Article pubs.acs.org/EF
Role of Asphaltenes and Additives on the Viscosity and Microscopic Structure of Heavy Crude Oils Lilian Padula,† Lia Beraldo da Silveira Balestrin,† Nelson de Oliveira Rocha,‡ Carlos Henrique Monteiro de Carvalho,‡ Harry Westfahl, Jr.,§ Mateus Borba Cardoso,§ Edvaldo Sabadini,† and Watson Loh*,† †
Institute of Chemistry, University of Campinas (UNICAMP), Campinas, São Paulo 13084-970, Brazil Leopoldo Américo Miguez de Mello Research and Development Center (CENPES), Petrobras, Rio de Janeiro, Rio de Janeiro 21941-915, Brazil § Brazilian Synchrotron Light Laboratory (LNLS), Campinas, São Paulo 13083-100, Brazil ‡
S Supporting Information *
ABSTRACT: An attempt to understand the microscopic origin of the high viscosity of Brazilian heavy crude oils was made combining macroscopic (rheological measurements) and microscopic [small-angle X-ray scattering (SAXS) measurements] techniques. A clear relationship between the asphaltene content and viscosity was found, while the removal of asphaltene via flocculation led to a large viscosity drop, confirming them as the origin of high viscosity. The SAXS analyses of crude oils confirmed the presence of asphaltene aggregates as fractal-like particles of colloidal dimensions. Afterward, a systematic investigation was performed on the effects of a series of additives and physical treatments on the crude oil viscosity. Physical methods did not cause any significant viscosity drop as well as more than 80 additives tested. SAXS measurements on oil samples containing toluene and heptane indicated little effect on the asphaltene nanoaggregates within the dimensions probed by SAXS, confirming a general mode of action based on aggregate dilution instead of disruption.
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On the basis of the findings mentioned above, there is growing interest in assessment of procedures capable of affecting (ideally reducing) the viscosity of heavy oils. In principle, perturbations of the asphaltene aggregate structure may result in variations on the viscosity of heavy oils. Some reports describe the possible effect of some substances on the asphaltene structure with such a purpose. For example, Argilier et al. verified that, except for solvents with large hydrogenbonding Hansen parameter, the solvents having polar functional groups enhance the efficiency of heavy oil dilution.6 Additives containing phosphorus were also studied as a result of their bitumen flow modifier characteristics.7 For example, polyphosphoric acid (PPA), as speculated by Masson and Gagné, affects the flow characteristics by raising molecular stiffness through N−N bridging.8 Additives, such as dodecylbenzenesulfonic acid (DBSA), which are known to stabilize asphaltene molecules in solutions of aliphatic solvents, proposedly through an acid−base interaction,9 were also investigated. Wang et al. noticed a limit concentration of DBSA, below which the asphaltenes start to aggregate because DBSA acts as a good dispersant. However, they also reported that the DBSA dispersant capability depends upon the properties of the asphaltene oil source.10 Chang and Fogler11 also observed that p-nonylphenol amphiphiles could disperse
INTRODUCTION
Heavy oils are characteristic for displaying densities close to that of water and an elevated viscosity (above 0.1 Pa s), which limits their exploration by conventional means. Despite their abundance and relevance, the physical properties of heavy oils are not yet fully understood and differ even when samples with different American Petroleum Institute (API) gravity values are compared.1,2 Their high viscosity is normally related to their elevated asphaltene content. Asphaltenes, which are defined as the oil fraction soluble in aromatic solvents and insoluble in saturated hydrocarbon solvents,3 have been the subject of extensive investigation for their key role in various other properties than viscosity, with most of them related to their capacity to self-assemble in some solvent systems (and perhaps in crude oils too), as well as for their surface-active properties that arise from their aromatic/aliphatic dual character and give raise to their strong tendency to adsorb at interfaces. Many studies have confirmed the relationship between the viscosity of crude oils and their asphaltene content. For some authors, there is a threshold asphaltene concentration, typically around 10%, above which the oil viscosity increases more intensely.4 In some cases, an increase in the elastic rheological character of these oils or a greater sensitivity to the temperature was reported to occur above this limit.5 According to these studies, this threshold could be thought of as similar to the critical concentration, C*, observed in polymer solutions as the limit between their dilute and semi-dilute regimes, above which particle−particle interactions control their rheological behavior.5 © 2016 American Chemical Society
Special Issue: 16th International Conference on Petroleum Phase Behavior and Fouling Received: September 16, 2015 Revised: December 22, 2015 Published: January 11, 2016 3644
