Determination of the kinetics underlying the p K a shift for the 2-aminoanthracenium cation binding with cucurbit [ 7 ] uril †

The binding dynamics of the 2-aminoanthracenium cation (AH) and 2-aminoanthracene (A) with cucurbit[7]uril (CB[7]) was studied using stopped-flow experiments. The kinetics was followed by measuring the fluorescence changes over time for AH and A, which emit at different wavelengths. The studies at various pH values showed different mechanisms for the formation of the AH@CB[7] complex, with this complex formed either by the binding of AH or by the initial binding of A followed by protonation. In the latter case, it was possible to determine the protonation ((1.5 0.4) 10 M 1 s ) and deprotonation (89 7 s ) rate constants for complexed A/AH, which showed that the pKa shift of +3.1 for A/AH + in the complex is mainly due to a lower deprotonation rate constant.


Introduction
2][3][4][5][6][7] One of the key features of supramolecular systems is their dynamics, 8 which can be directly related to the intended function of a supramolecular system.CB[n]s have been developed for a wide variety of applications, such as photocatalysis 9 or catalysis, [10][11][12][13] drug stabilization and delivery, [14][15][16][17] self-sorting and stimuli responsive systems, 3,[18][19][20][21] tandem enzyme assays, 22,23 and control of supramolecular polymerization. 24,25he dynamics of guest complex formation with CB [7] occurs over a wide time range, from milliseconds to hours, 10,[26][27][28][29][30][31][32][33][34][35] with rate constants for the association process as high as one order of magnitude below the diffusion controlled limit.The binding dynamics is affected by the size of the guest and the presence or absence of charges on the guest. 10,26,30,34Exclusion complexes can be formed between the positive charge of the guest and the carbonyl moieties at the portals of CB[n] before inclusion of the guest into the interior of the CB[n] cavity. 27,30,31owever, in other cases, the formation of an exclusion complex is not detected in kinetic studies. 32,34There are still too few reported studies on guest binding dynamics to develop a mechanistic understanding of how the guest binding dynamics can be controlled.Such an understanding is required for the rational design of systems containing CB [n]s where the dynamics is directly related to the intended function.
The objective of the current work is to explore one aspect of the guest-CB[n] dynamics, namely, the protonation and deprotonation reactions of a guest@CB[n] complex.This aspect is important because CB[n]s were shown to stabilize positively charged guests.7][38] Therefore, CB[n]-guest complexation alters the protonation and deprotonation rates of bound guests compared with this reactivity in water.Understanding the origins for this change in kinetics is relevant to the design of supramolecular systems that alter chemical reactivity, including the ability to affect acid-base catalysis.In this context, CB[n]s were shown to catalyze the hydrolysis of included guests. 39,40he increase in the hydronium cation concentration at pH values where the guest is protonated led to slower kinetics when binding of the hydronium cation with CB[n] was competitive with guest binding. 27,30,32The protonation state of the guest affects its binding dynamics with CB[n]s.For example, the association and dissociation rate constants of the cyclohexylmethylammonium cation with CB [6]  are lower than the same rate constants for cyclohexylmethylamine because, in the case of the cation, an exclusion complex is formed before the guest is included within the cavity. 30,31For pH values between the pK a values of the guest in water and in the complex, the association process corresponds to the binding of the neutral amine followed by fast protonation of the amine@CB [6] complex, whereas dissociation corresponds to the exit of the ammonium cation from CB [6]. 30The kinetics for the cyclohexylmethylamine/CB [6] system occur on hour to day time scales, depending on the pH.Therefore, the acid-base equilibria for the guest in water or within the complex were fast compared to the complexation dynamics with CB [6].On the other hand, no evidence for the formation of an exclusion complex was observed for the binding of the 2-naphthyl-1-ethylammonium cation with CB [7]. 32n this work, we chose a guest, the 2-aminoanthracenium cation (AH + ), with a lower pK a (4.0) 41 than that of cyclohexylmethylamine (10.5) 30 to study the effect of pH on the guest binding dynamics with CB [7] (Scheme 1).The pH values of the solutions were varied between 2.0, where the guest is completely protonated (AH + ), and pH 5.5, where the guest is mostly deprotonated (A).The singlet excited state of AH + , which emits with a maximum at 422 nm ("blue" emission), has a much lower pK * a (À5.4 in 1 : 1 water : ethanol), 42,43 leading to the formation of singlet excited A, which emits with a maximum at 503 nm ("green" emission). 38hese photophysical properties provide a means of following the concentrations of AH + and A separately.
AH + was shown to form a 1 : 1 complex with CB [7] resulting in a shi in the pK a for ground state AH + from 4.0 to 7.1, while the estimated excited state pK * a shied from À5.4 to between 4.7 and 5.2. 38In acidic solution, AH + was stabilized by complexation to CB [7], and its blue emission was observed. 38The changes in the pK a values for free and CB [7]-complexed AH + , as well as the ability to independently follow the concentrations of AH + and A, were used to characterize the guest binding dynamics at pH values where only AH + or predominantly A were present.At low pH, the kinetics was slower than at high pH because AH + forms an encounter complex with CB [7], whereas at high pH, neutral A is in fast equilibrium with CB [7], and A@CB [7] is then protonated.Kinetic studies led to the determination of a protonation rate constant of (1.5 AE 0.4) Â 10 9 M À1 s À1 for the A@CB [7] complex and a deprotonation rate constant of 89 AE 7 s À1 for AH + @CB [7], showing that the large pK a shi is mainly a reection of the slow down of the deprotonation step.

