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J. Phys. Chem. B 2005, 109, 23896-23904
Fragmentation of the Lamellae and Fractionation of Polymer Coils upon Mixing Poly(dimethylacrylamide) with the Lamellar Phase of Aerosol OT in Water Isabel E. Pacios,*,†,‡ Carmen S. Renamayor,† Arturo Horta,† Bjo1 rn Lindman,‡ and Krister Thuresson‡ Departamento de Fisicoquı´mica (CTFQ), Facultad de Ciencias, UniVersidad a Distancia (UNED), 28040 Madrid, Spain, and Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund UniVersity, SSE-2211 00 Lund, Sweden ReceiVed: July 15, 2005; In Final Form: October 21, 2005
The lamellar mesophase formed by surfactant 1,4-bis(2-ethylhexyl) sodium sulfosuccinate (AOT) in deuterated water is mixed with poly(dimethylacrylamide) (PDMAA) polymers of low molecular weight (M h n ) (2-20) × 103). The mixtures separate into microphases (lamellar plus isotropic polymer solution). Their microstructures are studied by microscopy, small-angle X-ray scattering (SAXS), and deuterium NMR (2H NMR). According to SAXS, the lamellar phase fractionates the molecular weight distribution of the polymer, by dissolving only chains with coil sizes smaller than the thickness of the water layers between lamellae, and keeping larger chains segregated from the lamellar phase. The fraction of polymer that is segregated from the lamellar phase grows with M h n of the polymer. In 2H NMR, there are two signals, a quadrupolar doublet (water molecules hydrating the anisotropic lamellar phase contribute to this doublet) and a singlet (water molecules in the isotropic polymer solution contribute to this singlet). These two signals are deconvoluted to analyze the phases. Mixing with the polymer produces the partial dispersion of the lamellar phase into small fragments (microcrystallites). The structure of these microcrystallites is such that they conserve the regular long period spacing of the macrophase, and are thus identified in SAXS, but they are smaller than the minimum size required to produce quadrupolar splitting (about 4 µm), and therefore, in 2H NMR, they contribute to the singlet. 2H NMR can thus not distinguish between small microcrystallites and an isotropic polymer solution segregated from the lamellar phase; instead small microcrystallites are detected as an apparent increase of the isotropic solution. The degree of dispersion produced by the polymer in the lamellar phase is correlated with the degree of segregation that the polymer suffers. Thus, much greater dispersion into microcrystallites is produced by the higher M h n polymers than by the lower M h n polymers (in the range covered by the present samples, although with a much higher molecular weight sample (3 × 106) that is totally segregated no such microcrystallites were detected).
Introduction Investigations of polymers combined with lyotropic liquid crystals have received great attention in recent times because many industrial products1 and biological processes2 contain mixtures of surfactants and polymers. Depending on the interactions between the polymer and the surfactants (and/or the solvent), when the surfactant forms a lyotropic lamellar phase, the polymer can be localized in the membrane,3,4 localized both in the membrane and in the solvent,5 adsorbed onto the bilayer surface,6-9 localized entirely in the solvent,10-12 or excluded from the lamellar phase in an isotropic phase.13 In other cases, the polymer induces a phase separation into two lamellar phases.14 The combination of poly(dimethylacrylamide) (PDMAA) with the surfactant/water systems deca(ethylene glycol) hexadecyl ether15 and 1,4-bis(2-ethylhexyl) sodium sulfosuccinate (AOT)16 are typical examples of mixtures without strong associations. These surfactant/water systems form ordered mesophases having hexagonal and lamellar structures. The repeat order or spacing of these structures is in the range of a * To whom correspondence should be addressed. E-mail: ipacios@ ccia.uned.es. † UNED. ‡ Lund University.