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Table 1. Properties of the Five Oils Studied the API Gravity, the SARA Contents Determined by the SARA Method, the Water Content in the Oil, and the Asphaltenes C5I and C7I That Represent the Asphaltene Fraction Insoluble in n-Pentane and the Asphaltene Fraction Insoluble in n-Heptane, Respectively oil
OF1
OF2
API gravity (deg) saturates (wt %) aromatics (wt %) resins (wt %) asphaltenes (wt %) water content (wt %) viscosity (mPa s) (measured temperature, °C) asphaltenes C5I (wt %) asphaltenes C7I (wt %)
11.0 39.5 27.5 21.9 11.1 30.0 3 × 105 (40) 18.8 12.0
12.3 37.7 34.7 23.3 4.3 12.0 7 × 104 (25) 11.5 6.5
OF4
OF5
18.3 43.4 24.6 30.4 1.6
23.0 68.8 13.4 17.8 90 nm (setting Rg2 > 90 nm does not affect the level 2 fitting profile of our data). On the other hand, the maltene-C5 curves (red circles in panels A and B of Figure 2) cannot be described using the same two-level unified fit model. This drastic change in the scattering profile is likely due to the asphaltene extraction process. However, a smaller fraction of soluble asphaltene (or structurally related molecules) still remains in the maltene 3646
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Table 2. Values for Rg1 and P1 for the First Level of Aggregation, Obtained Using the Unified Equation for OF1 and OF2 Oils with Different Concentrations of Toluene and n-Heptanea n-heptane
toluene concentration (wt %) OF1
OF2
a
0 1 3 10 0 1 3 10
Rg1 (nm)
P1 (nm)
± ± ± ± ± ± ± ±
2.7 2.8 2.2 2.2 1.5 1.8 1.7 1.9
2.7 2.5 3.2 3.1 4.6 4.0 4.2 3.5
0.2 0.2 0.3 0.5 0.2 0.3 0.3 0.2
Rg1 (nm)
P1 (nm)
± ± ± ± ± ± ± ±
2.7 2.9 2.2 3.2 1.5 2.2 2.0 1.8
2.7 2.4 3.3 2.4 4.6 3.2 3.4 4.0
0.2 0.2 0.3 0.2 0.2 0.2 0.3 0.2
The error indicates the deviation from the fitting model.
the model based on our results, aggregates consist of fractal mass structures (given by the exponent P1) with gyration radius Rg1 that arrange in a large structure with gyration radius Rg2 bigger than 90 nm, as shown in the scheme of Figure 2C. In addition, SAXS experiments were carried out in the presence of different solvents. First, we used toluene or heptane in different concentrations (between 1 and 10%) to investigate the relationship between the solvent quality and the aggregate structure (SAXS curves are presented in the Supporting Information). Table 2 also shows the obtained structural parameters for OF1 and OF2 aggregates as the concentration of toluene and heptane is increased. Although it is possible to observe a significant heavy crude oil viscosity variation when concentrations of toluene or heptane are above 5%, as will be discussed later, no substantial structural aggregate changes are observed from SAXS results for both oils upon dilution with these two solvents. Thus, viscosity changes cannot be directly correlated to the structure of these aggregates. Also, SAXS results cannot differentiate the oil behavior in the presence of good (toluene) or bad (heptane) solvents, as might be expected if their addition produced aggregate flocculation or redissolution/redispersion. It clearly indicates that these additives are not able to change the basic aggregate objects because only subtle changes are seen. In parallel, the structure of heavy crude oils in the presence of commonly used aggregation inhibitors [DBSA or nonylphenol (NP)] was also studied. Table 3 shows the obtained structural parameters derived from SAXS curves for OF1 and OF2 aggregates as the concentration of DBSA and NP is changed (SAXS curves are shown in the Supporting Information). Similar to what was previously discussed, the parameters for oil OF1 display only very subtle changes in the presence of these two inhibitors. On the other hand, there seems to be a slight but general Rg1 reduction trend for the size of particles in oil OF2 as the inhibitor concentration increases. Recent studies have shown that the average molar mass of asphaltene is 750 g mol−1, which can form oligomers mainly by π−π interactions.30 However, beyond this stage of aggregation, the understanding of asphaltene self-assembly is not well established. Dependent upon the nature of the interactions between the particles that form the aggregates and the continuum medium, sharp variations on the energy applied should result in partial disruption of the aggregates. To investigate this hypothesis, the effects of two different physical perturbation methods were investigated. In Figure 3,
Figure 2. SAXS curves obtained for (A) OF1 and (B) OF2 (black circles) and their respective maltenes-C5 (red circles) at 25 °C. Unified levels are presented as different color lines: the blue line corresponds to the fitting of the first level of organization; the green line is the same but for the second level; and the orange line represents the fitting when both levels are taken together. (C) Schematic representation of the hierarchical structure proposed for asphaltene aggregates. The error bars are smaller than the symbols used for the data points.
