J. Phys. Chem. 1995,99, 17877-17885
17877
Formation of Highly Stable Heterodimers in Aqueous Solution between P-Cyclodextrin Derivatives Bearing Multiple Opposite Charges Bertrand Hamelin? Ludovic Jullien,*7+9*FrbdCrique Guillo? Jean-Marie Lehn,**tAlain Jardy,” Laurence De Robertis,” and Hugues Driguez” Laboratoire de Chimie des Interactions Molkculaires (CNRS UPR 285), Colltge de France, 11, Place Marcelin Berthelot, F-75005 Paris, France, Dtpartement de Chimie URA 1679, Ecole Normale Suptrieure, 24, rue Lhomond, F-75231 Paris Cedex 05, France, Laboratoire de Chimie Analytique des Processus Industriels (CNRS URA 437), Ecole Suptrieure de Physique et de Chimie Industrielles, 10, rue Vauquelin, F-75231 Paris Cedex 05, France, and Centre de Recherches sur les Macromoltcules Vkgktales (CERMAV-CNRS) BP53X, F-38041 Grenoble, France Received: February 23, 1995; In Final Form: August IO, 1995@
Two water-soluble perfunctionalized B-cyclodextrins bearing amino or carboxyl groups were used to examine the possibility of obtaining stable heterodimers in water. The acidobasic properties of both compounds may be accounted for on the basis of a theoretical interpretation of the potentiometric titration of polyelectrolytes. The association constants between positively and negatively charged B-cyclodextrins were determined by potentiometric titrations. The Gibbs energies of association between cyclodextrins are shown to depend on the product of elementary charges borne by each interacting species. The results obtained are significant for evaluation of electrostatic contributions to molecular recognition.
Introduction The design of thermodynamically stable molecular assemblies in solution is a topic of active current research.’-7 Approaches have been developed to obtain aggregates of amphiphilic molecules possessing overall geometries that may be rationalized according to a single structural parameter.8 However, control over self-assembly processes requires the correct and precise manipulation of intermolecular forces in a sort of “molecular programming” procedure. To this end, geometrically directed interactions, such as hydrogen bonding and metal-ion ligand coordination, have been used to spontaneously generate desired supramolecular architectures by self-assembly. Despite the biological relevance of water as solvent and with the exception of coordination complexes, comparatively few studies have concerned the buildup of oligomeric organized assemblies in aqueous solution, and most of them have been based on the hydrophobic intera~tion.~On the other hand, electrostatic interactions have already been extensively used in the field of host-guest chemistry to form stable In these species, the guest is more or less surrounded by the host bearing an opposite charge. It was of interest to extend the use of electrostatic forces to obtain small organized mays by lateral interaction between oppositely charged faces of conveniently designed molecular units and to study the physical description of these binding forces. Electrostatic interactions in water between ions of low valency are generally weak because of the high dissociating power of water.I2-l4 On the other hand, surface force measurements have shown that the potential between surface distributions of opposite charges was strongly attracti~e.’~ This suggests that there exists a range of charges for which ions should exhibit significant interactions in water, even at low concentrations.
* To whom all correspondence should be addressed. +
Collbge de France.
* Ecole Normale Superieure. 0
Ecole Suptrieure de Physique et de Chimie Industrielles. de Recherches sur les Macromolecules Vkgetales. Abstract published in Advance ACS Abstracts, December 1, 1995.
I’ Centre @
Figure 1. Hypothetical heterodimer formation from interaction between two oppositely charged units.
Several studies have already shown that highly charged ions do give stable complexes in Furthermore, these studies have provided an incremental approach to predict the stability of new species with satisfying results. Because of its significance and its potential biological relevance (e.g., DNApolycation interactions), it appeared interesting to investigate new model systems exhibiting a larger number of charges and a well-defined spatial distribution. To this end, we have investigated the formation of heterodimers between conveniently functionalized P-cyclodextrins bearing n charges (n E[ 1;7]), either positive or negative (Figure 1).
Results Due to its high relative permittivity el, water is known to act as a strongly dissociating solvent; strong electrolytes do not form tight ion-paus in ~ a t e r . ’ ~ In . ‘ ~order to observe a significant amount of association, species bearing a large number of charges may be devised. To control the degree of association at the dimerization step, we have chosen to work with rigid bodies bearing well-defined distributions of charges localized on a single face. Under considerations that (i) the resulting dimer should be more or less neutral and (ii) the zwitterionic zone linking the dimer components should be small compared to the volume of each unit and thus would not determine water solubility, we decided to work with totally hydrophilic units to prevent any possible precipitation resulting from the neutralization accompanying the association. Cyclodextrins appear as suitable candidates to fulfill the preceding requirements. These cyclic oligomers of a-(1-4)
0022-365419512099-17877$09.00/0 0 1995 American Chemical Society
Hamelin et al.
17878 J. Phys. Chem., Vol. 99, No. 51, 1995
Figure 2. Chemical structure of CD7(Am) (left) and CD7(Ac)(H)7 (right).
