Electron Spin Resonance of Slowly Rotating Vanadyls–Effective Tool

Nov 28, 2016 - The approach for quantitative estimation of asphaltene sizes in crude oils in situ via precise simulation of electron spin resonance (E...
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Electron Spin Resonance of Slowly Rotating Vanadyls−Effective Tool to Quantify the Sizes of Asphaltenes in Situ Sergey N. Trukhan,† Sergei G. Kazarian,‡ and Oleg N. Martyanov*,† †

Boreskov Institute of Catalysis, Academician Lavrentiev Avenue 5, Novosibirsk 630090, Russia Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

‡

ABSTRACT: The approach for quantitative estimation of asphaltene sizes in crude oils in situ via precise simulation of electron spin resonance (ESR) spectra of the slowly rotating VO2+-containing fragments was developed. The method is based on the correlation between the size of the paramagnetic particles and their characteristic rotational time that can be determined by ESR in situ while incomplete averaging of anisotropic hyperfine interactions is observed. The precise simulation of the ESR spectra of heavy molecules, labeled naturally with vanadyl ions, allows one to find their size distribution in crude oils. In particular, the method is demonstrated to be an effective tool for the quantitative determination of the asphaltene sizes in different oil fractions in situ.

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INTRODUCTION One of the most intractable problems in recovering and refining of heavy oils and their components is the formation of deposits inside the equipment used for transportation and processing, which leads to inefficient heat transfer and loss of energy and raw materials during the process.1,2 It became clear that the essential step for the creation of effective technologies for production and processing of heavy oils is understanding and monitoring of the key factors that determine aggregate stability of the oil disperse systems and behavior and chemical transformations of their main components in different external conditions, including elevated temperature and pressure.3,4 It is generally accepted that asphaltenes play a key role in fouling processes.5 Asphaltenes have a tendency to selfassociate and form aggregates that can flocculate and precipitate under certain operating conditions. At the same time, it should be conceded that the key factors that determine the aggregative stability of asphaltenes in various heavy crude oils are still the subject of intensive discussions. Despite the number of advanced techniques and novel methods that have been developed and applied for studying the asphaltene structure and properties at both molecular and aggregate levels, including two-step laser mass spectrometry,6 atomic force microscopy,7 and magnetic circular dichroism,8,9 which is a predictive approach that reveals the mechanisms of asphaltene aggregation in heavy crude oils, they still require further development.3,10 The behavior of asphaltenes in crude oils largely depends on their local environment and intermolecular interactions with distinct chemical constituents, where numbers can easily reach over 100,000 in real crude oils.2,11 Therefore, asphaltene dynamics in crude oils cannot be described using any model system comprising few components and extracted asphaltenes. The relationship between the heavy oil composition and its stability may be established only using an in situ regime.12 Complementary in situ methods with different spatial and temporal resolution are needed to elucidate and separate the key factors that are crucial for the stability of asphaltenes in crude oils.13−15 © 2016 American Chemical Society

Among advanced techniques that have been used to study the structure, size, and properties of asphaltenes in situ the most popular methods are small-angle X-ray (SAXS) and neutron scattering (SANS),16−19 nuclear magnetic resonance imaging,20,21 and Fourier transform infrared (FTIR) spectroscopy.22,23 Occasionally, dynamic light scattering,24 timeresolved fluorescence depolarization,25 and atomic force microscopy (AFM)7 are used to determine some characteristics of the size distribution function of aggregates in oils. Each method has its limitations. For example, along with the great advantage of FTIR spectroscopy for providing chemical analysis of oil composition, it requires relative infrared transparency of the samples for measurements in transmission and the use of a very short path length that is challenging for achieving with heavy oil species. In the case of SAXS and SANS, the scattering function I(θ) depending on the size and shape of the scattering particles can be used for an unambiguous determination of the asphaltene sizes only if they have similar shape and are localized in sufficiently diluted solutions.26 Thus, small-angle scattering techniques can guarantee the estimation of the asphaltene parameters (gyration radius, fractal dimension, etc.) only based on a preassumed model. Kazarian and co-workers have applied, for the first time, attenuated total-reflection Fourier transform infrared (ATR FTIR) spectroscopy for chemical imaging of the deposit formation in heavy crude oils under different conditions in situ.27,28 Application of ATR FTIR spectroscopy realized in chemical imaging mode allowed the precipitates to be monitored and chemically analyzed. ATR FTIR imaging probes a thin layer (from a few to several micrometers) of the sample in contact with the measuring surface of the ATR crystal.13 To look into the bulk and investigate behavior and phase stability of the oil, nuclear magnetic resonance imaging (MRI) can be successfully used.29,30 It is a noninvasive and nondestructive Received: October 5, 2016 Revised: November 21, 2016 Published: November 28, 2016 387

