Complexation of Pyrene by Poly (allylamine) with Pendant β

J. Phys. Chem. B 1998, 102, 2947-2953

2947

Complexation of Pyrene by Poly(allylamine) with Pendant β-Cyclodextrin Side Groups Markus Hollas, Myung-Ae Chung, and Jo1 rg Adams* Institut fu¨ r Physikalische Chemie, Technische UniVersita¨ t Clausthal, Arnold-Sommerfeld-Strasse 4, D-38678 Clausthal-Zellerfeld, Germany ReceiVed: NoVember 4, 1997; In Final Form: February 5, 1998

The complexation of pyrene into the cavity of β-cyclodextrin (β-CD) has been studied in aqueous solutions of pure β-CD and β-CD substituted poly(allylamine) by using fluorescence spectroscopy. Two different approaches to obtain the association constant, both already described in the literature, are compared. It is shown that the evaluation of the fluorescence intensities of the first and third vibronic band of the pyrene fluorescence spectrum gives the correct result because the different quantum yields of free and complexed pyrene are considered correctly. The sole analysis of the Ham effect of pyrene leads to too high values of the association constant. A subsequent formation of 1:1 and 2:1 complexes between β-CD and pyrene was confirmed. The synthesized β-CD polymers exhibit a significant change in the complexation behavior depending on the degree of substitution (DS). At high DS (up to 23%) only 2:1 complex formation was observed, an evidence for intramolecular, chelate-like complexes due to the high local β-CD concentration. At low DS (below 5%) 2:1 complexes are formed only intermolecularly. Compared with pure β-CD, the overall complexation constant of the β-CD polymers increases by more than 2 orders of magnitude with increasing DS and is independent of the polymer molecular weight. The supramolecular structure of the complex is not changed due to the linkage of the cyclic oligosaccharide to the polymer chain.

Introduction In recent years supramolecular structures of water soluble polymers containing cyclodextrin (CD) groups gained increasing popularity because of their enhanced complex stability toward organic guest molecules.1-8 Potential application like chromatography, water cleanup, drug-delivery, or catalysis make these materials interesting. At the moment, the research still focuses on the basic influences of the polymer chain on the complexation behavior of the various CDs attached to or incorporated into a polymer. In the case of a 1:1 complex, i.e., one cyclodextrin ring forms an inclusion complex with one guest molecule, no significant change in the complex stability and complex structure is to be expected. Only if the polymer bears special groups, which are able to interact with the CD molecule or the whole complex, the complex stability should change. Just these interactions or even reactions between the guest and a part of the polymer structure can be used for catalysis or stereoselective reactions. 2:1 complexes (2 CDs and 1 guest) should show a higher sensitivity of the complex stability on the polymer structure. Here three molecules or segments have to interact cooperatively with each other. Because of the linkage to the polymer the two CD molecules already interact cooperatively to a certain extent. As a consequence the overall complex stability can be controlled by the flexibility and the structure of the polymer segments. Requirements for a systematic investigation of the polymer influence on the formation of 2:1 complexes are the use of well-characterized, preferably linear polymers and suited guest molecules. The better the guest fills the hydrophobic CD interior, the more stable is the supramolecular complex. Furthermore, the * Address correspondence to this author: e-mail: [email protected].

