Kinetics and Mechanism of Cyclodextrin Inclusion Complexation

The kinetics of cyclodextrin (CD) inclusion complexation has been usually analyzed in terms of a one-step reaction or a consecutive two-step reaction ...
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J. Phys. Chem. B 2006, 110, 24915-24922

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Kinetics and Mechanism of Cyclodextrin Inclusion Complexation Incorporating Bidirectional Inclusion and Formation of Orientational Isomers Joon Woo Park* Department of Chemistry, Ewha Womans UniVersity, Seoul 120-750, Korea ReceiVed: August 14, 2006; In Final Form: September 27, 2006

The kinetics of cyclodextrin (CD) inclusion complexation has been usually analyzed in terms of a one-step reaction or a consecutive two-step reaction involving intracomplex structural transformation as a second step. These schemes presume the inclusion of guest molecules through only one side of the CD cavity and the formation of unidirectional CD complexes. However, there has been increasing experimental evidence for the inclusion of guests through both sides of the CD cavity and the formation of orientational isomers for noncentrosymmetric guest molecules. This article presents a novel parallel reaction scheme for CD inclusion complexation, incorporating bidirectional inclusion and the formation of orientational isomers into the scheme. It is shown that the parallel reaction scheme gives the same concentration versus reaction time relationship as the consecutive two-step reaction scheme. The experimental methods for determining the microscopic directional rate constants are presented. The kinetic parameters of the two-step reaction scheme are expressed as functions of the directional rate constants. The ratios of orientational isomers of R-CD-based [2]pseudorotaxanes and the microscopic directional rate constants of the threading and dethreading reactions are estimated from the reported thermodynamic and kinetics data obtained by using either the one-step or twostep reaction scheme. It is shown that the thermodynamic preference of an isomer over the other is mainly due to the slow dethreading rate of the isomer.

1. Introduction Cyclodextrins (CDs) are cyclic oligosaccharides that have a hollow, torus-shape cavity. They are widely used as host moieties in supramolecular chemistry1 and as wheel components for supramolecular structures such as pseudorotaxanes and rotaxanes.2 Guest molecules can enter and exit the CD cavity through both sides of the cavity. Thus, the complexation of a noncentrosymmetric guest molecule with CD can give two orientational isomers having opposite orientations of the guest in the CD cavity.3-9 If the complexation and decomplexation reactions proceed by passing CD through a hydrophilic or bulky end of a guest, the reactions are usually under the slow exchange regime, compared to the NMR time scale, and the complex exhibits separate peaks from the free guest in an NMR spectrum.4-11 The presence of two orientational isomers of various R-CD-based [2]pseudorotaxanes with noncentrosymmetric thread molecules has been confirmed by 1H NMR spectroscopy.4-9 Two orientational isomers of [2]rotaxanes have been prepared by capping the isomeric [2]pseudorotaxanes.4,12 Recently, it was shown that the [2]pseudorotaxane isomers exhibit quite different kinetic and thermodynamic stabilities.4,5,7,9 The kinetic study of the CD inclusion complexation/decomplexation reaction is expected to provide mechanistic insight of the process as well as the information necessary for designing, assembling, and controlling CD-based supramolecular assemblies. Kinetics of the inclusion complexation reaction with CD have been extensively investigated using a variety of methods.10,11,13-26 The kinetic traces were usually analyzed with a one-step10,11,13-16,24 or a consecutive two-step reaction * Corresponding author. Phone: +82-2-3277-2346. Fax: +82-2-32772384. E-mail: [email protected].

scheme.17-23,25,26 These schemes presume the unidirectional inclusion complexation and do not consider the formation of orientational isomers. The observations of isomeric complexes and the biphasic behavior of the complexation reaction were explained in terms of the inclusion from two different ends of guests20 or intracomplex structural transformation.22,23 The activation parameters ∆H‡ and ∆S‡ 10,14,16-18,20-23 as well as ∆V‡ 21-23 have been reported for the reaction steps of the schemes. Despite some success in explaining the experimental observations, these reaction schemes have serious drawbacks in their inability to account for the bidirectional complexation/ decomplexation of CD with guest molecules and the formation of orientational isomers for noncentrosymmetric guests.3-12 Considering the importance of the structures and the kinetic processes in the molecular recognition of CD and the operation of CD-based supramolecular machines,1,2 a new approach for kinetics of CD inclusion complexation is critically required. In this article, a novel parallel reaction scheme incorporating the bidirectional complexation and the formation of orientational isomers with noncentrosymmetric guests is presented. The rate equations are derived for the scheme, and the methods for the determination of the microscopic directional rate constants are described. The rate constants of the previous one-step and twostep reaction schemes are expressed as functions of the microscopic directional rate constants. The reported results of the kinetic and thermodynamic studies on the threading and dethreading reactions of R-CD with various noncentrosymmetric guests are reexamined. The ratios of orientational isomers of R-CD complexes of the guests at equilibrium are estimated. Also, the microscopic directional rate constants for the complexation reactions are evaluated from the reported thermodynamic and kinetic parameters. It is also shown that the

10.1021/jp065238+ CCC: $33.50 © 2006 American Chemical Society Published on Web 11/15/2006

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Park extensive investigations on the kinetics of R-CD complexation of azo and related compounds have followed.14,15,17-23,26 The kinetic measurements were usually made by conventional or stopped-flow spectroscopic technique. Deviation of the kinetic behavior from that expected from the one-step reaction was found, and the one-step reaction scheme was elaborated to a consecutive two-step reaction scheme in the early 1980s.17 However, the one-step scheme is still being used, presumably due to its simplicity.15,28-30 3.1. One-Step Reaction Scheme. The one-step reaction between a guest (G) and CD is expressed as k+1

G + CDy\ zG/CD k -1

(1)

The reaction following this scheme would show a single exponential kinetic trace with an observed rate constant (k1,obs), which is related to the microscopic rate constants by eq 2.