Sample preparation
A 1 mM stock solution of 2-aminoanthracene was prepared in methanol.For the experiments at pH 2.0, 3.8, and 4.3, aqueous solutions were prepared by dissolving the required amounts of NaCl and 2.0 N HCl in water to achieve a nal NaCl concentration of 20 mM and the required pH.The buffer solutions at pH 5.0 and 5.5 were prepared by adding the required quantity of 2.0 N NaOH to water to achieve a nal sodium ion concentration of 20 mM and then titrating the solution with glacial acetic acid until the required pH was achieved.Aqueous AH + or A Scheme 1 Structures of cucurbit [7]uril (CB [7]) and the 2-aminoanthracenium cation (AH + ), equilibria between protonated AH + , neutral A, and CB [7], and pK a values for the ground (pK a , pK CB a ) and singlet excited state (pK * a , pK CB* a ) of AH + in the absence [41][42][43] and presence of CB [7]. 38olutions were prepared by diluting the methanol stock solution into the aqueous solutions of the required pH.CB [7] stock solutions (850 mM) were prepared by dissolving an appropriate amount of the solid in the aqueous solution of the required pH.The CB [7] stock solutions were titrated as described previously.47 For the binding isotherm experiments, small aliquots of the CB [7] stock solution were injected directly into 3 mL of the AH + /A solution with a gastight syringe.For stopped-ow experiments, a series of CB [7] solutions were prepared by diluting the stock solution into aqueous solutions of the required pH.

Equipment
Absorption spectra were recorded on a Cary 100 UV-Vis spectrophotometer.Steady-state uorescence measurements were performed on a PTI QM-40 spec-trouorimeter.Samples were excited at 365 nm and the emission was collected between 380 and 650 nm.A bandwidth of 2 nm was used for the excitation and emission monochromators.A baseline spectrum for a solution containing all chemicals except the uorophore was subtracted from all emission spectra to obtain corrected spectra.All measurements were performed by maintaining the sample temperature at 20 C. For the binding isotherm experiments, the area under each spectrum was integrated from 380 to 456 nm for the "blue" region and from 456 to 650 nm for the "green" region, corresponding to the emission of AH + and A, respectively.These integrated intensities were then normalized by assuming unity for the integrated intensity in the absence of CB [7].Time-resolved uorescence decays were recorded with an Edinburgh OB920 single photon counting system.The excitation source was a light emitting diode (EPLED-360, l ex ¼ 365 nm).The emission from the sample was collected at 405 or 510 nm using a monochromator with a bandwidth of 16 nm.The number of counts in the maximum intensity channel was 2000.The instrument response function (IRF) was recorded using a Ludox solution by collecting the emission at the excitation wavelength.The FAST (Edinburgh Instruments) soware was used to t the uorescence decay traces.The IRF was reconvoluted with the decay during the tting process.The quality of the t was judged by the randomness of the residuals and the c 2 values (0.9-1.2). 48The data were t to either a monoexponential decay (i ¼ 1, eqn (1)) or to a sum of two exponentials (i ¼ 2, eqn (1)), where each species has a lifetime (s i ) and a corresponding pre-exponential factor (A i ).A 10 Â 10 mm quartz cell was used for the absorption, steady-state, and timeresolved uorescence measurements.
Binding dynamics studies were carried out with an Applied Photophysics SX20 stopped-ow system.The solutions were excited at 365 nm with a Hg-Xe vapor lamp.This wavelength was chosen because it corresponds to a peak of the Hg-Xe lamp and leads to a higher excitation efficiency of the sample, increasing the signal-to-noise ratio for the measurements.The excitation monochromator bandwidth was set to 2 nm.The monochromator wavelength was calibrated by comparing the wavelength reading for the maximum intensity reading for water with the wavelength for the maximum intensity provided by the manufacturer of the lamp.The emission was detected using an interference lter (385-423 nm) with a maximum at 405 nm for the "blue" region and a 515 nm cut-off lter for the green region.The solutions were mixed in a 1 : 1 ratio in the mixing chamber.The temperature of the solutions was maintained at 20 C throughout the experiment, and the samples were incubated at this temperature for 10 min before the start of an experiment.A minimum of 25 traces were averaged for each experiment performed on the stopped-ow.The intensity of the stopped-ow for a solution containing all chemicals except the uorophore and CB [7] was taken as the baseline and subtracted from the stopped-ow traces to obtain the corrected traces.
