Thermodynamic Properties of a Diblock Copolymer of Poly

E. Villar-AlvarezSilvia BarbosaJ. F. A. SolteroV. MosqueraP. TaboadaY. Rharbi. The Journal of Physical Chemistry C 2018 122 (15), 8553-8563. Abstract ...
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Langmuir 2004, 20, 8903-8908

8903

Thermodynamic Properties of a Diblock Copolymer of Poly(oxyethylene) and Poly(oxypropylene) in Aqueous Solution Pablo Taboada, Silvia Barbosa, and Vı´ctor Mosquera* Grupo de Fı´sica de Coloides y Polı´meros, Departamento de Fı´sica de la Materia Condensada, Facultad de Fı´sica, Universidad de Santiago de Compostela, Santiago de Compostela E-15706, Spain Received April 5, 2004. In Final Form: July 20, 2004 Apparent molar volumes, expansibilities, and adiabatic compressibilities have been determined by density and ultrasound velocity measurements, in the temperature range of 5-50 °C, of aqueous solutions of the diblock copolymer denoted P94E316, where E denotes oxyethylene, P denotes oxypropylene, and the subscripts denote block lengths. The critical micelle concentration (cmc) was determined at 20 °C from ultrasound velocity data by an analytical method based on the Phillips definition of the cmc; it was impossible to use the method at other temperatures due to the high or low values of the cmc. Critical micelle temperatures were derived for different concentrations from ultrasound velocity measurements applying the same procedure as that for the cmc.

1. Introduction Commercially available diblock copolymers of ethylene oxide and propylene oxide have provided many copolymers for academic research, and the range has been significantly extended by laboratory synthesis. Block copoly(oxyalkylene) polymers comprising a hydrophilic poly(oxyethylene) block and a second hydrophobic oxypropylene block have interesting properties including micellization in dilute solution and the gelation of concentrated micellar solutions and are commercially available under the trade names Pluronics and Polaxamers. They are denoted as PmEn, where E denotes the oxyethylene unit, OCH2CH2, P denotes the oxypropylene unit, OCH2CH(CH3), and the subscripts m and n denote the number-average block lengths in repeat units. The order of appearance in the formula denotes the sequence of polymerization in the preparation. Aqueous solutions of PmEn diblock copolymers have attracted great interest in the past years attributed in part to their great suitability for industrial processes. Their micellization in aqueous solution is initiated at a given temperature by increasing the concentration beyond the critical micelle concentration (cmc) or at a given concentration by increasing the temperature beyond the critical micelle temperature (cmt). It is established, both experimentally1 and theoretically,2 that diblock copolymers micellize more readily and form micelles with larger hydrophobic cores than corresponding triblock copolymers. Consequently, diblock copolymers have advantages in many applications, not least in the solubilization of sparingly soluble substances, including drugs. As discussed elsewhere,1 for reasons connected with the chemistry of their sequential anionic polymerization, diblock PnEm copolymers are considerably more uniform in chain length and composition than the corresponding triblock copolymers, which may even contain a proportion of diblock copolymer. Consequently, the concentration range be* To whom correspondence should be addressed. E-mail: [email protected]. Tel: 0034981563100 ext 14056. Fax: 0034981520676. (1) Booth, C.; Attwood, D. Macromol. Rapid Commun. 2000, 21, 501. (2) Altinok, H.; Yu, G.-E.; Nixon, S. K.; Gorry, P. A.; Attwood, D.; Booth, C. Langmuir 1997, 13, 5837.

