Island versus Archipelago Architecture for Asphaltenes - American

Article pubs.acs.org/EF

Island versus Archipelago Architecture for Asphaltenes: Polycyclic Aromatic Hydrocarbon Dimer Theoretical Studies Fernando Alvarez-Ramírez and Yosadara Ruiz-Morales* Instituto Mexicano del Petróleo, Programa de Ingeniería Molecular, Eje Central Lázaro Cárdenas Norte 152, Mexico City 07730, Mexico ABSTRACT: To shed some light on the problem of the most likely architecture, island or archipelago, of the polycyclic aromatic hydrocarbon (PAH) core in asphaltenes, molecular orbital (MO) calculations have been carried out considering two PAHs per asphaltene molecule cross-linked (archipelago model) and the same two PAHs aggregated in a parallel fashion and not cross-linked (island model of interacting PAHs). The calculated highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gaps (H−L gaps) are compared to the 0−0 band experimental fluorescence emission data of asphaltenes. The calculations of the H−L gap were performed at the semi-empirical ZINDO approach using density functional theory (DFT) dimer-optimized structures (relaxed structures). This methodology was validated against experimental data and it was proven to have a good predictive power. A total of 48 PAHs with 5−10 fused aromatic rings (5FAR−10FAR) were calculated, as well as all of their possible combinations in dimers formed by large core (5FAR−10FAR)−large core (5FAR− 10FAR) systems (large−large core dimers). In total, 1176 systems in the archipelago architecture, crossed linked with a C5 alkane chain, and 1176 systems in the island-stacked interaction were calculated. Also, island and archipelago models were constructed with the 48 PAHs, interacting in both architectures, with 10 PAHs that contain 1−4 fused aromatic rings in the structure (1FAR−4FAR), thus comprising 960 calculations of large core (5FAR−10FAR)−small core (1FAR−4FAR) dimers (large−small core dimers). Therefore, a total of 3312 systems are calculated in this work. For both cases, large−large and large−small dimer systems, and for both architectures, island and archipelago, statistical analysis of the results was carried out. It is found that the calculated H−L gap of the dimers with the archipelago architecture is similar to the H−L gap of the monomers. For the case of the island dimers (stacked dimers), there is a dependency of the H−L gap upon both the size of the monomers, in terms of the number of fused aromatic rings, and the type of interlayer geometries or stacking arrangement between the monomers composing the island (stacked) dimer. The stacked dimers are more stable in most of the cases than the archipelago dimers. The higher stability in turn produces larger H−L gaps. The remarkably broad variation of the energy gap, of 0.9 eV, between the island and archipelago architectures for the large−large dimers strongly depends upon the dimer size and the stacking arrangement. In the later, the π−π interactions play a role but have a minor influence. The stacked island systems that fall inside the experimental range of asphaltenes are, in general, dimers composed with the same monomer in hexagonal (H) arrangement and 6FAR−10FAR combinations with parallel displacement (PD) arrangement, mainly without fjords or coves in the structure. Of all of the PAH systems that fall inside the experimental range of asphaltenes when interacting with any other PAH, to form a dimer, in either island or archipelago architecture, the 7FAR PAHs are more abundant in agreement with the former literature. When the percentage of all the calculated dimers, large−large and large−small, is compared, in both architectures, and whose H− L gap falls inside the experimental asphaltene fluorescence range, the large−large dimers are more abundant than the large−small dimers. The large−large dimers are more abundant by 20.6% in island architecture, and by 17.9% in archipelago architecture. It is concluded that indeed, if two asphaltene core PAHs are directly bound via a single bond, then optical methods, such as timeresolved fluorescence depolarization (TRFD) studies, would identify this as a single chromophore, thereby blurring the distinction between island versus archipelago. Some decomposition studies might find this single-bonded pair of PAHs as a single entity as well.

1. INTRODUCTION

molecular weights, only one PAH of seven rings can comfortably fall within this constraint, the so-called island architecture. If asphaltene PAHs have fewer than seven fused rings, then more than one ring system can be compatible within the molecular weight constraint. When much larger asphaltene molecular weights were considered correct, molecular structures

Asphaltene science has advanced significantly in recent years. Recent advances in the field of asphaltene science have been codified in the Yen−Mullins model, specifying the dominant asphaltene molecular structure and the hierarchical aggregate structures of asphaltenes in crude oils and in laboratory solvents.1−3 Indeed, some molecular structural issues are difficult to address. After much debate, the asphaltene molecular weight is largely resolved: the centroid of the distribution is 750 Da, with a full width half maximum of 500−1000 Da. The number of polycyclic aromatic hydrocarbons (PAHs) per asphaltene molecule has also been debated. For the known asphaltene © 2013 American Chemical Society

Special Issue: 13th International Conference on Petroleum Phase Behavior and Fouling Received: September 15, 2012 Revised: February 20, 2013 Published: February 21, 2013 1791

dx.doi.org/10.1021/ef301522m | Energy Fuels 2013, 27, 1791−1808

Energy & Fuels

Article

upon the number of fused rings in the PAH in accordance with a quantum particle in a box.28,29 This quantum principle explains the huge red shift in going from colorless benzene to black graphite. In addition, the PAH spectra depend critically upon the geometry of the PAH and its projection into the Clar-type representation, with aromatic sextet carbon versus isolated double-bond carbon.28−33 Carbon X-ray Raman studies have determined that the bulk of asphaltene aromatic carbon is aromatic sextet carbon.34,35 This result has also been obtained with molecular orbital (MO) calculations, which have been compared to the asphaltene optical absorption and electronic emission properties.36−39 In these studies, concentration effects were explored and ruled out much optical contribution from charge transfer.37 Analysis of PAHs with heteroatoms showed small differences in electronic structure from non-heteroatomcontaining PAHs. 38 A quantitative comparison of MO predictions matched asphaltene absorption and emission spectra reasonably well when using an asphaltene PAH distribution with seven fused rings as most probable, with the bulk of the population with 4−10 fused rings, as shown in Figures 1 and 2.38 This is consistent with all direct molecular imaging24,25 and the (infrared) Raman spectroscopy mentioned above.26,27 Moreover, a seven fused ring PAH (7FAR), with requisite alkane

were proposed with many PAHs per asphaltene molecule, the socalled archipelago model. The name has been retained even for proposed molecular structures with only two PAHs. Indeed, if two asphaltene PAHs are directly bound via a single bond, then optical methods, such as time-resolved fluorescence depolarization (TRFD) studies,4−9 might still identify this as a single chromophore, thereby blurring the distinction between island versus archipelago. In addition, some decomposition studies might find this single-bonded pair of PAHs as a single entity as well. Non-destructive optical spectroscopy yields fairly uniform cross-sections, and a large fraction of the oscillator strength is at or near the first allowed electronic transition. This relative uniformity of cross-section is in contrast to destructive separation methods, where cross-sections vary enormously. The first studies to indicate that the island model applies to asphaltenes are the TRFD studies.4−9 These non-destructive studies indicated that small blue-emitting asphaltene chromophores undergo rotational diffusion 10 times faster than large red-emitting chromophores; thus, it was concluded in these studies that the asphaltene chromophores (PAHs) are not crosslinked.4−9 These TRFD molecular diffusion results are consistent with those from fluorescence correlation spectroscopy10,11 and Taylor dispersion.12 Recently, several studies from several groups employing unimolecular decomposition of asphaltenes and model compounds have shown that the island molecular architecture is likely dominant. 13−19 The instability of archipelago compounds is likely why they are not strongly represented in asphaltenes, which are formed in decomposition reactions at elevated temperature and survive geologic time. However, bulk decomposition studies of asphaltenes appear to indicate the presence of smaller ring systems. Some bulk decomposition experiments of asphaltenes have been interpreted as being consistent with the archipelago molecular architecture.20 However, it has recently been established that bulk decomposition of various model compounds results in copious synthesis of archipelago compounds.21 Specifically, pyrolysis of island model compounds yields archipelago compounds for up to half of the sample. Laser-induced acoustic desorption (LIAD) mass spectrometry using electron impact ionization has been reported.22 In this study, archipelago model compounds were shown to undergo large mass loss upon fragmentation, while asphaltenes and island model compounds showed much smaller mass loss. In another study, asphaltene samples with different origins were examined via tandem mass spectrometry. The dissociation behavior of asphaltene molecular ions derived from different samples indicated structural differences but also similarities. The spectra indicated losses of alkyl radicals from the molecular ions, in support of the island-type molecular structure, with chains of varying lengths. However, many ions showed a predominant loss of a neutral molecule C10H7, which, according to the authors, indicates the presence of archipelago-type structures.23 Direct molecular imaging of asphaltenes by scanning tunneling microscopy obtained most likely asphaltene PAHs of six to seven fused aromatic rings (6FAR−7FAR).24 High-resolution electron transmission microscopy obtained similar results at lower resolution.25 Raman spectroscopy obtained similar PAH results.26,27 One of the best methods to interrogate the size of PAHs is to determine their electronic properties and, thus, optical spectra, because asphaltenes are inherently colored. To explore asphaltene PAHs, first, the governing principles of PAH electronic transitions needed to be sorted out in a systematic way.28,29 The electronic spectra depend critically

Figure 1. Comparison of MO calculated (top) and experimental (bottom) ultraviolet (UV)−visible−near-infrared (NIR) spectra of asphaltenes.38 The calculated spectra consisted of the sum of MO calculated electronic spectra from 523 PAHs with seven fused rings (7FAR) as most probable, with the bulk of the population in the range of 4−10 fused rings (4FAR−10FAR). The H−L gap was calculated with the ZINDO methodology at 0 K and with no solvent included. Good agreement is obtained for the spectral shape and overall increase in optical density over a very broad range, supporting the presumed asphaltene PAH distribution.38 1792


Energy & Fuels

Article

Quantitative analysis requires detailed examination of the architecture of the aromatic core, island and archipelago, and this is best accomplished by molecular orbital calculations. The challenge is to perform such an analysis on the large number of PAHs that can potentially contribute. The objective of the present study is to shed some light on the most predominant asphaltene aromatic core architecture, island versus archipelago, using theoretical MO calculations. The fluorescence emissions of the 0−0 band, i.e., the highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gap (H−L gap), for a total of 3264 dimer systems constructed by PAH in both architectures, island and archipelago, have been calculated and compared to the observed asphaltene experimental data to conclude about the most predominant architecture in oil asphaltenes.

