Partial Thermal Dethreading of [3]pseudorotaxanes of Î±-Cyclodextrin

2664

J. Phys. Chem. B 2001, 105, 2664-2671

Partial Thermal Dethreading of [3]pseudorotaxanes of r-Cyclodextrin with Linear Aliphatic r,ω-Amino Acids in Aqueous Solution Achilleas Tsortos,† Konstantina Yannakopoulou,‡ Kyriaki Eliadou,‡ Irene M. Mavridis,‡ and George Nounesis*,† I/RRP and Institute of Physical Chemistry, National Center for Scientific Research “Demokritos”, 15310 Aghia ParaskeVi, Athens, Greece ReceiVed: NoVember 1, 2000; In Final Form: January 29, 2001

The partial dethreading of stable host/guest, 2:1 [3]pseudorotaxanes of R-cyclodextrin with 12-aminododecanoic acid in aqueous solutions has been studied by high-precision differential scanning calorimetry (DSC) and NMR spectroscopy. For samples in which crystallization of the 2:1 complex had taken place at 10 °C, DSC heating scans revealed a heat capacity (Cp) anomaly at temperatures higher than the dissolution temperature (∼60 °C). This endothermic Cp peak is strongly dependent upon the heating rates used and is characterized by a net enthalpy change ∆H ) 17.15 ( 1.67 kJ/mol. The peak is attributed to the dethreading of one of the R-cyclodextrin rings and conversion to a [2]pseudorotaxane. Analysis of available thermodynamic data reveals that following this partial decomplexation, 3-4 methyl groups are exposed to the aqueous solvent. The dissociation kinetics have been analyzed via a one-step Arrhenius model leading to an activation energy Ea ) 140.1 ( 8.1 kJ/mol and a frequency factor A ) 1.7 ( 0.1 × 1017 s-1. The reaction rates are very slow, 3.8 (0.6 × 10-5 s-1 at 65 °C, compared to dissociation rates of other cyclodextrin complexes. These slow rates have been attributed primarily to the breaking of the hydrogen bonds between the two cyclodextrin rings in the dimer of the [3]pseudorotaxane and also to the high hydrophilicity of the end groups of the guest molecules. The observed partial dethreading process is not reversible; it is reproducible after recrystallization of the 2:1 complex. This thermodynamic behavior was not observed for an analogous R-cyclodextrin/11-aminoundecanoic acid complex in aqueous solution because crystallization of the 2:1 complexes could not be achieved.

Introduction

SCHEME 1 (CDs)1

Cyclodextrins are cyclic oligosaccharide molecules, the most common of which are composed of six (RCD), seven (βCD), and eight (γCD) D-glucopyranose units that have the shape of a truncated hollow cone (Scheme 1). CD molecules have the ability to form inclusion compounds, acting as hosts, by allowing other molecules (guests) into their hydrophobic cavity. In various sizes and chemical characteristics they are being used in pharmaceutical chemistry as drug delivery systems,1,2 in chromatography,2b and as enzyme catalysis models or assistants in protein folding (chaperone mimics).3,4 Complexation occurs through noncovalent interactions between the guest and the host. This is a dynamic process as shown in the following scheme: kf

CD + G y\ z CD/G k d

In general, but with many notable exceptions, kf rate constants range on the order of 107 to 108 M-1 s-1 and kd around 105 s-1, thus leading to a complex lifetime τ in the order of microseconds.5 Linear, long-alkyl-chain molecules possessing amino and/or carboxylic terminals have been one of the favorite inserts into RCD cavities (the narrowest of the cyclodextrin family). Several * Corresponding author. Tel. +301-6503936. Fax: +301-6543526. E-mail: [email protected]. † I/RRP. ‡ Institute of Physical Chemistry.

