Aggregation of Cesium Perfluorooctanoate on Poly(ethylene glycol

able to interact with shorter PEG oligomers. The average number of surfactant molecules bonded per polymer chain at the saturation is about twice that...
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J. Phys. Chem. B 2006, 110, 9112-9121

Aggregation of Cesium Perfluorooctanoate on Poly(ethylene glycol) Oligomers in Water Paolo Gianni,* Arianna Barghini, Luca Bernazzani, Vincenzo Mollica, and Pietro Pizzolla Dipartimento di Chimica e Chimica Industriale, UniVersita` di Pisa, Pisa, Italy ReceiVed: January 31, 2006; In Final Form: March 23, 2006

The interaction of cesium perfluorooctanoate (CsPFO) with poly(ethylene glycol) (PEG) of different molecular weight (300 e MW e 20000 Da) has been investigated at 298.15 K by isothermal titration calorimetry (ITC), density, viscosity, and conductivity measurements. Calorimetric titrations exhibited peculiar trends analogous to those already observed for sodium dodecyl sulfate (SDS). Micelles of the perfluorosurfactant, as compared to those of SDS, yield complexes with the polymer of similar thermodynamic stability but are able to interact with shorter PEG oligomers. The average number of surfactant molecules bonded per polymer chain at the saturation is about twice that observed for SDS. ITC data at 308.15 K indicate a larger thermodynamic stability of the aggregates but an almost constant stoichiometry. The peculiar thermal effects and the viscosity trend observed during the titration of an aqueous PEG solution with the surfactant appear consistent with a conformational change of the polymer. The PEG chain would evolve from a strained to an expanded conformation, induced by the growing of the surfactant micellar clusters bonded to the polymer, as suggested in a previous study of the PEG/SDS/H2O system.

Introduction Polymer-surfactant (P-S) systems in aqueous solution attracted the interest of many researchers owing to their wide application in many industrial formulations.1-3 Among the systems containing a water soluble nonionic polymer and anionic surfactants, many investigations were devoted to ascertain the different behavior of surfactants in which the hydrocarbon chains are replaced by fluorinated ones. In this paper, we investigate the process of aggregation on oligomers of poly(ethylene oxide) (PEO) of a perfluorosurfactant and compare its behavior with that exhibited by sodium dodecyl sulfate (SDS) previously studied in our laboratory.4 The characteristics of PEO-SDS aggregates in water have been clearly established. Particularly, small-angle neutron scattering measurements by Cabane and Duplessix5-7 confirmed the necklace model originally proposed by Shirahama8 and Nagarajan.9 Recent, pertinent bibliography is summarized in refs 4 and 10. Some authors10-12 highlighted a peculiar behavior of PEO-SDS aggregates formed by PEO polymers of low molecular weight, that is, poly(ethylene glycol) (PEG). Particularly, a recent paper by us4 revealed, through isothermal titration calorimetry (ITC) measurements, the binding of successive micelles on a series of PEG polymers with increasing chain length. Our calorimetric measurements also quantified the evolution of the energetics of the interaction of SDS with these polymers allowing us to determine the precise molecular weights which proved critical to observing the arising and settling of PEG-SDS interactions and also suggested to interpret the peculiar sequence of endo and exo heat effects of ITC titrations in terms of a conformational change of the polymer chain. In this respect, ITC proved a particularly sensitive technique. In fact, modern instruments are able to measure the heat associated with the addition of such small volumes of the titrant solution * To whom correspondence should be addressed. Fax: 39 050 2219260. Tel: 39 050 2219263. E-mail: [email protected].

as to allow us to practically determine directly partial molar enthalpies, which are very sensitive to the different interactions in solution. Since these interactions are mainly hydrophobic in nature, it seemed interesting to examine fluorinated surfactants, which interact more strongly with PEG owing to the higher hydrophobic character of CFn vs CHn groups. An extensive bibliography has been collected and rationalized relative to P-S systems employing this family of surfactants.13 The possible fate of fluorinated surfactants in the environment14 and the related risks for humans15,16 have been also recently reviewed. In this work, we aimed to check whether the characteristic behavior displayed by PEG-SDS complexes with different PEG molecular weights was peculiar of this system or whether the PEG polymers might display analogous behavior when interacting with a fully fluorinated surfactant. As the perfluorosurfactant we chose cesium perfluorooctanoate (CsPFO). The aggregation process of perfluoroalkanoate surfactants on the PEG polymeric chain in dilute aqueous solution has been already suggested17 to fit the necklace model above evidenced for SDS. Complexes formed by perfluorooctanoates with PEG were studied calorimetrically in the case of the Na+ counterion limited to two PEG molecular weights, 400 and 35 000.17 The data were analyzed in terms of a mass action model which allowed the authors to calculate formation constants, enthalpies of aggregation, and aggregation numbers for two different P-S complexes. The complete phase diagram of the binary system CsPFO/H2O is known,18,19 and the relevant micellization process has already been investigated through density20,21 and conductivity22 measurements. Most investigations concerned the surfactant concentration range 25-60% w/w, where this system exhibits a micellar nematic phase. For those interested, the aggregation number, shape, and charge of CsPFO micelles in this region of the phase diagram have been extensively studied through SAXS,23 NMR,24 conductivity,25,26 density and expansion coefficient,24,27 surface tension,28,29 and ultrasonic relaxation studies.30