few nanometers (2-10 nm),16 similar to the size of polymer coils of intermediate molecular weights. Because of its neutrality and lack of amide hydrogens, PDMAA shows no specific or binding interaction with these surfactants (deca(ethylene glycol) hexadecyl ether is neutral and AOT anionic), and one expects that the ability for the surfactant mesophase and the polymer to mix will depend on steric or geometric factors. The polymer mixes with the mesophase when the macromolecular coils can penetrate inside the ordered structure, their diameters being small enough to reside inside the spacing of the structure; on the contrary, the polymer stays segregated from the mesophase when the coil diameters are larger than the spacing of the lamellar structure. In this way, the ordered structure acts as a grating that sieves the polymer coils according to their size relative to the spacing of the structure.17 The spacing of the lamellar structure depends on the AOT content; thus, for a given AOT concentration, PDMAA will mix only up to a certain limit of molecular weights of the polymer, but this limit can be varied by changing the concentration of surfactant. Additionally, when polymer and surfactant are both present, the spacing of the lamellar structure depends also on the polymer concentration. Again, the influence of polymer concentration on lamellar spacing is determined by the relative
10.1021/jp0539019 CCC: $30.25 © 2005 American Chemical Society Published on Web 11/24/2005
Polymer-Surfactant Microstructures size macromolecules/spacing. Thus, the presence of the polymer is expected either to increase or to decrease the lamellar spacing, depending on such relative sizes. If the coil diameters are small and the macromolecules are allowed inside the lamellae, we expect that their inclusion will increase the spacing between lamellae, in analogy with an increasing amount of solvent. Contrarily, if the coil diameters are so large that the macromolecules are excluded from the lamellae, we know that the polymer decreases the interlamellar spacing, because it forms a separate polymer/water phase, taking with it part of the water from the lamellar phase, resulting in a partial deswelling of the lamellae by osmotic compression due to the polymer. In any given polymer sample, there is always a mixture of molecules with different molecular weights, thus the fraction of the molecular weight distribution that corresponds to chains larger than the spacing is excluded from the lamellar structure, while the rest of the polymer is able to penetrate inside. Therefore, the lamellar structure acts as a sieve that fractionates the polymer according to the size of the chains relative to the spacing. For the PDMAA/AOT/water system the phase formed by the segregated polymer is isotropic and its separation from the lamellar phase may take place only at the microscopic level (with no macroscopic boundaries), because of the high viscosity of the system. One of the ways of detecting the separation between an ordered and an isotropic phase, at the microscopic level, is through deuterium nuclear magnetic resonance spectroscopy (2H NMR). This technique allows distinguishing water molecules that are in an anisotropic environment and water molecules that are in an isotropic environment, which here means water molecules in the lamellar and in the polymer microphases, respectively. We report here 2H NMR results on the mixing between AOT and PDMAA for different molecular weights of the polymer. These molecular weights span the whole range of mixing behaviors, from total penetration of the polymer in the lamellar structure of AOT by low molecular weights, to partial penetration and partial exclusion for intermediate molecular weights, and finally practically total segregation of the polymer for the highest molecular weights.17 Here the samples have deuterated water to study the evolution of the microphases (lamellar, isotropic) by means of the 2H NMR technique. Additionally, small-angle X-ray scattering (SAXS) will be used to determine the degree of penetration of the polymer coils inside the lamellar spacing. The present results with 2H NMR provide a deeper insight on the nature of the coexisting microphases, information that was not available before.17 As we shall see, the degree of dispersion of the ordered phase turns out to be a key factor in understanding our experimental findings. We also compare the composition of the phases as obtained with the two techniques 2H NMR and SAXS. Experimental Section Materials. AOT (1,4-bis(2-ethylhexyl) sodium sulfosuccinate) was obtained from Sigma. Deuterated water (99.5% purity) was purchased from Dr. Glaser, Basel. Polymers employed are enumerated in Table 1 with molecular weights and radii (details about their synthesis and characterization are explained elsewhere).17 Sample Preparation. The AOT/PDMAA/D2O mixtures were prepared by weighing proper amounts of the three components directly into glass tubes that were then flame-sealed. The samples were homogenized by repeated centrifugation of the mixtures back and forth for more than 2 h and then were allowed to equilibrate for 42 days, at 25 °C, before any measurements
J. Phys. Chem. B, Vol. 109, No. 50, 2005 23897 TABLE 1: Characterization of PDMAA Samples: Number Average Molecular Weight (M h n) and Polydispersity Index (r )M h W/M h n) Determined by Size Exclusion Chromatography (SEC) and M h n Determined from Vapor Pressure Osmometry (VPO) M h n × 10-3 polymer
VPO
SEC
r SEC
6 5 4 3 2 1
20 6.3 5.0 2.2 2.3 2.2
18 7.3 7.6 3.0 2.8 2.6
2.25 1.65 1.65 1.70 1.48 1.34
were conducted. The concentration of AOT was set at an approximately fixed AOT/water ratio of 25% (vol/vol) and the concentration of PDMAA was allowed to vary in the approximate range 0.2-3.3% (vol/vol). 2H NMR. Deuterium spectra were recorded using a Bruker DMX 100 spectrometer operating at a deuterium resonance frequency of 15.35 MHz. The pulse length was 10.5 µs and the receiver dead time was set to 100 µs, and the time between scans was 0.27 s. These conditions render a good signal/noise ratio, although they are not optimum for quantitative estimations. The temperature was kept at 25 ( 0.2 °C by a flux of air through the sample holder. The samples were kept in 8-mm test tubes that had been flame-sealed. The quadrupolar splittings, ∆, were measured as the peak-to-peak distance and are reported in hertz. Small-Angle X-ray Scattering (SAXS) and Optical Microscopy. The procedures used have been described in detail elsewhere.17 Texture of Samples The textures of the samples were analyzed with the same methods as was used for similar samples prepared in natural water.17 AOT/D2O samples containing PDMAA appear clear when polymers 1, 2, and 3 (lower molecular weights) are used, but they are turbid with polymers 4, 5, and 6 (higher molecular weights). This turbidity increases with the polymer content and could indicate the presence of at least two phases. The corresponding micrographs without crossed polarizers confirm a phase separation pattern (see Figure 1a), which becomes more obvious on increasing molecular weight and concentration of the polymer. Generally, micrographs with crossed polarizers show typical oil streaks characteristic of lamellar texture LR (Figure 1b), which provides evidence for the presence of a phase with this order. Lamellar Spacing and Polymer Penetration Since in this investigation the solvent is deuterated water, and we have in a previous publication investigated closely related samples prepared with normal water, it is possible that a comparison of the results can reveal if the isotope substitution has any influence on the sieving of macromolecular coils by the lamellar structure. Our results will indicate if substituting hydrogen for deuterium has influence on the lamellar structure or on the osmotic equilibrium between the two microphases: lamellar and isotropic. To our knowledge, there is not much information on isotope effects in polymer/surfactant/water systems. We have only found a few investigations related to surfactant systems that deal with structure and dynamics of the micellar state18,19 and nothing with regards to the lamellar state. Regarding polymer solutions, we have found even less.20 SAXS diffraction patterns of these samples are similar to those previously studied in natural water. After the repeat
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Figure 1. Optical micrographs of AOT/D2O sample (25% v/v AOT) containing 3.2% v/v of polymer 5: (a) without crossed polarizers; (b) with crossed polarizers. Bar: 100 µm.