DOI: 10.1021/acs.energyfuels.6b02572 Energy Fuels 2017, 31, 387−394

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Energy & Fuels

quantitative data about dynamics of vanadyl complexes in the real solutions. This is probably due to rather complicated numerical procedures and results in the same concerns, especially for more complex systems like oils containing a mixture of various molecules with different sizes enclosing the vanadyl ions. In previous years, scientists have made some attempts to use ESR spectra of slowly rotating vanadyl fragments to evaluate the behavior of asphaltenes on a qualitative level. Usually, analysis of the spectra has been limited to determination of the relative peak-to-peak intensity of the nonoverlapping components related to the anisotropic and isotropic spectra46−49 or to the estimation of spectral resolution of certain spectrum components.39 The temperature dependence of the spectrum components ratio was used even for the estimation of the association energy of vanadyl complexes with asphaltenes.46−48 Unfortunately, the proposed approach does not take into account changes in the width and shape of the resonance lines occurring in the intermediate regime of slow rotation that can be caused by different reasons, including changes in the local viscosity and gradual aggregation processes of asphaltenes. These reasons in fact did not allow the ESR technique to become an effective and quantitative tool for monitoring the size distribution of asphaltenes and their behavior in situ. Here, we report for the first time an approach for quantitative estimation of asphaltene sizes in situ via precise simulation of ESR spectra of oils, which are the sum of the individual spectra of slowly rotating VO2+-containing fragments having different sizes and rotation speeds. It is demonstrated that ESR of slowly rotating vanadyl fragments is an effective tool for quantifying the size distribution of asphaltenes when partial averaging of the anisotropic hyperfine interaction is observed and the rigidlimit anisotropic spectrum is gradually transformed into an eight component isotropic one. The internal consistency of the method developed is proven experimentally using analysis of the ESR spectra of complementary components (soluble and insoluble in n-heptane) isolated from the heavy oil sample.

