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J. Phys. Chem. B 2002, 106, 2166-2174
Effect of Cations and Anions on the Formation of Polypseudorotaxanes Pierandrea Lo Nostro,† Josias R. Lopes,‡ Barry W. Ninham,§ and Piero Baglioni†,* Department of Chemistry and CSGI, UniVersity of Florence, Via della Lastruccia 3 Sesto Fiorentino 50019 Florence, Italy, Instituto de Quı`mica, UniVersidade Estadual de Campinas, Caixa Postal 6154, 13083-970 Campinas (Brasil), and Department of Applied Mathematics, Research School of Physical Sciences, Australian National UniVersity, Canberra, A. C. T., Australia 0200 ReceiVed: July 27, 2001; In Final Form: December 13, 2001
Aqueous solutions of R-, β-, or γ-cyclodextrin form stable and crystallizable inclusion complexes (polypseudorotaxanes) when added to long chain polymers such as PEG, PPG, and alkanols. This process consists of the threading of several cyclodextrin molecules around a single chain, with a kinetic profile that depends on temperature and solvent nature. We have studied the effect of salts on this threading process for a polypropylene glycol derivative with β-cyclodextrin at 25 °C. What emerges is that changes in the threading time are strongly dependent on the nature of both cations and anions. The formation of a polypseudorotaxane is then a process where hydrophobic forces clearly play a dominant role, and in this paper, we show that the diversity of salt effects is related to the microscopic frequency dependent dielectric properties of the ion pair, that account for the dispersion potential experienced by the different ions in solution.
Introduction Polypseudorotaxanes are supramolecular adducts produced by linear polymers that penetrate the empty cavities of cyclic host molecules, such as cyclodextrins (see Figures 1a and 1b). When an aqueous dispersion of a long chain polymer such as poly(ethylene oxide) is added to a water solution of cyclodextrin, after a few minutes, the mixture becomes turbid. Eventually, a white crystalline solid precipitates.1 Polypseudorotaxanes are the starting chemical architectures from which a set of other interesting molecules can be produced, such as molecular necklaces, molecular trains, and molecular tubes. All these entities possess the same inclusion properties of their originating ligands, and constitute a very important tool for the study of biological complexes2 and “smart” materials.3 The formation of polypseudorotaxanes is affected substantially by the chemical structure of the reactants, temperature, and solvent nature. To prepare inclusion compounds with high yields, the first requirement is an optimal ratio between the cross-section of the guest molecule and the host’s cavity. The kinetics of the process is strongly affected by temperature.1 The solvent also plays a crucial role in favoring or inhibiting the formation of the threaded structures as we detected in the case of PEG with R-CD, or PPG with β-CD, in D2O, H2O, and 0.1 M urea.4,5 The dynamics of R-CD, of the molecular necklace and the molecular tube, formed from the threading process of R-CD with PEG have been also investigated by 13C NMR relaxation.6 The effect of ions on the formation of a multimolecular linear complex such as a polypseudorotaxane is an ideal “Guineapig” to investigate probably one of the deepest yet unsolved key problems in surface chemistry: the Hofmeister mystery. * To whom correspondence should be addressed. Fax: +39 055 4573036. E-mail:
[email protected]. Internet: http://www.csgi.unifi.it. † Department of Chemistry and CSGI, University of Florence. ‡ Instituto de Quı`mica, Universidade Estadual de Campinas. § Department of Applied Mathematics, Research School of Physical Sciences, Australian National University.