.
linked D-glucose monomers have received considerable attention, mainly because of their ability to form inclusion c ~ m p l e x e s . ' ~ -They ' ~ combine the repetitive structure and the high degree of functionalization of polymers without the drawback associated with the relative lack of conformational definition. We have already made use of their intermediate size to investigate energy transfers20~2and antenna effects2* in multichromophoric cyclodextrins. The cyclodextrin reactivity has been extensively investigated and numerous water-soluble derivatized cyclodextrins have already been ~ynthesized.,~The high symmetry and degree of functionalization and the rigidity of the cyclodextrin torus associated with the possibility of introducing potential positive and negative functionalities without a long spacer on the primary rim are some features that lead us to choose cyclodextrin as a convenient unit to build a heterodimer in water, based on two components that can be satisfactorily described as relatively rigid circular crowns of regularly spaced opposite charges. Furthermore, because of the circular repartition of charges on the cyclodextrin primary rims, face to face dimerization may be reasonably considered as the most probable arrangement of heterodimers (Figure 1). Two P-cyclodextrin derivatives were synthesized: CD7(Am) and CD7(Ac) (Figure 2 ) . CD7(Am) was isolated as its heptachlorhydrate salt CD7(Am)(H)7(C1)7.2425CD7(Ac) was obtained in two or three steps and isolated as the monoacid hexasodium salt C D ~ ( A C ) ( H ) ( N ~Because ) ~ . ~ ~ of their acidobasic properties, both CD7(Am) and CD7(Ac) display different states of ionization (between 1 and 7) depending on the pH of the aqueous solution. A priori, this feature allows us to investigate all types of ionic interactions involving i+ and j - charges, with i and j varying from 1 to 7. In order to visualize any electrostatic interaction in the system, we chose to work without adding a supporting electrolyte. Indeed, high ion concentrations are known to efficiently screen ionic interactions between charged species. 12,13 Nevertheless, for all measurements reported in this paper, the species concentrations remained low (millimolar range). Furthermore, potentiometric titrations of CD7(Am)-CD7(Ac) mixtures have been done at almost constant and identical ionic strengths (vide infra). The molarity of the basic titrating reactant was chosen to reach high enough pH values in order to measure the highest pK,s of CD7(Am)(H)7(C1)7. The issue of describing heptacharged cyclodextrins either as large "small electrolytes" or as small polyelectrolytes was first addressed. In order to obtain some insight into the strength of interaction between the ionized forms of CD7(Am) and CD7(Ac) and their respective counterions (Cl- and Na+), the spinlattice relaxation time T I of the sodium cations was determined by 23Na-NMR, in the presence or absence of CD7(Ac), at the same sodium cation concentration (7 mM) in water at 25 "C. Such experiments have been performed for the investigation of the counterion condensation effect on p ~ l y e l e c t r o l y t e s . ~At~ , ~ ~ pH 6, where CD7(Ac) is hexa- or heptacharged (vide infra), the longitudinal relaxation times T1 of Na+ cations were found to be identical ( T I = 37 ms) for both CD7(Ac) and NaCl
aqueous solutions. This result suggests that no strong Na+CD7(Ac) binding occurs in the concentration range that was covered in our experiments. Potentiometric titrations were then carried out to determine the stepwise deprotonation constants of the CD7(Am) heptachlohydrate and of CD7(Ac)(H)7. Figure 3 displays the titration curves of acidified solutions of CD7(Am) and CD7(Ac) by 0.05 M NaOH together with the corresponding best computer simulations resulting from the introduction of seven acidity constants K, (Y ~ [ 1 ; 7 ] corresponding ) to the equilibria [CD~(AC)(H)(~-,,]'~-')f H,O == H30' -t [CD~(AC)(H)(,-~,)I~-
K, =
~ ~ c ~ ~ ~ ~ c ~ EH30+1 ~~~(,-,)l"l (14
[ [ c D 7 ( A C ) ( H ) ~ ~ - , ~]'-I l(~-
[CD7(Am)(H)(,-,,] (8-v)+ -k H,O
H,O+
+
[CD7(Am)(H)(7-,,]'7-"'f
A satisfying agreement between simulated curves and experimental points was found. The CD7(Am) and CD7(Ac) acidity constants K , are listed in Table 1. Acidity constants of CD7(Ac)(H)7 increase steadily, the pK,s being regularly distributed between 2 and 6.4. The same trend is found for CD7(Am)(H)7(C1)7, its pK,s varying from 6.1 to 9.3. These data yield the distribution curves of CD7(Am)- and CD7(Ac)-derived species shown in Figure 4. They indicate that, although there is no pH domain in which the positive and the negative units exhibit seven charges at the same time, the hexa- and heptacharged species are present at similar concentrations around pH = 6.2 and should thus interact. Potentiometric titrations of CD7(Am)-CD7(Ac) mixtures were eventually done to detect the presence of possible complexes and to determine their stoichiometry and their stability. Assuming that CD7(Am) and CD7(Ac) do not interact in solution at any pH, it is possible to simulate the titration curves of mixtures of both species. Figure 5 compares this simulation to experimental points for a 111.8 [CD7(Am)]/[CD7(Ac)] mixture. The strong deviation arising in the range pH 3-9 strongly supports the presence of an interaction between CD7(Am) and CD7(Ac) in this pH range. In order to account for the observed deviation, further equilibria involving the interaction between ionized forms of CD7(Am) and CD7(Ac) were introduced. Under the assumption that the stoichiometry of interaction between the positive and the negative units was 1/1 as suggested by the CD7(Am) and CD7(Ac) structures, a satisfying fit of the experimental points was found after introduction of five h e t e r h e r s [CD~(A~)CD~(AC)(H)I~-,~(~-')+ (n from 5 to 9) (Figure 6a), the formation of each being described by a phenomenological formation constant P, corresponding to the equilibria [CD7(Am)(H)i4-i-J
(14-i-n)+
+ [CD~(AC)(H)~](~-')--L
[CD~(AI~)CD~(AC)(H),,-,]'~-"'+ (2) where sup(7 - n,O) 5 i 5 inf(l4 - n,7) and n ~ [ 5 ; 9 ] .It was checked that at least these five heterodimers were necessary to obtain a convenient fit. However, it is impossible to exclude the possibility that supplementary heterodimers with lower stabilities are not involved.29 In order to assess the relevance
Formation of Highly Stable Heterodimers
8
I0
J. Phys. Chem., Vol. 99, No. 51, 1995 17879
a
I
S V C1)
:
3
4
5
6
7
8
9
1
0
PH
u IS IO
Figure 4. Repartition of CD7(Am)- and CD7(Ac)-derived species as a function of pH. The symbols 5+, 6+, and 7+ correspond, respectively, to the CD7(Am) species bearing 5 , 6 and 7 protons, whereas 5-, 6-, and 7- correspond, respectively, to the CD7(Ac) species bearing 5, 6, and 7 negative charges. 12
a
I1
m
IO
' 8 9
m
e
I 4
7
a
6
I
8
S
0
V C11
I
8 4
Figure 3. (a) Titration curve of a CD7(Am) solution by 0.05 M NaOH (see Experimental Section). Experimental points are displayed as crosses and the fit to determine pKas as a solid line. (b) Titration curve of a CD7(Ac) solution by 0.05 M NaOH (see Experimental Section). Experimental points are displayed as crosses and the fit to determine pK,s as a solid line.