method that does not require optical and IR transparency of the samples. Unfortunately, despite high sensitivity of MRI to the small alteration of the system parameters (density, phase concentration, diffusion, viscosity, environment of the protons, etc.), it can provide spatial resolution usually up to a few tenths of a micrometer only.13,31 For the asphaltene aggregation mechanism to be determined, it is necessary to look for the local environment and intermolecular interactions of asphaltene molecules that are occurring on a molecular scale. It is well-known that electron spin resonance (ESR) spectroscopy is a powerful tool for the investigation of the dynamics of the local environment of paramagnetic species in various media,32 including systems at elevated temperature and pressure,33 and is recognized as a complementary method for monitoring oil behavior.12,34 An analysis of the resonance absorption line shape and the averaging of hyperfine or spin− orbital anisotropic interactions are usually used to obtain information about the interactions between the radicals35 and local concentration phenomena including those observed in sub- and supercritical fluids.36,37 Recently, it was shown that the ESR technique can be effectively used to study the behavior of the asphaltenes and their aggregates at elevated temperatures in case they contain an unpaired electron of vanadyl ion incorporated in the asphaltenes.38,39 Within a certain temperature range, the sufficiently slow rotation of the asphaltenes can lead to gradual averaging of the anisotropic interactions of the vanadyl unpaired electron with the vanadium nuclear spin that can be registered as the transformation of the anisotropic hyperfine structure of V4+ ESR spectrum to the isotropic one. Analysis of the resonance spectra of vanadyl-containing asphaltenes observed at elevated temperature allows us in principle to separate the contributions of asphaltene molecules of different sizes that move with different characteristic rotational times.38 Thus, the VO2+ fragment in asphaltenes can serve as a natural spin probe to monitor in situ their dynamics in crude oils on the molecular scale as well as the size evolution of asphaltenes caused by the aggregation (disaggregation) processes and local environment changes at elevated temperatures and pressure. So far, vanadyl ions have been used as a spin probe to estimate the sizes of small molecules mostly via analysis of isotopic ESR spectra possessing incomplete averaging when the relative intensity of eight hyperfine components of the spectrum can be calculated according to the Kivelson’s formula:40 I(mI) = a + bmI + cmI2, where mI is the projection of the 51V nucleus spin moment to the external magnetic field, and a, b, and c are the coefficients proportional to the correlation times.41,42 The potential possibility of using electron spin resonance of slowly rotating vanadyl ions for similar purposes was shown quite a long time ago.43,44 The slow rotation means that V4+ ESR spectrum has an intermediate shape between the isotropic and anisotropic spectra. In this case, the spectrum cannot simply be described by either isotropic or anisotropic g-factor and hyperfine interaction (HFI) of an unpaired electron with the 51V nucleus spin moment of 7/2.41 This regime is realized at an intermediate rotational correlation time τc: 10−10 s ≲ τc ≲ 10−8 s. In this case, one can register the transition of well-known anisotropic vanadyl spectrum observed at τc ≫10−8 s45 to the eight component almost isotropic one observed for τc smaller than ∼10−10 s. Despite understanding of the phenomenon occurring, precise simulation of the ESR spectra in the intermediate regime of slow motion unfortunately was not realized to obtain

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EXPERIMENTAL SECTION

Experiments were performed with heavy oil having an API gravity of 16.4 and composition listed in Table 1. 5,10,15,20-Tetraphenyl-

Table 1. Composition and Physical Properties of the Heavy Oil property

value

saturates (wt %) aromatics (wt %) resins (wt %) asphaltenes (wt %) API gravity (deg) kinematic viscosity at 20 °C (mm2/s) density at 20 °C (g/cm3)

21.0 37.2 35.1 6.7 16.4 3868 0.957

21H,23H-porphine vanadium(IV) oxide (VOTPP) was purchased from Aldrich and used without further purification. All solvents used were reagent grade or higher. The initial crude oil was divided into two fractions (soluble and insoluble in n-heptane) according to the following procedure. The oil was mixed with n-heptane at an oil/heptane ratio equal to 1:10 with permanent stirring that resulted in the precipitation of the asphaltenes. For the process of deposit accumulation to be accelerated, the oil/ heptane mixture was centrifuged for 15 min at 2000g. The forced precipitation allowed us to easily separate the solid residue from the 388

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Energy & Fuels liquid part of the sample; afterward, the fractions were dried at room temperature to remove the n-heptane used for the separation. The final amount of the dry precipitate was 17% of the initial oil mass and was inevitably comprised of asphaltenes along with some accompanying compounds like resins. The procedure described is similar to ASTM method D6560-00 for the asphaltene extraction from the oil.50 The smaller 10-fold excess of heptane allowed us to divide the most and least stable asphaltenes,13 which have different characteristic sizes, as will be demonstrated below. It was checked that vanadyl ions registered in the precipitate are mostly incorporated into the asphaltenes. Samples for the high-temperature ESR experiments were prepared in the following way. The initial crude oil and soluble or insoluble in nheptane fractions were dissolved in toluene at a volume ratio of 1:20 (marked below as samples IO, S, and R, respectively) were introduced into the quartz capillary at room temperature. The ESR spectra were recorded with a Bruker X-band EleXsys 500 spectrometer equipped with ER 4105DR double rectangular cavity and digital temperature control system ER 4131VT. A double resonance cavity was used for quantitative measurements and precise determination of the ESR spectrum parameters using Mn2+/MgO as reference sample51,52 with spin Hamiltonian parameters g = 2.0011 ± 0.0001 and A = 243.5 ± 0.1 MHz. Field calibration was performed with help of the ER 036TM Teslameter. The viscosities of the samples at different temperatures were measured by Stabinger viscosimeter SVM 3000 (Anton Paar GmbH, Austria) following ASTM method D7042.53