The stopped-ow traces were analyzed by tting the individual traces to a sum of exponential functions (eqn (2)) or by using a global analysis method where all traces are simultaneously t to a dened model.The t to a sum of exponentials is dened by an offset (a 0 ) and the sum of exponentials terms, each of which has a corresponding observed rate constant (k obsi ) and an amplitude of a i . (2) The analysis of the individual stopped-ow traces at pH 2.0 and 3.8 was done as follows: to obtain the rate constant for the slow relaxation time, the traces were t to a mono-exponential function by starting the t at incrementally longer times until the residuals became random and the observed rate constant was constant.The rate constant for the fast relaxation time was then obtained by tting the traces to a sum of two exponentials and xing the rate constant for the slow relaxation process.The stopped-ow traces at pH 5.0 and 5.5 were t to a monoexponential function to yield one relaxation time.In the global analysis method, all the kinetic traces for a particular experiment were t simultaneously to a model dened in the Prokineticist II soware from Applied Photophysics.The goodness of the t was judged by the randomness of the residuals.

Results
The AH + /A absorption and emission spectra depend on the solution's pH.At pH 2.0, where only AH + is present in the ground state, a small emission intensity is observed from AH + around 400 nm in addition to the predominant emission centered at 510 nm from A formed adiabatically from excited AH + (Fig. 1a).The emission from AH + is absent at pH 6.0, which is two pH units higher than the pK a of AH + /A.At this pH, only A is present in solution.The absorption spectrum shows sharp peaks at pH 2.0 (Fig. 1b), whereas a broad absorption around 400 nm appears as the pH is raised (Fig. 1c and d).This broad absorbance is related to the presence of A. 41 In the presence of 25 mM CB [7], where 91% AH + (5 mM) is bound at pH 2.0, a red shi was observed in the absorption spectrum of AH + .At pH 3.8, with an approximately 3 : 2 mixture of AH + and A in water, the shoulder around 400 nm decreased in the presence of CB [7], and the sharp peaks shied to the same wavelengths observed at pH 2.0 in the presence of this host.These absorption spectra show that the equilibrium shis toward AH + when the guest is bound to CB [7].At pH 5.5, the amount of AH + is low (3%), and the absorption spectrum showed smaller changes in the presence of CB [7].These results are consistent with the stabilization of AH + when bound to CB [7].The binding of AH + with CB [7] was characterized at pH 2.0 where all of the guest molecules are protonated in water.0][51] The addition of Na + cations was also required to adjust the solution's pH.The system is described by the equilibria between Na + or AH + with CB [7] (Fig. 2a).The competitive binding of Na + to CB [7] was shown to slow the kinetics of AH + binding with CB [7] and to decrease the amplitude of the kinetics (Fig. 2b).This behavior is the same as that previously reported for the 2-naphthyl-1-ethylammonium cation binding to CB [7]. 32The smaller amplitude is due to the involvement of CB [7] in Na + bound complexes.The slow down of the relaxation kinetics is a consequence of a slower bimolecular association process because of the lower effective concentration of free CB [7] in the presence of Na + cations, while the dissociation is unaffected as it is a unimolecular reaction.Stopped-ow experiments were performed to determine the optimal Na + cation concentration for the kinetic studies.The kinetics were followed in the "blue" region where AH + emits because its excited state is not deprotonated owing to the higher pK * a of AH + @CB [7].A concentration of 20 mM of Na + cations was chosen for all experiments because the kinetics was sufficiently slow to be detected in stopped-ow experiments with reasonable amplitude.
Any parameter that is dependent on the concentration of CB [7] is an overall or apparent parameter because a fraction of the CB [7] molecules was non-reactive owing to the formation of CB [7] complexes with Na + cations (Fig. 2a).The binding isotherms led to the determination of the overall binding constants (b), while the bimolecular rate constants for the reactions involving CB [7] are apparent rate constants and denoted k 0 .The individual equilibrium constants (K) or bimolecular rate constants (k) can be obtained following the procedure previously  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
described. 32We chose to present the b and k 0 values in the results section as these are the values derived directly from the experiments.The addition of increasing concentrations of CB [7] to AH + (1.0 mM) at pH 2.0 led to a decrease of the "green" emission of A around 510 nm and an increase of the AH + emission below 450 nm (Fig. 2c).The dependencies of the intensities in the "blue" and "green" regions with the CB [7] concentration (Fig. 2d) were numerically t to an overall equilibrium constant (b 11 , see ESI † for details) dened by the equations shown in Fig. 2a, where [CB [7]] GF corresponds to the guest-free CB [7] concentration that is not complexed to AH + .The residuals between the experimental data and the ts were random.The recovered average b 11 values from two independent experiments were (4.92 AE 0.09) Â 10 5 M À1 when the emission intensity for A was followed and (4.8 AE 0.2) Â 10 5 M À1 when the intensity changes for AH + were measured, leading to an overall average b 11 value Fig. 2 Top left: Equilibria for CB [7] binding to Na + cations and AH + , and the definition of the overall equilibrium constant.Top right: Kinetics for the formation of the AH + @CB [7]  complex ([AH + ] ¼ 2 mM, [CB [7]] ¼ 7 mM) at pH 2.0 in the presence of increasing Na + cation concentrations: (a) 2, (b) 10, (c) 20, (d) 100, (e) 200 mM.Trace "f" corresponds to the baseline measurement in the absence of CB [7].Bottom left: Fluorescence spectra for AH + at pH 2.0 in the presence of increasing CB [7] concentrations from 0 to 19 mM.Bottom right: Binding isotherms (top panel) for the intensity changes for the "blue" (integration from 380 to 456 nm, open circles) and "green" (integration from 456 to 650 nm, solid circles) emission.The black lines correspond to the numerical fits of the data.The residuals between the experimental data and calculated values are shown in the middle panel ("blue" emission) and lower panel ("green" emission).
of (4.9 AE 0.1) Â 10 5 M À1 .The determination of the same b 11 values for the two different emission bands and the presence of an isoemissive point support the assignment of the bands in the uorescence spectra to AH + and AH + @CB [7].