TABLE 1: Protonation Equilibrium Constants -log K, (pK,) and Corresponding Protonation Equilibrium Constants -log after Statistical Correction of CD7(Ac)(H), and CD7(Am)(Hh(CI)7 (See Text)
(pm
P Z
PKU u
1 2 3
4 5
6 7
CD7(Ac)(H)7 > b, where b represents the average charge-charge distance within cyclodextrin molecules, the cyclodextrin may be assimilated to a point charge bearing the total charge borne on the cyclodextrin rim. Nevertheless, for the aqueous solutions of the most highly charged cyclodextrins, the Debye-Hiickel linearization of the Poisson equation is not valid anymore33and K - I cannot be calculated from the traditional formula: 2. I
7.5 k 1.5 8.35 1 10.25 zk 0.5 8.6 & 1 6.6 & 1.5
*
organic molecules and polymers. Accordingly, CD7(Am)- and CD7(Ac)-derived species may be viewed u priori (i) as polyelectrolytes or small ionic species or (ii) in the latter case as small circular arrangements of monovalent ions or highly charged single ions. Polyelectrolytes are characterized by the phenomenon of “counterion condensation” arising at concentrations for which the corresponding monomeric unit behaves as a strong electrolyte.31s32The critical concentration for observing this phenom-
Its calculation requires a numerical resolution. A crude estimate can be found in recent calculations that have shown extrema of the monovalent counterion-polyion correlation functions to be in the 2 nm range for solutions of polyions bearing 10-15 charges in the absence of a supporting electrolyte and in the same concentration range as that for the present s t ~ d i e s . ~ ~ , ~ ~ Since this estimate of K-’ is superior by only a factor of 2 or 3 to the internal cyclodextrin charge-charge distance b, the preceding discussion suggests that (i) under the present conditions, it is probably better to describe the charged cyclodextrin
J. Phys. Chem., Vol. 99, No. 51, 1995 17881
Formation of Highly Stable Heterodimers species CD7(Am) and CD7(Ac) as highly charged and unbalanced electrolytes than as local concentrations of small individual 1/1 electrolytes and (ii) the discrete charges bome on the cyclodextrin rim may not necessarily be smeared out when applying the electrostatic treatment to the experimental data. Another issue concerns the meaning of the thermodynamic data determined in the absence of a supporting electrolyte. Potentiometric titrations of CD7(Am) and CD7(Ac) solutions provide “apparent” thermodynamic constants corresponding to equilibria la, lb, and 2. Indeed, these constants Kk are obtained from iterative calculations where the concentrations are considered to be identical to activities aj. [H30+] is estimated from the pH along the titration, and the other concentrations are estimated from the total species concentrations, the number of ionizable sites, and the diverse conservation laws. In fact, the pH directly provides aH30+. Consequently, the constants Kk are linked to the standard Gibbs free energies A,GL of the corresponding reactions k by the following relation:
where the y, values designate the activity coefficients of the species involved in the reactions. Generally, the addition of a supporting electrolyte in a large amount allows to fix the ionic strength of the solution, and the application of a suitable theory, e.g., Debye-Hiickel, provides the value of the activity coefficient term, thus permitting to determine the true thermodynamic constants and to determine ARGi. The Debye-Hiickel linearization being not systematically valid during our experiments, the concept of ionic strength I is not very useful for describing the evolution of aqueous solutions in the course of the titrations of CD7(Am)-CD7(Ac) mixtures. According to the preceding description of CD7(Am) and CD7(Ac), the traditional formula for small electrolytes,
I = c ; c1 i z i2
(3)
should thus be used to calculate the ionic strength I , where the designate the total charges borne by each species. Along this line, constant values of I should be considered as the necessary condition to determine true thermodynamic data. The titrations of the CD7(Am)-CD7(Ac) mixtures do respect this condition; ionic strengths estimated from eq 3 are comparable for both titrations and remain constant along the titrations (see Experimental Section). On the other hand, the titrations of the solutions of pure CD7(Am) and CD7(Ac) do not fulfill the preceding requirement; the large variation of the charge of the CD species along the titrations causes a large change of I , and these latter titrations should thus be discarded to extract thermodynamic data since the activity coefficients continuously evolve during the titration according to an unknown law. In the present case, it is indeed more fruitful to address the problem in another way by asking whether the solutions are diluted or not and whether they remain diluted during titrations. In the former case, the thermodynamic data should reflect the behavior at zero concentration, that is, the Henry ideal case, for which activity coefficients are equal to unity. This question can be answered by comparing the averaged cyclodextrin-cyclodextrin distance (R) to the Debye-Hiickel reciprocal length K-’ since electrostatic interactions are reasonably supposed to play the major role in our case to account for the deviations from ideality. If one assumes a random distribution of cyclodextrins in aqueous
zi
solution, the range of concentrations that has been used for our experiments ((6-8) x M) corresponds to an average distance (R) equal to 12.5-15 nm, which has to be compared to K-’ in the 2 nm range.34%35 To consider the CD7(Am)-CD7(Ac) solutions as diluted therefore appears to be a reasonable assumption. Considering the infinitely diluted solution as the reference state, it follows that under our conditions of titrations, one can consider the activity coefficients to be equal to unity and thus that the constants Kk do represent true thermodynamic constants. One has
