1738
J. Phys. Chem. 1996, 100, 1738-1745
Effect of Cosolvents and Cosolutes upon Aggregation Transitions in Aqueous Solutions of the Poloxamer F87 (Poloxamer P237): A High Sensitivity Differential Scanning Calorimetry Study Jonathan Armstrong,†,‡ Babur Chowdhry,† John Mitchell,§ Anthony Beezer,§ and Stephen Leharne*,⊥ School of Biological and Chemical Sciences, UniVersity of Greenwich, Wellington Street, Woolwich, London SE18 6PF, U.K., The Chemical Laboratory, The UniVersity, Canterbury, Kent CT2 7NH, U.K., and School of EnVironmental Sciences, UniVersity of Greenwich, Creek Road, Deptford, London SE8 3BW, U.K. ReceiVed: May 19, 1995; In Final Form: September 26, 1995X
The effects of a number of different cosolvents and cosolutes upon the micellization of the oxyethylene/ oxypropylene/oxyethylene block copolymer F87 (P237; 70% oxyethylene and 30% oxypropylene) have been investigated using high-sensitivity differential scanning calorimetry (HSDSC). The calorimetric output has been analyzed using a model fitting procedure to obtain estimates for various thermodynamic parameters which characterize the micellization event as observed by HSDSC. These important parameters include T1/2, the temperature at which the micellization process is half-completed, ∆Hcal, the calorimetric enthalpy for the process which is measured by integration of the calorimetric output; ∆HvH, the van’t Hoff enthalpy; and n the aggregation number. From this data it has been possible to measure critical micelle concentrations (cmcs). The experimental investigations reveal that methanol, ethanol, urea, and formamide prevent the onset of micellization, while butanol and hydrazine favor micelle formation. Finally a thermodynamic model simulation is developed and presented which appears to be capable of explaining the major effects of methanol upon micellization.
Introduction ABA type block copolymers based upon ethylene oxide (the A block) and propylene oxide (the B block) are of significant commercial interest. They find numerous uses in a variety of industrial and pharmaceutical applications, such as in the formulation of aqueous preparations of non-water soluble drugs and cosmetics. A great deal of attention has been paid to increasing our understanding of their interesting physicochemical properties in aqueous solution. For example these systems exhibit the unusual property of gelation upon heating.1 Gelation, however, only occurs in concentrated solution. For example poloxamer P407 (F127) (chemical formula EO108PO69EO108), used as obtained from the manufacturer, gels at concentrations greater than 170 g kg-1.2 The aggregation or micellization properties of the poloxamers in more dilute solution have been the focus of numerous recent research reports.2-10 Micellization has been studied using a wide variety of techniques. In previous contributions to the literature we have explored the use of NMR and more importantly high-sensitivity differential scanning calorimetry (HSDSC) to characterize these phenomena.11-15 More recently, we have successfully fitted the observed HSDSC signals to a mass action based aggregation model.16 The information obtained from the model fitting has enabled us to suggest that the aggregation phenomenon observed by HSDSC is characterized by the aggregation of material that has already aggregated. It would appear that, for an extensive range of block copolymers in dilute solution (varying in concentration from 1 * Author to whom correspondence should be addressed. † School of Biological and Chemical Sciences, University of Greenwich, Woolwich. ‡ Present address: Department of Physiology and Biophysics, School of Medicine, University of Southern California, Los Angeles, CA 90033. § The University, Canterbury. ⊥ School of Environmental Sciences, University of Greenwich, Deptford. X Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-1738$12.00/0
to 20 g dm-3), assemblies, typically of about three aggregates, themselves consisting, on average, of between two and three molecules, are formed.16 To date, HSDSC measurements of these thermodynamic properties have not been made in the presence of cosolvents and cosolutes. It therefore appears appropriate to measure some fundamental thermodynamic parameters characterizing cosolvent interactions with these copolymers. Furthermore given that the poloxamers are often used in proprietary pharmaceutical formulations that contain a number of other materials, it is also important to investigate how additives may alter aggregation processes in these block copolymers. Indeed the solubilization of insoluble solutes is very often purposely influenced by the presence of a cosolvent17 which in many cases may be an alcohol. The object then of this paper is to report data which indicate the effects of alcohols on the aggregation processes, as followed by HSDSC for the poloxamer P237 (EO61PO40EO61 containing 70% oxythylene). The study is complemented by observations of the effect of other cosolutes on the aggregation process. Materials and Methods Poloxamer P237 was obtained as a gift from ICI (Cleveland, U.K.). It was used as supplied. The alcohols (methanol, ethanol, propanol, and butanol) and urea were AnalaR Grade obtained from BDH (Poole, Dorset, U.K.), AnalaR formamide and hydrazine were obtained from Aldrich (Dorset, U.K.). Solutions were prepared by dissolution of the poloxamer in doubly distilled water and cosolvent mixture. Solution phase HSDSC studies were carried out using a Microcal MC2 microcalorimeter (Microcal, Amherst, MA). The MC2 contains a fixed pair of matched tantalum cells which are filled with the sample and reference solutions, respectively. The cell volumes measure 1.1902 mL. Pressure in the cells was maintained by © 1996 American Chemical Society
Aggregation Transitions in Poloxamer F87 Solutions
Figure 1. HSDSC traces obtained for P237 in various aqueous methanol solution mixtures. The concentration of P237 in each case was 5 g dm-3.