10.1021/jp0606614 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/18/2006

Aggregation of CsPFO on PEG Oligomers

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We investigated the PEG/CsPFO system in dilute aqueous solution through calorimetry, density, conductivity, and viscosity measurements. Calorimetric ITC titrations of aqueous solutions of PEG with different molecular weights (300 e MW e 20 000 Da), hereafter indicated as PEG MW, were performed at 298.15 and 308.15 K. For a few polymers, viscosity and conductivity data at 298.15 K and density data at 288.15, 298.15, and 308.15 K were also collected. The data were compared with our previous measurements on the PEG/SDS system,4 pointing out particularly the similar behavior of the calorimetric data. Experimental Section Materials. Poly(ethylene glycol) (PEG) samples with nominal molecular weight of 300, 600, 900, 1500, 2000, 3400, 4600, 8000, 10 000, and 20 000 Da were obtained from Aldrich. Standard samples of PEG of certified molecular weight, characterized by a low polydispersity index (D ) Mw/Mn) were Fluka products. For these samples, the effective molecular weight was chosen as the average between Mw and Mn: PEG 6000 (D )1.03), PEG 8300 (D ) 1.02), and PEG 11200 (D ) 1.07). Pentadecafluorooctanoic acid 99% (Fluorochem) was neutralized with cesium hydroxide 99.7% (Aldrich) in aqueous solution. After water removal, the salt was crystallized from a n-butanol/n-hexane mixture and finally dried at 80 °C under vacuum for 2 days. Doubly deionized water was used as the solvent. All solutions were prepared by weight. The concentration of CsPFO was measured as moles per kilogram of water (m). PEG solutions were allowed to stand overnight before use, and their concentration was expressed as weight percent (wt %). Isothermal Titration Calorimetry. The isothermal titration calorimeter was a Thermal Activity Monitor 2277 (TAM) from Thermometric, equipped with a 612 Lund syringe pump. Titrations were performed at 298.15 (or 308.15 K) ( 0.02 K by adding aliquots of a few microliters (5-50) of a concentrated solution of surfactant into a 20 mL cell containing 15-16 g of the aqueous solution of the polymer. Observed heat effects were measured mostly on the 300 µW full-scale detection range, allowing an average uncertainty of (1%. A slightly larger scatter of experimental data was observed at 35 °C owing to the not perfectly constant temperature of the titrant contained in the Lund syringe. Titrations at 298.15 K involved the addition of 0.9204 m (0.6962 m at 308.15 K) aqueous CsPFO to 0.1% w/w PEG solutions and covered a surfactant concentration range 0 < mS < 0.08 mol kg-1. The concentration of PEG (mEO), intended as the molality of the repeat unit (-CH2-CH2-O-), was 0.0227 mol kg-1, obviously constant for all 0.1% PEG solutions. Density. Density measurements were carried out by means of a high-precision vibrating-tube densimeter Anton Paar DMA 5000. The instrument has a built-in thermostat for maintaining the desired temperature with a precision of (0.001 K and an accuracy of (0.01 K. The densimeter was calibrated by dry air and freshly degassed water at 298.15 K. The measured densities have a precision of (3 × 10-6 g cm-3 and are accurate within (5 × 10-6 g cm-3. Conductivity. Conductivity measurements were carried out at 298.15 ( 0.10 K with an Amel 160 apparatus. The cell constant (1.041 cm-1) was determined with a 0.01 M KCl aqueous solution. Viscosity. Viscosity measurements were performed by means of a Ubbelohde viscosimeter equipped with an optical system for flow detection. The temperature was controlled by a water bath maintained at 298.15 ( 0.05 K. Data were collected during

Figure 1. (a) Typical curves of heats of dilution of a concentrated CsPFO aqueous solution. (b) Enthalpy of transfer of surfactant S from water to PEG 8000 solution: (O) ∆trfH(S), eq 1; (b) ∆trfH(S,m), eq 2.

a stepwise titration in which aliquots of a concentrated solution of the surfactant were added to a polymer solution through a Hamilton syringe driven by a Cole Parmer 74900 pump. The reproducibility of any single experiment was usually better than 0.5%. The results were expressed as relative viscosity (ηrel ) η/ηo) where η and ηo are the viscosities of sample solution and solvent, respectively. Owing to the low concentration of the surfactant, and the consequent almost constant density of the solutions, the relative viscosity was approximated to the ratio of experimentally measured flow times: ηrel ) t/to. The density actually changes monotonically up to less than 1% in the most concentrated solution: this does not bias the trend of the function ηrel ) f(mS). Results Isothermal Titration Calorimetry. Typical enthalpy of dilution (∆dilH) curves obtained by adding concentrated aqueous CsPFO, containing micelles, to water in the presence or absence of some PEG polymer are shown in Figure 1a. In this and in the other figures reporting experimental data as a function of the surfactant concentration, the lines are drawn as a mere guide for the eyes. The figure indicates the critical surfactant concentrations pertinent to polymer-surfactant systems: the critical micellar concentration (cmc) in the absence of the polymer, the critical aggregation concentration (cac) at which the interaction with the polymer begins, and the saturation concentration (C2) at which no additional interaction between surfactant and polymer chains is revealed. A further critical concentration, Cm, represents the concentration at which free micelles begin to form in the presence of P-S aggregates. The distinction between C2 and Cm is made possible by the EMF determination of the free surfactant concentration as proposed by Wyn-Jones et al.31,32

