Bertrand Plainchont

Jonathan Farjon

Nicolas Giraud

Magnetic Field Dependence of Spatial Frequency Encoding NMR

Keywords: high-resolution NMR, spatial frequency encoding, selective pulses, magnetic field gradient, magnetic field, sensitivity, resolution, pure shift, J-edited

The influence of the strength of the static magnetic field on pulse sequences based on the concept of spatial frequency encoding is addressed. The evolution of the slice selection process occurring during encoded excitation and refocusing pulses, as well as pure shift and J-edited refocusing blocks, is studied both theoretically and experimentally on a model ABX 1 H spin system. It is shown that carrying out gradient-encoded pulse sequences at higher field enhances the quality of the spin dynamics that is locally triggered in each encoded slice and results in spectra of better resolution and sensitivity.

Introduction

Spatial frequency encoding (SFE) NMR is at the root of a series of methodological developments that have paved the way to the acquisition of 1 H 1-D and 2-D experiments with unprecedented high resolution. This method is based on the general concept of gradient-encoded pulses, which have been extensively used for a wide range of applications in NMR spectroscopy, depending on whether the time evolution of a spin system (single scan or ultrafast NMR 1 ), the local spin composition (imaging 2 , diffusion 3 ), or more generally, any spin dynamics process need to be edited throughout the sample. 4 In the latter case, a SFE is needed to control locally the selectivity of the excitation, the decoupling, or the refocusing of individual spin nuclei from each site of the analyzed molecule, in contrast to the spatial encoding of a time domain that is performed in ultrafast NMR. 5 In this spirit, Zangger and Sterk had first shown that broadband homonuclear decoupling sequences based on a SFE can be performed efficiently by implementing a pure shift (also known as 𝛿-resolved) refocusing block. 6 More recently, we have shown that the selective refocusing of homonuclear scalar or residual dipolar couplings can also be encoded along the sample, according to the resonance frequency of each coupling partner. 7,8 We have also demonstrated that it is possible to combine pure shift and J-edited spin evolutions into fully tailored experiments and produce ultrahigh-resolution correlation spectra with exactly the desired analytical content. 9,10 The high flexibility of SFE methods has also opened the way to an implementation of both pure shift and J-edited blocks into real-time acquisition schemes. [11][12][13] In a recent paper, we have reported the acquisition of highresolution gradient-encoded correlation experiments on an oligomeric saccharide sample showing a highly crowded 1 H spectrum. 14 We have experimentally shown that operating at higher magnetic field leads to a better efficiency of pure shift as well as J-edited refocusing blocks based on a SFE, leading to noticeable resolution enhancements on this spectroscopically challenging sample. In the present work, we study the magnetic field dependence of SFE NMR on a model ABX 1 H spin system. Notably, we describe the evolution of spatial resolution and sensitivity when going to higher field. We use the theoretical formalism that we have introduced recently 15 to simulate the spatial properties of the investigated irradiation schemes throughout the sample during a slice selection process.

Magnetic Field Dependence of the Slice Selection Process

Excitation Step

SFE results from the simultaneous application of a selective pulse and a pulsed magnetic field gradient. The basic idea underlying this irradiation scheme is that proton spins with different resonance frequencies are selectively irradiated in different 'slices' of the sample. The key features of this process can be understood through the basic single gradient-encoded excitation pulse sequence depicted in Figure 1(a). In the following, 3-hydroxy-4,4,4-trichlorobutyric 𝛽-lactone 1 (Figure 1b) is chosen as a model system to study the magnetic field dependence of the SFE. During a gradient-encoded pulse, the strength of the total magnetic field depends on the position z in the sample due to the application of a pulsed field gradient (Figure 1c). As a result, each proton site H A , H B , and H X will interact with the encoded selective pulse only around the position z A (respectively, z B and z X ) that satisfies the relation: where 𝜈 A and 𝜎 A (respectively, 𝜈 B and 𝜎 B , and 𝜈 X and 𝜎 X ) are the resonance frequency and the shielding of H A (respectively, H B and H X ), B 0 the external static magnetic field generated by the superconducting magnet, 𝛾 H the gyromagnetic ratio of the proton, and G z the strength of the magnetic field gradient taken here along the z-axis.

𝜈 A,B,X = 𝛾 H 2π ⋅ { B 0 + G z ⋅ z A,B,X } { 1 -𝜎 A,B,X } (1)
Figure 2 shows the spatial distribution of the magnetization corresponding to the coherences A + B 𝛼 X 𝛼 and A 𝛼 B 𝛼 X + of H A and H X calculated at the end of a gradient-encoded excitation step, at 14.1 T (𝜈 H = 600 MHz) and 23.5 T (𝜈 H = 1 GHz). For each magnetic field strength B 0 , the strength of the encoding gradient G B 0 is set so that the same range of chemical shifts, corresponding to the spectrum of the analyzed compound, is encoded along the virtual NMR sample. A larger spectral width 𝛾G B 0 l, where 𝛾 is the gyromagnetic ratio and l the length of the sample that is detected by the receiver coil, is thus encoded along the sample at higher field. Moreover, the same E-Burp2 pulse of identical duration is used at both fields, which ensures the same spectral bandwidth 𝛺 B . For H X first, the region around 𝜈 X within which the corresponding transverse magnetization is created is found to be thinner at 23.5 T than at 14.1 T, which is coherent with the fact that at first approximation the fraction of the sample that is selected by the gradient-encoded pulse is proportional to 𝛺 B /(𝛾G B 0 l). 16 We also remark that the shape of the phase distribution within the region encoded around 𝜈 X is comparable at both fields, although being thinner at 23.5 T. Moreover for H A , it is apparent that at 14.1 T, a selectivity issue arises as transverse magnetization corresponding to the A + B 𝛼 X 𝛼 term is observed not only around 𝜈 A but also around 𝜈 B , which means that the gradient-encoded excitation pulse cannot select H A and H B in spatially resolved cross sections. For the simulation carried out at 23.5 T, the thinner region that is observed around 𝜈 A , combined with the greater difference between the Larmor frequencies of H A and H B , contributes to improve the selectivity of the excitation pulse. As a result, very few residual magnetization is detected around 𝜈 B , which indicates that at 23.5 T the selectivity of the gradientencoded pulse is good enough to excite H A and H B in distinct slices of the sample. Furthermore, the 1 H spectra resulting from the SFE described above can be reconstructed by adding the NMR signals that are locally encoded for each observable coherence of the model spin system 1. In Figure 3, the spatial distribution of NMR spectra generated locally by the gradient-encoded excitation pulse is shown as a pseudo-2-D plot at 14.1 and 23.5 T. At 14.1 T, we note that H A and H B are encoded in overlapped cross sections, as it is highlighted by the amplitude profile displayed within the NMR tube. The overall spectrum that is the sum of these subspectra shows distorted lines, which arises directly from this spatial resolution issue. Again, it is apparent that operating at higher field allows for solving this problem, as at 23.5 T two cross sections are clearly distinguishable at