thermodynamic studies of RCD complexes with guest molecules of the type X-(CH2)n-Y where X and Y are carboxylic, carboxylate, amine, hydroxyl, and alkyl groups have been published.6-9 Calorimetric studies on such mono- or dihydroxyl or carboxyl derivatives with RCD indicate that for n ) 6-7, it is the alkyl chain that penetrates the cavity while the terminal groups of the guests form hydrogen bonds with the external (rim) OH groups of RCD. Moreover, these studies have suggested that in order for the guest molecule to span the full length (∼8 Å) of the cavity, five to six methylene (or neutral) groups are the minimum requirement, something that makes perfect geometrical sense. Crystallographic studies of RCD with long aliphatic guests10,11 have confirmed that an RCD head-tohead dimer fully accommodates a 12 carbon atom aliphatic chain. Charged or hydroxyl groups or branches at some point along the guest chain do not favor but rather prevent penetration of the cavity by the chain up to that point.7b,8,12,13 Regarding the question of what chain length can maximally be accom-

10.1021/jp004015v CCC: $20.00 © 2001 American Chemical Society Published on Web 03/14/2001

Partial Thermal Dethreading of [3]Pseudorotaxanes

J. Phys. Chem. B, Vol. 105, No. 13, 2001 2665

modated by a single RCD cavity in aqueous solutions, experiments indicate a “saturation” length of ∼8 for alkanes,9a ∼8 for aliphatic amines,8 and ∼9 for monocarboxylates,7 or even up to 10 CH2 groups in some cases.6 These results are explained either by suggesting the existence of kinks along the guest chain within the CD cavity (especially in the case of βCD) and/or by the notion of an “extended hydrophobic cavity” for the cyclodextrin. This “extension” of the cavity length is the result of water molecules organized via hydrogen bonds with the hydroxyls at the rims of the CD.6 For chains of about ten to twelve7,9,14,15 and even for as low as seven7,16 CH2 groups, published thermodynamic and solubility data imply that it is not a 1:1 complex that forms but rather a 2:1 host/guest complex is realized. Long polymeric17 as well as very short18 guests may also complex more than one CD molecule. X-ray crystallographic studies have so far proven the existence of only [3]pseudorotaxanes in the crystalline state of 1,12-diaminododecane10 and 12-aminododecanoic acid11 complexes with RCD as well as of 1,12-dodecanedioic acid and 1,13-tridecanedioic acid with βCD.19 Recent NMR studies11 have also demonstrated the simultaneous formation of a mixture of both 1:1 and 2:1 adducts in solution, for the 11-aminoundecanoic and 12-aminododecanoic acids, the 1,12-diaminododecane and the 1,13-tridecanedioic acid complexes with RCD. The goal of the present study is the investigation of the thermodynamic behavior of [3]pseudorotaxanes of RCD with 11-aminoundecanoic and 12-aminododecanoic acids (Scheme 1) in aqueous solutions using high-precision differential scanning calorimetry (DSC) and NMR spectroscopy. The energetics and the kinetics of the thermally induced, partial dethreading of the [3]pseudorotaxanes and their conversion to [2]pseudorotaxanes are presented. The dethreading process is slow compared to other linear guest molecules in [2]pseudorotaxane RCD complexes.20,21

the DSC cell at 25 °C. Heating scans followed immediately after loading and were carried out from 25 to 110 °C. (B) The prepared solutions were kept at 50 °C until loading into the DSC cell at 10 °C. At this temperature the samples remained for approximately 24 h before heating scans from 10 to 110 °C were initiated. For either type of experiment, the following heating rates were used: 0.5, 1.7, 6.8, 12, 20, and 30 K/h. Buffer reference scans were subtracted from the RCD complex scans, and baseline fits were performed to obtain the excess heat capacity ∆Cp, using the Origin 5.0 software supplied by MicroCal. Baseline correction was applied separately within the temperature range of each Cp anomaly, including linear, quadratic, and for the very wide (>20 °C) temperature ranges, cubic terms. The solutions prepared with RCD/12amo ratio 40mM/10mM and 40mM/20mM crystallized, as detected optically, after a period of a few hours at 10 °C (loading procedure B). These crystals were characterized as having a host/guest ratio of 2:1 by 1H NMR spectroscopy in DMSO-d6. The 11amo complexes never crystallized at any ratio tested. NMR Experiments. 1H NMR spectra were obtained at 250 MHz on a Bruker AC 250 instrument. The samples acquired the desired temperature by sitting in the probe for a period of 20-30 min. To parallel the DSC experiments, a buffered D2O solution of RCD/12amo 40mM/20mM, of exactly the same volume as that injected in the DSC cell, was maintained at 10 °C for 24 h. Crystallization occurred, the crystals were collected, air-dried, weighed (yield 55 ( 3%), and the ratio of their components was confirmed by 1H NMR in D2O to be 2:1. On the other hand, the supernatant liquid was examined at 5 °C by 1H NMR in order to characterize the nature of species in solution and found to contain both 1:1 and 2:1 species as expected.11