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We operationally identified cmc, cac, and C2 values as the intersections of the straight segments represented in Figure 1a. Ultimately, cmc and cac are associated with the beginning of aggregation (as suggested by Seng et al. with support of EMF data33) whereas the C2 and Cm values were chosen according to Dai and Tam.12 The curve relative to the dilution in water at 298.15 K allows us to determine the cmc value (cmc ) 0.0234 mol kg-1) which compares well with literature data collected at 303.15 K: 0.0268 mol kg-1 and 0.024 mol kg-1 through NMR19,34 and 0.0218 mol dm-3 through surface tension measurements.29 An analytical deconvolution of the same curve also allows us to determine the enthalpy of micellization (∆micH ) 5.1 kJ mol-1) never measured before for this surfactant. A larger value (∆micH ) 8.7 kJ mol-1) has been measured by Fisicaro et al. for the sodium salt.35 Figure 1b reports the enthalpy of transfer at 298.15 K of 1 mol of CsPFO from water to 0.1% w/w PEG 8000 solutions (∆trfH) as a function of surfactant (S) concentration. The data were obtained by combining the dilution enthalpies in water and water containing PEG, measured at the same S concentration

∆trfH(S)WfPEG ) ∆dilH(S)PEG - ∆dilH(S)W

(1)

Use of eq 1 for the calculation of the difference between the surfactant partial molar enthalpy in water and in PEG aqueous solution is justified by the very small titrant additions which cause a negligible dilution of the PEG concentration. The function ∆trfH(S) is an operational thermodynamic quantity for which the starting state of the surfactant changes from monomeric to micellar below and above the cmc, respectively. The usefulness of this quantity relies on the fact that its departure from the zero value, apart from small deviations related to dilution enthalpies, is a clear indication of the interaction of the surfactant with the polymer. Figure 1b also shows the trend of the enthalpy of transfer of the surfactant in its monomeric form, which may be obtained by correcting the ∆trfH(S) data for the micellization effect

∆trfH(S,m)WfPEG ) ∆trfH(S)WfPEG + δmicH

(2)

The quantity δmicH represents the contribution of micellization to the enthalpy of transfer. This contribution was calculated via a proper function which is null at low surfactant concentrations (mS) whereas approaches ∆micH at large mS values. In a small range around the cmc, the δmicH value increases steeply, matching the trend of ∆dilH(S)W.36 The quantity defined by eq 2 has the advantage of avoiding apparent exothermic effects caused by the shift of the micellization equilibrium (open circles of Figure 1b) and of being associated with the same thermodynamic process (S monomer f S aggregated) over the whole surfactant concentration range. When not otherwise specified, throughout the paper, the transfer enthalpy of the surfactant from water to PEG solutions will be simply indicated as ∆trfH, meaning with this symbol the property calculated from eq 2. Figure 2 reports values of ∆trfH at 298.15 K as a function of surfactant concentration for all polymers examined in this work. The enthalpies of transfer point out that this surfactant is able to interact with very short polymers. The cac value (0.021 m) slightly lower than cmc observed for MW ) 300 is a first indication, even if possibly related with the formation of mixed micelles. But, at MW ) 600, this system already exhibits a large endothermic peak before the cmc. This endo effect tends to be larger and shifted to lower S concentration for polymers with increasing molecular weight. For MW g 4600, the endo peak becomes larger or is followed by a second peak or a small

Figure 2. Enthalpy of transfer, ∆trfH, of CsPFO from water to 0.1% PEG (eq 2) at 25 °C as a function of surfactant concentration for polymers of different molecular weight.

shoulder. At very large concentrations, all of the curves tend to the constant value of the heat of micellization, since consistently the surfactant added after the saturation of the polymer is present in the form of free micelles. It is meaningful that, for all polymers, the graphical estimation of the difference between C2 and Cm (see Figure 1a) practically equals the difference between the cac and the cmc. This is what one would expect if, after the saturation of the polymer, the free micelles begin to form only when the concentration of free surfactant is increased up to the cmc value. Transfer enthalpies are found to be negligibly influenced by molecular weight distribution. A few measurements with polymer samples characterized by a very low polydispersity index (D < 1.07) did provide results consistent with those of the other samples. Particularly, a standard sample of PEG 8300 with D ) 1.02 yielded practically the same enthalpy curve as a normally polydispersed sample of PEG 8000. As a first observation, we notice that the general pattern of the transfer enthalpy data of CsPFO as a function of PEG molecular weight resembles that already observed for SDS.4 Transfer enthalpies reported for SDS in ref 4 are not corrected for micellization enthalpy (eq 2) but are comparable with present data owing to the practically null micellization enthalpy of this surfactant at 298.15 K. The main differences between the two systems are (i) CsPFO exhibits an earlier interaction with the polymer, being able to interact feebly with chains as short as 7 monomers (MW ) 300), while SDS revealed aggregation only for PEG 600 and (ii) SDS exhibited a clearer distinction between multiple peaks, as exemplified by its enthalpy curve for the transfer to a PEG 8000 solution.4 Table 1 lists the values of critical concentrations relevant to the various PEGs, together with an estimate of the enthalpy and free energy of formation of the CsPFO-PEG aggregate

