J. Phys. Chem. B 2008, 112, 1071-1081
1071
Threading, Growth, and Aggregation of Pseudopolyrotaxanes Pierandrea Lo Nostro,*,† Luca Giustini,† Emiliano Fratini,† Barry W. Ninham,‡ Francesca Ridi,† and Piero Baglioni† Department of Chemistry and CSGI, UniVersity of Florence, Via della Lastruccia 3, 50019 Sesto Fiorentino (Firenze), Italy, and Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Institute of AdVanced Studies, Australian National UniVersity, Canberra, Australia 0200 ReceiVed: July 10, 2007; In Final Form: October 1, 2007
The formation of supramolecular inclusion compounds (pseudopolyrotaxanes) produced by cyclodextrins and polymers can be monitored through turbidimetry. In this paper, we studied the kinetics of the threading of linear poly(ethylene glycol) chains of different molecular weights and of a four-arm star-like polymer as a function of temperature. The main thermodynamic parameters are extracted. The aggregation and precipitation of pseudopolyrotaxanes are described in terms of the Avrami-Erofe’ev model, which provides relevant information on the mechanism of these processes. SAXS and TGA experiments confirm the structure and hydration of the final products obtained from the different polymers. A new hypothesis for the interaction between pseudopolyrotaxanes that leads to aggregation and precipitation, based on the spatial dielectric anisotropy, is proposed.
Introduction Pseudopolyrotaxanes are supramolecular inclusion complexes obtained by the threading of a linear polymeric guest through strings of cyclic host molecules. One typical example of pseudopolyrotaxanes (PPR) forms when a poly(ethylene glycol) (the guest) and cyclodextrins (CD, the hosts) are dissolved and mixed in water. As a result of the inclusion process, the polymer guest chains are forced to stretch, are confined in the host cavities, and cannot interact directly with other adjacent polymer molecules.1 The formation of PPR from R-CD and poly(ethylene glycol) (PEG) polymers was reported first by Harada.2 Since then, PPR have been studied by several authors with a variety of techniques.1,3-5 Cyclodextrins (CD) are 1 f 4 R-linked cyclic oligomers of glucopyranose and possess a typical toroidal shape with the primary hydroxyl groups at the narrow rim and the secondary -OH residues at the wider edge of the macromolecule (see Figure 1).4 Molecular modeling shows that the two rims are not equivalent in the sense that the larger rim is more hydrophilic while the narrow one is more hydrophobic. Therefore, according to some MD calculations, the CD molecule should possess a nonzero dipole moment directed from the secondary to the primary edge.6-8 PPR are interesting tools for different reasons. They are studied as models for supramolecular assemblies where noncovalent interactions are responsible for highly specific processes (e.g., molecular recognition).1,4 They can be exploited as carriers for drug delivery9 and in organic chemistry for the separation of cyclic products from linear precursors.10 The process that leads to the formation of a PPR is driven by enthalpy. This is because of the more hydrophobic character of the cyclodextrin cavity that generates attractive hydrophobic and van der Waals interactions between the polymer and the * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: +39 055 457-3036. Website: http://www.csgi.unifi.it. † University of Florence. ‡ Australian National University.
Figure 1. Structure of a cyclodextrin made up of “n” 1f 4 R-linked glucose moieties. The green area represents the narrow rim occupied by the primary -OH groups, and the yellow shaded portion indicates the hydrophobic internal cavity of the macrocycle.
CD and is attributed to the formation of hydrogen bonds between adjacent CD rings. Since these forces rapidly vanish with increasing distance between the included guest and the internal surface of the host cavity, inclusion compounds are readily formed when the ratio between the polymer cross section and the internal area of the CD cavity, the so-called space-filling coefficient Φ, is between 0.9 and 1.2.4 In addition, the threading of the polymer requires the release of water molecules into the bulk phase, both from the hydration sheath of the polymer and from the host cavities. Other parameters that affect the formation of PPR are the molecular weight of the polymer, the concentration of the reactants, the temperature, the composition of the solvent (i.e., the presence of other solutes), the state of the guest molecules and the crystalline packing of the host species, and the surface of the vessel where the reaction is taking place.1,11-13 The formation of these supramolecular adducts has been investigated for different systems. In particular, the formation of inclusion complexes from cyclodextrin and PEG or poly(caprolactone) (PCL) is favored when the polymer chain length is increased.1,14,15 In competition experiments, two guests are
10.1021/jp075380q CCC: $40.75 © 2008 American Chemical Society Published on Web 01/09/2008
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Figure 2. Threading of a polymer and of a preaggregate of cyclodextrins, resulting in the formation of pseudopolyrotaxanes (PPR).
simultaneously present in solution, for the same host molecules, in a controlled stoichiometric ratio. Interestingly, these studies reveal the balance between kinetic and thermodynamic control.1 In the case of PEG and PCL with R-CD, the threading seems to take place under kinetic control,14,15 while with poly(Nacetylethylenimine) (PNAI) and γ-CD, the same process is dominated by thermodynamics.16 R-CD forms inclusion compounds also in the presence of neat liquid PEG chains, with a solid-state phase transition from the cage to the channel structure in the host species.17 Similarly, in a previous study, we showed that inclusion compounds are formed when an aqueous solution of β-CD is in contact with molten F(CF2)8(CH2)16H, a diblock, very hydrophobic, semifluorinated n-alkane, above 53 °C. The host-guest complexes immediately aggregated and precipitated in the vial. The elongated and assembled structure of the collected material was confirmed through AFM.18 These experiments show that the mobility of the guest molecule is a key factor; in fact, increments in temperature and/or the amount of polymer accelerate the reaction, while a higher PEG molecular weight results in a decrement of the complexation rate.17 Macroscopically, the whole process proceeds in two steps. First, there is an onset of consistent turbidity after mixing the two reactants. Then follows a precipitation of a white hydrated powder. In case the polymer chain is very long, a thermoreversible gelation occurs, and this prevents a full covering of the guest.19 Due to their very poor solubility in water, once formation is initiated, the inclusion complexes act as nucleation centers and crystallize into channel structures.1,20 The X-ray structures of PPR indicate that the inclusion complexes obtained from R-CD possess a hexagonal symmetry. Further, the CD macromolecules are piled up with a head-to-head and tail-totail order that maximizes the number of hydrogen bonds between the two different rims of CDs, as depicted in Figure 2.4,21 More recently, Goh and Sabadini have reported the formation of PPR starting from different CDs with star-shaped PEOs.22,23 In particular, Goh confirmed that the (EO unit/R-CD) stoichiometry of the PPR in the case of a four-arm poly(ethylene glycol) is slightly larger than the typical 2:1 ratio. This is due to a “linking point effect” that derives from the inaccessibility of the more central EO units by the threading CD macromolecules due to steric restrictions. The same authors report that the final product adopts the classical columnar structure. The time evolution of turbidity at a fixed wavelength (for example, 400 nm) during the formation and precipitation of PPR provides some interesting information on the mechanism and thermodynamics of these processes. The plot is characterized by a sigmoid-shaped curve that shows the presence of different regions (see Figure 3). In the first region (a), for 0 < t < tth, no absorbance change is recorded (Ath). A parameter tth has been
Figure 3. Turbidity plot recorded at 400 nm during the formation, aggregation, and precipitation of PPR. The inset shows the same graph with a linear x-axis scale. The pictures illustrate the turbidity of the same solution at different times. The arrows locate the threading time (tth), the inflection time (ti), and the initial and final absorbance values (Ath and A∞).