complex stability depends on the hydrophobic interaction between the CD rings and the guest. The association constant K is a measure of the thermodynamic stability of an inclusion complex. To determine K, a physical property of the guest or host sensitive to the inclusion complex is chosen. From the group of guest molecules that are able to form 2:1 complexes, pyrene is often used together with β-cyclodextrin.9 Its overall fluorescence intensity and the shape of the emission spectrum of pyrene change significantly when incorporated into the cavities of two β-CDs. Protection from quenching processes and dipolar interactions are the reasons for an increase in absolute fluorescence intensity and lifetime.10 Dipole T induced dipole interactions (Ham effect) between pyrene and its microenvironment are responsible for the changes of the intensity ratio of the first and third vibronic transitions.11-14 Because of this marked sensitivity even very high association constants at low cyclodextrin concentrations can be determined easily. Figure 1a shows schematically how pyrene (8.2 Å wide and 10.4 Å long) can be encapsulated either partially by one β-CD (inner diameter 7.8 Å, depth 7.8 Å)15 or nearly completely by two β-CDs. There is still a debate in the literature on the importance of the first complexation step, the formation of the 1:1 complex.5,16 The group of Warner16 analyzed their data by considering only the direct formation of the 2:1 complex from 1 pyrene and 2 β-CDs. The 1:1 complex is assumed to be only an intermediate product with a negligible role in the overall complexation process and the fluorescence signal. Hence, only the association constant K0f2 is calculated. In contrast to this approach, Xu et al.5 and Kusomoto et al.17 also consider the 1:1 complex as an important and detectable structure. Therefore, they calculated K0f1 and K1f2. Detailed investigations of the polymer influence on the complex formation have so far been made by Harada et al.,2 Xu et al.,5 and Martel et al.6 They used pyrene or 2-p-

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2948 J. Phys. Chem. B, Vol. 102, No. 16, 1998

Hollas et al. SCHEME 1: Synthesis of the Cyclodextrin Containing Poly(allylamine)

TABLE 1: Synthesized Poly(allylamine) Compounds and Yields Pn Figure 1. Schematic representation of the 2:1 complex formation between β-cyclodextrin and pyrene: (a) pure β-cyclodextrin; (b) polymer-bound β-cyclodextrin.

toluidinylnaphthalenesulfonate (TNS) as guest molecule and supposed that polymer-bound cyclodextrins only favor the formation of 2:1 complexes according to Figure 1b. Two covalently linked cyclodextrins form a ring with the fluorescence probe. This is the typical structure of chelate complexes whose association constants (KCh) are usually several orders of magnitude higher than for conventional complexes because of an entropic effect (chelate effect).18 Limiting factors for the chelate complex stability are the ring size and the local CD concentration. However, the influence of the degree of substitution (DS) and the polymer chain length on complexation have so far not been investigated in detail. For example, Martel et al.6 investigated complexation behavior of β-cyclodextrin substituted poly(vinylamine) and TNS but could not rule out any influence of electrostatic interactions between the polymer and the incorporated dye molecule. In this paper we want to present our systematic investigation on the complexation behavior between β-cyclodextrin substituted poly(allylamine) and pyrene. As mentioned above, two different methods of data treatment of the steady-state fluorescence spectra are described in the literature,5,16,17 leading to different results for the complexation constants between β-cyclodextrin and pyrene. Therefore, before discussing our results on the polymeric CDs, the pure β-CD/ pyrene complexation is analyzed regarding the association process and its temperature dependence. Experimental Section Materials. Aldrich pyrene (g99%) and poly(allylamine hydrochloride) (Mn ) 50 000-65 000 g‚mol-1 and Mn ) 850011 000 g‚mol-1) were used without further purification. β-Cyclodextrin (pharmaceutical grade) was obtained from WackerChemie GmbH, Munich. Synthesis of Cyclodextrin Substituted Poly(allylamine). Monotosylation of β-cyclodextrin in the 6-position was carried out according to a procedure described by Petter et al.19 The polymer analogous reaction of the monotosylated β-CD (CDOTs)

900-1150

150-200

CDOTs/poly(allylamine) compound molar ratio for synthesis DS,a % yield, % A1 A2 A3 A4 A5 A6 A7 A8 B1 B2 B3 B4 B5

0.005 0.02 0.05 0.1 0.15 0.33 0.33 1.0 0.005 0.02 0.05 0.10 0.32

0.5 2 5 10 15 18 20 23 0.5 2 5 9 18

54 73 50 77 54 67 44 29 32 55 51 50 57

a

Degree of substitution of the amine groups by CDOTS, calculated from NMR spectra and for A5-A8 from NMR spectra and elemental analysis.

