3.1. Composition and Crystallinity Characterization.
From the quantitative point of view, PGAA delivered the sulfur-to-carbon (S/C) ratio of 0.065 and 0.155 for the two uniaxially deformed sPS films studied in this work. Following the method reported in [40
], which was used also in our previous study [28
], sulfonation degrees of S = 19.5 and 46.3% (molar fraction of sulfonated monomer units) were determined for the samples, which were later subjects of doping with C60 and C70 fullerenes, respectively.
The FTIR spectra of the films doped with C60 (blue curves) or C70 (black curves) fullerenes are shown in Figure 2
in parallel to that from a δ-form sPS film (red curve). Due to the multitude of characteristic bands of sPS, only weak differences between fullerene-free and fullerene-doped films could be observed, similar to those indicated in the region 1440–1470 cm−1
a). However, it is not clear that the origin of these infrared bands can be attributed to fullerenes. An experimental FTIR characterization of fullerenes in bulk or functionalized polymers can be found in [41
] for C60 or [42
] for C70, while theoretical calculations were done in [43
The region of symmetric and asymmetric stretching of the SO3−
group is shown in Figure 2
b. The bands corresponding to the sulfonic group were observed at around 1240 and 1040 cm−1
, which is in good agreement with early reports on sulfonated copolymers [44
From the evaluation of the bands that are characteristic to crystalline and amorphous sPS, the amount of polymer in the ordered TTGG sequences can be satisfactorily estimated following the procedure described in [46
]. This would give a rough indication of the crystallinity of the sample. Information about the FTIR spectra from deuterated sPS either in film or solution/gel samples is very scarce in the literature. Therefore, for this exercise, we considered the bands in the range 500–600 cm−1
, which is a range that was never discussed before in the case of the deuterated sPS system and, which, according to our investigations on crystallization from solution (results to be published soon), contains information about either the helical or amorphous polymer chain conformation. Assuming that the two peaks shown in Figure 2
c for each sample could be assigned to the sPS in crystalline (556 cm−1
) or amorphous (545 cm−1
) phases, the fraction of conformationally ordered polymer obtained from the interpretation of the areas of the peaks would be about 35 and 22% for the films with a higher sulfonation degree (loaded with C70) and lower sulfonation degree (loaded with C60), respectively. A more accurate evaluation of the crystallinity can be obtained from the WAXD spectra.
In Figure 3
a, the UV-Vis absorption spectra of the three samples are shown in parallel. The polymer characteristic absorption features occur below 300 nm; therefore, the strong but rather featureless absorption observed in the region 300–700 nm in the case of fullerenes-doped polymers may be considered indicative for the incorporation of fullerenes in the membranes. Although some broad features may be observed in the 300–350 nm and 500–600 nm regions, however, the characteristic absorption bands for C60 or C70 fullerenes [42
] are not clearly visible in these spectra. At this stage of the study, we do not have yet a clear explanation for this observation, remaining that the behavior of fullerenes incorporated into the s-sPS by the dipping of polymer films in saturated fullerene solution will be investigated in detail in a forthcoming study. Nevertheless, the prompt-gamma activation analysis (PGAA), FTIR, and UV-Vis results confirmed the successful sulfonation and loading of the sPS membranes with either C60 or C70 fullerenes.
WAXD spectra from the s-sPS films containing fullerenes are presented in the Figure 3
b in parallel with the pattern from the s-sPS film with only protonated toluene loaded in the crystalline regions (clathrates). The pair of peaks at around 8 and 10° in 2θ is indicative for the formation of the crystalline δ-form of the clathrates [29
]. The presence of these peaks in the patterns collected on the samples loaded with fullerenes indicates that the sPS crystalline habit is preserved in these samples, too. Their slight enhancement when C60 or C70 fullerenes were added may relate to anchoring of the fullerenes to the sPS chains, as it was discussed in [49
]. The positions of the diffraction peaks are the same in all WAXD patterns, which indicates that the addition of fullerenes does not change the parameters of the polymer crystalline lattice. Since the formation of the crystalline regions in the membranes is a consequence of the initial exposure of the film samples to the action of toluene from solution [28
] and the fullerenes may replace the toluene molecules in the δ-form sPS co-crystals via the guest exchange mechanism, we assume that the subsequent incorporation of fullerenes does not significantly alter the crystalline degree of the membranes. This is different from the situation of the films that are produced by common gelation of the sPS and fullerenes [49
], when the incorporation of the fullerenes into the sPS lattice was evidenced by the slight changes that were observed in the position of the diffraction peaks from the polymer film containing fullerenes compared to the fullerenes-free polymer film. From the fitting of the diffraction patterns, the Ac
(peaks) and Aa
(background) areas were estimated, and the crystallinity of the membranes could be evaluated according to [33
]. This was about 33 and 24% for the films with a higher sulfonation degree (loaded with C70) and lower sulfonation degree (loaded with C60), respectively, which is quite close to the results obtained from the analysis of the FTIR spectra.