defined as the “threading time”. It is directly related to the threading process that involves a certain number of cyclodextrins per single polymer.24 Thereafter, for tth < t < ti, the absorbance starts increasing progressively (region b). For t > ti, the rate decreases until the absorbance levels off (region c) and reaches a more or less constant value (A∞). Threading Process. The threading region, where the absorbance A does not change with time, reflects a multistep process.12,24 This involves (1) the diffusion of the polymer and cyclodextrin molecules in the solvent medium; (2) the initial threading of the host molecules on the guest chain that requires at least a partial stretching of the random coiled polymer chain in solution; (3) the simultaneous release of solvating water molecules from the surface of the polymer and from the cyclodextrin cavities; (4) the sliding of the cyclodextrin molecules along the polymer chain and penetration of more cavities; in this step, CDs force the polymer chain to stretch further and avoid a direct contact between the polymer and the aqueous environment; (5) a partial dethreading of a few cyclodextrins from the polymer’s ends; however, once the CDs molecules have complexed the guest, dethreading is inhibited because of hydrophobic interactions and because the vicinal threaded CD units act as physical stoppers;15 and (6) the
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aggregation of several pseudopolyrotaxanes in bundles that eventually precipitate. The steps of this schematic process are differently effected by temperature.11,25 Recently, on the basis of cryo-TEM, light scattering, and ESR experiments on water solutions of β-CD,26,27 we inferred that, as depicted in Figure 2, cyclodextrins associate in preformed aggregates in water solutions above a certain critical concentration. Such preformed aggregates, whose existence has also been postulated in previous papers,28-31 would act as templates for the formation of pseudopolyrotaxanes.12 Several CD molecules would then thread the polymer chain all at once and not in a “one-by-one” sequence. This process can be repeated depending on the polymer’s chain length. In this way, the correct headto-head/tail-to-tail sequence of CD rings and the relatively short time required for the threading process to occur would be reasonably accounted for. Working with a large excess of cyclodextrin, the threading reaction would then be interpreted as a pseudo-first-order process: polymer + mCD a σ* f pseudopolyrotaxane Here, σ* represents the transition state of the process (rate step), an unstable intermediate structure that corresponds to the activation energy and which then evolves into the final product. With this model, the threading time tth depends on temperature T as24
( )
ln(T‚tth) ) -ln
∆Gqth 3kB - m‚ln[CD] + 2h RT
(1)
In this equation, kB, h, and R are the Boltzmann constant, the Planck constant, and the universal gas constant, and [CD] is the concentration of cyclodextrins; “m” and the Gibbs free energy of activation for the threading process (∆Gqth) can be obtained as fitting parameters. The enthalpic, entropic, and ∆Cqp,th parameters can then be extracted from the data as12
∆Hqth ) -T2‚ ∆Sqth
[
]
∂(∆Gqth/T) ∂T
∆Hqth - ∆Gqth ) T
∆Cqp,th )
( ) ∂∆Hqth ∂T
P
(2)
(3)
Figure 4. Chemical structure of the four-arm STAR polymer.
the same PPR and between different chains are considered to be responsible for the precipitation of the supramolecular adduct.25 Moreover, if the existence of a dipole moment in the CD cavity is confirmed,6-8 this may generate water-mediated attractions between PPR structures and result in aggregation and precipitation of larger aggregates from the solution. We have used the Avrami equation to describe such aggregation/precipitation phenomena.32-34 The Avrami-Erofe’ev and the Prout-Tompkins kinetic models were introduced, and are commonly used, for solid-state reactions like the crystallization or thermal decomposition of inorganic salts.35 However, they hold also in other cases. For example, they apply to the hydration of cement,36 to pharmaceuticals,37,38 coagel phase transitions,39 kinetics of the growth of organogels,40 melting and crystallization of polymers from their cyclodextrin inclusion complexes after removal of the host molecules,41 and encapsulation and release of CO2 from R-CD.42 In this paper, we report our investigation on the kinetics of threading of a four-arm star-shaped PEG (abbreviated as STAR15k), of poly(ethylene glycol) dimethyl ether (DMPG2k), and of PEG1M with R-CD as a function of temperature. From the turbidity curves, we obtain the threading time and the values of m, ∆Gqth, ∆Hqth, ∆Sqth, and ∆Cqp,th. An additional effect that has not been previously considered has also been explored. It is known that dissolved atmospheric gas changes the flocculation rates of hydrophobic colloids, polymerization of lattices, emulsion stability, and other phenomena involving hydrophobic effects.43-45 Consequently, the effect of dissolved atmospheric gases on the threading process is examined in the cases of DMPG2k/R-CD and explored at three different temperatures. In addition, we show that the aggregation and precipitation of the pseudopolyrotaxanes produced by STAR15k and DMPG2k with R-CD in pure water at different temperatures can be described by the Avrami theory. Experiments with TGA and SAXS provide results that elucidate the structure and hydration of the PPR formed.
(4)
The assumptions of the model are (1) the region of the turbidity plot with no change in absorbance is strictly related to the threading time; and (2) the concentration of cyclodextrin is so large that it is hardly changed. Assumption 1 implies that all polymer chains form the PPR during the threading lapse time, tth. The model has been successfully tested with several systems by varying the nature of the polymer, its molecular weight, and the size of the CDs: PEG3.35k + R-CD, (NH2)2PPG2k + β-CD, Pluronic6.5k + γ-CD, PEG8k + R-CD, and DMPG2k + R-CD.11,12,24 We also checked the effect due to the solvent composition (water, heavy water, urea, sugars, and salts).11,12,24 Interestingly, all systems show a negative value of ∆Cqp,th, which reflects hydrophobic effects, and m ranges between 15 and 22. In all of these systems, CD molecules can thread the polymer chain from both ends, independently. Growth and Aggregation. With this as background, we now turn our attention to the phenomena that take place when PPR are formed, start to aggregate, and eventually precipitate. The hydrogen bonds between adjacent CD molecules belonging to
Materials and Methods R-CD (purity g 98%), poly(ethylene glycol) with Mv ≈ 106 (PEG1M), and the end-capped poly(ethylene glycol) dimethyl ether with Mn ≈ 2000 (DMPG2k) were purchased from Fluka (Milan, Italy). The four-arm star-shaped poly(ethylene glycol) with Mw ≈ 15000 (STAR15k) was received from SunBio Inc. (Orinda, CA). All chemicals were used as received. For all experiments, we used bidistilled water purified with a MilliQ system (Millipore) to remove colloidal impurities. The molecular structures for DMPG2k and STAR15k are H3C(O-CH2-CH2)n-OCH3 and C-[CH2-O-(CH2-CH2-O)mH]4, with n ≈ 44 and m ≈ 84, respectively. The structure of the STAR polymer, which has a pentaerythritol core, is depicted in Figure 4. The purity of this polymer is greater than 90%, as declared by the manufacturer. The powder contains 95% of the four-arm molecule, and the remaining 5% is mostly the threearm analogue. Fixed volumes of the guest and of the host water solutions were gently mixed in the cell, and the absorbance measurement (at λ ) 400 nm) was started immediately after, and recorded
1074 J. Phys. Chem. B, Vol. 112, No. 4, 2008
Lo Nostro et al. TABLE 1: The tth (sec), ∆Gqth (kJ/mol), ∆Hqth (kJ/mol), ∆Sqth (J/mol‚K), ∆Cqp,th (J/mol‚K), and m for STAR15k (2.5 mM) + r-CD (0.140 M); χ2 ) 4.0 × 10-3
Figure 5. Y-shaped Pyrex glass vial used for the dissolved gas experiment.