k1,obs ) k+1[CD]o + k-1

Figure 1. Structures of the guests listed in Table 1.

observations, which were not easily accounted for by the previous schemes, are successfully explained by the new reaction scheme. 2. General Information First, the one-step and consecutive two-step reaction schemes that have been used to analyze and interpret the kinetics of CD complexation reactions by many investigators are described. Some reported experimental observations that are not easily explained by the schemes are presented. Then, a novel parallel reaction scheme incorporating bidirectional inclusion and formation of orientational isomers is presented, and the rate constant equations are described. The rate constants of the one-step and consecutive two-step reaction schemes are expressed in terms of the microscopic directional rate constants of the present scheme. Though the results of this work can be applied to any CD complexation systems, our discussion and examples are mostly restricted to the threading and dethreading reactions of R-CD with noncentrosymmetric threadlike molecules, the kinetic processes of which can be followed by conventional methods and would be important in the assembly and operation of CDbased supramolecular machines.2 For convenience of presentation and discussion, the reported thermodynamic and kinetic parameters of the extensively studied systems, R-CD complexes of phenyl azo compounds and an aliphatic chain-linked dyad compound (Figure 1), are summarized in Table 1. Unless otherwise specified, all relationships are written under the condition of large excess of CD with respect to the guest G, and [CD]o denotes the total concentration of CD. 3. Previous Reaction Schemes and Some Unaccountable Observations Cramer and co-workers investigated the kinetics of the inclusion complexation of a series of 1-naphthylazobenzenes with R-CD by a temperature-jump method in 1967.13 They followed the reaction with the absorbance change and analyzed the kinetics with a one-step reaction scheme. Since then,

(2)

The k1,obs versus [CD]o plot would yield a straight line, and forward (k+1) and backward (k-1) rate constants are determined from the plot. The data for guests 1, 7, 8, 12, and 19 in Table 1 were obtained from this scheme.11,13,15,18,20 The data of 1 and 12 were fitted to a biexponential function, but the authors could not detect the signal of the second component.18,20 Several kinetic parameters obtained by using the one-step scheme cannot be soundly explained by chemical principles. One is that the equilibrium constant calculated from the rate constants using the relationship K ) k+1/k-1 is usually much smaller than the corresponding value determined by spectroscopic titration or from NMR spectra.11,13,15,20,27 This can be ascertained by comparing K and k+1/k-1 of 7, 8, 12, and 19 in Table 1. In addition, inflection was often observed in the log k+1 or log(k+1/T) versus 1/T plots.13,14,20 It was also found that the observed rate constant does not depend linearly on [CD]o as predicted in eq 2, but shows a saturation behavior.17,25 The kinetic traces for the reactions of R-CD with a number of azo compounds fit better to a double exponential function than to the single exponential.18-23 3.2. Consecutive Two-Step Reaction Scheme. To account for the experimental observations that deviate from those expected from the one-step reaction scheme, the consecutive two-step scheme (eq 3) was introduced to interpret the kinetic behavior.17-23,25 k+1

k+2

z G/CD* y\ z G/CD G + CD y\ k k -1

-2

(fast)

(slow)

(3)

The scheme assumes a fast association process between G and CD to form an intermediate complex G/CD*, and the subsequent intracomplex structural reorganization of G/CD* to a more stable complex G/CD. As the first step appeared to be very fast compared to the second step, the two steps were considered to be independent in the kinetic time scale. The observed rate constant for the second step (k2,obs) was derived as in eq 4 by assuming pre-equilibrium for the first step.

k2,obs )

k+2K1[CD]o (1 + K1[CD]o)

+ k-2

(4)

where K1 denotes the equilibrium constant of the first step and is equal to k+1/k-1.

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TABLE 1: Reported Equilibrium (K) and Rate Constants (k+1, k-1, k-2, k-2) Based On the One-Step or Two-Step Mechanism; First (k1,obs) and Second (k2,obs) Rate Constants Calculated at [r-CD] ) 1.0 × 10-3 M; and Equilibrium Isomer Ratio (R) for Inclusion Complexation Reactions of Selected Guests with r-Cyclodextrin in Aqueous Mediaa guest

K/M-1 b

1 2 3 4 5 6 7 8 9 10 11 12 13

8300 10000 8300 4500 5600 1900 4000 450 14000 9800 5000 1200 4170 2800 5800 5400 910 4500 6500 15100 2500

14 15 16 17 18 19

k+1/M-1 s-1

k-1/s-1

700000 77 21000 6.5 20000 6.0 12000 9.4 11000 14 460 0.55 5000 7.7 6000 19 22000 3.0 20000 5.5 5400 4.0 570 1.3 15200(15400)g 25.4(26.6)h k+1/k-1 ) 430 13600(13400)g 13.3(15.1)h 11000 4.0 550 0.7 167000 380 >107 >103 12200(12300)g 1.84(2.05)h 0.35 2.7 × 10-4

k1,obs/s-1 c 777 27.5 26.0 21.4 25 1.01 12.7 25 25 25.5 9.4 1.87 40.6 26.9 15.0 1.25 547 14.0 6.2 × 10-4

k+2/s-1

k-2/s-1

e f 0.87 0.58 0.8 f

e f 0.55 0.28 0.16 f

f f >0.3 e 1.83 1.6 0.70 0.47 f 58 18.5 0.20

∼0.8 f ∼0.3 e 0.17 0.28 0.22 0.28 f 4.8 4.5 0.09

k2,obs/s-1 c

1.22 0.61 0.51

0.86 0.76 0.57 0.64 22.5 0.26

Rd

ref

i 5.2 4.0(3.6) 6.0(4.1) 13(10) i 12 i 2.8 4.4 6.4 i 13(22)(11.6)j 12(11) 11(6.4)(8.1)j 3(3.4) i 19(24) (8.2) 3.6(4)(2.6)j 2.9