Binding isotherms were also measured at pH values of 3.8, 5.0, and 5.5 (Fig. S1 and Table S1 in the ESI †).The determined average b 11 values from the binding isotherms measured for the "blue" and "green" emissions were (2.83 AE 0.03) Â 10 5 , (3.49AE 0.09) Â 10 4 , and (1.52 AE 0.04) Â 10 4 M À1 at pH values of 3.8, 5.0, and 5.5, respectively.At pH values of 3.8, 5.0, and 5.5, the percentage of AH + is 61, 9, and 3%, while the percentage of A is 39, 91, and 97%, respectively.The decrease in the overall equilibrium constants as the pH was raised is a reection of the lower equilibrium constant for the binding of A to CB [7] compared with that for the binding of AH + .The equilibrium constant for the binding of A to CB [7]  (3) Time-resolved uorescence experiments are used to identify uorophores with different lifetimes; in the case of supramolecular systems, the same uorophore in different environments can have different lifetimes. 8,52The decays for systems containing uorophores with different lifetimes are t to a sum of exponentials, where each term has an associated lifetime and pre-exponential factor A i (eqn (1)).The A i values are related to the abundance of each species; a positive value indicates the disappearance of the uorophore, while a negative value indicates the formation of the uorophore.The lifetime of excited A measured at 510 nm and pH 6.0 was 24.8 AE 0.1 ns.This value is of the same order of magnitude as the lifetimes previously determined in water : ethanol (14 ns) 43 or cyclohexane (25-33 ns). 53At pH 2.0, the kinetics at 510 nm for the emission of A showed a growth in kinetics with a lifetime of 1.0 AE 0.2 ns followed by a decay with a lifetime of 24.6 AE 0.1 ns (Fig. S4 and Table S2 in the ESI †).The growth corresponds to the adiabatic deprotonation of excited AH + to form excited A, which decays with the same lifetime as excited A at the higher pH.This assignment at pH 2.0 is supported by the equal absolute values of the pre-exponential factors, which were À0.49AE 0.02 and 0.51 AE 0.02 for the short-and long-lived components, respectively.The equal preexponential factors indicated that all the excited states of A were formed from AH + , as would be expected at a pH where the uorophore is in the protonated form.
In the presence of 16 mM CB [7] at pH 2.0, where all AH + is bound, the uorescence decay could only be measured at 410 nm because AH + is stabilized in the complex and is the predominant species in the system.The decay was monoexponential with a lifetime of 7.6 AE 0.1 ns, which corresponds to the emission of excited state AH + complexed with CB [7].This lifetime is not limited by the deprotonation of AH + @CB [7] because pH 2.0 is lower than both the pK CB a and pK CB* a values.In the presence of 2.6 mM CB [7], 50% of AH + is bound to CB [7] and the remainder is free in water.For this reason, the uorescence kinetics could be measured at 410 nm for the emission of AH + and at 510 nm for the emission of excited A. The emission decay for AH + at 410 nm led to the recovery of 0.9 AE 0.1 and 7.7 AE 0.1 ns lifetimes.The short lifetime corresponds to the deprotonation of AH + in water, while the long lifetime corresponds to the emission of AH + in the AH + @CB [7] complex.At 510 nm, where excited A emits, a growth with a 1.1 AE 0.1 ns lifetime was observed followed by a decay with a 24.5 AE 0.1 ns lifetime.This kinetics is the same as that observed for AH + in water, and the absence of a longerlived growth with a lifetime close to 8 ns suggested that AH + @CB [7] was not deprotonated during the excited state lifetime of AH + .Therefore, the intensity changes at 510 nm are diagnostic for the changes in the AH + concentration in water and do not have a contribution from the concentration changes for AH + @CB [7].
The longest lifetime observed for the AH + /A system in the absence and presence of CB [7] is 25 ns, and the dynamics of the excited state occurs on a much faster time scale than the millisecond time scale for the formation of the AH + @CB [7]  complex (see below).Therefore, the changes in emission intensity can be seen as instantaneous when analyzing the kinetics of AH + @CB [7] complex formation, and the excited state dynamics of AH + is decoupled from the dynamics of CB [7]  complex formation.