every second, until a thick, solid, white gel was formed. The reference sample was pure water. The final concentration of R-CD was 0.140 M, close to its solubility limit; the concentrations of STAR15k, DMPG2k, and PEG1M were fixed at 2.5, 100, and 0.019 mM, respectively. UV spectra were recorded with a Lambda 5 spectrophotometer (Perkin-Elmer), using a thermostated bath to control the temperature of a Hellma quartz cell ((0.1 °C). The temperature effect was investigated at 15, 20, 25, 30, and 35 °C for STAR15k and DMPG2k. For PEG1M, the turbidity curves were recorded at 15, 18, 20, and 25 °C. In order to study the effect of dissolved gases on the kinetics of threading, the solutions of the reactants (DMPG2k, 100 mM and R-CD, 0.14 M) were transferred in the two separated compartments of a Y-shaped ultrahigh vacuum (UHV) vial (see Figure 5), frozen in liquid nitrogen at atmospheric pressure, brought to 10-5 hPa using an ultravacuum setup connected to a turbomolecular pump, and then warmed up in a thermostated bath at 15, 25, and 35 °C. The freeze-pump-thaw cycle was repeated four times. Then, the two solutions were mixed by rotating the Y-shaped vial, and the turbidity was estimated by visual inspection, against a standard sample, at constant temperature. Each result is the average over 10 measurements. We report in passing that all of the attempts at running the turbidity experiment in Hellma quartz cells (divided in two small compartments to keep the two reactants separated before mixing) at 10-5 hPa were unsuccessful, as the cells broke down during the freeze-pump-thaw cycle. Therefore, the experiment was carried out using the more-resistant Pyrex Y-shaped vials and followed by visual inspection. Thermogravimetry. DSC-TGA measurements were performed with an SDT Q600 apparatus (TA Instruments, Milan, Italy) between 30 and 250 °C, with a scan rate of 20 °C/min and under a nitrogen flux (100 mL/min). About 3 mg of each sample were sealed in an aluminum hermetic pan with a laserdrilled pinhole in the lid. The pinhole prevents early vaporization from the sample and provides a controlled outlet of the vapor. The extra pressure created inside of the pan by increasing the temperature produces a delay in the temperature-dependent weight loss of the sample. This procedure can be used to distinguish between different kinds of water molecules that are differently bound to the sample and that can be sequenced during the TGA scan. Small and Wide-Angle X-ray Scattering. SWAXS measurements were performed on a HECUS SWAX instrument (Kratky camera) with two position-sensitive detectors (OED 50 M, 1024 channels of width 54 µm). A Seifert ID-3003 X-ray
T (°C)
tth ((6%)
∆Gqth ((5%)
∆Hqth ((5%)
∆Sqth ((10%)
∆Cqp,th ((10%)
m
15 20 25 30 35
16 21 26 30 36
-31.8 -31.6 -31.6 -31.7 -31.8
-29.6 -30.6 -31.7 -32.7 -33.8
7.7 3.5 -0.2 -3.3 -6.8
-212.6
23 ( 1
generator provided Cu KR radiation (λ ) 1.542 Å). A 10 mm thick nickel filter was used to remove the Cu Kβ radiation. The sample-to-detector distance was 273 mm. The volume between the sample and the detector was kept under vacuum (P < 1 mbar) during the measurements to minimize scattering from the air. The Kratky camera was calibrated using silver behenate, which is known to have a well-defined lamellar structure (d ) 58.48 Å).46 The scattering angle in the WAXD detector was determined against a LUPULEN standard sample. The experimental setup resulted in a scattering vector (Q ) 4π/λ sin 2θ) range from 0.008 to 0.5 Å-1 in the small-angle and a scattering angle (2θ) range from 18 to 27° in the wide-angle region. The hydrated solid was transferred into a 1 mm X-ray glass Mark tube using a syringe and a centrifuge (about 1000 rpm for 2 min). Measurements were performed at 25 ( 0.1 °C by using a Peltier element. Spectra were acquired for both samples at 40 kV and 30 mA for 7200 s. All scattering curves (slit smeared data) were corrected for the background contribution (glass capillary filled with water) and iteratively slit desmeared according to the procedure described by Lake.47 Results and Discussion Turbidity. All isothermal turbidity curves for PEG1M, DMPG2k, and STAR15k/R-CD show a sigmoidal profile, similar to that illustrated in Figure 3, where the absorbance at 400 nm is plotted versus t on the log scale. The inset shows the same curve with the x axis on the linear scale. The pictures show the evolution of turbidity in the dispersion at different times. The time ti represents the inflection (or inversion) point, where the second derivative changes sign. The reaction between the polymer chain and cyclodextrins is a multistep process that can be summarized in the following manner. (a) The polymer chain penetrates the emptied cavities of the macromolecular hostssafter displacement of the water molecules from the CDs cavitiessand forms the PPR (threading process, region a in Figure 3). (b) The formation of the first stable nuclei takes place, when they reach a critical size,48 and then start growing (region b). (c) Eventually, for t > ti, the particles aggregate into bigger structures and separate from the solution (region c). We will analyze the threading and the aggregation processes separately. Kinetics of Threading. The values of the threading time (tth), the thermodynamic parameters (∆Gqth, ∆Hqth, ∆Sqth, and ∆Cqp,th), and the fit parameter “m” relative to the transition state σ* are listed in Tables 1-3 as a function of temperature for STAR15k, DMPG2k, and PEG1M, respectively. The threading time tth increases with T, confirming that the threading process is favored at low temperature. The Arrhenius plot (∆Gqth/T versus 1/T) for the three cases is shown in Figure 6. The experimental results show the following features. (i) The threading process is controlled by enthalpy (exothermic). The value of ∆Sqth is small for STAR15k and DMPG2k, ranging between -16 and 10 J/mol‚K.