A α B α X + A α B α X + A + B α X α ν X ν X ν B ν A ν B ν A 100 °100 °A+ B α X α
X ν B ν A ν X ν X ν B ν A ν A ν B ν X ν B ν A Figure 3.
The amplitude profile of the NMR signal evaluated on the first point of each locally generated free induction decay is represented in cylindrical coordinates at 14.1 T (a) and 23.5 T (b). For each magnetic field, the spatial distribution of virtual proton spectra is reported in pseudo-2-D plots where the vertical axis refers to the position z in the NMR sample. On these maps, blue and red contours are positive and negative, respectively 𝜈 A and 𝜈 B , respectively, leading to a 1 H spectrum showing the classical roof effect expected for a second-order spin system.

In conclusion for this part, the implementation of a SFE at higher magnetic field allows for improving the spatial resolution of the slice selection process, by selecting thinner cross sections throughout the sample.

Influence of the Shape of the Gradient-encoded Pulse

In a previous paper, we had shown that among the different shaped pulses designed for the purpose of selective irradiations, not all of them are suitable for undergoing a SFE. 15 We had established that a key feature for yielding a proper slice selection process is the ability for a given shape to maintain the distribution of magnetization coherent along the encoded cross section. Figure 4 shows the evolution of the slice selection process simulated at 14.1 and 23.5 T for a series of excitation shaped pulses. Their duration was set so that they all have the same spectral bandwidth. For every shape, we observe a thinning of the encoded slices when going to higher field, as it can be monitored on the signals located at 𝜈 X . An improvement of the slice selection process is notably observed at higher field for E-Burp2 (90 ∘ ), Esnob (270 ∘ ), as well as Gaussian pulses calibrated for both 90 ∘ and 270 ∘ , as it is illustrated by the presence at 23.5 T of two distinct slices at 𝜈 A and 𝜈 B . We note that this was less predictable for the Gaussian 90 ∘ pulse that had been previously shown to suffer from a problem of phase coherence upon gradient encoding. These results highlight the suitability of E-Burp2, Esnob, and Gaussian shapes for SFE NMR.

Influence of B 0 on a Gradient-encoded Refocusing Pulse

Gradient-encoded refocusing pulses are key actors of the spin dynamics that is locally triggered in each region of the sample, because they have been shown to improve greatly the spatial selectivity of the refocusing blocks within which they are implemented. In order to evaluate the influence of B 0 on this kind of selective pulse, we have simulated the action of a gradient-encoded Reburp π pulse on transverse magnetization initially taken along the y-axis and composed of selected coherences of H A and H X , at 14.1 and 23.5 T. In Figure 5, the spatial distribution of the resulting magnetization is shown for both magnetic fields. Similarly to what is observed for the excitation case, the cross sections within which the magnetization is properly refocused by the refocusing block are found to be thinner at higher field for both proton sites, whereas outside of these regions the initial transverse magnetization is fully dephased. We also note that the height of the cross section encoded at 𝜈 A at 23.5 T allows for refocusing with a high

B α X + (b) 23.5 T A α B α X + ν X ν B ν A A + B α X α A + B α X α

From 1-D to 2-D Spatial Frequency Encoding NMR

Following on from the above, the study of the magnetic field dependence of SFE NMR can be extended to the general case of a pulse sequence composed of several gradient-encoded pulses.

As an illustration, we have acquired a 2-D 𝜔 1 -homonuclear decoupled experiments 17 at two different magnetic fields, on 10 mg of 1 dissolved in 700 μl of deuterated chloroform. We remind that this pulse sequence implements a pure shift block during the indirect evolution delay, which yields a 2-D phased spectrum with only diagonal peaks showing a singlet structure in the indirect domain, and a normal multiplet structure in the direct domain. For this experimental part, we have chosen to monitor the resolution enhancement that can be achieved in the pure shift dimension when going from 7.05 T (𝜈 H = 300 MHz) to 14.1 T. The resulting spectra are shown in Figure 6 together with the amplitude profiles that were calculated after the excitation step and at the end of the pure shift block of this pulse sequence. At 7.05 T, we observe that neither the excitation step nor the pure shift block can achieve a slice selection process of sufficient spatial resolution for H A and H B . On the resulting 2-D spectrum, it is apparent both protons were encoded in the same cross section, as it is illustrated by the shape of the distorted correlation appearing around 𝜈 A and 𝜈 B . Conversely, at 14.1 T, we note that the efficiency of the refocusing block allows for refining the slice selection process initially created during the excitation step, to a point where H A and H B can be selectively decoupled. The better spatial resolution that is reached at this field can be straightforwardly correlated with the high spectral resolution achieved at 𝜈 A and 𝜈 B . The projection displayed along the indirect domain allows for observing the singlet structure of each correlation, which highlights the higher efficiency of the homonuclear decoupling sequence at 14.1 T than at 7.05 T.