Figure 1. Experimental ESR spectra (shown in black) of 5 × 10−4 M vanadyl porphyrin complex 5,10,15,20-tetraphenyl-21H,23H-porphine vanadium(IV) oxide (VOTPP) solution in toluene registered at different temperatures (shown near the spectra for convenience). The spectral components were multiplied by T to compensate for the Curie−Weiss effect. The spectra calculated for different correlation time τc are shown in red. The rotational correlation time τc′ determined for the VOTPP complex dissolved in toluene independently using the Stokes−Einstein−Debye equation is shown on the left for each temperature. The microwave frequency is ν = 9.538 GHz. Six approximately equidistant narrow lines appearing in the spectra are the lines of the reference Mn2+/MgO used in the ESR experiment.

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RESULTS AND DISCUSSION The essential step for the successful development of the method for quantitative analysis of the asphaltene sizes in situ based on ESR spectra is precise simulation of the V4+ spectrum (regarding the width, shape, and intensity of all resonance lines) of a model system: an individual VO2+ complex at intermediate values of τc. It is necessary to check the physical model and numerical procedure for the spectrum simulation within the temperature range when it is gradually transformed from the anisotropic to isotropic state. Figure 1 shows the ESR spectrum of 5 × 10−4 M vanadyl porphyrin complex 5,10,15,20-tetraphenyl-21H,23H-porphine vanadium(IV) oxide (VOTPP) solution in toluene registered at different temperatures. The shape of the spectrum varies significantly depending on the speed of rotation of VOTPP molecule. At T = 150 K, well-known anisotropic ESR spectrum of V4+ is observed that is the sum of anisotropic spectra for various values of mI.54 This spectrum can be considered as a limited case of immobilized paramagnetic molecules whose characteristic rotation frequency ν = 1/(2πτc) is much smaller than the difference of hyperfine interaction constants AHFI: ν ≪ ΔAHFI, that is τc ≫ 1/(2π(A∥ − A⊥)) ≈ 5 × 10−10 s. In this case, we can register the anisotropy of the g and the HFI tensor and identify all their components. At T = 365 K, the eight-component isotropic spectrum (Figure 1) is registered that is the manifestation of the effective averaging of the anisotropic interactions because of the sufficiently fast rotation of the paramagnetic molecules. The residual asymmetry of the hyperfine structure of VO2+ and different width and peak-to-peak intensities of the eight HFI lines are attributed to the incomplete averaging of the anisotropic interactions at this temperature.40 In the intermediate temperature range from 150 to 365 K, the gradual transition from anisotropic to isotropic spectra is realized that corresponds to the so-called slow rotation regime with characteristic correlation time τc being in the range of ∼10−10 to 10−8 seconds. The precise calculation of the

resonance spectrum shape in this case is a rather complex problem. The Redfield theory used for the spectrum simulation of the fast rotating molecules cannot be applied for the slowly rotating vanadyl molecules. In the latter case, we face a dynamics problem that can be solved using the stochastic Liouville equation.55 The computational procedure for the ESR spectrum calculation in this temperature range was developed using public software package EasySpin56 that appeared to be a comprehensive and adequate software package to handle this task satisfactorily. Figure 1 shows the result of the simulation of the ESR spectra over the whole temperature range when gradual averaging of the anisotropic interactions is observed. The g and HFI tensors parameters were identified using rigid-limit spectrum registered at 150 K: g⊥ = 1.9845, g∥ = 1.9615, A⊥ = 167 MHz, and A∥ = 479 MHz, which agree well with previously published data.57 The best agreement between the experimental and simulated spectra at 150 K is achieved when a single line has Gaussian form and line width ΔHfwhm = 32 MHz. These parameters were used for calculating the spectra at all other temperatures. The only fitting parameter was the correlation time τc. The criterion for the best fitting was the minimal value of the standard deviation of the simulated spectrum from the experimental one. One can see that the experimental spectrum at certain temperature can be described by the calculated one with particular correlation time that is seen by eye as an almost perfect repeating of the entire spectrum shape (Figure 1). 389