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TABLE 2: The tth (sec), ∆Gqth (kJ/mol), ∆Hqth (kJ/mol), ∆Sqth (J/mol‚K), ∆Cqp,th (J/mol‚K), and m for DMPG2k (100 mM) + r-CD (0.140 M); χ2 ) 1.2 × 10-2 T (°C)
tth ((6%)
∆Gqth ((5%)
∆Hqth ((5%)
∆Sqth ((10%)
∆Cqp,th ((10%)
m
15 20 25 30 35
21 30 35 43 60
-39.0 -38.7 -39.0 -39.0 -38.8
-36.2 -37.5 -38.8 -40.1 -41.4
9.5 4.2 0.6 -3.5 -8.6
-260.4
25 ( 1
TABLE 3: The tth (sec), ∆Gqth (kJ/mol), ∆Hqth (kJ/mol), ∆Sqth (J/mol‚K), ∆Cqp,th (J/mol‚K), and m for PEG1M (0.019 mM) + r-CD (0.140 M); χ2 ) 3.8 × 10-3 ∆Gqth
∆Hqth
∆Sqth
∆Cqp,th
T (°C)
tth ((3%)
((5%)
((5%)
((10%)
((10%)
m
12 15 18 20 25
240 364 516 673 1094
-84.0 -83.9 -83.9 -83.8 -84.0
-81.2 -82.9 -84.7 -85.8 -88.8
9.9 3.3 -2.7 -7.0 -16.1
-583.1
36 ( 1
(ii) The number of CD molecules that participate in the transition state, m, is about 24 for STAR15k and DMPG2k and 36 for PEG1M. This finding confirms previous results that show that m changes with the molecular weight and hydrophobicity of the polymer. In fact, for (NH2)2PPG2k/β-CD, PEG3.35k/R-CD, and PEG8k/R-CD, we found that m is 16, 20, and 31, respectively.12 (iii) On the other hand, m depends also on the initial concentration of cyclodextrin. In an earlier study on the formation of PPR from DMPG2k(1.67 mM)/R-CD(49 mM) mixtures, we obtained a lower value for m (15).12 In the same paper, we showed that for [R-CD] below 40 mM, there is no onset of turbidity, and the PPR formed are in equilibrium with free polymer and host molecules.12 More recently, Horsky and Porsch found that the precipitation of a PPR from R-CD and different PEG polymers occurs when the concentration of the host molecule is larger than about 44 mM.49 These effects are probably related to the formation of the preassembled aggregates of CD. This occurs only above a critical concentration, depending on temperature, the kind of macrocycle (R, β, or γ), and the presence of other cosolutes.12,26,27 In the present study, we are working with more concentrated solutions of R-CD, close to its solubility limit. Hence, we can reasonably expect the stability of the preassembled aggregates to be greater than that in a more-diluted solution of CD, and the number of cyclodextrin rings that participate in the transition state is expected to be larger. (iv) The heat capacity change is negative. This reflects a hydrophobic effect that controls the threading process.50 (v) ∆Hqth and ∆Sqth decrease with T. Although these parameters almost balance and produce small changes in ∆Gqth, the negative value for ∆Cqp,th indicates an enthalpy/entropy compensation. In particular, the slope of T∆Sqth versus ∆Hqth is 0.998 for STAR15k and DMPG2k and 1.005 for PEG1M, reflecting the larger entropy contribution in the latter case.51 (vi) Table 4 shows the values of ∆Gqth (at 298 K) and m obtained in this and in previous studies on different systems, PEG, DMPG, poly(propylene glycol) bis(2-aminopropyl ether) (shortly (NH2)2PPG), Pluronic (PLU), and STAR with R-, βor γ-CD, and in different solvents (H2O, D2O, and urea, 0.1 M).12 Briefly, ∆Gqth/m reaches the maximum absolute value for (NH2)2PPG/β-CD (-6.5) and PLU/γ-CD (-5.3) PPR, compared to the PEG-based/R-CD adducts (about 3), probably due to the
Figure 6. Arrhenius plots for STAR15k (b), DMPG2k (0), and PEG1M (O).
TABLE 4: Values of ∆Gqth and ∆Gqth/m for Different Polymer/CD Complexes at 298 K guest
host
solvent
∆Gqth (kJ/mol)
DMPG2k (NH2)2PPG2k (NH2)2PPG2k (NH2)2PPG2k (NH2)2PPG2k PEG3.35k PEG3.35k PEG3.35k PEG3.35k PLU6.5k PEG8k STAR15k PEG1M
R-CD β-CD β-CD β-CD β-CD R-CD R-CD R-CD R-CD γ-CD R-CD R-CD R-CD
H2O H2O H2O/D2O 1:1 D2O urea 0.1 M H2O H2O/D2O 1:1 D2O urea 0.1 M H2O H2O H2O H2O
-39.0 -104.4 -93.7 -131.9 -98.5 -53.7 -53.5 -70.8 -38.8 -101.7 -101.5 -31.6 -28.1
m
∆Gqth/m
25 16 15 18 16 20 21 22 19 19 31 23 36
-1.6 -6.5 -6.3 -7.3 -6.1 -2.7 -3.0 -3.2 -2.0 -5.3 -3.3 -1.4 -0.8
better matching between the polymer cross section and the cavity available area in the former cases.4 In the case of PEG derivatives, ∆Gqth/m increases with the polymer chain length, confirming that the threading process is favored for highmolecular-weight guests,1,14 with the exception of STAR15k (-1.4). However, it must be noted that STAR15k carries four independent threading sites instead of two. For PEG1M, the very low value of ∆Gqth/m is probably due to the partial covering of the very long polymer chain.4,23 It is interesting to note that the solvent composition plays a role in determining ∆Gqth. With respect to pure water, D2O favors and urea does not favor the threading process due to the different stabilization of hydrogen bonds.11 (vii) It is interesting to note that when plotting ∆Hqth versus T, the data for the three different polymers produce straight lines that all intersect at about 150 K (see Figure 7). This observation confirms the results found in previous studies.12,50 (viii) The effect of degassing on the kinetics of threading for DMPG2k/R-CD at 15, 25, and 35 °C is shown in Table 5. The results indicate that after removing the dissolved gases, the threading process is about 40% faster than that in the presence of atmospheric dissolved gases. Although the experiment was carried out through a visual observation, the acceleration of the threading reaction is evident and significant. The number of CD molecules involved in the formation of the transition state (m) remains practically constant. The calculation of the Gibbs free energy, enthalpy, entropy, and specific heat capacity changes after degassing indicates that the threading process is more favored when dissolved gases are depleted from the reaction medium. It is driven by enthalpy, and controlled by hydrophobic interactions. Although the variations are small due to the apparently small influence of such interactions, the effect is real and reproducible. The mechanism of such an effect can
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Figure 7. ∆Hqth versus T for STAR15k (b), DMPG2k (0), and PEG1M (O).
