Fast Fourier Transform and autocorrelation function for the analysis of complex mass spectra

International Journal of Mass Spectrometry 338 (2013) 30–38

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Fast Fourier Transform and autocorrelation function for the analysis of complex mass spectra B. Apicella a,∗ , A. Bruno b,1 , X. Wang c , N. Spinelli b a b c

Istituto di Ricerche per la Combustione – CNR, P.le Tecchio 80, Napoli, Italy CNISM and Dipartimento di Scienze Fisiche, Università degli Studi di Napoli “Federico II”, Napoli, Italy SPIN-CNR, Napoli, Italy

a r t i c l e

i n f o

Article history: Received 12 August 2012 Received in revised form 9 January 2013 Accepted 9 January 2013 Available online 19 January 2013 Keywords: Asphaltene Pitch Fast Fourier Transform Autocorrelation function Mass spectra analysis

a b s t r a c t Mass spectrometry is useful for structural investigation of molecules as it is able to give simultaneously molecular weight (MW) distributions, chemical functionalities and fragmentation and/or reaction growth paths. However, in the case of very complex mixtures it can be very difficult to interpret a mass spectrum and to individuate manually the gap among the peaks. In the present work, for the first time two mathematical methodologies, Fast Fourier Transform (FFT) and autocorrelation function (AF), have been applied to the mass spectra analysis of complex carbonaceous mixtures, like naphthalene pitch and asphaltenes, whose structure and MW are object of pitched debates in literature. The potentiality of this mathematical approach was shown for improving the spectra interpretation whichever the mass spectrometer used. It was found that in general FFT analysis is more accurate with denser peaks and lesser resolved spectra but fails in accuracy when few/sharp peaks are present. On the other hand, AF analysis is more accurate in the determination of main periodicities when the spectrum presents just few peaks and a higher resolution. Structures and MW have been derived for naphthalene pitch and asphaltenes, on the basis of the match of their FFT and AF spectra. Naphthalene pitch was found to be constituted of many compounds arriving up 1000 Da, with different unsaturation degrees and the presence of naphthenic rings and aliphatic bridges. Asphaltenes have been found to present a polymeric structure with aromatic moieties with no more than 4–5 rings linked by aliphatic chains and their MW extending up to 1000 Da. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The refinement and upgrading of mass spectrometry techniques have provided a considerable impulse to the determination of the composition, molecular weight distribution and structure of always more high molecular weight and complex materials. Mass spectrometry has currently achieved a mass resolution capable of discerning chemical composition and structure in complex mixtures, especially when applied in combination with chromatographic separation. High molecular weight (MW) aromatic species are commonly present in heavy fractions of coal- and petroleum-derived fuels as well as in the tarry carbonaceous particulates generated from fuel-rich combustion. For these species, the high molecular weight coupled with their insolubility in most common organic solvents

∗ Corresponding author. Tel.: +39 0817682254; fax: +39 0815936936. E-mail address: [email protected] (B. Apicella). 1 Present address: Italian National Agency for New Technologies, Energy and SustainableEconomic Development (ENEA), Portici (NA), Italy. 1387-3806/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijms.2013.01.003

make the chromatographic techniques coupled to mass spectrometry not suitable for the analysis. In alternative, the analysis of these compounds can be performed by direct injection into the source of mass spectrometer with ionization by electron impact, electrospray or photoionization [1–3], deposition on metallic plates followed by laser desorption and ionization [4–7] or by an on-line transfer as a molecular beam directly from the source to the mass spectrometer followed by electron impact or laser ionization [8,9]. Anyway, whatever is the mass spectrometric system used, complex mixtures produce spectra with a huge number of peaks which generally make difficult the data analysis. This motivates the application of mathematical methods, capable of rapid and repeatable processing of mass spectral data that give repeated spacing patterns throughout the entire mass range. Correlation analysis, as autocorrelation function (AF), of chemical data has been used since many years [10], even if the specific application of correlation methods to mass spectrometric data has been mainly limited to mass spectral library matching, substructure searching, smoothing for improving quantitative analysis by GC–MS, as deeply described in a review paper [11] and to synthetic polymer structural analysis [12]. Applications to more