tween onset and completion of micellization is narrower for the diblock architecture. Altinok et al.3 have examined the micellization and micelle properties of a set of copolymers prepared with different E-block and P-block architectures but similar overall composition and chain length. They used several techniques to characterize the aggregation process of copolymer P94E316 in water where it undergoes aggregation as the classical surfactants do. Booth and Attwood1 have realized a systematic study of the effect of P-block length within a series of EP copolymers. Kelarakis et al.4 have studied the effect of P and E block lengths on the micellization of different diblock copolymers, among them P94E316, by gel permeation chromatography, tube inversion, and light scattering. In a previous work,5 we have studied the enthalpy of demicellization, ∆Hdemic, of copolymer P94E316 at different temperatures using isothermal titration calorimetry. A literature search for the aqueous solutions of copolymer P94E316 revealed that its volumes, expansibilities, and compressibilities have not been investigated over wide concentration and temperature intervals. Moreover, the data have often been obtained in a temperature-scanning mode at few fixed concentrations.6 So, the aim of this work is to complete the study of diblock copolymer P94E316 with direct thermodynamic data. Apparent molar volumes and adiabatic compressibilities were obtained by using density and speed of sound measurements in the temperature range of 5-50 °C in the dilute concentration region. At temperatures higher than 20 °C, the values of the cmc are so low that the concentration data were out of the resolution of the equipment, and for temperatures below 20 °C, the critical concentration is so high that it is necessary to work with a great quantity of solute to measure the critical concentration. (3) Altinok, H.; Nixon, S. K.; Gorry, P. A.; Attwood, D.; Booth, C.; Kelarakis, A.; Havredaki, V. Colloids Surf., B 1999, 16, 73. (4) Kelarakis, A.; Yang, Z.; Pousia, E.; Nixon, S. K.; Price, C.; Booth, C.; Hamley, I. W.; Castelletto, V.; Fundin, J. Langmuir 2001, 17, 8085. (5) Taboada, P.; Mosquera, V.; Attwood, D.; Yang, Z.; Booth, C. Phys. Chem. Chem. Phys. 2003, 5, 2625. (6) Yang, Z.; Pousia, E.; Heatley, F.; Price, C.; Booth, C.; Castelletto, V.; Hamley, I. W. Langmuir 2001, 17, 2106.

10.1021/la0491302 CCC: $27.50 © 2004 American Chemical Society Published on Web 08/25/2004

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2. Experimental Section 2.1. Materials. The copolymer P94E316 was prepared by the sequential anionic polymerization of propylene oxide followed by ethylene oxide. The methods used in preparation and characterization followed closely that described by Kelarakis et al.4 The formula of the copolymer was obtained accurately from the molar mass of the precursor poly(oxypropylene), Mn ) 5450 g mol-1, and the overall compositions (E ) 77.1 mol %). The molar mass-average calculated from overall Mn and Mw/Mn was 20 700 g mol-1, and the mass fraction of E was 0.718. The molar mass distribution has no significant influence on properties such as volumes contrary to some other more sensitive techniques such as light scattering.7,8 Solutions observed during the tube inversion tests (concentration range, 0-25 wt %) for the copolymer remained clear to the eye throughout the temperature range investigated in the present work. 2.2. Equipment. Density and ultrasound velocity measurements were realized using a commercial density and ultrasound velocity measurement apparatus (Anton Paar DSA 5000 densimeter and sound velocity analyzer) equipped with a new generation stainless steel cell. Temperature control was maintained by the Peltier effect with a resolution of (0.001 °C, giving rise to uncertainties in density of ca. (1 × 10-6 g cm-3. The ultrasound velocity resolution was (10-2 m s-1. Solutions were prepared by mass at room temperature, using a Mettler AT20 balance with a precision of 0.001 mg. Water was double distilled and deionized. The densimeter and the ultrasound equipment were calibrated using deionized and doubly distilled water, whose densities and velocities were taken from the literature,9 and a vacuum. The calibration densities of water were 0.999 964 at 5 °C, 0.999 699 at 10 °C, 0.999 09 at 15 °C, 0.998 203 at 20 °C, 0.997 043 at 25 °C, 0.995 645 at 30 °C, 0.994 029 at 35 °C, 0.992 212 at 40 °C, 0.990 208 at 45 °C, and 0.988 030 g cm-3 at 50 °C. 2.3. Calculations. The apparent molar volume, Vφ, of the copolymer in water was calculated by means of the following equation:10

Vφ )

3 M 10 (F - F0) F mFF0

(1)

m and M are the molality and molecular weight, respectively, of the copolymer, F is the density of the solution, and F0 is the density of water. To obtain reliable volume data, it is necessary to measure densities with great precision.11 By differentiating eq 1 with respect to m at constant F, one obtains a probable error in Vφ of (M/F - Vφ)(δm/m)F that gives a maximum error of (0.2 cm3 mol-1 in the concentration range studied. If eq 1 is now differentiated with respect to F at constant m, we obtain a probable error in Vφ of (1000/mF0 + Vφ)(δF/F)m that will cause a maximum error of about (40 cm3 mol-1 in the range of data measured. The apparent molar expansibilities, Eiφ, were calculated from the dependence of the apparent molar volume on temperature, T:

Eiφ ) (∂Vφ/∂T)p

(2)

where p is the pressure and i ) 0 for monomers and m for monomer in the aggregate. Density and ultrasound velocity, u, measurements were combined to calculate isentropic compressibilities, ks, using the Laplace equation:10 (7) Paterson, I.; Armstrong, J.; Chowdhry, B.; Leharne, S. Langmuir 1997, 13, 2219. (8) Reddy, N. K.; Fordham, J.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1990, 86, 1569. (9) Lide, D. R. In Handbook of Chemistry and Physics, 76th ed.; CRC Press: Boca Raton, FL, 1995-1996. (10) Harned, H. S.; Owen, B. B. In Physical Chemistry of Electrolyte Solutions; Chapman and Hall: London, 1957; Chapter 8. (11) Hφiland, H. In Thermodynamic data for biochemistry and biotechnology; Hinz, H.-J., Ed.; Springer-Verlag: Berlin, 1986.

1 106 ks ) - (∂Vφ/∂T)s ) 2 V Fu

(3)

V and S refer to volume and entropy, respectively. The isentropic compressibility coefficient is expressed in bar-1 when u is expressed in cm s-1 and F is expressed in g cm-3. The isentropic apparent molar compressibility, Kφ(S), can be calculated from ultrasound measurements:12

Kφ(S) )

103(ks - k0s ) + ksVφ mF0

(4)

where ks and k0s are the isentropic coefficients of compressibility of the solution and water, respectively. The maximum error obtained in the range of concentration studied was about (0.05 cm3 bar-1 mol-1. The same method followed to calculate the volume error was used to calculate the error of Kφ(S), now with the variables F, m, and u. All these quantities provide a thorough description of the thermodynamic properties of aqueous solutions of the diblock copolymer P94E316.

3. Results and Discussion 3.1. Apparent Molar Volumes. Solute-solute and solute-solvent interactions can be obtained from the concentration dependence of the apparent molar thermodynamic quantities. The dependence of the apparent molar volume, Vφ, of copolymer P94E316 on concentration, c, and temperature is shown in Figure 1. These plots give a general overview of the aggregation behavior of the copolymer. Plots of Vφ against concentration reveal structural changes occurring in solution at 20, 25, and 30 °C and show that the aggregation process is strongly dependent on temperature. As the cmc decreases with the temperature and low concentrations affect volume calculations by a large error, at 35, 40, 45, and 50 °C it was impossible to detect structural changes. At temperatures below 20 °C, the idea of working at concentrations higher than the cmc was rejected due to the high quantity of solute necessary to reach the critical concentration. The concentration dependence of apparent molar volumes, Vφ, reflects the nature of solute-solute interactions. Three regions are observed in the plot of Vφ against c for aqueous solutions of the copolymer Vφ: (i) At concentrations below the cmc, the copolymer is nearly independent of concentration until the cmc; this region is characteristic of the monomeric state. (ii) After the cmc, there is a steep rise in Vφ that increases with the concentration up to an upper limit of measurement that represents the change of monomeric to micellar state. (iii) Vφ becomes nearly independent of concentration; this last behavior is characteristic of the aggregate state and indicates that the micelle-only domain has been reached. Figure 1 shows only the three regions at 20 °C. The first region is observed at 5, 10, and 15 °C; the other two regions were impossible to work due to the high quantity of copolymer necessary to reach the cmc. The first region has not been detected at temperatures higher than 20 °C because the cmc decreases with the temperature and low concentrations affect volume calculations by a large error. The second and third regions are observed at 25 and 30 °C. As can be observed at 20, 25, and 30 °C, the aggregation process extends over a wide concentration range, as a consequence of the reduced hydrophobicity of the oxypropylene chains when compared with that of purely aliphatic surfactants,13 (12) Franks, F.; Quickenden, M. J.; Ravenhill, J. R.; Smith, H. T. J. Phys. Chem. 1968, 72, 2668. (13) Senkow, S.; Mehta, S. K.; Douhe´ret, G.; Roux, A. H.; RouxDesgranges, G. Phys. Chem. Chem. Phys. 2002, 4, 4472.

