Langmuir 1999, 15, 1891-1892
1891
Thermodynamic Calculations on Micellization and Micellar Structure of a Poly(ethylene oxide)/Poly(propylene oxide)/Poly(ethylene oxide) Triblock Copolymer in Water Solution, As Studied by the Spin Probe Technique
cases correspond, on the contrary, to opposite effects on the Helmholtz free energy F of the system.
Cesare Oliva,* Horia Caldararu,† and Agneta Caragheorgheopol†
P h 2 is a dimensionless parameter varying between 0 and 1, and not a true physical quantity.4 Therefore, it is difficult to attribute any physical meaning to its variation. However, a few years ago a procedure was proposed5,6 that was able to overcome this difficulty, on the basis of statistical thermodynamic calculations. Following the h 2 is the Maier-Saupe theory,4 the order parameter P average of the Legendre polynomial P h 2(cos β), that is,
Dipartimento di Chimica Fisica ed Elettrochimica, Universita` di Milano, e Centro C.N.R., Via Golgi 19, 20133 Milano, Italy, and Romanian Academy, Institute of Physical Chemistry “I.G.Murgulescu”, Splaiul Independentei 202, 77208 Received October 22, 1998. In Final Form: December 10, 1998
Introduction During an investigation1 on micellization and micellar structure of the poly(ethylene oxide)27 (PEO) and poly(propylene oxide)39 (PPO) triblock copolymer PEO-PPOPEO (Pluronic P85), the low degree of P85 micellization occurring at 298 K was pointed out by the fact that at this temperature the spin probe TEMPO-hexanoate (C6-NO) in 10% w/w aqueous solution of P85 distributed between water and micelles giving two electron paramagnetic resonance (EPR) spectra overlapping each other in approximately a 1:1 ratio. By contrast, only the EPR spectrum due to C6-NO in P85 micelles was recorded at T > 303 K, indicating that an almost complete micellization occurs at these temperatures, as already reported by other authors.2 C6-NO spin probing of P85 provided also qualitative evaluations of the (local viscosity related) fast-tumbling correlation time τc, which resulted from the same order of magnitude (10-10 s) of the ones obtained3 by NMR analysis. These data were also confirmed1 by using other spin probes. Furthermore, complementary information were obtained with 5-doxylstearic acid (5DSA) in an alkaline aqueous solution. In fact, in this case fast isotropic rotational diffusion did not affect the EPR spectra. Therefore, the last provided an evaluation of the Maier and Saupe order parameter4 S (hereafter indicated h 2 refers to the local order at by P h 2) (Figures 1a and 2a). P the probed position along the micellar radius. In these triblock water-soluble copolymers, PPO is hydrophobic, while PEO is hydrophilic, and water molecules act as binders between EO chains giving them an ordered structure. At higher temperatures partial dehydration occurs, resulting in a P h 2 decreasing. As a consequence, also the entropy and the free energy of the system change. In the previous work on this subject1, the authors observed that the addition of alcohols had similar effects with a temperature increase, as both these experiments promote micellization, reduce the hydration, and cause an analogous decrease of P h 2. In the present note we deepen this subject by showing that the analogous variation of P h 2 observed in the two * To whom correspondence should be addressed at the Universita` di Milano. † Romanian Academy. (1) Caragheorghepol, A.; Caldararu, H.; Dragutan, I.; Joela, H.; Brown, W.: Langmuir 1997, 13, 6912. (2) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Macromolecules 1994, 27, 2414. (3) Godward, J.; Heatley, F.; Booth, C. J. Chem. Soc. Faraday Trans. 1995, 91, 1491. (4) Meier, V. W.; Saupe, A.; Z. Naturforsch., Tail A 1958, 13, 564; 1959, 14, 882; 1960, 15, 287.