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Energy & Fuels The correlation time at given temperature T for the VOTPP complex dissolved in toluene can be determined independently using the Stokes−Einstein−Debye equation τc′ = (πD3 /6)η(T )/(kBT )

The characteristic sizes of asphaltenes in the different solutions and especially their size distribution function are still a point of discussion.61 Some data indicate the log-normal distribution of asphaltenes deposited in n-heptane,62 whereas other authors follow the Schultz distribution function for asphaltenes in toluene-containing solutions.60,63,64 To prove the consistency of the model and reliability of the quantitative data extracted from the analysis, we applied a numerical simulation for the ESR spectra of complementary heavy oil components that are soluble or insoluble in nheptane, samples S and R, respectively. Figure 2a (black lines)

(1)

where η(T) is the dynamic viscosity of the toluene, and D is the characteristic size of the rotating VOTPP complex. For D = 1.1 nm, which is the typical size of the VOTPP complex in a plane parallel to the porphyrin ring, the τc′ value calculated according to eq 1 is virtually identical to the parameter τc identified from the numerical simulation of the experimental spectra at the same temperature within the range 190−365 K (Figure 1). At lower temperature, a difference between τc and τc′ values is observed. The difference between the τc and τc′ values at T < 200 can be caused by the increase of the effective VOTPP molecule size near and below the melting point of toluene (T = 178 K) due to the aggregate formation of VOTPP and toluene molecules.59 This phenomenon naturally leads to slowing of the molecular rotation according to eq 1. Thus, verification of the approach using a model solution of the individual vanadyl complex in toluene demonstrated the possibility of the ESR technique to precisely define the effective correlation time τc originating from the molecular rotation at certain temperatures. The spectrum simulation demonstrates high sensitivity to the small alteration of the effective molecule size or to the local viscosity of its environment within the temperature range where the slow rotation regime is observed. The τc value allows us to calculate the effective size of the rotating molecule at certain temperatures in the solution with a known viscosity or to determine the local viscosity of the environment of the paramagnetic molecule with specific size. The encouraging results obtained for the model system enable us move forward and adapt the numerical procedure for the determination of the particle sizes in more complex multicomponent systems such as crude oil samples. Before proceeding with the simulation of ESR spectra of oil and its components, it is necessary to make some basic assumptions, which take into account the multicomponent nature of the system. With a certain degree of accuracy, we can make the following statements that will allow us to quantify the sizes of the asphaltenes. 1. V4+ ESR spectra registered in oil are the sum of the spectra of the individual vanadyl-containing molecules (mostly asphaltenes) of different sizes whose spin Hamiltonian parameters and line widths are similar to each other over the whole temperature range discussed. 2. All vanadyl-containing species move in a medium with similar local viscosity. Differences of the diffusion mechanisms for different molecules in principle may slightly change the shape of the spectrum lines at τc ≈ 1 ns. However, it makes an almost insignificant contribution to the line shapes of the resulting vanadyl spectra.44 3. For sufficiently diluted solutions, the changes in the spectrum shape within the slow-motion regime are mainly associated with changes in the effective correlation time due to the temperature dependence of the medium local viscosity. The dissociation of the asphaltene aggregates with increasing toluene solution temperature may slightly shift the size distribution function to smaller sizes.60 It should be taken into account if best fitting of the spectrum is necessary. 4. The integral intensities of the ESR spectra of all individual vanadyl-containing molecules are equal to each other (in the nonsaturated ESR regime) and follow the Curie law (I∼1/T). 58,59