The kinetics for the formation of the AH + @CB [7] complex was studied in stopped-ow experiments.Two solutions, one containing CB [7] and a second containing AH + /A, were mixed in a 1 : 1 volume ratio.The concentrations stated are those for the nal mixed solution.The kinetics was studied at pH 2.0, where only AH + was present in water, and at pH 5.5, where A corresponds to 97% of the species present in water.A higher pH could not be used because the signals in the stopped-ow experiments became too small.The kinetics was also studied at intermediate pH values where a mixture of AH + and A was present (pH 3.8: 61% AH + and 39% A, pH 5.0: 9% AH + and 91% A).At all pH values, mixing of the guest (AH + /A) with CB [7] led to a decrease of the emission intensity at 510 nm (Fig. 3a for pH 2.0 and Fig. S5 in the ESI †) and an increase of the emission intensity at 410 nm (Fig. S6 in the ESI †).It is important to note that at pH 2.0, the emission intensity at 510 nm corresponds to the concentration of AH + in water, where excited A is formed from the deprotonation of excited AH + , as AH + in the CB [7]  complex is not deprotonated.The intensity increase at 410 nm corresponds to the formation of AH + @CB [7].At pH 5.5, the emission intensity at 410 nm corresponds to the concentration of AH + @CB [7] because, at this pH, AH + in water deprotonates readily.The intensity at 510 nm corresponds to the sum of the intensities of A in water and A@CB [7].At the intermediate pH values of 3.8 and 5.0, the intensity at 510 nm corresponds to the concentrations of A in water, A@CB [7], and AH + in water that forms excited A adiabatically.At all pH values, the same observed rate constants were recovered from the kinetics measured at 410 and 510 nm, indicating that the kinetics are coupled, as would be expected for the relaxation kinetics of a system where the various species are in equilibrium.
Two control experiments were performed: (i) comparison of the amplitudes for the kinetic and binding isotherm measurements and (ii) kinetic measurements with buffered and unbuffered solutions.
(i) It is important to establish whether the kinetics are measured for a sufficiently long time for the system to reach equilibrium.The normalized amplitudes from the stopped-ow experiments at 0.2 s were the same as the amplitudes from the binding isotherm experiments at all pH values (Fig. S7 and S8 in the ESI †).This result shows that the system is equilibrated within 0.2 s.Kinetic processes faster than the 1 ms mixing time of the stopped-ow experiment appear as initial offsets in the kinetic traces.In the current system, such a fast process would involve CB [7], and the amplitude of the offset would increase as the host concentration was raised.The kinetics at all pH values did not show a progressively increasing offset, indicating the absence of a relaxation process that occurred faster than 1 ms (Fig. S5 and S6 in the ESI †).Therefore, the whole kinetics of the system is captured in the stopped-ow experiments.
(ii) Experiments at pH 2.0 and 3.8 were performed in unbuffered solutions, where the pH was adjusted with the addition of HCl in the presence of 20 mM NaCl, while measurements at pH 5.0 and 5.5 required the use of sodium acetate as a buffer ([Na + ] ¼ 20 mM).A control experiment was performed at pH 4.3, where samples were prepared in the presence of HCl/NaCl or acetate buffer, and the kinetics for complex formation was measured.The dependence of the observed rate constants with CB [7] was similar, with a slightly lower slope observed for the experiments performed in acetate buffer (Fig. S9 in the ESI †).This difference is very similar to the variation observed between independent experiments, but it could also reect the weak binding of acetic acid to CB [7].However, this control experiment showed that the large differences in the dependencies of the observed rate constants with the CB [7] concentration (Fig. 3b) are not due to a counter-ion effect.
The kinetic behavior is different at the different pH values studied (Fig. 3b).A qualitative description will be provided rst to guide the reader through the detailed analysis.The kinetics at pH 2.0 and 3.8 were t to the sum of two exponentials, while the kinetics at pH 5.0 and 5.5 were mono-exponential.The relaxation kinetics for the lowest observed rate constant at pH 2.0 and 3.8 was slower than the relaxation kinetics at pH 5.5, and a steeper dependence of the observed rate constant with the CB [7] concentration was observed at the lower pH values.The errors for the measured rate constants are higher at pH 5.5 because the signal-to-noise ratio was lower, reecting the smaller amount of CB [7]  complex formed.
The slower kinetics observed at pH 2.0 is consistent with a mechanism where an exclusion complex is formed, denoted AH + $CB [7], in which the positively charged guest interacts with the carbonyl groups at the portal of CB [7] without the inclusion of the anthracene moiety into the CB [7] cavity in addition to a pathway where the anthracene moiety is included directly.Inclusion of the anthracene moiety to form AH + @CB [7] occurs either from the exclusion complex (pathway "z", Fig. 3c) or directly ("pathway "x").
At pH 5.5, deprotonated A is the predominant species in water (97%), but the hydronium ion concentration is sufficiently high to protonate the A@CB [7]  complex and form AH + @CB [7].The mechanism includes the fast equilibration between A and CB [7] followed by slow protonation and deprotonation steps (Fig. 3d).Deprotonation of AH + @CB [7] and the exit of AH + from AH + @CB [7] are competitive, and the latter reaction needs to be accounted for in the tting of the data.
The kinetics at pH 2.0 was t to the sum of two exponentials, from which two observed rate constants, k obs1 and k obs2 , were obtained.Similar dependencies were observed for the k obs2 values with the CB [7] concentration when the kinetics were measured for the "blue" and "green" emission intensity changes.The values for k obs1 were scattered, and this pattern is a reection of the small amplitude of this component at low CB [7] concentrations.To improve the precision of the ts, the kinetics was t to a mono-exponential function by starting the t at incrementally longer delays aer the start of the reaction until a constant value for k obs2 was obtained and the residuals were random (Fig. S10 and Table S3, see ESI † for details).These k obs2 values were then xed for the t of the entire kinetic trace to recover the values for k obs1 .