TABLE 5: The tth Ratio between the Degassed and the Nondegassed Samples, ∆Gqth Change (kJ/mol), ∆Hqth Change (kJ/mol), ∆Sqth Change (J/mol‚K), and ∆Cqp,th (J/mol‚K) for DMPG2k (100 mM) + r-CD (0.140 M) after Degassing T (°C)
tth,deg/tth,gas ((10%)
∆∆Gqth ((10%)
∆∆Hqth ((10%)
∆∆Sqth ((20%)
∆∆Cqp,th ((20%)
15 25 35
0.39 0.46 0.47
-6.9 -6.8 -7.0
-6.2 -6.6 -7.1
2.6 0.4 -0.4
-45
be presumably ascribed to the interaction of microbubbles with the polymer and the R-CD molecules before the formation of the PPR and/or to the release of gas molecules (mainly carbon dioxide) included in the CD cavity.52 Upon degassing, the (hydrophobic) microbubbles are depleted from the surface of the guest chain and from the cavity of the host rings, and the threading process can take place at a faster rate with respect to the same reaction carried out in the presence of the dissolved atmospheric gases. The degassing procedure would also deplete gas molecules (especially CO2) associated to the internal cavity of CDs and therefore make the threading of the polymer easier. In any case, this dissolved gas effect parallels the phenomenon that we observed in the cloud point temperature of a short-chain lecithin in water dispersion 53 and mimics the accelerating effect induced by the presence of poorly hydrated (chaotropic) anions (such as NO3-, I-, and SCN-) on the formation of PPR from poly(propylene glycol) and β-CD.54 Growth and Aggregation of PPR. For an isothermal process, the relative change in absorbance (R) denotes the fraction of reactant (PPR) transformed at time t, and we can write
R(t) )
[PPR]t - [PPR]th [PPR]∞ - [PPR]th
)
A - Ath A∞ - Ath
(5)
A, Ath, and A∞ are the absorbance values at time t, at time tth, and the final constant value when the aggregation process is complete, respectively. At time t e tth, R ) 0, and when t . ti, R ) 1. According to the Avrami theory, we have
ln[-ln(1 - R)] ) M‚ln k + M‚ln(t - tth)
(6)
where k is the rate constant and M is the exponent associated with the nucleation type and related to the dimensionality of the product phase, type of growth, and nucleation rate. Figure 8 shows, as an example, R and ln[-ln(1 - R)] versus ln(t - tth) for the formation of PPR from STAR15k and R-CD at 15 °C. The other cases are similar. The dotted lines identify the point of inversion (ti) at which R ≈ 1/2. The values of ti for the different cases are reported in Table 6. Since the curve (open
Figure 8. Plot of ln[-ln(1 - R)] (b, left y axis) and R (O, right y axis) versus ln(t - tth) for STAR15k/R-CD at 15 °C. The intersection of the two straight lines identifies the value of ti, where R ) 1/2.
circles) that describes R(t) is symmetrical with respect to ti, we can use the Avrami equation to describe the variation of R as a function of t.35 The plot shows that the slope M of the curves before and after ti is significantly different, indicating that two different processes take place.55 Figure 9 shows all of the ln[-ln(1 - R)] versus t curves obtained for STAR15k/R-CD (a) and DMPG2k/R-CD (b) pseudopolyrotaxanes in water at different temperatures. A perusal of the curves shows that the two systems behave differently, as in previous findings.55 In both cases, the whole reaction involves two steps, a fast process for t < ti, related to the nucleation and growth of the first nuclei, followed by a slower process (for t > ti) that involves the precipitation of large aggregates. The values of ln k and M extracted from the fitting of the experimental curves according to eq 6 are listed in Table 6. The Avrami exponent M provides interesting information on the mechanism involved in the process described by the model6
M ) a + bc
(7)
where a is the nucleation index and indicates the time dependence of the number of nuclei per unit volume of reactant (a ) 0 for zero nucleation rate, and a ) 1 for constant nucleation); b is the dimensionality of the growth (b ) 1, 2, 3 for mono-, bi- and tridimensional growth, respectively); and c is a growth index that depends on the rate-determining step of the transformation (c ) 1 for phase boundary control, and c ) 1/ for diffusion-controlled processes). For a given value of M, 2 different combinations of (a,b,c) are possible, in principle. We will discuss the results for STAR and DMPG separately. STAR12k/R-CD. In this case, the values of M are 1.5 and 1.0 for the growth and precipitation processes, respectively. The M ) 1.5 can be obtained by two possible combinations, by (1,1,1/2) or by (0,3,1/2). Given the linear structures of the PPR, it is reasonable to expect that once formed, they start to aggregate side-by-side.25 Since this aggregation occurs at the extended surface of the cylinders, the process is optimized by the correct parallel orientation of the rods. As depicted in Figure 10, the maximum number of contacts between the four arms of the threaded polymer is obtained when the PPR pile up and form a ribbon. This would confirm the combination (1,1,1/2), constant nucleation rate and monodimensional, diffusioncontrolled growth. For similar reasons, in the slow process where M ) 1, the combination (0,1,1) should be selected (no nucleation, linear growth under phase boundary control). DMPG2k/R-CD. For this system, the values of M are calculated as 2.5 and 1.0 for the two steps. Since the PPR have a rod-like structure (see Figure 10), the correct combination of
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J. Phys. Chem. B, Vol. 112, No. 4, 2008 1077
TABLE 6: Values of ti (in sec, (10%), ln k, and M for the Growth and Precipitation Processes of STAR15k and DMPG2k/r-CD, Calculated from the Experimental Turbidity Curves and from Eq 6 STAR15k/R-CD T
ti
ln k
M
15° 20° 25° 30° 35°
150 370 640 860 1100
growth -8.77 ( 0.04 -8.65 ( 0.16 -8.49 ( 0.07 -8.25 ( 0.08 -8.07 ( 0.04
1.6 1.5 1.4 1.3 1.3
DMPG2k/R-CD ln k precipitation -4.15 ( 0.15 -5.28 ( 0.11 -6.12 ( 0.07 -6.94 ( 0.04 -7.70 ( 0.07
(a,b,c) seems to be (0,2,1/2) for the precipitation (zero nucleation rate, bidimensional diffusion-controlled growth) and (3/2,2,1) for the growth (increasing nucleation rate, bidimensional growth under phase boundary control). These results indicate that the growth and aggregation of PPR are controlled by the architecture of the polymer chain, which determines the structure of the supramolecular adducts, and the extension of their binding sites. Activation Energy. According to the Eyring model for a thermally activated process, we have
ln k ) ln
( )
kBT ∆Gq h RT
(8)
from which we obtain
ln
() ( )
kB k ∆Sq ∆Hq ) ln + T h R RT
(9)
so that the values of ∆Hq and ∆Sq can be evaluated by plotting ln(k/T) versus 1/T (see Table 7 and Figure 11). The variation of the heat capacity is calculated as ∆Cqp ) (∂∆Hq/∂T)p. The results indicate that the growth of pseudopolyrotaxanes, which involves the breaking of hydrogen bonds, release of hydration water molecules into the bulk phase, and intermolecular interactions between the associating PPR, is driven by an enthalpic contribution, with a positive value of ∆Cqp. The entropic term is quite small and positive in the case of DMPG2k, while its value is negative and larger for STAR15k, a result that reflects the particular order built up during the formation and
M
ti
ln k
M
0.8 0.9 1.0 1.1 1.1
220 280 315 350 400
growth -16.13 ( 0.01 -15.23 ( 0.04 -14.55 ( 0.03 -13.74 ( 0.02 -12.90 ( 0.10
2.4 2.7 2.5 2.3 2.4
M
precipitation -2.31 ( 0.01 -3.86 ( 0.01 -4.57 ( 0.01 -5.77 ( 0.01 -6.58 ( 0.07