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complex samples or to mixture of many unknown compounds are still missing. In the present work, Fast Fourier Transform (FFT) and autocorrelation function analysis have been applied to mass spectra in order to individuate periodicities that can indicate preferential growth roots and/or fragmentation patterns. The potentiality of the simultaneous application of both FFT and AF for spectra interpretation has been firstly tested on mass spectra of standard materials as polystyrenes of different masses. After then, FFT and AF have been applied to data analysis of the mass spectra of high-MW aromatic mixtures, as naphthalene pitch and asphaltenes, which are very complex and more difficult to be interpreted with respect to synthetic polymers. Indeed, their complex composition is not completely known and it is still the object of many investigations [13–21]. It has been shown that the application of these methods does not require a specific software created “ad hoc” but a commercial graphic software can be used and in this way it is possible to have a higher flexibility in the parameters choice for data analysis. Moreover, it has to be underlined that the FFT and AF analysis methods regard the spectra interpretation and as such they can be used to analyze spectra obtained with any kind of mass spectrometer. Indeed, in this work the two techniques have been applied on mass spectra from different mass spectrometric systems, differing for both the ionization source and the mass analyzer. It is worth to note that the methodology of mass spectra analysis based on FFT presented in this paper has not to be confused with the Fourier Transform mass spectrometry (FT-ICR MS and Orbitrap FTMS) that is a type of high resolution mass spectrometry based on the cyclotron frequency of the ions in a fixed magnetic field [22–24]. Both in the case of low resolution and high resolution mass spectra FFT and AF analysis gives gaps of periodic features that can help to individuate series and/or growth or fragmentation paths. Therefore, the goal is not the identification of a single peak as in the case of the high-resolution FTMS. Moreover, since there is not a mass limit for the application of such mathematical methods, they are of concern also for the data analysis of very high resolution spectra acquired by mass spectrometers based on ion cyclotron resonance. Indeed, in such a kind of instruments, accurate mass measurements allows for the unambiguous assignments of molecular formulas for ions up to ∼400 Da [24]. For assignment of species observed at higher masses, it is necessary a close inspection of the spectrum for detecting repeated spacing patterns and for this, the application of FFT or AF should be extremely helpful. The general outline of the present work is the following. We report first on the case of polystyrenes that have been chosen as standard for checking the information that FFT and AF analysis can give for mass spectra interpretation when high repetitive sequences are present and which advantages and shortcomings each method presents. The application to other standard samples with increasing complexity, like water clusters and ovalene clusters, are reported in the Supporting Information. Naphthalene pitch and asphaltenes have been chosen as examples of application of methods on complex samples with high scientific interest. On naphthalene pitch and asphaltenes it has been shown how the information obtained by applying FFT and AF analysis to the mass spectra interpretation can add a relevant contribution to the scientific debate on molecular weight and structure of the samples.

2. Data analysis methods: FFT and AF A commercial and very user friendly software, Origin 9.0 (OriginLab Corporation), has been used in this paper for FFT and AF calculation, without any necessity of writing a dedicated program.

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Some outlines on the mathematical theory involved in the application of these methods are reported in the following. Correlation analysis is a calculation technique used to extract information about the coherence within one or between two signals [11]. Methods of calculating correlation functions (Fast Fourier Transform and autocorrelation) are described in detail in the literature [11,25], and only the basic principle will be described in the following. 2.1. Fast Fourier Transform The Discrete Fourier Transform (DFT) is a mathematical operation transforming one discrete function of the independent variable into another function, which is the representation of the original function in the domain of the inverse of the independent variable. In the case of mass spectra, the independent variable is represented by the mass m and therefore the Fourier transform will be a function of mass frequency (f = 1/m). The DFT requires an input function that is discrete and whose non-zero values have a limited (finite) duration, moreover the data should be equally spaced. If mass spectral data points are not equally spaced, as in TOF mass spectrometry, the input function should be interpolated at a suitable uniform mass interval comparable with the instrumental resolution for the smallest ion mass in the spectrum. A Fast Fourier Transform is an efficient way to compute the Discrete Fourier Transform. Therefore, the result of a FFT is simply equal to that of a DFT performed on the same input. Many FFT software packages can give us several output results, such as the magnitude, power, phase and amplitude of the transformed data. Among these results, the mean square amplitude power, FFTf , represents the number of ions contributing to the mass frequency (f = 1/m). In order to have a clearer physics meaning, the independent variable, the frequency f, may be converted to the mass period (m = 1/f) and the m depending mean square amplitude power (FFTm ) can be got from the equation FFTm · m = FFTf · f