CD7(Am) and CD7(Ac) Acidobasic Properties. Several theoretical models have been developed to account for pHtitration curves of polyacids. The main challenge of these models was to determine the local environment of titratable groups from assumptions based on the molecule shape, the dielectric constant, etc.36-38 Cyclodextrinsprovide ideal systems for testing such models since the knowledge of atomic positions or atom environments is much better than, for example, for proteins or polyelectrolytes. In CD7(Am) and CD7(Ac), the transition from a 8 - v times protonated molecule to a 7 - v times protonated is governed in principle by the 8 - v dissociation constants characterizing each of the 8 - v undissociated acidic group^.^^,^^ If one assumes all titratable groups on the P-cyclodextrin to be intrinsically identical and independent, except for electrostatic interaction, the deprotonation constant may adequately be described by a single dissociation constant K,, as defined in relations l a and lb. The protonation constants K , are directly obtained from the analysis of the titration curves. In order to extract the dissociation constants % of a single acid group in a 8 - v times protonated molecule, the K , must be corrected by a statistical factor taking into account the number of protonated and deprotonated positions in the molecule. The Gibbs free energies ARG: and AR& respectively associated with K , and % both correspond to reactions l a and l b but differ in that for A,Gz, the protonation sites are considered discemable whereas for AR&; they are not. In the latter case, only the total number of protons borne by the molecule is of significance. An entropic term of configuration originates from application of this discernability criterion and a simple combinatory calculation thus provides 8-v Ku = %(?)
(4)
where % is a measure of the free energy change accompanying the removal of a proton from one acid group of a 8 - v times protonated molecule according to the equation A& = -RT In %. The free energy change may be regarded as composed of two more or less independent terms: (i) the energy expended in the removal of a proton from the acid groups, e.g., A& = -RT In s;(ii) the work to be introduced in removing the dissociated proton from the field of the ionized groups of the ,f3-cyclodextrin core to infinity AS;. Thus,
%=
exp(-A&i/RT)
Introducing this into eq 4, one obtains
If the entropic terms are neglected, a crude estimate of A&:
17882 J. Phys. Chem., Vol. 99, No. 51, 1995 11
Hamelin et al.
1
9 t
t
I
1 ‘
1
3
2
7
6
5
4
v Figure 7. Variation of the dissociation constants p%$ of a single acidic group in a 8 - u protonated molecule for CD7(Am)(H)7(C1)7(solid
line) and for CD7(Ac)(H)7(dotted line). may be calculated as the work to remove a proton from the center of the P-cyclodextrin core (radius RCD)to infinity. In this model, the organic ion is treated as a cavity embedded in the solvent, which is considered to be a continuum with its macroscopic dielectric constant. Assuming that the charged groups are tightly bound on the CD rim, the following relations are obtained:
A&: =
(v - 1)Le2
for CD7(Ac)
~~EOEPCD
ag;= -
(7 - v)Le2
for CD7(Am)
47~~05%~
where L designates Avogadro’s number, e the elementary charge of the proton, EO the vacuum permittivity, and cr the relative permittivity of the medium. Thus, according to this model, the dependence of p Z on v should be linear and eventually given by the relations
p K = 4n In 1 0 k T ~ o ~ &( v ,- 1) + pG e’
for CD7(Ac) (5a)
e2 p K= 4x In lOkT~,Q?,, (v - 7)
+p
q for CD7(Am)
(5b) where k is the Boltzmann constant?I One notices that the slopes of both pK,(v) functions should be the same, provided that the relative permittivities cr in the proximity of charges borne on the P-cyclodextrins are the same for the positive and the negative derivatives. Furthermore, the relations 5a and 5b provide an interpretation for p%[CD7(Am)l and for p%[CD7(Ac)]. p%[CD7(Am)] should give the typical value of the pKa of a primary ammonium group in a sugar environment, whereas p%[CD7(Ac)] should give that of an a-thioalkyl-substituted carboxylic acid. Figure 7 displays the p z s as calculated with relation 4 from the experimental results. The p s s do depend linearly on v, and the slopes of both straight lines for CD7(Am) and CD7(Ac) compare well (0.4 for CD7(Ac) and 0.3 for CD7(Am)) as suggested by the relations 5a and 5b. Considering that CD7(Am)- and CD7(Ac)-derived species can be satisfactorily described as relatively rigid circular crowns of regularly spaced charges with an average linear charge spacing b in the 1 nm application of the preceding theoretical treatment to the present potentiometric study provides a rough estimate of the local relative permittivities close to CD7(Ac) (cr x 50)
and CD7(Am) (er 70). These values are in satisfactory agreement with the permittivity relative to water of concentrated solutions of sodium chloride where the dielectric constant decreases continuously to become equal to 50 beyond 4-5 M.I3 Indeed, charged groups linked to the P-cyclodextrin primary rim by a short spacer (i) may be considered to be surrounded by the aqueous medium and (ii) are locally highly concentrated (1- 10 M range). Furthermore, this simple theoretical treatment accounts satisfactorily for the p% values. Thus, p%[CD7(Am)] is equal to 8.5 and lies in the range of pKa values of alkylammoniums in sugar environment^.