Thermodynamic Properties of a Diblock Copolymer

Langmuir, Vol. 20, No. 20, 2004 8905 Table 2. Partial Molar Volumes at Infinite Dilution, V0φ, Obtained by the Group Contribution Scheme and Apparent Molar Volumes of the Copolymer in the Aggregate, Vm φ 0 0 T Vφc Vm T Vφc Vm φ φ (°C) (cm3 mol-1) (cm3 mol-1) (°C) (cm3 mol-1) (cm3 mol-1)

5 15 20 25 30

Figure 1. Apparent molar volume, Vφ, as a function of the concentration c for aqueous solutions at (]) 5, ([) 10, (+) 15, (b) 20, (O) 25, (9) 30, (0) 35, (2) 40, (4) 45, and (1) 50 °C. Table 1. Parameters V0φ, BV, and CV for Fits of Equation 5 T (°C)

V0φ (cm3 mol-1)

BV (cm3 kg mol-2)

CV (cm3 kg2 mol-3)

5 10 15

16 227 ( 2 16 324 ( 2 16 449 ( 3

0.8 ( 0.6 1.5 ( 0.8 2.2 ( 0.9

-0.04 ( 0.03 -0.055 ( 0.04 -0.095 ( 0.04

and becomes steeper with temperature, indicating that the process is more highly cooperative. In the copolymer PmEn aqueous solutions, the cooperativity of aggregation is much less important so that the self-assembly extends over a wider concentration range. The micellization occurs when the attractive forces between oxypropylene blocks dominate the oxyethylene repulsive interactions14 and the hydrophilic-hydrophobic balance favors the association. The extrapolation to infinite dilution of the apparent molar volume of the block copolymer monomer, V0φ, leads to its limiting partial molar volume that provides information on the hydration of the solute. Solute-solute interactions are obtained from the concentration dependence of the thermodynamic quantities. Usually, a virial expansion is used for partial or apparent molar quantities. For nonionic amphiphilic solutes, the expansion of the volume at premicellar concentrations gives the equation15

Vφ ) V0φ + BVm + CVm2

(5)

which was applied at the temperatures of 5, 10, and 15 °C. The parameters BV and CV are two adjustable parameters equivalent to the second and third virial coefficients, respectively. BV and CV measure the nonelectrostatic solute-solute interaction.16 Values of V0φ, BV, and CV obtained are shown in Table 1. A useful approach if the standard partial molar properties cannot be determined from the experimental data is modeling by group contribution schemes.3,18 Contributions (14) Malmstein, M.; Lindman, B. Macromolecules 1992, 25, 5440. (15) Desnoyers, J. E.; Perron, G.; Roux, A. H. In Surfactant Solutions; Zana, R., Ed.; Marcel Dekker: New York, 1987; Chapter 1. (16) Brun, T. S.; Hφiland, H.; Vikingstad, E. J. Colloid Interface Sci. 1978, 63, 89. (17) Gutierrez-Pichel, M.; Taboada, P.; Varela, L. M.; Attwodd, D.; Mosquera, V. Langmuir 2002, 18, 3654. (18) Harada, S.; Nakajima, T.; Komatsu, T.; Nakagawa, T. J. Solution Chem. 1978, 7, 463.