distance or long period (d) of the lamellar stacking from the position of the first Bragg peak is calculated, k1 (using the simple relationship d ) 2π/k1), we evaluated the variations of lamellar spacing with polymer concentration, which differ widely depending on the molecular weight of the polymer, as expected. The lowest molecular weights (1, 2) produce increase of spacing at constant AOT/D2O, the highest molecular weights (5, 6) produce the largest decrease of such spacing, and the intermediate molecular weights (3, 4) produce a moderate decrease, clear in 4 and almost unnoticeable in 3, according to their order of molecular weights (4 > 3). The macromolecular coils of the two lower molecular weights (1, 2) are small enough to penetrate freely inside the lamellar structure of AOT, and in this way the spacing at constant AOT/D2O increases as polymer is incorporated between lamellae. The macromolecular coils of the other molecular weights are larger and somewhat restricted to such penetration, suffering segregation to an isotropic microphase that partially deswells the lamellae and gives the decrease of lamellar spacing at constant AOT/D2O. This degree of segregation starts very weak in 3, grows in 4, and gets very strong in 5 and 6. As deduced previously, the spacing of the ordered phase changes, both with surfactant and with polymer concentration, in the following way17
1/d ) (1/d0)(φS + KφP)
(1)
where φS and φP are the experimental surfactant and polymer volume fractions in the ternary surfactant-polymer-solvent system, respectively, and K is a coefficient which reflects the partition between the two phases of the components present in both of them, namely, the solvent and the fraction of the polymer molecular weight distribution with coil diameters falling below the cutoff distance imposed by the lamellar spacing. This K was written as K ) fK∞, where f is the fraction of polymer that is excluded from the ordered structure and K∞ the limiting value of K for total exclusion.21 In a practical application of eq 1, we shall plot (dφS)-1 as a function of φP/φS (Figure 2). From the intercept we obtain the bilayer thickness (d0) and from the slope the value of K. The present results in deuterated water are similar to those found in natural water. Regarding the value for d0, it is within the range given in the literature for d0 in natural water, 1.95-2.05 nm,22 and the same d0 is obtained for all the molecular weights (d0 ) 1.93 nm, polymers 1-3; d0 ) 1.97 nm, polymer 4; d0 ) 1.95 nm, polymer 5; d0 ) 1.94 nm, polymer 6). This invariance of d0 means that the polymer does not disturb appreciably the bilayer structure of AOT, as expected if there is no strong association polymer-surfactant.
Figure 2. Interlamellar spacing of AOT, d, as function of PDMAA concentration for polymers of different molecular weights. φS and φP are AOT and PDMAA volume fractions, respectively, in the AOT/ PDMAA/D2O ternary system.
TABLE 2: Partition Coefficient, K, for the Equilibrium between the Lamellar and Isotropic Microphases, Determined in D2O, from the Linear Plots of Figure 2, As Compared with K Determined17 in H2O K polymer
D2O
H2O
1 2 3 4 5 6
-0.05 -0.12 0.46 1.38. 1.63 2.14
0.09 0.09 0.19 0.85 1.37 1.69
Regarding the values of K, they vary strongly with the molecular weight of the polymer, and the trend of this variation is similar to that found in natural water, although with some noticeable differences. The values of K for all the polymers in deuterated water are given in Table 2 (we have not considered the point of highest φP with polymer 5 as it deviates too much from the trend suggested by a straight line), where they are compared with those obtained in normal water. For the two polymers with lowest molecular weights (1, 2) that penetrate freely in the lamellar structure, K should be zero, but the slope of Figure 2 gives a negative value (very small) for K, which could mean some kind of attraction (very weak) of the polymer with the AOT bilayer in the case of deuterated water. For these same polymers in normal water, we have previously obtained K ) 0, which is in contrast to the present negative K. As we can see, there is a progressive increase of K with the molecular weight of the polymer, indicating that a higher fraction of the polymer, f, is being excluded from the lamellar structure. This tendency is the same in deuterated and normal water, but the precise values of K for each polymer differ in the two solvents.