18 18 18 18 18 18 15 13 20 20 20 20 22 17 22 19 18 22 19 22 11

a Data were taken at 25 °C except 8 (at 14 °C), I ) 0.1 M, and at neutral or mild acidic pH where phenolic -OH is not dissociated. b Macroscopic equilibrium constant for 1:1 complexation, determined by spectroscopic titration, and the data of 1-6 are from ref 27. c Calculated from the reported data using eqs 2 and 4. d Estimated from the reported K, k+1, and k-1 values. Numbers in the parentheses without a suffix are estimated values by using R ) 2k+2/k-2 (see text for details). e The authors could not detect a signal. f The authors reported that the amplitude of the second component was too small to obtain reliable rate constants. g (k1f + k2f) from the plots in Figure 3. h (k1r + k2r) from the plots in Figure 3. i Reasonable values of R could not be obtained from the reported data. j From 1H NMR spectra (see Table 2).

Two types of [2]pseudorotaxane formation reactions with R-CD have been analyzed with the two-step reaction scheme. One is the reaction with the centrosymmetric L-(CH2)n-L type guests, where the hydrophilic end group L has substantial binding affinity to R-CD.25 The threading of R-CD with the guest proceeds with inclusion of the group L into the R-CD cavity to form the L-(CH2)n-{L-CD} complex. The complex transforms slowly to the L-{(CH2)n-CD}-L complex. The rate of the first step reaction is too fast to determine the rate constants, but the reaction is characterized by the dependence of the observed rate constant on [R-CD] as eq 4. The second reaction type is with the noncentrosymmetric Y-S-X type guests: S is the station for R-CD in the [2]pseudorotaxanes, and the X and Y groups behave as block or bumper for the passage of R-CD. This shows the biphasic behavior in the kinetic traces, even when no appreciable binding affinity of the terminal X or Y group to R-CD is expected.18-23 The reaction is characterized by two observed rate constants, k1,obs (eq 2) and k2,obs (eq 4). The kinetic independence of the two steps seems to be justified from the observation of k1,obs/k2,obs > 20 (see Table 1). Discussion on the two-step reaction scheme in this article is restricted to the latter type reaction. The macroscopic equilibrium constant (K) for the complexation is defined as K ) {[G/CD*] + [G/CD]}/{[G][CD]} and becomes K ) K1 + K1K2, where K2 denotes the equilibrium constant of the second step and is equal to k+2/k-2. The K values calculated from the kinetics data had appeared to agree reasonably well with those obtained by spectroscopic measurements.17-20,22 Also, the existence of two isomeric R-CD inclusion complexes that could be assigned to G/R-CD* and G/R-CD were revealed in the 1H NMR spectra of R-CD complexes of a number of noncentrosymmetric thread molecules.4-9,20,22-24 Thus, the two-step reaction has been accepted as a general scheme for the CD complexation mechanism.26 However, the scheme has several critical drawbacks in fundamental aspects of cyclodextrin chemistry, and many of

the experimental observations do not support the reaction mechanism. (1) The scheme, as well as the one-step scheme, assumes the unidirectional threading of CD onto the guest, but it is certain that CD forms complexes with guest molecules bidirectionally to yield orientational isomers with noncentrosymmetric guests.3-9,12 An unequivocal evidence for this is the preparation of the two orientational isomers of R-CD[2]rotaxanes with thread molecules that have only one open end for the threading of R-CD.4,12 (2) The slow second step, which requires higher activation energy than the first step, was interpreted as solvational and conformational changes,18,22,26 but no supporting evidence for this has been provided. (3) The isomers are also observed with R-CD complexes of thread molecules with aliphatic chains as the station (analogous of 19 having different end groups),4,6,7,9 where an intracomplex structural transformation would not be feasible. (4) NMR traces of the complexation reaction have indicated the simultaneous formation of two isomers at an early stage of the reaction,4,5,7,9 whereas the scheme predicts the formation of one isomer and its slow transformation to another isomer. Therefore, it is obvious that an alternative reaction scheme is necessary to account for these experimental observations. 4. Novel Parallel Reaction Scheme Involving Bidirectional Inclusion Now, a novel, parallel reaction scheme, in which a guest molecule enters and exits both sides of the CD cavity, is presented.31 The generalized reaction scheme is represented in Figure 2. First, the reactions with centrosymmetric guests, X-S-X, and then reactions with noncentrosymmetric guests, Y-S-X, are considered. Rate constant equations and methods for the determination of the directional microscopic rate constants are presented, and then the rate constants of the previous one-step and two-step reaction schemes are expressed in terms of the microscopic rate constants. For clarity of

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Park complexation of R-CD with this type of guest has been widely studied.7-11,13-15,17-22 The reaction between a guest G and CD occurs via two parallel routes and gives two orientational isomers PI and PII. k1f

G + CDy\ zPI k

(6)

1r

k2f

zPII G + CDy\ k

(7)

2r

The general solution for the two parallel reactions is a double exponential function characterized by two observed rate constants k1,obs and k2,obs.32,33

[G]/[G]total ) C1 exp(-k1,obs‚t) + C2 exp(-k2,obs‚t) + k1r‚k2r/q (8) Figure 2. Schematic representation of inclusion complexation reactions of CD with a threadlike guest, X-S-Y. CD molecule encircles the station S, and the bulky and/or hydrophilic X and Y groups are protruded in the complex. (A) Threading and dethreading through both X and Y groups are allowed. (B) Threading and dethreading through Y are blocked due to the large size of Y.

presentation, no appreciable binding affinity of X or Y with CD is assumed. 4.1. Centrosymmetric Guest Molecules. The complexation of a CD with a centrosymmetric thread molecule gives only one [2]pseudorotaxane species, although CD can thread and dethread via four different routes, bidirectionally through both ends of the thread molecule as depicted in Figure 2A: PI and PII are identical as X ) Y. The microscopic rate constants have the relationships k+12 ) k+11, k+21 ) k+22, k-21 ) k-11, and k-12 ) k-22. The reaction can be described as a one-step reaction (eq 1) with the following relationships for the rate constants.