a nitrogen cylinder normally set at 1 atm. The instrument is capable of measurement in the temperature range of 5-95 °C. Dedicated software (DA2, Microcal) is used to control the calorimeter and acquire data. Samples were normally scanned at 60 K h-1. The instrument is however capable of scanning down to 10 K h-1. Scanning at several different scan rates was undertaken. The lack of scan rate dependence of the measured calorimetric parameters of ∆Hcal (the area obtained by integration of the calorimetric trace) and T1/2 (the temperature at which the area under the curve is equal to 1/2∆Hcal) indicates the process to be under strict thermodynamic control. Water base lines were run periodically. These were always flat.
J. Phys. Chem., Vol. 100, No. 5, 1996 1739 saturated concentration of molecularly dispersed species.23 The fact that measurements of surface tension as a function of surfactant concentration for a number of the poloxamers3,10 show that in the region of micellization the surface tension does not remain constant but changes quite markedly indicates that the concentration of surfactant monomer is dependent upon the number of micellar aggregates and as such contradicts a phase separation interpretation. In calorimetric terms it should also be expected that phase separation should give rise to an extremely sharp rise in the apparent excess heat capacity of a HSDSC trace.19 Such a sharp rise would occur because at some temperature infinitesimally smaller than the phase separation temperature the heat capacity of the system would be determined by the presence of unaggregated surfactant in water. At some temperature infinitesimally greater than the phase separation temperature, the heat capacity of the system would include a further contribution from the micellar phase. Thus, phase separation, because of its abrupt nature, should give rise to a discontinuity in apparent excess heat capacity. Alternatively it could be argued that phase separation can be thought of as the formation of an aggregate of infinite size.21 HSDSC simulation can be used to demonstrate that this produces a vertical leading edge for the HSDSC signal. The leading edge in the HSDSC traces in Figure 1 show that although the increase in apparent excess heat capacity is fairly sharp, it cannot be described as discontinuous, which is what a phase separation model would demand. It is therefore concluded that the HSDSC signals should be analyzed using an aggregation model in which the aggregation numbers are quite modest. Such an equilibrium description of aggregation, in which n molecules of X form an aggregate, may be written as21
nX a Xn
Results and Discussion Data Assessment and Model Fitting the DSC Output to an Aggregation Process. A typical example of the HSDSC output obtained in this study is shown in Figure 1. The calorimetric outputs were obtained for aqueous solutions of P237 (concentration, 5 g dm-3) consisting of various amounts of methanol. A number of important features should be noted. The calorimetric transitions are fully reversible, and the measured thermodynamic parameters are independent of scan rate. Scan rate independence convincingly indicates that the process under investigation is under strict thermodynamic control.18 The heat capacity of the posttransitional portion of the transitions is lower than the pretransitional portion. Such behavior provides evidence that the process is accompanied by a permanent decrease in the heat capacity of the system. The decrease in heat capacity can be taken to signify a reduction in water structure. Such a result would be anticipated given the nature of the process under investigation (see below). The shapes of the heat capacity vs temperature outputs are indicative of an aggregation process.19 The formation of micellar aggregates is normally considered to be an example of a phase separation process, and the aggregation of poloxamer compounds has been analyzed using thermodynamic relationships that describe phase separation.2,20 There are, however, problems with such an analysis. Phase separation implies that formation of micelles is an abrupt process21 since there cannot be any prephase separation aggregation.22 Thus, under isothermal conditions, the process should be characterized by a single value for the concentration of unaggregated surfactant in aqueous solutionsthe so called critical micelle concentration (cmc). The cmc should be independent of the number of micelles present in solution21 and is assumed to represent the
If we now define the extent of aggregation, R, as the fraction of polymer chains present in micelles, we can obtain the following expressions:
[Xn] ) Rc/n
(1)
[X] ) (1 - R)c
(2)
where c is concentration. The equilibrium constant, K, for the process may then be written as
K ) [Xn]/[X]n ) R/n(1 - R)ncn-1
(3)
If we assume that over the temperature range within which the transition occurs the enthalpy change is independent of temperature, then the expression for K may be substituted into the following indefinite integral form of the van’t Hoff isochore
ln K )
-∆HνH + IC RT
(4)
to produce
ln
(
)
-∆HνH R ) + IC n n-1 RT n(1 - R) c
(5)
where T is temperature, ∆HvH is the van’t Hoff enthalpy, R is the gas constant, and IC is the integration constant. The integration constant may be found by setting T ) T1/2 (T1/2 being the temperature at which the extent of reaction R is equal to 0.5). Substituting for the integration constant and subsequent
1740 J. Phys. Chem., Vol. 100, No. 5, 1996
Armstrong et al.