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J. Phys. Chem. B, Vol. 109, No. 50, 2005 23899 leave less possibility for the polymers to penetrate, resulting in higher K values. Shape of 2H NMR Spectra
Figure 3. Fraction of long chain polymer (in total polymer) excluded from lamellar phase, f, as function of volume fraction of total polymer, φ p.
Noticeably, the values of K are higher in deuterated water. Higher K means that, for a given total polymer concentration, the fraction of polymer that is segregated, f, takes with it more solvent. This is a possible solvent isotope effect, but we have to be aware of the large error in the values of K (the points in the plots of Figure 2 show a substantial scatter and also we have fewer points in the case of deuterated water), this error being likely conditioned by the difficulty in attaining a true equilibrium between the two microphases (see below). At any rate, the main unifying conclusion is that K grows with the molecular weight of the polymer the same way in deuterated as in natural water. Fraction of Polymer Excluded from the Lamellae It is possible to calculate, for each polymer sample, the fraction of polymer chains that are excluded from entering the AOT/D2O lamellar structure (f), by comparing the distribution of molecular weights in the polymer, W(M), with the cutoff distance imposed by the spacing between lamellae
f)
∫M∞ W(M) dM
(2)
C
where MC is the molecular weight value which corresponds to chains having dimensions equal to the spacing between lamellae (see ref 17 for further details). The values of f thus calculated are depicted in Figure 3, as function of polymer concentration. Again, the polymers cover the whole range of degrees of exclusion from the lamellae: polymers 1 and 2 practically not excluded, polymer 3 slightly excluded, polymers 4 and 5 about half excluded, and polymer 6 almost totally excluded. For a given polymer, its degree of exclusion grows with polymer concentration. As pointed out above, this is a consequence of a cooperative effect of the polymer in its own exclusion, since the polymer deswells the lamellar structure, and thus contributes to shorten the interlamellar distance, which then excludes more polymer. When comparing these values of f in deuterated water with those in natural water shown in Figure 5 of ref 17, we can see that they are very similar, especially the ones close to the limit of total penetration (polymers 1 and 2) or close to the limit of total exclusion (polymer 6), which are almost identical in the two solvents, while the ones for intermediate exclusions (polymers 3, 4, and 5), turn out to be somewhat higher in deuterated water. This could point to an isotope solvent effect: if AOT were more strongly hydrated in deuterated water and/ or the volume of polymer coils were slightly higher, it would
The 2H NMR spectra show two signals: one is a doublet due to quadrupolar splitting; the other is a single peak situated in the middle of the two wings of the quadrupolar doublet (see Figure 4). The quadrupolar splitting arises from the anisotropic environment that the water molecules experience in the lamellar phase, while the central peak is expected to arise from the isotropic solvent molecules in the isotropic polymer solution phase. However, a contribution to the central peak could also come from fragments of the ordered phase being small enough for solvent molecules to map longer distances than their size due to diffusion during the experimental time. (Another possibility, that the central peak is due to a new splitting not resolved, should be rejected, because this would be associated with the appearance of corresponding diffraction peaks in SAXS, which is not found here.) It is expected that the two signals should appear whenever there is coexistence of the two microphases, lamellar and isotropic. Especially, the lamellar phase of AOT is present in all of the samples, and the isotropic phase should be present only in those cases where some polymer is segregated from the lamellae. However, the quadrupolar doublet is missing at some concentrations of the polymers with the higher molecular weights, and the central peak appears even for the polymers with the lowest molecular weights, where no segregation is expected as concluded from SAXS. The absence of quadrupolar splitting enters in contradiction with the observations by optical microscopy that all samples have textures typical of lamellar phase, and the presence of the central peak in the lowest molecular weight samples, if assigned entirely to solvent molecules in an isotropic environment, is likewise in conflict with the results from SAXS, which show that total penetration of polymer coils in the lamellar phase takes place with the lowest molecular weights. To analyze this contradiction, we shall now describe the details of the 2H NMR spectra, sample per sample. First, we shall give a mere qualitative description of the spectra. Then, we shall analyze the form of the signals in the spectrum, by deconvoluting the central peak from the quadrupolar doublet, to estimate the relative contributions from the two microphases, lamellar and isotropic. In our description of the spectra, we shall focus on the changes with polymer concentration and with molecular weight of the following characteristics of the spectra: the appearance or not of the quadrupolar doublet and the central peak, the relative heights of these two signals, and the width of the central peak. Separately, we shall discuss the magnitude of the quadrupolar splitting. In the low molecular weight polymers 1, 2, and 3, there is always a clear quadrupolar doublet, and the central peak appears in most, but not all, of the cases. In polymer 1 the central peak (very small) is seen at concentrations 0.6 and 1.0%, and can be anticipated (because of the flat bottom in the valley inbetween the doublet) at the other concentrations (Figure 4). In polymer 2 the central peak is not seen at concentration 0.2%, it appears very small at 0.6%, and grows progressively with increasing concentration at 1.0, 2.0, and 3.0%; it always stays lower than the wings of the doublet. In polymer 3 the central peak is detected only by the flat bottom of the doublet at concentration 0.2%, it is clearly seen at 0.6%, and it becomes higher at 1.0 and 2.0% (similar in both), and finally at 3.0% the central peak is higher than the doublet wings (Figure 4). So on comparison with polymer 2, we can
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Figure 4. 2H NMR spectra from AOT/D2O (25% v/v AOT) containing PDMAA at different polymer concentrations (shown as % v/v polymer in the figure), for the polymers 1, 3, 4, and 6.
