J. Phys. Chem. 1995, 99, 5094-5101
5094
SANS Study of the Micellar Structure of PEO/PPO/PEO Aqueous Solution Guangwei W U , ~Benjamin Chu,*Jt' and Dieter K. Schneidero Chemistry Department, State University of New York at Stony Brook, Stony Brook, New York 11 794-3400, Department of Materials Science and Engineering, State University of New York at Stony Brook, Stony Brook, New York 11 794-2275, and Biology Department, Brookhaven National Laboratory, Upton, New York 11973 Received: September 23, 1994; In Final Form: December 22, I994@
Small-angle neutron scattering ( S A N S ) was used to investigate the micellar structure formed by a poly(oxyethylene-oxypropylene -oxyethy lene) (PEO 13PP03oPEO13, Pluronic L64) copolymer in D20 over a temperature range of 8.4-35.0 "C. The intermicellar interactions were corrected by using an equivalent hard sphere approximation with an equivalent hard sphere radius. The aggregation number of the micelles decreased with decreasing temperature. The micellar scattering behavior could be well described by a coreshell structure. Based on the core-shell model, the volume fraction of the polymer segments in the micellar shell was less than 0.2. The micellar molar mass became larger after having introduced an organic solvent (xylene) into the system and increased with increasing amount of solubilized xylene. The maximum amount of solubilized xylene in the micelle was of the order of 0.3-0.4 xylene molecule per PO unit.
Introduction PEOPPO triblock copolymers are widely used nonionic polymer surfactants in cosmetic and pharmaceutical industries; for example, see review of Schmolka.' In the last decade, fundamental studies on the micellar formation of PEOPPO triblock copolymers in water or in organic solvents have attracted considerable a t t e n t i ~ n . ~In - ~ aqueous ~ most of the studies focused on information related to the critical micelle concentration, the micellar size, temperature effects, and the phase diagram. The micellar structure has not been investigated in detail partially because of limited facilities which are accessible to the colloid scientists. The micellar size of PEOPPO aqueous solution is of the order of 10-20 nm. Thus, only small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) are the appropriate scattering techniques. As the electron densities of PEO and PPO are very close to that of water, the signal-to-noise ratio of even synchrotron SAXS on such a system is relatively low. SANS should be the best technique to explore the micellar structure of PEOPPO triblock copolymers in water. Although the micellar structure formed by triblock copolymers has been well studied during the last 2 decades (e.g., see the review by Tuzar and K r a t o ~ h v f l ~the ~ ) , copolymers used are rather large, with the block length consisting of the order of a few hundred segments.30 In contrast, the block length of Pluronic copolymers is relatively short. For example, L64 has a total length of only -70 segments. Thus, the micellar structures formed by short-segment-length copolymers could differ from those of larger copolymers. For example, the larger copolymers can form starlike blob structures31which seem to be less likely for such short-segment-length copolymers. On the other hand, a clear distinction in the supramolecular structure is not expected since the chain length and solvent quality as well as many parameters can be varied continuously. SANS1'J2 and SAXS2I have been used to study the micelle formation and the gel structure of PEOPPO copolymers in
* Author to whom correspondence
@
should be addressed. Chemistry Department, SUNY. Department of Materials Science and Engineering, SUNY. Brookhaven National Laboratory. Abstract published in Advance ACS Abstracts, February 15, 1995.