(1)

Eq. (1) indicates that even if the variable domain changes, the number of ions to the mass frequency does not change.  contributing  From f /m = 1/m2 , we can get: FFTm = FFTf

   f  FFTf  m  = 2 m

(2)

In order to enhance features corresponding to larger mass period, in this paper we directly used the FFT output, i.e. the mean square amplitude power, which has a physical meaning of: FFTf = m2 · FFTm 2.2. Autocorrelation function The autocorrelation function (AF) is the correlation function calculated between two couples of the signal delayed each other by the increment  of the independent variable t (i.e.  is a delay if the independent variable is the time). It is appropriate to analyze the self-similarity as function of , because it illustrates how much the signal resembles a shifted (delayed) version of itself. Let f(t) be a discrete signal of length M. The autocorrelation function can be defined as:



i=M−1

y() =

f (ti )f (ti − )

i=0

The magnitude of the correlation represents the degree of similarity between the signal and its delayed copy as a function of the

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delay between them. If the magnitude of the autocorrelation function is large, the delayed signal will be considered to be very similar to the original one. Alternatively, if it is close to zero, the signal will be considered not to keep its linear relation increasing the distance between two points. When the correlation is normalized, its magnitude will range from 0 to 1. The autocorrelation function can be easily computed using a fast algorithm based on the convolution theorem, which can be expressed as follows:



i=M−1

y() =

f (ti )f (ti − ) = iFFT (FF ∗ )

i=0

where F is the Fourier transform of f(t), * means complex conjugation and iFFT stands for the inverse FFT. Therefore, three steps are required to calculate the autocorrelation function: (1) The Discrete Fourier Transforms of f(t) is computed using FFT; (2) Multiply the Fourier transform of f(t) with the conjugated transform of f(t − ); (3) Perform inverse Discrete Fourier Transform of the product. 2.3. Time of flight mass spectra In principle FFT and AF methods can be used to analyze mass spectra obtained with any experimental set-up, apart from the ionization or mass analyzer employed, nevertheless the application to time of flight mass spectra requires a special attention in order to preserve quantitative information. In fact, when a time depended time-of-flight mass spectrum (TOFt ) is converted into a mass depended time-of-flight mass spectrum (TOFm ), the TOFm has to be renormalized through the equation: TOFm = TOFt

t (m/z)

(3)

where t is the instrument time resolution and (m/z) is the corresponding mass interval. Usually, TOF mass spectrometers give out TOFt with a constant time sampling interval. So, for a general case, we can get TOFm ∝

TOFt (m/z)

(4)

For a conventional TOF mass spectrometer, different ions with the same charge are accelerated to have the same kinetic energy, independently on the mass. The relation between the m/z and flight time t is then: t∝



(m/z).



Then t ∝ (m/z)/ TOFm ∝

TOFt



m/z

(5) (m/z) and we can get: (6)

Therefore, the area of each peak in normalized TOFm mass spectrum is proportional to the relative abundance of the correspondent ion. 3. Experimental 3.1. Samples Polystyrenes (PS) of different average molecular weights (1700 Da; 5050 Da; 11,600 Da) were purchased from Polymer laboratories.