Materials and Methods

Representative Cp vs T profiles (raw data) of RCD/11amo and RCD/12amo complexes examined by DSC under the two experimental protocols described above, are presented in Figure 1. It can readily be observed that within the temperature range studied, Cp remains featureless (trace [1]), for all the samples for which protocol A was followed, i.e., no time for crystallization of the 2:1 complexes was allowed by immediate initiation of the heating scans at 25 °C. Featureless, nonanalyzable Cp profiles were also exhibited by several samples for which protocol B was followed, (traces [2] and [5]). These include samples for which crystallization of the 2:1 complex could not be achieved prior to the heating runs. Such is the case for all of the solutions of RCD/11amo complexes regardless of guest/host ratios (trace [2]), as well as all the RCD/12amo samples with host/guest ratios X outside the range 40 mM/20 mM e X e 40 mM/10 mM (trace [5]). Indeed, any attempt to induce crystallization of the 2:1 complex in samples with ratios X such as 40 mM/30 mM, 40 mM/5 mM, or 40 mM/40 mM was unsuccessful. On the other hand, RCD/12amo solutions with X within this range exhibit the characteristic reproducible Cp behavior of traces [3] (40 mM/20 mM) and [4] (40 mM/10 mM). For these samples, crystalline complexes precipitated in the DSC cell prior to the heating scans and 1H NMR analysis confirmed that they were crystals of the 2:1 RCD/12amo complexes, i.e., [3]pseudorotaxanes, as it has already been described. Moreover, the NMR spectrum of the supernatant liquid showed both 1:1 and 2:1 species.11 The characteristic peak sequence of the Cp vs T profiles is presented in detail in Figure 2 for an RCD/12amo sample with

11-Aminoundecanoic acid (11amo) and 12-aminododecanoic acid (12amo) were purchased from Aldrich, R-cyclodextrin (RCD) was purchased from Janssen and used without any further treatment. Deuterium oxide (D2O) and deuterated dimethyl sulfoxide (DMSO-d6) were purchased from Cortec, Paris. Buffered aqueous solutions (pH 7.3) were prepared from sodium dihydrogen phosphate (64 mM)/potassium hydrogen phosphate (145 mM) salts in distilled H2O (or D2O); the interaction of phosphate ions with RCD is known to be negligible.22,23 Working solutions were prepared by the slow addition of the R,ω-amino acid into the buffered RCD aqueous solution under stirring, at 40 °C. An ultrasound sonicator was also used to aid complete dissolution, especially at the higher concentrations. For both the RCD/11amo and the RCD/12amo systems, solutions at five different concentration ratios were tested: 40 mM/5 mM, 40 mM/10 mM, 40 mM/20 mM, 40 mM/30 mM and 20 mM/20 mM. Microcalorimetry Experiments. Microcalorimetric measurements were performed on a VP-DSC scanning calorimeter (MicroCal Inc., Northampton, MA). The instrument active cell volume is 0.514 mL. Temperature and heat calibrations were performed as described elsewhere.24 Prior to scanning, all solutions were degassed for ∼15 min under vacuum. During the experiments, the pressure was automatically kept at ∼30 psi. Two types of sample loading procedures were followed. (A) The prepared solutions were kept at 50 °C, until loading into

Results and Discussion

2666 J. Phys. Chem. B, Vol. 105, No. 13, 2001

Tsortos et al.