2. METHODOLOGY Computational chemistry approaches have revolutionized our understanding of the structure and reactivity of molecules, and computation has become the third apex of the triangle representing how we do science, with experiment and theory representing the other two apexes. Applications of theoretical chemistry have played a role in the understanding of the structure, in terms of the number of fused aromatic rings, of the aromatic region in asphaltenes.28,29,36−39 MO calculations coupled with the ubiquitous optical absorption and emission data for asphaltenes have been used28,29,36−39 to identify the number of fused aromatic rings and their types of ring geometries in asphaltenes by virtue of understanding their electronic structure. In addition, this method naturally gives the stability of the ring systems, thereby enabling one to determine why asphaltenes have certain ring geometries.28,29,36−39 If one considers that asphaltenes are essentially stable for geologic time, then unstable aromatic structures as determined by MO calculations are ruled out. The optical absorption spectra of asphaltenes exhibit an exponential decrease in the neighborhood of 650 nm, showing that large graphitic structures with very low energy electronic absorption do not constitute a significant component of the asphaltene fraction. Likewise, asphaltene fluorescence emission spectra, which exhibit significant intensity in the range of 400−650 nm (1.9065−3.0981 eV),41−43 reflect the nature and type of FAR structures present in asphaltenes. However, these optical absorption and emission data when consider alone have limited use, in particular for the determination of aromatic structures. The utility of this data is greatly expanded when comparing it to the MO calculations of the electronic structure for the many possible candidates, catacondensed and pericondensed PAHs, for asphaltenes. Understanding the implications of different ring geometries and sizes on the stability also provides essential information about governing heuristics for the asphaltene aromatics. The characterization of the stability of the FAR systems in terms of kinetic and thermodynamic stability is primary. The defining terms pericondensed and catacondensed are subordinate to the stability considerations. The Clar model, which states that the most important representation of a PAH is one having the maximum number of disjoint π-sextets, depicted by inscribed circles, and a minimum number of fixed double bonds, captures the essence of the kinetic and thermodynamic stability arguments, enabling a simple heuristic for assessing stability. FARs with more sextet carbon are more aromatic and more kinetically and thermodynamically stable; that is, they gain in stability because of delocalization of π-electrons within the resonant sextets. FARs with increased isolated double-bond carbon are much more reactive and unstable; that is, they are kinetically and thermodynamically less stable. These concepts are extended using a methodology with the simple sobriquet “the Y-rule”.28,29,32,33 The Y-rule establishes the most important and most kinetically and thermodynamically stable representation, in terms of π-sextets and double bonds, for any pericondensed PAH. With regard to reactivity, it is well-known that a PAH is attacked at the position of the double bonds because it requires less energy to break these bonds than to break a π-sextet. Thus, the Clar-

Figure 2. (Top) Simulated fluorescence emission spectrum of asphaltene.38 The calculated spectra consisted of the sum of MO calculated electronic spectra from 523 PAHs with seven fused aromatic rings as most probable, and the bulk of the population with 4−10 fused aromatic rings. The H−L gap was calculated with the ZINDO methodology at 0 K and with no solvent included. (Bottom) Measured emission spectra of several asphaltenes and one condensate are shown. There is a good agreement between the calculated data and the experiment.

carbon and heteroatom content for asphaltenes, matches the most probable molecular weight.29,36,38 In another study,36 the quantitative comparison of asphaltene PAHs and the color that they impart is accomplished by a comparison of ubiquitous asphaltene spectra to predictions from MO calculations. Many (258) candidate PAHs were analyzed by MO calculations. Polydispersity was considered at the outset. Candidate PAHs were considered within the context of molecular stability and measured aromatic sextet carbon versus isolated double-bond carbon. The polydispersity of asphaltene ring systems was considered within optical spectral constraints of PAH population distributions. A consistent picture emerged; most probable asphaltene PAHs have seven fused rings. Also, a comparison of the MO analysis with measured dispersion in the asphaltene diffusion constant supported the “monomer” or “like your hand” description for the bulk of asphaltene molecules. The archipelago model was largely ruled out for the bulk of asphaltenes as being incompatible with the asphaltene color. Also, it was found that heteroatoms do not significantly modify the results.36 This study showed that two fundamental parameters largely control PAH optical properties: (1) the number of fused rings and (2) the ratio of isolated double-bond carbon/sextet carbon, and several fundamental conclusions were drawn regarding asphaltenes. Petroleum asphaltenes consist of PAHs mostly with 6−8 FARs. Asphaltene molecules span a range having appreciable molecular populations with 4−10 fused aromatic rings (4FAR−10FAR). 1793


Energy & Fuels

Article

Figure 3. Structures of the 48 benzenoid PAHs with 5−10 FARs used to construct the island and archipelago large−large dimers. The hydrogen atoms are not shown for clarity of the structures. These 48 PAHs were previously determined as most likely aromatic regions in asphaltenes.28,29 The electronic structure is shown in terms of the most important Clar structure,28,29,31−33 where the π-electronic density is distributed in resonant sextets, inscribed in the circle notation, and in isolated double bonds. The most important Clar structures were determined using the Y-rule.28,29,31−33 type structures found with the Y-rule also give information about where it is most likely that chemical reactivity would take place. These simple methods are tied to stability arguments and shown to yield asphaltene structures found experimentally.28,29,36−38 In particular, in previous works,28,29,36 it has been found that (1) acenes are not allowed as the asphaltene FAR region based on stability, (2) fully resonant PAHs, i.e., PAH systems with only resonant sextets in their structure, are not allowed either based on their high energy transitions, unless unrealistically large ring systems are assumed; that is, the fully resonant systems are colorless or pale yellow, unlike

asphaltenes, (3) almost fully resonant pericondensed structures are stable and compatible to the large volume of optical absorption and emission data of asphaltenes, and (4) mostly FARs with 5−10 fused aromatic rings and 2−4 π-sextets satisfy the requisite of stability, satisfy the requisite of optical absorption and emission transitions, and satisfy the FAR size constraints imposed by direct molecular imaging and measurement of the rotational diffusion constants. Finally, 56 PAHs29 were identified, out of thousands of possible isomers, with 5−10 fused aromatic rings that fulfill all of the experimental asphaltene constraints 1794


Energy & Fuels

Article

Figure 4. Structures of the 10 small benzenoid PAHs with 1FAR−4FAR used to construct the island and archipelago small−large dimers composed by one of these small PAHs and one of the large PAHs, shown in Figure 3. The hydrogen atoms are not shown for clarity of the structures. The electronic structure is shown in terms of the most important Clar structure.28,29,31−33 and that are most likely structural candidates of the FAR region in asphaltenes. In ref 38, the results of MO calculations on 523 selected PAHs were used to create an ensemble of possible asphaltene molecular structures. A simple distribution of these PAHs as a model distribution for asphaltene PAHs had seven fused aromatic rings as the most probable, with a symmetric distribution falling off to 3 and 11 fused aromatic rings, respectively. Also, a large fused ring “tail” of up to 15 fused aromatic rings was included. This PAH distribution coupled with the individual PAH absorption spectra were used to create a weighted optical absorption profile for the model asphaltene. In addition, this PAH distribution is coupled with the individual HOMO−LUMO transition energies and the energy gap law to derive a predicted fluorescence emission spectrum. Despite of the fact that all of the calculations were carried out at 0 K and with no solvent, there is good agreement between the experimental data and the calculations, as shown in Figures 1 and 2. Analysis of PAHs with heteroatoms showed small differences in the electronic structure from non-heteroatom-containing PAHs. In the present theoretical work, we have only concentrated in studying dimers in island and archipelago architectures constructed with neutral even-numbered PAHs with fused six-member rings, that is, benzenoid-type PAHs. A total of 48 PAHs, chosen from the 56 set published in ref 29 and mentioned above, with 5−10 fused aromatic rings (5FAR−10FAR), were calculated, and they are presented in Figure 3. All of their possible combinations considering two PAHs per asphaltene aromatic core, which are cross-linked with a C5 alkane chain to simulate the archipelago model, and the same two PAHs aggregated in a parallel fashion and not cross-linked, to simulate the island model of interacting PAHs, were calculated. In total, 1176 systems in archipelago structure and 1176 systems in island stacked interaction were calculated with aromatic cores that contain 5−10 FARs for a total of 2304 calculations. The theoretical estimates are derived from a single “frozen” molecule in the gas phase at 0 K without corrections for thermal motions and solvent effects. No heteroatoms have been included in the structures for simplicity of the calculations. Experimentally, it is known that the replacement of carbon in PAH compounds with heteroatoms typically results in a red shift (higher wavelength) of the fluorescence maximum, if there is any spectral effect.40 Because of the fact that bulk decomposition studies of asphaltenes appeared to indicate the presence of smaller ring systems (see the Introduction), we have also considered the study of the same 48 PAHs with 5FAR−10FAR bonded to smaller PAH cores, which contain