aqueous solution. Nevertheless, there is yet no clear picture about the micellar structure. In the reports by Mortensen et a1.,*lJ2a simplified model which assumed the micellar core to be the only scattering source was used to analyze the SANS scattering profiles. Thus, the detailed micellar structure could not be extracted from this simplified model. Recently, based on the mean-field lattice theory, Linse13-15 and Hatton et aL20 have reported the theoretical predication on the micelle formation and the phase behavior of PEOPPO triblock copolymers in aqueous solution, with the micelle consisting of a compact PPO core and a loose PEO shell. The volume fraction of the copolymer segment in the micelles has a plateau region and then decreases in the radial direction. We have thoroughly studied the temperature-induced micelle f ~ r m a t i o n ~and , ~ the solubilization effect' on the micellar structure of L64 in aqueous solution as well as the water-induced micelle formation and the micellar ~ t r u c t u r e ~of~ -L64 ~ ~ in xylenelwater mixtures. In the present work, the micellar structure formed by L64 in D20 and the effect of solubilization were studied by using S A N S at different temperatures ranging from 8.4 to 35.0 "C. In order to achieve a reasonable signalto-noise ratio and the micelle formation at low temperatures, the copolymer concentrations used in this work were not in the dilute regime. The effects due to interparticle interactions were studied by using four different copolymer concentrations (8.0%, 16.0%, 23.9%, and 31.9% wt/v). Based on the scattering profiles after correction for interparticle interactions, the micellar structure could be retrieved from a core-shell model. The Teubner-Strey was used to estimate the intermicellar distance, the micelle number density, and the micellar molar mass.
Experimental Methods Materials and Sample Preparation. Pluronic L64, PEOW PP030PE013, was obtained as a gift from BASF Co. and used without further purification. The nominal molar mass of this copolymer is 2900 g mol-', and the weight fraction of PEO is 40%. Our measured weight-average molar massz4 was 3.7 x lo3 g mol-l. Deuterium water (D2O) with 99.9% D was purchased from Cambridge Isotope Laboratories. A stock solution (with copolymer concentration 3 1.9%) was prepared
0022-365419512099-5094$09.00/0 0 1995 American Chemical Society
Micellar Structure of PEOPPOPEO Aqueous Solution
9 2500,
.
/a-= , . . . . ,
. . . , . . . .
4
J. Phys. Chem., Vol. 99, No. 14, 1995 5095 4 0 0 ~ .. .
.
I
. .
.
, .
.
.
.
.
I
.
.
.
.
,
. ,
,
4 /am-' 3
20 t .
.
,
.
,
/--'
4 /--' Figure 1. Excess S A N S scattered intensity profiles of L64 aqueous solution at denoted copolymer concentrations and temperatures. The scattered intensity had been normalized to an incident neutron intensity of 1 million counts. The solid lines are the best fitting of the T-S modeL3*
by dissolving L64 in D20. After having stood for several days, the stock solution was diluted to the required copolymer concentrations. For the samples used to study the solubilization effect, a certain amount of HPLC-grade o-xylene (Aldrich Chemical Co.) was added to L64D20 solution. Small-Angle Neutron Scattering (SANS). SANS experiments were performed by using the biology small-angle neutron scattering ~pectrometer~~ located at H9B in the high-flux beam reactor (HFBR) of Brookhaven National Laboratory. Cold neutrons were derived from a liquid-hydrogen cold-neutron source located in the beam thimble of H9 beam line. The wavelength was set at 7.2 A with a spread in MIA of less than 10%. The sample to detector distance was 175 cm. Samples were placed in capped quartz cells, and the path length of the sample was 2 mm. With the current setup, the desmearing effect was negligible. The experimental temperature was controlled to h0.2 "C. Measured scattered intensity profiles were corrected for detector nonlinearity, incident neutron intensity variation, sample absorption, and environmental background contributions. For comparison, the scattered intensity was normalized to 1 million incident neutron counts. The scattered intensity of unimer was very weak when compared with the micellar scattering as shown in Figure 1. At the two higher temperatures of 35.0 and 29.8 "C, the critical micelle concentration (cmc) of L64 aqueous solution was 3.8 x and 1.76 x g/mL, respectively. Therefore, the scattered intensity contribution from the unimers was relatively small and could be corrected together with the incoherent scattering (Zinc). This approach would have a larger uncertainty at 23.2 "C because of the larger cmc value. The contribution of I,,, was removed by using the Porod law,34the
scattered intensity in the high q range being assumed to obey the relation
I = A/q4
+ Zinc
(1)
where A is a constant related to the surface-to-volume ratio of the particle and q is the scattering vector whose magnitude is equal to (4x/A) sin(B/2). We also tried to use the modified Porod l a ~ and 3 ~found the interface scattering to be negligible for the studied system within the q range used. The incoherent scattering contribution from the two approaches agreed with each other to within the fitting error limits. The scattering length densitiesz9of PEO, PPO, and D20 are 0.595, 0.361, and 6.40 x 1Olo cm-2, respectively. The ratio of the scattering length density difference between PEO and D20 to that between PPO and D20 is close to 1. Therefore, no correction was made for the scattering length difference between PEODzO and PPO/
D20. Results and Discussion Critical Micelle Concentration (cmc). It is well-known that the cmc decreased with increasing temperature for the PEO/ PPO triblock copolymer in aqueous solution. The cmc value from different research groups*J9 could be slightly different because of the difference in sample chemical composition, preparation methods, and/or detection techniques. Most recently, Hatton et al.19 and Wanka et aL8reported the cmc values by using dye solubilization and surface tension experiments, respectively, for different PEOPPOPEO triblock copolymers in aqueous solution over a range of temperatures. For Pluronic
5096 J. Phys. Chem., Vol. 99, No. 14, 1995
L64,19a ln(cmc) vs l/T(absolute temperature) plot showed good linearity over the temperature range of 23.5 to 44.5 "C.