rearrangement produces the following expression:
[
T ) 1/
[
]]
1 0.5n-1R R ln T1/2 ∆HνH (1 - R)n
(6)
In this form, R is made the independent variable and T is the dependent variable. This unusual way of expressing the relationship makes the model fitting procedure very much easier. The establishment of this equilibrium description of the process allows the data to be analyzed in the following way. DSC measures the power required to maintain the temperature of the sample cell at the same temperature as the reference cell as the temperature of both is raised. The output obtained from the instrument is thus a data set of power as a function of temperature. The power data are readily converted to heat capacity using the following equation:
φCp,xs ) P/σm
(7)
where φCp,xs is the apparent excess heat capacity, P is power, σ is the scan rate, and m is the number of moles of sample. φCp,xs can also be formulated as follows:
φCp,xs ) ∆Hcal
dR dT
(8)
where ∆Hcal is the enthalpy obtained by integrating the area under the DSC signal. Equation 8 shows that the heat capacity of the system can be related to fractional enthalpy changes as a function of temperature. The derivative dR/dT is readily obtained by converting eq 3 to a logarithmic form and differentiating ln K with respect to R:
(∂ ∂Rln K)
n,c
)
1 n + R 1-R
(9)
Combining this derivative with the van’t Hoff isochore produces:
∆HνH 1 ∂ ln K ∂R n dR ) 1/ + ) 2 dT ∂T p,n ∂ ln K p,c,n R 1 R RT
(
) (
)
((
Figure 2. Model fitting the HSDSC output obtained for P237 in a 5% methanol water solution mixture.
))
(10)
Calculating dR/dT using eq 10 allows the excess heat capacity to be calculated using eq 8. These equations form the basis of the simulation process outlined later in the text. For model fitting, the DSC data output was first numerically transformed using eq 7 to produce a data set of heat capacity as a function of temperature. The data were further transformed to provide a data set of R vs T. The extent of aggregation at any particular temperature is considered to be the enthalpy released at that temperature divided by the entire enthalpy change for the process. A nonlinear least squares curve fitting program was used to fit the extent of aggregation vs temperature data to eq 6 and thereby provide best fit values for n, T1/2, and ∆HvH. Sturtevant24 has pointed out that at the start and end of a transition there may be a distribution of van’t Hoff enthalpy values, including some relatively small values; thus, R values between 0.1 and 0.7 were used for the model fitting exercise. An example of the fit is shown in Figure 2, where it is clear that the model is reasonably representative of the aggregation process under investigation. Nature of the Aggregation Process. A number of workers have investigated the aggregation process in aqueous poloxamer solutions. There is a widely accepted agreement that the oxypropylene core of the macromolecule provides the hydrophobic portion,25 while the oxyethylene ends provide the hydrophillic portions. Physical modeling has been used to show
that both oxyethylene and oxypropylene blocks are capable of fitting into ice structures and are thus hydrated in aqueous solutions by a “structured” water shell.26 The fit for oxyethylene is good, whereas that for oxypropylene is strained because of the pendant CH3 group.26 This results in a lower enthalpy release associated with hydrogen bond formation. As the temperature is increased, a number of processes combine to give rise to the dehydration of the oxypropylene core. The entropic gain to be made by the destruction of the structured water shell is commonly credited as providing the driving force for the process. At higher temperatures the entropic gain is greater than the enthalpic gain; thus, the free energy for the process becomes negative. However, there appear to be good reasons for believing that, mechanistically, the process may also be related to changes in the polarity of the oxypropylene core as the chain conformation changes. At low temperatures oxyethylene is believed to adopt a polar conformation. As the temperature increases, there become available a greater number of nonpolar conformations which thus provide an entropic driving force for conformational change.27,28 The eventual adoption