As the detailed analysis of WAXD spectra and of fullerenes behavior in s-sPS films is beyond the goal of this work, we limit ourselves here to a qualitative conclusion. Based on the characterization methods applied prior to SANS on our samples, we can confirm the presence of the crystalline δ-form in all films and the loading of samples with fullerenes, and we may only suppose that in some of the cavities between the sPS helices in the crystalline region, the protonated toluene initial guest was replaced by the fullerenes.
3.2. SANS on Dry Films
The main objective of this work is the microstructural characterization of the s-sPS membranes under hydration and the understanding of the formation and evolution of morphologies at te nanoscale and mesoscale. In our previous study [28
], we discussed the indirect observation on the preservation of crystallinity in such systems during the chemical treatment and hydration procedures. A direct observation of this effect together with a detailed microstructural characterization of the membranes over a wide length scale can be achieved by using the contrast variation SANS over a wide Q-range. This enables the collection of the scattering features from the crystalline ordering in the range of nanometers up to the micrometer size large-scale domains in one experiment. For this purpose, the novel approach that involves careful SANS measurements at high angle was checked first at the KWS-2 SANS instrument in combination with the contrast variation method on two δ-clathrate sPS films with toluene as the guest in the cavities between the polymer helices: one film was investigated as produced, while the other one was investigated after subsequent sulfonation and loading with C70 fullerenes.
In Figure 4
, the scattering patterns from the uniaxially deformed sPS film containing clathrate co-crystalline δ-form with either protonated toluene or deuterated toluene are shown in two-dimensional (Figure 4
a,b) and one-dimensional (Figure 4
c) presentations, respectively, following the averaging over the meridian and equatorial sectors. In Figure 4
a, two strong maxima can be observed in equatorial sectors at high angles, while two local maxima can be distinguished at low scattering angles in the meridian direction, above and below the beam stop, which is visible in the middle of the detector. These 010 reflections appear on the equator and the interlamellar reflections appear on the meridian, respectively, as depicted in the sketch presented in Figure 1
. In Figure 4
b, these features are either barely observable (the 010 reflections) or vanished (the interlamellar reflections). These features are also depicted by the one-dimensional patterns in Figure 4
c. The 010 reflections are yielded by the correlation between polymer sheets that sandwich in between the guest molecules. The SLD of deuterated crystalline sPS is ρ = 6.47 × 1010
, while that of the toluene is ρ = 0.94 × 1010
and ρ = 5.66 × 1010
for the protonated and deuterated species, respectively. Thus, protonated toluene molecules hosted between deuterated sPS helices provides a high neutron contrast, which is most apparent from the correlation between 010 planes (see Figure 1
, the crystalline lattice details). In case of using deuterated toluene guests, the neutron contrast is much lower, and the peaks on the equator become less obvious in the scattering pattern.