AGO = RT ln(Xcmc)
AG" = AH" - TAS"
(24 (2b)
where AGO, AZP, and AS" are the micellization free energy, enthalpy, and entropy, respectively, R is the gas constant, and X,,, is the critical micelle concentration in mole fraction. Equation 2a was also expressed as AGO = RT ln(cmc) in other literature, for example, ref 6. The derived thermodynamic constants are AH" = 230 kJ/mol and AS" = 0.835 kJ/(mol K). The enthalpy of micellization is in good agreement with the value (210 iz 11 kJ/mol) reported by Zhou and Chu6 by using light scattering on a different sample. The entropy of micellization is different because of the difference in the expression used (eq 2a). Equation 2 assumes that the measurements are performed at a constant temperature or AH" and AS" are temperature independent. For PEOPPO copolymers in aqueous solution, the hydrogen bond which is temperature dependent plays an important role. Therefore, the temperature range over which a linear ln(cmc) vs l/Trelation exits should be important to our understanding of the micelle formation. Figure 1 shows the excess SANS scattering profiles of L64/ D20 solution at four different L64 concentrations (0.319,0.239, 0.160, and 0.080 g mL-') and five different temperatures (8.4, 16.1, 23.2, 29.8, and 35.0 "C). The scattered intensity of the micelles is much stronger than that of the unimers. It is reasonable to assume that the micellization process has not been altered by changing H20 to D20. On the basis of the scattered intensity profile, we can judge whether micelles were formed at the selected temperature and concentration. At 8.4 "C, L64 existed as unimers at all four concentrations. Thus, the cmc value, if it exists, should be larger than 0.32 g mL-' at 8.4 "C. The cmc values should be between 0.32 and 0.24 g mL-' at 16.1 "C and between 0.08 and 0.16 g mL-' at 23.2 "C. At the two higher temperatures, the cmc values were less than 0.08 g mL-'. On the basis of the cmc data reported by Hatton and co-w~rkers,'~ we can find out the cmc values corresponding to our experimental temperatures by interpolation, with the values being equal to 0.0038,0.0176, and 0.135 g mJ.-', respectively, at 35.0, 29.8, and 23.2 "C, in agreement with the observed results. Interparticle Interactions. The concentrations studied were not in the dilute region. Interparticle interactions should be considered in order to extract the single-particle scattering behavior. The simplest approach was by using an equivalent hard-sphere model to correct for the interparticle interactions. Although neither micelles nor unimers were real hard spheres, this approach was shown to be valid.28 The equivalent hardsphere radius of the micelles formed by L64 in xylene in the presence of water was equal to the micellar core radius, plus one-half of the micellar shell thickness. The measured scattered intensity is proportional to the particle form factor P(q) and the structure factor S(q,C) and has the relati~nship~~
Z = As2MCP(q)S(q,C)
(3)
where A@ is the scattering length density difference between particle and solvent background, M is the molar mass of the particle, and C is the particle concentration. Even if we were to use the equivalent hard-sphere model to correct for interparticle interactions, there would be no simple expression for the structure factor S(q,C). Only in some special cases, e.g., in the
u 1op
y
Wu et al.