of a nonpolar conformation would in turn be expected to affect interactions with water. More recently8,31 the assumption that similar conformational changes occur in oxypropylene has produced a model which is qualitatively capable of reproducing poloxamer phase behavior. Several studies have recognized that the aggregation process is fairly complex in that several aggregation states have been noted.5-7,29 Preceding micelle formation light scattering has detected the formation of extremely large aggregates whose generation has been attributed to the presence of a relatively hydrophobic diblock impurity.6,7,29 These aggregates break up on warming, and the diblock impurity is thought to become incorporated into the micelles. Finally it should be recognized that the thermodynamic model outlined in the previous section suggests that the concentration of micellar aggregates is continually increasing with rising temperature. Mortensen35 using small angle neutron scattering has shown this to be true for P235 (poloxamer F85). Effects of Cosolvent and Cosolute Concentration upon the Thermodynamic Data. The data obtained for the effect of cosolvents and cosolutes on the poloxamer P237 are shown in Table 1. A number of key points emerge from a scrutiny of the data. It is clear that methanol, ethanol, urea, and formamide tend to raise the temperature range over which aggregation occurs. Propanol, butanol, and hydrazine decrease this temperature range. The specific effects will be examined in more detail below. Values for the van’t Hoff enthalpy (which is evaluated from the change in the equilibrium constant character-
Aggregation Transitions in Poloxamer F87 Solutions
J. Phys. Chem., Vol. 100, No. 5, 1996 1741
TABLE 1: Effect of Various Cosolvent and Cosolute Concentrations on the HSDSC Data Obtained for Pluronic P237a concnb (%) methanol 5 10 15 17.5 20 ethanol 5 10 15 20 propanol 2.5 5 7.5 10 butanol 2.5 5 7.5 [urea] (M) 1 2.034 4.107 6.15 8 hydrazine 5% 10% 15% 20% formamide 10 20 30 40
T1/2 (K)
∆Hcal (kJ mol-1)
∆HvH (kJ mol-1)
n
∆HvH/∆Hcal
319.2 321.6 324.4 325.8 328.8
158 126 119 92 53
628 582 381 397 474
3.6 3.6 2.5 2.7 2.9
4 4.6 3.2 4.3 8.9
319.3 321.2 324.3 329.6
143 106 59 10.9
599 526 458 731
3.5 3.2 2.8 3.0
4.2 5 7.8 67
317.0 315.1 315.1 314.8
170 159 90 77
732 669 772 614
4.2 4.0 3.7 3.1
4.3 4.2 8.6 8.0
311.8 304.8 296.1
193 230 280
693 560 575
3.7 2.7 2.5
3.6 2.4 2.0
323.8 324.3 327.6 331.6 335.6
148 138 119 131 157
587 586 469 422 401
4.7 4.3 2.9 3.1 4.1
4.0 4.3 3.9 3.2 2.6
312.0 307.6 302.4 296.8
200 254 237 230
669 747 721 821
3.7 5.3 4.7 5.9
3.4 2.9 3.0 3.6
320.7 324.2 328.7 333.9
166 133 105 89
557 492 461 413
3.8 3.4 3.4 3.5
3.4 3.7 4.4 4.6
a The following uncertainities are estimated for the data: T , (0.1 1/2 K; ∆Hcal, (3%; n, (5%; ∆HvH (5%. b The concentrations of urea, [urea], are in molar units.
izing the aggregation process with temperature) and calorimetric enthalpy (obtained by integration of the HSDSC trace) are also shown. T1/2 is a particularly important parameter characterizing the stability of the system. Since it is, by definition, the temperature of half-completion of the aggregation process, it is associated with a definite free energy. Using eq 3 this can be shown to be
∆G ) RT1/2 ln(0.5n-1cn-1n)
(11)
For a constant value for c and n, ∆G is solely dependent upon T1/2. Aggregation arises from a reversal of the process of hydrophobic hydration.17 Thus, T1/2 can be linked to the stability of the solvation sphere. Changes in the stability of the solvation sphere brought about by the incorporation of a cosolvent/ cosolute can thus be demonstrated by changes in T1/2. Under these circumstances changes in ∆HvH and ∆Hcal may be linked to the changes in T1/2 and reflect the fact that the aggregation process is accompanied by a permanent change in heat capacity, ∆Cp. If this is the case, then a plot of either ∆HvH or ∆Hcal against T1/2 should produce a straight line. All of the data obtained for both ∆HvH and ∆Hcal have been plotted with the corresponding T1/2 values and are shown in Figure 3. The figures obtained show a moderate amount of scatter but do suggest a reasonably linear relationship between the enthalpies
Figure 3. Plots of the van’t Hoff and calorimetric enthalpies as a function of T1/2.