In principle, the two relaxation times could correspond to two different processes.If k obs2 was related to the reaction of AH + with CB [7] without the formation of an encounter complex, then the ratio of the slope of a linear dependence between k obs2 and the CB [7] concentration ((3.4 AE 0.2) Â 10 6 M À1 s À1 , average from two kinetic studies with the emission collected in the green region and one in the blue region) and the intercept (14.6 AE 0.8 s À1 ) should correspond to b AH 11 .However, this ratio ((2.3 AE 0.2) Â 10 5 M À1 ) is much lower than the b AH 11 value of (4.9 AE 0.1) Â 10 5 M À1 determined from the binding isotherm studies.This analysis showed that the kinetics for the two relaxation processes are coupled.
Based on the precedence for the formation of exclusion complexes followed by cavity inclusion with CB[n]s as the host, 27,30 the kinetics was analyzed using the mechanism shown in Fig. 3c.The formation of AH + $CB [7] was assumed to be in fast equilibrium.With this assumption, the two relaxation processes are related to the three equilibria (eqn (4) and ( 5)), where k 0 + (AH) and k À (AH) are dened in Fig. 3c: Fits of the dependence of k obs2 with the CB [7] concentration to eqn (5) (see Fig. S11 and Table S4 in the ESI † for individual values) led to an average b y value of (2.6 AE 0.6) Â 10 4 M À1 , a k 0 + (AH) value of (4.9 AE 0.4) Â 10 6 M À1 s À1 , and a k À (AH) value of 10 AE 1 s À1 .The ratio between k 0 + (AH) and k À (AH) is (4.9 AE 0.6) Â 10 5 M À1 , which is equal to the b AH 11 value ((4.9 AE 0.1) Â 10 5 M À1 ) determined from the binding isotherm.The equality of these values suggests that the mechanism proposed is consistent with the kinetic and the binding isotherm data.
The k obs1 values increased with the CB [7] concentration; however, the data had large errors and showed signicant scatter, indicating that tting of the data was not warranted (Fig. S12 in the ESI †).The value of k Ày is estimated to be between 100 and 130 s À1 , which is ten times higher than the rate constant for the exit of AH + from the inclusion complex (k À (AH) ¼ 10 s À1 ), supporting the assumption that the formation of the exclusion complex occurs as a fast equilibrium.The value for k y estimated from the b y and k Ày values is between 2.7 Â 10 6 and 3.5 Â 10 6 M À1 s À1 , which would lead to an increment for the k obs1 value of ca. 30 s À1 for a 10 mM increase in the CB [7] concentration.This increment is within the scatter observed for the experimental data.
The data at pH 5.5 were analyzed using a global analysis method (Scheme S1 in the ESI †), where the kinetics at all CB [7] concentrations for two independent experiments collected for the "green" emission were analyzed simultaneously.The data from the kinetics in the "blue" region were not used because of the poor signal-to-noise ratio.
The value for the equilibrium constant for A@CB [7] was xed as 390 M À1 , and this equilibrium was assumed to be fast.Assuming that the association rate constant of A with CB [7] will be at least as high as the overall association rate constant for AH + of 4.9 Â 10 6 M À1 s À1 , then the dissociation rate constant for A from A@CB [7] will be at least 1.3 Â 10 4 s À1 , which is ten times faster than the time resolution of the stopped-ow experiment.This calculation is consistent with the assumption of a fast equilibrium for A@CB [7].
The dissociation of AH + @CB [7] needs to be included in the model because the value for the rate constant of this process (10 s À1 ) corresponds to 10% of the observed rate constant.This value was also xed in the model.The protonation and deprotonation reaction for A/AH + in water is faster than the time resolution of the experiment, and the concentration of the hydronium ion is constant as the solution was buffered.For this reason, the deprotonation reaction for AH + in water is not included in the model used for tting the kinetics.
Global analysis of the kinetics at pH 5.5 (see Fig. S13 in the ESI † for the residuals) led to a recovery of the protonation rate constant (k H + ) of (1.5 AE 0.4) Â 10 9 M À1 s À1 for A@CB [7] and a deprotonation rate constant of (k H À ) of 89 AE 7 s À1 for AH + @CB [7].The pK CB a value calculated from these rate constants is 7.3 AE 0.2, which is in agreement with the reported value of 7.1 AE 0.2 determined from a pH titration experiment. 38 quantitative analysis of the kinetics at pH 3.8 and 5 is not feasible because the model requires the inclusion of both the low and high pH mechanisms observed for the binding of AH + and A; the model would include too many parameters to t the data.However, the changes can be explained qualitatively based on the relative contributions from the formation of the exclusion complex AH + $CB [7] and the complex with neutral A, A@CB [7].The overall equilibrium constant for the formation of the former is 69 times higher than that for the latter.At pH 3.8, where 61% of the guest in water is in the protonated form and the remaining 39% is deprotonated, the kinetics is dominated by the binding of AH + with CB [7] and the observed decay did not t to a mono-exponential function.However, the amplitude of the fast component is smaller at pH 3.8 than at pH 2 (Table S5 in the ESI †).This difference increased from 11% for a CB [7] concentration of 5 mM to 32% for a CB [7] concentration of 13 mM.This increase is expected because the formation of A@CB [7] will be more prominent at a higher CB [7] concentration.The formation of A@CB [7] is followed by immediate protonation of the complex ($2.4 Â 10 5 s À1 ) because of the high hydronium ion concentration at this pH.This reaction path leads to a decrease in the contribution from AH + @CB [7] formation through the exclusion complex.This effect is observed as a decrease in the slope for the dependence of k obs2 with the CB [7]  concentration without a large change in the intercept.