16287.4 16488.56 16585.3 16660.9 16743.5

16656.8 16888.8 17005.3

35 40 45 50

16826.4 16907.4 16969.9 17056.9

17105.0 17192.4 17267.4 17337.6

to the volumes at infinite dilution from ethylene oxide, δV(E), and propylene oxide, δV(P), have been determined at several temperatures13,19 (δV(E) ) 36.08, 36.55, 36.74, 36.92, 37.11, 37.28, 37.45, 37.63, and 37.81 cm3 mol-1 and δV(P) ) 51.98, 52.54, 52.93, 53.13, 53.37, 53.68, 53.97, 54.03, and 54.35 cm3 mol-1 at 5, 15, 20, 25, 30, 35, 40, 45, and 50 °C, respectively). Therefore, limiting partial molar volumes of the monomers of the diblock copolymer P94E316 0 can be calculated. The values are shown in Table 1 as Vφc . The hypothesis of additivity of the group contribution schemes is not of general validity and, then, can lead to incorrect values of the volume and the expansibility of micellization, ∆Vm and ∆Em (not reported in this work). The maximum difference obtained in the present work between the apparent molar volumes calculated by the virial expansion model and the group contribution scheme of the copolymer P94E316 was 39 cm3 mol-1, which makes a difference of 0.2%. Pluronics associate as uniform spherical micelles20,21 with the core formed by P groups, while the hydrated PE blocks constitute the outer shell with an aggregation number that increases with temperature.4 As can be observed in Figure 1, Vφ tends to a near constant value, Vm φ , that can be taken as the apparent molar volume of the monomer in the aggregate. Values of Vm φ obtained after lineal fitting are shown in Table 2, where it can be observed that an increment of the temperature increases Vm φ , but the increment is shorter for each temperature increment. This shows that in the temperature range of 20-50 °C, the micellar size increases with temperature, confirming previous reported data.20,21 The high values of Vm φ , if compared with those apparent molar volumes at high concentration reported of other Pluronics13 (E13P30E13 and E20P69E20, 2545 and 5260 cm3 mol-1 at 20 °C, respectively), reflect the interaction of different hydrophilic/hydrophobic ratios and also the geometric contribution. The cmt was analyzed at concentrations of 0.1, 0.25, 1, and 10 g dm-3 in the temperature range of 20-50 °C. In Figure 2 are shown plots of concentrations 1 and 10 g dm-3 at different temperatures. Similar plots were obtained for the other concentrations. The sharp increase in Vφ shown in Figure 2 illustrates the aggregation process that results from the gradual dehydration of the monomer species, coupled with the enhanced attractive hydrophobic interactions between propylene oxide chains.13 The cmt was determined as the concentration when the apparent molar volume departs from the straight line. The values so obtained are shown in Table 3 and are in agreement with the cmt values previously obtained using other experimental techniques, such light scattering and dye solubilization.6 It is clearly (19) Simek, L.; Bohdanecky, M. Eur. Polym. J. 1996, 32, 129. (20) Mortesen, K.; Pedersen, J. S. Macromolecules 1997, 26, 8805. (21) Chu, B.; Zhou, Z. In Nonionic Surfactants; Nace, V. M., Ed.; Marcel Dekker: New York, 1996.

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Figure 2. Apparent molar volume, Vφ, as a function of temperature, T, in kelvin, for aqueous solutions of (b) 1 and (9) 10 g dm-3. The arrows denote the cmt. Table 3. Critical Micelle Temperature Values Obtained by Apparent Molar Volumes and Sound Velocity apparent molar volumes c (g

dm-3)

0.1 0.25 1 10 a

sound velocity

cmt (°C)

c (g

26 25 22 (22)a 18 (18)a

dm-3)

0.01 0.25 1 10

cmt (°C) 31 25 22 19

Values in parentheses are from ref 6.

Table 4. Effect of the Pressure on the Standard Partial Molar Enthalpy of the Copolymer in Water, DH0/Dp, and on the Apparent Molar Enthalpy of the Copolymer in the Aggregate, DHm/p T ∂H0/∂p ∂Hm/∂p T ∂H0/∂p ∂Hm/∂p (°C) (cm3 mol-1) (cm3 mol-1) (°C) (cm3 mol-1) (cm3 mol-1) 5 10 15 20 25

8871.1 8949.6 9068.2 9654.1 9969.2

6763.0 8316.0

30 35 40 45 50

10303.4 10649.8 11006.4 11356.5 11743.0

9805.5 11327.2 12886.6 14183.6 16125.8

observed in the figure that (a) higher copolymer concentrations lead to lower cmt’s and that (b) the volume after aggregation at a given temperature is independent of the concentration for T > 300 K. 3.2. Apparent Molar Expansibilities. Apparent molar expansibilities in aqueous solution are very sensitive to hydrophobic and hydrophilic solute-solute interactions.13,22 As can be seen in Figure 1, Vφ increases with temperature and, therefore, the apparent expansibility of the monomers and aggregates is positive in both cases. The slopes of the plots of Viφ (i ) 0, m for monomers and aggregates, respectively) versus temperature were E0φ ) 3 -1 94 - 0.24T and Vm K-1, where T φ ) 326.9 - T cm mol is the thermodynamic temperature, with a correlation coefficient of 0.997 and 0.991, respectively. The dependence on temperature may reflect the different states of hydration of the micellar core. De Lisi and Milioto23 have reported for copolymer L64 an expansibility of micellization of -1.74 ( 0.08 cm3 mol-1 K-1, negative as is observed for the surfactant systems. In our case, the positive value indicates the predominance of hydration of the hydrophobic solute molecules.24 (22) Desnoyers, J. E.; Caron, G.; de Lisi, R.; Roberts, D.; Roux, A.; Perron, G. J. Phys. Chem. 1983, 87, 1397. (23) de Lisi, R.; Milioto, S. Langmuir 2000, 16, 5579. (24) Eagand, D.; Crowther, N. J. Faraday Symp. Chem. Soc. 1983, 17, 141.