Aggregation of CsPFO on PEG Oligomers

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TABLE 1: Thermodynamic Data Obtained from Calorimetric Titrations of 0.1% PEGs with CsPFO in Water PEG MW (Dalton)

caca,b (mmol kg-1)

no PEG 300 600 900 1500 2000 3400 4600 6000 8000 10000 11200 20000

23.4 (cmc) 21.1 18.4 16.2 14.0 12.0 11.0 9.2 10.4 9.4 9.3 9.3 9.0

no PEG 300 600 1500 3400 4600 6000 8000 10000 11200 20000

21.0 (cmc) 19.2 15.3 10.1 8.5 8.5 8.3 7.5 7.1 6.8 7.5

∆trfHmaxc (kJ mol-1)

∆aggG°md (kJ mol-1)

Cmaxe,b (mmol kg-1)

C2f (mmol kg-1)

-39.72 -40.35 -41.08 -41.84 -42.27 -43.16 -42.55 -43.05 -43.11 -43.11 -43.27

23.0 20.8 17.4 15.6 14.3 12.0 12.5 12.4 11.5 11.9 11.2

60 50 48 45.5 39.0 41.6 36.4 41.2 39.8 40.3 40.8 39.6

-40.89 -42.10 -44.13 -45.01 -45.01 -45.13 -45.65 -45.93 -46.16 -45.65

21 10 12.9 11.5 11 10.4 9.7 9.2 9.2 9.5

80 47 37 37.2 36.5 36.4 36.2 34.4 34.3 37.4

298.15 K 3.03 2.50 2.77 3.13 3.30 4.25 4.41 3.93 3.61 3.15 2.77 308.15 K 0.35 0.20 0.56 0.65 0.9 0.91 1.1 1.31 1.4 1

a Critical aggregation concentration. b Uncertainty (0.2 mmol kg-1. c Calculated through eq 2 at the maximum of the endothermic peak. d Calculated as ∆aggG°m ) 2RT ln cac, standard state unit mole fraction. e Concentration corresponding to ∆trfHmax. f Concentration of saturation of the polymer; uncertainty (0.5 mmol kg-1 when MW g 2000 Da.

which is first formed at low surfactant concentrations. The cac values are regularly decreasing as the PEG molecular weight is increased, reaching an almost constant value of 9 mmol kg-1 for MWs higher than 4600 Da. According to the charged phase separation model,37 values of the standard free energy of formation of this aggregate, starting from the free monomers, can be calculated as ∆aggG°m ) 2RT ln cac. In the hypothesis that the surfactant added in correspondence of the maximum of the endothermic peak is 100% aggregated, the corresponding value of the transfer enthalpy (∆trfHmax, see Table 1) can be identified with the enthalpy of aggregation of CsPFO monomers, ∆aggHm. The corresponding entropy of aggregation can be calculated from the Gibbs equation. The values of these thermodynamic properties and of critical concentrations are plotted in Figure 3 as a function of the molecular weight of the polymers. The figure indicates that at high molecular weights all of the curves point approximately to a constant value, that is, the aggregates probably reach a steady composition and thermodynamic stability. The function ∆aggG°m, and the related cac, identify the value MW ∼ 2600 Da as the threshold molecular weight for displaying this constant behavior. Unfortunately, different from the PEG/SDS system, the analogous indication by the ∆trfHmax function appears uncertain, probably due to the partial overlapping of the endothermic peaks in the case of low MW polymers. As a conclusion, the condensation of CsPFO molecules on the PEG chains seems to reach an almost stable condition after MW ∼ 2600, that is, a chain of about 60 monomer units would be able to bind a fully formed micellar cluster. A few measurements in our laboratory on the system PEG/LiPFO seem to support this finding. A comparison with SDS,4 which exhibits constant thermodynamic parameters for MW g 3800 Da, would indicate a smaller size of the micellar clusters of CsPFO. Experimental data on the aggregation number (Nagg) of CsPFO in these

Figure 3. Thermodynamic parameters for CsPFO aggregation on PEG as a function of PEG molecular weight at 25 °C: (a) surfactant concentrations at the critical aggregation (cac), at the maximum of the endothermic peak (Cmax), and at the saturation of the polymer (C2); (b) ∆aggG°m, ∆aggHm () ∆trfHmax), and T∆aggSm, see Table 1 and text.

aggregates are not available. A value Nagg ) 5 was calculated by De Lisi et al.17 for NaPFO, through a fitting procedure to a thermodynamic model involving six unknown parameters.

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Figure 4. Effect of polymer concentration on the heats of transfer of CsPFO from water to aqueous PEG 8000 solutions at 25 °C.