1FAR−4FAR (mostly catacondensed systems). A total of 10 small PAHs are considered and presented in Figure 4. Individually, these small cores do not fulfill all of the asphaltene size, structural, and optical data; however, here, they are being considered to assess their effect on the H− L gap when bonded to a larger PAH. There are in total 480 calculations in archipelago architecture and 480 calculations in island stacked interaction involving the 5FAR−10FAR cores interacting with the 1FAR−4FAR cores for a total of 960 calculations. In previous studies,28,29 the validation of the best combination of theoretical methods (optimization method/excited-state calculation method and optimization method/single-point calculation method) that agree better with the experimental fluorescence emission data of monomer PAHs was carried out. To find the best method for the geometry optimization of the structures, three different methods were tested: (1) using COMPASS FF-based minimization, (2) using the semi-empirical PM3 method, and (3) using density functional theory (DFT) and the B3LYP functional. The excited electronic states (including the frontier orbital π−π* transition) were calculated also using different methods: (1) the semi-empirical electronic structure method ZINDO/S, (2) the semi-empirical PM3 method, (3) a singlepoint calculation at the Hartree−Fock (HF) self-consistent field level, (4) a single-point calculation with the DFT with the B3LYP functional, and (5) the time-dependent density functional theory (TDDFT) to calculate the transition energy. In general, the method combinations (optimization method//single-point H−L energy calculation method) B3LYP//B3LYP, PM3//B3LYP, PM3//TDDFT, PM3//ZINDO, FF//B3LYP, and FF//ZINDO give a H−L gap that compares well to the experimental data, while the other methods (B3LYP//HF or PM3 and PM3//HF or PM3) give bad results. The optimization of structures using the B3LYP functional is expensive as well as the calculation of transition states with TDDFT. It was concluded that the best agreement between the theory and experiment is observed for the case of the FF/ ZINDO calculations,28,29 which is the cheapest calculation method because ZINDO is a semi-empirical method. However, this methodology has not been validated for dimers. Therefore, in this paper, we carried out the validation of the best method to calculate the H−L gap of dimers with the high level method TDDFT and the semi-empirical method ZINDO, using DFT optimized structures. All of the structures, monomers and dimers, in both, island and archipelago, architectures were geometry-optimized (structure relaxation) using the high quantum level DFT approach with the selfconsistent generalized-gradient GGA and the Perdew−Wang 91 1795


Energy & Fuels

Article

Figure 5. Some structures of the dimer island PAH interacting cores. The numbers make reference to the PAH structures in Figure 3 used for the construction of the systems.

Figure 6. Some structures of the archipelago dimers. The numbers make reference to the PAH structures in Figure 3 used for the construction of the systems. (PW91)44 exchange-correlation potential (DFT GGA−PW91) with a DNP basis set (triple numerical basis set)45,46 with a radial cut off of 3.0 Å, as implemented in the DMol3 code47 and instrumented in the interface of Materials Studio.48 For the case of all monomer PAHs, presented in Figures 3 and 4, the calculation of the H−L gap was carried out at two levels of theory: (1) at the semi-empirical ZINDO/S49 approach, which is a semi-empirical quantum chemistry method calibrated for calculating excited states, as implemented in the Cerius II program,50 and using the DFT optimized structures (previously, this method has been proven to provide a good agreement with experimental values for the calculation of optical properties of PAHs)28,29,38 and (2) at the quantum TDDFT51 approach using the DFT optimized structures. The past decade has seen TDDFT linear response theory become the most widely used electronic structure method for calculating vertical electronic excitation energies.52 For the TDDFT calculations, we have used the DFT GGA−PW91 method44 together with the DNP basis set,45,46 with a radial cut off of 3.0 Å. The adiabatic local density approximated (ALDA) kernel is used in the TDDFT functionality with exchange-correlation terms included as implemented in the DMol3 code47 and instrumented in the interface of Materials Studio.48

For the case of the dimers, in both island and archipelago architectures (see Figures 5 and 6), the calculation of the H−L gap has to be validated. In a first approach, the dimer H−L gap was calculated at the two levels explained above: (1) at the semi-empirical ZINDO/S approach, employing the DFT optimized structures, and (2) at the high quantum level TDDFT approach, using the ALDA kernel with exchange-correlation terms included, together with the optimized DFT structures. The obtained results were compared to the very few experimental data available in the literature, and from this comparison, the best calculation method is determined and used throughout the present work in the case of the dimer systems. The H−L gap in the dimer systems was calculated at their equilibrium interlayer separations.

3. RESULTS AND DISCUSSION In the following text, the notation large−large dimer is used for the PAHs constructed with two PAH cores where each PAH core contains from 5 to 10 fused aromatic rings (5FAR−10FAR). In the case of the island architecture or also called stacked dimers in the text, both PAH cores are interacting face to face, as shown in Figure 5. In the case of the archipelago architecture or also called connected dimers in the text, both PAH cores are crossed link 1796


Energy & Fuels

Article

with a C5 alkane chain, as shown in Figure 6. Also, the abbreviation H−L gap is used to define the HOMO−LUMO gap. 3.1. H−L Gap of Monomer PAHs with 5FAR−10FAR. In Figure 7, the calculated H−L gaps with TDDFT and ZINDO

Figure 8. Calculated H−L energy gap for some of the PAH monomers, presented in Figure 3, and comparison to the available experimental data. All of the structures are optimized DFT. The data shown here are also tabulated in Table 1.

average error for the case of ZINDO is 0.2693 eV. Thus, the difference between methods is 0.0451 eV, which is negligible. The ZINDO method overstimates the H−L gap for the monomers, while the TDDFT method understimates the H−L gap (see Figure 8). The theoretical estimates are derived from a single “frozen” molecule in the gas phase at 0 K without corrections for thermal motions and solvent effects. The difference between the theoretical and experimental data could be due to the Stokes shift, which involves the reconfiguration of the solvent cage for the ground electronic state once the excited molecule of PAH undergoes photoemission.40,59,60 The Stokes shift to red is reported to be around 10−45 nm for solvents with low polarity.59,61 The inclusion of solvent in the calculations would shift the result of the calculated H−L gaps to smaller energies or larger wavelengths by around 0.3 eV (∼40 nm).28 Therefore, many of the systems that fall right above the upper limit of the experimental range of asphaltenes, in the case of the ZINDO calculations, would fall into the experimental range, and a few of the systems would fall out the experimental asphaltene range in the case of the TDDFT calculations. On the other hand, the inclusion of heteroatoms would also red shift the calculated H−L gap. In a previous theoretical study,28 when the calculated H−L gap for the different asphaltene structures was compared to their corresponding PAH cores, it was found that the effect of the presence of the alkyl chains and the heteroatoms in the asphaltene structures on the H−L gap is almost negligible. It is found that the difference in the calculated H−L gap with the different methodologies is a constant. It means that results from one method can be extrapolated to the other method by this constant (see Figure 9). The difference between TDDFT and ZINDO is 0.596 eV on average for the monomer PAHs. 3.2. H−L Gap of PAH Dimers for Systems Large Core (5FAR−10FAR)−Large Core (5FAR−10FAR): Large−Large Dimers. As seen in Figures 5 and 6, some of the dimer DFT optimized structures are not planar. In a previous study,28 it was found that, as the number of fused hexagonal rings in PAHs increases, there is a slight distortion from planarity. From 9FAR on, this distortion is more significant. Also in ref 28, it is presented that the deviation from the planarity is related to the stability of the PAH structure, which is decreased when there are present bays or coves or fjords (Figure 10), following the stability order: bay > cove > fjord, because of steric hindrance between hydrogen atoms in these regions.28 As mentioned in the Methodology for the case of the dimers, in both island and archipelago architectures (see Figures 5 and

Figure 7. Calculated H−L gaps for the 48 PAH systems, presented in Figure 3, using the ZINDO and TDDFT methodologies. The green region represents the experimental fluorescence of asphaltenes. The statistical analysis is shown together with the percentage of molecules that fall inside the experimental range for each theoretical methodology.

methodologies for the 48 PAH monomer systems (Figure 3) are presented. The green region represents the experimental fluorescence range of asphaltenes,41−43 which is reported to be in the range of 400−650 nm or 1.9065−3.0981 eV. As seen in Figure 7, the calculated H−L gap depends upon the calculation methodology. The percentage of molecules that fall inside the asphaltene experimental range for each theoretical methodology is shown. With TDDFT, 93.8% of the 48 PAHs (Figures 3 and 7) fall inside the experimental range of asphaltenes, while with the semi-empirical ZINDO method, 43.7% of the 48 PAHs fall inside the experimental range. The ZINDO methodology has previously been proven to have a good prediction power for the calculation of the H−L gap of PAHs.28,29,38 However, TDDFT excitation energies are generally remarkably accurate, typically within a fraction of an electron volt.53 TDDFT calculations are time- and cost-consuming, computationally speaking, while ZINDO is cheaper and faster. In Figure 8 and Table 1, the validation of the calculation methods is carried out for several of the monomer PAH compounds, with 5−7 fused aromatic rings and one system with 9 fused aromatic rings. The calculated gaps are compared to the reported experimental λ0−0 fluorescence emission band. There is, in general, a good agreement between both theories and the experiment, with deviations of 40 nm on average or less. The average error for the case of TDDFT is 0.2242 eV, and the 1797


Energy & Fuels

Article

Table 1. Validation of the Calculation Methods for PAH Monomer H−L Gapsa system

TDDFT

ZINDO

experimental data

1 2

2.8600 2.5800

3.3342 3.1594

3

2.5600

2.9967

4

2.9200

3.4691

5 7 11

2.5600 2.7700 2.9300

3.1479 3.3687 2.9810

15 2.6500 44 1.9900 average error

3.2018 2.6012

3.0598−3.0225b,c 2.8178d 2.8164e 2.8516d 2.8392f 2.8752g 2.8686e 3.0995g 3.0598−3.0225b,g 3.1058e 2.8293g 2.9576g 2.9090g 3.0131e 3.0237h 2.9505g 2.3294g

average experimental data

difference of TDDFT − experimental data

difference of ZINDO − experimental data

3.0412 2.8171

0.1812 0.2371

0.2930 0.3423

2.8586

0.2986

0.1381

3.0719

0.1519

0.3972

2.8293 2.9576 2.9819

0.2693 0.1876 0.0519

0.3186 0.4111 0.0001

2.9505 2.3294

0.3005 0.3394 0.2242

0.2513 0.2718 0.2693

a See Figure 3 for system numbers. bDependent upon the solvent. cFrom ref 54. dFrom ref 40. eFrom ref 55. fFrom ref 56. gFrom ref 57. hFrom ref 58.

Figure 10. Schematic representation of the structural parameters in PAH compounds.