Figure 2. Experimental ESR spectra (shown in black) of the complementary heavy oil components that are soluble or insoluble in n-heptane dissolved in toluene at an oil/toluene ratio of 1:20 registered at different temperatures for samples (a) R and (b) S. The intensities of the ESR spectra shown considering different relative contents of vanadyls in samples S and R as compared to those of sample IO. The simulated spectra are shown in red. The temperatures are shown near the spectra for convenience. The spectra components were multiplied by T to compensate for the Curie−Weiss effect. The central region of the ESR spectra with the intense symmetrical singlet (g = 2.003 ± 0.001) traditionally associated with the carbon π-systems is shaded for convenience. The Schultz size distribution functions that gave us the best fitting of ESR spectra registered at different temperatures for samples (c) R and (d) S.

shows the experimental ESR spectra of samples S and R registered at different temperatures. The intensities of the spectra are normalized to the Curie factor of 1/T(K). The central regions of all ESR spectra, where the intense symmetrical singlet (g = 2.003 ± 0.001) traditionally associated with the absorption of carbon π-systems in asphaltenes is observed, are shaded for convenience. The integral intensity of the ESR spectra of the sample R is 6.3 ± 0.5 times as much as that of sample S registered at the same temperature. Taking into account the mass ratio of soluble and insoluble in n-heptane oil fractions, it means that 390

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the ESR spectrum of samples R and S can be described satisfactorily only using considerably different size distribution functions of the asphaltenes. The mean size of the vanadylcontaining species in sample S is almost one-half of that of sample R. At the same time, the width of the appropriate size distribution in sample S is more than twice as narrow as that of sample R. This result is quite predictable and corroborates the above qualitative considerations of the differences between ESR spectra of samples S and R in the intermediate temperature range. The phenomenon relates to the precipitation of the least stable asphaltenes in the 20-fold excess solution of oil in nheptane.13 One can find that the size distribution function slightly shifts to the smaller size range with increasing temperature. This phenomenon can be explained by the gradual dissociation of less stable asphaltenes that is more pronounced for sample S and leads to the formation of smaller vanadyl-containing molecules. At the same time, larger and more stable asphaltene molecules presented in sample R are subjected to this process to much smaller extent, which is in a good agreement with previously reported data.13,65 At the same time, one can see that the size distribution functions obtained are always limited by Dmin ≈ 1 nm from the smallest size edge. This size corresponds as expected to the smallest possible size of the porphyrin complex identified in oil, namely vanadyl etioporphyrin. Figure 3a (black lines) shows the experimental ESR spectra of the initial heavy oil dissolved in toluene at an oil/toluene ratio of 1:20 (sample IO) registered at different temperatures. To check the self-consistency of the developed method, we simulated the ESR spectra of sample IO using just the sum of the size distribution functions of the asphaltenes in samples S and R deduced from the best fitting of their ESR spectra taking into account different relative content of vanadyls in samples S and R (Figures 3b). It appeared that the calculated spectrm (Figure 3a, shown in red) adequately repeat all features of the experimental ones. The standard deviation of the simulated spectrum from the experimental ones in this case has almost the same value as for the spectra represented in Figure 2a. Of course, such checking of the method is reasonable only for sufficiently diluted systems in case there is no considerable aggregation process of asphaltenes taking place in the system, or it occurs in a similar way for both fractions. Actually, that is why we deal with the diluted fractions of the oil prepared in the manner described above. To be on a safe side, we verified the relevancy of this assumption by the verification of additivity of the experimental ESR spectra of samples S, R, and IO. Figure 4 shows the results of subtraction of the spectrum of the R sample from the appropriate spectrum of the IO sample registered at different η(T)/T values that are approximately equal to the appropriate ratio for the S sample. The intensity of these spectra was normalized to the vanadyl content in the initial oil sample. One can find that the difference spectra of samples IO and R are very similar to the experimental spectra of the S sample despite the fact that, at TS = 230, 260, and 290 K, the latter one has a few times lower peak-to-peak intensities as compared to those of samples IO and R. It proves that the spectrum of the IO sample is indeed the sum of the spectra of samples R and S. The results obtained confirm the consistency between the simulated spectrum and the size distribution function. The shape of the ESR spectra reflects the actual content of vanadylcontaining molecules with a certain size, and precise simulation of registered spectra allows one to obtain reliable data on their