Magnetic Field Dependence of Sensitivity

One frequent reservation that is sometimes expressed about the relevance of SFE techniques regards their low sensitivity.

To tackle this problem, it is important to discuss here whether acquiring spatially encoded spectra at higher field has an overall beneficial effect on sensitivity. In this section, we aim thus at quantifying the relationship between the sensitivity of a gradient-encoded experiment and B 0 . We have studied, for eight different magnetic fields that are representative of the range of NMR spectrometers commercially available to date, the evolution of the sensitivity of a single gradient-encoded pulse experiment. The integration of the signal of H X and H A has been calculated for each magnetic field and normalized by the signal arising from the same semiselective excitation pulse without SFE (Figure 7). The resulting ratio I encoded /I selective provides a direct quantification of the fraction of the sample within which H X and H A are encoded, while allowing to throw off the contribution of the intrinsic probehead sensitivity and the Boltzmann population of the observed spin. Again, we have set the gradient strength so that the spectral width that is encoded along the virtual sample matches exactly the proton spectrum of 1. As expected, I encoded /I selective values range from 4 to 18% and decrease with B 0 , which reflects the thinning of the encoded cross section with the strength of the magnetic field. Furthermore, as I encoded is proportional to the spectral bandwidth of the encoded pulse, the resulting ratio should, to a first approximation, be proportional to B 0 -1 . Figure 7(a) shows the corresponding trend curve described by Pell and Keeler 16 that we have adjusted to the ratio calculated at 23.5 T to account for the contribution of the shaped pulse to the slice selection process. For H X , the evolution of the ratios is in agreement with this trend curve. For H A , however, although the ratios obtained at higher field (14.1-23.5 T) follow the trend curve, those determined at lower field (7.05, 9.4, and 11.7 T) are higher than expected, which is explained by the fact that the slice selection induced by the SFE could not be operated properly, resulting in an overlap of the two slices within which H A and H B are encoded, and hence the observed deviations. From this result, it is now possible to extrapolate the overall dependence of the sensitivity of a single gradient-encoded pulse experiment on B 0 . For the homonuclear case, and if we

3.6 ν X ν X ν X ν B ν A ν A ν B ν X ν B ν A ν A ν B
S∕N ∝ n ⋅ 𝛾 5∕2 H ⋅ B 3∕2 0 (2)
where n is the number of observed proton nuclei in the sample. The value of the integration that can be derived from I encoded to account for (i) the influence of the magnetic field on the Boltzmann population of the observed proton spins, (ii) the signal induced in the receiver coil at detection, and (iii) the noise has been calculated for different B 0 s (Figure 7b). On the one hand, we note that the overall sensitivity of the spatially frequency-encoded experiment increases with the strength of the magnetic field, despite the selection of thinner slices upon the gradient-encoded excitation step. On the other hand, for H A , the NMR signal acquired at lower field is weaker than what could be expected from the ideal curve adjusted to the sensitivity measured at 23.5 T, which underlines again the spatial resolution issue previously described at lower field. These results highlight the relevance of implementing spatially frequency-encoded pulse sequences at higher magnetic field, in so far as it contributes to enhance the three inextricably linked features that are the dispersion of the resonance frequencies (i.e., the spectral resolution), the spatial resolution of the slice selection process, and the sensitivity -although this latter point is modulated by the slice selection issue.

Conclusion

In this article, we have described the magnetic field dependence of NMR pulse sequences based on a SFE of the sample. We have highlighted the evolution of the key features that drive sensitivity and resolution in gradient-encoded pulse sequences, from the basic irradiation schemes, to state-of-the-art refocusing blocks that are nowadays routinely implemented in high-resolution experiments dedicated to the extraction of 1 H chemical shifts and/or homonuclear couplings. We have shown that operating at higher field leads to a better spatial resolution of the slice selection process, together with a moderate sensitivity enhancement of the resulting data. The combination of SFE techniques with high magnetic fields shades a new light on the trade-off that has classically to be found between sensitivity and resolution in SFE NMR. Indeed, the main limitation of high-resolution techniques based on this method regards the sensitivity penalty that has to be paid when protons with very close chemical shifts have to be decoupled, because it implies the use of highly selective pulses. [START_REF] Foroozandeh | [END_REF] We remark that operating at higher field amounts to increasing the chemical shift dispersion while keeping the same selectivity for the gradient-encoded pulses, which is a way to address this issue without sacrificing sensitivity. The implementation of SFE methods on high field spectrometers should thus be particularly suitable for the analysis of larger molecular systems showing overcrowded 1 H spectra.

1 Figure 1 .

 11 Figure 1. (a) The single gradient-encoded pulse sequence. The delays t rec. and t acq. are the recovery and the acquisition times, respectively. The black ellipsoidal shape on the proton channel ( 1 H) corresponds to a shaped excitation pulse. The white rectangular bar on the pulsed field gradient (PFG) channel refers to the application of a rectangular-shaped z field gradient. (b) The structure of the model 1 H ABX spin system 1. (c) Schematic representation of the spatial frequency encoding performed during the single gradient-encoded shaped pulse experiment shown in (a). The receiver coil is represented in orange in order to materialize the total height of the sample that is detected. The z gradient coils are pictured in red. Yellow arrows symbolize the magnetic field gradient

Figure 2 .