b
0 3 5 . 0 *C
8
h
104
0
I
u
v
\>o.J
'0.k'0.k '0.25
l O 8 O L . O 6 ~'0.b
C-cmc /gmL-'
Figure 2. Reduced scattered intensity at q = 0 vs concentration at
different temperatures. The corresponding unimer concentration (cmc) had been subtracted in the micelle solutions. case of uniform spheres, could eq 3 be used to fit the experimental data directly in order to keep the number of adjustable variables in eq 3 to within a reasonable number, for example, to no more than four. In the present work, the approach used to extract the particle form factor P(q) was different from the one used by Mortensen and Pedersen," who used a direct nonlinear least-squares fitting of eq 3 by assuming that the micellar core was responsible for all the SANS scattering. In other words, the P(q) they used was the form factor of a uniform sphere. In our case, the interparticle interactions S(q,C) were corrected first by using an equivalent hard-sphere model, and then the net scattering intensity profile (after correction for interactions) was compared with different theoretical particle form factors. It should be noted that both approaches suffer from the hard-sphere approximation. The method by Mortensen and Pedersen is simpler, but it yields less information. While our approach may appear to be quite logical and yields more detailed information, it assumes that S(q,C) values are based on arbitrary equivalent hard spheres, and thus, the results on details which go beyond the hard-sphere approximation are less reliable and may be subject to criticism. The expression of scattered intensity Z(q) at zero scattering angle ( q = 0) is much simpler than eq 3 because, with P ( q = 0) = 1, S(q = 0,C) = (1 - ~ , ) ~ / ( l 2 ~ where ) ~ Q, is the equivalent hard-sphere volume fraction of the particles. After having taken these factors into account and expanded S(q = O,C), the Z(q = 0) can be expressed by the relation
+
log(Z(q = O)/o log(Aq2M) - 3 . 4 8 ~
-
(4)
The error caused by neglecting the higher-order terms of S(q = 0,C) is less than 5% up to Q, 0.4. The equivalent hardsphere volume fraction of the particle is related to the equivalent hard-sphere radius RHS,the molar mass, and the concentration of the particle by the relation Q, = (4nR~s3/3)N~c/M kC with N A being Avogadro's number. It should be noted that C represents the micellar concentration, not the copolymer concentration. When considering the micellar system, the cmc needs to be subtracted. Figure 2 shows the log[l(q = O)/C) vs
J. Phys. Chem., Vol. 99, No. 14, 1995 5097
Micellar Structure of PEOPPOPEO Aqueous Solution
TABLE 1: Summary of the Results Based on Z(q = 0) of SANS" tl"C
k intercept RHslnm N Rclnm a
35.0 1.44 f 0.08 4.69 f 0.07 5.3 69 4.6
29.8 1.45 f 0.05 4.59 f0.03 4.9 55 4.3
23.2 1.77 f 0.03 4.44 f 0.01 4.7 39 3.8
16.1 1.42 f 0.05 2.85 f 0.03 1.3 1
8.4 1.9 f 0.2 2.83 f 0.1 1.4 1
The error of N is -lo%, and the errors for RHSand Rc are -5%.