with poly(allylamine) follows the partially modified procedure (Scheme 1) of Seo et al.4 To a solution of 1.2 g of potassium hydroxide in 15 mL of methanol was added in small portions 0.37 g (4 mmol repeat units) of poly(allylamine hydrochloride). The solution was stirred for 1 h at room temperature and then kept at 5 °C for 12 h. The precipitated potassium chloride was filtered off and the filtrate evaporated to dryness. The polymer (4 mmol) was dissolved in 10 mL of water and small portions of a calculated amount of CDOTs (Table 1) were added while stirring at 75 °C. When the solution turned clear again the next portion was added. After the addition of the last portion the solution was stirred for 12 h at 75 °C. Finally the reaction mixture was filtered and dialyzed. For the dialysis, the crude, aqueous reaction solution was diluted 10 times, filled into a dialysis tube (KALLE, average pore size diameter 24 Å), and dialyzed for 12 days against deionized water under continuous exchange of the dialysate. After freeze-drying a white powder was obtained. Table 1 lists all synthesized polymers. IR, NMR, and Elemental Analysis of Compound A7. IR (KBr): ν 3372 (O-H, in H-bridges); 2917 (C-H aliphatic); 1568 (NH2); 1490 (NH); 1320 (C-N); 1153 (C-O-C). 1H NMR (400 MHz, D2O): δ 1.68 (b, 2 H, CH2-a); 2.0 (b, 1 H, CH-b); 2.77 (s, 3 H, CH3-TsO); 3.10 (b, 2 H, CH2-c); 3.46 (b, 1 H, N-H); 3.68-4.43 (b, 42 H, CH-2, CH-3, CH-4, CH-5, CH6, CH-6′); 5.43 (bd, 1 H, CH-1); 7.70 and 8.13 (2d, 4 H, ar H).

Complexation of Pyrene [C11.4H20.6NO6.8‚1.2 H2O]n anal. Calcd: C, 45.32; H, 6.87; N, 4.64; S, 0. Found: C, 43.49; H, 6.76; N, 4.18; S, 0.80. Preparation of the Solutions. Aqueous pyrene solutions of 2 × 10-7 mol‚L-1 were used as solvent for all fluorescence experiments. Special care was taken to obtain pyrene solutions free of any microcrystals. The following procedure showed reproducible results:16 2.5 mL of a 1 × 10-5 mol‚L-1 solution of pyrene in cyclohexane were evaporated under nitrogen in a 250-mL flask and 100 mL of deionized and distilled water were added. After the solution was shaken for 12 h the flask was filled up with water and sonicated for 2 h. The absence of pyrene microcrystals was proved by fluorescence spectra, showing no detectable excimer emission. The stock solutions containing either β-CD or CD polymers were prepared by adding aqueous pyrene solutions (for manual dilution series) or deionized and distilled water (for automatic dispensing) to the appropriate amount of β-CD or CD polymer and shaking at 40 °C over 12 h. The pH of the β-CD solution was 7 and the polymer solution showed a pH between 7.5 and 9, depending on the degree of substitution. Fluorescence Spectra. Corrected fluorescence spectra were taken at room temperature with a SPEX FLUOROLOG 2, using a photon counting technique. The excitation slit was set to 5.4 nm and the emission slit to 0.9 nm. The excitation wavelength was 335 nm, and the emission spectra were taken from 350 to 450 nm. To increase the emission intensity, cells with aluminum coated windows were used. All sample solutions were aerated. Except for the temperature dependent measurements, all spectra were taken at 293 K. Dilution series were prepared on two different ways, manual or automatic. In the case of manual preparation, 2-mL flasks were filled with calculated volumes of the aqueous pyrene solution and the pyrene containing CD stock solution. Afterward the flasks were shaken for several hours. Automatic preparation of the titration experiment was carried out with an EPPENDORF electronic dispensing system EDOS 5221. Definite volumes of a CD stock solution were dispensed directly into the fluorescence cell inside the spectrometer. This cell was filled with a definite volume of the aqueous pyrene solution. A small glass stirrer was used to mix the sample solution during a delay of 3 min between dispensing of the CD solution and the measurement of the fluorescence intensity. The spectrometer and the dispensing system were controlled by the same computer. The stock solution did not contain pyrene, because otherwise uncomplexed pyrene would have been adsorbed onto the polyethylene surface of the syringe and the tubing. For the calculation of the association constant, the measured fluorescence intensities were corrected regarding the decrease of the pyrene concentration in the fluorescence cell due to dilution. Results and Discussion β-Cyclodextrin. Intensity changes of the pyrene fluorescence based on complexation by β-CD play a key role in the evaluation of the steady-state fluorescence data. This requires a known pyrene concentration in all sample solutions. Spectra of the pyrene fluorescence taken in aqueous solutions of varying β-CD concentration are shown in Figure 2. The absolute intensity increases and the intensity ratio of peaks 1 and 3 (I1/I3) decreases due to the transition of pyrene molecules from the polar solvent water into the hydrophobic cyclodextrin cavities. According to the literature, the determination of the association constants from either the absolute fluorescence intensity