k+1 ) 2(k+11 + k+21); k-1 ) 2(k-11 + k-21)

(5)

From the kinetic studies with X-S-X guests, k+1 and k-1 are determined but the microscopic directional rate constants cannot be obtained separately. If the two X groups are far apart, the threading reaction can be considered to occur independently through the two groups. The directional threading rate constants, k+11 and k+21, would be the same as those for reactions via the narrow primary side and the wider secondary side, respectively, of CD with a noncentrosymmetric guest Z-S-X, where Z is a bulky group causing threading to occur only through the group X (see section 4.2). The sum of the two directional threading rate constants of Z-S-X would be about half of the apparent threading rate constant k+1 of X-S-X.7 However, it is necessary to be cautious when applying the rate constant relationships to the dethreading rate constants, as the X and Z groups may interact differently with the encircled CD of the [2]pseudorotaxane and the dethreading rate would be influenced by such an interaction. As the reaction is not an elementary reaction, it is quite possible to observe the deviation from the linearity in the log k+1 versus 1/T, log k-1 versus 1/T, or log K versus 1/T plots: K denotes the macroscopic equilibrium constant of the complexation reaction and is expressed as K ) (k+11 + k+21)/(k-11 + k-21). 4.2. Noncentrosymmetric Guest Molecules with a Bulky End Group. For a guest of the Y-S-X type, where Y is larger than the cavity size of CD, CD can thread and dethread the guest only through X, as represented in Figure 2B. The guests 4-8 and 11-19 in Table 1 are of this type. The kinetics of

with

k1,obs )

p + xp2 - 4q p - xp2 - 4q and k2,obs ) 2 2

(9)

where p ) (k1f + k2f)‚[CD]o + (k1r + k2r) and q ) (k1f‚k2r + k2f‚k1r)‚[CD]o + k1rk2r. The sum of k1,obs and k2,obs is p and is expressed as eq 10 in terms of the microscopic rate constants.

k1,obs + k2,obs ) (k1f + k2f)‚[CD]o + (k1r + k2r)

(10)

The plot of (k1,obs + k2,obs) versus [CD]o would yield a straight line with the slope and intercept equal to (k1f + k2f) and (k1r + k2r), respectively. To obtain the k1f and k2f values from their sum, it is necessary to find the k1f/k2f ratio. The ratio is the same as the [PI]/[PII] ratio in the early stage of the threading reaction and can be determined from the dethreading kinetics described below. The dethreading kinetics also gives the values of k1r and k2r. The dethreading reactions of G/CD complexes, PI and PII, can be induced upon the addition of a competitive guest S to a solution of the G and CD mixture.7 Binding of S to CD depletes the free CD and results in the dethreading reactions of PI and PII. The reactions can be written as KS

S + CDy\zS/CD k1r

PIy\ zG + CD k

(11) (12)

1f

k2r

zG + CD PIIy\ k

(13)

2f

A required condition for following the dethreading reactions conveniently after the addition of S is that the reaction rate between S and CD is much faster than the rates of dethreading reactions. Another necessary characteristic of S for using it as a competitive guest is that S does not interact appreciably with G as well as the G/CD complexes. If S has a high binding affinity to CD and is added to high concentration, the concentration of free CD remains low during the dethreading reaction, and thus rethreading of CD with G becomes negligible.34 In these conditions, the dethreading reactions can be treated as two independent irreversible first-order reactions. The k1r and k2r values can be obtained from fitting of the kinetic traces of [PI] and [PII], respectively. An example for this is the determination of the dethreading rate constants of orientational isomers of [2]-

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pseudorotaxanes composed of R-CD and dicationic threads by 1H NMR spectroscopy.7 Monitoring the concentration of each isomer is usually not feasible. Instead, the concentration of free G or the sum of the concentrations of both isomers can be traced. The time dependence of [G] is given as

[G] ) [G]total - [PI]o exp(-k1r‚t) - [PII]o exp(-k2r‚t) (14) where [PI]o and [PII]o are the initial concentrations of the corresponding isomers. The fitting of the [G] versus time profile to eq 14 gives the microscopic dethreading rate constants, k1r and k2r, as well as [PI]o and [PII]o. For many CD/noncentrosymmetric guest systems at equilibrium, one orientational isomer appears to be predominant over the other.4,5,10,11,22 Therefore, the addition of S to a solution of G and CD at equilibrium would give reliable dethreading rate constants for the thermodynamically more stable isomer, but the rate constant for the less stable isomer might have a large uncertainty due to the small amplitude. It would be often desirable to add S at an early stage of the threading reaction for the determination of the reliable dethreading rate constant of the less stable isomer. Particularly, if the addition of S is made at t < 1/(k1r + k2r), the [PI]o/[PII]o ratio would be the ratio of threading rate constants for the isomers, k1f/k2f. Thus, all four microscopic directional rate constants in Figure 2B can be obtained from the combination of the results of threading and dethreading kinetics. Now, it is time to relate the rate constants with the equilibrium properties and to discuss the general trend of the CD inclusion complexation reaction of noncentrosymmetric guests. As the microscopic rate constants are obtained from the threading and dethreading kinetics, the microscopic equilibrium constants KI and KII for the formation of PI and PII complexes, respectively, are calculated from the relationships KI ) k1f/k1r and KII ) k2f/ k2r. The KII/KI ratio is the same as the equilibrium ratio (R) of the orientational isomers, [PII]/[PI]. The macroscopic equilibrium constant (K) becomes (KI + KII). Conversely, the microscopic rate constants can be calculated from the results of the threading experiments, which give kf () k1f + k2f) and kr () k1r + k2r), and the equilibrium measurements, which give the values of K and R, without the results of dethreading experiments. The microscopic equilibrium constants KI and KII are related to K and R by KI ) K/(1 + R) and KII ) K‚R/(1 + R). The microscopic dethreading rate constants are calculated from KI, KII, kf, and kr by using the relationships k1r ) (KII‚kr - kf)/(KII - KI) and k2r ) (kf - KI‚kr)/(KII - KI).35 Once these are calculated, the microscopic threading rate constants are obtained from k1f ) KI‚k1r and k2f ) KII‚k2r. This method would be useful for various guest/CD systems when the isomers are distinguishable in 1H NMR spectra,4-9,22 as the dethreading experiments are not necessary for the determination of the microscopic rate constants. Abou-Hamdan and co-workers observed the existence of two isomers in the R-CD complexes of the guests 13, 14, and 18 and assigned them to the G/R-CD* and G/R-CD complexes of the two-step mechanism (eq 3).22 However, it is believed that the isomers are indeed orientational isomers. From the k1,obs and k2,obs data provided by the authors,36 (k1,obs + k2,obs) values are plotted against [CD]o (Figure 3), and the kf () k1f + k2f) and kr () k1r + k2r) values are obtained. These are included in Table 1, in the column of k+1 and k-1, respectively. Then, the directional rate constants for the complexation reactions between R-CD and these guests are calcu-