 2 Figure 2. The spatial variation of the magnetization calculated at (a) 14.1 and (b) 23.5 T at the end of a gradient-encoded excitation pulse is represented with 2 viewing angles inside the NMR tube, for (top) A 𝛼 B 𝛼 X + and (bottom) A + B 𝛼 X 𝛼 coherences. An E-Burp2 pulse of duration 60 ms was used for the selective irradiation. The virtual sample was divided into 401 slices of equal height around each region of interest, to which a positiondependent magnetic field value was assigned

  chemical shift (ppm) Encoded spectral width ~ 2000 Hz Encoded spectral width ~ 2000 Hz

  ν

Figure 4 .

 4 Figure 4. The evolution of the amplitude profile generated by a gradient-encoded excitation step is represented at 14.1 and 23.5 T for (a) an E-Burp2 90 ∘ pulse of 60 ms, (b) an Esnob 270 ∘ pulse of 20 ms, (c) a Gaussian 90 ∘ pulse of 20 ms, and (d) a Gaussian 270 ∘ pulse of 20 ms

Figure 5 .

 5 Figure 5. The spatial variation of the magnetization calculated at the end of gradient-encoded Reburp 180 ∘ pulse of 60 ms at (a) 14.1 T and (b) 23.5 T, for (top) A 𝛼 B 𝛼 X + and (bottom) A + B 𝛼 X 𝛼 coherences

Figure 6 .

 6 Figure 6. The amplitude profiles calculated after the gradient-encoded excitation pulse and at the end of the pure shift block of a 2-D 1 H 𝜔 1 -homonuclear decoupled experiment simulated on 1 at (a) 7.05 T and (b) 14.1 T. The corresponding experimental 2-D spectra acquired are also shown at both fields. E-Burp2 and Reburp pulses of 60 ms were used for the gradient-encoded excitation and the pure shift block, respectively. The strength of the gradient coil was set so as to encode along the sample a spectral width of 6.4 and 6.3 ppm at 7.05 and 14.1 T, respectively

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Volume 5, 2016 © 2016 John Wiley & Sons, Ltd.

© 2016 John Wiley & Sons, Ltd.Volume 5, 2016

© 2016 John Wiley & Sons, Ltd.

© 2016 John Wiley & Sons, Ltd. Volume 5, 2016

Acknowledgment

This work was supported by the French Research Agency (ANR-2011-JS08-009-01).

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Optimization of laser-induced breakdown spectroscopy parameters from the design of experiments for multi-element qualitative analysis in river sediment

Keywords: LIBS, Design of experiments, Central composite design, Fractional factorial design, Sediment

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Laser-induced breakdown spectroscopy (LIBS) is a fast, low analytical cost, and environmentally clean technique, which does not require the use of reagents for sample preparation [START_REF] Pasquini | Laser-induced breakdown spectroscopy[END_REF]. However, limitations of LIBS, compared to classical analytical techniques, are lower sensitivity and precision, due to matrix effects. The sensitivity of the single pulse (SP) LIBS system can be increased using different kinds of experimental setups, such as double pulse (DP) LIBS [START_REF] Nicolodelli | Signal enhancement in collinear double-pulse laser-induced breakdown spectroscopy applied to different soils[END_REF][START_REF] Nicolodelli | Double-pulse laser induced breakdown spectroscopy in orthogonal beam geometry to enhance line emission intensity from agricultural samples[END_REF], resonance-enhanced LIBS [START_REF] Goueguel | Investigation of resonance-enhanced laser-induced breakdown spectroscopy for analysis of aluminium alloys[END_REF][START_REF] Nicolodelli | Determination of Pb in soils by double-pulse laser-induced breakdown spectroscopy assisted by continuum wave-diode laser-induced fluorescence[END_REF], microwave-assisted LIBS [START_REF] Liu | Elemental analysis by microwave-assisted laser-induced breakdown spectroscopy: Evaluation on ceramics[END_REF], spark discharge LIBS [START_REF] Nassef | Spark discharge assisted laser induced breakdown spectroscopy[END_REF][START_REF] Lima | Determinations of phosphorus in fertilizers by spark discharge-assisted laser-induced breakdown spectroscopy[END_REF], spatial confinement of laser-induced plasma [START_REF] Popov | Spatial confinement of laser-induced plasma to enhance LIBS sensitivity for trace elements determination in soils[END_REF], and the use of a micro-torch [START_REF] Liu | Laserinduced breakdown spectroscopy enhanced by a micro torch[END_REF]. In addition to instrumental techniques to improve the sensitivity of LIBS, strategies involving sample pretreatment have been used, such as the deposition of nanoparticles onto samples [START_REF] De Giacomo | Nanoparticle-enhanced laser-induced breakdown spectroscopy of metallic samples[END_REF] and the addition of a salt containing easily ionizable elements [START_REF] De Morais | Laser-induced breakdown spectroscopy determination of K in biochar-based fertilizers in the presence of easily ionizable element[END_REF].