Table 2. Comparison of Calculation Methods to Available Experimental Dataa difference between experimental data and calculated data island dimer system

Figure 9. Difference in the calculated H−L gaps for the 48 monomer PAHs (see Figure 3) depending upon the calculation method. (a) Difference between the energies calculated with TDDFT and ZINDO. The statistical analysis is shown in panel b. The difference between calculation methods is equal to a constant value of 0.596.

EH−L (eV) TDDFT

1−1 2.1800 2−2 1.8000 3−3 1.7400 4−4 2.3200 average error

6), the results from the calculation of the H−L gap have to be validated by comparing to the experimental data available in the literature, and from this comparison, the best calculation method is determined. There is a lack in the literature of data to validate computational results against the experiment. We were able to find very few experimental data and just enough for the case of the island dimer configuration with the same stacked monomer. In Table 2, the validation of the calculation methods TDDFT versus ZINDO for dimers is presented together with the very few available experimental data.

a b

EH−L (eV) ZINDO

EH−L (eV) experimental

TDDFT − experimental

ZINDO − experimental

3.2000 2.9340 2.6869 3.3726

3.0388b 2.7862c 2.8833c 3.0996c

0.8588 0.9862 1.1433 0.7796 0.9420

0.1612 0.1478 0.1964 0.2730 0.1946

All of the structures (Figure 3) are optimized at the DFT level. From ref 62. cFrom ref 63.

It can be seen in Table 2 that the best agreement between theory and experiment corresponds to the ZINDO method, while the TDDFT method produces, in general, energies underestimated by up to 0.9 eV with respect to the experimental data. In Figure 11, the graphic representation of the information in Table 2 is presented for a direct visual comparison. On average, 1798


Energy & Fuels

Article

first-order correction to the H−L gap energy calculation. As discussed later on, the effect of the π−π interaction on the calculated H−L gaps is almost negligible, at least for the case of dimers. In Figure 12a, the calculated H−L energy gap for the 1176 dimers in island architecture are presented. The green region

Figure 11. Calculated H−L energy gap for some of the stacked dimer structures (interacting islands) for the systems 1−1, 2−2, 3−3, and 4−4 and comparison between calculation methodologies, TDDFT, ZINDO, and available experimental data. All of the structures are optimized with DFT. The data shown here are also tabulated in Table 2.

the error obtained with the TDDFT is 0.9420 eV (up to 200 nm), and for the ZINDO method, it is equal to 0.1946 eV (around less than 30 nm). If solvent were included in the calculations, a red shift of around 0.3 eV (∼30 nm) would be observed (see section 3.1), which would make, in turn, the TDDFT calculated energy gap to worsen, and the ZINDO energy gap would be almost equal to the experiment. Extension of DFT to electronically excited states, namely, TDDFT, stands, as its ground-state counterpart, as the most widely used theoretical approach to compute the transition energies to the electronically excited state as well as to evaluate related properties. However, despite its successes and versatility, TDDFT suffers from, at least, a major practical limitation: the reliability of the results depends significantly upon the selected exchange-correlation (xc) functional. The vast majority of functionals have been developed, parametrized, and optimized for ground-state properties.64,65 Because of this limitation, the results of the calculation of the singlet excited state, that involves the H−L gap in our TDDFT computations, do not agree with the experimental results. Hybrid functionals have emerged as a reliable computational model for predicting excitation energies and oscillator strengths for large molecular systems.52 However, it is not possible for the number of systems and sizes calculated in the present work to use a hybrid functional because the calculations become computationally expensive and take a longer time to finish. Therefore, the methodology used in the present work for the calculation of the H−L energy gap for the dimers, in both architectures, is ZINDO and using the DFT optimized geometries. As seen in Figure 11, this combination DFT/ ZINDO (optimized structure/energy gap calculation) produces a good result. 3.2.1. H−L Gap of Large−Large PAH Dimers in Island Architecture: Island Large−Large Dimers. In Figure 5, some examples of the island large−large PAH dimer structures are shown. These structures are constructed using two interacting PAHs in face to face conformation to emulate the island architecture of the aromatic core in asphaltenes. The PAHs used contain 5−10 fused aromatic rings (5FAR−10FAR), and the island interacting models are constructed with combinations of the 48 PAH systems presented in Figure 5. Therefore, there are a total of 1176 systems obtained from the monomer combinations into dimers. The construction of the island models in this way also involves the introduction of the π−π interaction, which is a

Figure 12. (a) Calculated H−L gaps for a sample of 1176 dimers in island architecture (see Figure 5). (b) Calculated H−L gaps for 1176 dimers in archipelago architecture (see Figure 6). The green region represents the experimental fluorescence of asphaltenes. The statistical analysis is shown together with the percentage of molecules that fall inside the experimental range.

represents the experimental fluorescence range of asphaltenes.41−43 The statistical analysis, also presented in Figure 12a, displays a total of 67.1% of the island architecture population in the asphaltene experimental region, whereas 32.8% falls above the fluorescence experimental asphaltene region. No solvent and no heteroatoms have been included in the calculations for simplicity. As discussed above, the replacement of carbon in PAH compounds with heteroatoms typically results in a red shift of the fluorescence maximum if there is any spectral effect observed,28,40,41 but it is theoretically found to be negligible.28 On the other hand, the Stokes shift, because of the solvent, to red is reported to be around 10−45 nm for solvents with low polarity.59,61 The inclusion of solvent in the calculations would, in principle, shift the result of the calculated H−L gaps to smaller energies or larger wavelengths by around 0.3 eV.25 Therefore, those systems with a H−L gap above the upper borderline of the experimental range of asphaltenes will fall inside the experimental range, thus increasing the percentage in the green region in the statistical analysis. However, to conclude about the effect of the solvent on the H−L gap, it is necessary to carry on a systematic study considering the dielectric constant of the solvent. It is not possible to define, without performing the systematic study, that the shift to red would be the same for all of the dimers. 1799


Energy & Fuels

Article

Figure 13. (a) Color map of PAH compounds conforming the island dimers (stacked model). (b) Color map of PAH compounds conforming the archipelago dimers (connected model). The yellow color represents the systems that fall inside the asphaltene fluorescence experimental range, while the blue color represents the systems that do not fall into the asphaltene experimental range. The color information shown right on the axes represents the monomer H−L energy gaps.

the percentage of population of archipelago dimers in the green region. In Figure 13b, a color map for the calculated H−L gaps for the archipelago dimers is presented in terms of the PAH combinations used to construct the dimers. The yellow color represents the systems that fall inside the experimental range of asphaltenes, while the blue color represents the systems that do not fall inside the experimental range. As it was the case in the island dimers, the dominant factor for an archipelago dimer to fall into the experimental range of asphaltenes is determined by the H−L gap, of the involved monomers, which is shown in Figure 13b on the axes. Again, as it was the case for the island dimers, three cases are observed: (1) when both monomers have a H−L gap that falls inside the experimental range, the H−L gap of the formed dimer also falls into the experimental range; (2) when one of the monomers presents a H−L gap that falls into the experimental range, the dimer also falls into the experimental range; and (3) when none of the monomer H−L gaps falls into the experimental range, the dimer H−L gap also does not fall into the experimental range. 3.2.3. H−L Gaps of Large−Large Island Dimers versus Large−Large Archipelago Dimers. When the color maps presented in Figure 13 for the different architectures, island (stacked) and archipelago (connected), are compared, it is observed that the maps are almost similar, despite the architectures. There are bands of regions of PAH systems that fall inside the experimental range of asphaltenes (yellow color) when interacting with any other PAH; these PAH compounds are as follows (see Figures 3 and 13): 3, 6, 13, 16, 18, 20−23, 30, 35−37, 41−44, and 46−48. The PAHs 3 and 6 are 6FAR; they contain six aromatic fused rings in their monomeric structure and present carbon ratios of 0.8333 and 1.0, respectively. The carbon ratio is the ratio of carbon atoms in isolated double bonds to those in aromatic sextet rings.28,35−38,66 In Figure 3, the aromatic sextet is depicted with the circle notation.28−33 The number and position of resonant sextets in the PAH structures in Figure 3 were determined using the Y-rule (see the Methodology). The systems 13, 16, 18, 20−23, and 30 are 7FAR, with carbon ratios that are mainly 0.4444 and 0.5555. The systems 35−37, 41, and 42 are 8FAR, with carbon ratios between 0.5555 and 0.6666. The

In Figure 13a, a color map for the calculated H−L gap is presented for each PAH combination used to construct the island dimers. The yellow color represents the systems that fall inside the experimental range of asphaltenes, while the blue color represents the systems that do not fall inside the experimental range. As seen in Figure 13a, in general, the dominant factor for an island dimer to fall into the experimental range of asphaltenes is determined by the H−L gap of the involved monomers. If the H−L gaps of both monomers fall inside the experimental asphaltene range, then the island dimer H−L gap also falls into the experimental range and vice versa, i.e., if the H−L gaps of the monomers do not fall into the experimental asphaltene range, then the island dimer H−L gap also does not fall into the experimental range. Finally, if the H−L gap of only one of the monomers, composing the dimer, falls into the experimental range, then the island dimer H−L gap also falls into the experimental range. 3.2.2. H−L Gap of Large−Large PAH Dimers in Archipelago Architecture: Large−Large Archipelago Dimers. In Figure 6, some examples of archipelago large−large dimer structures are shown. These structures are constructed using two interacting PAHs cross-linked with a C5 alkyl chain to simulate the archipelago architecture of the aromatic core in asphaltenes. The PAHs used contain 5−10 fused aromatic rings (see Figure 3). There are a total of 1176 systems obtained from the combinations. The construction of the archipelago models does not involve π−π interactions, as it was the case for the island dimers (see the former section). In Figure 12b, the calculated H−L gaps for the 1176 archipelago dimers are presented. The green region represents the experimental fluorescence range of asphaltenes.41−43 It is found that 65.6% of the 1176 calculated dimer H−L gaps fall inside the experimental range of asphaltenes. No solvent and no heteroatoms have been included in the calculations for simplicity. The inclusion of solvent in the calculations would, in principle, shift the result of the calculated H−L gaps to smaller energies by around 0.3 eV.28 Therefore, the systems with a H−L gap above the upper borderline of the experimental range of asphaltenes would fall inside the asphaltene experimental range, increasing 1800