On the other hand, the interlamellar correlation peaks appear due to the difference in SLD between the amorphous and crystalline regions of the sPS co-crystals with guest molecules. The SLD of the amorphous sPS is ρ = 6 × 1010
. Loading the crystalline regions with protonated toluene will provide those regions with a lower SLD than the interlamellar amorphous regions, which will evidence the interlamellar correlations. In contrast, by using deuterated toluene, the difference in SLD between the crystalline lamellae and interlamellar amorphous regions will become much smaller than in the case of using protonated toluene. This will cause the interlamellar peaks on the meridian direction in the scattering patterns to vanish. Detailed SANS studies on the exchange of small guest molecules in sPS co-crystals are reported in [31
This contrast variation SANS investigation has proven that the status of the crystalline lattice can be monitored during the s-sPS sample treatment by observing the scattering features yielded at high angles. In Figure 5
, we show the high Q scattering patterns from a dry s-sPS film. The film is characterized by a high sulfonation degree (S = 46.3%) and a crystallinity of roughly 35%, and was clathrated with protonated toluene and subsequently loaded with C70 fullerenes. The data are presented two-dimensionally (Figure 5
a) and averaged over the equatorial and meridian sectors (Figure 5
b). The 010 reflections are well visible in the equatorial sectors, while the ionomer peak, which for the dry membrane is indicative of the mean distance between the sulfonic ionic clusters [51
], shows an isotropic distribution. The interlamellar reflections appear at much lower Q values in the case of the sulfonated samples, and are thus not visible in this experimental configuration. This is due to the swelling of the interlamellar amorphous regions, as already reported in [28
]. A correlation distance of ξion
= 14.95 Å was obtained from the evaluation of the ionomer peak position in Q. This distance is smaller than the one determined for dry Nafion [52
]. Taking into account the fact that the neutron SLD of fullerenes is very different from that of protonated toluene, but close to that of deuterated toluene [53
], we may conclude that the replacement of the initial protonated toluene guest in the deuterated sPS crystalline region by the subsequently loaded fullerenes took place to a very small extent only, since the scattering features characteristic of the crystalline lattice were not affected apparently. Otherwise, the 010 reflections should have been reduced drastically, as in the case of using deuterated toluene as the guest in the sPS co-crystals. Thus, the scattering features from the crystalline regions in the s-sPS films can be still observed after the loading of samples with fullerenes.
3.3. SANS on Hydrated Films—Variation of Hydration Level
With this information at hand, two s-sPS samples with different degrees of sulfonation and crystallinity, which were loaded with either C60 or C70, were investigated at the TOF SANS diffractometer TAIKAN during hydration at different RH levels and with different mixtures of H2O/D2O.
presents a selection of one-dimensional scattering data from the same s-sPS sample that was discussed in Figure 5
, and which was hydrated with H2
O at different RH levels. The data were averaged over the meridian and the equatorial sectors. The scattering patterns present three distinct peak-like features, which are observable for all hydration levels. These features are indicative of structural levels occurring at different length scales in the complex morphology of the polymer films. In the high Q range, the 010 crystalline peak appears in the equatorial sectors at around Q010
= 0.6 Å−1
, as in the case of the sPS clathrates (Figure 4
c) and the dry s-sPS sample (Figure 5
b). This peak, which denotes a mean repeating distance between the sPS sheets of about 10–11 Å, does not change its position and intensity with the increase of the RH. This observation led to the conclusion that the hydration does not affect the crystalline structure. Again, the neutron contrast is provided by the protonated toluene guest molecules, which occupy the cavities between the deuterated s-PS helices to a larger extent.
The ionomer peak is present in data on both the meridian and equatorial sectors, as it represents a scattering feature characteristic of the hydration occurring in amorphous regions, and is thus isotropically distributed on the detection area. The peak position Qion
depends on the level of the film hydration [54
]; thus, it moves toward lower values of Q with the increasing RH. A detailed presentation of the high Q scattering range from dry and hydrated films is given in Figure 7
. In our sample, the correlation between the hydrated ionic clusters increases from about ξion
= 14.95 Å for dry film to about ξion
= 23.7 Å for hydrated film at RH = 80%. A close inspection of the ionomer peak profile reveals a shoulder-like feature on the high Q side of the peaks, which becomes clearer with increasing humidity, due to the shift of the peak position to lower Qs. The Q-position of this shoulder seems to remain constant, regardless of the RH, and corresponds to the Q-position of the ionomer peak that is characteristic of a dry membrane. Apparently, the part of the ionic clusters that gives rise to the occurrence of the ionomer peak in dry conditions is still not hydrated, even for higher RH values.
In the low Q region, the interlamellar peak characteristic of the oriented lamellar stacks (Figure 1
) can be observed in the meridian scattering patterns. The peak position Qlam
moves only slightly to lower Q values with increasing RH, and denotes an interlamellar correlation of about 170–200 Å. In contrast, the equatorial scattering patterns exhibit at low Q a kind of plateau and a shoulder-like feature at around Q = 0.05 Å−1
, which resemble characteristics of weakly correlated spherical morphologies. We propose that they represent loosely correlated large hydrated regions that include the ionic clusters. The scattering from these water domains should appear isotropically on the detector. However, in the meridian sectors, the scattering from the lamellar stacks is superimposing over it.