In LIBS, the measurement precision is affected by matrix effects [START_REF] Noll | Laser-Induced Breakdown Spectroscopy -fundamentals and applications[END_REF], the intensity of the emitted nanosecond laser, and the nonlinear interaction between the nanosecond laser and the sample matrix [START_REF] Noll | Laser-Induced Breakdown Spectroscopy -fundamentals and applications[END_REF]. One of the ways to overcome this limitation is to obtain tens or hundreds of spectra distributed in different regions of the sample, to decrease the matrix effects and increase precision [START_REF]Laser-Induced Breakdown Spectroscopy: Theory and Applications[END_REF]. Some parameters that affect the plasma, such as accumulated pulses [START_REF] Castle | Variables influencing the precision of laser-induced breakdown spectroscopy measurements[END_REF][START_REF] Gondal | The role of various binding materials for trace elemental analysis of powder samples using laser-induced breakdown spectroscopy[END_REF], the wavelength [START_REF] Hahn | Laser-induced breakdown spectroscopy (LIBS), part I: Review of basic diagnostics and plasmaparticle interactions: Still-challenging issues within the analytical plasma community[END_REF] and energy of the nanosecond lasers [START_REF] Vadillo | Effect of plasma shielding on laser ablation rate of pure metals at reduced pressure[END_REF][START_REF] Singh | Laser-Induced Breakdown Spectroscopy[END_REF], and the temporal parameters (delay time and gate width) [START_REF] Ciucci | Trace pollutants analysis in soil by a timeresolved laser-induced breakdown spectroscopy technique[END_REF] play important roles in the optimization of the signal-to-noise (S/N) ratio, with their ideal values varying according to the sample composition. In DP LIBS, the inter-pulse delay is an important factor to consider for improving plasma emission [START_REF] Nakamura | Determination of an Iron Suspension in Water by Laser-Induced Breakdown Spectroscopy with Two Sequential Laser Pulses[END_REF].

Design of experiments (DOE), a methodology based on mathematical and statistical theory, is used to plan and conduct experiments by means of the analysis and interpretation of data obtained from the experiments. DOE allows input variables to be manipulated to investigate their effects on the measured response variable [START_REF] Durakovic | Design of experiments application, concepts, examples: State of the art[END_REF]. When there are many factors to be optimized, it is necessary to select the variables that have the greatest effects. Fractional factorial designs can be used to perform the screening of factors [START_REF] Atkinson | Optimum Experimental Designs[END_REF], but since they only allow fitting of first order models, another DOE is needed to detect curvature. A three-level design (3k factorial design) is often performed to fit a second order model, but as the number of factors increases, it becomes inefficient and impractical, so a central composite design (CCD) may be used instead.

CCD is a fraction of the 3k factorial design, but it does not use unnecessary degrees of freedom (which increases the cost of the experiment) [START_REF] Mason | Statistical Design and Analysis of Experiments: With Applications to Engineering and Science[END_REF]. The main advantage of adopting a DOE strategy, instead of testing all the different combinations of experimental parameters, consists in evidencing interactive effects among multiple parameters, reducing analysis time and costs [START_REF] Yu | Response surface methodology for optimizing LIBS testing parameters: A case to conduct the elemental contents analysis in soil[END_REF]. The DOE approach has been combined with LIBS to define the most appropriate analytical parameters. For example, factorial design was used for samples of sugar cane [START_REF] Romera | Expeditious prediction of fiber content in sugar cane: An analytical possibility with LIBS and chemometrics[END_REF] and cassava flour [START_REF] Costa | Direct Determination of Ca, K and Mg in Cassava Flour Samples by Laser-Induced Breakdown Spectroscopy (LIBS)[END_REF], fractional factorial design for fertilizers [START_REF] Andrade | Direct Determination of Contaminants and Major and Minor Nutrients in Solid Fertilizers Using Laser-Induced Breakdown Spectroscopy (LIBS)[END_REF], and CCD for soils [START_REF] Yu | Response surface methodology for optimizing LIBS testing parameters: A case to conduct the elemental contents analysis in soil[END_REF][START_REF] Costa | Qualitative and Quantitative Analysis of Soils Using Laser-Induced Breakdown Spectroscopy and Chemometrics Tools[END_REF]. However, no studies have used DOE to optimize instrumental parameters in LIBS, considering SP LIBS with different lasers and the DP LIBS configuration.

The LIBS technique has been applied to investigate the elemental compositions of marine [START_REF] Barbini | On board LIBS analysis of marine sediments collected during the XVI Italian campaign in Antarctica[END_REF][START_REF] Lazic | Self-absorption model in quantitative laser induced breakdown spectroscopy measurements on soils and sediments[END_REF][START_REF] Lazic | Underwater sediment analyses by laser induced breakdown spectroscopy and calibration procedure for fluctuating plasma parameters[END_REF], river [START_REF] Austria | Laser-induced breakdown spectroscopy for the quantitative analysis of metals in sediments using natural zeolite matrix[END_REF], and mining [START_REF] Austria | Spectral fitting approach for the determination of enrichment and contamination factors in mining sediments using laser-induced breakdown spectroscopy[END_REF] sediments. However, there have been no studies concerning optimization of the key parameters affecting the analysis of complex samples such as sediments, whose matrix effects are increased by the fact that they present different characteristics in terms of texture, granulometry (contents of sand, silt, and clay), and chemical composition [START_REF] Han | Application of laser-induced breakdown spectroscopy to Arctic sediments in the Chukchi Sea[END_REF]. LIBS combined with DOE has excellent potential for applications involving sediments.

In the present work, the key parameters influencing the LIBS spectra for multielement analysis of river sediment were optimized using CCD for SP LIBS with different wavelengths, and the combination of two DOE for DP LIBS, 2 6-2 fractional factorial designs (one-quarter fraction) and CCD. The optimization was done to qualitatively analyze the main elements present in the river sediments. The parameters considered were laser energy, delay time, gate width, and the number of accumulated pulses. For DP LIBS, the inter-pulse delay time was also evaluated.