say that the central peak grows both with increasing polymer concentration and with increasing molecular weight (Figure 4). Following with this same trend, in polymer 4 the central peak is already of similar height as the wings of the doublet at 0.2% and gets much higher than these wings at 0.6%, and finally, at 1.0%, the signal consists only of the central peak, slightly distorted at the position of the wings (Figure 4). However, for the next two higher concentrations, the situation reverses: at 2.0% the doublet is recovered as shoulders of the central peak, and at 3.0% the two wings of the doublet are again clear but are much smaller than the central peak. The width of the central peak shows also a peculiar change: this peak broadens when polymer concentration is increased from 0.6 to1.0%, but further increase of concentration produces the opposite effect, the peak gets narrower as the concentration increases in the series 1.0, 2.0, and 3.0%. In polymer 5, the trend is similar. At 0.2% the central peak is larger than the doublet wings, at 0.6 the signal is almost exclusively the central peak with shoulders at the positions of the doublet wings, and at 1% the shoulders are even smoother. Then the situation reverses: the wings appear again as very small peaks at 2.0% and are a little more pronounced at 3.0%. The width of the central peak also evolves similarly to polymer 4, it broadens from 0.2 to 0.6%, but then it gets narrower as the concentration increases in the series 0.6, 1.0, 2.0, and 3.0%. With polymer 6 only at the lowest polymer concentration, 0.2%, there appears a quadrupolar doublet (much lower than the central peak). For the rest of the concentrations, the signal is just one peak (with only a faint distortion in the case of 0.6%) (Figure 4). The width of the peak evolves similarly to central peaks from polymers 4 and 5 (Figure 5): The peak broadens from 0.2 to 0.6%, but then it gets progressively narrower as the concentration increases in the series 0.6, 1.0, 2.0, and 3.0%. Regarding the relative heights of the central peak with respect to the height of the quadrupolar wings, we can see that increasing molecular weight and increasing polymer concentration both enhance the central peak over the quadrupolar wings. Thus, the wings are higher at all concentrations of polymers 1
Figure 5. Width at half-maximum, whm, of the central peak in 2H NMR spectra, as a function of polymer volume fraction, φP, for AOT/ D2O samples containing polymers 4, 5, and 6: filled points, measured directly on the peak; open points, calculated from the peak as explained in the section Microcrystallites.
and 2, at all concentrations for polymer 3 (except for the highest one), only at the lowest concentration for polymer 4, and never for polymers 5 and 6. The progressive increase in the central peak relative to the quadrupolar doublet as the molecular weight of the polymer increases can be easily assigned to the greater degree of segregation from the lamellar phase suffered for the longer polymer chains. The increase of the central peak with increasing polymer concentration could be traced also to a greater degree of segregation, since we have seen (Figure 3) that the fraction of each polymer segregated increases with concentration. It can be deduced from the experiments that these polymer/ surfactant mixtures are metastable, with phase separation taking place at the microscopic level only, and that the microphases undergo progressive evolution over long periods of time, which modifies the shape of the 2H NMR spectra. The results described above correspond to spectra obtained at least one year after the preparation of samples. Along this period, the shape of spectra from samples with 0.6-3% of polymer 6 kept constant (see Figure 6a), but in all the other cases the shapes changed, with the central peak becoming relatively less intense in comparison with the peaks from the quadrupolar splitting (see Figure 6b). The extension of this variation depends on the size of the polymer and on its concentration. For example, most of samples with polymers 1, 2, and 3, present at the beginning a central peak higher than the peaks from the quadrupolar splitting, and
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J. Phys. Chem. B, Vol. 109, No. 50, 2005 23901
Figure 6. Time evolution of NMR spectra from samples with 2.1% of polymer 6 and 1 (parts a and b, respectively). Numbers in the top indicate the number of months since the sample was prepared.