0.7 0.7 0.8 1.0 1.0
growth of the nuclei (see Figure 10). Moreover, the lower value of ∆Hq for STAR15k (5 times smaller than that for DMPG2k) is related to the partial covering of the star-like polymer and is also the results of the steric and geometric constraints imposed by the central cross-linking branch. The different values of ∆Hq for the growth processes of STAR15k and DMPG2k reflect also the fact that in the former case, the process is controlled by diffusion, while the latter is under phase boundary control.57 Interactions. Different kinds of intermolecular interactions and structural features are supposed to be responsible for the formation of the polymer/CD inclusion complexes. They include dipolar interactions, van der Waals and hydrophobic forces, hydrogen bonding, conformational changes and crystalline packing in the hosts, the space-filling coefficient, and depletion of cavity-bound water molecules.1,4 In particular, as we reported in the Introduction, hydrogen bonding is thought to be responsible for the aggregation and precipitation of PPR. However, a more subtle mechanism can be invoked to justify such behavior. The key factor is spatial dielectric anisotropy. In fact, a PPR composed of a PEG chain threaded by a sequence of CD macrocycles possesses different dielectric properties along the main axis (|) and in the perpendicular direction (⊥). In the parallel direction, the molecular structure of the PPR is composed of many repeated -O-CH2-CH2- units, with a continuous coaxial coating of CD rings. In the perpendicular direction, the dielectric properties are those of a single cyclodextrin that includes the EO groups. While a monomeric PEG in solution can adopt a coiled conformation and decrease the dielectric anisotropy, in the PPR state, the polymer chain is forced to remain in a tubular stretched conformation by the surrounding coordinating cyclodextrin rings. This dielectric anisotropy gives rise to an interaction that can be calculated.58 According to the formula obtained by Parsegian and Mitchell,59-61 the van der Waals interaction energy per unit length between long parallel cylindrical rods separated by distances (R) much larger than their thickness (2a) depends on the rod radius, temperature (T), and dielectric susceptibility of the embedding medium (m) as a summation over the rods
g(R) ) -
Figure 9. Plots of ln[-ln(1 - R)] versus ln(t - tth) for STAR15k/RCD (a) and DMPG2k/R-CD (b); 9: 15 °C; b: 20 °C; 2: 25 °C; [: 30 °C; 1: 35 °C.
ln k
9πa 4kBT 16R5
∞
[
∆2⊥ + ∑ ν)0
(
∆ ⊥ | - m 4
)
- 2∆⊥ + m 3 | - m - 2∆⊥ 128 m
(
)] 2
(10)
where ν is the frequency at which is measured and ∆⊥ ) (⊥- m)/(⊥ + m). For skewed rods, the equation includes also the angular dependence. The formula accounts correctly for the temperature dependence of the interaction. In fact, the experiments have shown that the aggregation (and precipitation) of the PPR increases at higher temperatures, which is justified by the temperature dependence of g(R) in eq 10. A rough
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Lo Nostro et al.
Figure 10. Schematic aggregation of PPR produced by STAR15k (a) and DMPG2k (b) with R-CD. The arrows indicate the directions of growth of the aggregates that optimize the contact between adjacent PPR.
TABLE 7: Values of ∆Hq (kJ/mol), ∆Sq (J/mol‚K), and ∆Cqp (J/mol‚K) for the Growth of PPR Aggregates as Obtained from Eq 9, by Fitting the Data Reported in Table 6 STAR15k/R-CD DMPG2k/R-CD
∆Hq
∆Sq
∆Cqp
23.9 ( 2.0 114.7 ( 2.8
-235 ( 7 20 ( 10
161 771
calculation shows that g(R) is always negative, and therefore, a strong attraction between parallel cylindrical PPR is generated.58-61 Although a more refined calculation of the dielectric constant components in the parallel and perpendicular directions is necessary, nonetheless, g(R) provides an interesting explanation at the microscopic level of the cooperative, nonadditive, attractive interaction, which leads to the aggregation of the formed PPR in solution simply due to their molecular architecture and dielectric properties. Tonelli’s group has shown that dioxane solutions of poly(caprolactone) (PCL) and of poly(L-lactic acid) (PLA) both produce inclusion compounds with aqueous R-CD.62 However, when the two polyesters are simultaneously present in the dispersion and compete for the same R-CD cavities, only PCL forms inclusion adducts with R-CD and not PLA, despite the longer PLA chain (Mw ) 285000) with respect to the PCL polymer (Mw ) 65000). Moreover, PLA has a small capacity to displace PCL from preformed inclusion compounds, while PCL is more efficient in causing the dethreading of PLA from complexes with R-CD.62 This effect can be explained in terms of difference in hydrophobicity between PCL and PLA, which is the major driving force for inclusion into R-CD cavities. On the other hand, the interaction expressed by g(R) in eq 10, which we propose to be responsible for the PPR aggregation, emerges only when the PPR are already formed and originates from the dielectric anisotropy of the cylindrical long structure of pseudopolyrotaxanes. Thermogravimetric Analysis. TGA experiments were run between 30 and 260 °C on pseudopolyrotaxanes obtained from STAR15k and DMPG2k with R-CD, after centrifugation to get rid of the water excess. In this temperature range, the samples loose about 87 (for DMPG2k) and 90% (for STAR15k) of their mass due to water evaporation. The sample holder (pan) possesses a laser-drilled tiny pinhole that prevents fast vaporization of water from the sample and allows us to distinguish
Figure 11. Plot of ln(k/T) versus 1000/T for the growth process of STAR15k/R-CD (O) and DMPG2k/R-CD (0).
different kinds of water that may be present in the sample. A blank TGA measurement was carried out on pure water as a reference (data not shown). The measurements are very reproducible. The experimental points (open circles and squares in Figure 12) were fitted with four Gaussian contributions
y ) y0 +
1
x2π
4
yi
[
‚exp ∑ i)1 σ i
]
(T - Ti)2 2σ2i
(11)
where y0, yi, Ti, and σi are fitting parameters extracted from the experimental data. For each peak, Ti, σ2i , and yi represent the mean, the variance, and the weight of that contribution to the total curve (y), respectively. The extracted fitting parameters suggest that when PPR precipitate, they associate with two different kinds of water molecules. One type is strongly bound to the PPR aggregates and evaporates at a higher temperature (126.7° for DMPG2k and 134.6 °C for STAR15k). The other is retained less and is released at a lower temperature (118.3° for DMPG2k and 115.3 °C for STAR15k). Note that the temperature difference between DMPG and STAR is larger in the case of the strongly interacting water molecules. Interestingly, Table 8 shows that while the mass fraction of strongly bound water molecules for DMPG is about 19.3%, it is 39.3% for STAR. This evidence reflects the different structures and arrangements of the PPR produced by the two polymers. In fact, DMPG aggregates are organized in a tighter packing, but STAR carries many more
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J. Phys. Chem. B, Vol. 112, No. 4, 2008 1079
Figure 12. Thermograms for STAR15k/R-CD (0) and DMPG2k/R-CD (O). The full black lines are the fitting curves obtained from eq 11. The colored lines are the four Gaussian curves deconvoluted from the data (blue for 1, full red for 2, green for 3, and dotted red for 4).