^^ p%[CD7(Ac)] is similarly in agreement with the value one should expect for a poly(a-thioalkyl-substitutedcarboxylic acid), which should form hydrogen bonds and thus show a decrease in its first pKa as malonic acid does.43 Eventually, the coherence of the experimental results and the theoretical treatment is in line with the simple description of CD7(Am) and CD7(Ac) as rigid symmetrical arrangements of positively or negatively ionizable groups. CD7(Am)-CD7(Ac) Ion Pairing in Water. The titrations of mixtures of CD7(Am) and CD7(Ac) have shown that protonated forms of CD7(Am) and deprotonated forms of CD7(Ac) interact in a broad range of pH values. The introduction of a set of five heterodimers [CD~(A~)CD~(AC)(H)I~-,](’-~)+ (n from 5 to 9) was sufficient to satisfactorily fit the experimental points. However, the method that is used to determine the nature of heterodimers to be taken into account does not provide the precise charge distribution in the interacting species (i remains undetermined in eq 2) but only the total number of protons involved in the heterodimer. Hence, the five sets of equilibria describing the interaction between CD7(Am) and CD7(Ac) require, respectively, five (Ps), six (P6), seven (P7), eight (Ps), and nine (Pg) protons. That means that each experimentally accessible constant P, is indeed an average of several constants P,,,,, which remain individually unknown. The contribution of each equilibrium (i,n)in equilibria 2 to P, may nevertheless be estimated from the examination of the distribution of the protonated forms of CD7(Am) and CD7(Ac) as a function of pH (Figure 4)and from the nature of the forces that are involved in the interaction and that determine the Pi,, values. One can thus reasonably suppose that (i) only equilibria involving species present in significant amounts in the range of pH values examined will significantly contribute to the constant P, and (ii) because of the electrostatic nature of the interaction, the equilibria involving the CD7(Am) or CD7(Ac) derivatives bearing the maximal number of charges will display the largest contributions to P,. Taking into account these considerations, Figure 4 suggests a limitation of the equilibria contributing to each constant P, to a single equilibrium involving the cyclodextrin derivatives bearing separately the maximal number of opposite charges. Under these conditions, the constants P, are unambiguously related to five equilibria described by the constants P,,, where i (respectivelyj ) designates the number of positive (respectively, negative) charges on CD7(Am)(respectively, CD7(Ac)). The relation between n and (ij) pairs is given in Table 3. It is therefore possible to determine the Gibbs energies ARG; associated with the formation of each pair of ions (Table 3). The stability constants Po thus obtained and the corresponding standard affhities of reaction -ARC; are remarkably high for ionic interactions in water and thus demonstrate the potential use of electrostatic interactions to assemble oligomeric systems in aqueous solutions. In view of the preceding discussion of the validity of the Debye-Hiickel approximations for aqueous solutions of cyclodextrin-derived charged species, it is not surprising that ion-
J. Phys. Chem., Vol. 99, No. 51, I995 17883
Formation of Highly Stable Heterodimers TABLE 3: Equilibrium Constants Pu and Corresponding Gibbs Energies of Reaction ARGO, between CD7(Am) and CD7(Ac) at 298 K n i j log Pij ARGO~. (kJ.mo1-I) 7 7 7 10.25 f 0.5 -59 f 3 -49 f 6 8 7 6 8.6 f 1 5 6.6 f 1.5 -38 f 9 9 7 6 6 7 8.35 f 1 -47 f 6 -43 f 9 5 5 7 7.5 f 1.5 pairing constants do not conform to the B j e r ” ion-association constant K 1 3
n
L
50 40
-10
0
10
20
30
40
50
60
Figure 8. Gibbs energy ARGO~of ion pair formation between the i
where Ab) is a function containing the minimum and the effective mean distance between oppositely charged ions. The P, values do not depend on the third power of ij. In fact, it seems more appropriate to consider that a sort of condensation takes place between the highly charged positive and negative cyclodextrin-derived species. This description is strengthened if one considers the meaning of the Pu determination. As previously emphasized, K - I measures the range of the electrostatic interactions and thus scales the solution for electrostatic interactions. The Pg constants are obtained from sensing the solution potential by protons, by measuring the deviation from the Henry ideal behavior of CD7(Am)-CD7(Ac) mixtures (infinitely diluted solutions; (R)>> K - ~ ) . Consequently, the Pu values reflect the presence in the solution of cyclodextrin heterodimers with an interparticle distance inferior to K - I ( e 2 nm). Since the cyclodextrin molecular sizes lie in the same range (1-2 nm), it seems reasonable to assume that the Pu constants describe the formation of “tightly bounded” CD7(Am)-CD7(Ac) pairs and do not only result from integration on a diffuse counterionic cloud as it is done to derive the B j e r ” ion-association constant. To gain some insight into the nature of the interaction between species of opposite charges, a thermodynamic cycle was envisaged.4 Since experimental results obtained for common ions suggest that the enthalpy and the entropy changes associated with ion pair formation are linearly related, only the enthalpy change was conside~ed.4~ Both solvated ions derived from CD7(Am) and CD7(Ac) are removed from their coordinated water shell and placed in the gas phase (step 1). The two bare ions are then brought into adjacent positions (step 2). Eventually, the ion pair is returned to the solution (step 3). Because of the large size of the ions obtained from CD7(Am) and CD7(Ac), it seemed reasonable to consider in a f i s t approximation that the difference between the sum of the solvation enthalpies of both CD(Am) and CD(Ac) and the solvation enthalpy of the heterodimer CD(Am)-CD(Ac) was small compared to the energy of bringing the bare ions in contact, Le.,
= ARH;(step 1)
+ ARiY;(Step 2) -k ARH;(step 3) ARH;(step 2)
ARHi (step 2), resulting from electrostatic attractions between individual charges borne on cyclodextrin rims, should be proportional to the number ij of pairs of opposite charges. Since common factors determine both enthalpy and entropy changes associated with ion-pair formation, the preceding reasoning suggests that the Gibbs free$nergy of reaction for CD7(Am)CD7(Ac) association ARG,j should be proportional to ij?6 Figu5e 8 displays the experimental corrFlation between ARG, and lijl. The dependence of ARGOon ij can be
times protonated species from Cb7(Am) and the j times ionized species from CD7(Ac) as a function of lgl. Experimental points from this study are represented as triangles and the average values as filled circles; the data from ref 47 is represented as a filled square. The solid line corresponds to the best linear fit of the experimental points, whereas the dotted lines constitute the limits of the bundle of acceptable linear fits.