C plot at low temperatures (unimers) and high temperatures (micelles). The slope ( k ) and the intercept of the linear fitting of Figure 2 are listed in Table 1. By using the weight-average molar mass of the unimers measured by static light scatteringz4 (3.7 x lo3 g mol-'), the equivalent hard-sphere radius of the unimers could be estimated from the slopes based on eq 4 at low temperatures and is equal to 1.3 and 1.4 nm at 16.1 and 8.4 "C, respectively. These values are very close to the equivalent hard-sphere radius (1.2 nm) of a single L64 chain in o-xyleneZ4 at 26.2 "C. It is reasonable to assume that the scattering length density of the copolymer has remained the same before and after micellization and the Ae's of the unimers and the micelles are the same. The latter assumption could cause a larger error at 23.2 "C than at the other two higher temperatures because the considerable cmc value at 23.2 "C could change the scattering length density of the background slightly. The aggregation number or the molar mass of the micelles could be calculated from a comparison of the intercepts at high temperatures and those at low temperatures. The results are listed in Table 1. With known micellar molar mass, the equivalent hard-sphere radius (RHs)of the micelles could be estimated from the slopes at high temperatures. The computed aggregation number of the micelles was reasonable when compared with reported literature values5~7,17.2z as measured by other techniques and the result obtained by a direct model fitting (Teubner-Strey modeP2) of the experimental data. The aggregation number increased with increasing temperature as expected. The equivalent hard-sphere radius of the micelles was in reasonable agreement when compared with the result reported by Mortensen et a1.11,12or the Rh value6 for L64 micelles. By assuming that the micellar core was dominated by the PPO block and was liquidlike, the micellar core radius (Rc) could be estimated by using the relation
I
lOOC 100
h
lo-'
00.319 gmLI' A 0.239 gmL-' +0.160 gmL-: 00.080 g m L
7
cr a
v
10-2 -
11 n-3 0-~
0.0
0.5
1.0
1.:
q /nm-'
Figure 3. Micellar form factor P ( q ) profiles at different copolymer concentrations and 35.0 "C. P(q) was obtained from the scattered intensity profile by first correcting the intermicellar interactions and then normalizing the scattered intensity at q = 0 to unity.
6
v
a
t0.0
0.5
1 .o
1.5
q /nm-'
Rc = (3Mc/4~NAdppo)1'3
Figure 4. Comparison between experimental data (symbols) and the
where dppo = 1.05 g cm-3 is the density of the PPO block and MC (=0.6 M) is the molar mass of the PPO blocks. The estimated liquidlike micellar core radius is also listed in Table 1. RHSwas larger than the micellar core radius but smaller than the reported R h (-10 nm). This result is in agreement with the core-shell micelle structure and the SANS results29 of L64 micelles formed in xylene in the presence of water. The micellar core was relatively compact, while the micellar shell was heavily solvated. Particle Form Factors. After having found out a way to correct the interparticle interactions, the particle form factor could be retrieved by normalizing the corrected scattering profile to unity at q = 0. Figure 3 shows plots of the micellar form factors at 35.0 "C and four different concentrations. The micellar form factors were similar except for the one with the highest concentration which displayed a shoulder at q 0.7 nm-'. The volume fraction of micelles was estimated to be -0.45 at C = 0.319 g mL-' and 35.0 "C. A possible explanation for the shoulder was that the hard-sphere approximation was insufficient to account for the complete
-
theoretical uniform sphere form factor (solid lines) and the Gaussian coils (dashed lines). The radii of the uniform spheres used in the form factor were 2.2 and 2.3 nm, respectively, at 16.1 and 8.4 "C. The R, values used in Debye function were 1.7 and 1.8 nm, respectively, at 16.1 and 8.4 "C.
structure factor. In addition, the micelles could be in a partially ordered state as reported in the literature. Micelles of PEO/ PPOPEO in aqueous solution could form ordered structures11J2~8 such as a body-center-cubic structure at high micellar concentrations. The micellar scattering profiles at different micellar concentrations could not have the exact same profiles because of the difference in the osmotic interaction even though the micelles could have the same aggregation number and shape as we reported previously.28 At low micellar concentrations, the intermicellar distance should be larger and the osmotic interaction weaker. Therefore, the micelles were relatively more swollen at low micellar concentrations and the scattered intensity decayed relatively faster, as shown in Figure 3. Figure 4 shows the form factors of L64 unimer at 16.1 and 8.4"C. Good agreement was obtained between the experimental data (diamonds) and the theoretical form factors (solid lines)
Wu et al.