Statistical Thermodynamic Calculation Procedure
P h2 )
∫0πP2(cos β) f(β) sen β dβ
(1)
where f (β) is the orientational distribution function:
f(β) ) exp[-aP h 2P2(cos β)/kT]/Z
(2)
in which the internal energy U(β) at the orientation is expressed approximately by
U(β) = -a P h 2 P2(cos β)
(3)
and Z is the canonical partition function. When eqs 3 and 2 are substituted together with the experimental value of P h 2 into eq 1, a new equation is obtained in which the only unknown is a. By this way, the partition function Z can be easily calculated5,6 as well as the thermodynamic parameters entropy S, internal energy U, and Helmholtz free energy F ) U - TS, at each temperature T. Results In Figure 1a the order parameters P h 2 obtained1 from the anisotropic spectra of 5-DSA monitoring P85 at room temperature are reported as a function of added C6OH concentration. In parts b, c, and d of the same figure entropy, internal energy, and Helmholtz free energy values are reported, as obtained from P h 2 by eqs 1-3. In Figure 2a some P h 2 values are reported versus temperature for a P85 sample in the absence of C6OH. In parts b-d of the same figure the corresponding thermodynamic parameters are also shown. We can observe that P h 2 decreases at both increasing alcohol concentration and temperature, and that, correspondingly, S and U increase in both the cases. When a 3% v/v of C6OH is added to the system at 298 K, its entropy value S increases by about 2 J K-1 mol-1, half the value measured upon a temperature increase from 298 K up to 373 K. At the same time, U increases by about 1. kJ mol-1 in the first case, and of twice such a value in the second case. However, the most interesting parameter to be considered is F, which indicates the thermodynamic “stability” of the system. The difference at each temperature between the internal energy and TS provides the values of the free (5) Oliva, C.; Marchesini, S.; Cervato, G.; Viani, P.; Cestaro, B. Il Nuovo Cimento 1985, 6D, 585. (6) Oliva, C.; Viani, P.; Marchesini, S.; Cestaro, B. Il Nuovo Cimento 1988, 10D, 793.
10.1021/la981485w CCC: $18.00 © 1999 American Chemical Society Published on Web 02/02/1999
1892 Langmuir, Vol. 15, No. 5, 1999
Notes
v v
Figure 1. (a) Experimental order parameters P h 2, measured with 5-doxyl stearic acid probing a 5% w/w aqueous 0.1 N NaOH solution of a triblock copolymer (Pluronic P85), and calculated (b) entropy S, (c) internal energy U, and (d) Helmholtz free energy F, versus the percentage (v/v) of added C6OH at room temperature.
energy displayed in Figures 1d and 2d as a function of added C6OH and of the temperature, respectively. Discussion It is worth noting that, in the series versus added C6OH, the system has the lowest F value, that is, is more stable, when it has the highest P h 2 value, that is, when no C6OH is added. On the contrary, in the series versus T the highest stability is observed in correspondence of the lowest P h2 value, that is, at the highest temperature. Therefore, addition of C6OH and increasing temperature have a similar influence on P h 2 variation, but the opposite effect on the free energy of the system, and therefore on its stability. The fact that higher F values are measured at higher contents of C6OH indicates that the examined system loses in part its stability by interacting with added C6OH molecules. In particular, in the range between 0 and 3%
Figure 2. (a) Experimental order parameters P h 2, measured with 5-doxyl stearic acid probing a 10% w/w aqueous 0.1 N NaOH solution of a triblock copolymer (Pluronic P85), and calculated (b) entropy S, (c) internal energy U, and (d) Helmholtz free energy F, versus temperature.
v/v of added C6OH, the addition of 1% v/v of C6OH to the system would cause a mean increase of the free energy of about 180 J mol-1. However, we must outline that the above calculated change of entropy and of free energy due to increasing temperature or to alcohols addition are just a small part of the total amount of the standard value (∆S° ) 842 J mol-1 and ∆G° ) -25.5 kJ mol-1) required for P85 micellization at its critical micellization temperature (reported2 for a 1% solution). At last, we can outline that statistical thermodynamic calculations based on experimental P h 2 values lead to more detailed information on the examined system than the rough consideration of its P h 2 parameters alone. In particular, such a procedure leads to a quantitative evaluation of the configurational free energy contribution to the stability of disordered systems. LA981485W