TABLE 8: Fitting Parameters Obtained According to Eq 11 from the DSC-TGA Measurements for STAR15k and DMPG2k (see Figure 9) T1 (°C) T2 (°C) T3 (°C) T4 (°C) χ2 R2 mass fraction 1 mass fraction 2 mass fraction 3 mass fraction 4
STAR15k
DMPG2k
102.4 107.3 115.3 134.6 2.6472 0.9989 6.1% 54.4% 35.2% 4.3%
103.7 107.7 118.3 126.7 1.3647 0.99957 7.2% 73.5% 4.1% 15.2%
EO units per arm (about 84) than DMPG (about 44) and therefore threads more cyclodextrin units. The thermogravimetric analysis shows that the hydrated DMPG2k/R-CD PPR lose about 87% of their initial weight due to the loss of water upon heating between 50 and 250 °C. Of this, 19.3% is strongly bound water according to Table 8 (peaks 3 and 4). The weight fraction of strongly bound water is given by the formula
MwnwNCD ) P‚∆W Mpol + MwnwNCD + MCDNCD
(12)
where Mw, Mpol, and MCD are the molecular masses of water, of the polymer, and of R-cyclodextrin, respectively. The nw and NCD indicate the number of strongly bound water molecules associated to each CD moiety and the number of CD rings that thread one single polymer chain. P and ∆W are the percentage of strongly bound water (detected from the deconvolution of the TGA curve) and the water loss during the heating, respectively. From eq 12 and the thermogravimetric data, it is easy to calculate that the number of strongly bound water molecules per CD comes out to be 11 if 22 CD rings thread each DMPG polymer. These strongly bound water molecules are sandwiched between the CD molecules in the PPR, stabilize the structure, and strengthen the intermolecular interactions between adjacent cyclodextrins.12,29 In the case of STAR12k/R-CD, considering that the EO/CD stoichiometric ratio is about 2.2:1,22 we can calculate the number
of CDs that thread each single arm to be about 38. Since the hydrated STAR12k/R-CD PPR releases 90% of its weight as water vapor and since 39.5% of this amount is strongly bound to the supramolecular assembly, then the number of bridging water molecules per CD unit comes out to be about 8. These values are different from that reported by Tonelli et al. in their study on “air-dried” R-CD columnar structures (about 6.7 molecules of water per CD).63 However, it is important to recall that in Tonelli’s work, the (pure) R-CD powder was obtained by pouring the R-CD aqueous solution into cold chloroform and after vacuum filtration and overnight exsiccation under vacuum draft. Instead, in the present work, we investigated the behavior of pseudopolyrotaxanes obtained by the linear DMPG and the four-arm STAR polymers with R-CD. Furthermore, our PPR were simply centrifuged to remove the excess water and not dried in a more vigorous manner. This difference in the samples’ composition and preparation can justify the discrepancy between the final results. In any case, the number of water molecules per single CD reported by Tonelli is quite close to what we found for the STAR/R-CD PPR. Small- and Wide-Angle X-ray Scattering. SAXS measurements were performed on hydrated PPR obtained from DMPG2k/ R-CD and STAR15k/R-CD. Figure 13a shows the SAXS profiles for both samples. At low Q values (below 3 × 10-2 Å-1), the I versus Q log/log plot shows a linear trend with a slope of -2.5 for STAR15k/R-CD and -4 for DMPG2k/R-CD. In the case of DMPG2k/R-CD, the profile accounts only for the scattering of a smooth surface (i.e., the overall dimension of the aggregate is greater than the instrumental resolution, 50 nm).64 For STAR15k/R-CD PPR, a preliminary analysis of the very low Q region according to the Guinier approximation gives an apparent radius of gyration (Rg) of 23 nm. A peculiarity of this spectrum is the abrupt change of slope at about 0.03 Å-1 that corresponds to a characteristic dimension of about 10 nm. If we consider this dimension as the thickness (t) of a discoid structure
R2g )
t2 r 2 + 12 2
(13)
then its radius (r) comes out to be 32.5 nm, which matches very well the length of one single arm in the fully stretched conformation (15000/4)‚0.375 ≈ 31.6 nm (see Figure 10). Figure 13b shows the wide-angle X-ray diffraction patterns of the DMPG2k/R-CD and STAR15k/R-CD hydrated solids. Both WAXD spectra are different from those of the host and of the guest species (data not shown).65 In particular, for DMPG2k/RCD, the peaks observed at scattering angles of about 20 (d ) 4.44 Å) and 22.6° (d ) 3.96 Å) are usually assigned to the 210 and 300 reflections from a hexagonal lattice with a characteristic dimension of 13.6 Å. The reflection at about 7.60° (d ) 11.6 Å) in the expanded view of the SAXS spectra (Figure 13c) agrees with the proposed lattice structure depicted in Figure 10 and can be indexed as 100. The strong 210 reflection is a typical feature observed for polymer inclusion complexes with R-CD65,66 and agrees with the overall external diameter dimension of R-CD molecules, about 14 Å. The overall molecular architecture is consistent with a channel-type crystalline structure due to the long-chain nature of the guest molecules that can be referred to as a columnar crystalline structure.65 It is important to note that all reflections appear as a doublet, confirming the coexistence of two distinct columnar structures with different amounts of bound water and hence different dimensions. Furthermore, the intensity ratios show that the more abundant peak corresponds to the more hydrated and bigger
1080 J. Phys. Chem. B, Vol. 112, No. 4, 2008
Lo Nostro et al. sandwiched between the CD rings. Again, the presence of a doublet confirms the presence of two different hydrations of the columnar structure also in the axial direction. All of these characteristic reflections appear, but less defined and less intense, in the profile for the STAR15k/R-CD hydrated solid. In this case, the columnar structure is less ordered as a result of the branched nature of the parent polymer (see Figure 10). In the axial direction, a strong displacement disorder is reflected by the very broad peak at 5.0°. As expected, DMPG/ R-CD PPR possess a higher degree of crystallinity compared to those obtained from STAR15k/R-CD. The experimental results suggest that the strongly bound water is bridging the adjacent cyclodextrin macrocycles and stabilizes the entire structure of the single PPR through hydrogen bonding. Conclusions
Figure 13. SWAXS spectra for STAR15k/R-CD (0) and DMPG2k/RCD (O) PPR. (a) SAXS profiles for 0.01 < Q < 0.5 Å-1. (b) WAXD spectra for 18° < 2θ < 25°. (c) Enlargement of the SAXS spectra between 0.3 and 0.55 Å-1.