5098 J. Phys. Chem., Vol. 99, No. 14, 1995 of a uniform sphere having a radius RU of 2.2 and 2.3 nm, respectively, for a and b of Figure 4, with the superscript U being used to emphasize the radius to be that of a unimer. However, the form factor of a Gaussian coil based on the Debye function34(dashed lines) was unable to fit the experimental data over the whole q range. The radii of gyration (R,) were estimated by using the Guinier approximation (not shown) to be 1.7 and 1.8 nm, respectively, at 16.1 and 8.4 "C. From a comparison between experimental data and theoretical P(q) or the relation between RU and R,, the scattering behavior of L64 unimers appeared to be different from a Gaussian coil. The radius RHSof a L64 unimer in D20 was only 1.3 nm, which was almost the same as the RHSof L64 in xylene, and was much smaller than the RU or R, size from the scattering profile. By comparing RHSwith RU or R,, it is not difficult to conclude that the unimer was not a hard sphere but could be a penetratable sphere, a reasonable picture for the single chain unimolecular micelle. In comparison with the L64 single chain, the micellar structure could be examined in more detail by SANS over the available q range. At first, we used a classic micelle model: the core-shell structure to fit our experimental data. In view of the lack of information on the segment density distribution in the micelle, we used a simplified core-shell model which was assumed to have a uniform segment density distribution within the micellar core and that of the micellar shell. Therefore, the particle form factor can be expressed as
q /nm-'
0.239 gml-' where p = A&(Aec - Ags) with Ags and Agc being the scattering length density difference of the micellar shell and of the micellar core, respectively. There are only three adjustable parameters in eq 6: the micellar core radius (Rc), the micellar shell outer radius (Rs), and the contrast ratio (p). In the special case of p = 0, eq 6 becomes the form factor of a uniform sphere. The micelles had a relatively narrow size di~tribution.~ To the first-order approximation, the polydispersity of the micellar size was not taken into account when comparing experimental data with the theoretical form factor by using a nonlinear leastsquares fitting procedure. Figure 5 shows the comparison between the theoretical form factor based on eq 6 and the experimental data obtained by normalizing Z(q = 0) to unity after correction for the intermicellar interactions. The agreement between the experimental data and the theoretical curve was reasonably good. The values of the parameters obtained are listed in Table 2. For comparison purposes, we also used a simpler model: a uniform sphere to fit the experimental data. In this case, the micellar size (or the micellar core size, Rm) was the only adjustable parameter. The fitting results are shown in Figure 6 and the value of Rm is also listed in Table 2. In the low-q region, e.g., q < 0.6 nm-', the fitting by the simpler model was reasonably good. At higher q values, the agreement between the experimental data and the theoretical curve based on the simpler uniform sphere model was not as good as that based on the core-shell model. Similar results were obtained at other copolymer concentrations. As we expected, RHS of the micelles was between Rc and Rs. It is interesting to find that RHSwas almost equal to Rc plus one-half of the shell thickness (Rs - Rc) at 35.0 and 29.8 "C, the same picture as the micelles formed by L64 in xylene in the presence of water.28 At 23.2 "C, the RHSvalue was about 10% lower than that predicted by the above picture because of lower aggregation number. Rc remained almost unchanged at
0.5
1.o
1.5
q /nm-l
Figure 5. Comparison between experimental data (symbols) and the theoretical core-shell form factor (solid line). The parameters used in the core-shell model fitting are listed in Table 3.