J. Phys. Chem. B, Vol. 102, No. 16, 1998 2949

Figure 2. Emission spectra of pyrene in aqueous solutions under variation of the β-cyclodextrin concentration, [CD]0 ) (2 × 10-4) (1 × 10-2) mol‚L-1.

or the intensity ratio R ) I1/I3 leads to different results.5,16,17 This difference is a consequence of the observed intensity increase during a titration experiment. Independent of whether the intensities of the different pyrene species in an aqueous pyrene-CD solution are controlled by quenching processes or the local microenvironment, individual quantum yields have to be assigned to each of them.5 Because the 1:1 complexes cannot be neglected from the start, three species of pyrene with their different quantum yields have to be considered, namely, free pyrene (py), pyrene in 1:1 complexes (py-CD), and pyrene in 2:1 complexes (CD-py-CD). Hence, the measured spectrum is a sum of the individual spectra of these three species, weighed according to their concentration, as already described by Xu et al.5 For the two intensities of interest, I1 and I3, this consideration results in the two following expressions:

I1 ) fpyRpyI3,py + fpy-CDRpy-CDI3,py-CD + fCD-py-CDRCD-py-CDI3,CD-py-CD (1) I3 ) fpyI3,py + fpy-CDI3,py-CD + fCD-py-CDI3,CD-py-CD (2) with Ri being the intensity ratio I1,i/I3,i of an individual species i and fi being the molar fraction of the species i.

fpy )

1 1 + K0f1[CD]0 + K0f1K1f2[CD]02

fpy-CD )

K1[CD]0 1 + K0f1[CD]0 + K0f1K1f2[CD]02

fCD-py-CD )

K0f1K1f2[CD]02 1 + K0f1[CD]0 + K0f1K1f2[CD]02

(3)

(4)

(5)

To obtain eq 3-5, it is assumed that the consumption of uncomplexed β-CD due to complexation can be neglected compared to the initial CD concentration [CD]0. This simplification is true as long as [CD]0 is significantly larger than the total pyrene concentration. This condition was assured in all our experiments. To calculate the association constants K0f1 and K1f2 from the measured intensities I1 and I3, nonlinear least-squares fits according to eq 1-5 with eight fit parameters, namely, I3,i, Ri, K0f1, and K1f2, were performed.

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Hollas et al.

Figure 3. Fluorescence intensity I1 ([) and I3 (2) as a function of β-cyclodextrin concentration (automatic titration). The solid lines show the calculated fits according to eqs 1-5.