Unfortunately, the aggregation number is dependent on the nature of the counterion, as suggested from the values determined for the free micelles of LiPFO (Nagg ) 15-20)38 and NaPFO (Nagg ) 23-30 near cmc)39 and also from a direct dynamic fluorescence study of PEG-SDS aggregates.40 A rough estimate of the aggregation number of free CsPFO micelles, Nagg ) 50,21 coupled with the observation that generally micellar clusters of surfactant bonded to a macromolecule are slightly smaller than the corresponding free micelles,41 would suggest that the aggregation number of CsPFO-PEG aggregates is little smaller than the SDS-PEG ones. Since the average radius of the micelles, and also of micellar aggregates, is mainly determined by the length of the surfactant hydrophobic tail, the perfluorooctanoate aggregates bonded to PEG are probably smaller than the dodecyl sulfate ones and it is therefore reasonable that they are fully wrapped by a shorter polymeric chain. The reaction of micellization of CsPFO and its aggregation on PEG were also investigated in the presence of 0.1 m NaCl. As already known for other surfactants, the higher ionic strength causes a clear decrease of the critical concentrations: the cmc drops from 0.0234 to 0.0120 mol kg-1 and the cac in 0.1% PEG 8000 from 0.0095 to 0.0040 mol kg-1. A minor effect is observed on the micellization enthalpy, ∆micH, which changes from 5.1 to 5.8 kJ mol-1 whereas a net increase of the endothermic aggregation enthalpy, ∆trfHmax, is observed for PEG 8000: 5.5 kJ mol-1 as compared with 3.93 kJ mol-1 in the absence of NaCl. Curves of the dilution and transfer enthalpies of CsPFO in 0.1% PEG 8000 and PEG 4600 in the presence of 0.1 m NaCl can be seen in Supporting Information, Figure S1. In Figure 4, the effect of varying the polymer concentration is finally shown. The curves of ∆trfH at increasing PEG 8000 concentration clearly reveal similar trends. As already noticed by others,12 an increase in polymer concentration does not affect the value of the cac but causes an increase of the maximum and a broadening of the endothermic peak. The area of this peak, related to the integral heat of aggregation, results thus proportional to the polymer concentration indicating involvement of a proportionally larger number of surfactant molecules. Consistently, C2, the stoichiometric surfactant concentration necessary to saturate the polymer, is also gradually shifted to larger values indicating a proportionally larger concentration of surfactant bonded to the polymer at the saturation (C2 - cac). To reveal the effect of temperature on the micellization and aggregation processes, analogous titrations were performed at

Gianni et al.

Figure 5. Dilution enthalpies of CsPFO at different temperatures: filled symbols, T ) 25 °C; hollow symbols, T ) 35 °C.

Figure 6. Enthalpies of transfer of CsPFO from water to 0.1% PEG aqueous solutions at 35 °C.

308.15 K with PEG polymers already taken into consideration. Figure 5 shows the effect of temperature on the dilution enthalpies of the aqueous surfactant in water and in water containing PEG 8000. The curve relative to water allows us to calculate cmc ) 0.0211 mol kg-1 and ∆micH ) 1.2 kJ mol-1. The lower cmc value, as compared with that found at 25 °C, indicates a larger stability of the micelles at higher temperatures and is consistent with the endothermic micellization enthalpy. The observed change with temperature of micellization enthalpy allows us to calculate a micellization heat capacity ∆micCp ) -392 J K-1 mol-1, consistent with the calorimetric value of -522 J K-1 mol-1 given by De Lisi et al. for the sodium salt42 on the basis of experimental data of ref 43 but quite different from the value -1255 J K-1 mol-1 found by Mukerjee et al.38 The latter value however, as already suggested,44 is probably biased by the successive differentiations of cmc experimental data at different temperatures. A comparable ∆micCp value, -500 J K-1 mol-1, was also measured for lithium perfluorononanoate.44 The transfer enthalpies of CsPFO monomers from water to PEG aqueous solution at 35 °C are shown in Figure 6 for some selected PEG polymers. The complete set of critical concentrations and thermodynamic data of aggregation is reported in Table 1. The curves of ∆trfH as a function of concentration (see Figure 6) display a trend similar to that exhibited at 25 °C, with an initial endothermic effect very similar for all PEG polymers

Aggregation of CsPFO on PEG Oligomers

Figure 7. Thermodynamic parameters for CsPFO aggregation on PEG as a function of PEG molecular weight at 35 °C (see legend to Figure 3).

and a subsequent exothermic effect. All the curves are practically shifted toward lower enthalpy values: for instance, in the case of PEG 8000, the endo peak, chosen as representative of the P-S aggregate which is first formed at low surfactant concentration, decreases from the value ∆trfHmax ) 3.93 kJ mol-1 at 25 °C to the value 1.10 at 35 °C. These data allow us to calculate a heat capacity change for aggregation of the surfactant to the polymer ∆aggCp ) -283 J K-1 mol-1, which confirms the hydrophobic nature of the aggregation process. A second effect of temperature is observed on the values of the critical concentrations and enthalpies and free energies of aggregation, which are plotted as a function of MW in Figure 7. We may notice that critical concentrations and the standard free energy of aggregation reach a plateau at the higher temperature for lower values of the molecular weight: MW ∼ 2000 against ∼2600 at 25 °C. The ∆aggHm data indicate no critical point at all, probably due to their low absolute values. Consistently with a larger stability of the aggregates at the higher temperature, a stable situation is observed for shorter length polymers. If one calculates the ratio of the surfactant bonded to the PEG monomeric unit at the saturation, RC2, which may be approximated as (C2 - cac)/mEO, then the average values 1.4 at 25 °C and 1.3 at 35 °C are obtained for polymers with MW > 4000 Da. This indicates that the higher temperature favors the early formation of the aggregate, but the stoichiometry of the aggregate at the saturation is about the same at both temperatures. Conductivity. The conductivity of aqueous solutions of CsPFO at 298.15 K has been measured in water and water containing 0.1% of a few selected PEGs. The experimental results are reported in Supporting Information, Figure S2. The curve in water clearly displays two straight lines, which do intersect at the cmc value of 0.024 m. The trend of the curves in the presence of PEG allows us to identify three linear