The scattering from these sulfonated s-sPS films is characterized by a high sulfonation degree and a relatively high crystallinity, which are loaded with C70 fullerenes, and resemble that from the fullerene free s-sPS films discussed in [28
]. We may conclude that the partition of fullerenes between the amorphous and crystalline regions of these s-sPS films has a negligible effect on the scattering properties of the samples. As qualitatively concluded before, the C70 fullerenes seem to be located mostly in the amorphous regions rather than in the co-crystalline phase.
On the other hand, the scattering from fullerenes or fullerene assemblies dissolved in solution or amorphous polymer environment, similar to the deuterated polystyrene in the present case, is very weak [56
]. Therefore, we can consider it negligible compared to the contribution from other morphologies that form and evolve in our samples during the sulfonation and hydration processes. The experimental results in Figure 6
were interpreted via structural models: the data on equatorial sectors were described by Equations (1)–(3), while the meridian patterns were described by a superposition of scattering from spherical domains and lamellar stacks (Equations (4)–(6)). The water domains were characterized by a spherical form factor combined with the hard-sphere structure factor, which is an approach that is usually employed for the interpretation of scattering data from spherical polymeric micelles [57
], but is also applied for the characterization of ionic aggregates in PEMs [59
]. Thus, four free parameters are used for describing the scattering from water domains in the Q range between 0.008 and 0.2 Å−1
according to Equations (1)–(3), namely the “forward scattering” (I0
from the ensemble of the spherical water domains, the radius R of these domains, the hard sphere volume fraction ηHS
, and the hard-sphere radius RHS
. Additionally, we added a Gaussian term for the description of the ionomer peak at high Q and the constant background (Equation (1)). The three parameters of the Gaussian function describing the ionomer peak—amplitude, width, and position—were left free during the fitting procedure, while the background was kept fixed, as given by the flat behavior of the scattering curves in the high Q range. The ionomer peak description was included in the model because of its presence in the meridian pattern, too, which will help for an accurate modeling of these data in a subsequent step. The 010 peak was excluded from the fitting procedure. Despite the multitude of parameters, we consider that the fitting procedure offers reliable results, because the two structures that are modeled appear at very different length scales, therefore without influencing one another to a significant extent. If only the form factor is used for modeling the water domains, the experimental data cannot be properly described. The weak correlation effects between the water domains seem to be a consequence of the high sulfonation degree of this sample, when water clusters are densely formed in the amorphous region. Detailed discussions of the formation, growth, and percolation of water clusters as a function of the hydration level and functionalization of PEMs can by found in [9
The “forward scattering” from the ensemble of the spherical water domains and the size of these domains is of direct interest for the characterization of our system. We should note that a large polydispersity in size (σR
≈ 20%) of the water domains had to be considered in the fitting procedure in order to obtain a good fit in the Q region 0.1–0.2 Å−1
. Knowing the size and the SLD of the scattering objects—the water domains, and the SLD of their environment—and the sulfonated segments of s-sPS (Table 1
), we could extract information about the volume fraction ϕsph
occupied by the scattering objects in the sample (Equation (1)), in a similar way to [62
]. The volume fraction occupied by water in the whole amorphous region, (ϕwater
, is reported in Table 2
. From the water volume fraction in the sample volume estimated from the interpretation of the (I0
, the reported value for each RH is obtained by taking into account the crystallinity of the film, which was estimated at 35%, and the fact that only the amorphous regions are hydrated.
The data measured on the meridian sector were modeled for a morphology consisting of oriented crystalline-amorphous lamellar stacks, which are “embedded” in a bulk amorphous environment (Figure 1
). The scattering was described by combining Equations (1) and (4)–(6), and was superimposed over the scattering from water domains (including the ionomer peak contribution), which is isotropic and is known from the model interpretation of the equatorial data. Assuming a very large lateral extension of the lamellae, Rl
> 1000 Å—thus out of the size domain that is covered by the SANS window—and a constant thickness of the crystalline lamellae d = 60 Å, which is an average value of what is reported in the literature for sPS crystals with different degrees of crystallinity and subjected to different treatments [63
], only two free size parameters were used in the fitting procedure. These were, namely, the thickness of the interlamellar layer, Lb
, and the dispersion (smearing) parameter, σD
, of the interlamellar spacing, LD
= d + Lb
. As discussed in Section 2.3
, the SLD of the crystalline and interlamellar amorphous layers, ρlam
, were considered free during the fitting procedure, while that of the bulk region ρbulk
was considered that of the amorphous sPS (Table 1
). Finally, the volume fraction of the lamellar stacks in Equation (1) was considered fixed and taken from the assumed crystalline degree of the material (35%).