Figure 1. Raw Cp vs T data from heating runs of [1] RCD/12amo (40/20) for which the 2:1 complex was not given time to crystallize prior to heating, [2] RCD/11amo (40/20) (does not crystallize), [3] RCD/ 12amo (40/10), and [4] RCD/12amo (40/20), [5] RCD/12amo (40/30). For both [3] and [4], the 2:1 complex had crystallized prior to heating as described in the text. For [5], the complex does not crystallize. The heating rate was 10 K/h for trace [1] and 1.7 K/h for all the other runs presented in the figure. The Cp traces have been shifted vertically for clarity.

Figure 3. Raw Cp vs T data from heating runs of the crystallized RCD/ 12amo (40/20), at various heating rates. [1] 20 K/h, [2] 6.8 K/h, [3] 1.7 K/h, and [4] 0.5 K/h. The arrows indicate the limits of the Td peak. The Cp traces have been shifted along the y axis for clarity.

Figure 2. Raw Cp vs T data for one heating run of an RCD/12amo (40/20) solution for which the 2:1 complex had crystallized prior to heating. The heating rate was 6.8 K/h. Four Cp peaks can be readily identified. The endothermic peak at T1∼25 °C, the exothermic peak at T2 ∼ 46 °C, the sharp endothermic dissolution peak at Tdis ∼ 60 °C and the high-temperature endothermic dethreading peak at Td ∼ 80 °C.

ratio 40 mM/20 mM, heated at 6.8 K/h. The sharp endothermic peak at ∼60 °C, marked as Tdis, corresponds to the dissolution of the crystals of the 2:1 complex. This has also been confirmed by direct optical observations carried out in parallel to the DSC experiments and at similar heating rates. At lower than 60 °C temperatures, two reproducible characteristic features occur: the endothermic peak at ∼25 °C marked as T1 and the exothermic peak at ∼46 °C marked as T2. The sequence of an endotherm

followed by an exotherm and then by a sharp endotherm has been observed frequently in DSC heating scans of polymeric, crystalline samples. It is considered to correspond to crystal melting, followed by recrystallization, and then by the final melting peak.25 The most interesting, for the present study, Cp feature appears at temperatures higher than Tdis. The reproducible, endothermic, weak and broad peak marked as Td (Figure 2) extends in temperature for a few decades of degrees. Its most striking property is the Cp dependence upon the heating rates of the DSC scans. This is depicted by the various DSC profiles of RCD/12amo samples, 40 mM/20 mM, heated at the various rates that are presented in Figure 3. For the range of heating rates u ) 0.5 to 30 K/h, Td (temperature at maximum Cp) shifted by 23 °C and the temperature span of the peak increased from ∼8 to ∼33 °C. This strong heating rate dependence uniquely characterizes the peak in question, indicating its different nature from the three low-temperature peaks of the Cp profile. This is clearly demonstrated in Figure 4 where Kissinger plots for the dissolution (Tdis) and the high-temperature (Td) peaks are presented. While these plots will be discussed in more detail later (see Analysis of Kinetics), it can be observed directly at this point that the dissolution peak is characterized by much faster reaction times and approximately five times larger activation energy Ea (slope of the linear fits). Excess heat capacity (∆Cp) data derived by normalization of the raw Cp to the number of moles of 12amo that participated in crystal formation are presented in Figure 5. The very pronounced effect of the heating rate upon the Cp profile is clearly demonstrated. For the crystallization procedure described


Figure 4. Kissinger plots for the dethreading (9) and the dissolution (O) Cp peaks depicting the very different dependence upon the heating rate u. Tm is the temperature at maximum Cp (Tm ) Tdis for the dissolution and Tm ) Td for the dethreading peak). From the linear fits shown, estimates of Ea may be obtained: Ea ) 118.4 ( 9.2 kJ/mol for the dethreading and Ea ) 600 ( 61 kJ/mol for the dissolution peak (see text).