In contrast to this approach, Munoz de la Pena et al.16 and Kusumoto et al.17 neglected the different quantum yields for free and complexed pyrene and evaluated only the intensity ratio R. As a consequence the number of fit parameters is reduced. This calculation of K0f1 and K1f2 neglects the individual contribution of the different pyrene species to the measured R values, leading to a non-properly-weighed R with regard to the fluorescence intensities of the different species. In the case of a dominant 2:1 complex, as suggested by Munoz de la Pena et al., the association constant K0f2 is overestimated by the factor Q2, the ratio of the quantum yield between pyrene in the complexed state and free pyrene. Thus, from eq 1-3 and 5 under neglect of the terms including the 1:1 complex R is calculated as

R)

Rpy + RCD-py-CDQ2K0f2[CD]02 1 + Q2K0f2[CD]02

(6)

with Q2 ) I3,CD-py-CD/I3,py. In comparison to eq 6, Munoz de la Pena et al.16 calculated the complex stability according to the following equation:

R)

Rpy + RCD-py-CDK0f2[CD]02 1 + K0f2[CD]02

(7)

Evaluation of the data under the assumption of 1:1 and 2:1 complexes17 introduces a further error because the intensity ratio Q1 for the 1:1 complex is another unknown factor. Another disadvantage of fitting I1/I3 is the fact that the number of data points is divided by 2 compared to a direct fit of the individual intensities.5 Therefore, investigation of the pyrene complexation should consider the absolute intensities I1 and I3. Nevertheless, according to Xu et al. problems arise from the high number of fit parameters when only few concentrations are measured. By use of the computer controlled dispensing system we were able to investigate the pyrene complexation with a large number of data points. Intensities I1 and I3 with increasing CD concentration measured at 293.1 K are shown in Figure 3. The curves are in good agreement with those of Xu et al.5 and the experimental data can be fitted quite well. I1 and less significant I3 show a decrease of the fluorescence intensities at low CD concentrations. This is a hint for the initial formation of the 1:1 complex, which has an intensity nearly 3 times lower than that of free pyrene according to the fit result listed in Table

2. At higher CD concentrations the fluorescence intensity increases due to the formation of the 2:1 complex which has an intensity about 6 times higher than that of free pyrene (Table 2). The fitted intensity ratios R have values of 0.68 for the 2:1 complex, 0.90 for the 1:1 complex, and 1.80 for free pyrene. The empirical polarity scale of Dong et al.13 assigns 0.68 to a very nonpolar, 0.90 to a semipolar, and 1.80 to a polar environment. This corresponds with the microenvironment of pyrene for the three different species. Unfortunately, a separate investigation of K0f1 and K1f2 did not succeed because of a wide scattering of both parameters. Despite the high number of data points, the ratio K1f2/K0f1 varied from 0.5 to 2.0 for several measurements at 293.1 K (Table 2). About the same range was observed by Xu et al. Therefore, it is not possible to discuss K0f1 and K1f2 in detail. However, the product K0f1K1f2 leads to reproducible values, which are about a factor of 6 lower than the overestimated K0f2 resulting from R-fits according to eq 7. This factor corresponds well with the intensity ratio between the 2:1 complex and free pyrene. A plot of ln(K0f1K1f2) versus 1/T shows a decrease of the complex stability with increasing temperature (Figure 4). Enthalpy and entropy changes on complexation were calculated to ∆H ) -34.4 kJ‚mol-1 and ∆S ) -29.2 J‚mol-1‚K-1. The complex formation is enthalpy controlled and leads to an expected decrease in entropy due to the unfavorable, highly ordered structure of the complex. Results of the intensity fits at different temperatures are listed in Table 2. As expected, the Ri values of the different species are almost temperature independent. Only a slight linear decrease was observed. This decrease is the typical behavior of R versus temperature for pyrene. Furthermore the 1:1 complex has a lower and the 2:1 complex a higher intensity than free pyrene over the whole temperature range. Quite interesting is the tendency of the temperature dependence of the ratio K1f2/K0f1. The decrease of this ratio with increasing temperature indicates a change in weighing of both constants in favor of K0f1. In Figure 5 the temperature dependence of K0f2 is compared with the product K0f1K1f2. As expected, the association constants calculated by fitting the polarity signal of pyrene are higher than the product resulting from the intensity fits. It is worth noting that with increasing temperature the difference between the two data sets decreases. This is a result of the decreasing contribution of the stronger fluorescent 2:1 complex on K0f2 at higher temperature. In conclusion, we believe that only fits of the absolute intensities I1 and I3 enable the correct determination of complex stability as shown by the calculation and experiments. Furthermore subsequent formation of 1:1 and 2:1 complexes is evident. Investigations on the thermodynamic properties show that the complexation is enthalpy controlled. In agreement with Xu et al.5 both association constants are of the same order of magnitude. Despite the still high inaccuracy of K0f1 and K1f2, an increasing importance of the 1:1 complexes with increasing temperatures has been detected. Cyclodextrin-Substituted Poly(allylamine). On the basis of the knowledge about the β-cyclodextrin/pyrene system, a detailed investigation of the complexation behavior of cyclodextrin-substituted poly(allylamine) was possible. It has to be noted, that even after 12 days of dialysis and constant flushing of the dialysate, there were still noticeable amounts of tosylate ions detected by NMR and elemental analysis. Even with changing the pH of the water or its salt