Figure 3. Plots of the sum of two observed rate constants (k1,obs + k2,obs) vs [R-CD] (eq 13) for inclusion complexation reactions of the guests 13(4), 14(O), and 18(0). The k1,obs values are also shown as ×’s for comparison. The observed rate constant data taken at 25 °C are from the Supporting Information of ref 22. The (k1f + k2f) and (k1r + k2r) values obtained from these plots are included in Table 1.

lated from the rate constants, K, and the ratios of the isomers via the aforementioned procedure. The results are given in Table 2. Table 2 shows that the k1f and k2f values of the guests 13, 14, and 18 for the complexation reactions with R-CD are similar: all of the reactions proceed through the 4-benzenesulfonate groups. In contrast, the k1r and k2r values are highly sensitive on the substituents on the phenyl ring, which acts as a blocking group for R-CD, though the reactions also occur through the same group, 4-benzenesulfonate. The similarity between the two directional threading rate constants and a large difference between the two directional dethreading rate constants agree with the previous reports on the R-CD [2]pseudorotaxanes of aliphatic chain-linked carbazole-viologen pair,4 and of stilbene or azobenzene compounds.5 This trend of the directional rate constants was also revealed in the R-CD complex of E-4-tbuthylphenyl-4′-oxyazobenzene, in which the ratio of the dethreading rate constants of the orientational isomers is the same as the ratio of areas in 1H NMR of the isomers, 2.86, suggesting that k1f ≈ k2f and k1r/k2r ) 2.86.8 The structures of CD complexes are usually elucidated from 2D NMR spectra. The NMR spectra usually led researchers to conclude that the complexes exist as a single isomer.10,11,37,38 The formation of R-CD-based [2]rotaxanes as a single orientational isomer via capping of the corresponding [2]pseudorotaxanes also suggests the presence of the [2]pseudorotaxanes as a single isomer.39,40 However, the time dependence of the 1H NMR spectra of the mixtures of the guests and R-CD showed that the two directional threading rate constants to form the isomers of the precursor [2]pseudorotaxanes are not much different, but the dethreading rate constants of the isomers are quite different, resulting in the thermodynamically more stable isomer to be predominant at equilibrium.4,5 The apparent mistaken conclusions of the formation of CD complexes as a single isomer and thus unidirectional threading of CD based on 2D NMR could be because the spectra are taken in nearequilibrium conditions and the 2D NMR spectra are not sensitive enough to detect the cross-peaks from the minor isomer unequivocally. The interior of the CD cavity is not a smooth cone, but has constrictions near the middle of the cavity.41 The constricted region may act as bottleneck in the passage of a guest through

24920 J. Phys. Chem. B, Vol. 110, No. 49, 2006 TABLE 2: Microscopic Directional Rate Constants Calculated from Reported Kinetic and Thermodynamic Dataa

Park but the same estimation cannot be made for the dethreading rate constants. 5. Relationships of Kinetic Parameters of Previous and Present Reaction Schemes

a Thermodynamic and kinetic data are from ref 22 and are given in Table 1. b Ratio of isomers from 1H NMR spectra (from ref 22). c Recalculated from 1H NMR spectra (the original reported value was 3.3).

the CD cavity. This might be a reason why the threading rate constants exhibit little dependence on the CD face. Therefore, in the CD complexes with noncentrosymmetric guests at equilibrium, the predominance of one orientational isomer is largely due to the slow dethreading rate of the isomer. It might be a general trend in CD complexation that k1f ≈ k2f and k1r >> k2r.42 This implies that k1f and k2f contribute about equally to k+1, whereas k1r contributes much more to k-1 than k2r does. This accounts for the reason why the log k+1 versus 1/T plot often deviates from linearity, while log k-1 versus 1/T plot exhibits good linearity.13,14,18 4.3. Noncentrosymmetric Guest Molecules for Which CD Threads through Both Ends. If the sizes of both end groups, X and Y, are not large enough to block the passage of CD, a CD molecule can thread and dethread through both ends of the guest as depicted in Figure 2A. The reactions of R-CD with the guests 1-3, 8, and 9 (Table 1) might belong to this case. The kinetics can be studied and analyzed in the same way as described in section 4.2. However, the obtained rate constants for orientational isomers are not the microscopic rate constants, but the sums of the microscopic rate constants for reactions through X and Y groups: k1f ) (k+11 + k+21); k1r ) (k-11 + k-12); k2f ) (k+12 + k+22); k2r ) (k-21 + k-22). If the X and Y groups in Y-S-X are far apart from each other, the threading reactions occur through the two groups independently. In this case, the microscopic rate constants through the X and Y groups can be estimated from the kinetics studies of guest molecules Z-S-X and Y-S-Z, respectively, where Z is a bulky group. This strategy is similar to that mentioned in section 4.1 for the estimation of the microscopic rate constants of the reactions with centrosymmetric guests. As the substitution of Y of Y-S-X to Z would not affect the threading kinetics through X, the k1f and k2f values of Z-S-X would not be much different from the k+21 and k+12 values, respectively, of Y-S-X. Similarly, the k1f and k2f values of Y-S-Z can be taken as the k+22 and k+11 values, respectively, of Y-S-X. To apply the above strategy to the evaluation of the microscopic dethreading rate constants, it is necessary to ascertain that the end groups (X, Y, and Z) do not affect the thermodynamic stability of the resulting complexes (i.e., no appreciable interaction between the end group and the encircled CD). However, this condition would be met rarely. The microscopic rate constants in Table 2 support our argument that the microscopic threading rate constants through a group (e.g., X) in the reactions with Y-S-X type guest would be similar to those with Z-S-X type guest where Z is a blocking group,