The whole threading process can be envisaged according to a stepwise model: the free end of the guest molecule must face the cavity with a proper geometry so that the threading of the first CD molecules can start. Then, the host will move toward the center of the polymer; in this step, the polymer chain unfolds and stretches, and the threaded host molecules establish two main interactions: hydrophobic interactions with the polymer repeating units, i.e., O-CH2-CH2 in the case of PEG, and hydrogen bonds between neighboring CD molecules. New CD molecules take part in the reaction via a cooperative mechanism. Molecular dynamics calculations showed that cyclodextrins arrange preferentially in a closely packed head-to-head and tailto-tail sequence, presumably in order to optimize the number of hydrogen bonds that they form.7 The process goes on until the whole guest is totally covered with host molecules. NMR experiments, kinetic data, and structural parameters provide the same values for the number of threaded CD molecules per single chain of polymer, and indicate an averaged 2:1 stoichiometric ratio between the polymer’s repeating units and CD.7-9 For PPG-Am2/β-CD polypseudorotaxanes in water, we found that about 16 cyclodextrin molecules are threaded by a single guest chain.5 Because X-ray crystal structure data shows that 6.5 water molecules are averagely bound in the β-CD cavity,10 the total volume of replaced water molecules is 6.5 × 16 × 30 ) 3120 Å3, very close to the volume of a single PPG-Am2 in the liquid state, calculated from the average molecular weight and density (3334 Å3). This shows that PPG-Am2 fully occupies the empty cavity of the host, and that cyclodextrins cover the entire polymer stretched chain. In general, hydrophobic interactions remove hydrophobic surfaces from contact with water and organize macromolecular assemblies:11 this is exactly what happens during the formation of a polypseudorotaxane from CD rings and a polymer chain. Because the solvent composition effectively affects the kinetics of the process, we can conclude that the driving force resides not just in the hosting capability of cyclodextrin. It must somehow be related to the solvent-solute interactions as well.
10.1021/jp012915l CCC: $22.00 © 2002 American Chemical Society Published on Web 02/02/2002
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Figure 1. (a) Structure of a polypseudorotaxane obtained from a polypropylene oxide polymer and β-cyclodextrin. (b) Formation of a polypseudorotaxane and of a polyrotaxane from a linear polymer guest and several host molecules.
The entire threading process results from the interplay of different kinds of interactions: the internal, hydrophobic cavities of cyclodextrins interact strongly with the repeating groups of the guest, and shield the polymer from water. Moreover,
threaded cyclodextrins interact through hydrogen bonds (on the average three hydrogen bonds on the larger rims and two on the narrower rims), and several water molecules are expelled during the formation of the polypseudorotaxane. The aqueous
2168 J. Phys. Chem. B, Vol. 106, No. 9, 2002
Figure 2. Absorbance variation (λ ) 400 nm) during the formation and precipitation of a polypseudorotaxane. Plot 2a corresponds to pure water, the arrow indicates the region where absorbance remains constant, and in which the threading phenomenon takes place. Plot 2b shows the retarding and accelerating effect of sodium sulfate and sodium iodate, respectively, on the threading process.
solvent leads to the formation of the final assembly in a manner reminiscent of micellization, where hydrophobic interactions between the host and the guest are optimized, and the repulsion between the hydrophobic guest and the water molecules are minimized. The formation of the final supramolecular assembly is then ruled by enthalpy more than entropy.2 Ionic solutions produce significant salting-in or salting-out phenomena in a wide range of biological and physicochemical observations. Their effects often depend on the cation-anion pair, with a typical trend that traditionally has been denominated as the “Hofmeister series”.12 Whether Hofmeister ions produce their effects by changing the hydrogen bonding of water or not is still a debated issue.13 The number of experimental evidences where the same trends have been confirmed, and where “ion specificity” (especially for anions) has been observed is really large. Depending on their effect, ions have been defined as “kosmotropic” or “chaotropic”, and the sign inversion along the lyotropic sequence depends on the particular system studied.14 Since the first observations reported by Hofmeister at the end of the 19th century, salting-out and solubility of proteins,13,15,16 hydrophobic chromatography,17,18 floc volumes of hydrophobic particles,19 ion binding20 and counterion condensation21 for micelles and polyelectrolytes, cloud points of nonionic aqueous dispersions,22 phase inversions in microemulsions,23 bubble-bubble interactions at the air/water interface,24 collagen structural stability,25 shape and size of metal nanoparticles,26 liquid-gel transitions of pluronic solutions,27 conformation of protein-coupled receptors,28 transport properties of proteins,29 phase behavior of phospho- and glyco-lipids,14 water-amphiphile interactions,30 drug’s controlled release,31 and