Figure 3. Apparent molar expansibility, Eφ, as a function of temperature, T, for aqueous solutions of copolymer P94E316 at (b) 0.025, (O) 0.1, (9) 0.5, and (0) 1 g dm-3.

Accurate volume and expansibility data can provide information regarding the effect of the pressure on the enthalpy, because

∂V ∂H )V-T ∂p ∂T

(6)

m If V0φ, E0φ and Vm φ , Eφ are inserted into eq 6, then the enthalpy term will be the standard partial molar enthalpy of the copolymer in water and in the aggregate. Table 4 shows values of the effect of the pressure on the molar enthalpy of the copolymer in water and in the aggregates. An increment of the pressure, just as an increase in temperature, renders the solution and the aggregation processes exothermic from 20 to 30 °C and endothermic at higher temperatures. The effect of the pressure is to decrease the intermolecular distances so that the energetic interactions become more favorable. Figure 3 shows, for selected concentrations of the copolymer, the variation of Eφ with temperature at different copolymer concentrations. The expansibilities were calculated directly from the temperature dependence of apparent molar volumes. At lower temperatures, when only monomers should be present, Eφ remains positive with a value that shows the presence of preaggregates. At high temperatures that favor complete association of monomers, similar values of Eφ are seen. This gives rise to a large increase in Eφ that shows a sharp maximum, progressively shifted to lower temperatures as the copolymer concentration increases. This clearly indicates that the transition from monomers to aggregates is correlated with decreasing hydration of the low hydrophobic P units. 3.3. Sound Velocity and Compressibilities. For a nonscattering system, there is a simple relationship between the ultrasonic velocity of a solution and its physical properties. Assuming that the wavelength of sound is much greater than the particle size and independent of the frequency, the compressibility can be described by eq 3. For systems where scattering is important, the velocity is dependent on the particle size and frequency and appreciable velocity dispersion may occur. Rassing and Attwood25 and Wen and Verrall26 have shown that the speed of sound is very sensitive to the

(25) Rassing, J.; Attwood, D. Int. J. Pharm. 1983, 13, 47. (26) Wen, X. G.; Verrall, R. E. J. Colloid Interface Sci. 1997, 196, 215.

Thermodynamic Properties of a Diblock Copolymer

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Figure 5. Isentropic apparent molar compressibilities, Kφ(S), as a function of the concentration, c, at (]) 5, ([) 10, (+) 15, (b) 20, (O) 25, (9) 30, (0) 35, (2) 40, (4) 45, and (1) 50 °C. Table 5. Apparent Molar Adiabatic Compressibilities at 0 Infinite Dilution, Kφ(S) , Isentropic Apparent Molar Adiabatic Compressibilities of the Monomer in the m Aggregate, Kφ(S)

Figure 4. (a) Sound velocity, u, vs concentration, c, for aqueous solutions of copolymer P94E316 at 20° C. The dotted line represents the Gaussian fit of the second derivative of the ultrasound-concentration curve. The arrow denotes the cmc. (b) Sound velocity, u, vs temperature, T, at concentrations of (O) 0.25 and (b) 10 g dm-3. The arrows denote the cmt’s.