Complexation of Pyrene

J. Phys. Chem. B, Vol. 102, No. 16, 1998 2951

TABLE 2: Fit Results for Complex Formation of β-Cyclodextrin and Pyrene in Aqueous Solutions at Different Temperatures T, K

K0f1, L‚mol-1

K0f1‚K1f2, 103 L2‚mol-2

K1f2/K0f1

Rpy

Rpy-CD

RCD-py-CD

I3,py-CD/I3,py

I3,CD-py-CD/I3,py

276.4 283.9 288.7 293.1

124.4 154.8 334.9 354.5

100.9 71.6 40.8 37.4

1.99 1.96 1.92 1.80

1.4 1.06 1.73 0.90

0.66 0.73 0.66 0.68

0.76 0.87 1.18 0.35

3.5 3.6 5.4 6.1

306.8 315.4

234.7 262.9

19.6 16.8

6.52 2.99 0.36 0.54 (0.5-2.0) 0.36 0.24

1.83 1.79

1.42 1.70

0.60 0.50

1.03 0.90

4.8 3.4

Figure 4. ln(K0f1K1f2) versus 1/T. Thermodynamic data for the complex formation from linear regression (solid line): ∆H ) -34.4 kJ/mol-1 and ∆S ) -29.2 J‚mol-1/K.

Figure 6. R versus poly(allylamine) concentration, amine form, Mn ) 8500-11 000 g‚mol-1.

Figure 5. Temperature dependence of the overall pyrene complexation constant with and without consideration of the intensity changes. Trend lines are added. (2) K0f2 according to eq 9; (9) K0f1K1f2 according to eqs 1-5.

Figure 7. R versus [CD]0 for β-CD (2) and polymer B4 ([).

concentration the tosylate groups could not be removed. We assume that these groups are not linked covalently to either the polymer backbone or the CD groups but rather form a complex or salt with the CD polymer. The water solubility of the synthesized polymers is generally lower than that for free poly(allylamine) and depends on the degree of substitution (DS) and chain length. Solubility increases with DS (up to DS ) 10%) but finally drops rapidly when reaching the synthetic upper limit of 23%. A comparison of polymers with different chain lengths shows better water solubility for the shorter chain. Viscosity measurements showed a decrease of the intrinsic viscosity for the CD polymers compared to pure poly(allylamine). This decrease is understandable when considering that the attached CD molecules do not contribute to the hydrodynamic radius of the polymer to the same extend as the polymer backbone. A second reason, already discussed by Martel et