Naphthalene pitch (Mitsubishi Gas-Chemical Company) is a black solid prepared by pyrolysis of naphthalene at 600 ◦ C, using HF/BF3 as catalyst [26]. It is a 100% synthetic mesophase pitch and it is considered to consist of oligomers of naphthalene. The synthesis route for naphthalene pitch involves only pure naphthalene-based polyaromatic species, therefore there are only very low amounts of heteroelements (0.23 wt.% sulphur and below 0.1 wt.% for nitrogen and oxygen) [26]. Asphaltenes are defined as the petroleum fraction insoluble in low-boiling solvents (n-pentane and n-heptane) and soluble in toluene. Asphaltenes used in this work were separated from a commercial heavy fuel oil by n-pentane using ASTM (D200-75) separation methods. Water clusters have been produced using as source distillate water from a reservoir where a nitrogen flow, bubbling inside the liquid, acts as transfer gas. It was kept at a temperature of 28 ◦ C in nitrogen atmosphere. More details have been given in the Supporting Information. Ovalene (Schmidt, s.rl.) is a polycyclic aromatic hydrocarbon (PAH) with the formula C32 H14 , which consists of ten peri-fused six-membered rings. 3.2. Methods Polystyrenes (PS), ovalene and naphthalene pitch have been analyzed by different laser desorption mass spectrometric instruments. PS and ovalene were analyzed by laser desorption ionization time of flight mass spectrometer (LDI-TOF-MS) and naphthalene pitch by atmospheric pressure laser desorption ionization ion trap mass spectrometer (AP-LDI-ITMS). In the case of PS, dithranol has been used as the matrix and silver trifluoroacetate as the cationizing agent, whereas for ovalene and naphthalene pitch no matrix has been used. Ovalene spectrum and FFT and AF analysis are reported in the Supporting Information. The samples were dissolved in N-methyl pyrrolidone (NMP) and deposited on a metallic plate substrate (target). The target was prepared by depositing of about 1 ml of a solution of the sample dissolved in NMP on the 25 mm diameter aluminum stub. The solvent was evaporated in an oven at T = 60 ◦ C and then pumped by a turbo-molecular pump to remove the last traces of solvent (in the case of NMP). The metallic target was set into the sources of the two different MS equipments described in the following. Asphaltenes, dissolved in toluene solutions, were directly injected into the atmospheric pressure photoionization source of an ion trap mass spectrometer (APPI-ITMS) by using a syringe pump. 3.2.1. LDI-TOF-MS A Bruker Daltonics Reflex IV MALDI-TOF mass spectrometer instrument (Warwick, UK) was used for laser desorption ionization time of flight-mass spectrometry (LDI-TOF-MS) measurements of PS spectra in reflector mode. The instrument features the 337 nm wavelength of a nitrogen laser with a pulse length of 3 ns and an acquisition, automation and data processing software package. The spectra were acquired over a range of ion accelerating voltages between 20 and 25 kV. More details are given in a previous work [5]. 3.2.2. AP-LDI-ITMS In the Atmospheric Pressure Laser Desorption Ionization Mass Spectrometry (AP-LDI) the ions are produced at normal atmospheric pressure differently to the conventional MALDI and LDI ion source where ions are formed inside the vacuum system of the mass spectrometer. The ionization source is a nitrogen laser (337 nm), mounted inside a laser and stage control box, producing a 10-Hz

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pulsed beam. The mass analyser is an Ion Trap (IT). More details are reported in a previous work [27]. 3.2.3. APPI-ITMS The Atmospheric Pressure Photoionization Ion Trap mass spectra were obtained with an Agilent 1100 Series MSD Trap (Agilent Technologies, Palo Alto, CA, USA). A PhotoMate orthogonal APPI spray source (Syagen Technology) was installed on the mass spectrometer. The APPI source was based on a radio frequency (RF) discharge of a gas mixture consisting primarily of krypton and operated on the atomic emission lines at 10.0 and 10.6 eV. More details are reported in a previous work [7]. 4. Results and discussion The spectra reported in this paragraph represent examples with increasing complexity for showing the advantage in applying FFT and AF for data analysis of the spectra. 4.1. Polystyrenes In Fig. 1 the spectra acquired by LDI-TOFMS of synthetic polystyrenes with different average MW are reported (Fig. 1a (1700 Da), b (5050 Da), and c (11,600 Da)). The TOF mass spectra have been interpolated in order to produce a regularly spaced discrete function of the independent variable m/z. Then FFT and AF analysis have been applied to these spectra and the resulting FFT and AF periodicity spectra are reported in Figs. 2a–c and 3a–c, respectively. The transformed function has been evaluated as a function of m/z and reported as a function of the corresponding periodicity.