Lo Nostro et al. restriction enzymes' activity32 are the most familiar examples where a strong dependence of different physicochemical parameters on the kind of ion pairs was consistently found. Dissolved atmospheric gas effects in colloidal systems have also been reported lately: although they have been usually ignored; however, recent experimental results show that their role in mediating interactions is crucial.33 Besides the effect of several inorganic compounds, some organic chemicals have shown similar behavior, leading to many experimental studies where water solvation, water structure, and ion-dipole interactions have been invoked in order to justify the findings, with a view to designing microenvironments for optimizing biological functions such as enzymatic catalysis, biorecognition, and conformational stability.12 The direct and ineluctable evidences of such trends have been explained with a variety of semiempirical treatments that show relationships between the experimental observables and some thermodynamic properties (such as hydration energy, ionization potential, surface tension increment, etc.), without the assistance of a self-consistent theoretical framework. This task is not easy as the range of experimental conditions and chemicals under study is very wide,34,35 and a clear, unified, theoretical approach is still to come.36 Facing this issue, Ninham and Yaminsky35 argue that ions respond to an electrostatic potential near the interface as well as to a potential that is due to dispersion forces. The effects occur particularly when the salt concentration is higher than 0.1 M. Dispersion forces are generally neglected in the treatment of experimental data, according to the usually recalled theories (DLVO, Onsager, Lifshitz).36 On the other hand, when the image potential experienced by ions is calculated by taking into consideration the number of electrons they possess, and therefore their polarizabilities and their response to dipolar dispersion electric fields,35,37 at that point the Hofmeister’s salts sequence acquires a physical meaningfulness and can be quantified in terms of microscopic physicochemical parameters. The correlation between Hofmeister’s salts effects and the electric properties of ions was already proposed by Voet in his paper: “since the heat of hydration of ions depends on the electric field which surrounds them, the lyotropic effects are beyond doubt caused by the different electric field strengths of the ions”.38 Because in the formation of polypseudorotaxanes hydrophobic and solvent-solute interactions appear to be the ruling factors, these inclusion assemblies can be considered among the simplest models for complex biological entities such as proteins, enzymes’ structures, ribosomes and so on, and may represent a valid tool for the study of some of their properties. The effect of salts on the formation of polypseudorotaxanes has so far been neglected. In one of his first papers, Harada stated that the solubility of aqueous R-CD/PEG complexes (with PEG molecular weight lower than 1000) did not change when the reaction medium was added with NaCl or KCl.2 In our experiments, we detected a significant salt effect on the kinetics of formation of polypseudorotaxanes, with remarkable changes that depend on the kind of ions added to the aqueous solvent. In this paper, we have studied the salt effect induced by different salts on the threading process of β-cyclodextrin (βCD) with poly(propylene glycol)-bis-2-aminopropyl ether (PPGAm2). By recording absorbance at 400 nm as a function of time on β-CD/PPG-Am2 mixtures, a typical trend is shown: at the beginning absorbance remains constant, and then it sharply increases as the threaded polypseudorotaxanes aggregate and precipitate. As we proposed and discussed in previous papers, we define as “threading time” (tth) the time interval in which
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J. Phys. Chem. B, Vol. 106, No. 9, 2002 2169
Figure 3. Threading time for different anions (a) and cations (b).