TABLE 2: Micelle Parameters from the Form Factor Fitting t/"C
Rclnm Rdnm P RVnm 9s
35.0 3.2
6.9 0.11
5.0 0.1 1
29.8 3.2 7.0 0.09 4.8 0.08
23.2 3.0 7.4 0.05 4.7 0.05
the three temperatures and was smaller than the radius of the sphere consisting of all PPO blocks, implying that not all PO segments were located inside the compact micellar core as predicted in the mean-field lattice model. 13-15,20 The micellar outershell radius was almost temperature independent and increased very slightly with decreasing temperature. Based on the results of Rc and Rs at different temperatures, it was not hard to find that the micellar size was mainly determined by the conformation of the copolymer chains. The copolymer chain was more extended at low temperatures because water was a better solvent at low temperatures for the copolymer, especially for the PPO block. Therefore, the micellar size was slightly larger at low temperatures. The PPO block could be loopedi3-'5 or straight,l1-l2while the PEO block could be in zigzag, helix, or meander c~nformation.~ Our present data could not yet make a definitive determination on the conformation. p decreased with decreasing temperature, in agreement with the fact that the micellar aggregation number decreased with decreasing temperature while the micellar size remained almost unchanged. The scattering length density difference of the PPO block and the PEO block was very small. The scattering length ratio of
Micellar Structure of PEOPPOREO Aqueous Solution
J. Phys. Chem., Vol. 99, No. 14, 1995 5099
TABLE 3: Aggregation Number of Micelle after Solubilization of Xylene at tl°C X Y W
0 25 50 75 100
q /nm-'
35.0
29.8
23.2
48 59 76 94 105
42 54 68 82 95
28 35 43 51 61
but much larger than the values of the micellar core radius from the core-shell model as listed in Table 3. Furthermore, the values of Rm from a uniform sphere fitting were also larger than the micellar core radii based on the assumption that all PPO blocks were located in the micellar core as listed in Table 2. Both of these two comparisons implied that the sphere derived from a uniform sphere fitting was equivalent to that of the whole micelle, not only the micellar core. Model Fitting. It is not always possible to maintain the same conditions while varying the copolymer concentration. Then, the aggregation number or the molar mass of the micelles could not be determined by extrapolation of the concentration to infinite dilution as we have used implicitly in the previous section. However, the micellar molar mass (M) could still be estimated semiquantitatively if we knew the intermicellar distance (d)by the relationship
h
CT
Y
a
q /nm-'
M = CNAh
q /nm-'
Figure 6. Comparison between experimental data (symbols, same as Figure 5) and the theoretical uniform sphere form factor (solid lines). The radii of the uniform spheres used were 5.0, 4.8, and 4.5 nm, respectively, at 35.0, 29.8, and 23.2 "C. PPOREO blocks was 1.04. If the solvation in the micellar core was assumed to be negligible, the volume fraction ( q s ) of the polymer segment in the micellar shell could be estimated from p because Aes is proportional to p s :
llp = AeclAQs - 1 = 1.041~s- 1
(7)
Thus, the estimated q s values were 0.11, 0.084, and 0.048, respectively, at 35.0,29.8, and 23.2 "C. These values appeared to be too small. But these values represented an average of ~ J S with the volume of the micellar shell being about 10-15 times the volume of the micellar core. Thus, the actual amount of copolymer segments in the micellar shell was much larger and the ratio of the amount of copolymer segment in the micellar shell to that in the micellar core could be estimated to be 0.95, 0.80, and 0.67, respectively, at 35.0, 29.8, and 23.2 "C. These values were larger or close to the volume ratio of EO to PO based on chemical composition, which should be (0.4/0.6) 0.67, with the densities of PEO and PO being about the same. Based on the theoretical p r e d i c t i ~ n , ' ~ - there ' ~ . ~ ~was a small portion of the PO units in the micellar shell and a small portion of the EO units in the micellar core. The EORO ratio of copolymer segments in the shell to that in the core could be larger than the EOPO composition ratio (0.67) if more PO units were located in the micellar shell than the EO units located in the micellar core. The values of R" from the form factor fitting of a uniform sphere were very close to the values of the RHSof the micelles
Cd3NA
(8)
where n is the number density of the micelles. The TeubnerStrey (T-S) modeP2is one of the models which is able to obtain the intermicellar distance based on the excess scattered intensity profile. Based on the T-S model, the scattered intensity of the micellar system could be expressed as Ifq) = a/( 1
+ c,q2+ c2q4)
(9)
and d could be calculated from constants cl and c2 by the relation
The fitting was very good when the scattered intensity had a well-defined peak. The solid lines in Figure 1 were a nonlinear least-squares fitting of the T-S model by means of eq 9. The difference in M thus obtained among the different micellar concentrations was less than lo%, and the average micellar aggregation numbers were 48,42, and 28, respectively, at 35.0, 29.8, and 23.2 "C. The micellar aggregation number decreased with decreasing temperature, which was the same conclusion as based on the results from the concentration extrapolation. All the micellar aggregation numbers obtained from the intermicellar distance were about 25-30% smaller than that obtained from the concentration extrapolation. This difference could come from the assumption that n l/&. Fortunately, the difference was more or less systematic. Solubilization of Organic Solvent (0-Xylene). Only a few report^^,^^ have studied the effect of solubilization on the micellar behavior of PEORPO triblocks in aqueous solution. The aggregation number of the micelle increased with increasing amount of solubilized xylene. The maximum solubilization ability of the L64 PEOPPO micelle in water was of the order of 0.3-0.4 xylene molecule per PO unit in the micelle. In comparison with the reported solubilization result35of 10% PPO/ PEO diblock (70:30) aqueous solution at 25.0 "C, the maximum
5100 J. Phys. Chem., Vol. 99, No. 14, 1995
Wu et al.