Fig. 1. Polystyrenes mass spectra with different average MW: 1700 Da (a); 5050 Da (b); 11,600 Da (c) acquired by LDI-TOF-MS in reflectron mode.

Fig. 2. FFT periodicity spectra of polystyrenes with different average MW: 1700 Da (a); 5050 Da (b); 11,600 Da (c).

In every MW investigated range, the PS presents a polymer typical mass spectrum with well defined periodic peaks. The FFT and AF analysis puts in evidence the typical mass periodicity gap of polystyrenes, around 104 Th, and corresponding to a styrenic unit. In the case of FFT periodicity spectrum (Fig. 2a) the main peak is at 104 Th and other minor peaks with decreasing intensities are present due to higher harmonics (2nd, 3rd, etc.) and placed at masses that are 1/2, 1/3, 1/4, etc. of the gap mass, respectively. The AF has a local maximum for each periodic separation of peaks in the original mass spectrum: the first peak corresponds to the gap 104 Th whereas strong correlation peaks appear also at multiples of 104 Th, extending up to 2000 Th (Fig. 3b). The intensity of the highest peaks is close to 1 indicating that mass values corresponding to multiples of 104 Th are strongly correlated, as expected from a highly periodic structure. However, it is interesting to note how the FFT identification of the correct gap (104 Th, styrene unit) improves going from PS having lower MW, with a less dense spectrum, up to the PS having higher MW (Fig. 2a–c). Moreover, as expected, for the spectrum with higher peak density, the higher harmonics are less intense, with a simplification of the FFT spectrum. By contrast, AF peaks are narrower and closer to 104 Th in the case of the lower MW PS (Fig. 3a) whereas their full width at half maximum (FWHM) increases going toward higher MW (Fig. 3b and c). This trend is better shown in Table 1, where the values at the peak maximum for FFT and AF (in this case for the first peak) are reported, along with the error estimated as ±HWHM (half width at half-maximum) value. Overall, it can be concluded that, as expected from mathematical considerations, the FFT analysis is more accurate with more dense peaks spectra, but it fails in accuracy when few peaks are present.

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Fig. 3. AF spectra of polystyrenes with different average MW: 1700 Da (a); 5050 Da (b); 11,600 Da (c).

Fig. 4. Water clusters mass spectra acquired in linear and reflectron mode (a) and their FFT (b) and AF (c) spectra.

Indeed, FFT analysis is not only sensitive to the periodic components in mass spectra, but also sensitive to the shape of peaks. It will give the distribution of power of each pure sine wave component. Because a typical peak in mass spectra is far from a sine wave, the FFT results contains both the information of fundamental mass periods and its second, third, etc., harmonic components. In general, the higher dense the mass spectra is, the less high order harmonic components will be in FFT. Thus, FFT is suitable for higher dense and poorly resolved mass spectra and AF is more accurate in the determination of the main periodicity when the mass spectrum presents narrow peaks. Moreover, also the main background present in the AF spectrum depends on the density of peaks in the spectrum. In particular, denser is the mass spectrum higher is the continuum unstructured background in the AF spectrum, indicating a stronger correlation among components.

In order to show this effect in Fig. 4a the spectra of water clusters with very different resolution are reported, whereas in Fig. 4b and c there are their FFT and AF spectra. More details on water clusters spectra are reported in the Supporting Information. The two water clusters spectra here reported are detected in linear and reflectron mode, obtaining a resolution around 160 and 1000, respectively. The resolution is calculated as the ratio of the mass of interest, m, to the lowest resolved difference in mass, m, as defined by the width of a peak at 50% of the peak height: m/m [28]. In Fig. 4b and c it can be observed that the spectrum with a higher resolution (the reflectron one) presents a FFT spectrum (Fig. 4b) complicated by the presence of a large number of harmonics, whereas it has an AF spectrum (Fig. 4c) with a very high resolution that can allow detecting a second gap, 19 Th, more than the main gap (18 Th) reported also in FFT spectrum. It is so evident the advantage of using AF instead of FFT in the case of higher resolution spectra and by contrast of using FFT instead AF for lower resolution spectra. When the spectra are complex, with a large number of peaks and small gaps among them, the advantage of using FFT and AF for the spectrum analysis is much more evident, as shown in the following with the analysis of more complex carbonaceous samples as naphthalene pitch and fuel oil asphaltenes.