absorbance remains constant and that can supposedly be related to the formation of the polypseudorotaxane1,5 (see Figure 2a). As a matter of fact, by using this definition of tth we were able to determine the number of β-CD molecules threaded per single chain, and the Gibbs' free energy for the process as fitting parameters of the experimental data.4 We measured tth at 25 °C during the formation of polypseudorotaxanes in the presence of 0.1 M water solutions of different salts. The effect of anions was checked with different sodium salts, and that of cations was investigated by using different chlorides. Materials and Methods NaF, NaCl, NaBr, NaI, NaIO3, NaOH, NaSCN, NaHCO3, Na2CO3, NaH2PO4, NaNO3, CH3COONa, Na2SO4, sodium citrate, and sodium succinate, LiCl, KCl, CsCl, NH4Cl, CaCl2, β-cyclodextrin, and PPG-Am2 (MW ≈ 2000) were from Fluka (Milan, Italy), and used as received, without further purification. Bidistilled water has been purified with a MilliQ system (Millipore) to remove colloidal impurities. UV spectra were recorded with a Lambda 5 spectrophotometer (Perkin-Elmer), using a thermostated bath to control the temperature of the cuvette (25° ( 0.1 °C). The concentration of PPG-Am2 was 7.5 × 10-5 mol/L, and that of β-CD was 8.37 × 10-3 mol/L. All salt solutions were 0.1 M in water. Fixed volumes of the guest and of the host molecules’ water solutions were mixed in the cuvette, and the absorbance
measurement (at λ ) 400 nm) was started immediately after. The reference sample was pure water. The threading time (tth ( 10 s) was determined from the UV spectra (see Figure 2a). Results and Discussion Figure 2a shows the variation of absorbance (at 400 nm) as a function of time for a mixture of PPG-Am2 and β-CD in water, at 25 °C. The plot indicates the presence of three regions: the first (indicated by the arrow) with no variation of absorbance (A) with time, which corresponds to the formation of the polypseudorotaxane, then A steeply increases, because of the aggregation of large particles that produce a consistent light scattering, and finally absorbance remains almost constant with small oscillations, due to the precipitation of the final adduct. As we already outlined in previous papers,1,4,5 the whole process presumably starts with the threading and sliding of CD molecules over the linear chain (as illustrated in Figure 1b), and ends when the large polypseudorotaxanes aggregate, produce a strong turbidity (Rayleigh scattering), and eventually separate from the solution. We showed that the initial time in which absorbance remains constant ((0.001) is related to the threading process, that is when cyclodextrin molecules get penetrated by the linear polymeric guest, and we denominated it “threading time” (tth); after this initial time aggregates are quickly formed and absorbance strongly increases. Salt solutions significantly change tth for β-CD/PPG-Am2 mixtures by either accelerating or retarding the formation of
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TABLE 1: Lyotropic Numbers (N),a Molal Surface Tension Increments (σ),b,c Free Energies of Hydration (∆GHydr),d Ionic Polarizability (r), Partial Molar Volumes (νs),e and Threading Times (tth) for the Studied Anions and Cations anion (sodium salt)
N
carbonate sulfate 2.00 acetate fluoride 4.80 hydroxide chloride 10.00 bromide 11.30 dihydrogenphosphate hydrogencarbonate nitrate 11.60 iodide 12.50 thiocyanate 13.25 iodate lithium 115 sodium 100 ammonium potassium 75 cesium 60 calcium
σ (mN‚kg/m‚mol) -∆Ghydr νs tth b c (kJ/mol) R (Å3) (cm3/mol) (sec) 2.73
2.65 2.60
1.64 1.32
1.60f 2.12 1.57 1.23
1300 1145 300 345 345 270 250 245
2.39 18.99 41.06 1.050 3.687 4.813
310 1.06 1.02 0.54g
1.08 0.96
1.63 1.64 1.39 1.40 1.39 3.66
1.57 1.26 1.30 3.46
275 220 230 270 511 412 339 337 284 1588
7.163 0.03 0.18 0.84 2.44
18.39 24.81
147 146 131 118 103 79 63 55
23.36
40
29.67 35.82 39.04
36 35 30 25 65 79 111 120 124 71
18.93 18.39 37.66 28.37 40.22 24.64
a
From Voet A. Chem. ReV. 1937, 20, (2), 169. b From Melander, W.; Horvath, C. Arch. Biochem. Biophys. 1977, 183, 200. c Data obtained by calculating σ as the slope of the γ vs molality plot from data found in International Critical Tables of Numerical Data, Physics, Chemistry and Technology, C. J. West Ed., US National Research Council, McGraw-Hill Book Co., New York, 1933. The original ∆γ vs molarity values where converted into ∆γ vs molality by using the density data found in the same reference. The discrepancy between the two sets of σ is within 6%. d Values obtained from Marcus, Y. J. Chem. Soc. Faraday Trans. 1991, 87 (18), 2995. e Values for 0.5 M salt solutions at 25 °C (for HCO3- and SCN- at 18 °C); they were obtained by using the density data reported in International Critical Tables of Numerical Data, Physics, Chemistry and Technology, C. J. West Ed., US National Research Council, McGraw-Hill Book Co., New York, 1933, to determine VM, and then calculating νs according to Gonza´lez-Gaitano, G.; Guerrero-Martı´nez, A.; Ortega, F.; Tardajos, G. Langmuir 2001, 17, 1392. f The σ value for F- might be affected by the formation of difluoride ions in the solution (2F- + H2O ) OH- + HF2-), as reported by Scha¨fer, K.; Masia`, A. P.; Ju¨ntgen, H. Z. Elektrochem. 1955, 59, 425. g From Jarvis, N. L.; Scheiman, M. A. J. Phys. Chem. 1968, 72, 74.