one year later the situation is the opposite, while with polymers 4, 5, and sample with 0.2% of polymer 6, the variation is less strong and the central peak is always the most important while the splitting, not very clear at the beginning of this study, became more evident one year later (especially in sample with 0.2% of polymer 6 and with 0.6 to 2% of polymer 4 or 5). Gathering all the above results, we can speculate that in most of the samples the central peak contains the contribution not only from isotropic water but also from water in small microcrystallites of the lamellar phase (i.e., small fragments of the lamellar phase). These “microcrystallites” are probably formed by dispersion at the moment of mixing the polymer with the surfactant. Later, once at rest, these microcrystallites grow in size, which gives the small decrease with time of the central peak in regard to the quadrupolar doublet. The influence of microcrystallites will be discussed in more detail below, when we have an estimation of the central peak. However we call attention to that some of the changes in the 2H NMR line shape that occur here upon mixing AOT/water with polymer are similar to the ones that were observed in the neat AOT/water system when it was disturbed by mechanical stresses.23 There the perturbation also produced a reduced size of the lamellar domains. Microcrystallites The results above depict the relative importance of the central peak and the quadrupolar doublet. Since all the spectra were done in the same experimental conditions (see 2H NMR), it is possible to estimate a relative proportion of the two components and obtain at least a relative numerical comparison of the influence of molecular weight and concentration of the added polymer. But the two signals overlap, so we need a deconvolution method. To this end, we can use a function adequate to represent a three-dimensional (3D) powder spectrum24 plus a Lorentzian. The deconvolution is done by fitting the experimental NMR spectra of our samples with these two functions. The data were fitted by a method of least-squares deviation between experimental and calculated results. The Lorenztzian should be in the center of the splitting, but small deviations are found in some spectra. Fittings with and without taking this into account do not give significant differences. Fitting parameters at hand are the following: from the 3D powder spectrum, the splitting, ∆, a relaxation constant, R, and a constant to normalize the intensity with the experimental results, N1; from the Lorentzian, full width of the peak at half-height and a constant to normalize the intensity with the experimental results, N2.
TABLE 3: Ratio of Areas, (central peak area)/(total area), in the Deuterium Signal of 2H NMR Spectra from AOT/ D2O/PDMAA, as a Function of Polymer Concentration OP × 100 for the Six Polymer Studieda concn polymer polymer polymer polymer polymer polymer φP × 100 1 2 3 4 5 6 0.2 0.6 1 2 3
0.00 0.04 0.01 0.00 0.00
0.00 0.01 0.10 0.12 0.11
0.00 0.09 0.09 0.07 0.23
0.07 0.55 0.86 0.71 0.38
0.16 0.76 0.87 0.52 0.37
0.35 (1) (1) (1) (1)
a The ratio of areas is calculated by the least-squares fitting described in the text. In parentheses, values attributed to spectra without splitting (where the fitting to a powder spectrum makes no sense).
Once the spectrum is adjusted, we can obtain the ratio of the central peak area to total area. This ratio of areas in the spectrum could, in principle, be associated with the ratio between the water in the isotropic phase to the total water in the sample (ignoring, in the first instance, the possible contribution from small microcrystallites to the central peak, which will be discussed later).23 The estimated fraction of isotropic water thus calculated from the 2H NMR spectra is almost zero for polymer 1, between 0 and 23% for polymers 2 and 3, between 7 and 87% for polymers 4 and 5, and between 35 and 100% (considering that there is no splitting in most of its samples) for polymer 6 (see Table 3 for details). From this, we can deduce that the fraction of isotropic water increases with the polymer size, as expected. From 2H NMR we have thus estimated a fraction of water experiencing an isotropic environment, FW ()water in the isotropic phase/total water). From SAXS we can get the fraction of water in the lamellar phase,1 - FW, by using the spacing of the lamellar structure, d, the dilution law, and the global composition of each sample, as
1 - FW ) [φS/(1 - φS - φP)] (d - d0)/d0
(3)
Then, we directly get also from SAXS the fraction of water in an isotropic environment, FW. Let us compare now the results from these two techniques. In Figure 7 is represented the value of FW, obtained from the ratio of the central peak area to total area from NMR fitted curves, FW (NMR), as a function of the FW calculated from SAXS by means of eq 3, FW (SAXS), for all the samples studied here. Also included are results from previous studies of the system D2O/AOT/PDMAA where the polymer has a high molecular weight of 3 × 106 and is, from a previous investigation, known to be located in the isotropic phase.25 Almost all
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Pacios et al. SCHEME 1. Partial Distribution of the Lamellar Phase as Microcrystallites and the Polymer in the Isotropic Phase
Figure 7. Fraction of water in the isotropic phase with respect to total water (in volume fraction), FW, obtained from SAXS and 2H NMR measurements: filled circles, previous results25 for a polymer with a high molecular weight 3 × 106; squares, samples with polymers 4 and 5 and sample with 0.2% of polymer 6; triangles, samples with polymer 3. Solid line is the identity, dotted line is the best fit of filled circles, and dashed lines are the corresponding prediction of the range.