All three experimental curves in Figure 6
b were modeled simultaneously. Since the crystalline lamellae are not changing during hydration, the ρlam
free parameter was considered the same for all curves, while the other free parameters were left to vary specifically to each RH condition. The model lines in Figure 6
b describe rather well the experimental data, and the fitting procedure delivered the main parameters reported in Table 2
. As we already noted, the sulfonation of the amorphous regions in the sPS film induced a swelling of the interlamellar domains in comparison with the non-sulfonated films, as reported in [28
]. Therefore, the slightly larger value for the thickness of the interlamellar layer, Lb
, and resulting interlamellar spacing, LD
, was obtained in our case. This quantitative analysis indicates a certain swelling of the interlamellar regions with increasing hydration, which was deduced from the slight increase in the thickness of the interlamellar layer Lb
. However, we should note that the model interpretation of the current data also indicates an increase in the smearing σD
of the fitted interlamellar correlation distance between the oriented lamellae LD
= d + Lb
, which makes the actual swelling of the amorphous interlamellar layer difficult to assess.
To obtain semi-quantitative information about the volume fraction of water accumulated in the interlamellar amorphous region, the fitted SLD was further interpreted based on the assumptions made on the polymer and water volume fractions in these regions (Section 2.3
). Thus, at a low hydration level, the water fraction in the interlamellar space is rather similar to that in the whole amorphous regions of the film sample. With increasing RH, the water domains grow in size and number, apparently (Table 2
). From the evaluated values for (ϕwater
, we can conclude that the formation and growth of the water domains with increasing hydration seem to happen almost only in the amorphous bulk region, while the water volume fraction in the interlamellar amorphous layers remains quite constant. This may also explain the aspect of the ionomer peak (Figure 7
), due to ionic clusters that remain dry still at high RH values. In addition, keeping in mind that the hydrated regions are characterized by a large polydispersity in size, we can assume that smaller water domains are present in the interlamellar regions compared to the bulk regions. These effects may be caused by the increased flexibility of the sPS chains in the bulk amorphous domains compared to that of the amorphous sPS chains between the crystalline lamellae, which favors the formation and growth of water domains mostly in the bulk amorphous region. For very high hydration levels, RH > 85%, a growth and percolation of water domains takes place in the bulk region, which ultimately leads to changes in the orientation and position of lamellar stacks, as reported before [25
]. The preservation of the lamellar stacks arrangements even at a very high hydration level (saturation) is indicative of the lower water uptake in the interlamellar amorphous regions as in the bulk amorphous ones.
Finally, the fitting procedure delivered the value ρlam
= 6.012 × 1010
for the SLD of the crystalline lamellae, a value which is lower than that of crystalline sPS (Table 1
). If we consider that the sPS lamellae are loaded with a protonated toluene guest, from the interpretation of the fitted value, we obtain a volume fraction of about 8.2% protonated toluene hosted between the sPS helices in the crystalline region, which is a value that is in very good agreement with what is reported in the literature [30
3.4. SANS on Hydrated Films—Neutron Contrast Variation
The equatorial and meridional scattering patterns from of the s-sPS film with a low degree of sulfonation (S = 19.3%) and lower crystallinity (22%) loaded with C60 fullerenes are presented in Figure 8
. They were collected at a constant hydration level, RH = 80%, which was achieved using different H2
O mixtures. Three neutron contrast conditions corresponding to the H2
O ratios (vol%) of 100/0, 68/32, and 0/100 were investigated. The middle ratio corresponds to the matching SLD calculated for the sulfonic acid terminal group (SO3
For the 100/0 H2
O case, the same scattering features as in the case of the sample with a high degree of sulfonation (Figure 6
) can be observed: the 010 crystalline peak that is revealed only in the equator direction, the isotropic ionomer peak that is visible in both the equatorial and meridian scattering patterns, and the interlamellar peak that is observed only in the meridian direction, at a lower Q value than the ionomer peak. The profile of the interlamellar correlation peak is not as strong as in the case of the sample with a higher sulfonation degree (Figure 6
), which may be due to the lower crystallinity in the present sample. Unlike for the high sulfonation degree sample, in the present case, the scattering from the water domains (equatorial sectors) does not show a shoulder-like feature at around Q = 0.05 Å−1
. Instead, a strong upturn appears toward the low Q region. A similar feature was observed in the very low Q region of the scattering patterns from highly sulfonated films [28