the polypseudorotaxane, in fact some ions stabilize the reactants in the aqueous environment and slow the reaction, whereas others favor the formation of the polymeric inclusion assembly and increase the reaction rate. Figure 2b shows the effect due to the presence of sodium sulfate or sodium iodate in the reaction medium: Na2SO4 produces a longer tth (slower threading), whereas NaIO3 results in a shorter threading time (faster reaction), as compared to pure water. Figure 3a and 3b shows the trend of tth for a set of different ions
CO3) ≈ SO4) > CH3COO- > cit3- > succ2- > F- > OH- > H2O > Cl- > Br- > H2PO4- > HCO3- >NO3- ≈ I- > SCN- > IO3where cit3- ) citrate; succ2- ) succinate
Cs+ > K+ > NH4+ > H2O > Na+ > Ca2+ > Li+ Anions affect the kinetics of the polypseudorotaxane’s formation more than cations, divalent ions are more effective than monovalent species,13 and the effects induced by cations and anions are totally different. To discuss our data, we will analyze the variation of tth as a function of some physicochemical
Figure 4. Threading time as a function of the lyotropic number as defined by Voet for anions (a) and cations (b).
parameters: the lyotropic number (N), the molal surface tension increment (σ), the Gibbs' free energy of hydration (∆Ghydr), ionic polarizability (R) and partial molar volume (ns); these parameters were either obtained directly or calculated from the literature,39,40 and are reported in Table 1. Figure 4a and 4b shows the plot of tth versus N for anions and cations, respectively. N, the lyotropic number, is an empirical parameter introduced by Voet,38 that quantifies the effect of different salts in salting-out experiments that involve lyotropic effects. We found that tth always decreases when N increases, indicating that our system involves the same kind of lyotropic activity performed by ions in other phenomena, such as polymer swelling, gelation of lyophilic colloids, esters reactivity, viscosity of electrolyte solutions, and so on.38 Processes where a hydrophobic effect plays the dominant role, such as salting-out of aromatic hydrocarbons41 or of polar amides,42 go with a significant dependence on the molal surface tension increments, σ.13,43 This parameter is strictly related to the energy (∆Gcav) required for creating a spherical cavity within the solvent, ∆Gcav ) A × γ, where A and γ are the cavity’s surface area and the solvent surface tension, respectively. Therefore, as Melander and Horva´th stated,43 σ quantifies the hydrophobic free energy involved in the process. The σ values were either taken directly from the literature,43 or calculated from surface tension change and density data for different aqueous salt solutions between 20° and 25 °C (see Tables 2 and 3). Figure 5a and 5b indicates tth as a function of σ (mN × kg × m-1 × mol-1), and shows that the formation of the polypseudorotaxanes is accelerated by anions with the smallest σ and by cations with the highest surface tension increment, and Vice Versa. In our system, at the end of the threading process, the volume occupied by the hydrophobic PPG-Am2 molecule
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J. Phys. Chem. B, Vol. 106, No. 9, 2002 2171
TABLE 2: Densities and Molalities of Some Aqueous Salt Solutions between 20° and 25 °C at Different Weight Percentagea P % (w/w) 1.0000 2.0000 4.0000 6.0000 8.0000 10.000 12.000 14.000 16.000 18.000 20.000 22.000 24.000 25.000 30.000 40.000