satisfactorily described as linear and is in line with the results of other studies.1° Furthermore, the extrapolated value at ij = -1 compares well with the experimental value of equilibrium constants of ion pair formation for monovalent strong electrolytes in water at 25 OC, which lies in the 0.1 range?’ In addition, the extrapolation of the ARGO~ curve at ij = 0 shows that the CD7(Am)-CD7(Ac) interactions are mostly driven by chargecharge interactions since no net attraction is observed for ij = 0, thus strongly suggesting the absence of other contributions (van der Waals, hydrophobic, ...) to the CD7(Am)-CD7(Ac) attraction. Conclusion The present study of CD7(Am) and CD7(Ac) P-cyclodextrin derivatives illustrates some solution properties of acidobasic molecules of intermediate size that may be considered simultaneously as large organic molecules and as small polymers. Although they did not exhibit several characteristics of polyelectrolytes, such as counterion condensation, the acidobasic features of these molecules conform to the behavior expected from application of polyelectrolyte theories. In this respect, it is interesting to note that the uses of a single intrinsic pKa and of statistical corrections are sufficient to account for the titration of /?-cyclodextrin-derived species. This observation is in line with the intermediate size of the mesomolecular cyclodextrins, whereas the concept of multiple discrete pKas applies well for small organic molecules and emphasizes the role of specified acidobasic sites. A single intrinsic pKa and the extent of neutralization are currently used to describe the acidobasic properties of polyelectrolytes. On the other hand, application of macroscopic polyelectrolyte theories to better conformationally defined molecules of intermediate size, such as cyclodextrins, should provide some empirical values of local macroscopic parameters like the dielectric constant illustrated here. This could be important if one considers the significance of such information, for molecular dynamics simulations for instance. In addition, although electrostatic interactions are efficiently screened in water, the present study shows that it is nevertheless possible to assemble molecules via lateral interaction between oppositely charged faces, provided that the number of charges involved is large enough and that their spatial distribution is suitable. Further studies will be undertaken in order to determine the detailed structure of the CD7(Am)-CD7(Ac)
Hamelin et al.
17884 J. Phys. Chem., Vol. 99,No. 51, 1995
heterodimers and to analyze the limitations associated with this mode of lateral interaction to organize molecules in aqueous solution (role of molecular size and shape, of the shape of the charge distribution, of temperature, of the presence of supporting salts, etc.). Experimental Section Synthesis. CD7(Am(H)7)(C1)7 was synthesized as previously d e ~ c r i b e dand ~ ~ ,characterized ~~ by its melting point and 'Hand I3C-NMR spectra. Its microanalysis agreed with the formula (C6H1204NC1)7-13H20, which was used for d l titration experiments (Anal. calcd for (C6H1204NC1)7*13H20: c , 31.18; H, 6.85; N, 6.06. Found: C, 31.23; H, 6.82; N, 5.65). CD7(Ac) was synthesized according to a procedure that will be described elsewhere26and characterized by 'H- and I3C-NMR. Its microanalysis was in agreement with the formula [(CgHj1 0 6 SNa)6.(C&1206S)]*4NaC1'15H20,which was used for the titration experiments (Anal. calcd for [(C~H1106SN~)~.(CSHI~~~S)I.~N~C~.~~H~O: C, 29.31; H, 4.73; Na, 10.02; C1, 6.19. Found: C, 29.39; H, 4.47; Na, 9.91; C1,6.29). 23Na-NMR. 23Na-NMR spectra were recorded at room temperature (22 f 2 "C) on a Bruker AM 200SY spectrometer equipped with a broad band probe at 52.9 MHz. Each sodium salt, CD7(Ac) (3 mg) or NaCl (0.7 mg), was dissolved in 2.00 mL of D20, and the longitudinal relaxation times TI of Na+ ions were measured by the partial inversion recovery technique by applying the relation, T I 1 . 5 - 1 . 