Though the consecutive two-step reaction scheme and the present two parallel reactions scheme start from widely different mechanistic assumption, the schemes are quite analogous. Mathematically, both schemes predict the same kinetic profile, the double exponential function for [G] versus t trace. The kinetics is characterized by the two observed rate constants, k1,obs and k2,obs. Before deriving the kinetic parameters of the previous consecutive two-step scheme in terms of the microscopic directional rate constants of the present scheme, it is necessary to point out a few common features found in the kinetic behaviors of extensively investigated R-CD inclusion complexation systems (see Table 1 for examples). One is that the macroscopic equilibrium constant is quite large and on the order of 103-104 M-1. Another is that most kinetic measurements were carried out under the condition of a large excess of R-CD over G: an exception to this is guest 8 in Table 1. The other is that the k1,obs value is generally more than 20 times greater than the k2,obs value at the concentration of R-CD commonly used for kinetic measurement, 1.0 × 10-3 M (Table 1). As k1,obs >> k2,obs, the (k1,obs + k2,obs) would be insignificantly different from k1,obs. Thus, the slope and intercept of the (k1,obs + k2,obs) versus [R-CD] plot (eq 10) for the present scheme would not be significantly different from the corresponding values of the k1,obs versus [R-CD] plot (eq 2) for the two-step scheme. This is demonstrated in Figure 3 for the complexation reactions of R-CD with guests 13, 14, and 18 (for data, see Table 1). On this basis, one can regard the k+1 and k-1 values from the two-step reaction scheme (Table 1) as (k1f + k2f) and (k1r + k2r) values, respectively, of the present reaction scheme. The observations of k1,obs >> k2,obs suggest that the (p2 4q)1/2 term in eq 9 is close to p (i.e., 4p/p2 > k2r,42 K1 is approximated as (k1f + k2f)/k1r. On the basis of the general trend of k1f ≈ k2f, it can be said that K1 is about twice the microscopic equilibrium constant (KI) for the formation of the less stable isomer, PI. Similarly, k+2 is approximated as k2f‚k1r/(k1f + k2f),

Kinetics and Mechanism of Cyclodextrin Complexation which corresponds to the apparent rate constant for the conversion of PI isomer to the more stable isomer PII isomer, and becomes k1r/2 if k1f ≈ k2f. The k-2 value is about the same as k2r. The K2 () k+2/k-2) of the previous two-step scheme is expressed approximately as k2f‚k1r/[(k1f + k2f)‚k2r] and becomes about KII/2KI. The macroscopic equilibrium constant (K) for the complexation reaction is expressed as (K1 + K1‚K2) for the two-step reaction, whereas it is given as (KI + KII) in the present parallel reaction scheme. On the basis of the results of the above analysis, we find that K1 ≈ 2KI and K2 ≈ KII/2KI, K for the two-step scheme becomes 2KI + KII. This differs from the value for the present parallel reaction scheme by KI. As the ratio of isomers appears to be usually greater than 3 (Table 1), the K values calculated from the kinetic data assuming the consecutive two-step reaction would agree with the true K value within 25%, which is within the range of experimental uncertainty.17,22 This might be a reason why the two-step reaction scheme usually appears to be successful in accounting for the experimental observations. The later stage of the complexation reaction forming two orientational isomers would appear as if the PI isomer isomerizes to a thermodynamically favored one (PII).7,9,42 If one takes the steady-state approximation for G, the rate of the isomerization process is expressed as eq 19. The isomerization reaction is expected to follow the single exponential function with observed rate constant kiso ) (k2f k1r + k1f k2r)/(k1f + k2f). This is the limiting k2,obs value at high concentration of CD.

∂[PI]/∂t ) -k2fk1r/(k1f + k2f)‚[PI] + k1fk2r/ (k1f + k2f)‚[PII] (19) It is quite often that the kinetic trace of CD complexation reaction appears to fit better to single exponential function than to a double exponential function, misleading one to conclude that the reaction is a one-step process.18-20 The complexations of guests 1, 6-8, 12, and 15 with R-CD (Table 1) are examples of this. Though the complexation reaction of guests 4-7 and 13-15 would proceed through the same group, 4-benzenesulfonate, the k+1 values for 6 and 15 appeared to be much smaller than the corresponding values for others. Similarly, the k+1 value for 12 was reported to be much larger than that for 11, though the threading of R-CD with these guests would occur through the same 2-naphthalenesulfonate. Yoshida and coworkers attributed this to the difference in the mechanism of molecular recognition:18,19 they classified the R-CD complexation mechanism into the fast one-step (A), the consecutive twostep (B), and the slow one-step mechanisms (C). Such different kinetic behaviors can be observed in the present parallel reaction scheme depending on the relative magnitudes of rate constants and microscopic equilibrium constants, but without a change in the reaction mechanism. The amplitudes C1 and C2 of the kinetic trace (eq 8) depend on the initial conditions and the rate constants. If G and CD are mixed at t ) 0, they are expressed as eqs 20 and 21 (see SI for derivation), where K′ denotes K‚[CD].