Materials and methods

Sample

One sediment sample from the Piracicaba River in Brazil (22°36'01.8" S, 48°17'53.5" W) was employed in this work to carry out all the experiments, to analyze only the effect of the instrumental variables on the response. The sample was collected using a core sampler to a depth of 15 cm in the sediment layer. The sample was freezedried, ground, and sieved through a 100-mesh sieve. Portions (500 mg) of the sample were compacted into pellets, using a pressure of 5 tons for 1 min.

LIBS instrumentation

The LIBS system used in this study was assembled in the laboratory, using two Nd:YAG pulsed lasers, and could operate in two different modes: (i) SP LIBS with a 1064 nm laser (Q-switched Ultra, Quantel) reaching the sample at an angle of 90°, or with a 532 nm laser (Brilliant, Quantel) reaching the sample at an angle of 45°, and (ii) DP LIBS in crossed beam configuration, combining the two different wavelength lasers, with the first pulse at 1064 nm and the second pulse at 532 nm, or with the first pulse at 532 nm and the second pulse at 1064 nm. The 1064 nm laser pulse had maximum energy of 50 mJ, width of 8 ns, and repetition rate of 20 Hz, while the 532 nm laser pulse had maximum energy of 180 mJ, width of 4 ns, and repetition rate of 10 Hz, coupled with a second harmonic generator module. In the case of SP LIBS, a pulse delay generator (model 9618, Quantum Composers) was used for temporal control of the laser and the data acquisition system, while for DP LIBS, it was used for temporal control of the two lasers, and the data acquisition system. An echelle spectrometer (Aryelle Butterfly 400, LTB) was used to detect and select the wavelengths. The highresolution spectrometer was equipped with an intensified charge-coupled device (ICCD) with 1024 × 1024 pixels, operated in two spectral bands (175-330 and 275-750 nm, with a resolution of 13-24 and 29-80 pm, respectively).

Spectra reproducibility

A study was carried out to evaluate how the number of spectra affects the precision of the average S/N ratio, through the simulation method consisting of the resampling of subsamples [START_REF] De O. Leite | Sample size for full-sib family evaluation in sugarcane[END_REF][START_REF] Da Silva | Tamanho de amostra para caracterização morfológica de frutos de pimenteira[END_REF]. The sediment sample was analyzed by SP LIBS, and the parameters were chosen at random from the experimental runs of the CCD for SP LIBS with the 1064 nm laser. Therefore, the 1064 nm laser energy fixed at 46 mJ, the delay time at 0.5 µs, and the gate width at 5 µs. A total of 61 spectra were acquired for different regions of the pellet, with the accumulation of 9 laser pulses.

The spectra were processed using software developed in the Python programming language. After excluding outliers, using the scalar product between the average and each measured spectrum, baseline correction was performed close to each peak evaluated (Table 1) [START_REF] Marangoni | Phosphorus quantification in fertilizers using laser induced breakdown spectroscopy (LIBS): A methodology of analysis to correct physical matrix effects[END_REF]. The S/N ratio for each analyte was calculated by dividing the maximum intensity of each emission line (peak height) by the standard deviation of the noise adjacent to the peak [START_REF] Hahn | Laser-induced breakdown spectroscopy (LIBS), part II: Review of instrumental and methodological approaches to material analysis and applications to different fields[END_REF], resulting in 61 S/N ratios being obtained. The R program (version 3.6.0) [START_REF] Core | R: A language and environmente for statistical computing[END_REF] was used to estimate the 95% confidence interval (CI) for the mean S/N ratio of the 61 spectra. Random subsets of the 61 spectra were simulated, with sizes ranging from 2 to 60 spectra. For each subset size, 1000 random samples were simulated. For each analyte, the mean of the S/N ratio outside the 95% CI as a function of the number of spectra for each measurement is shown in However, when the number of spectra per sample increased, the analysis time is also increased, so it is essential to establish a quantity of pulses needed to ensure the desired precision of the measurements, without losing the rapid analysis advantage of the LIBS technique. Use of this method enables determination of the number of spectra required in each measurement, bypassing the problems of lack of homogeneity of solid and complex samples, such as sediments, and plasma variables, which change from shot to shot, affecting the measurement precision [START_REF] Miziolek | Laser Induced Breakdown Spectroscopy (LIBS): Fundamentals and Applications[END_REF][START_REF] Wachter | Determination of Uranium in Solution Using Laser-Induced Breakdown Spectroscopy[END_REF]. With the aim of increasing the precision of the measurements and overcoming the sampling problems that affect the spectral reproducibility of the LIBS analyses, while preserving the advantages of the LIBS technique in allowing rapid multi-element analysis, the number of spectra was fixed at 45 for performing all the DOE.

Design of experiments 2.4.1 Central composite design for SP LIBS with 1064 and 532 nm lasers

The central composite design (CCD) was implemented for optimization of the S/ N ratio for all the elements evaluated (Table 1) in a fluvial sediment sample, with the aim of obtaining information about the linear, interaction, and quadratic effects, in order to identify a condition suitable for most of the elements. Four independent factors that influence LIBS analysis were selected for optimization: (i) laser energy (LE), (ii) delay time (DT), (iii) gate width (GW), and (iv) accumulated pulses (AP). These factors were optimized for the SP LIBS system operating with the 1064 nm laser and with the 532 nm laser.

