time of NMC with increasing PEO300 concentration coincides with the previous results in the higher viscosity region of C > C . The dynamical modes in the vicinity of polymer side chain become slower at more concentrated PEO solution. It indicates that the interpenetration process of PEO300 into P(St–Cz) sphere will proceed with increasing of PEO300 concentration above C region. In closing, we would like to sum some new knowledge in this report as follows: (1) The fluorescence emission anisotropy ratio decay curves of P(St–Cz) in a mixture of PEO300 and 1,2dichloromethane are expressed very well by the W€ oessner model. (2) Our original ‘v2 -map method’ estimates the validity of the W€ oessner model. Using this analytical technique, we selected the effective parameters of the W€ oessner model, that is, the angle between the excited transition dipole moment and the rotation axis of chromophore attached to a polymer side chain a, the rotational relaxation time of a polymer side chain h1 , and the relaxation time of three-bond
crankshaft h3 . The schematic diagram is shown in Fig. 7. (3) The values of a, h1 , and h3 are 85.5–90.8, 5–12, 0.4– 0.6 ns, respectively, and they are considered to be reasonable in the higher viscosity region of C > C. (4) Our original estimation technique based on the W€ oessner model is very excellent to clarify various dynamical modes of a flexible polymer in the region of semi-concentrated polymer concentration.
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