Energy & Fuels

Article

Figure 14. Difference between the calculated H−L gaps for island architecture dimers (stacked) and archipelago dimers (connected). See the text for a description.

systems that do not fall inside the experimental range of asphaltenes (blue color) for the case of the island architecture (stacked; Figure 13a) than for the case of the archipelago architecture (Figure 13b). The formation of the stacked dimer will cause the reorganization of the electronic density, and the effect is more pronounced as the number of fused aromatic rings increases, as in the case of 10FAR, and as the number of sextets in each PAH monomer increases. However, how important is the π−π interaction effect on the H−L gap in the stacked systems? In panels a and b of Figure 12, the calculated H−L gaps for both architectures are shown. In both architectures, it is observed that the lowest energy of the H−L gap for the dimers starts at around 2.25 eV. Therefore, it seems, in principle, that the π−π effect does not play an important factor in the H−L gap of the stacked dimers; otherwise, both architectures would not have a similar lowest H−L gap energy. The highest energy of the H−L gap for the dimers goes up to, in general, 3.50 eV for the case of connected dimers and as far as 3.90 eV in the case of the stacked dimers. The H−L gaps of the island dimers go to higher energies than the gap of the archipelago dimers (see Figure 12). In Figure 14, the difference in the calculated H−L gaps for both architectures is presented. As seen in Figure 14a, there are many cases where the difference is around zero and many other cases where the difference is not zero. In Figure 14b, a Gauss distribution of the H−L gap difference between both architectures is shown together with the fitting equation and the obtained parameter values. The full width at half maximum (FWHM) of the Gauss distribution is equal to 0.07 eV, and the maximum of the curve is centered at 0.04 eV. Thus, it could be considered that, in general, the difference in the H−L gap between both architectures goes from 0.04 to 0.07 eV, and it could also be considered that this might be the value of the effect of the π−π interactions on the H−L gap of the stacked (island) architecture, which is negligible.

systems 43 and 44 are 9FAR, with a carbon ratio of 0.6666. Finally, the systems 46−48 are 10FAR and present carbon ratios between 0.3333 and 0.4166. Of all of these PAH systems that fall inside the experimental range of asphaltenes when interacting with any other PAH, in either island or archipelago architecture, the 7FAR PAHs are more abundant, and this result is in agreement with reports in the literature.1−3,24−26,35−38 There is a recent Raman paper of asphaltenes that also agrees with 7FAR PAHs as a maximum.67 X-ray Raman spectroscopy (XRRS) has used the 1s−π* transition of a large number of PAHs and asphaltenes, and these studies show that the PAHs of asphaltenes are predominantly sextet carbon.35,66 This observation is in accordance with the stability that asphaltenes have exhibited by surviving for geologic time at elevated temperatures in oil reservoirs. The exact ratio of carbon atoms in isolated double bonds to those in aromatic sextets is a bit difficult to determine from XRRS but is on the order of 1:3 (0.3333) for isolated double-bond carbon/sextet carbon for the bulk asphaltene sample. The 7FAR systems found in here, which fall inside the experimental range of asphaltenes (yellow color in Figure 13), when interacting with any other PAH have a carbon ratio of, in general, 0.4444−0.5555. This carbon ratio is obtained by analyzing the electronic density distribution in monomeric structures and was obtained using the Y-rule (see the Methodology), but it will change in the case of stacked dimers (island architecture) because of the possibility of π−π interactions. When panels a and b of Figure 13 are compared, it is observed that the major differences are mainly in the regions that involve the systems 14−19 interacting with 14−19 (14−19/14−19), which are 7FAR-type systems, where more systems fall inside the region of asphaltenes in the island architecture (yellow color), and the regions 45−48/45−48. The 45 system is 9FAR, and the systems 46−48 are 10FAR. In this last region, there are more 1801


Energy & Fuels

Article

Because of the fact that the π−π electronic clouds are somehow perturbed when the PAH chromophores interact face to face, in the island models, we would expect that the H−L gaps show some changes when comparing architectures. The presence of a molecule on top of another slightly distorts the geometry, which is the same as introducing a defect that, in turn, would diminish the H−L gap because of a lowering in stability of both chromophores. However, as observed in Figure 14b, the energy difference between architectures sometimes goes down and sometimes goes up. The main energy difference between both architectures is observed around 0.04 eV, but there is a distribution in the energy difference between both architectures that goes from 0.3 to −0.6 eV (see region inside the horizontal purple bars in Figure 14a), i.e., a maximum difference of 0.9 eV. This energy difference cannot be attributed to π−π interactions alone. The π−π effect is less pronounced in some systems than in others, but in general, it is not that important. The energy difference distribution between architectures of 0.9 eV is due to the arrangement of the monomers with respect to each other in the stacked dimer. After free optimization of the stacked dimer structure, without any restriction, a minimum is found where the monomers composing the dimers are arranged face to face but in such a way that the stacked dimers are more stable in many cases than the archipelago dimers. The higher stability in turn produces larger H−L gaps.28 If the stability is too high, then the H−L gap of the stacked dimer goes out of the experimental range of asphaltenes. Four types of interlayer geometries or stacking orders are observed in the optimized island dimers (see Figure 15): (a)

of a distance equal to half of the size of one hexagonal ring. In the S structure, one-half of the carbon atoms in one monomer lies directly above the carbon atoms in the other monomer, while the other half lies over the centers of hexagonal rings in the other monomer. We found that, in the case of the island dimers (stacked dimers), there is a dependency of the H−L gap upon both the size of the monomers, in terms of the number of fused aromatic rings, and the type of interlayer geometries or stacking orders presented in Figure 15. It is found that, in general, there is a trend of the energy gap with increasing monomer sizes for the different stacking orders. The energy gaps tend to decrease with an increasing size of the monomers for the case of the more planar hexagonal rings, in agreement with previous work,28,29,36−38 and the energy gap follows the order with respect to the arrangement: S > P > SH > H, in agreement with the literature.68 By close analysis of the calculated H−L gaps and the optimized structures of the dimer, it is found that the energy of PAH dimers depends upon not only their size but also the topological arrangement of the hexagonal rings in the monomers. Different monomer combinations produce different types of dimer interlayer geometries. It is found that dimers with S and PD stacking provide similar energy gaps, with the former being slightly larger, whereas the gaps obtained for dimers with H stacking are smaller by about 0.2−0.3 eV. Then, in the H stacked dimers, the π−π interaction is weaker. It is also found that the change in the H−L gap energy between S and H dimers is smaller than that induced by the change in size. When the H−L gaps of the monomers are analyzed with respect to the H−L gap of the stacked dimers, in general, there is a reduction of the H−L gap because of the fact that the interlayer π−π interaction leads to the degenerate HOMO and LUMO of the monomers splitting into non-degenerated HOMO and LUMO, and the net result of this effect is to close the gap of the HOMO and LUMO in the dimer. The effect is larger for the case of the S dimers than the H dimers, as shown in Figure 16. In Figure 16, the effect on the island dimer H−L gap because of interlayer π−π interactions in H and S type of dimers is shown for the case of a dimer formed with the same monomer, n, (panels a and b of Figure 16, respectively) and for a dimer formed with different monomers, n and m, (with different monomeric H−L gap) and in a different arrangement, H and S (panels c and d of Figure 16, respectively). The π−π interactions in the H arrangement are smaller than in the S arrangement, and as seen in Figure 16, the splitting of the degenerated HOMO and LUMO in the dimer is smaller in the H arrangement than in the case of the S dimer. Our findings agree with reports in the literature on models of graphene.68,69 As seen in Figure 16, dependent upon the combination of the monomer size and type of arrangement, the H−L gap of the formed dimer can have a different value. That is why, in Figure 14, a distribution of difference in the H−L gap is observed between the island and archipelago architectures. The H−L gap of the archipelago architecture is similar to that of the monomers, but in the case of the island structure, it depends upon the size of the monomers and the type of arrangement between them in the dimer. In Table 3, the effect on the H−L gap because of dimer formation is presented. It can be seen that the formation of the stacked system lowers the energy of the gap, except for system 11 (coronene). The H−L gap of the archipelago with a C5 chain is similar to the gap of the monomer. When a stacked system is formed but with a C13 chain bonding the monomers, there is an increase of the energy to a higher energy than the one calculated

Figure 15. Top views of stacking arrangements of monomers with respect to each other in face to face dimers (island architecture or stacked dimers): (a) H, (b) TH, (c) PD, and (d) S.

hexagonal stacking (H), (b) twisted hexagonal stacking (TH), (c) parallel displaced stacking (PD), and (d) staggered stacking (S). In the H structure, the atoms in one PAH occupy positions directly above the atoms of the other PAH. The TH structure corresponds to a hexagonal stacked structure with a rotation angle between the two monomers. The PD structure involves the parallel displacement of one of the monomers in the H structure 1802


Energy & Fuels

Article

Figure 16. Splitting into non-degenerate HOMO and LUMO orbitals involved in the formation of island (stacked) dimers due to interlayer π−π interactions in H- and S-type dimers: (a) dimer formed with the same monomer (n) in the H arrangement, (b) dimer formed with the same monomer (n) in the S arrangement, (c) dimer formed with different monomers (n and m, with different H−L gap) in the H arrangement, and (d) dimer formed with different monomers (n and m) in the S arrangement.