F(CaCl2)
m(CaCl2)
1.0135 1.0302 1.0471 1.0643 1.0818 1.0997 1.1180 1.1366 1.1557 1.1753
0.18388 0.37542 0.57512 0.78349 1.0011 1.2287 1.4668 1.7162 1.9778 2.2525
1.2260 1.2790 1.3927
3.0034 3.8615 6.0068
F (NH4Cl)
m(NH4Cl)
F (LiCl)
m(LiCl)
F (NaCl)
m(NaCl)
F (NaBr)
m(NaBr)
1.0002 1.0033 1.0093 1.0153 1.0212 1.0270 1.0327 1.0383 1.0439 1.0494 1.0549 1.0603 1.0657
0.188 83 0.381 52 0.778 93 1.1933 1.6256 2.0772 2.5492 3.0433 3.5608 4.1036 4.6736 5.2728 5.9035
1.0029 1.0087 1.0202 1.0316 1.0430 1.0545 1.0660 1.0776 1.0894 1.1013 1.1134
0.23828 0.48142 0.98289 1.5057 2.0512 2.6210 3.2167 3.8401 4.4932 5.1782 5.8973
1.0041 1.0111 1.0253 1.0396 1.0541 1.0688 1.0836 1.0987 1.1140 1.1295 1.1453
0.17283 0.34919 0.71293 1.0922 1.4879 1.9012 2.3332 2.7854 3.2591 3.7559 4.2776
1.0048 1.0125 1.0284 1.0446 1.0613 1.0785 1.0961 1.1142 1.1329 1.1522 1.1721
0.098 163 0.198 33 0.404 92 0.620 31 0.845 06 1.0798 1.3252 1.5820 1.8511 2.1333 2.4295
P % (w/w)
F (NaI)
m(NaI)
F (Na2SO4)
m(Na2SO4)
F (NaNO3)
m(NaNO3)
F (Na2CO3)
m(Na2CO3)
1.0000 2.0000 4.0000 6.0000 8.0000 10.000 12.000 14.000 16.000 18.000 20.000
1.0047 1.0125 1.0284 1.0448 1.0616 1.0790 1.0969 1.1154 1.1344 1.1541 1.1745
0.067347 0.13607 0.27781 0.42557 0.57977 0.74081 0.90918 1.0854 1.2700 1.4636 1.6668
1.0061 1.0151 1.0332 1.0515 1.0701 1.0890 1.1083 1.1279 1.1479 1.1683 1.1890
0.071113 0.14368 0.29334 0.44937 0.61219 0.78224 0.96002 1.1461 1.3410 1.5454 1.7600
1.0037 1.0104 1.0239 1.0376 1.0515 1.0656 1.0799 1.0945 1.1094 1.1246 1.1402
0.11884 0.24011 0.49022 0.75098 1.0231 1.3073 1.6044 1.9153 2.2410 2.5826 2.9413
1.0073 1.0176 1.0381 1.0588 1.0797 1.1008 1.1223 1.1442
0.095302 0.19255 0.39312 0.60222 0.82042 1.0483 1.2866 1.5359
P % (w/w)
F (NaHCO3)
m(NaHCO3)
F (CH3COONa)
m(CH3COONa)
F (NaSCN)
m(NaSCN)
F (KCl)
m(KCl)
1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 10.000 12.000 14.000 16.000 18.000
1.0059 1.0132 1.0206 1.0280 1.0354 1.0429 1.0505 1.0581
0.12024 0.24293 0.36816 0.49599 0.62651 0.75982 0.89598 1.0351
1.0021 1.0072
0.12313 0.24877
1.0038 1.0090
0.12459 0.25173
1.0034 1.0098
0.13548 0.27373
1.0173
0.50791
1.0196
0.51394
1.0225
0.55887
1.0275
0.77808
1.0303
0.78731
1.0354
0.85614
1.0377 1.0479 1.0582 1.0686 1.0790 1.1001
1.0600 1.3544 1.6623 1.9844 2.3219 2.6758
1.0411 1.0520 1.0630 1.0741 1.0853 1.0966
1.0726 1.3705 1.6820 2.0080 2.3494 2.7076
1.0485 1.0617 1.0751 1.0886 1.1025 1.1165
1.1663 1.4903 1.8290 2.1835 2.5548 2.9443
P % (w/w)
F (CsCl)
m(CsCl)
F (NaOH)
m(NaOH)
F (NaF)
m(NaF)
1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 10.000 12.000 14.000 16.000 18.000
1.0047 1.0125
0.059997 0.12122
1.0284
0.24749
1.0100 1.0213 1.0324 1.0435 1.0545
0.25254 0.51023 0.77323 1.0417 1.3159
1.0092 1.0198 1.0304 1.0409 1.0515
0.24056 0.48604 0.73657 0.99232 1.2535
1.0447
0.37913
1.0615 1.0788 1.0967 1.1151 1.1340 1.1536
0.51650 0.65997 0.80996 0.96693 1.1314 1.3038
a Data obtained from International Critical Tables of Numerical Data, Physics, Chemistry and Technology; West, C. J., Ed.; US National Research Council, McGraw-Hill Book Co.: New York, 1933. Molarity is given by 10‚P‚F/M, and molality is given by 10‚P/(M-P) Where P, F, and M are the weight percentage and density of the solution, and the molecular weight of the solute, respectively.