J. Phys. Chem. B, Vol. 110, No. 18, 2006 9117 segments whose intersections allow us to locate the cac (first and second lines) and the C2 (second and third ones). The cac and C2 values thus determined are less precise than those determined by ITC but are consistent with the values reported in Table 1. The ratios of the slopes of the straight lines allow us to determine the values of the dissociation degree R of the counterions,45 which result as R ) 0.42 for the free micelles and 0.70, 0.72, and 0.71 for the aggregates formed on PEG 3400, PEG 8000, and PEG 20000, respectively. The R value of the free micelles is lower than the value 0.58 calculated at the cmc by Iijima et al. on the basis of NMR46 and SAXS/SANS47 measurements. This latter value, however, decreases with surfactant concentration. The ionic dissociation of the aggregates appears independent of PEG molecular weight but clearly increases when passing from the free micelles to the micellar clusters bound on the polymer, as already noticed for other P-S complexes.1 For instance, in the case of SDS-PEG complexes, the R value increases from 0.37 to an average value of 0.59 for the PEG polymers with the above molecular weights.48 Density. Measurements were performed in aqueous CsPFO solutions at 288.15, 298.15, and 308.15 K. The trend of the apparent molar volume of the surfactant as a function of its concentration in water and in PEG 8000 solution at 25 °C is reported in the Supporting Information, Figure S3. The volume change associated with micellization (∆micV) was evaluated as the difference between the values of the apparent molar volumes of the surfactant in the monomeric (VΦ,m) and micellar (VΦ,M) form, extrapolated at the cmc. The VΦ,M values of CsPFO in the micelles were calculated as

[

1000 + mSMS 1000 - VΦ,mcmc δ δ0 VΦ,M ) mS - cmc

]

(3)

where mS and MS are the surfactant molality and molecular weight and δ and δ0 the density of the solution and the solvent, respectively. The trend of apparent molar volumes and the graphical estimation of ∆micV are shown in Figure 8a. The ∆micV values (10.3, 9.9, and 8.5 cm3 mol-1 at 15, 25, and 35 °C, respectively) decrease with temperature, as already observed by Gonzalez-Martin et al.20 The value at 25 °C is lower than the value of 12.8 cm3 mol-1 found by others.20,21 However, these authors considered the average value of the partial molar volume of the solute over a large concentration range20 or found no concentration dependence of this quantity.21 The low value of the cac in 0.1% PEG 8000 solutions prevented a precise determination of the concentration dependence of VΦ,m in the pre-micellar region: the few data collected were fitted to a straight line with the same slope observed in the absence of the polymer. Apparent molar volumes of the surfactant aggregated on the PEG chain (VΦ,agg) were calculated, at concentrations larger than the cac, according to eq 3 where the values of VΦ,M and cmc were replaced by VΦ,agg and cac, respectively, δ0 was the density of the 0.1% PEG solution, and VΦ,m the apparent molar volume of the monomer in the latter solution. These data are plotted in Figure 8b. Values of the volume change associated with S aggregation on the polymer, ∆aggVm, calculated analogously to ∆micV, were 7.4, 5.9, and 6.0 cm3 mol-1 at 15, 25, and 35 °C, respectively. Thus, the process of aggregation of monomeric surfactant molecules on the PEG chain also involves a positive volume change, though smaller than that observed for micellization. Viscosity. Some measurements were performed on CsPFO solutions in the presence of 0.1% PEG 4600, covering the

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Gianni et al. concentrations. The decrease falls in the same region where the ITC curves display the first endothermic effect (see Figure 2). At larger CsPFO concentrations, the relative viscosity reaches a minimum and then increases steeply and monotonically. Discussion

Figure 8. Apparent molar volume of the surfactant in the monomeric and associated form in water (a) and 0.1% PEG 8000 (b): (O) 15 °C, (b) 25 °C, and (X) 35 °C. Associated form of S: (a) micelle for mS > cmc (VΦ,S ) VΦ,M) and (b) aggregate with PEG for mS > cac (VΦ,S ) VΦ,agg).

Figure 9. Relative viscosity of 0.5% PEG 8000 aqueous solutions as a function of CsPFO concentration at 25 °C. The dotted vertical line corresponds to the cac value determined by ITC.

surfactant concentration range explored during ITC titrations. The viscosity of the solutions was found to increase slowly and monotonically with surfactant concentration. However, in these conditions, the possible incidence of the structure of micellar aggregates with PEG on the overall viscosity of the medium is expected to be small owing to (i) the low concentration of the polymer and (ii) the feeble effect on viscosity by the not sufficiently long polymeric chain. An analogous titration with a longer polymer at larger concentration exhibited a different pattern. In Figure 9, the change in relative viscosity (ηrel ) η/ηo, with being η the viscosity of the sample solution and ηo the viscosity of the solvent) with surfactant concentration for 0.5% PEG 8000 solutions is reported. The viscosity presents an initial small increase followed by a clear decrease at still low CsPFO