The design had a total of N=k 2 +2 k +c p experimental runs, where k is the number of factors and c p is the number of replicates at the central point. In this work, the numbers of experimental runs at factorial, axial, and central points were 16, 8, and 2, respectively, so N was 26. The CCD model was as follows [START_REF] Mason | Statistical Design and Analysis of Experiments: With Applications to Engineering and Science[END_REF]:

y=β 0 + ∑ i=1 k β i x i + ∑ i=1 k β ii x i 2 ∑ ∑ i< j=2 k β ij x i x j +ε (1)
where, y is the response variable, β are the regression coefficients of the model, x is the independent variable, and ε is the random error component. The model errors were assumed to be a random variable, normally and independently distributed, with zero mean and σ² constant variance.

The upper and lower limits for the factors were based on previous studies [START_REF] Nicolodelli | Signal enhancement in collinear double-pulse laser-induced breakdown spectroscopy applied to different soils[END_REF][START_REF] Nicolodelli | Double-pulse laser induced breakdown spectroscopy in orthogonal beam geometry to enhance line emission intensity from agricultural samples[END_REF].

As the CCD model used was rotatable, the distance from the axial points to the central point, α, was ± 2. The values for the critical factors were calculated and studied at five levels (Zα, Z1, 0, +1, + α). The choice of α depends on k, and can be calculated by the following equation [START_REF] Mason | Statistical Design and Analysis of Experiments: With Applications to Engineering and Science[END_REF]:

α =(2¿¿ k ) 1 4 ¿ (2)
For the SP LIBS system operating with the 1064 nm laser, the levels studied for each factor were as follows:

Factors optimization for DP LIBS

The optimization of the S/N ratio for the same analytes studied using SP LIBS (Table 1) was performed for the fluvial sediment sample using DP LIBS, combining two DOE, because there were 6 factors to be optimized. First, two 2 6-2 fractional factorial designs (one-quarter fraction) were implemented for DP LIBS in the crossed beam configuration, with different laser sequences (one sequence was 1064 and then 532 nm, and the other was 532 and then 1064 nm), for screening in order to discard non-significant variables. A CCD was then performed to maximize the response using the best laser sequence.

The 2 6-2 fractional factorial designs were performed to screen six independent factors that influenced the analysis using DP LIBS: (i) LE (1064 nm), (ii) LE (532 nm), (iii) AP, (iv) GW, (v) inter-pulse delay (ID), and (vi) DT. This design has resolution IV, so no main effects are aliased with any other, but 2-factor interactions are aliased with other 2-factor interactions. The number of experimental runs was 16, but two runs were also carried out at the central point, in order to estimate the experimental error, so the total number of runs was 18. The linear model for the fractional factorial designs was as follows [START_REF] Mason | Statistical Design and Analysis of Experiments: With Applications to Engineering and Science[END_REF]:

y=β 0 + ∑ i=1 k β i x i + ε (3)
where, y is the response variable, β are the regression coefficients of the model, x is the independent variable, and ε is the random error component. The model errors were also assumed to be a random variable, normally and independently distributed, with zero mean and σ² constant variance.

Previous studies have been carried out to identify the maximum and minimum factor limits [START_REF] Nicolodelli | Signal enhancement in collinear double-pulse laser-induced breakdown spectroscopy applied to different soils[END_REF][START_REF] Nicolodelli | Double-pulse laser induced breakdown spectroscopy in orthogonal beam geometry to enhance line emission intensity from agricultural samples[END_REF]

Data analysis

The spectra have been analyzed as described in section 2.3. The coefficient of variation (CV) for each element was calculated for all DOE performed to assess the variability of the data and, thus, to know if the change in the values of the factors causes variation in the response. The regression models were evaluated by analysis of variance, using R software (version 3.6.0) [START_REF] Core | R: A language and environmente for statistical computing[END_REF]. The coefficients of determination (R 2 ) were calculated for the models and the relative importance (RI) for model components [START_REF] Groemping | Relative Importance for Linear Regression in R: The Package relaimpo[END_REF].

R 2 is a measure of the fit quality of a model, when the value of R 2 is low, it means that little of the variation in the response is attributable to its dependence on the factors. For linear models, RI provides a decomposition of the explained variation of the model into non-negative contributions, calculated based on the covariance matrix [START_REF] Lindeman | Introduction to Bivariate and Multivariate Analysis[END_REF].