points fall above the identity line, and this discrepancy can be associated to an overestimation of anisotropic water by SAXS, an overestimation of isotropic water by NMR, or a combination of both. Let us evaluate each one of these two possibilities. (1) Overestimation of Anisotropic Water by SAXS. An overestimation would arise if the surfactant molecules were not only in the lamellar phase but also in the isotropic phase. This is not expected from the phase behavior of AOT since only a very low concentration of monomer is expected in equilibrium with the lamellar phase. Furthermore, in the case of the very high molecular weight polymer, it was previously shown16 that the polymer concentration obtained assuming that all surfactant molecules are in the lamellar phase agrees well with the experimental results, so it seems that this contribution can be neglected. Additionally, for the polymers that are partially excluded from the lamellar phase (i.e., 4 and 5) there is another source of error that underestimates the amount of water in the isotropic phase, because to obtain the isotropic water from SAXS data we have assumed that there is no polymer in the lamellar phase. But, as we have seen above, some coils penetrate in the water layers of the lamellar phase. However, the contribution from this mechanism should be small because the global amount of polymer is small (around 3% in volume, or less) in comparison with the global amount of water (around 72% in volume, or more). Figure 7 shows that the deviation of the data points corresponding to samples with polymers 4, 5, and 6 (squares) does not follow a linear variation with the concentration, which means that we can reject the possibility that this explains the divergence. (2) Overestimation of Isotropic Water by NMR. The observed behavior would suggest that the samples can contain lamellar microcrystallites, which are not large enough to give splitting but instead increase the width of the central peak. The fitted results of NMR data from samples prepared with PDMAA of molecular weight 3 × 106 (filled circles) show that the width of the Lorentzian is approximately constant with an average value of 8 ( 3 Hz. Then, the slight scattering of these results from the identity line seems to be related not so much with the Lorentzian broadening but with differences in the 3D powder spectrum that could be associated with the size of the ordered domains23 and/or with the experimental settings (see 2H NMR).
After comparison of the data from the other samples (squares and triangles) with the previous results (filled circle points), the most important difference is the broadening of the Lorentzian (now between 11 and 46 Hz). This can be due to the presence of microcrystallites in the system being too small to induce splitting but contributing to the width of the Lorentzian. Influence of microcrystallites is modulated by their size, and they can either increase the width of the Lorentzian or induce changes in the powder spectra. In the case of samples with polymers 2 or 1 (data not show in Figure 7), SAXS results (see above) indicate clearly that only one phase is present, so the small Lorentzian peak observed in their NMR spectra can be related only with some microcrystallites present in these samples. From the above discussion, FW obtained from NMR spectra could be associated with the sum of contributions from water in sufficiently small microcrystallites and water in an isotropic phase, while FW from SAXS corresponds to water not being in lamellar microcrystallites or in a lamellar phase but being in an isotropic environment. A tentative estimate of the fraction of lamellar phase which is in the form of microcrystallites, FM, can be calculated as
∆FW ) FW(NMR) - FW(SAXS)
(4)
FM ) ∆FW/(1 - FW(SAXS))
(5)
As was explained above, a fraction, f, of polymer (given in Figure 3) is excluded from the lamellae and separates in to an isotropic phase. In this isotropic phase, the effective polymer concentration is then given by fφP. Since there is not a macroscopic phase separation, it seems reasonable that this fraction of polymer would be the responsible to distort the lamellar structures producing microcrystallites (Scheme 1). Figure 8 depicts the estimated fraction of lamellar phase that is in the microcrystallites, as a function of the polymer volume fraction in the isotropic polymer-rich phase, fφP. It seems that there are two clear regions. In the first one, the fraction of microcrystallites increases strongly, and in the second one, it decreases or keeps constant. First, the fraction of microcrystallites increases with polymer concentration, due to the disturbance produced by the presence of polymer chains (with polymers 1, 2, and 3, this variation is not very significant, because these oligomers keep preferentially in the lamellae and only a small fraction outside distorts the ordered structures).
Polymer-Surfactant Microstructures
Figure 8. Estimated fraction of lamellar microcrystallites, FM (eq 5), as a function of the polymer volume fraction in the isotropic polymerrich phase, fφP.
Figure 9. Experimental quadrupolar splitting, ∆, as function of polymer concentration, φP, for all samples showing such splitting; namely, all the concentrations of polymers 1, 2, 3, 4, and 5 and concentration 0.2% of polymer 6.
Quadrupolar Splitting The next point to consider is the magnitude of the quadrupolar splitting, ∆, as a function of polymer concentration and polymer molecular weight. The data of ∆, for the samples which present such splitting, are given in Figure 9. The first point to note is that the splitting remains constant, independent of polymer concentration and equal to the value of ∆ for AOT/D2O free of polymer, with the lower molecular weight polymers. According to theory, the quadrupolar splitting is proportional to the number of solvent molecules hydrating the ordered component relative to the total number of solvent molecules in the ordered phase. In the AOT/water lamellar structure, when macromolecular coils penetrate between lamellae, the number of hydrated solvent molecules and the number of total solvent molecules both remain constant, so there is no reason for a variation in ∆ by adding polymer. Thus, a constancy of ∆ is expected for the lower molecular weights, because the coils of these polymers can penetrate the water domains of the lamellae. Apparently, the same trend with virtually constant ∆ is maintained also with polymers with higher molecular weights (although this may be only apparent since the quadrupolar doublet is not well resolved, or even disappears as was the case with high molecular weight polymers (6), as explained above). Constancy of ∆ for the high molecular weights is not the expected behavior, because these polymers suffer partial segregation from the lamellar phase and polymer segregation induces partial deswelling of the lamellae (as detected by X-ray as a decreasing lamellar spacing). On the other hand, previous results with a very high molecular weight polymer that is totally segregated from the lamellar structure showed that ∆ indeed increased with polymer concentration.25 In fact, it was shown that the increase in ∆ produced by polymer segregation was well correlated with the concomitant decrease in total water of the lamellar phase, as measured by the thickness of the water
J. Phys. Chem. B, Vol. 109, No. 50, 2005 23903
Figure 10. Experimental quadrupolar splitting, ∆, as function of the inverse thickness of the water layers in the lamellae, (d - d0)-1, for all concentrations of polymers 1, 2, 3, 4, and 5 and 0.2% of polymer 6: full circles, previous results for a polymer of molecular weight 3 × 106.16,25 (d0 ) 1.96 nm.)