and T1/2 values. R2 for the ∆HvH vs T1/2 plot is 75%, while for the ∆Hcal vs T1/2 plot it is 58%. ∆Cp,vH, the heat capacity change obtained from the ∆HvH vs T1/2 plot, is -12.6 kJ mol-1 K-1. ∆Cp,cal, the heat capacity change obtained from the ∆Hcal vs T1/2 plot, is -4.75 kJ mol-1 K-1. Changes in heat capacity are indicative of changes in structure which is related to changes in cohesion.32 It is therefore concluded that changes in T1/2 occur because the cosolvents/cosolutes produce cohesional changes. The shift of the transition to different temperatures and the permanent change in heat capacity result in changes in ∆HvH and ∆Hcal, in agreement with Kirchoff’s law.33 The values obtained for ∆HvH and ∆Hcal for each aqueous solution are different and reflect the difference in the way they were evaluated. More precisely they reflect a difference in what is perceived to be the molar unit in the enthalpic dimensions. ∆Hcal is obtained directly by integration of the HSDSC trace. The mole referred to in its units is obtained from the apparent excess heat capacity, which is calculated using eq 1. The number of moles, m, is the number of moles of chains and is given by the ratio mass/molar mass of P237. It can be shown, using the above equations, that ∆HvH is given by the following equation:
∆HνH )
2(n + 1)Cp,1/2RT1/2 ∆Hcal
(12)
where Cp,1/2 is the apparent excess heat capacity at T1/2 and the other symbols have their previously defined meanings. Equation 12 clearly demonstrates that both Cp,1/2 and ∆Hcal have the same molar definition which cancels out. The molar definition for ∆HvH is thus supplied by the gas constant, R, which is the proportionality constant obtained from the van’t Hoff isochore.
1742 J. Phys. Chem., Vol. 100, No. 5, 1996
Armstrong et al. aggregation by HSDSC16 these block copolymers are encountered predominantly as unimers, dimers, and trimers. The values obtained for n, the aggregation number, are also small. If we accept that the aggregation process is in fact the aggregation of aggregates, we can estimate that the micellar aggregates formed during the HSDSC experiments comprise in the main of somewhere between 5 and 26 molecules, depending upon the identity and concentration of cosolute/ cosolvent. The results obtained are comparable to those obtained by Brown for P237 (poloxamer F87) of 14. It has been demonstrated that the aggregation numbers increase with increasing temperature for the poloxamers,4,29 yet the analysis outlined in this paper clearly shows that the HSDSC signal can be modeled quite satisfactorily by assuming a constant aggregation numbersat least in the region of R values between 0.1 and 0.7. This seeming disparity can be resolved by suggesting that the further addition of molecules to the micellar aggregates is, by and large, a calorimetrically silent event. Effects of Cosolvent and Cosolute Concentration upon Micellization Parameters. The effect of alcohol type and concentration upon aggregation is outlined in Table 1. Increasing concentration of methanol and ethanol causes an increase in T1/2 (see Figure 4). The cmc can be thought of as being the aqueous concentration of monomeric surfactant which is in equilibrium with the micellar form of the surfactant. Then at T1/2 the concentration of monomer is half the total concentration of surfactant used to prepare the solution (c). This concentration, 1/2c, must therefore be considered to be the cmc at this temperature. Since the HSDSC outputs show no measured kinetic limitation and are therefore thermodynamically controlled, it must also be concluded that if a solution was prepared using the quantity 1/2c of surfactant, then, on warming, aggregation would occur at T1/2. T1/2 may therefore be thought of as being a critical micelle temperature for this concentration of surfactant. Thus, it is clear that for any particular cmc the addition of methanol and ethanol increases the critical micelle temperature. The cmc at any particular temperature may also be obtained from the HSDSC trace in the following way. Consider the following mass balance for the system:
c ) [X] + n[Xn]
(13)
If we substitute for [Xn] using the equilibrium constant for the process, we obtain Figure 4. Plots of T1/2, obtained from the HSDSC output as a function of cosolvent and cosolute concentration.