al.6 for CD-poly(vinylamine), is the formation of numerous hydrogen bonds between the CD OH groups and the NH2 groups of the polymer, leading to a more compact polymer coil. To measure the influence of the polymer backbone on R the behavior of pyrene in the presence of poly(allylamine) was investigated. As shown in Figure 6, R is independent of the poly(allylamine) concentration up to 1.0 mmol‚L-1 at 293.1 K. All measurements with CD polymers were made below this concentration. The influence of the backbone can therefore be neglected. A reason for the decrease of R at high poly(allylamine) concentrations is presumably an interaction between the pyrene and the hydrophobic aliphatic segments of the polymer backbone. Compared to pure β-cyclodextrin the complexation of pyrene with CD polymers is shifted to lower concentrations with increasing DS and rises within a much smaller concentration range. A comparison of the R-curve of B4 with that of pure CD is shown in Figure 7. The required CD concentration decreases about 2 orders of magnitude for the polymer. As a

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Hollas et al.

Figure 8. Fluorescence intensity I3 normalized to I3 at [CD]0 ) 0 versus cyclodextrin concentration for polymers of different DS.

consequence the complex stability increases. Complex stoichiometry and association constants of the polymers were determined by evaluation of the intensity curves. As shown in Figure 8 the normalized intensities I3 for different polymers are shifted to lower CD concentrations with increasing DS and show significant changes in their shape. For a DS of 0.5 and 2% (compounds A1 and A2) I3 first decreases with increasing CD concentration before an increase was observed. Quite good fits were achieved for these compounds under the assumption of a subsequent formation of 1:1 and 2:1 complexes. Because of the broadness of the minimum the 1:1 complex seems to be dominant and 2:1 complexes are only formed at high CD concentrations. A reason for this behavior could be a hindered intramolecular formation of 2:1 complexes because of a too long distance between adjacent CD moieties in these polymers: big changes of the chain conformation and hence a too high loss in entropy would be required for an intramolecular 2:1 complex, making this type of complex unfavorable. The final intensity increase should be caused by the formation of intermolecular 2:1 complexes from neighboring polymer chains at high concentrations. Following these assumptions 2:1 complexes should be more favorable at higher DS because of the smaller distance between adjacent CD groups. In fact, the intensity curves show no minimum with increasing CD concentration for polymers with DS larger 5% (Figure 8). To visualize the change in complexation behavior as a function of DS the normalized intensities I1 of the exemplarily chosen compounds A1 (DS ) 0.5%) and A6 (DS ) 18%) are compared in Figure 9. For a better comparison of the two data sets differently scaled abscissas are used. Similar to Figure 8, a low degree of substitution leads to a decrease of the fluorescence intensity, whereas at high DS I1 always increases. As a consequence, intensity fits for the polymers with DS g 5% under the assumption of subsequent 1:1 and 2:1 complex formation led to physically meaningless values of K0f1, K1f2, and Ri. Only fits without a quadratic term of the CD concentration resulted in reproducible and meaningful association constants. This is an indication for the formation of 2:1 chelate complexes whose equilibrium constants are generally calculated according to18

K)

[ML-L] [M][L-L]

(8)

(M, complex core; L, ligand) and for CD polymers according

Figure 9. Fluorescence intensity I1 normalized to I3 at [CD]0 ) 0 as a function of [CD]0 of compounds A1 ([) and A6 (2). The solid lines are added trend lines.

to Figure 1b

KCh )

[CD-py-CD] [CD-py-CD] ) [py][CD-CD]0 [py]0.5[CD]0

(9)