layers (d - d0), such that ∆ was proportional to (d - d0)-1. If we plot our present results together with previous ones (see Figure 10), it appears that the low molecular weight polymers fall close to the trend marked by the very high molecular weight, although now the range of values covered is so small that it by itself would say little if not compared with the previous trend. To estimate the size of the microcrystalites, where a crossover from spectra with only a central peak to spectra having a quadrupolar doublet is expected, we note that molecular diffusion limits the range in which 2H NMR is sensitive. According with this, the mean-square displacement, z2, of water due to diffusion, during the time t can be obtained as, z2 ) 2Dt, where D is the self-diffusion coefficient of water (2.25 × 10-9 m2/s at 25 °C). The diffusion time (t) associated with the crossover can be estimated from the quadrupolar splitting, t ) 1/∆. In the present samples the expected value of z2 can then be calculated to 14 µm2, which indicates that the minimum size of the ordered domains to appear in the NMR spectra as a quadrupolar splitting26 should be about 4 µm. One independent way to confirm the presence of microcrystallites and to obtain the average of the crystal sizes could be through SAXS diagrams if obtained in an instrument with a proper primary beam (i.e., a synchrotron). Conclusions The mixing of PDMAA (e3% PDMAA) with the lamellar phase of AOT/deuterated water (25% AOT) produces partial segregation. The degree of this segregation increases with the molecular weight of the polymer. According to SAXS and microscopy, very low molecular weight polymers dissolve in the water layers of the lamellar phase, but high molecular weight polymers are excluded from the lamellae and form a separate isotropic microphase. For a given molecular weight distribution, the lamellar spacing acts as a grating that fractionates the polymer chains, and only the fraction of chains having macromolecular dimensions smaller than thickness of water layers in the spacing are dissolved in the mesophase. As a result of mixing, part of the lamellar phase is dispersed in small fragments (microcrystallites). These microcrystallites conserve the regular long period spacing, which is detected in the diffraction patterns by SAXS, but the microcrystallites are smaller than the minimum size required to produce quadrupolar splitting in 2H NMR spectra (about 4 µm). Hence, 2H NMR gives an overestimation of the isotropic polymer solution which is segregated from the lamellar phase, while SAXS yields more reliable results.
23904 J. Phys. Chem. B, Vol. 109, No. 50, 2005 In this way, very low molecular weight polymers, which get preferentially dissolved in the water layers of the lamellar phase, give an apparent contribution from a separate isotropic phase in 2H NMR, which is actually due to the dispersed lamellar microcrystallites. Similarly, with the high molecular weight polymer, which gets preferentially excluded from the lamellae, the quadrupolar signal of anisotropic water disappears, because the lamellar phase is in the form of microcrystallites. The distribution of microcrystallites evolves toward larger sizes, since the signal ratio isotropic/anisotropic of 2H NMR spectra decreases with time (>1 year). Acknowledgment. I.E.P. thanks members of the Department at Lund for help and advice during her visiting stays. Financial support from the Spanish Ministerio de Educacio´ n y Ciencia (project CTQ2004-05706/BQU), from a Marie Curie European Re-integration Grant (MERG_CT-2004-006316), and from UNED are acknowledged, as well as support from the Swedish Research Council and the Center for Amphiphilic Polymers (CAP) at Lund University. References and Notes (1) Holmberg, K.; Jo¨nsson, B.; Kronberg, B.; Lindman, B. Surfactants and polymers in aqueous solution, 2nd ed.; John Wiley & Sons, Ltd.: Chichester, England, 2003. (2) Petrov, A. G. The Lyotropic State of Matter, Molecular Physics and LiVing Matter Physics; Gordon and Breach Science Publishers: Amsterdam, 1999. (3) Radlinska, E. Z.; Gulik-Krzywicki, T.; Lafuma, F.; Langevin, D.; Urbach, W.; Williams, C. E.; Ober, R. Phys. ReV. Lett. 1995, 74, 4237. (4) Radlinska, E. Z.; Gulik-Krzywicki, T.; Lafuma, F.; Langevin, D.; Urbach, W.; Williams, C. E. J. Phys. II 1997, 7, 1393.
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