vanadyl-containing species are presented in samples R and S in comparable amounts (56 and 44%, respectively). The ESR spectra for the toluene solution of both fractions at first glance look rather different except for the low temperature region. Visual comparison of the sample spectra at temperatures from 230 to 350 K shows strong differences in the shapes of the resonance lines. At T = 230−260 K, the peak-to-peak intensity of the spectrum lines of sample S decreases faster as compared to sample R despite the fact that, at T = 200 K, the spectra have almost equal integral intensities (Figure 2a and b). The phenomenon observed points to the comparatively narrow size distribution function of asphaltenes presented in sample S. The absence of vanadyl-containing asphaltene species having significantly different sizes results in temperature behavior that is similar to the behavior of the model system (Figure 1). Indeed, the transition from the anisotropic to the isotropic spectrum in the case of narrow size distribution takes place at almost the same temperature for all vanadyl-containing molecules. Hence, one should observe simultaneous broadening of all resonance lines within the narrow temperature range that registered as a strong decrease of peak-to-peak line intensities. This mechanism explains the registration of isotropic spectrum at 320 K for sample S, whereas the presence of larger asphaltenes in sample R makes the anisotropic component noticeable in the spectrum even at this temperature. The simulation of the spectra registered in samples R and S is shown in red in Figure 2a and b. The simulated spectrum is the sum of the spectra with different values of τc(D) taken with relative weights corresponding to the distribution function. Correlation time τc(D) was calculated using Stokes−Einstein− Debye eq 1. The individual spectra are calculated using regular EasySpin “chili()” function used for modeling cw EPR at slow motion regimes with the following parameters: g⊥ = 1.9835, g∥ = 1.9635, A⊥ = 158 MHz, and A∥ = 470 MHz and line form Gaussian ΔHfwhm = 42 MHz, which were determined by fitting the experimental spectrum at T = 150 K when all the molecules are fixed, i.e., τc = ∞. The local dynamic viscosity of each sample at temperatures below 250 K was evaluated from the linear approximation of experimentally measured relative dynamic viscosities η/ηtoluene (Table 2). The fitting parameters Table 2. Relative Dynamic Viscosities of the Samples at Different Temperatures η/ηtoluene temperature sample

250 K

300 K

350 K

IO S R

1.264 1.213 1.329

1.249 1.204 1.310

1.253 1.198 1.308

were the average size and polydispersity of the size distribution function for each sample at the temperature considered. The criterion for the best fitting was the minimum of the standard deviation of the simulated spectrum from the experimental one. The important point here is that we can get the size distribution function using precise simulation of the single spectrum only in the case that vanadyl-containing aggregates are in the slow rotation regime, which is true in our case. Among the different types of distribution functions, the numerical method allowed us to obtain the best fit for samples R and S using the Schultz size distribution function shown in Figure 2c and d. It appeared that the temperature behavior of 391

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Figure 4. ESR spectra of sample S registered at different temperatures (black line). The resulting spectra (blue line) obtained by the subtraction of the spectrum for the R sample from the appropriate spectrum of the IO sample registered at the same η(T)/T value as for the S sample considering different relative content of vanadyls in samples S and R as compared to that of sample IO. All spectra were multiplied by T to compensate for the Curie−Weiss effect. The central region of the ESR spectra with the intense symmetrical singlet (g = 2.003 ± 0.001) traditionally associated with the carbon π-systems is shaded for convenience. Figure 3. (a)Experimental ESR spectra (shown in black) of the initial heavy oil dissolved in toluene at an oil/toluene ratio of 1:20 (sample IO) registered at different temperatures. The simulated spectra are shown in red. The spectral components were multiplied by T to compensate for the Curie−Weiss effect. The temperatures are shown near the spectra for convenience. The central region of the ESR spectra with the intense symmetrical singlet (g = 2.003 ± 0.001) traditionally associated with the carbon π-systems is shaded for convenience. (b) The size distribution functions used for the simulation that is the sum of the size distribution functions of samples R and S is shown for different temperatures.