]. The absence of the shoulder-like feature indicates that there is no correlation effect between the water domains. This may be due to the lower sulfonation degree in the present sample, which makes the water domains form and grow in the amorphous regions well separated from each other. On the other hand, the upturn at low Q, which appears stronger on the equator direction due to the stretching of a sample on the vertical axis, arises from the large-scale fractal-like character of the membranes. This feature is not visible toward low Q values in the patterns reported in Figure 6
. This may be a consequence of the stronger correlation effects between the lamellae in the stack in that case: the strong structure factor peak induces an intensity drop toward low Q, and consequently, the intensity upturn is becoming observable at lower Q values. The intensity upturn at low Q values can be described by a power law [28
], which should be added to the model equations that are used for fitting the experimental data, but is less important for the data interpretation in this work. The 70/30 H2
O data show basically the same scattering features that are shown by the 100/0 H2
O patterns, only the global intensity is lower, due to the lower contrast achieved between the hydrated and non-hydrated components of the film morphology. No matching of any scattering feature is visible. The data measured under the 0/100 H2
O contrast show a different behavior from the other two contrast conditions. The first striking effect is the vanishing of the ionomer peak. We assume that the matching of the scattering properties of ionic clusters and surrounding water is achieved, which renders the correlation between the ionic clusters no longer visible. From this observation, a very important conclusion may be drawn: the ionic clusters that are promoting the water uptake by the membrane consist of an association of larger sections of neighboring s-sPS chains in the region of the benzene ring and the sulfonic acid terminal group, which are correlated over the distance 2π/Qion
. With increasing hydration, the water domain grows, and the correlation distance between these groups increases. The correlation effects are vanishing in the scattering patterns when the hydration medium has a similar SLD to that of the sulfonated sPS segment, which is roughly the D2
Another peculiarity of the scattering data in this contrast condition is the low Q behavior, where a Q−1
power law behavior of the scattered intensity may be roughly identified in the equatorial profile, rather than the spherical form factor profile combined with a low-Q steeper power law feature as for the other contrast conditions, or the case of the highly sulfonated sample [28
]. The Q−1
power law behavior is indicative of the one-dimensional structures present in the sample. If we consider that the water accumulates along groups of elongated s-sPS chains in the amorphous region, this will highlight the hydrated regions as one-dimensional arrangements in contrast to the surrounding crystalline or non-sulfonated sPS environment, which is in agreement with the observed scattering behavior.
The interpretation of the experimental data was done in a similar way as for the sPS film with a higher sulfonation degree (Figure 6
). The equatorial data were described by the combination of a spherical form factor of the water clusters (Equation (2)) and a Gaussian feature of the ionomer peak. An additional Q−3
power-law term was added to describe the low-Q data behavior. The meridian data were fitted by a superposition of the scattering features from the water clusters and the correlated lamellar stacks (Equations (4)–(6)). The modeling of the experimental data was quite successful, and has delivered the parameters reported in Table 2
. For the description of the equatorial data, only a spherical form factor was considered, as no tracks of correlation between the water clusters were observed. The experimental data were separately fitted on the equatorial sectors first, to obtain the water domains parameters, and then on the meridian direction, simultaneously for all contrast conditions. The fitting procedure was carried out as discussed in Section 3.3
. The Lb
parameter was fitted, but kept the same for all contrast condition, since they were measured at the same RH. The low-Q power law behavior was considered only for the equatorial data interpretation, where it is more prominent due to the uniaxial sample deformation in the vertical direction.
The volume fraction that is occupied by water in the whole sample is roughly the same for all contrast conditions, about 18%, which is to be expected since all measurements were carried out at the same RH.
From the fitted SLD of the interlamellar layers, semi-quantitative information about the volume fraction occupied by water in these regions could be obtained. Thus, the water occupies between 5% and 7%, as delivered by the fit of the 100/0 and 70/30 contrast conditions. The fitted results for the 0/100 contrast condition could not be further interpreted in a reliable way. A value with no physical meaning was obtained; therefore, we believe that in this case, a more specific model should be used for the interpretation of the experimental data. Nevertheless, all the values obtained for the lamellar stacks in the other two contrast conditions are consistent with each other. Therefore, the model interpretation of this data is considered realistic. Finally, the value ρlam
= 6.003 × 1010
for the SLD of the crystalline lamellae delivered a volume fraction of about 8.5% protonated toluene hosted between the sPS helices in the crystalline region, which again is a value that is in very good agreement with what is reported in the literature [30