Table 2 summarizes the thermodynamic data for the micellization reaction of CsPFO in water, together with literature data relative to other perfluorooctanoates. A close look at this table shows that most properties are feebly dependent on the nature of the alkaline counterion and often a larger difference is found among data pertaining to the same system but given by different authors. The typically hydrophobic character of micellization is confirmed by the large and positive values of the entropy change and the large and negative values of the change in heat capacity. The binding of CsPFO to PEG of different molecular weight, examined in this work, closely resembles that exhibited by SDS.4 In both cases, the calorimetric curves of the transfer of the surfactant from water to an aqueous PEG solution (∆trfH ) f(mS), see Figures 2 and 6 of the present work and Figure 2 of ref 4) display a clear endothermic maximum at low surfactant concentration, followed by minima at larger concentrations which become exothermic in the case of SDS. This trend appears typical of the polymer. It might indicate the formation of two different aggregates or some transition of the aggregate which is initially formed. In the case of SDS, this behavior was explained by Dai and Tam12 in terms of dehydration of the polymer caused by the aggregation of the low concentrated surfactant on the polymeric chain driven by hydrophobic interactions, followed by rehydration of the polymer which would associate with the surfactant through ion-dipole interactions at higher concentration. The explanation was consistent with the evaluation of the endothermic effect associated with the dehydration of the polymer repeat unit -CH2-CH2-Ooriginally proposed by Olofsson.62 We suggested that an alternative, or additive, explanation might be the initial coiling of the polymer around a small micellar cluster leading to a strained high-energy conformation, which evolves to a more extended conformation as the cluster bonded to the polymer grows with increasing surfactant concentration.4 This explanation was consistent with a viscosity decrease of the solution at low SDS concentration. The decrease of viscosity of CsPFO-PEG 8000 aqueous solutions (see Figure 9) parallels the enthalpy increase of the ITC curves and is consistent with the formation of a compact, strained high-energy conformation of the polymer around a small micellar cluster of the surfactant. One might object that the viscosity minimum (mS ) 0.030 mol kg-1) unexpectedly corresponds to the S concentration at which the calorimetric curve exhibits a minimum (see Figure 2), that is, the region of supposed relaxation of the initially strained polymeric chain. But we like to observe that this is due to the different nature of the properties being compared. The enthalpy of transfer, being a difference of partial molar enthalpies, is a probe sensitive to the environment found by the few molecules actually added in each step of the titration, while the viscosity, being a bulk property, reflects the average situation of all molecules present in the solution. So, correctly, the minimum of the η ) f(mS) function falls close to the surfactant concentration at which the partial molar enthalpy of the further added surfactant indicates the beginning aggregation of S on an expanded conformation of the polymer. In Figure 10, the reduced viscosity (ηred ) (ηrel - 1)/mS) is plotted together with the ∆trfH data for the same

Aggregation of CsPFO on PEG Oligomers

J. Phys. Chem. B, Vol. 110, No. 18, 2006 9119

TABLE 2: Thermodynamic Data for the Micellization of Perfluorooctanoates in Water T (°C)

cmc (mol kg-1)

LiPFO

25

NaPFOg

30 8 25

0.0334d, 0.037e, 0.0341f 0.013e 0.036h 0.0306d, 0.035e, 0.0306f, 0.030i, 0.033j, 0.0356k 0.032q, 0.031r 0.0375j, 0.040k 0.0287d, 0.0300s 0.027h,0.0274t 0.027r 0.028h 0.024u 0.0234V 0.0234x

S

KPFO RbPFO CsPFO

30 55 25 30 35 20 50 20 25 30

NH4PFO N(CH3)4PFO N(C2H5)4PFO

35 3 25 35 25

∆micG° a (kJ mol-1)

∆micH° (kJ mol-1)

∆micS° (J K-1 mol-1)

-28.45j (-26.15j,l)

8.9i, 9.20j, 8.70m

-30.41j (-28.28j,l)

-13.8j

126j (117j,l)

56j (46j,l)

∆micCp (J K-1 mol-1)

∆micV (cm3 mol-1)

Nb

Rc

-522i, -1255j, -587k

11.2k 13.3n, 15j, 12.8o 23p

0.56i, 0.455j

-586j, -363k

19.4q 3.4k

0.473j

(-27.61m,l)

0.52t

-30.44x

5.10x

0.024u, 0.0218V, 0.027w, 0.0268z 0.0198x 0.033h 0.030aa, 0.025bb 0.015r 0.00719f

-392x

119x

12.9°, 9.9x, 12.79y

0.42x 0.57w

1.18x

b a Standard free energy of micellization according to the charged phase separation model: ∆ micG° ) (2 - R)RT ln(cmc/55.5). Aggregation number of the micelle near to cmc. c Dissociation degree of the counterion. d Reference 49. e Reference 50. f Reference 51. g Further cmc data are quoted in refs 34 and 52. h Reference 53. i Calculated from data of ref 43 or quoted therein. j Reference 38. k Reference 54. l Given by the author according to a different model. m Reference 35. n Reference 55. o Reference 21. p Reference 39. q Reference 56. r Reference 57. s Reference 58. t Reference 59. u Reference 34. V Reference 29. w Reference 22. x This work. y Reference 20. z Reference 19. aa Reference 60. bb Reference 61.