The fact that the ratio ∆HvH/∆Hcal is greater than 1 for all the solutions studied indicates that the molar unit involved in the aggregation process is composed of several chains. This result is not entirely unexpected since premicellization aggregation has been noted using light scattering.6,7,29 It is further reported that these premicellization aggregates are in equilibrium with the micelles.7 The major discrepancy, however, between this study and the light scattering data is related to estimates of the size of these aggregates. From the van’t Hoff enthalpy to the calorimetric enthalpy ratio our work suggests in the main between two and five molecules comprise these premicellar aggregates, though at high concentrations of methanol, ethanol, and propanol this value becomes much larger. Brown’s work, however, reports that the premicellar aggregates may comprise thousands of monomers.7 Work described by Hergeth34 on the other hand proposes that at very low poloxamer concentrations and thus at temperatures below which we would observe
nK[X]n + [X] - c ) 0
(14)
The equilibrium constant K at any temperature is given by
[ (
K ) exp
)]
∆HνH 1 1 /0.5n-1cn-1n R T1/2 T
(15)
Using the data in Table 1 and the above equation, Figure 5 was produced, which shows how the cmc varies with alcohol concentration at 320 K. It is interesting to note that both methanol and ethanol have a parallel effect upon cmc and critical micelle temperature (CMT). Though the effect is fairly modest, both alcohols increase cmc and cmt. A 20% methanol solution increases T1/2 by some 11 K. The result is not unexpected. It has been observed, for example, that methanol raises the cloud point for aqueous solutions of polyoxyethylene p-tert-octylphenyl ether.17 Clouding is brought about by desolvation of the oxyethylene block. The effect has been interpreted in terms of the “structure-breaking” effects of methanol upon water.17
Aggregation Transitions in Poloxamer F87 Solutions
Figure 5. Plots of estimated critical micelle concentrations as a function of cosolvent and cosolute concentration.
The net result of which is to decrease the standard chemical potential of the amphiphile in water, µ°water. There is, however, no comparable reduction in µ°micelle.21 The standard free energy of transfer of an amphiphilic molecule from aqueous solution to a micelle (µ°micelle - µ°water) will therefore increase, which means, in thermodynamic terms, that micellization can only occur at higher amphiphile concentrations resulting in an increase in cmc. The increase in cmc and cmt suggests, from a thermodynamic view point, that both ethanol and methanol favor the unaggregated form of the copolymer. This effect may be rationalized by considering that addition of both alcohols to the bulk solvent results in changes to the solvation sphere that surrounds the propylene oxide block. Indeed methanol and ethanol may be considered as ligands which can replace water in the solvation sphere30 and thus bind to the copolymer molecule in much the
J. Phys. Chem., Vol. 100, No. 5, 1996 1743 same way as inorganic ligands bind to metal ions in coordination compounds. A small change in interaction energy is all that is required to bring about a change in the temperature at which oxypropylene desolvation occurs. The effects of propanol and butanol upon cmc and T1/2 indicate that these alcohols favor the aggregated form of the copolymer since increasing concentrations of both decrease the cmc and T1/2. Indeed it is quite possible that both alcohols form mixed micellar aggregates with P237. The effects of urea upon water structure has been dealt with in the literature quite extensively. Urea is usually considered to be a water structure breaker,36 though a recent report of the results obtained by neutron diffraction finds no evidence for this belief.43 Indeed it appears that urea seems to be quite capable of fitting fairly comfortably into the structure of bulk water. Its ability as a protein denaturant which is generally attributed to structure breaking may therefore be a manifestation of some other phenomenon. However, urea clearly decreases the thermodynamic driving force for hydrophobic interaction and is thus a potent destabilizer of protein structure. Hydrophobic interaction is the driving force for micellization;21 thus, it should be anticipated that increasing urea concentration will increase both the cmt and cmc, which is found to be the case. Urea has previously been shown to increase the cmc of n-dodecyltrimetylammonium bromide and sodium docecyl sulfate37 and would therefore appear to be a general property of the material. Structurally formamide is similar to urea, and this similarity is translated into a parallel effect upon cmc and cmt. Hydrazine on the other hand does not possess a carbonyl group. It appears that this deficiency results in a decrease in both the cmc and cmt. This may be the result of an increase in water structuring which will produce an increase in hydrophobic interaction. Hydrazine, in physical terms, is very similar to water,38 especially in terms of its ability to form hydrogen bonds. As a consequence, surfactants are capable of micellizing in hydrazine solution.38,39 However, reported data suggest that cmcs are greater in hydrazine than in water.38 It therefore seems surprising that, in mixtures of the two, cmcs are actually reduced and must point to some process by which water activity is reduced. Such a reduction will increase surfactant activity, which increases the thermodynamic driving force for micellization and thereby reduces the cmc. For urea, formamide, and hydrazine it may therefore be concluded that the suppression of micellization is brought about by the presence of the carbonyl group. It might therefore seem appropriate to examine to what extent this is true for other carbonyl containing compounds such as aldehydes, ketones, and sugars. Finally one aspect of the cmc data that does need to be addressed is the effect that impurities may have. A number of workers have commented upon the fact that commercial samples of poloxamers contain diblock impurities which may have some impact upon thermal aggregation2,5,29 and almost certainly give rise to premicellization aggregation.6,7 However, it is interesting to note that for the poloxamer P407 there is no evidence that the presence of these impurities significantly affects cmc and cmt values.2 Indeed the fact that both cmc and cmt values remain very nearly constant suggests that enthalpies are constant too. DSC Simulations. It is possible to obtain some indication of the size of the interaction between the cosolutes and cosolvents and the copolymer by simulation of the HSDSC output. This can be achieved in the following way. Methanol and ethanol may be considered to be ligands which replace water in the solvation sphere30 and thus bind to the copolymer
1744 J. Phys. Chem., Vol. 100, No. 5, 1996
Armstrong et al.