architecture, the percentage of dimers with a H−L gap that fall inside the experimental range of asphaltenes is 67.1% compared to 65.6% for the case of the archipelago systems. The difference is 1.5%, with more abundance of systems in the island architecture. However, if the solvent is included in the calculations, a red shift of about 0.3 eV would be observed and most of the systems would fall inside the experimental range of asphaltenes, despite the architecture. Therefore, for the case of large−large dimers, the optical methods, such as TRFD studies, indeed might not be able to distinguish between island and archipelago dimer systems. 3.3. H−L Gap of PAH Dimers for Systems Small Core (1FAR−4FAR)−Large Core (5FAR−10FAR): Small−Large Dimers. Because of the fact that bulk decomposition studies of asphaltenes appeared to indicate the presence of smaller ring systems (see the Introduction), we have also considered the study of the same 48 PAHs with 5FAR−10FAR (Figure 3) interacting with smaller PAH cores, which contain 1FAR−4FAR (mostly catacondensed systems). A total of 10 small PAHs with 1FAR−4FAR are considered and presented in Figure 4. Individually, these small cores do not fulfill all of the asphaltene size, structural, and optical data;28,38 however, here, they are being considered to assess their effect on the HOMO−LUMO gap when interacting with a larger PAH. Thus, there are in total of 480 calculations in archipelago architecture and 480 calculations in island stacked interaction involving the 5−10 FAR cores and the 1−4 FAR cores for a total of 960 calculations. The systems in both architectures are constructed and optimized in the same way as explained in the Methodology. In Figure 17, the calculated H−L gaps for the small−large dimers in both architectures are presented. In the case of the

Table 3. Effect on the H−L Gap Because of Dimer Formation system

energy gap (eV)

3 monomer 3−3 stacked dimer (islands with no chain) 3−3 edge−edge dimer with a C5 aliphatic chain 3−3 stacked dimer with a C13 aliphatic chain 5 monomer 5−5 stacked dimer (island with no chain) 5−5 edge−edge dimer with a C5 aliphatic chain 5−5 stacked dimer with a C13 aliphatic chain 11 monomer 11−11 stacked dimer (island with no chain) 11−11 edge−edge dimer with a C5 aliphatic chain 11−11 stacked dimer with a C13 aliphatic chain

2.9967 2.6870 2.9330 3.0510 3.1479 3.0040 3.1980 3.0530 2.9810 3.8970 3.1360 3.9820

for the stacked with no chain system. Therefore, as mentioned above, the gap is a function of the structure. Most of the island dimers after optimization have S or PD arrangent, and mostly, the island dimer formed with the same monomer presents a H conformation. The stacked island systems that fall inside the experimental range of asphaltenes are, in general, dimers composed of the same monomer in the H configuration and 6FAR−10FAR combinations with PD conformations. It is also found that, in general, the stacked island systems that do not fall inside the experimental range of asphaltenes have a S structure and 9FAR−10FAR monomer combinations and a H structure with 5FAR combinations. In panels a and b of Figure 12, the percentage of dimers that fall inside the experimental range of asphaltenes for both architectures is shown. In the case of the island (stacked) 1803


Energy & Fuels

Article

Figure 18. (Top) Color map of PAH compounds conforming the island dimers (stacked model) in the small−large dimers. (Bottom) Color map of PAH compounds conforming the archipelago dimers (connected model) in the small−large dimers. The yellow color represents the systems that fall inside the asphaltene fluorescence experimental range, while the blue color represents the systems that do not fall into the asphaltene experimental range. The color information shown right on the axes represents the monomer H−L energy gaps.

In Figure 19, the difference in the H−L gap for the small−large dimers in both architectures is presented. The difference between

Figure 17. Calculated H−L gaps for the small−large dimers in both architectures: island or stacked (top) and archipelago or connected (bottom). The structures are constructed with the 5FAR−10FAR PAHs (see Figure 3) interacting with the 1FAR−4FAR PAHs (see Figure 4). There are a total of 480 systems in each architecture. The green region represents the experimental fluorescence of asphaltenes. The statistical analysis is shown with the percentage of molecules that fall inside the experimental range.

island (stacked) architecture, the percentage of dimers with a H− L gap that falls inside the experimental range of asphaltenes is 46.5% compared to 47.7% for the case of the archipelago (connected) systems. The difference in the percentage of systems that fall inside the experimental range of asphaltenes between both architectures is 1.2%, and there is more abundance of archipelago architecture. However, more than 50% of the calculated H−L gaps for the large−small dimers, in both architectures, falls outside of the range of asphaltenes. When the percentage of all of the calculated systems large− small and large−large is compared, in both architectures, that falls inside the asphaltene experimental range, (see Figures 12 and 17) the large−large systems are more abundant by 20% in island structure and 17.9% in archipelago architecture than the large−small dimers. In Figure 18, color maps for the calculated H−L gaps for the small−large island dimers (stacked; see top of Figure 17) and for the small−large archipelago dimer (connected; see bottom of Figure 17) are presented in terms of the PAH combinations (Figures 3 and 4) used to construct the dimers. The yellow color represents the systems that fall inside the experimental range of asphaltenes, while the blue color represents the systems that do not fall inside the experimental range. As was the case for the large−large dimers, the dominant factor for a dimer to fall into the experimental range of asphaltenes is determined by the H−L gap of the involved monomers, also shown in Figure 17 on the axes. No substantial difference is observed in the color maps between different architectures for the small−large dimers.

Figure 19. Difference between the calculated H−L gaps for island architecture dimers (stacked) and archipelago dimers (connected) for the small−large dimers.

the two architectures is, in most of the cases, equal to zero. There are 8 systems out of the 480 small−large systems with a H−L gap energy difference between architectures of 0.2−0.5 eV. These systems are the dimers formed by tetracene (V; Figure 4) with 8FAR−10FAR systems with a carbon ratio between 0.25 and 0.41. The dimer composed of VI (pyrene) and 34 (8FAR) (Figures 3 and 4) has the highest H−L gap difference between architectures (0.5 eV). Both PAHs (VI and 34) are highly symmetric with carbon ratios between 0.3 and 0.2, respectively. Most of these structures have a S and P arrangement (see Figure 15). 1804


Energy & Fuels

Article

4. CONCLUSION The H−L gap of 3264 PAH dimer systems in island and archipelago architectures were carried out in this work using the semi-empirical ZINDO method and DFT quantum level optimized dimer structures. Large−large dimers with 5FAR− 10FAR PAH cores (Figure 3) and large−small dimers with 5FAR−10FAR interacting with 1FAR−4FAR PAH cores (Figure 4) were calculated in both architectures. Statistical analysis was carried out in each group, large−large and large−small dimers, in both architectures, island and archipelago. The calculated HOMO−LUMO gaps were compared to the experimental 0− 0 band fluorescence emission of asphaltenes to conclude about the most likely architecture of asphaltenes. The DFT/TDDFT and DFT/ZINDO methodologies (optimization of structure/calculation of the H−L gap) produce a H− L gap for the monomer PAHs, calculated in this study, which compares well with the experiment. However, the DFT/TDDFT method underestimates the H−L gaps, while DFT/ZINDO overestimates the gaps. Therefore, the addition of solvent into the calculations would, in principle, produce results that compare better to the experiment when using the ZINDO method. For the case of the dimers, the calculation of the H−L gap has been validated by comparing to the experimental data available in the literature, and it is found that the best agreement between theory and experiment corresponds to the DFT/ZINDO method, while the DFT/TDDFT method gives, in general, energies underestimated by up to 0.9 eV. The average error obtained with TDDFT is 0.9420 eV (up to 200 nm), and for the ZINDO method, it is equal to 0.1946 eV (∼30 nm). If solvent were included in the calculations, a red shift of around 0.3 eV (∼30 nm) would be observed, which in turn would make the TDDFT calculated energy gap to worsen, and the ZINDO energy gap would be almost equal to the experiment. TDDFT suffers from, at least, a major practical limitation: the reliability of the results depends significantly upon the selected xc functional, and the vast majority of functionals have been developed, parametrized, and optimized for ground-state properties. Hybrid functionals would provide a better result than the TDDFT used here; however, the computations would become too expensive and lengthy that it would be unrealistic to try to calculate as many systems as the number calculated in this work. Therefore, the DFT/ZINDO methodology (optimization of the structure/calculation of the H−L gap) has been used to calculate the H−L gap of the dimers in both architectures, island and archipelago. Because of the amount of calculations involved in this work and the computationally difficult optimization of structures at the DFT level, we have studied only dimers. It is concluded that, in general, the dominant factor for an island or archipelago dimer to present a H−L gap that falls into the experimental range of asphaltenes is determined by the H−L gap of the involved monomers. Three cases are observed: (1) when both monomers have a H−L gap that falls inside the experimental range, the H−L gap of the formed dimer also falls into the experimental range; (2) when one of the monomers presents a H−L gap that falls into the experimental range, the dimer also falls into the experimental range; and (3) when none of the monomer H−L gaps falls into the experimental range, the dimer H−L gap also does not fall into the experimental range. It is found that the calculated H−L gap of the dimers with archipelago architecture is similar to the H−L gap of the monomers. This observation is more evident when comparing the H−L gap of dimers formed with the same monomer. We