Figure 6. Analysis of thermodynamic data for the interaction of RCD with various linear hydrocarbon chains. The straight line is the linear fit by eq 1 in the text; (4) [3CNpyr(CH2)103CNpyr]2+ (ref 21); (*) -OOC(CH2)7NH3+ (ref 7c); (2) -OOC(CH2)12COO- (ref 20); ([) CH3(CH2)5COO- (ref 26); (O) CH3(CH2)4-7NH3+ (ref 8); (x) -OOC(CH ) NH + (ref 7c); and (0) cumulative average from a great 2 10 3 variety of guest molecules (ref 6).

SCHEME 2

place. Equation 1 represents a linear fit of the data26 plotted in Figure 6

-∆Hb(kJ/mol/CH2) ) 1.393 + 0.0544 T(°C)

Figure 5. ∆Cp vs T profiles of DSC heating runs of the crystallized RCD/12amo (40/20) at u ) 1.7 K/h (1), 6.8 K/h (2), 20 K/h (3), and 30 K/h (4) scan rates.

earlier, 55 ( 3% of the 12amo in solution crystallized in 2:1 RCD/12amo complexes for all the 40 mM/20 mM samples presented here. ∆H is found to be 17.15 ( 1.67 kJ/mol, independent of the heating rate. As discussed in the Introduction, the thermodynamics of the interaction of linear hydrocarbon chain molecules, bearing various chemical end-groups, with RCD has been investigated extensively.6,7,20,21,26 The energetics of the association (or dissociation) of complexes involving aliphatic guests (5-12 CH2 moieties and with no bulky end-groups) are analyzed here and presented in Figure 6. It appears, that a fairly good linear relationship exists between the enthalpy of the interaction and the temperature at which these host/guest interactions take

(1)

Using eq 1, ∆Hd ) 4.9 kJ/mol/CH2 is readily obtained for the dissociation at 65 °C. This in turn suggests that according to the net ∆H value measured here by DSC (17.15 ( 1.67 kJ/ mol), about 3-4 CH2 groups are released from the hydrophobic environment of the RCD cavity into the bulk water solution, implying the simultaneous release of one RCD macrocycle, i.e., the partial dissociation (dethreading) for the 2:1 complex. The other seven CH2 groups may be easily accommodated in the remaining cyclodextrin cavity, probably with some small rearrangement, as discussed in the Introduction (Scheme 2). The 65 °C temperature was chosen as a low limit for the dethreading peak at the slowest scan rates. The dissociation of the complex is suggested here to follow the thermal path: dissolution

dethreading

RCD/12amo/RCD 98 RCD/12amo/RCD 98 (solution) (crystal) RCD/12amo + RCD (solution) (solution) Through this path, the partial dethreading process is not reversible. It is reproducible though after recrystallization (of the same sample) of the 2:1 complex. The calorimetric analysis strongly implies that the broad hightemperature Cp peak corresponds to the dissociation of the 2:1


Tsortos et al.

Figure 7. 1H NMR spectra of (a) RCD, 40 mM buffered solution, D2O, 343 K; (b) RCD/12amo, 40 mM/20 mM, buffered solution, D2O, 343 K.

RCD/12amo complex. Apparently, the formation of solid RCD/ 12amo crystals prevents the 2:1 complexes from dethreading until the crystal final dissolution temperature is reached. After this temperature is crossed, the decomplexation process initiates. At these higher temperatures ∆H is large enough and thus measurable by DSC. Decomplexation at lower temperatures on the other hand (all noncrystallized samples) leads to undetectable ∆Cp peaks and ∆H, especially since the process is characterized by slow kinetics, and may be spanning several degrees. The conclusion that the Cp peak in question does indeed describe the dissociation of only one RCD ring from the 2:1 complex is also supported by NMR experimental results. The 1H NMR spectrum of a 40 mM/20 mM, RCD/12amo sample that was transferred directly from the DSC cell into an NMR tube and was observed at 70 °C corresponds to a system in which the RCD cavity is occupied by the guest molecule (Figure 7). This is signified by a chemical shift displacement of the cavity proton H3, relative to its frequency in the spectrum of RCD alone, whereas the signals of the outer protons H2, H4 remain at the same chemical shift. Simultaneously, peak broadening is indicative of the dynamic exchange process that takes place among the species at that temperature. However, it is not possible to discern whether [2]pseudorotaxanes or a mixture of [2]- and [3]pseudorotaxanes exist at this high temperature (broadened RCD peaks that cannot be resolved). Nevertheless, these results support the previously stated notion that above 65 °C one RCD ring slowly slips off leaving an inserted guest and that the process does not involve complete disassembling of the 2:1 complex. Analysis of Kinetics. Kinetic analysis of the DSC peaks was carried out according to well-established methodology;27,28 eq 2 gives the rate constant k for a particular scan rate u

k ) uCp/(Qt - QT)