4.2. Effect of spectra resolution on FFT and AF analysis FFT and AF analysis can be applied to spectra with any resolution, even if spectra resolution acts in a different and opposite way on the results obtained from the two methods.

Table 1 PS molecular weight, main periodicity identified with FFT and AF first maximum. PS MW (Da)

FFT maximum (Da)

AF first maximum (Da)

1700 5050 11,600

104 ± 4 105 ± 2 104 ± 1

104 ± 3 103 ± 8 105 ± 18

4.3. Naphthalene pitch Synthetic pitches are relevant as starting material for carbon fiber production. Carbon fiber, because of its high strength and low

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of the gap at 12.6 Th) support the conclusion that naphthalene pitch synthesis routes never led to a regular polymer with a regular growth path. Naphthalene pitch appears to be constituted of many compounds arriving up to MW of about 1000 Da with different unsaturation degrees, with naphthenic rings and aliphatic bridges (gap 12.6). Moreover, the aromatic moieties are probably smaller as the MW of the different compounds is lower than 1000 Da, with most of species having MW around 400 Da. Another important information derives from the comparison of FFT spectrum evaluated in the range 200–400 Th with that one evaluated in the range 400–2000 Th, reported in Fig. 6. It appears evident that the FFT applied in the first portion of the spectrum (Fig. 6a) presents all the periodicities of the total spectrum (Fig. 6b) whereas the higher molecular weight range spectrum (Fig. 6b) presents only the periodicity 1 and 2, and the absence of the gap at 12.6 is noticeable. This suggests that the growth paths for naphthalene pitch synthesis go on up to 400 Da with the regular increase of the MW due to aliphatic bridges insertion. After this limit, the mixed aliphatic/aromatic structures can combine in several ways, with no univocal path, therefore obscuring any periodicity in the spectrum. This change in the peaks patterns before and after the maximum is evident to a visual observation of the spectrum, but without a mathematical analysis of the spectrum it is not possible to evaluate the change in the spacing. 4.4. Asphaltenes

Fig. 5. Naphthalene pitch mass spectrum (a) acquired by AP-LDI-ITMS and its FFT spectrum (b) and AF spectrum (c).

weight, has become an important material for industry but a crucial point for its performance is to control the properties of the starting material. Naphthalene pitch is a good candidate for carbon fiber generation as it assures similar behavior of the anisotropic and isotropic portions on spinning because all molecules in the pitch are basically naphthalene oligomers of continuous molecular weight distribution [10]. The structure of naphthalene pitch is very complex and not well defined. Raman microspectroscopy [29] has suggested that naphthalene pitch is constituted of polyaromatic species characterized by smaller dimensions and by the presence of aryl–aryl C–C bonds, naphthenic rings and possibly also alkyl groups at the periphery of the molecules. The mass spectrum of naphthalene pitch obtained by LDI-ITMS is reported in Fig. 5a, adapted from the spectrum published in [27]. Due to the large number of peaks, it is very complicated to individuate the main periodicities in it. By contrast, the FFT spectrum reported in Fig. 5b shows some clear periodicities. The main FFT peaks are observed corresponding to mass differences of 1.00 ± 0.01 and 2.00 ± 0.06 Th and a minor peak at 12.6 ± 0.3 Th that can be interpreted as due to the presence of homologous series increasing by a carbon atom or CH and CH2 group (gap of 12–14 Th, with a prevalence of 12 Th) with a different degree of unsaturation (gap of 1 and 2 Th). The errors have been estimated as ±HWHM value. In Fig. 5c the AF spectrum calculated in the whole mass range is reported. The maximum value of correlation is above 0.9, indicating that all the masses in the spectrum are highly correlated. The absence in the AF spectrum of correlations for mass intervals greater than 1.0 ± 0.2 and 2.0 ± 0.3 Th and the main presence of the same gaps in FFT spectrum (with only a minor contribution