structures. The nonequatorial reflections (5.6°/001, 11.2°/002, etc.) of the PEG inclusion complex show an axial repeating distance of 15.8 Å, corresponding to the sequence of two R-CD macrocycles around the polymer chain (the height of each CD is 7.8 Å). Huh et al. reported that in the case of a PEG-grafted dextran inclusion complex hydrogel, this reflection (001) can shift to a lower diffraction angles (5.4°) due to an increase of the axial period (16.3 Å) associated with the presence of water molecules bound in the R-CD sequence of the hydrogel.67 Extra peaks are evident at 4.8 and 5.2° for DMPG2k/R-CD and correspond to the 100 nonequatorial reflection associated with axial periods of 18.3 and 16.9 Å. These distances account for the space occupied by the bridging water molecules that are
When mixed in an aqueous solution, R-cyclodextrins (R-CDs) and poly(ethylene glycol) chains produce host-guest complexes named pseudopolyrotaxanes (PPR), where several host rings thread one single polymer molecule. The threading, aggregation, and precipitation of these supramolecular entities can be followed by turbidimetry and studied as a function of temperature. The kinetic model for the threading process that we proposed in previous works was tested on two different linear and four-arm star-like PEG polymers. The number of cyclodextrin macrocycles involved in the formation of the activation state (m) was determined together with the thermodynamic parameters for the threading process (∆Gqth, ∆Hqth, ∆Sqth, and ∆Cqp,th) by fitting the experimental data. The main findings suggest the following conclusions. (1) The inclusion process is driven by enthalpy and favored by lower temperature. The value of ∆Cqp is always negative, indicating that the hydrophobic effect is dominating the entire inclusion process. (2) The number of R-CDs that participate in the transition state (m) depends on the molecular weight and hydrophobicity of the guest polymer and on the initial concentration of R-CD. When the concentration of R-CD is lower than 40 mM, PPR are not formed. This result confirms the hypothesis that the host molecules preaggregate in solution and thread the polymer chain all at once and not with a “one-by-one” stepwise mechanism. (3) When the reaction is carried out starting from degassed solutions, the threading time is much shorter (about 40%). This effect has been related to the depletion of gas molecules (especially CO2) from the internal cavity of R-CD and/or to the removal of microbubbles from the reactants molecules. The Avrami-Erofe’ev model was used to describe the mechanism that controls the aggregation and precipitation of PPR produced by R-CD with the linear DMPG2k and with the four-arm STAR15k polymers. In both cases, the fast aggregation of PPR proceeds with a mechanism that involves nucleation, while the dimensionality depends on the molecular structure of the starting polymer, monodimensional growth for STAR and bidimensional for DMPG. The thermodynamic parameters were calculated for the two processes and indicate that the aggregation occurs with a positive ∆H, while the precipitation of the aggregates is promoted at higher temperatures. TGA and SAXS experiments were performed to investigate the structure of the aggregates that separate from the solution and to obtain information on the hydration and packing of the PPR. Interestingly, the SAXS results confirm the packing arrangements formed by the PPR aggregates predicted by the calculation of the Avrami coefficient and the presence of bridging, strongly bound water molecules between adjacent cyclodextrin macro-
Threading, Growth, and Aggregation of PPR cycles. Finally, in order to justify the aggregation and precipitation of PPR, we propose that the spatial anisotropy of dielectric properties in PPR is responsible for the onset of a strong attractive interaction between these supramolecular structures in solution. This kind of interaction, which simply requires the presence of dielectric anisotropy in the dispersed particles, is proportional to temperature, as shown by the experiments. As pointed out by Tonelli,1 the threading of polymers in CDs seems to be a general phenomenon due to their long-chain structure. Specificity and discrimination operated by cyclodextrin during the inclusion process emerge clearly in competition experiments, where two or more guests compete for the same host cavities. Here, we propose that the organization of the long and thin PPR, where the included guests are forced in a stretched conformation, produces a spatial difference in the dielectric properties, which results in a net attractive interaction leading to aggregation and precipitation of the supramolecular assemblies. Acknowledgment. The Authors acknowledge the Consorzio Interuniversitario per lo Sviluppo dei Sistemi a Grande Interfase (CSGI, Florence) and the Ministero dell’Istruzione, dell’Universita` e della Ricerca (MIUR, Rome) for partial financial support. References and Notes (1) Rusa, C. C.; Rusa, M.; Peet, J.; Uyar, T.; Fox, J.; Hunt, M. A.; Wang, X.; Balik, C. M.; Tonelli, A. E. J. Inclusion Phenom. Macrocyclic Chem. 2006, 55, 185-192. (2) Harada, A.; Kamachi, M. Macromolecules 1990, 23, 2821-2823. (3) Harada, A. Coord. Chem. ReV. 1996, 148, 115-133. (4) Wenz, G.; Han, B.-H.; Mu¨ller, A. Chem. ReV. 2006, 106, 782817. (5) Huang, F.; Gibson, H. W. Prog. Polym. Sci. 2005, 30, 982-1018. (6) Lipkowitz, K. B. Chem. ReV. 1998, 98, 1829-1874. (7) Lichtenthaler, F. W.; Immel, S. Tetrahedron: Asymmetry 1994, 5, 2045-2060. (8) Yasuda, S.; Miyake, K.; Sumaoka, J.; Komiyama, M.; Shigekawa, H. Jpn. J. Appl. Phys. 1999, 38, 3888-3891. (9) Li, J.; Ni, X.; Leong, K. W. J. Biomed. Mater. Res. 2003, 65A, 196-202. (10) Singla, S.; Zhao, T.; Beckham, H. W. Macromolecules 2003, 36, 6945-6948. (11) Lo Nostro, P.; Lopes, J. R.; Cardelli, C. Langmuir 2001, 17, 46104615. (12) Becheri, A.; Lo Nostro, P.; Ninham, B. W.; Baglioni, P. J. Phys. Chem. B 2003, 107, 3979-3987. (13) Lo Nostro, P.; Ninham, B. W.; Baglioni, P. In Self-Assembly; Robinson, B. H., Ed.; IOS Press: Amsterdam, The Netherlands, 2003; ISBN: 1-58603-382-4. (14) Rusa, C. C.; Tonelli, A. E. Macromolecules 2000, 33, 1813-1818. (15) Rusa, C. C.; Luca, C.; Tonelli, A. E. Macromolecules 2001, 34, 1318-1322. (16) Rusa, M.; Wang, Z.; Tonelli, A. E. Macromolecules 2004, 37, 6898-6903. (17) Peet, J.; Rusa, C. C.; Hunt, M. A.; Tonelli, A. E.; Balik, C. M. Macromolecules 2005, 38, 537-541. (18) Lo Nostro, P.; Santoni, I.; Bonini, M.; Baglioni, P. Langmuir 2003, 19, 2313-2317. (19) Girardeau, T. E.; Zhao, T.; Leisen, J.; Beckham, H. W.; Bucknall, D. G. Macromolecules 2005, 38, 2261-2270. (20) Hunt, M. A.; Tonelli, A. E.; Balik, C. M. J. Phys. Chem. B 2007, 111, 3853-3858. (21) Topchieva, I. N.; Tonelli, A. E.; Panova, I. G.; Matuchina, E. V.; Kalashnikov, F. A.; Gerasimov, V. I.; Rusa, C. C.; Rusa, M.; Hunt, M. A. Langmuir 2004, 20, 9036-9043. (22) Jiao, H.; Goh, S. H.; Valiyaveettil, S. Macromolecules 2002, 35, 1980-1983. (23) Sabadini, E.; Cosgrove, T. Langmuir 2003, 19, 9680-9683. (24) Ceccato, M.; Lo Nostro, P.; Baglioni, P. Langmuir 1997, 13, 24362439.
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