samples, leading to an asymmetric background scattering in the high-q range of the SAXS. Also, the power-law decay in the lowq region of the SAXS curve still indicates the presence of objects larger than 90 nm (lower intensity). We suggest that this scattering structure has the same origin as the structure observed in the heavy crude oil samples. Therefore, the data confirm that a significant part of the scattering objects was removed (insoluble asphaltene fraction) through the extraction process with n-pentane. The results presented above agree with the modified Yen aggregation model proposed by Mullins et al.12,14 and with earlier reports using small-angle scattering techniques with crude oil or asphaltene solutions that produced particle dimensions in this size range, as will be discussed later. In 3647
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Energy & Fuels Table 3. Values for Rg1 and P1 for the First Level of Aggregation, Obtained Using the Unified Equation for OF1 and OF2 Oils with Different Concentrations of DBSA and NPa DBSA concentration (wt %) OF1
OF2
a
0 0.06 1 2.5 0 0.06 1 2.5
NP
Rg1 (nm)
P1 (nm)
± ± ± ± ± ± ± ±
2.7 2.2 2.4 2.8 1.5 1.4 2.4 2.1
2.7 3.2 2.9 2.6 4.6 5.6 3.0 2.6
0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2
display with the asphaltene molecules, resulting in partial disruption of their aggregates. Considering economic aspects related to the eventual use of such additives to improve heavy oil pumping, concentrations of 10 000 ppm were used, as an upper limit for real application. On average, viscosity drops around 27 and 16% for oils OF1 and OF2, respectively, after the addition of 10 000 ppm of these 80 additives (the values are indicated in Table I of the Supporting Information). As for their rheology, the shear thinning behavior remains. We can highlight the viscosity changes observed for some additive classes, for example, when ethoxylated NP, an asphaltene precipitation inhibitor, and DBSA, a good asphaltene dispersant, are added. Two concentrations (300 and 10 000 ppm) of these additives were tested, and it was observed that DBSA promoted a viscosity increase with both concentrations, while the opposite trend is observed for NP. In principle, for DBSA, an oil viscosity drop was expected because this additive interacts with asphaltenes through an acid−base reaction9 and, according to Wang et al.,10 DBSA promotes a decrease of the asphaltene aggregate size when dispersed in nheptane. Another interesting additive studied is polyphosphoric acid (PPA), which is usually used as a flow modifier in bitumen.7,31 The idea of using this additive is to promote a reaction of PPA with sites of the aggregates, causing hysterical hindrance that could obstruct the linkage to other asphaltene molecules and, thus, blocking the eventual aggregation process responsible for the high viscosity. Indeed, an increase in viscosity is observed when 10 000 ppm of PPA was used (around 400 and 300% for OF1 and OF2, respectively). This is interpreted as associated with a reticulation process of PPA and asphaltene molecules or aggregates.8 Considering the apparent non-specificity of the additives to promote viscosity changes at this level of 10 000 ppm, the investigation was extended to a wider concentration range for two solvents: toluene (a good solvent for asphaltene) and heptane (a bad solvent for asphaltene). The variations of the viscosity of OF1 with these two solvents are shown in Figure 4. As observed, the viscosity only drops significantly when the amount of toluene or heptane is above 5%.