The calculation of the equilibrium constant is analogous to calculations with 1:1 stoichiometry. Because of the chelate effect these constants are typically several orders of magnitude higher compared to conventional complexes. Harada et al.2 explained this effect for CD polymers with the already frozen translational motion of polymer bound CD, whereas the formation of a 2:1 complex from free β-cyclodextrin requires a higher loss of entropy, because the freely diffusing molecules have to associate. Due to the high association constants the 1:1 complex should be negligible in CD polymers if the spacing between two CD moieties allows the formation of a chelate-type structure. The fluorescence intensity of pyrene in the polymer chelate complex is about 6 times higher than that for free pyrene. This is the reason for the intensity increase. The average RCD-py CD value is 0.74. This is in good agreement with the R of 0.68 for the 2:1 complex of β-cyclodextrin and pyrene. There seems to be no influence of the polymer backbone on the pyrene microenvironment. Otherwise RCD-py CD should depend on the polymer concentration and differ significantly from the value for pure β-CD complexes. Such side effects of the polymer backbone were observed for CDsubstituted epichlorhydrin oligomers.5,8 It was not possible to prove the presence of chelate-type structures for these polymers.8 The calculated association constants K of the chelate complexes for all poly(allylamine) compounds are plotted in Figure 9 as a function of DS. For comparison the value of (K0f1K1f2)1/2 of pure β-CD is included. For the polymers with the lowest degree of substitution (K0f1K1f2)1/2 was also chosen because the intensities could not be fitted according to eq 9. The K values of polymers A1 and B1 (DS ) 0.5%) are unexpectedly high. A reason could be their low solubility in water indicated by already turbid stock solutions. Manual preparation showed no significant deviation from automatic preparation. This supports the reproducibility of this fast and automatic titration technique. The complex stability increases strongly with increasing degree of substitution and reaches 350 times the corresponding value for β-CD at the highest DS (limited by the synthesis). In

Complexation of Pyrene

Figure 10. Equilibrium constants K for the complexation of pyrene in poly(allylamine)s and β-CD. Closed symbols, KCh; open symbols, (K0f1K1f2)1/2. (9, 0) Pn ) 900-1150; (2, 4) Pn ) 150-200; (O): β-cyclodextrin. m: data points calculated from manual titration experiments.

J. Phys. Chem. B, Vol. 102, No. 16, 1998 2953 adjacent CDs encapsulate a pyrene molecule (short range) or two CDs separated by several polymer segments build the complex (long range). Long-range complexation should depend on molecular weight because short chains form more compact coils than long chains. Consequently, the complex stability should increase with decreasing chain length. In contrast to this, the distance of neighboring segments is controlled by the degree of substitution and not by the total length of the polymer chain. According to Figure 10, there is no dependence of the complex stability on the molecular weight. Therefore, we assume that short-range complexation is dominant for the polymers under investigation. In conclusion, our measurements give evidence for the formation of supramolecular, chelate-type structures in β-cyclodextrin substituted polymers with a poly(allylamine) backbone. Because of the chelate effect the association constants are several orders of magnitude higher than for β-cyclodextrin and can be controlled by the degree of substitution. The influence of polyelectrolytes and pH variations on the complexation will be the subject of following investigations. Acknowledgment. We gratefully acknowledge support by the DFG. We thank Prof. J. W. Park EWHA-University, Seoul, Korea, for numerous fruitful discussions. We are also thankful to Wacker-Chemie, Munich, for the supply of β-cyclodextrin. References and Notes

Figure 11. Intramolecular long-range and short-range complexation in CD polymers: (a) long-range complexation; (b) short-range complexation.

comparison, Xu et al.5 detected just a 20 times higher complex stability for cyclodextrins bound to the epichlorhydrin oligomers. Such a strong dependence of K on DS can only be explained by the chelate effect: increasing DS reduces the distance between CD moieties and leads to an increase in local CD concentration. Furthermore, a shorter distance between the CDs lowers the entropy loss due to a change of the chain conformation when encapsulating the pyrene guest molecule. An important result visualized in Figure 10 is the independence of KCh on the polymer chain length. This enables us to draw a schematic picture (Figure 11) of the kind of complex structure inside a polymer coil. Generally there are two possibilities to form an intramolecular 2:1 complex: either two

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