T (°C) 5

a

onset of association processes induced by increasing temperature or concentration. The velocity of sound is smaller in solutions containing aggregates and monomeric species than those containing monomeric species only. Consequently, isentropic compressibilities exhibit concentration dependence. Values of the cmc at 20 °C were detected by sound velocity and determined by an analytical method based on the Phillips definition of the cmc:27

( ) d3u dm3

)0

(7)

m)cmc

The numerical analysis of the data was made by means of a recently developed algorithm based on the RungeKutta numerical integration method and the LevenbergMarquardt least-squares fitting algorithm which allows the determination of precise values ((0.05%) of the cmc’s.28 Figure 4a shows the measured ultrasound velocity data and a Gaussian fit of its second derivative, at the temperature of 20 °C, from which a value of 2.34 g dm-3 for the cmc was calculated. The cmc’s obtained by apparent molar volumes, microcalorimetry,5 and surface tension6 are in agreement with the value obtained by ultrasound velocity. Variation of sound velocity with temperature was also studied. The temperature dependence of sound speeds at concentrations of 0.01, 0.25, 1, and 10 g dm-3 shows that u steeply increases as the temperature is raised, as is shown in Figure 5b for concentrations of 0.25 and 10 g dm-3. The cmt’s were calculated applying the same procedure as for the cmc’s. The values are shown in Table 2. Figure 5 shows plots of the isentropic apparent molar compressibility, Kφ(S), against concentration at different (27) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561. (28) Pe´rez-Rodriguez, M.; Prieto, G.; Rega, C.; Varela, L. M.; Sarmiento, F.; Mosquera, V. Langmuir 1998, 14, 4442.

10

15

20

25

30

35

40

45

50

0 a -0.59 -0.44 -0.31 Kφ(S) m a 12 0.19 0.32 0.35 0.37 0.41 0.46 Kφ(S) 0 m Kφ(S) and Kφ(S) are in cm3 bar-1 mol-1.

temperatures. Previous studies29,30 of Kφ(S) have shown that this quantity is large and negative for ionic compounds in water, positive for mainly hydrophobic solutes, and intermediate, small, and negative for uncharged hydrophilic solutes such as sugars. The values of Kφ(S) at concentrations above the cmc, at temperatures between 20 and 50 °C, are positive and those below the cmc, between the temperatures 5 and 25 °C, are negative, which reveals that monomers trapped in the micellar hydrophobic environment are more compressible than aqueous free monomer in solution. If the intrinsic compressibility of the solute is considered zero, the observed compressibilities are ascribed to the compressibility of the hydration sheath, and an increase of Kφ(S) characterizes the progressive hydration loss of propylene oxide blocks that accompanies the aggregation process, as has been seen previously by other authors for triblock EPE copolymers.13 Kφ(S) is negative at premicellar concentrations between 5 and 20 °C as corresponds for many uncharged solutes, increasing with concentration up to small and positive values as corresponds to hydrophobic solutes. As can be observed in Table 5, the positive isentropic apparent molar compressibilities of the monomer P94E316 m in the aggregate, Kφ(S) , increase with temperature due to a decrease in the amount of structured water in the vicinity of the copolymer, which is less compressible than bulk water. In the other hand, the negative values of the isentropic apparent molar compressibilities at infinite m , obtained are a consequence of the higher dilution, Kφ(S) resistance to pressure of the structured water around the monomer compared to that of bulk water. (29) Hφiland, H.; Vikingstand, E. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1441. (30) Franks, F.; Ravenhill, J. R.; Reid, D. S. J. Solution Chem. 1972, 1, 3.

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4. Conclusions The aim of the present work was to investigate the nature and magnitude of interactions in aqueous solutions of diblock copolymer P94E316 over a wide concentration and temperature range (5-50 °C). The volume data of the copolymer in the temperature range of 20-50 °C show that the aggregation process is strongly dependent on the temperature, the dependence of the volume of the monomer in the aggregate arising from the interactions of some oxypropylene chains with water. At low concentrations, the data reveal structural changes at 20, 25, and 30 °C. The micellization of the copolymer can be incited at a given concentration by increasing the temperature, and higher copolymer concentrations lead to lower values of the critical micelle concentration. Also, the volume after aggregation at a given temperature is independent of the concentration for T > 300 K.

Taboada et al.

It has been observed that the intrinsic apparent molar compressibilities of the aggregates increase with temperature due to a decrease in the amount of structured water in the vicinity of the copolymer, which is less compressible than bulk water. Acknowledgment. The project was supported by the Ministerio de Ciencia y Tecnologı´a through project MAT2001-2877 and Xunta de Galicia. P.T. thanks the Ministerio de Ciencia y Tecnologı´a for his Ramo´n y Cajal position. Supporting Information Available: Density and sound velocity of block copolymer P94E316 at different temperatures. This material is available free of charge via the Internet at http://pubs.acs.org. LA0491302