The kinetics at pH 5 was adequately t to a mono-exponential function.In water, 9% of the guest is in the form of AH + while 91% corresponds to A. The kinetics is dominated by the binding of A, but a slow down was observed for the kinetics when compared with the kinetics at pH 5.5.This slow down was caused by the formation of the AH + $CB [7] exclusion complex that removes A and free CB [7]  from solution.The lower free concentrations of A and CB [7] decrease the amount of AH + @CB [7] formed through the faster reaction pathway, which is the protonation of the A@CB [7] complex.

Discussion
The guest binding dynamics of AH + with CB [7] can be compared with the dynamics of previously studied guests.2-Naphthyl-1-ethylammonium (Scheme 2) has a positive charge located in one extreme of the molecule in a similar fashion to AH + , whereas the positive charge in berberine is centrally located.In both cases, the kinetics was associated to one process without the observing the formation of an exclusion complex.
The equilibrium constant K AH was calculated to be (2.3AE 0.3) Â 10 6 M À1 (eqn (6)) using the previously determined values of 130 AE 10 M À1 and 21 AE 2 M À1 for the binding of the rst and second Na + cation to CB [7], 32 and the average b 11 value of (4.9 AE 0.1) Â 10 5 M À1 .The same multiplication factor was used to calculate the value of the association rate constant (k + (AH)) as (2.3 AE 0.2) Â 10 7 M À1 s À1 from the overall association rate constant k 0 + (AH).It is important to note that the latter value includes the pathway for the formation of the exclusion complex.
A comparison of the binding of these three guests to CB [7] shows that the location of the positive charge and the size of the hydrophobic moiety of the guest inuence the binding dynamics.The two modes of association of AH + with CB [7], i.e. direct inclusion and formation of the exclusion complex, are probably related to the directionality of the approach of the guest with respect to the portal of CB [7].Direct inclusion likely occurs when the anthracene moiety approaches the portal, whereas the exclusion complex is formed when the positive charge on the amino group interacts rst with the carbonyl groups on the rim of the portal.In the case of the 2-naphthyl-1-ethylammonium cation, the guest is sufficiently small that if the exclusion complex is formed, the guest can rotate and enter the cavity.In this case, the rate constant of inclusion (k z in Fig. 3c) is higher than the dissociation of the exclusion complex (k Ày ), the association rate constant is high, and the exclusion complex is not detected as a dened intermediate.The association rate constant for AH + is a factor of $25 lower than that of the 2-naphthyl-1-ethylammonium cation, which accounts for the formation of an exclusion complex where the dissociation of the exclusion complex is competitive with inclusion.The dissociation rate constant is a factor of $5 lower for AH + than for the 2-naphthyl-1ethylammonium cation.This slow-down is probably related to the larger hydrophobic moiety of AH + .
The aromatic moiety of berberine is included in the CB [7] cavity, 34 and the central location of the charge likely precludes the formation of an exclusion Scheme 2 Structure, equilibrium constants and association and dissociation rate constants for the binding of berberine, 34 the 2-naphthyl-1-ethylammonium cation 32 and AH + with CB [7].The values of K and k + for AH + @CB [7] were calculated from the overall values (see text).This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
complex.The complexation of berberine to CB [7] shown to occur through constrictive binding, where the CB [7] needs to be distorted for inclusion of the guest to occur.This stereochemical effect led to lower association and dissociation rate constants.The association rate constant for berberine and AH + are the same, but different mechanisms led to these values being lower than the association rate constant for the 2-naphthyl-1-ethylammonium cation.Distortion of the host is also responsible for the lower dissociation rate constant observed for berberine compared to those of AH + and the 2-naphthyl-1-ethylammonium cation.These results show that the binding dynamics cannot be predicted from the values of the equilibrium constants because the mechanism for binding differs for the three guests.Berberine has a similar equilibrium constant to the 2naphthyl-1-ethylammonium cation, but the association and dissociation rate constants of berberine are decreased to a similar extent because of the constricted binding.On the other hand, AH + has a lower equilibrium constant because of the slow down of the association process where the exclusion complex is formed, but the dissociation rate constant is affected to a lesser extent because no constricted binding is operating.It is important to note that in the case of cyclohexylmethylamine binding to the smaller CB [6], the formation of an exclusion complex and constrictive binding were postulated, leading to very slow kinetics, 30,31 showing that the binding dynamics with CB[n]s can occur over very different time scales.The role of the protonation of the guest was previously studied for the cyclohexylmethylamine/CB [6] system, where the binding dynamics of the neutral and positively charged guest was uncoupled from the protonation/deprotonation dynamics. 30,31In the case of AH + and A binding to CB [7], the binding dynamics is coupled to the protonation/deprotonation reactions for the CB [7]-bound guest.In both systems, the dynamics is faster for the formation of the CB[n] complex with the neutral guest.However, in the case of AH + /A binding to CB [7], it was possible to measure the kinetics of the system at different pH values.These studies led to the determination of the different mechanisms, where an exclusion complex is formed when AH + binds to CB [7], whereas for A, complexation is fast and is followed by protonation of the complex (Scheme 3).