found that, in the case of the island dimers (stacked dimers), there is a dependency of the H−L gap upon both the size of the monomers, in terms of the number of fused aromatic rings, and the type of interlayer geometries or stacking orders between the monomers composing the island (stacked) dimer. Four types of interlayer geometries were found: H, TH, PD, and S (Figure 15). It is found that, in general, there is a trend of the energy gap with increasing monomer sizes for the different stacking orders. It is concluded that the energy gaps tend to decrease with an increasing size of the monomers for the case of the more planar hexagonal rings, in agreement with previous literature,28,29,36−38 and the energy gap follows the order with respect to the arrangement: S > P > SH > H. By close analysis of the calculated H−L gaps and the optimized structures of the island dimers, it is found that the energy of PAH dimers depend upon not only their size but also the topological arrangement of the hexagonal rings in the monomers. Different monomer combinations produce different types of dimer interlayer geometries. It is found that dimers with S and PD stacking provide similar energy gaps, with the former being slightly larger, whereas the gaps obtained for dimers with H stacking are smaller by about 0.2−0.3 eV. Then, in the H stacked dimers, the π−π interaction is weaker. It is also found that the change in the H−L gap energy between S and H dimers is smaller than that induced by the change in size. When the H−L gaps of the monomers are analyzed with respect to the H−L gap of the island dimers, in general, there is a reduction of the H−L gap because of the fact that the interlayer π−π interaction leads to the degenerate HOMO and LUMO of the monomers splitting into non-degenerated HOMO and LUMO, and the net result of this effect is to close the gap of the HOMO and LUMO in the island dimer. The effect is larger for the case of the S dimers than the H dimers (see Figure 16). Thus, the π−π effect is less pronounced in some systems than in others, but in general, it is not that important. For the case of PAHs as prototypes for graphene multilayers,68 the dependence of the energy gaps upon the number of stacked graphene sheet layers for monomers, dimers, trimers, and tetramers is reported in the literature. As we observe and discuss in this work, the energy gap is reduced when two same monomers interact to form a dimer, in any of the arrangements (S, PD, H, and TH). In ref 68, Feng et al. mentioned that, when a third layer is added to the second layer, the decrease in the energy gap is smaller (0.09 eV) and the energy gap of the tetramer is reduced only by 0.03 eV. This shows that the number of graphene sheets has little effect on the energy gaps of PAH multilayers beyond the bilayer. Here, it is found that the difference in the calculated H−L gap for the dimers between the island and archipelago architectures follows a distribution that is centered in 0.04 eV but that spans a range of up to 0.9 eV. This energy difference distribution between architectures is due to the arrangement of the monomers with respect to each other in the stacked dimer. The stacked dimers are more stable in most of the cases than the archipelago dimers. The higher stability in turn produces larger H−L gaps. The archipelago and island large−large dimers that fall inside the experimental range of asphaltenes contain monomers that have 7FAR, with carbon ratios that are mainly 0.4444 and 0.5555, 8FAR with carbon ratios between 0.5555 and 0.6666, 9FAR with a carbon ratio of 0.6666, and 10FAR with carbon ratios between 0.3333 and 0.4166. Mostly PAHs with no coves or fjords in the PAH monomer structure are preferred. These carbon ratios are calculated for the monomers, and from this work, it cannot be 1805


Energy & Fuels

Article

concluded about the final carbon ratio in the stacked dimers unless a formal systematic study of the π-electronic distribution, in resonant sextets and isolated double bonds, is carried out. However, because the H−L gap of these island dimer systems falls into the experimental asphaltene range, their final carbon ratio should be comparable to the one reported for asphaltenes, around 0.3333. Most of the island dimers after optimization have S or PD arrangement, and the island dimers formed with the same monomer present a H conformation. The stacked island systems that fall inside the experimental range of asphaltenes are, in general, dimers composed of the same monomer in H configuration and mainly without fjords or coves in the structure and 6FAR−10FAR combinations with PD conformation and mainly without fjords or coves in the structure. Of all of these PAH systems that fall inside the experimental range of asphaltenes when interacting with any other PAH, to form a dimer, in either island or archipelago architecture, the 7FAR PAHs are more abundant in agreement with former literature.1−3,24−26,35−38 The difference in the percentage of dimers with a H−L gap that falls inside the experimental range of asphaltenes between the island architecture and the archipelago architecture for the large−large dimers is 1.5%, with more abundance of systems in island architecture. However, if solvent is included in the calculations, a red shift of about 0.3 would be observed and most of the systems would fall inside the experimental range of asphaltenes, despite the architecture. Therefore, for the case of large−large dimers, the optical methods, such as TRFD studies, indeed would not be able to distinguish between island versus archipelago. However, it cannot be claimed that the H−L gap of all of the systems will be red-shifted the same amount of electron volts when solvent is included in the calculation through inclusion of the dielectric constant. The only way to conclude about the effect of the solvent is to carry out a systematic theoretical study. For the case of the large−small dimers, the difference in the percentage of systems that fall inside the experimental range of asphaltenes between both architectures is 1.2% and there is more abundance of archipelago architecture. However, more than 50% of the calculated H−L gaps for the large−small dimers, in both architectures, falls outside of the range of asphaltenes. If the effect of solvent is considered, as a constant change, still around 50% of the small−large systems would remain outside the experimental range of asphaltenes. When the percentage of all of the calculated dimers, large− small and large−large, is compared, in both architectures, and whose H−L gap falls inside the asphaltene experimental range, the large−large systems are more abundant by 20.6% in island structure, and by 17.9% in archipelago architecture, than the large−small dimers. It is concluded that, indeed, if two asphaltene core PAHs are directly bound via a single bond, then optical methods, such as TRFD studies, would identify this as a single chromophore, therefore as an island, thereby blurring the distinction between island versus archipelago. In addition, some decomposition studies might find this single-bonded pair of PAHs as a single entity.

■

Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Mullins, O. C. The modified Yen model. Energy Fuels 2010, 24, 2179−2207. (2) Mullins, O. C. The asphaltenes. Annu. Rev. Anal. Chem. 2011, 4, 393−418. (3) Mullins, O. C.; Sabbah, H.; Eyssautier, J.; Pomerantz, A.; Barré, L.; Andrews, A.; Ruiz-Morales, Y.; Mostowfi, F.; McFarlane, R.; Goual, L.; Lepkowicz, R.; Cooper, T.; Orbulescu, J.; Leblanc, R.; Edwards, J.; Zare, R. Advances in asphaltene science and the Yen−Mullins model. Energy Fuels 2012, 26, 3986−4003. (4) Groenzin, H.; Mullins, O. C. Asphaltene molecular size and structure. J. Phys. Chem. A 1999, 103, 11237−11245. (5) Groenzin, H.; Mullins, O. C. Molecular sizes of asphaltenes from different origin. Energy Fuels 2000, 14, 677−684. (6) Buenrostro-Gonzalez, E.; Groenzin, H.; Lira-Galeana, C.; Mullins, O. C. The overriding chemical principles that define asphaltenes. Energy Fuels 2001, 15, 972−978. (7) Groenzin, H.; Mullins, O. C.; Eser, S.; Mathews, J.; Yang, M. G.; Jones, D. Asphaltene molecular size for solubility subfractions obtained by fluorescence depolarization. Energy Fuels 2003, 17, 498−503. (8) Badre, S.; Goncalves, C. C.; Norinaga, K.; Gustavson, G.; Mullins, O. C. Molecular size and weight of asphaltene and asphaltene solubility fractions from coals, crude oils and bitumen. Fuel 2006, 85, 1. (9) Buch, L.; Groenzin, H.; Buenrostro-Gonzalez, E.; Andersen, S. I.; Lira-Galeana, C.; Mullins, O. C. Effect of hydrotreatment on asphaltene fractions. Fuel 2003, 82, 1075. (10) Andrews, A. B.; Guerra, R.; Mullins, O. C.; Sen, P. N. Diffusivity of asphaltene molecules by fluorescence correlation spectroscopy. J. Phys. Chem. A 2006, 110, 8095. (11) Schneider, M.; Andrews, A. B.; Mitra-Kirtley, S.; Mullins, O. C Asphaltene molecular size from translational diffusion constant by fluorescence correlation spectroscopy. Energy Fuels 2007, 21, 2875− 2882. (12) Wargadalam, V. J.; Norinaga, K.; Iino, M. Size and shape of a coal asphaltene studied by viscosity and diffusion coefficient measurements. Fuel 2002, 81, 1403−1407. (13) Sabbah, H.; Morrow, A. L.; Pomerantz, A. E.; Zare, R. N. Evidence for island structures as the dominant architecture of asphaltenes. Energy Fuels 2011, 25, 1597−1604. (14) Sabbah, H.; Morrow, A. L.; Pomerantz, A. E.; Mullins, O. C.; Tan, X.; Gray, M. R.; Azyat, K.; Tykwinski, R. R.; Zare, R. N. Comparing laser desorption/laser ionization mass spectra of asphaltenes and model compounds. Energy Fuels 2010, 24, 3589−3594. (15) Borton, D.; Pinkston, D. S.; Hurt, M. R.; Tan, X.; Azyat, K.; Tywinsky, R.; Gray, M.; Qian, K.; Kenttamaa, H. I. Molecular structures of asphaltenes based on their ions’ dissociation reactions in mass spectrometry. Energy Fuels 2010, 24, 5548−5559. (16) Lobodin, V. V.; Podgorski, D. C.; Nyadong, L.; Corilo, Y. E.; McKenna, A. M.; Rodgers, R. P.; Marshall, A. G. Determination of archipelago and island aromatic building blocks: The structural continuum of heavy petroleum. Proceedings of the 13th International Conference on Petroleum Phase Behavior and Fouling; St. Petersburg, FL, June 10−14, 2012. (17) McKenna, A. M.; Rodgers, R. P.; Robbins, W. K.; Marshall, A. G. Molecular characterization of asphaltenes and maltenes by FT-ICR mass spectrometry and implications to island and archipelago structural models. Proceedings of the 241st American Chemical Society National Meeting; Anaheim, CA, March 27−31, 2011. (18) McKenna, A. M.; Purcell, J. M.; Rodgers, R. P.; Marshall, A. G. Identification, characterization, and quantitation of vanadyl porphyrins in heavy crude oil by FT-ICR mass spectrometry. Proceedings of the 10th International Conference on Petroleum Phase Behavior and Fouling; Rio de Janeiro, Brazil, June 14−18, 2009. (19) McKenna, A. M.; Purcell, J. M.; Rodgers, R. P.; Marshall, A. G. Atmospheric pressure photoionization Fourier transform ion cyclotron resonance mass spectrometry for detailed compositional analysis of