(2)

Here, Qt is the total area under the ∆Cp peak and QT is the area up to a temperature T. Strictly speaking, this equation is valid for one-step/single-mechanism first-order reactions following the Arrhenius relationship regarding the temperature dependence of k

k ) A exp(-Ea/RT)

(3)

Figure 8. Arrhenius plot of the first-order dissociation rates k vs 1/T for the partial dethreading of the RCD/12amo [3]pseudorotaxanes. For the linear fit shown, Ea ) 140.1 ( 8.2 kJ/mol and A ) 1.7 ( 0.1 × 1017 s-1. The scan rates used were u ) 1.7 K/h (b); u ) 6.8 K/h (0); u ) 20 K/h (2), and u ) 30 K/h (O); (R ) 0.97).

Figure 8 shows the Arrhenius plot for the dissociation reaction of 2:1 complexes of RCD/12amo; Ea and A were calculated to be 140.1 ( 8.1 kJ/mol and 1.7 ( 0.1 × 1017 s-1 respectively. The corresponding estimates of the activation (Eyring) parameters, at 65 °C, are ∆Hq ) 137.3 ( 7.9 kJ/mol, ∆Sq ) 75.6 ( 4.5 J/K mol and ∆Gq ) 111.5 ( 6.8 kJ/mol. It can readily be seen that dethreading of one RCD from the complex is a very slow process having a rate constant k ) 3.8 ( 0.6 × 10-5 s-1 at 65 °C. Similar rates (10-4 to 10-6 s-1) are known for reactions involving breaking or making of covalent bonds such as nitration,29a decarboxylation,29b and deprotonation29c at similar temperatures, and cis-trans isomerization,29d Claisen rearrangement,29e and degradation29f at much higher temperature levels. In systems involving RCD [2]pseudorotaxane decomplexation, rate constants kd of ∼10-1 to 10-3 s-1 have been measured at 25 °C for guest molecules with charged pyridinium21 and bulky phenol30 end-groups. For the guest R,ω-alkanedicarboxylates, of similar length to the guest used in our study, kd was found to be ∼1 s-1 at 30 °C;20 these rates were calculated assuming dissociation of [2]pseudorotaxane to the free compound. The question still remains of what is the reason for the very slow dissociation rate observed here. It has long been known that the more hydrophilic the end group of the linear guest, the slower the kinetics for association and dissociation reactions, this group acting as a barrier. The introduction of charge at the guest’s termini is known to slow the rate constants by 102 to 103 times.20-22,30-32 In our case, the dehydration of the charged carboxylate or amine end-groups is expected to be even more difficult since, in contrast to other studies, no salt was added to the solutions. In addition, and more importantly, the existence of six hydrogen bonds between the two RCD molecules of the [3]pseudorotaxanes10,11 imposes a big barrier to the dissociation process. Although weakened at 65 °C it would still be greater than ∼26 kJ/mol, an estimate calculated from the data of Ross et al.8 concerning the “melting” of hydrogen bonds. Regarding the activation parameters now, we see that ∆Hq, ∆Sq, and ∆Gq all have positive values as observed in other cases too;21 in the case of -OOC(CH2)12COO- dethreading from RCD, ∆Sq is negative.20 A positive ∆Sq is believed to indicate a much