molecule. This process may be represented by the following mass action expression:
KL ) [XL]/[X][L]
(16)
KL is the ligand binding constant, [XL] is the concentration of polymer ligand “complex”, [X] is the concentration of polymer, and [L] is the concentration of the ligand. For the simulation a number of assumptions have been made. Firstly it is assumed that KL is independent of temperature. This implies that the enthalpy of binding is either very small or indeed zero and that as a consequence KL varies marginally, if at all, over the temperature range of interest. In these circumstances the free energy of binding must arise from an entropic effect. Since methanol is a structure breaker,19 the entropy decrease on binding may arise from a loosening of the structure of the solvation sphere. Secondly it is assumed that methanol, as a non-micelle-penetrating solvent,37 is desorbed from the solvation sphere prior to micelle formation. Finally, it is assumed that only one methanol molecule is linked to each oxypropylene molecular core. The justification for this comes from the observation that two water molecules are bound to each oxyethylene unit.42 It is assumed that this must also be the maximum number of water molecules that can bind to oxypropylene units. The oxypropylene core for P237 is 40 units long, which implies that at most some 80 water molecules are linked to the core. For a 1 M methanol solution the molecular ratio of water to methanol is 55 to 1. Thus, if the solvation sphere has the same composition as the bulk, then each oxypropylene block should contain approximately one methanol molecule. The aggregation equilibrium constant is dependent upon temperature. It is has been further noted that the enthalpy of the process is itself temperature dependent. The change in equilibrium constant with temperature should therefore be written as40
[ (
K(T) ) exp
)
(( ) )]
∆Cp,νH ∆HνH 1 T 1 - + ln + R T1/2 T R T1/2 T1/2 - 1 /0.5n-1Ctotaln-1n (17) T
where ∆Cp,vH is the value for the heat capacity obtained from the graph of ∆HvH against T1/2. The following mass balance expressions can be drawn up for Ctotal and Ltotal, the total concentrations of copolymer and ligand, respectively:
Ctotal ) [X] + [XL] + n[Xn] Ltotal ) [XL] + [L]
(18)
The other symbols retain the previous definitions. Combining these expressions with the mass action expressions for aggregation and ligand binding gives
Figure 6. Simulation of the effect of varying the composition of methanol water mixtures upon the aggregation transition of P237.