in water is replaced by water molecules that were initially bound to β-CD. Therefore, although there is no variation of volume in the solution, the solvent cavities that hosted PPG-Am2 before the threading, eventually disappear, they do so with a free energy variation that depends on the hydrophobic surface area and on the solvent surface tension. This accounts for the dependence of tth on σ. However at this point the different behavior of cations and anions is still unexplained.
Figure 6a and 6b shows tth as a function of the Gibbs' free energy of hydration, ∆Ghydr (kJ/mol) for anions and cations, respectively; the values of ∆Ghydr were taken from the literature.44,45 In the case of anions, tth increases with increasing -∆Ghydr, whereas in the case of cations the threading time lowers as -∆Ghydr increases. The most accelerated effects are induced by the anions with the smallest value of -∆Ghydr (IO3and SCN-), and by the cation with the highest free energy of
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TABLE 3: Surface Tension Change (∆γ) of Some Aqueous Salt Solutions between 20° and 25 °C as a Function of Molar Concentrationa M 0.025 0.050 0.100 0.200 0.250 0.500 0.700 1.000 1.500 2.000 2.900 3.000 4.000 5.000 6.000 7.000 9.000 11.000 14.000
NH4Cl CaCl2 NaOH NaCl NaBr NaI Na2SO4 NaNO3 Na2CO3 KCl 0.05 0.16
0.05 0.09 0.17
0.35
0.04 0.07 0.12
0.1550
0.54 0.35 0.71
0.78 1.52
1.39
3.20
0.42 0.82 0.65
0.30 0.60
0.65 1.28
0.36 0.70
2.65 4.00
1.40
1.30
6.90
14.95 18.40 25.10
0.70 1.64 1.30 1.01 2.80 1.97 1.52 3.28 3.80 4.90 6.54 10.00 8.17 9.80 14.70
1.36 2.73
22.80 27.60
a Data obtained from International Critical Tables of Numerical Data, Physics, Chemistry and Technology; West, C. J., Ed.; US National Research Council, McGraw-Hill Book Co.: New York, 1933. Molarity (M) was converted into molality (m) using Table 2, to obtain σ as the slope of the curve ∆γ vs m.
Figure 6. Threading time as a function of the Gibbs' free energy of hydration for anions (a) and cations (b). The curves are only meant to guide the eye through the data.
already been found for phospholipid vesicles and reported in the literature.29 The opposite behavior performed by anions and cations could be explained by invoking the fact that positive ions can interact with the donor oxygen atoms of the PPG chain and partially displace water of hydration from the polymeric chain. On the other hand, the least hydrophilic anions are expected to move from the aqueous environment and approach the more hydrophobic surface of the PPG chain, inducing surface charge perturbations that push the chain to penetrate the more friendly hydrophobic cavities of β-CD. As opposed to this, the most hydrophilic anions such as sulfate and carbonate, with a high free energy of hydration, would somehow reduce the interaction of water molecules with the polymer, and therefore, the threading process would be retarded with respect to pure water. To discuss the experimental data in terms of microscopic parameters, we have plotted tth as a function of the ionic polarizability (R, Å3) in Figure 7a and 7b, and of the partial molar volume (νs, cm3/mol) in Figure 8a and 8b, respectively. Ionic polarizabilities for halides and alkali ions were taken from the literature,46 and the apparent molar volumes were calculated as47 Figure 5. Threading time as a function of the molal surface tension increment obtained from literature data, for anions (a) and cations (b). In (a) the open circles refer to σ values obtained from ref 40; the filled circles relate to σ obtained from literature data36 of surface tension and density measurements as a function of concentration.