Figure 9. Enthalpy-entropy compensation plot for the dethreading of one RCD molecule off the [3]pseudorotaxane complex. Data points, for the guest molecule, refer to [3CNpyr(CH2)103CNpyr]2+ (4); -OOC(CH ) COO- (b); -OOC(CH ) NH + (O); (R ) 0.993). 2 12 2 11 3

bigger and/or looser activated form of the complex while negative ∆Sq a smaller and/or stiffer one. The tandem calculation of A ∼ 1017 (> 1013 s-1) indicates exactly that.33a Similar results for A have been reported both for solution and bulk decomposition studies.33 ∆Hq is also known to be smaller for the dissociation of neutral rather than of ionized molecules30 and is expected to get larger as the hydrophilicity increases; the magnitude of the value reported here indicates just this fact. Figure 9 shows an enthalpy-entropy compensation plot using data from the present work along with data from other dissociation studies of X-(CH2)n-X guest molecules with RCD hosts;20,21 a very good correlation can be seen (R ) 0.993). Such correlations have been interpreted to indicate that all of these dethreading reactions follow the same mechanism.6,30,34-39 The isokinetic temperature, Tiso (or β), as defined by eq 4, is calculated to be 821 K, whereas the coefficient R, as defined by eq 5, is found to be ∼0.37 (at 30 °C).

∆(∆Hq) ) β ∆(∆Sq)

(4)

T ∆(∆Sq) ) R ∆(∆Hq)

(5)

Calculations on the data presented by Watanabe et al.20 produce a value of 369 K and 0.81 for Tiso and R respectively, for the binding (equilibrium) reaction of -OOC(CH2)12COO- with RCD; these values are in excellent agreement with the cumulative result (Tiso ) 380 K and R ) 0.79) presented by Rekharsky and Inoue6 for the RCD reactions with a great variety of molecules; this fact, although indirectly, further supports the results produced in the present study. The intercept (T∆Sq)0 is negative (-27.7 kJ/mol), indicating the inherent unfavorability of the dissociation process;35 entropy loss mainly due to water organizing around the exposed part of the hydrophobic, alkyl guest molecule chain outbalances the gain from the acquired motional freedom. The implication of a common mechanism of dissociation for the inclusion complexes of this and other studies20,21 could then be taken to suggest, in a fashion similar to other reports,6,22,34,40

Figure 10. ∆Cp vs T profile of a heating run for the crystallized RCD/ 12amo (40 mM/20 mM) 2:1 complex at u ) 1.7 K/h (continuous line) and simulation fit (dotted line) using the parameters Ea ) 282.3 kJ/ mol, Tm ) 71.65 °C, and Qt ) 17.15 kJ/mol (see text). The inset describes the corresponding progress (%) of this dissociation reaction.

tandem steps of (a) guest end group dehydration and inter [3]pseudorotaxane electrostatic bond breaking (in our case between NH3+ and COO-) and counterion separation in the other studies, (b) simultaneous breakdown of hydrogen bonds between the two RCD molecules in our case19 and/or possible distortions between water and the RCD sugar molecules in the other studies, followed by (c) the dethreading of the RCD cavity from the guest and reorganization of water around the newly formed products. What makes the difference in kinetics is the relative magnitude and sign of the ∆Hq and ∆Sq parameters30,34,36 for each guest compound. In our case, stronger hydration and hydrogen bond breaking may lead to more positive ∆Hq values while exposure of shorter (3-4 instead of 10) hydrophobic (-CH2-) moieties to the water environment leads to higher ∆Sq values (see Figure 9). Coming to the shape of the dissociation peak, an apparent asymmetry is clearly observed (Figure 5). There is a fast rising part at the very start of the peak and an equally abrupt fall at the end. Clearly, a curve simulating first order kinetics of a one-step/single-mechanism reaction cannot produce a good fit of the experimental data (Figure 10), regardless of the fact that in the Arrhenius plot linearity is fairly good (R ) 0.97) given the extended temperature range. Good reasons for this have been put forth by many researchers, partially explaining the data presented here. Sanchez-Ruiz41 has described the situation where molecules (proteins), consisting of more than one unit (dimeric, trimeric, etc.) that undergo cooperative structural transformations, exhibit a similar abrupt fall at the end of the DSC peaks. This could be explained theoretically by models assuming either reversibility or irreversibility for the reaction. The possibility cannot be excluded here of such clusters (“dimers” etc.) made up of 2:1 complexes existing in the solution and dissociating in a coordinated, cooperative manner, although no direct experimental evidence is at hand. Kissinger,42 in kinetics modeling studies, points out that similar asymmetries occur if the order of the reaction is not one but zero (or approaching zero). Following Kurganov et al.43 in analyzing the DSC data points in the range of ∼5-95% of the whole peak (and ignoring the initial and final part of the curve), a very good fit was found,