7 ~ . ~ ~ . ~ ~ Titrations. Potentiometric titrations were carried out with a Solea-Tacussel TT2 titrimeter using a glass electrode for high alkalinity and a calomel reference Tacussel. All solutions were prepared from deionized and boiled water flushed with N2 upon cooling. The 0.05 M NaOH solution was prepared from a Titrisol set and kept free of carbon dioxide. The entire cell was thermostated at 25 "C. A stream of nitrogen, presaturated with water vapor by bubbling, was passed over the surface of the solution. The pH meter was calibrated with a solution of tartaric acid monopotassium salt at pH = 3.557 at 25 "C and a Tacussel buffer solution at pH = 7.001 at 25 "C. Aliquots of 1 M HCl were added if necessary to reach low pH in order to analyze the data in the widest pH range. The following conditions were used for the potentiometric measurements: (i) for titration of CD7(Am), 15.0 mg CD7(Am) in water (15.0 mL), [CD7(Am)lo = 6.4 x M, analyzed pH range 4-9.5, initial ionic strength50of 18 mM, ionic strength of 4 mM at pH = 9.5;50(ii) for titration of CD7(Ac), 15.6 mg CD7(Ac) in water (11.0 mL), 75 pL of 1 M HCl, [CD7(Ac)]o = 8.0 x M, analyzed pH range 2.5-9, initial ionic strength50 of 10 mM, ionic strength of 28 mM at pH = 9.5;50(iii) for titration of the mixture [CD7(Am)]/[CD7(Ac)] 1/13, 5.0 mg CD7(Am) and 12.91 mg CD7(Ac) in water (15.0 mL), 85 p L of 1 M HC1, [CD7(Ac)]o = 3.7 x M, [CD7(Am)]o = 2.0 x M, analyzed pH range 2.5-9.5, initial ionic strength50 of 13 mM, ionic strength of 17 mM at pH = 9.5;50(iv) for titration of the mixture [CD7(Am)]/[CD7(Ac)] 2.2/1, 10.0 mg CD7(Am) and 6.45 mg CD7(Ac) in water (15.0 mL), 110 pL of 1 M HCl, [CD7(Ac)]o = 1.8 x M, [CD7(Am)]o = 4.0 x lov4M, analyzed pH range 2.5-9.5, initial ionic strength50 of 14 mM, ionic strength of 13 mM at pH = 9.5.50 Data from all titrations were analyzed by the computer program TOT.5' Each point of the simulated curves is calculated by iteration. Once the acidobasic species are chosen, formation constants are determined from iterative comparisons between simulated curves and experimental points. Uncertainties in the formation constants are estimated from observation of significant deviations between the simulated curves and
experimental points after systematic introduction of increments to the constants. Acknowledgment. Our special thanks go to Dr. Luc Belloni and Dr. Marguerite Rinaudo for helpful discussions. We are grateful to Dr. Liliane Lacombe for performing 23Na-NMR measurements and to Dr. Josette Canceill for her permanent presence, help, and kindness. The RINGDEX Company is gratefully acknowledged for a generous supply of P-cyclodextrin. References and Notes (1) (2) (3) (4)
Lehn, J.-M. Angew. Chem., Int. Ed. Engl. 1988, 27, 89. Lehn, J.-M. Angew. Chem., Int. Ed. Engl. 1990, 29, 1304. Lindsey, J. S. New J. Chem. 1991, 15, 153. Philp, 0.;Stoddart, J. F. Synletr 1991, 445. (5) Whitesides, G. M.; Mathias, J. P.; Seto, C. T. Science 1991, 254, 1312. (6) Sauvage, J.-P.; Dietrich-Buchecker, C. 0. Tetrahedron 1990, 46, 503. (7) Constable, E. C. Tetrahedron 1992, 48, 10013. (8) Israelachvili, J. In Intermolecular and Surface Forces, 2nd ed.; Academic Press: London. San Diego. New York. Boston, Svdnev. Tokvo. and Toronto, 1991. (9) Betz. S. F.. Raleigh. D. P.; DeGrado. W. F. Curr. Ouin. Struct. Bzol. 1993, 3, 601. (10) For reviews see the following. Schneider, H.-J. Annew. Chem., Int. Ed.'Engl. 1991,30, 1417. Schneider,H.-J. Chem. SOC. Re; 1994, 227, and references cited therein. (11) Dietrich, B.; Hosseini, M. W.; Lehn, J.-M.; Sessions, R. B. J. Am. Chem. Soc. 1981, 103, 1262. Furuta, H.; Magda, D.; Sessler, J. L. J. Am. Chem. SOC. 1991, 113, 978. Yatsimirsky, A. K.; Eliseev, A. V. J. Chem. Soc., Perkin Trans. 2 1991, 1769. Kato, Y . ;Chu, F.; Flott, L. S.; Schneider, H.-J.; Schiestel, T.; Zimmermann, P. J. Am. Chem. Soc. 1992, 114, 7698. Eliseev, A. V.; Yatsimirsky, A. K. J. Org. Chem. 1994, 59, 264. Eliseev, A. V.; Schneider, H.-J. J. Am. Chem. SOC. 1994, 116, 6081. Anslyn, E. V. J. Am. Chem. Soc. 1994, 116, 4194. Morgan Conn, M.; Rebek, J., Jr. J. Am. Chem. Soc. 1994, 116, 3279. Worm, K.; Schmidtchen, F. P. Angew. Chem., Int. Ed. Engl. 1995, 34, 65. (12) Antropov, L. In Electrochimie thhorique; Mir Ed: Moscow, 1979. (13) Bockris, J. O'M.; Reddy, A. K. N. In Modern Electrochemistry, 6th ed.; Plenum Press: New York, 1977. (14) Reichaxdt, C. In Solvent Efsects in Organic Chemistry, 2nd ed. (1st reprint); VCH: Weinheim, Basel, Cambridge, and New York, 1990. (15) Ross, C. T.; Houston, J. E.; Crooks, R. M.; Kim, T.; Michalske, T. A. J. Am. Chem. Soc. 1995, 117, 3830. (16) Bender, M. L.; Komiyama, M. In Cyclodextrin Chemistry; Springer: Berlin, 1977. (17) Szeijtli, J. In Cyclodextrin Technology; Kluwer: Dordrecht, 1988. (18) Saenger, W. Angew. Chem., Int. Ed. Engl. 1980, 21, 344. (19) Wenz, G. Angew. Chem., Int. Ed. Engl. 1994, 33, 803. (20) Berberan-Santos, M. N.; Canceill, J.; Brochon, J.-C.; Jullien, L.; Lehn, J.-M.; Pouget, J.; Taw, P.; Valeur, B. J. Am. Chem. Soc. 1992, 114, 6427. (21) Berberan-Santos, M. N.; Pouget, J.; Valeur, B.; Canceill, J.; Jullien, L.; Lehn, J.-M. J. Phys. Chem. 1993, 97, 11376. (22) Jullien, L.; Canceill, J.; Valeur, B.; Bardez. E.; Lehn, J.