Asphaltenes are the heavy aromatic fraction of coal and petroleum. The detailed definition of their molecular structure and mass distribution is relevant for the processing of these materials and to control their behavior in refinery plant. Indeed, their mass spectra extend in a rather wide MW range and present repetitive units constituted by polyaromatic structures with different ring number and possibly with the presence of heteroatoms and therefore with peak gap not easily identifiable by chromatographic and mass spectrometric techniques. Therefore, their molecular structure and mass distribution are still now object of a pitched scientific debate [14–21]. Many authors proposed a relatively low MW range of m/z 500–1000 [15–19], whereas others [14,20,21] found basically bimodal distributions with two mass ranges: the former between m/z 100 and 3000 and the latter corresponding to masses higher

Fig. 6. FFT spectrum of naphthalene pitch up to 400 Da (a) and over 400 Da (b).

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Fig. 7. Asphalthenes mass spectrum (a) acquired by APPI-ITMS and its FFT spectrum (b) and AF spectrum (c).

than m/z 100,000. Even though the high MW range could be overestimated due to the three-dimensional conformation (or large hydrodynamic volumes) adopted by the larger asphaltene molecules, these authors claimed the presence of big molecule of at least 10,000 Da [14]. The mass spectrum of asphaltenes is very complex due to the presence of a large number of peaks differing for only 1 Th. Appling the FFT analysis it is possible to simplify the spectrum, isolating few main periodicities. Fig. 7a and b report the mass spectrum of the asphaltenes sample acquired by APPI-ITMS and its FFT periodicities spectrum, respectively. In a previous paper [7] a screening of different systems for spectra acquisition of asphaltenes has been performed, showing that the best combination of ionization system and mass analyzer in terms of detection range extension is the APPI-ITMS used in the present paper. The peaks in the region below 200 have to be neglected as they are due to reaction products of toluene with oxygen with one and two aromatic rings, respectively [7]. As in the case of naphthalene pitch, the main peaks in the FFT of asphaltenes correspond to mass differences of 1.000 ± 0.001 and 2.000 ± 0.004 Th with a minor peak at 12.7 ± 0.2 Th that can be interpreted as due to the presence of homologous series of aromatic polymers (gap of 12–13 Th) with a different degree of unsaturation (gap of 1 and 2 Th). More in detail, periodicity at 12.7 Th means a large contribution of 13 Th, due not only to isotopic contribution, but probably also to the presence of aliphatic bridges (CH) among the building block of the molecules. A small peak at 14.8 ± 0.1 Th indicates the possible presence of aliphatic bridges (CH2 ) and aliphatic chain terminal (CH3 ). The presence of FFT periodicities around 122 ± 8 Th and 240 ± 30 Th indicates the presence of asphaltenic polymeric chains through the addition of condensed