Cp,xs ) [∆Hcal + ∆Cp,cal(T - T1/2)][∆HνH + ∆Cp,νH(T - T1/2)] + 1 n RT2 + R 1-R R∆Cp,cal (21)
(
)
where ∆Cp,cal is the heat capacity change obtained from the graph of ∆Hcal vs T1/2 and ∆Cp,vH is the heat capacity change obtained from the graph of ∆HvH vs T1/2. Using these equations, it is possible to show how changes in the concentration of the ligand, L, affect the HSDSC output. This is shown in Figure 6. The figure was produced by using the thermodynamic data obtained for P237 in aqueous solution and combined with the analysis outlined above. The figure shows that the main features of the HSDSC data obtained are reproduced. Most importantly it is shown that relatively small changes in T1/2 would appear to be due to a relatively small ligand binding constant. For the simulation a value of 2 was used. The dimensions of the simulated outputs decrease because of the functional dependence of the calorimetric enthalpy upon T1/2. Comparison of Figure 6 with Figure 1 indicates that the dimensional alterations are not adequately modeled, implying that either the value for ∆Cp,cal is in error or that there is an important enthalpic component of methanol binding to the monomeric form of the copolymer. It is also clear that though the inclusion of a term accounting for the change in heat capacity for the process reproduces the negative trend of the posttransitional portion of the traces, it is not, however, adequately described by the model. Undoubtedly changes in aggregation number,4 changes from spherical to rodlike micelles,31,41 and any changes in solvation of the oxyethylene blocks are all likely to make their own separate contributions to the posttransitional heat capacity of the system. Conclusions
nK[X]n+1 + nKKL[X]n + (Ltotal + KL - Ctotal)[X] KLCtotal ) 0 (19) Solving for [X] allows values to be obtained for [L] and [XL]. From these values the extent of aggregation, R, can be calculated:
R)
Ctotal - ([X] + [XL]) Ctotal
(20)
Finally it can be shown that Cp,xs can be obtained from the following expression:
The effects of various cosolvents/cosolutes upon the thermal aggregation of the poloxamer P237 has been investigated. The data show that the addition of fairly large quantities of cosolvents/cosolutes is required before changes in thermodynamic parameters become apparent. The effects of the cosolvents/cosolutes may be rationalized either by invoking the concept of water structure changes or by postulating some direct interaction. Methanol, ethanol, formamide, and urea have been shown to raise cmc and cmt values, and this may occur either because they are behaving as structure breakers or possibly because they replace water molecules in the solvation sphere of oxypropylene. Propanol, butanol, and hydrazine reduce cmc
Aggregation Transitions in Poloxamer F87 Solutions and cmt values. This may occur either because they behave as structure promoters or because they comicellize with the polymeric surfactant. References and Notes (1) Gilbert, J. C.; Washington, C.; Davies, M. C.; Hadgraft, J. Int. J. Pharm. 1987, 40, 93. (2) Yu, G.-E.; Deng, Y.; Dalton, S.; Wang, Q.-G.; Attwood, D.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1992, 88, 2537. (3) Wanka, G.; Hoffmann, H.; Ulbricht, W. Colloid Polym. Sci. 1990, 268, 101. (4) Rassing, J.; Attwood, D. Int. J. Pharm. 1983, 47, 55. (5) Yang, L.; Bedells, A. D.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1992, 88, 1447. (6) Brown, W.; Schille´n, K.; Almgren, M.; Hvidt, S.; Bahadur, P. J. Phys. Chem. 1991, 95, 1850. (7) Brown, W.; Schille´n, K.; Hvidt, S. J. Phys. Chem. 1992, 96, 6038. (8) Linse, P.; Malmsten, M. Macromolecules 1992, 25, 5434. (9) Malmsten, M.; Lindman, B. Macromolecules 1992, 25, 5440. (10) Hecht, E.; Hoffmann, H. Langmuir 1994, 10, 86. (11) Mitchard, N. M.; Beezer, A. E.; Rees, N. H.; Mitchell, J. C.; Leharne, S.; Chowdhry, B. Z.; Buckton, G. J. Chem. Soc., Chem. Commun. 1990, 900. (12) Mitchard, N. M. Ph.D. Thesis, University of London, 1990. (13) Beezer, A. E.; Mitchell, J. C.; Rees, N. H.; Armstrong, J. K.; Chowdhry, B. Z.; Leharne, S.; Buckton, G. J. Chem. Res. 1991, 254. (14) Beezer, A. E.; Mitchard, N. M.; Mitchell, J. C.; Armstrong, J. K.; Chowdhry, B. Z.; Leharne, S.; Buckton, G. J. Chem. Res. 1992, 236. (15) Mitchard, N. M.; Beezer, A. E.; Mitchell, J. C.; Armstrong, J. K.; Chowdhry, B. Z.; Leharne, S.; Buckton, G. J. Phys. Chem. 1992, 96, 9507. (16) Armstrong, J. A.; Chowdhry, B. Z; Beezer, A. E.; Mitchell, J. C.; Leharne, S. J. Chem. Res. 1994, 364. (17) Sobisch, T.; Wu¨stnick, R. Colloids Surf. 1992, 62, 187. (18) Sanchez-Ruiz, J. M.; Lopez-Lacomba, J. L.; Cortijo, M.; Mateo, P. L. Biochemistry 1988, 27, 1648. (19) Armstrong, J. A.; Chowdhry, B. Z; O’Brien, R.; Beezer, A. E.; Mitchell, J. C.; Leharne, S. J. Phys. Chem., in press.
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