C1 ) {(k1f + k2f)[CD]o - K′‚k2,obs/(1 + K′)}/ (k1,obs - k2,obs) (20) C2 ) {K′‚k1,obs/(1+ K′) - (k1f + k2f)[CD]o}/ (k1,obs - k2,obs) (21) If the |C1/C2| ratio is very large or close to 0, the kinetic trace might appear as if it follows the single exponential function

J. Phys. Chem. B, Vol. 110, No. 49, 2006 24921 and the reaction is a one-step process. In the case of |C1/C2| >> 1, the reaction may appear as a fast one-step reaction (mechanism A)18,19 with the observed rate constants close to k1,obs. The condition of |C1/C2| >> 1 is met when (k1f + k2f)· [CD]o >> (k1r + k2r) (i.e., k+1‚[CD]o >> k-1). The reactions of guests 1, 9, and 10 in Table 1 belong to this case: C1/C2 ratios calculated from the reported data at 1.0 mM R-CD are about 100 for 1, 17 for 9, and 8 for 10. In the case of |C1/C2| ≈ 0, the kinetic trace would reflect mostly the slow second component, and the reaction appears to undergo by the type C mechanism. The reactions of guests 6, 12, and 15 in Table 1 might belong to this case. These guests exhibit much smaller K values than the other guests examined, suggesting the large dethreading rate constants and thus the small C1/C2 ratio. It seems that the authors misjudged the slow second component of the reaction as the first component for the guests. The closeness of the calculated k1,obs of these guests to the k2,obs values of other closely related guests strongly implies this possibility. If this is the case, the reported k+1 and k-1 values of the guests in Table 1 would correspond approximately to k+2K1 and k-2 values, respectively, of the consecutive two-step mechanism. Finally, the equilibrium ratios (R) of orientational isomers of R-CD complexes with guests shown in Figure 1 are estimated by using the reported kinetic and thermodynamic parameters given in Table 1. As K1 () k+1/k-1) is about twice that of KI, KII is approximated as (K - k+1/2k-1). The equilibrium ratio (R) of PII to PI isomers is equivalent to the KII/KI ratio. The ratio is easily estimated from K, k+1, and k-1 values by the relationship R ) (2K - k+1/k-1)/(k+1/k-1). R can also be estimated from k+2 and k-2 values by using the relationship R ) (k2f·k1r)/(k1f·k2r). Assuming k1f ) k2f and k1r >> k2r, R becomes k1r/k2r, which is given as 2k+2/k-2. The estimated R values are included in Table 1. Good agreement between the values obtained from the two different estimation methods is seen. It is also seen that the estimated R values for guests 13, 14, and 18 match well with the corresponding values determined from NMR spectra.22 These indicate the validity of our analysis based on the assumption of k1f ) k2f and k1r >> k2r. Conclusions A novel parallel reaction scheme for the cyclodextrin inclusion complexation reactions is described. This scheme incorporates the bidirectional threading and dethreading of CD and the formation of two orientational isomers with noncentrosymmetric guests. The kinetic trace of this scheme follows a double exponential function similar to that expected from the consecutive two-step reaction scheme that has been widely used. The microscopic directional rate constants and microscopic equilibrium constants can be obtained from kinetic studies of the threading and dethreading reactions or from kinetics studies of threading reaction and thermodynamic studies on the macroscopic equilibrium constant (K) and the ratio of isomers. The rate constants of the consecutive two-step scheme are expressed in terms of the microscopic directional rate constants. The equilibrium ratios of orientational isomers of R-CD [2]pseudorotaxanes of various noncentrosymmetric guests are estimated from the reported K values and kinetic parameters obtained by using the one-step or the two-step schemes. The various unaccountable observations based on the previous schemes are explained with the present scheme. As the dethreading process of a pseudorotaxane is analogous to the movement of CD along a polymer chain having multiple stations and bumpers, the microscopic directional rate constants that can be obtained by