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 1806


Energy & Fuels

Article

petroleum. Proceedings of the 9th International Conference on Petroleum Phase Behavior and Fouling; Victoria, British Columbia, Canada, June 15−19, 2008. (20) Rubinstein, I.; Spyckerelle, C.; Strausz, O. P. Pyrolysis of asphaltenes. Geochim. Cosmochim. Acta 1979, 43, 1−6. (21) Alshareef, A. H.; Scherer, A.; Tan, X.; Azyat, K.; Stryker, J. M.; Tywinski, R. R.; Gray, M. R. Formation of archipelago structures during thermal cracking implicates a chemical mechanism for the formation of petroleum asphaltenes. Energy Fuels 2011, 25, 2130−2136. (22) Borton, D.; Pinkston, D. S.; Hurt, M. R.; Tan, X.; Azyat, K.; Tywinsky, R.; Gray, M.; Qian, K.; Kenttamaa, H. I. Energy Fuels 2010, 24, 5548−5559. (23) Borton, D.; Hurt, M.; Gray, M.; Kenttamaa, H. A comparison of model compounds and asphaltenes, island vs. archipelago models. Proceedings of the 12th International Conference on Petroleum Phase Behavior and Fouling; London, U.K., July 10−14, 2011. (24) Zajac, G. W.; Sethi, N. K.; Joseph, J. T. Molecular imaging of asphaltenes by scanning tunneling microscopy: Verification of structure from 13C and proton NMR data. Scanning Microsc. 1994, 8, 463. (25) Sharma, A.; Groenzin, H.; Tomita, A.; Mullins, O. C. Probing order in asphaltenes and aromatic ring systems by HRTEM. Energy Fuels 2002, 16, 490−496. (26) Bouhadda, Y.; Bormann, D.; Sheu, E. Y.; Bendedouch, D.; Krallafa, A.; Daaou, M. Characterization of Algerian Hassi-Messaoud asphaltene structure using Raman spectrometry and X-ray diffraction. Fuel 2007, 86, 1855−1864. (27) Bouhadda, Y.; Fergoug, T.; Sheu, E. Y.; Bendedouch, D.; Krallafa, A.; Bormann, D.; Boubguira, A. Second order Raman spectra of Algerian Hassi-Messaoud asphaltene. Fuel 2008, 87, 3481−3482. (28) Ruiz-Morales, Y. HOMO−LUMO gap as an index of molecular size and structure for polycyclic aromatic hydrocarbons (PAHs) and asphaltenes: A theoretical study. J. Phys. Chem. A 2002, 106, 11283− 11308. (29) Ruiz-Morales, Y. Molecular orbital calculations and optical transitions of PAHs and asphaltenes. Asphaltene, Heavy Oils and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshall, A. G., Eds.; Springer: New York, 2007; Chapter 4. (30) Clar, E. The Aromatic Sextet; Wiley: London, U.K., 1972. (31) Ruiz-Morales, Y. The agreement between clar structures and nucleus-independent chemical shift values in pericondensed benzenoid polycyclic aromatic hydrocarbons: An application of the Y-rule. J. Phys. Chem. A 2004, 108, 10873−10896. (32) Ruiz-Morales, Y. Aromaticity in pericondensed cyclopenta-fused polycyclic aromatic hydrocarbons determined by density functional theory nucleus-independent chemical shifts and the Y-rule: Implications in oil asphaltene stability. Can. J. Chem. 2009, 87, 1280−1295. (33) Gutman, I.; Ruiz-Morales, Y. Note on the Y-rule in Clar theory. Polycyclic Aromat. Compd. 2007, 27 (1), 41−49. (34) Bergmann, U.; Mullins, O. C.; Cramer, S. P. Carbon Raman X-ray spectroscopy of asphaltenes. Anal. Chem. 2000, 72, 2609. (35) Bergmann, U.; Groenzin, H.; Mullins, O. C.; Glatzel, P.; Fetzer, J.; Cramer, S. P. Carbon K-edge X-ray Raman spectroscopy supports simple yet powerful description of aromatic hydrocarbons and asphaltenes. Chem. Phys. Lett. 2003, 369, 184. (36) Ruiz-Morales, Y.; Mullins, O. C. Polycyclic aromatic hyodrocarbons of asphaltenes analyzed by molecular orbital calculations with optical spectroscopy. Energy Fuels 2007, 21, 256. (37) Ruiz-Morales, Y.; Wu, X.; Mullins, O. C. Electronic absorption edge of crude oils and asphaltenes analyzed by molecular orbital calculations with optical spectroscopy. Energy Fuels 2007, 21, 944. (38) Ruiz-Morales, Y.; Mullins, O. C. Simulated and measured optical absorption spectra of asphaltenes. Energy Fuels 2009, 23, 1169−1177. (39) Klee, T.; Masterson, T.; Miller, B.; Barrasso, E.; Bell, J.; Lepkowicz, R.; West, J.; Haley, J. E.; Schmitt, D. L.; Flikkema, J. L.; Cooper, T. M.; Ruiz-Morales, Y.; Mullins, O. C. Triplet electronic spinstates of crude oils and asphaltenes. Energy Fuels 2011, 25, 2065−2075. (40) Berlman, L. B. Handbook of Fluorescence Spectra of Aromatic Compounds; Academic Press: New York, 1971.

(41) Structures and Dynamics of Asphaltenes; Mullins, O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998. (42) Groenzin, H.; Mullins, O. Asphaltene molecular size and structure. J. Phys. Chem. A 1999, 103, 11237−−11245 and references therein. (43) Groenzin, H.; Mullins, O. Molecular size and structure of asphaltenes from various sources. Energy Fuels 2000, 14, 677. (44) Perdew, J. P.; Wang, Y. Accurate and simple analytic representation of the electron−gas correlation energy. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244−13549. (45) Delley, B. An allelectron numerical method for solving the local density functional for polyatomic molecules. J. Chem. Phys. 1990, 92, 508−517. (46) Delley, B. From molecules to solids with the DMol3 approach. J. Chem. Phys. 2000, 113, 7756−7764. (47) Accelrys, Inc. DMol3, Release 4.0; Accelrys, Inc.: San Diego, CA, 2001. (48) Accelrys, Inc. MS Modeling 5.5; Accelrys, Inc.: San Diego, CA, 2010. (49) Zerner, M. C.; Correa de Mello, P.; Hehenberger, M. On the convergence of the self consistent field method to excited states. Int. J. Quantum Chem. 1982, 21, 251−259. (50) Accelrys, Inc. Cerius2, Version 4.6; Accelrys, Inc.: San Diego, CA, 2001. (51) Runge, E.; Gross, E. K. U. Density-functional theory for timedependent systems. Phys. Rev. Lett. 1984, 52, 997−1000. (52) Maitra, N. T.; Burke, K.; Appel, H.; Gross, E. K. U.; van Leeuwen, R. Ten topical questions in time-dependent density functional theory. In Reviews in Modern Quantum Chemistry: A Celebration of the Contributions of R. G. Parr; Sen, K. D., Ed.; World-Scientific: Singapore, 2002; Vol. 2, pp 1186−1225. (53) Casida, M. E.; Huix-Rotllant, M. Progress in time-dependent density functional theory. Annu. Rev. Phys. Chem. 2012, 63, 287−323. (54) Waris, R.; Street, K. W., Jr.; Acree, W. E., Jr.; Fetzer, J. C. Polycyclic aromatic hydrocarbon solute probes. Part IV: Effect of solvent polarity on the fluorescence emission fine structures of select pyrene and pentaphene derivatives. Appl. Spectrosc. 1989, 43, 845−850. (55) McKay, J. F.; Latham, D. R. Fluorescence spectrometry in the characterization of high-boiling petroleum distillates. Anal. Chem. 1972, 44, 2132−2137. (56) Trickey, S. B.; Diercksen, G. H. F.; Müller-Plathe, F. UV Atlas of Organic Compounds; Plenum Press: New York, 1967. (57) Acree, W. E., Jr.; Tucker, S. A.; Fetzer, J. C. Fluorescence emission properties of polycyclic aromatic compounds in review. Polycyclic Aromat. Compd. 1991, 2, 75−105. (58) Halasinski, T. M.; Hudgins, D. M.; Salama, F.; Allamandola, L. J. Electronic absorption spectra of neutral pentacene (C22H14) and its positive and negative ions in Ne, Ar, and Kr matrices. J. Phys. Chem. A 2000, 104, 7484−7491. (59) Mullins, O. C. In Asphaltenes, Fundamentals and Applications; Sheu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995; Chapter 2. (60) Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Springer: New York, 2006. (61) Wang, X.; Mullins, O. C. Fluorescence lifetime studies of crude oils. Appl. Spectrosc. 1994, 48, 977−984. (62) Fioressi, S. E.; Binning, R. C., Jr.; Bacelo, D. E. Effects of cluster formation on spectra of benzoapyrene and benzoepyrene. Chem. Phys. Lett. 2008, 454, 269−273. (63) Birks, J. B.; Christophorou, L. G. “Excimer” fluorescence IV. Solution spectra of polycyclic hydrocarbons. Proc. R. Soc. London, Ser. A 1964, 277, 571−582. (64) Jacquemin, D.; Planchat, A.; Adamo, C.; Mennucci, B. TD−DFT assessment of functionals for optical 0−0 transitions in solvated dyes. J. Chem. Theory Comput. 2012, 8, 2359−2372. (65) Jacquemin, D.; Wathelet, V.; Perpète, E. A.; Adamo, C. Extensive TD−DFT benchmark: Singlet-excited states of organic molecules. J. Chem. Theory Comput. 2009, 5, 2420−2435. 1807


Energy & Fuels

Article

(66) Bergmann, U.; Mullins, O. C. Carbon X-ray Raman spectroscopy of PAHs and asphaltenes. In Asphaltenes, Heavy Oils, and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshall, A. G., Eds.; Springer: New York, 2007; Chapter 5. (67) Abdallah, W. A.; Yang, Y. Raman spectrum of asphaltene. Energy Fuels 2012, 26, 6888−6896. (68) Feng, C.; Lin, C. S.; Fan, W.; Zhang, R. Q.; Van Hove, M. A. Stacking of polycyclic aromatic hydrocarbons as prototype for graphene multilayers, studied using density functional theory augmented with a dispersion term. J. Chem. Phys. 2009, 131, 194702. (69) Tyutyulkov, N.; Staykov, A.; Müllen, K.; Dietz, F. Symmetry breaking of full face-to-face arrangement of homonuclear π-electron molecules in 1-D stacks. Chem. Phys. Lett. 2003, 373, 314−318.

1808


Island versus Archipelago Architecture for Asphaltenes - American

Recommend Documents