TABLE 3: Thermodynamic Parameters for the Aggregation of Surfactants on PEG Chain in 0.1% PEG 8000 Aqueous Solution at 298.15 Ka surfactant SDS CsPFO

∆aggG°Mb (kJ mol-1) -0.17 -0.10

∆aggHMc (kJ mol-1) +4.66 -1.17

∆aggSM (J K-1 mol-1)

∆aggCp,M (J K-1 mol-1)

∆aggVMd (cm3 mol-1)

+16 -4

+292g

-1.4g

+109

-4.0

RC2e

Rf

R′f

0.76 1.38

0.37g

0.57g 0.72

0.42

∆aggXM values (X ) G, H, S, Cp, V) refer to the aggregation on the polymer of a preformed free micelle: SDS data (ref 4) and CsPFO data (this work). b From eq 4. c From eq 5. d Calculated as ∆aggVM ) ∆aggVm - ∆micV. e RC2 ) (C2 - cac)/mEO. It represents the ratio of bonded surfactant to PEG monomers. f Counterion dissociation degree of the micelle (R) and the P-S aggregate (R′). g Reference 48. a

Table 3 compares the thermodynamic data of the aggregation of surfactant micelles on the polymer for the PEG/CsPFO system with those previously obtained for the system PEG/SDS.4 For convenience, the data refer to the aggregate formed with PEG 8000, but practically all quantities maintain the same values for all molecular weights larger than 5000 Da. The standard free energy of formation of the aggregate, starting from preformed surfactant micelles, was calculated according to the charged phase separation model37 as

∆aggG°M(S - PEG) ) RT[(2 - R′)ln cac - (2 - R)ln cmc] (4)

Figure 10. Surfactant transfer enthalpy, ∆trfH, and reduced viscosity (ηred ) (ηrel - 1)/mS) for 0.5% PEG 8000 aqueous solutions as a function of CsPFO concentration at 25 °C.

0.5% PEG 8000 solution. The reduced viscosity, enhancing the contribution by the added solute, indicates a shift of the η minimum toward the region of the maximum of ∆trfH values. Thus, the initial formation of a compact P-S aggregate which expands at larger S concentration seems to give an account of the behavior of aggregates formed by PEG with both SDS and CsPFO surfactants.

where R and R′ are the ionization degrees of the micelle and the aggregate, respectively. The ∆trfHmax values (see Table 1) give a measure of the enthalpy of aggregation on the polymer of the surfactant in its monomeric form. Values of the enthalpy of aggregation of preformed micelles on the polymer, consistent with ∆aggG°M values calculated through eq 4, were obtained by correcting the ∆trfHmax data for the heat of micellization

∆aggHM ) ∆trfHmax - ∆micH

(5)

Combination of the free energy and enthalpy data yielded the corresponding entropy of micelle-PEG aggregation.

9120 J. Phys. Chem. B, Vol. 110, No. 18, 2006 We should stress that we are treating our data under the approximation of the charged pseudophase model.37 A more refined model would require experimental determination of the free surfactant concentration31 or application of a multiparameter fitting treatment17,63 which may be critical due to the mutual correlations of the parameters. Even the change in the number of aggregation of the surfactant, when this passes from the free micelle to the polymer aggregate, is here not expressly taken into consideration and its effect is therefore included in the values of the thermodynamic transfer properties. Nevertheless, we deem that our comparisons are still valuable on a relative basis. Following the general rule that the hydrophobicity of a CF2 group is about 1.5 times that of a CH2 group,64 CsPFO and SDS should exhibit a comparable hydrophobicity and thus a similar thermodynamic behavior in reactions mainly driven by hydrophobic interactions. Table 3 shows that the aggregation of preformed micelles of CsPFO and SDS on a chain of poly(ethylene glycol) of molecular weight higher than 5000 Da practically involves the same thermodynamic stability, but the dominant effect is entropic in the case of SDS while enthalpic for CsPFO. This aggregation is characterized as well by positive ∆aggCp,M and negative ∆aggVM values. These changes, showing the opposite sign with respect to micellization, are consistent with the decrease of the surfactant aggregation number generally associated with the aggregation of the micelles on polymers.41 However, we should underline that the ∆aggVM property, due to the way it was calculated, is not exactly consistent with other ∆aggXM properties of Table 3. While the latter refers to the complex formed at low surfactant concentration, the aggregation volume refers to the complex stable at large concentrations. Comparison of the ratios of the bonded S molecules to the PEG monomeric units at saturation (RC2) for the two surfactants indicates that the PEG chain, when saturated, binds a number of CsPFO molecules double those of SDS. Since the average aggregation number of a CsPFO micellar cluster bonded to PEG (a pearl in the pearl-necklace model2,5-7) was estimated to be lower than that of SDS, this necessarily involves a much larger number of these clusters in the case of CsPFO. This crowding of micellar units indicates that the lower screening provided by counterions (R′CsPFO > R′SDS) is more than compensated for by the smaller size of the units themselves and the larger screening effect associated with their stronger bond with the polymer. Conclusions We put in evidence that the aggregation reaction of CsPFO on PEGs of different molecular weight is very similar to that already observed with SDS. ITC and viscosity data at low S concentration are consistent with a P-S aggregate in which the polymeric chain wraps around a small surfactant cluster assuming a strained high-energy conformation, which relaxes to an expanded conformation as the surfactant concentration is increased. The thermodynamic parameters attributed to the aggregation of a free micelle on the PEG polymer chain again indicate the importance of hydrophobic interactions. In this process, CsPFO and SDS display the same increase in thermodynamic stability. The number of surfactant molecules bonded to the PEG polymeric chain at the saturation was found to be almost double that observed for SDS. Acknowledgment. The authors are grateful to the Ministero dell’Istruzione, dell’Universita` e della Ricerca (MIUR) for financial support (COFIN 2002).

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