Tsortos et al.

assuming a first-order reaction at each scan rate separately, and only some small deviation was observed at the highest scan rate used. Fitting the Cp data to models assuming zero-order reaction was unsuccessful (data not shown). However, given the capacity of Arrhenius diagrams to be linear and relatively insensitive to small influence factors (sometimes canceling each other out), the smaller-than-one reaction order cannot be completely ruled out. Figure 4 shows a Kissinger plot42 based on the theoretical relationship

d ln(u/Tm2)/d(1/Tm) ) -Ea/R

(6)

where Tm is the temperature at which the Cp maximum occurs and u is the scan rate employed; this relationship is valid for any reaction order.42 A good linearity (R ) 0.992) is observed giving an Ea value of 118.4 kJ/mol, within 15% agreement with the 140.1 kJ/mol value from the Arrhenius plot. The one-step/single-mechanism assumption may not indeed be a valid one. The two sides of the RCD molecule are quite asymmetric. Molecular modeling calculations44 have shown that the primary (narrower) end is hydrophobic, whereas the secondary (wider) end is much more hydrophilic.45 Other calculations have also indicated the existence of a dipole moment directed from the secondary toward the primary side of the RCD cavity.40,44 Dethreading could occur either through the carboxylate or through the amino end of the guest molecule, as discussed earlier, so that the apparent asymmetric shape of the DSC peak could be the result of these processes taking place simultaneously, but with smaller or larger differences in their kinetics. On the basis of this discussion, the partial dethreading rate constant k, presented here, can only be considered as an apparent one. Apparently, the very strong dependence of the Cp peak position and shape on the scan rate is inherent in situations where the scan rates used are faster than the actual kinetics for both reversible and irreversible reactions.46 For the present system, an excellent linear relationship exists (R ) 0.999, data not shown) between the activation energy and the preexponential factor, calculated at each scan rate separately, manifesting a kinetic compensation effect.47 This points out that the change in Ea is only apparent, and there is no change of mechanism in the reaction with changing of the experimental conditions (in this case the scan rate). Statistical analysis, as suggested by Krug et al.,48 verified that the observed correlation is not due to statistical, experimental, error propagation at the 95% level of significance. To our knowledge, this is the first attempt (to date) to thermodynamically characterize the dissociation of [3]pseudorotaxane of RCD in solution. As it was pointed out, this is only possible for complexes that can crystallize within the DSC cell. More studies involving similar guest/host complexes are underway in an effort to gain more insight for the decomplexation mechanisms of these self-organizing systems. References and Notes (1) (a) Saenger, W. Angew. Chem., Int. Ed. Engl. 1980, 19, 344. (b) Wenz, G. Angew. Chem., Int. Ed. Engl. 1994, 33, 803. (c) Chem. ReV. 1998, 98, 8, No 5, special issue on cyclodextrins. (2) Szente, L.; Szejtli, J. AdV. Drug DeliVery ReV. 1999, 36, 17. (b) Szejtli, J. Cyclodextrin Technology; Kluwer Academic Publishers: Dordrecht, 1988. (3) Karuppiah, N.; Sharma, A. Biochem. Biophys. Res. Com. 1995, 211, 60. (4) Breslow, R. Pure Appl. Chem. 1990, 62, 1859. (5) Stella, V. J.; Rao, V. M.; Zannou, E. A.; Zia, V. AdV. Drug DeliVery ReV. 1999, 36, 3. (6) Rekharsky, M. V.; Inoue, Y. Chem. ReV. 1998, 98, 1875.

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Partial Thermal Dethreading of [3]pseudorotaxanes of Î±-Cyclodextrin

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