The protonation rate constant for ammonia in water is 4.3 Â 10 10 M À1 s À1 , 55 and this value constitutes the highest possible rate constant for the protonation of A in water, which is unknown.The protonation rate constant for A@CB [7] of 1.5 Â 10 9 M À1 s À1 is $30 times lower than this upper limit, suggesting that protonation of A@CB [7] is not signicantly impeded, which is consistent with the location of the amino group at the portal of CB [7].The lower value for the protonation rate constant for A@CB [7] is probably related to fact that the approach of the hydronium ion towards the sides of CB [7] or the portal that does not contain the amino group leads to unproductive encounter complexes.In this respect, the protonation rate constant for a guest where the acid/base group was exposed to the water phase while a portion of the guest was bound to CB [7] was the same as for the guest in water, 56 probably because the attack of the hydronium ion was not impeded.The deprotonation rate constant of AH + @CB [7] is higher (89 s À1 ) than the rate constant for the exit of AH + from AH + @CB [7] (10 s À1 ).However, the deprotonation reaction is not observable at low pH values because the protonation process is too fast.For example, at pH 2.0, the protonation process for A@CB [7] has a pseudo-rst order rate constant of 1.5 Â 10 7 s À1 .
In conclusion, the studies on the binding of AH + and A with CB [7]  provided further evidence that different mechanisms occur for the binding of guests with CB[n].The binding dynamics of a neutral guest was shown to be faster than that for the corresponding positively charged guest.However, the binding constant is higher for the charged guest than for the neutral guest, mainly because of the charge-dipole interaction between the guest and the carbonyl groups at the portal of CB [n].The size of the guest and the position of the positive charge on the guest affect the type of mechanism for the binding dynamics and affect the magnitude of the association and dissociation rate constants.Positive charges located at one end of the guest are more likely to lead to the formation of exclusion complexes when compared to molecules with centrally located positive charges.In addition, the requirement for distortion of CB[n] to accommodate the guest can lead to a signicant slow down of the dynamics, but has a much smaller effect on the equilibrium constant as the required distortions of the host will occur for both the association and dissociation processes.
The coupling of the binding dynamics of A@CB [7] and AH + @CB [7] to the deprotonation and protonation reactions of these complexes made it possible to measure the protonation and deprotonation rate constants.The determination of these rate constants showed that the pK a shi observed for the CB [7]-bound guest was due mainly to a decrease in the deprotonation rate constant because of the stabilization of the charged species.This result has direct implications for the use of CB[n]s in any application, such as in catalysis, where the lifetime of a charged species is important.
can be calculated from the thermodynamic cycle shown in Scheme 1 since three of the equilibrium constants are known.It is important to note that the thermodynamic cycle is valid for overall equilibrium constants where the value for AH + (b AH 11 ) is the one determined at pH 2.0 and b A 11 is related to the other equilibrium constants (eqn (3), see ESI † for derivation), leading to a value for b A 11 of 390 AE 10 M À1 , where the error is related to the measurement of b AH11 .An attempt was made to measure directly the equilibrium constant between A and CB[7] at pH 12.The changes in the uorescence intensity were small (Fig.S2in the ESI †) and no saturation was achieved, which indicated the incomplete binding of A. The value of b A 11 and the quantum yield of A in A@CB[7] are correlated, and for this reason, no unique value for b A 11 could be obtained.Adequate ts were observed for b A 11 values xed between 100 and 700 M À1 (Fig.S3in the ESI †), which are of the same order of magnitude as the value determined from the thermodynamic cycle.

Fig. 3
Fig. 3 Top left: Kinetic traces at pH 2.0 for the mixing of AH + (1 mM) with CB[7] ((a) 0, (b) 3, (c) 5, (d) 7, (e) 9, (f) 11, and (g) 13 mM) measured for the "green" emission.Top right: Dependence of the observed rate constant with the CB[7] concentration at different pH values (pH 2.0: B, C, black; pH 3.8: >, A, red; pH 5.0: O, :, blue; and pH 5.5: ,, -, green).The solid and open symbols are the values recovered for the kinetics measured for the "green" and "blue" emission, respectively.For pH values where the open symbols are not shown, they are the same as the closed symbols.The error bars are smaller than the symbols for all pH values, with the exception of pH 5.5.The observed rate constants for pH 2.0 and 3.8 correspond to the lowest values recovered from a fit of the kinetics to the sum of two exponentials.The kinetics for pH 5.0 and 5.5 were fit to a mono-exponential function.Bottom left: Mechanism used to analyze the kinetic data at pH 2.0.Bottom right: Mechanism used to analyze the kinetic data at pH 5.5.