allows for determining the sizes of rigidly coupled fragments of asphaltene aggregates and may provide slightly small values for their sizes as compared to those of SAXS data and bigger than those obtained from AFM. The approach does provide a fine fit of the concordance between experimental and simulated spectra. However, consideration of the fitting on a deeper level of the accuracy displays the noticeable deviation of the simulated spectrum from the experimental one at least for some peaks of the ESR spectra for the model used. Further progress in more precise simulation of the oil fraction spectra in our opinion should take into account slight distribution of the g and HFI tensor parameters for different asphaltenes and different environments of V4+ ions. Furthermore, the shape of the distribution function taken a priory can be optimized that will actually lead to an increase in the calculation time. Finally, the diffusion processes can differ from the Brownian type that are used within the EasySpin package for the slow motion case. Taking into account all of these peculiarities will allow us to upgrade the method to obtain more detailed quantified data on asphaltene size distribution for different oil fractions at different temperatures and external conditions as well as during the aggregation process.

size distribution function. The reliability of the data obtained from the analysis of ESR spectra is determined by the fact that only a few variable parameters (mean size, distribution width, and local viscosity) should allow one to satisfactorily describe the spectra recorded at different temperatures within the whole temperature range of significant changes of the spectrum shape when it is modified from anisotropic to isotropic form. The size distribution functions corroborate the results obtained previously concerning the sizes of the asphaltenes and their aggregates. Sizes of asphaltene aggregates determined by complex methods lay in the ranges of 2−20,61 2−5,3 and 10−20 nm.18 According to SANS and SAXS data, the asphaltene aggregates in toluene solution are best described by a disk with 6.4 nm total diameter with 30% polydispersity and a height of 1.3 nm.66 Nanofiltration data gives asphaltenes aggregates in oil sizes from less than 5 nm up to 100 nm.34 It was also found by SANS that a 1% solution of asphaltenes in toluene at 298 K has asphaltene particles distributed in the size range of 7−13 nm and a range of 7−11 nm at 373 K.60 Differences in the data can be connected with the different kinds of the oils studied and with differences in the experimental methods used. In particular, the ESR approach

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CONCLUSIONS In conclusion, it was shown using VOTPP solution as a model system that precise simulation of ESR spectra of the slowly rotating vanadyl complexes allows one to quantify a small alteration of the effective molecule size or the local viscosity of its environment within the temperature range where incomplete averaging of anisotropic hyperfine interactions is observed. Precise analysis of the in situ ESR spectra of VO2+containing fragments incorporated into the heavy molecules 392

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Energy & Fuels with different sizes allows one to find the size distribution of the vanadyl-containing asphaltenes at elevated temperatures in oil components that are soluble or insoluble in n-heptane. The reliability of the data obtained from the analysis of ESR spectra is confirmed by the consistency between the simulated spectra and the size distribution of the asphaltenes. It is shown that the correct model allows one to use just a few variable parameters (mean size, distribution width, and local viscosity) for acceptable fit of the spectra recorded at different temperatures within the whole temperature ranges of significant changes of the spectrum shape when modified from anisotropic to isotropic form. The method is demonstrated to be an effective tool for the quantitative determination of the asphaltene size distribution in different oils and their fractions in situ.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Sergey N. Trukhan: 0000-0001-8403-5902 Oleg N. Martyanov: 0000-0001-9999-8680 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Russian Science Foundation (Project No. 15-19-00119). We thank D.D. Uvarkina for viscosity measurements.

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