Rg1 (nm)
P1 (nm)
± ± ± ± ± ± ± ±
2.7 2.2 1.9 2.0 1.5 2.0 2.7 2.0
2.7 3.3 3.9 3.6 4.6 3.4 2.8 3.3
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3
The error indicates the deviation from the fitting model.
Figure 3. OF2 flow curves at 25 °C before and after the physical treatments: ultrasound and thermal quenching (see the text for details). The error bars are smaller than the symbols used for the data points (experiments were performed as triplicates).
the flow curves for the sample OF2 are presented after being submitted to ultrasound or thermal quenching. As observed, both processes fail, promoting the decrease of the sample viscosity. In the case of ultrasound, there is a slight increase in heavy oil viscosity, which can be attributed to light fraction losses upon heating. Even in the case of the thermal quenching experiments, in which the temperature was changed by 280 °C in a few seconds, only small variation of the viscosity was observed. Overall, these samples display a shear thinning behavior, which is also not changed with the different treatments. Despite these drastic sample perturbations, only a negligible effect was induced on the aggregates by physical methods. We moved then to analyze the effect of eventual disruptions by adding different classes of substances (good and bad solvents, surfactants, polymers, etc.) to oils OF1 and OF2. These varied additives were chosen based on some of their intrinsic characteristics, for instance, acid−base properties and amphiphilic nature (a complete list of the additives used can be seen in Table I of the Supporting Information). In some cases, additives that promote reactions with chemical groups of the asphaltenes were also used. The main idea of using such additives is based on possible specific interactions that they may
Figure 4. OF1 viscosity reduction with toluene and n-heptane addition. The values of the viscosities were obtained at 25 °C and at a shear rate of 10 s−1. The error bars are smaller than the symbols used for the data points (experiments were performed as triplicates). 3648
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This finding does not mean that heavy oil viscosity cannot be affected by some additives. Indeed, it is possible to reduce oil viscosity, as shown in Figure 4, by adding solvents at a few percent volume fraction. For practical purposes, this strategy reduces their viscosity to values that allow for their transportation but at a significant cost considering the volume of diluent needed. Tests with a wide range of compounds did not reveal any specificity that could correlate their chemical properties to the observed viscosity reductions. It seems striking, however, that good (toluene) and bad (heptane) asphaltene solvents produce the same overall effect. It should be stressed that the amount of added heptane is well below the amount required for asphaltene flocculation; therefore, no significant formation of larger particles is expected. However, despite their different interactions with asphaltenes, added toluene or heptane, at this volume fraction, does not affect their nanoaggregates, as previously discussed in SAXS results. Another alternative for larger viscosity decreases, of course, would be the removal of asphaltenes, supported by the drastic viscosity drop shown in the Supporting Information, although this is not a process that seems feasible at industrial scale. In general, the present findings agree well with previous results and interpretation put forward by the group of Argilier et al.33 based on systematic studies on vacuum residues and their toluene solutions. That group has also performed studies within a wide temperature range, revealing that, at higher temperatures, viscosity is reduced but the colloidal structures are little affected, consistent with the picture presented here that assumes that these nanoaggregates are separated but not disrupted, much similar to the results that we observed upon oil dilution. With the present results, we can extend their proposal to a more comprehensive picture, in which perturbations caused by physical changes (temperature variation, high-energy mixing, or ultrasound) or by chemical means (addition of good or bad solvents or inhibitors) do not disturb their structure at the nanometric scale and, when viscosity reductions are observed, additives act by separating the jammed asphaltene aggregates.