aromatic rings, from two (116 Th with one 5-C ring and 128 Th with 2 6-C rings) to five (240 Th with a 5-C ring and 252 Th with all 6-C rings). The absence of periodicities of 12 Th and 24 Th, typical of large PAH sequences [6], also confirms the polymeric structure of asphaltenes, constituted by repetitive aromatic condensed moieties of different dimensions connected by aliphatic bridges, as hypothesized by several authors [14–21] as well as the small dimensions of the aromatic moieties. Therefore, the FFT analysis in the complex case of asphaltene spectrum can help the interpretation of the structure highly debated in the literature [14,15]. Indeed, as already reported before, some authors proposed a molecular weight range around 500–1000 Th [15] whereas others [14,21] found bimodal distributions with two mass ranges: the former up to 3000 Da and the latter corresponding to masses higher than m/z 100,000. The results here reported give quantitative support to the qualitative spectra interpretation we have already reported in a previous work [7]: asphaltenes have a polymeric structure with aromatic moieties with no more than 4–5 rings linked by aliphatic chains and their MW extends up to 1000 Da. Therefore, the molecular units appear not bigger than 1000 Da. Probably, in agreement with [30], it can be argued that the high MW found by some authors can be due to the occurrence of the supramolecular aggregation, which complicates a lot of the chemistry of asphaltenes, obscuring the domains of covalency. However, the possibility that small molecular units up to 1000 Da are linked among them forming bigger molecules with MW extending up to MegaDalton [14,20,21] more than merely aggregates cannot be completely ruled out. Indeed, even if the use for the mass spectra here reported of a soft ionization as a photoionization lamp makes the fragmentation of big molecules in mass spectrometry source poorly probable, the ion trap detector limit is 4000 Da, hindering the eventual presence of higher MW species. Moreover, the present work shows, in agreement with results reported by Liao [31], that there are multiple aromatic (PAH-like) units containing 2–5 rings inside asphaltene molecules and not only 1, as concluded by the work from the research group of Mullins [32]. Fig. 7c reports the AF spectrum. Also in this case a high correlation and the main periodicity of 1.0 ± 0.2 and 2.0 ± 0.3 Th, with the peaks at each 2 Th higher are shown. The other periodicities are not visible in the AF spectrum. The presence of periodicity of 1 and 2 Th, absent or very low in the case of large PAH samples spectra [9], confirm the polymeric nature of asphalthenes. Also in this case it is shown that the FFT for a complex spectrum can give more detailed information, nevertheless it is important to underline that it is mainly the matching of the two approaches (FFT and AF) which allows extracting information on the actual structure of the molecules, giving a simpler interpretation of the mass spectral data. It is also noteworthy that the periodicities of the asphaltene spectrum disappear for masses greater than that one corresponding to the maximum signal intensity (around 560 Th), as shown in Fig. 7 where the FFT spectra of the two parts of the spectrum (up to 560 Th, Fig. 8a and over 560 Th, Fig. 8b) are reported. The FFT of the first part of the spectrum (Fig. 8a) presents the same periodicities of the whole spectrum (1, 2, 12.7 and 14.8 Th), whereas the periodicities at 122 and 244 Th are absent. The FFT of the last part of the spectrum presents only periodicities at 1 and 2 Th. These results can be interpreted by considering the asphaltenes structure very regular up to MW of 560 Da, with structures with at maximum 4, 5 rings linked by aliphatic bridges. Bigger structures can be formed combining these molecules in many different ways, therefore presenting no periodicities into the spectrum. It is confirmed, however, that not only one kind of aromatic moieties is

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Acknowledgments The authors want to thank the MSE-CNR project on “Clean Carbon” for the financial support for the TOFMS system. The authors wish to thank Centro Regionale di Competenza ‘AMRA’ for financial support. We are also deeply grateful to Dr. Anna Ciajolo for helpful discussions and comments on the paper. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ijms.2013.01.003. References

Fig. 8. FFT spectrum of asphaltenes up to 560 Da (a) and over 560 Da (b).

present but there are multiple aromatic units containing 2–5 rings inside asphaltenes molecules.

5. Conclusions In the present work FFT and AF analyses have been employed for obtaining rapid and repeatable processing of mass spectral data that gives repeated spacing patterns throughout the entire mass range. The potentiality of the simultaneous application of both FFT and AF for spectra interpretation has been tested firstly on standard materials as polystyrenes with different masses. Afterwards, FFT and AF have been applied to the data analysis of the spectra of high MW aromatic mixtures, as naphthalene pitch and asphaltenes, which are very complex and more difficult to be interpreted with respect to synthetic polymers. The mass spectra were obtained by using three different MS systems (samples by other two MS system are reported in SI), showing the applicability of the mathematical approach for every kind of mass spectrum. The effect of peak density and resolution on the two different mathematical methods have been shown revealing that FFT is suitable for higher dense and lesser resolved mass spectra and AF is more accurate in the determination of the main periodicity when the spectrum presents few peaks and higher resolution. Complex carbonaceous materials, very important from a scientific point of view as naphthalene pitch and asphaltenes, have been studied comparing the two methods and showing how it is important to individuate the periodicities to explain growth or fragmentation paths in complex material. Structure and MW of naphthalene pitch and asphaltenes have been found, on the basis of their FFT and AF spectra. Naphthalene pitch has been found to be constituted of many compounds arriving just up MW of about 1000 Da, with most of compounds with MW around 400 Da, with different unsaturation degrees, and therefore the presence of naphthenic rings and aliphatic bridges. The findings from the present study indicate that asphaltenes present a polymeric structure with aromatic moieties with no more than 4–5 rings linked by aliphatic chains and with MW of molecular units extending up to 1000 Da.

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