hydration (Ca2+ and Li+). On the other hand, the most relevant inhibiting effects are played by anions with the highest free energy of hydration (CO32- and SO42-), and by cations with the smallest value of -∆Ghydr (Cs+ and K+). This trend has
VM )
M 1000‚(F - F0) F m‚F‚F0
from which the partial molar volumes are obtained as48 νs ) d(m‚VM)/dm, where M, m, F, and F0 are the molecular weight of the solute, the molal concentration of the solution, and the densities of the solution and of the solvent, respectively. The densities of salts aqueous solutions as a function of solute concentration at 25 °C were taken from the literature39 (see Table
Formation of Polypseudorotaxanes
Figure 7. Threading time as a function of the ionic polarizability for anions (a) and cations (b).
2). Although the number of available data for polarizability is very limited, the evidence is that tth decreases as R increases for anions, and increases for cations. The same trend is shown in the case of tth versus νs. It is important to recall that R as well as νs are ultimately connected to the capacity of ions to respond to dipolar electric fields changes. Because of hardness, F- is less sensitive to dispersion forces, and I- is more. Other parameters, such as the refractive index or the dielectric constant could be considered in order to test the validity of this interpretation. These findings may be explained by invoking dispersion forces in the solution as the primary actor in determining the Hofmeister effect. Conclusions The threading process that occurs when aqueous solution of polymers and cyclodextrins are mixed basically depends on the solvent properties and temperature. The driving force of the whole phenomenon is related to the hydrophobic interactions between the polymeric chain and the host cavities, that result in the removal of physical contact between the polymer and water. In other words, water molecules push the hydrophobic long chain toward the hydrophobic CD cavity, so that the formation of the resulting polypseudorotaxane will lead to a consistent stabilization of the entire system. On a microscopic level, the repulsion between solvent and solute concern the molecular water dipoles and the hydrophobic chain groups. This paper reports a study on the kinetics of formation of polypseudorotaxanes from a polypropylene-glycol derivative and β-cyclodextrin in water in the presence of different salts. Our results show that significant changes are induced by anions and cations, according to the Hofmeister’s sequence. The experimental
J. Phys. Chem. B, Vol. 106, No. 9, 2002 2173
Figure 8. Threading time as a function of the apparent molar volume for anions (a) and cations (b) calculated for 0.5 M salts solutions at 25 °C from literature data. The values for HCO3- and SCN- were obtained at 18 °C.
evidence shows that the threading process is strongly related to hydrophobic interactions, as in other lyotropic phenomena. We also determined a qualitative relationship between the threading time and two microscopic parameters, i.e., ionic polarizability and partial molar volumes, that depend on the dispersion forces experienced by the ions in solution, besides the classic electrostatic potential. In conclusion, our results show that the formation of a polypseudorotaxane can be described as a process where hydrophobic forces clearly play the dominant role, and that the extent of salt effects (Hofmeister’s series) is related to the complex microscopic dielectric properties of ions, ion pair, and substrate. Acknowledgment. The authors gratefully acknowledge MURST and CSGI for partial financial support. J.R.L. is grateful to the Brasilian Agency FAPESP Ph.D Program (99/023456). References and Notes (1) Ceccato, M.; Lo Nostro, P.; Baglioni, P. Langmuir 1997, 13, 2436. (2) Harada, A. Coord. Chem. ReV. 1996, 148, 115. (3) Fujita, H.; Ooya, T.; Yui, N.; Macromolecules 1999, 32, 2534. (4) Lo Nostro, P.; Ceccato, M.; Baglioni, P. “Preparation of Polyrotaxanes and Molecular Tubes for Host-Guest Systems” in Polysaccharide Applications, ACS Symp. Series 737, M. A. El-Nokaly and H. A. Soini Eds., ACS, Washington, 1999. (5) Lo Nostro, P.; Lopes, J. R.; Cardelli, C. Langmuir 2001, 17, 4610. (6) Lo Nostro, P.; Ceccato, M.; Rossi, C.; Baglioni, P. J. Phys. Chem. B 1997, 101(26), 5094. (7) Pozuelo, J.; Mendicuti, F.; Mattice, W. L. Macromolecules 1997, 30, 3685. (8) Fujita, H.; Ooya, T.; Yui, N. Macromol. Chem. Phys. 1999, 200, 706.
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