DISCUSSION The present results have clearly indicated the predominant role of asphaltenes in the high viscosity displayed by heavy oils based on the direct relationship evidenced between the asphaltene content and oil viscosity. It should be stressed that these results were obtained with different oils, also including mixtures of heavy oils and their maltenes. The latter finding broadens the reach of these results because it also supports that, regardless of the asphaltene structure observed in these oils, it is maintained upon their dilution with their maltenes. This relationship has already been proposed by Argilier et al.,27 with the only difference that their results were interpreted as indicating the presence of a critical asphaltene concentration, similar to a critical concentration for polymer solutions, above which their solution behavior resembled that of semi-dilute polymer solutions. When our results are plotted in a semi-log scale (Figure 1), our interpretation is that they point toward an exponential relationship between viscosity and asphaltene content that holds within the whole concentration interval investigated. The other clear evidence of the present results is that, in the crude heavy oils investigated, asphaltenes assemble to form colloidal structures conforming to fractal or hierarchical aggregation, as indicated by fit modeling the obtained SAXS curves. There seems to be a consensus in the literature that these aggregates exist, and there are many previous SAXS or SANS studies supporting this model, whose results are not too different from the present results.16−19 There are, however, only few reports of direct investigation using crude oils,16 which is one relevant aspect of the present report. It is not straightforward to directly relate the dimensions of these aggregates in crude oils to results obtained with the different model solvents used in earlier studies. Nevertheless, overall, one can observe that all previously published models and experimental results assume colloidal objects in the size range of a few nanometers, agreeing with the present results. Fogler et al. reported SANS studies on asphaltene solutions in different solvents, identifying asphaltene clusters that conform to fractal aggregates with sizes within 2−9 nm.17 They also studied crude oil samples and, in this case, reported objects with dimensions of a few nanometers that increase in size as the flocculant (heptane) is added or as time evolves.16 Barré and co-workers studied asphaltene aggregates in dilute toluene solutions by SAXS and SANS, observing disk-like aggregates around 3 nm (radius) and 7 nm (height).18 Sirota also reports SAXS and SANS studies on asphaltene solutions, interpreting the scattering results as arising from colloidal aggregates generated by concentration fluctuations that display a fractal morphology and solid-like nature (being below their Tg).19 Another interesting finding from the SAXS studies is that, in the range of the studied concentration, these nanoaggregates do not seem to be affected by the addition of either good or bad solvents (toluene and heptane) or of common additives that display inhibitory or dispersion capacity toward asphatene deposits, such as DBSA and NP. In addition, oil viscosity remains constant throughout the whole range of concentrations and additives listed as the Supporting Information. This observation deviates from common strategies for the design of asphaltene deposition inhibitors that target specific asphaltene−asphaltene interactions, such as π−π stacking, hydrogen bonding, or acid−base interactions, that are thought to be responsible for the formation of the nanoaggregates.32
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CONCLUSION The results presented and discussed here confirm the key role of asphaltene aggregates as an origin of the high viscosity displayed by heavy crude oils. SAXS results reveal that asphaltenes in crude oils appear as fractal aggregates formed by basic particles with dimensions of a few nanometers. These are then assembled into larger aggregates whose dimensions could not be determined with the present experimental setup. There were slight differences in sizes of these particles for the two Brazilian heavy oils investigated, but most interestingly, their dimensions in real systems were not affected by either good or bad solvents and only slightly by asphaltene dispersants. In combination of the macroscopic (rheological) and microscopic (SAXS) results presented here, we observe that additives reduce oil viscosity by a dilution effect rather than direct interference with the asphaltene aggregates, as characterized by specific interactions. In a more general perspective, the present results suggest that strategies to influence asphaltene aggregation should be more focused on their colloidal behavior rather than their molecular interactions, a trend that still needs to be confirmed for the various phenomena involving asphaltene in crude oils. In this context, emphasis on specific interactions, such as hydrogen bonding or π−π stacking, may not be as relevant as on 3649