24922 J. Phys. Chem. B, Vol. 110, No. 49, 2006 using equations and experimental methods described in this work would be used to simulate and understand the formation and dynamics of polypseudorotaxanes. This work also addresses that care should be taken in interpreting the thermodynamic parameters derived from the equilibrium constants and their temperature dependence. Acknowledgment. Part of this study was carried out during the author’s sabbatical stay at the Department of Chemistry, Yale University. The author acknowledges the hospitality of Professor W. L. Jorgensen’s group during his stay at Yale. Supporting Information Available: Derivation of the rate constant equations of the parallel reaction scheme. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) ComprehensiVe Supramolecular Chememistry; Szejtli J., Osa, T., Eds.; Pergamon Press: Oxford, 1996; Vol. 3. (b) Chem. ReV. 1998, 98, 1741-2076. (2) (a) Nepogodiev, S. A.; Stoddart, J. F. Chem. ReV. 1998, 98, 1959. (b) Raymo, F. M.; Stoddart, J. F. Chem. ReV. 1999, 99, 1643. (c) Harada, A. Acc. Chem. Res. 2001, 34, 456. (d) Huang, F. H.; Gibson, H. W. Prog. Polym. Sci. 2005, 30, 982. (e) Wenz, G.; Han, B.-H.; Mu¨ller, A. Chem. ReV. 2006, 106, 782. (f) Tian, H.; Wang, Q. C. Chem. Soc. ReV. 2006, 35, 361. (3) (a) Park, J. W.; Song, H. E.; Lee, S. Y. J. Phys. Chem. B 2002, 106, 7186 and references therein. (b) Park, J. W.; Lee, S. Y. J. Inclusion Phenom. Macrocyclic Chem. 2003, 47, 143. (4) Park, J. W.; Song, H. J. Org. Lett. 2004, 6, 4869. (5) Wang, Q.-C.; Ma, X.; Qu, D.-H.; Tian, H. Chem.-Eur. J. 2006, 12, 1088 and references therein. (6) Eliadou, K.; Yannakopoulou, K.; Rontoyianni, A.; Mavridis, I. M. J. Org. Chem. 1999, 64, 6217. (7) Baer, A. J.; Macartney, D. H. Org. Biomol. Chem. 2005, 3, 1448. (8) May, B. L.; Gerber, J.; Clements, P.; Buntine, M. A.; Brittain, D. R. B.; Lincoln, S. F.; Easton, C. J. Org. Biomol. Chem. 2005, 3, 1481. (9) Oshikiri, T.; Takashima, Y.; Yamaguchi, H.; Harada, A. J. Am. Chem. Soc. 2005, 127, 12186. (10) Yonemura, H.; Kasahara, M.; Saito, H.; Nakamura, H.; Matsuo, T. J. Phys. Chem. 1992, 96, 5765. (11) Toki, A.; Yonemura, H.; Matsuo, T. Bull. Chem. Soc. Jpn. 1993, 66, 3382. (12) (a) Isnin, R.; Kaifer, A. E. J. Am. Chem. Soc. 1991, 113, 8188. (b) Isnin, R.; Kaifer, A. E. Pure Appl. Chem. 1993, 65, 495. (c) Buston, J. E. H.; Young, J. R.; Anderson, H. L. Chem. Commun. 2000, 905. (d) Buston, J. E. H.; Marken, F.; Anderson, H. L. Chem. Commun. 2001, 1046. (13) Cramer, F.; Saenger, W.; Spatz, H.-Ch. J. Am. Chem. Soc. 1967, 89, 14. (14) Yoshida, N.; Fujimoto, M. J. Phys. Chem. 1987, 91, 6691. (15) Zheng, P.; Li, Z.; Tong, L.; Lu, R. J. Inclusion Phenom. Macrocyclic Chem. 2002, 43, 183. (16) Yim, C. T.; Zhu, X. X.; Brown, G. R. J. Phys. Chem. B 1999, 103, 597. (17) Hersey, A.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1 1984, 80, 2039. (18) Yoshida, N.; Seiyama, A.; Fujimoto, M. J. Phys. Chem. 1990, 94, 4246 and references therein. (19) Yoshida, N.; Hayashi, K. J. Chem. Soc., Perkin Trans. 2 1994, 1285.

Park (20) Yoshida, N. J. Chem. Soc., Perkin Trans. 2 1995, 2249. (21) Bugnon, P.; Lye, P. G.; Abou-Hamdan, A.; Merbach, A. E. Chem. Commun. 1996, 2787. (22) Abou-Hamdan, A.; Bugnon, P.; Saudan, C.; Lye, P. G.; Merbach, A. E. J. Am. Chem. Soc. 2000, 122, 592. (23) Saudan, C.; Dunand, F. A.; Abou-Hamdan, A.; Bugnon, P.; Lye, P. G.; Lincoln, S. F.; Merbach, A. E. J. Am. Chem. Soc. 2001, 123, 10290. (24) (a) Watanabe, M.; Nakamura, H.; Matsuo, T. Bull. Chem. Soc. Jpn. 1992, 65, 164. (b) Lyon, A. P.; Banton, N. J.; Macartney, D. H. Can. J. Chem. 1998, 76, 843. (25) (a) Macartney, D. H. J. Chem. Soc., Perkin Trans. 2 1996, 2775. (b) Smith, A. C.; Macartney, D. H. J. Org. Chem. 1998, 63, 9243. (c) Jin, V. X.; Macartney, D. H.; Buncel, E. J. Inclusion Phenom. Macrocyclic Chem. 2005, 53, 197. (26) Connors, K. A. Chem. ReV. 1997, 97, 1325. (27) Yoshida, N.; Seiyama, A.; Fujimoto, M. J. Phys. Chem. 1990, 94, 4254. (28) Examples of recent work on the CD/guest systems using the onestep scheme for the CD complexation are a dynamic study using an ultrasonic relaxation method29 and the control of diffusive motion with a periodic electric field.30 (29) Fukahori, T.; Kondo, M.; Nishikawa, S. J. Phys. Chem. B 2006, 110, 4487. (30) Alcor, D.; Allemand, J.-F.; Cogne´-Laage, E.; Croquette, V.; Ferrage, F.; Jullien, L.; Kononov, A.; Lemarchand, A. J. Phys. Chem. B 2005, 109, 1318. (31) Yoshida and co-workers noticed that the biphasic behavior of the R-CD complexation kinetics of noncentrosymmetric guests can be explained by a parallel reaction mechanism.18 They proposed the formation of orientational isomers by threading R-CD through two different ends (X and Y in Figure 2) of guest molecules, but assumed unidirectional threading through a given end of the guest. The parallel reaction scheme was not further elaborated, and they used the consecutive two-step scheme in the subsequent reports to analyze kinetic traces and interpret results.18,19 Recently, Baer and Macartney reported the kinetics of the reactions of two R-CD-based orientational isomers of dicationic thread molecules by following the formation and transformation of each isomer with 1H NMR spectroscopy.7 (32) Derivation of eqs 8 and 9 is given in the Supporting Information. Alternatively, two reactions in eqs 6 and 7 can be combined and expressed as the following series reaction, the solution of which was discussed by several authors and given as eq 8.33 k1f[CD]

k2f[CD]

-1

-2

PI y\ zGy\ zPII k k (33) Moore, J. W.; Pearson, R. G. Kinetics and Mechanism, 3rd ed.; Wiley: New York, 1981; pp 296-300. (34) When [CD]o