-M. Angew. Chem., Int. Ed. Engl. 1994, 33, 2438. (23) Croft, A. P.; Bartsch, R. A. Tetrahedron 1983, 39, 417. (24) Tsujihara, K.; Kurita, H.; Kawazu, M. Bull. Chem. SOC.Jpn. 1977, 50, 1567. (25) Boger, J.; Corcoran, R. J.; Lehn, J.-M. Helu. Chim. Acta 1978, 61, 2190. (26) Guillo, F.; Hamelin, B.; Jullien, L; Canceill, J.; Lehn, J.-M.; DeRobertis, L.; Driguez, H. Bull. SOC. Chim. Fr. 1995, 132, 857. (27) Kielman, H. S.; Van Der Hoeven, J. M. A. M.; Leyte, J. C. Biophys. Chem. 1976, 4, 103. (28) Manning, G. S. J. Chem. Phys. 1975, 62, 748. (29) It is essentially the uncertainty associated with the stability estimate of these supplementary heterodimers that forbids us to use experimental data to determine more heterodimer stabilities. Indeed, for these species, the range of uncertainties becomes of the same ord$r of magnitude as the formation constants as extrapolated from the ARG,,-ij correlation (vide infra). (30) The mathematical treatment of the data does not differentiate between a 111 and a d n stoichiometry if, in the latter case, association constants for pairing are identical. Polymer formation cannot be excluded at this stage. (31) Manning. G. S. Acc. Chem. Res. 1979, 12, 443. (32) Magdalgnat, H.; Turq, P.; Tivant, P.; Chemla, M.; Menez, R.; Drifford, M. J. Chem. Educ. 1978, 55, 12.
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Formation of Highly Stable Heterodimers (33) In our case (monovalent counterions), this approximation is valid as long as ( ~ e * ) / ( 4 n € ~ ~ 5 nm, which is not satisfied for all counterions present in solution (the external diameter of the P-cyclodextrin lies in the 1.5 nm range). (34) Vlachy, V.; Marshall, C. H.; Haymet, A. D. J. J. Am. Chem. SOC. 1989, 111, 4160. (35) Rescic, J.; Vlachy, V.; Haymet, A. D. J. J. Am. Chem. SOC.1990, 112, 3398. (36) Tanford, C.; Kirkwood, J. G. J. Am. Chem. SOC. 1957, 79, 5333. (37) Tanford, C. J. Am. Chem. SOC. 1957, 79, 5340. (38) Tanford, C. J. Am. Chem. Soc. 1957, 79, 5348. (39) B j e r r " , N. Z. Phys. Chem. 1923, 106, 219. (40) Katchalsky, A,; Gillis, J. Red. Trav. Chim. Pays-Bas 1949, 68, 879. (41) Such a linear dependence with the same slope is maintained even if the entropic term is different from zero as long as ASu is linearly related to AH". Moreover, a similar equation can be obtained if one considers a continuous variation of the charge bome by the cyclcdextns, that is, instead of considering the solution as a mixture of cyclodextrins bearing various integral numbers of charges, it is replaced by a solution of a single kind of ion with a continuously variable charge. Such a mathematical treatment leads to a slope equal to those in (5a) and (5b) and therefore to the same erRc~ estimate. (42) estimated from CPK models. (43) The uncertainty associated with this extrapolated value is larger for CD7(Am) than for CD7(Ac). Furthermore, pK, values of primary ammoniums in sugars are very much sensitive to chirality and possible
hydrogen bonding. See the following. Pemn, D. D: In Dissociation Constants of Organic Bases in Aqueous Solution: Supplement 1972; Butterworths: London, 1972. Kortiim, G.; Vogel, W.; Andrussow, K. In Dissociation Constants of Organic Acids in Aqueous Solution; Butterworths: London, 1961. Albert, A,; Serjeant, E. P. In Ionization Constants of Acids and Bases; Methuen & Co and John Wiley & Sons, Inc.: London and New York, 1962. (44)Thq Structure of Electrolytic Solutions; Hamer, W. J., Ed; John Wiley & Sons, Inc. and New York, Chapman & Hall, Limited: London, 1959. (45) As for a preceding reasoning, under the assumption that there is a linear energy relationship between enthalpic and entropic terms, the slope on lijl, which is here of interest, is not modified. (46) Under the assumption that activities are equal to concentrations, the ARGO, that are measured by potentiometry and the ARGO~that &e estimated #rom the thermodynamic cycle can be directly compared. Contrary to the theoretical treatment for acidobasic properties, no statistical correction of the association constant has to be made. Provided that the protons remained localized on the same sites for the interacting and noninteracting species, the two entropic terms arising from the nondiscemability of sites cancel in the thermodynamic treatment. (47) Kay, R. L. J. Am. Chem. SOC.1960, 82, 2099. (48) Colebrook, L. D.; Hall, L. D. Can. J. Chem. 1980, 58, 2016. (49) Cookson, D. J.; Smith, B. E. Anal. Chem. 1982, 54, 2593. (50) Estimated as explained in the text. (51) Rosset, R.; Bauer, D.; Desbarres, J. In Chimie analytique des solutions et infonnatique; Masson, Paris, Milan, Barcelone, and Bonn, 1991. Jp950529W