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(10) Wang, J.; Li, C.; Zhang, L.; Que, G.; Li, Z. The Properties of Asphaltenes and Their Interaction with Amphiphiles. Energy Fuels 2009, 23, 3625−3631. (11) Chang, C.-L.; Fogler, H. S. Stabilization of Asphaltenes in Aliphatic Solvents Using Alkylbenzene-Derived Amphiphiles. 2. Study of the Asphaltene-Amphiphile Interactions and Structures Using Fourier Transform Infrared Spectroscopy and Small-Angle X-ray Scattering Techniques. Langmuir 1994, 10, 1758−1766. (12) Loh, W.; Mohamed, R. S.; Santos, R. G. Crude Oil Asphaltenes: Colloidal Aspects. In Encyclopedia of Surface and Colloid Science, 2nd ed.; Somasundaran, P., Ed.; CRC Press (Taylor & Francis Group): Boca Raton, FL, 2007; Vol. 1, pp 1−18, DOI: 10.1081/E-ESCS120012618. (13) Mohamed, R. S.; Ramos, A. C. S.; Loh, W. Aggregation behavior of two asphaltenic fractions in aromatic solvents. Energy Fuels 1999, 13, 323−327. (14) Andreatta, G.; Bostrom, N.; Mullins, O. C. High-Q ultrasonic determination of the critical nanoaggregate concentration of asphaltenes and the critical micelle concentration of standard surfactants. Langmuir 2005, 21, 2728−2736. (15) Goual, L.; Sedghi, M.; Wang, X.; Zhu, Z. Asphaltene Aggregation and Impact of Alkylphenols. Langmuir 2014, 30, 5394− 5403. (16) Hoepfner, M. P.; Vilas Bôas Fávero, C.; Haji-Akbari, N.; Fogler, H. S. The Fractal Aggregation of Asphaltenes. Langmuir 2013, 29, 8799−8808. (17) Hoepfner, M. P.; Fogler, H. S. Multiscale Scattering Investigations of Asphaltene Cluster Breakup, Nanoaggregate Dissociation, and Molecular Ordering. Langmuir 2013, 29, 15423− 15432. (18) Eyssautier, J.; Levitz, P.; Espinat, D.; Jestin, J.; Gummel, J.; Grillo, I.; Barré, L. Insight into Asphaltene Nanoaggregate Structure Inferred by Small Angle Neutron and X-ray Scattering. J. Phys. Chem. B 2011, 115, 6827−6837. (19) Sirota, E. B. Physical Structure of Asphaltenes. Energy Fuels 2005, 19, 1290−1296. (20) Institute of Petroleum. IP 143/84, Asphaltene Precipitation with Normal Heptane. Standard Methods for Analysis and Testing of Petroleum and Related Products; Institute of Petroleum: London, U.K., 1988; Vol. 1. (21) Santos, R. G.; Bonet, J. E.; Silva, J. A. Processo de desidrataçaõ de compostos orgânicos e produtos compreendendo composto orgânico desidratado (Dehydration of organic compounds and products comprising dehydrated organic compound). BR PI0804392-2, Oct 13, 2008. (22) ASTM International. ASTM D4124, Standard test methods for separation of asphalt into four fractions. Annual Book of ASTM Standards; ASTM International: West Conshohocken, PA, 2001. (23) Ilavsky, J.; Jemian, P. R. Irena: tool suite for modeling and analysis of small-angle scattering. J. Appl. Crystallogr. 2009, 42, 347− 353. (24) Nelson, A. Co-refinement of multiple-contrast neutron/X-ray reflectivity data using MOTOFIT. J. Appl. Crystallogr. 2006, 39, 273− 276. (25) Beaucage, G. Approximations Leading to a Unified Exponential/ Power-Law Approach to Small-Angle Scattering. J. Appl. Crystallogr. 1995, 28, 717−728. (26) Kline, S. R. Reduction and analysis of SANS and USANS data using IGOR Pro. J. Appl. Crystallogr. 2006, 39, 895−900. (27) Argillier, J.-F.; Coustet, C.; Henaut, I. Heavy Oil Rheology as a Function of Asphaltene and Resin Content and Temperature. Proceedings of the SPE International Thermal Operations and Heavy Oil Symposium and International Horizontal Well Technology Conference; Calgary, Alberta, Canada, Nov 4−7, 2002; SPE 79496, DOI: 10.2118/ 79496-MS. (28) Maqbool, T.; Balgoa, A. T.; Fogler, H. S. Revisiting Asphaltene Precipitation from Crude Oils: A Case of Neglected Kinetic Effects. Energy Fuels 2009, 23, 3681−3686.
properties such as colloidal stability and coagulation kinetics, especially for the design of asphaltene inhibitors or dispersants for crude oils.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.5b02103. Flow curves for different oil samples (Figure 1), SAXS curves for oil samples containing different amounts of organic solvents (toluene or n-heptane; Figures 2 and 3) and additives (NP and DBSA; Figure 4 and 5), and a list of additives tested to change the oil viscosity as well as the resulting viscosity values (Table I) (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge the support of Petrobras to this project in its beginning. Lilian Padula, Lia Beraldo da Silveira Balestrin, Watson Loh, Mateus Borba Cardoso and Edvaldo Sabadini thank the Brazilian agency CNPq for a Ph.D. scholarship and senior research productivity grants. The authors also thank LNLS for access to the SAXS beamlines and for the competent support of their technical staff.
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REFERENCES
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