Conclusions
1.2~ 10'
-
1.0
*! 0.0
d
"0
0.0
I
0.4
I
0.2 0.0 0.0
0.5 q
1.0
1.5
/nm-'
1.0~10~
0.0 h
0.0 c'10
70.4 c1
0.2 0.0 0.0
0.5
1.o
1.5
q /nm-' Figure 7. Excess SANS scattered intensity profiles of L64 in aqueous solution with denoted amount of o-xylene at different temperatures. Initial copolymer concentration and the sample volume were the same, being 0.319 g mL-' and 2 mL, respectively. The scattered intensity had been normalized to incident neutron intensity of 1 million counts. The solid lines were the best fitting of the T-S model.
solubilization was 0.23 xylene per PO unit. Thus, our result was reasonable. Figure 7 shows S A N S scattered intensity profiles after adding different amounts of xylene to 0.319 g mL-' L64 in aqueous solution at different temperatures. The scattered intensity became stronger and the maximum position shifted to lower q values with increasing amount of solubilized xylene. The volume fraction of the micelles did not change considerably because the cmc value was much smaller than the copolymer concentration at the two high temperatures and the amount of added xylene was negligible. In other words, the value of S(q = 0,C) should not change dramatically with different amounts of solubilized xylene. Qualitatively, the micelles became larger with increasing amounts of solubilized xylene, in agreement with literature results. In order to obtain some semiquantitative results, the T-S model was used to fit the scattering profiles in order to derive the intermicellar distance. The solid lines in Figure 7 represented the best fitting curves based on the T-S model. To the first-order approximation, the cmc values were assumed to remain unchanged after the solubilization. The molar mass of the micelles after solubilization of xylene could be estimated by using eq 8. The corresponding aggregation number of the micelles is listed in Table 3. The aggregation number of the micelles increased with increasing amount of solubilized xylene and/or increasing temperature.
Based on the S A N S study of L64 in aqueous solution at different temperatures, some information about the micelle formation and structure could be concluded as follows. (1) The critical micelle concentration over a large range of temperatures may not be able to be extrapolated from the thermodynamic functions because the entropy and/or the enthalpy of micellization could be temperature dependent at lower temperatures. (2) The intermicellar interactions could be corrected by using an equivalent hard-sphere model with an equivalent hard-sphere radius (RHs). The RHS,located between the micellar core and the outer micellar shell, was almost equal to the micellar core radius plus one-half of the micellar shell thickness. (3) The micellar molar mass and the corresponding aggregation number increased with increasing temperature. (4) L64 unimers existed as (non-Gaussian)coils in the solvent. However, the scattering behavior of the unimers could be fitted by using a uniform sphere approximation. (5) The micelle structure could be described by a core-shell model. The micellar size was almost temperature independent and increased only very slightly with decreasing temperature. The volume fraction of the polymer segment in the micellar shell was very low, being less than 0.2. Not all the PPO segments were located in the micellar core. Therefore, there was no clear core-shell boundary. (6) The maximum solubilization amount of xylene in the L64 micelles was of the order of 0.3-0.4 xylene molecule per PO unit in the micelles. The aggregation number of the micelles increased with increasing amount of solubilized xylene. The result is in contrast with the micellization behavior of the same L64 dissolved in xylene in the presence of water.24In the latter case, the micellar core is mainly made up of EO units and water, and the maximum amount of solubilized water can be of the order of 2.7 water molecules per EO unit.
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