Results and discussion

Central composite design for SP LIBS with 1064 and 532 nm lasers

The results of the central composite design (CCD) for the SP LIBS system operating with the 1064 nm laser showed that the linear and quadratic effects of laser energy (LE) explained at most 10% of the variability for V (Table 2), with the contour graphs showing that its influence was very small (Figure 2). Hence, the lowest LE value corresponded to the optimized value. The delay time (DT) variable influenced the responses for all the elements, with the exception of Cu (Table 2), with the elements most affected being B (RI = 70%), Co (RI = 75%), and Fe (RI = 39%). For B and Co, the minimum DT value maximized the S/N ratio, while the opposite effect was observed for Fe (Figure 2). The highest coefficients of variation (CV) were found for B and Co, so the optimized DT corresponded to its lowest value. The gate width (GW) variable showed effects for 7 elements (Ca, Cr, Mg, Mn, Na, Sr, and V) (Table 2), with higher GW values resulting in maximization of the S/N ratio (Figure 2). The accumulated pulses (AP) variable showed effects for all the analytes, except Fe and Sr (Table 2). In cases where AP was significant, maximization of the S/N ratio occurred at the maximum AP value (Figure 2). The sum of the interactions between the factors represented less than 10% for all the elements, except Fe, where the LE*GW interaction represented 14%, and Zn, where DT*GW represented 21%. Therefore, the optimized factors for the SP LIBS system operating with the 1064 nm laser were LE = 34 mJ, DT = 0.2 μs, GW = s, GW = 20 μs, GW = s, and AP = 10. For the SP LIBS system operating at 532 nm, the CCD results showed that LE only affected the responses for B, Fe, Co, and Zn, with RI of 10, 11, 8, and 13%, respectively (Table 2). Among these elements, Fe presented the highest CV of 64%, corresponding to the greatest effect of LE. Since the lowest LE value maximized the S/ N ratio for Fe (Figure 3), while for the other elements LE had little or no effect, the lowest value of LE was adopted as the optimum. An effect of DT was observed for all the elements (Table 2). Since the lowest value was only indicated for B and Co (Figure 3), the highest value of DT was adopted as optimal. Among the elements whose response was affected by GW (Table 2), all showed the highest response at the maximum value, with the exception of Cr (Figure 3). All the elements showed an effect of AP (Table 2), with the highest response at the maximum value, with the exception of Fe (Figure 3). The sum of the interactions between the factors represented less than 10% for all elements, except for Co, where the LE*DT and GW*AP interactions both represented 6.5%, and for Cu, where the LE*GW, LE*AP, and GW*AP interactions represented 14, 8, and 10%, respectively. For the SP LIBS system operating at 532 nm (Table 2 andFigure The optimization of the factors that influenced the multi-element analysis of sediment by SP LIBS (1064 and 532 nm lasers) showed that in cases where the CV was less than 10%, the response variation in all the runs did not have a significant effect, regardless of the combination of values studied for each factor. In LIBS, the breakdown events dramatically change the spectral line intensities, consequently increasing the CV of the measurements. For geochemical analyses, CV values between 5 and 20% are generally acceptable [START_REF]Laser-Induced Breakdown Spectroscopy: Theory and Applications[END_REF]. The RI of the factors studied for each element helped to identify the most important variables from the percentage contributions.

For both SP LIBS systems, the lowest LE value was chosen as the optimum, because LE in the studied range had little or no influence on the S/N ratio of the elements evaluated. Studies have shown that the intensities of the emission lines of the LIBS spectrum increase with the laser energy, under constant irradiance [START_REF] Aguilera | Characterization of laser-induced plasmas by emission spectroscopy with curve-of-growth measurements. Part II: Effect of the focusing distance and the pulse energy[END_REF][START_REF] De Carvalho | Effects of laser focusing and fluence on the analysis of pellets of plant materials by laser-induced breakdown spectroscopy[END_REF].

However, increasing the intensity of the emission lines can lead to increased noise, so it is important to evaluate the S/N ratio [START_REF] Hahn | Laser-induced breakdown spectroscopy (LIBS), part II: Review of instrumental and methodological approaches to material analysis and applications to different fields[END_REF].

For both SP LIBS systems, the highest GW and AP values maximized the S/N ratio. However, for the 1064 nm laser, the lowest DT value maximized the S/N ratio for most elements, while for the 532 nm laser the highest value of this factor maximized the response for most elements. These results were related to the mechanisms of plasma generation and formation. The cascade-like growth of the electron density (inverse bremsstrahlung) is more favorable for longer wavelength lasers [START_REF] Cabalin | Experimental determination of laser induced breakdown thresholds of metals under nanosecond Q-switched laser operation[END_REF], while multiphoton ionization plays an important role for short wavelength lasers [START_REF] Singh | Laser-Induced Breakdown Spectroscopy[END_REF].

Factors optimization for DP LIBS

Two 2 6-2 fractional factorial designs were implemented for DP LIBS with different laser sequences (one sequence was 1064-532 nm, and the other was 532-1064 nm), for choosing the best laser sequence and screening to discard non-significant variables. The 2 6-2 fractional factorial design with the 1064-532 nm laser sequence (Table 3) showed that the 1064 nm LE had no influence on the S/N ratio, for any element, while the 532 nm LE explained at most 10% of the variability (for Fe). The other factors had greater effects on the S/N ratio, with effects ≤43% for AP (10 elements: B, Ca, Co, Cr, Mg, Mn, Na, P, V, and Zn), ≤29% for GW (4 elements: Cr, Mg, Mn, and Na), ≤66% for inter-pulse delay (ID) (6 elements: B, Co, Mg, Ni, P, and Zn), and ≤58% for DT (10 elements: B, Co, Cu, Fe, Mg, Mn, Ni, P, Sr, and Zn). The 2 6-2 fractional factorial design with the 532-1064 nm laser sequence (Table 3) again showed that the 1064 nm LE had no influence on the S/N ratio for any element, while the 532 nm LE explained at most 20% of the variability (for Zn). The other factors had greater influence on the S/N ratio, with effects ≤42% for AP (11 elements: B, Ca, Co, Cu, Cr, Mg, Mn, Ni, P, V, and Zn), ≤41% for GW (4 elements: Cr, Mg, Mn, and Sr), ≤85% for ID (6 elements: B, Ca, Co, Fe, Mg, and Na), and ≤43% for DT ( The 2 6-2 fractional factorial design with the 532-1064 nm laser sequence showed better performance (higher S/N ratios), compared to the 1064-532 nm laser sequence.

This was expected, because the background emission was higher when the 1064 nm laser was used for sample ablation [START_REF] Nicolodelli | Signal enhancement in collinear double-pulse laser-induced breakdown spectroscopy applied to different soils[END_REF]. Hence, the 2 6-2 fractional factorial design with the 532-1064 nm laser sequence, where the 1064 nm laser was used to reheat the plasma, was optimized using a CCD.

According to the results obtained by 2 6-2 fractional factorial design with the 532-1064 nm laser sequence, the values of the factors that were fixed were chosen, and then the factors that had the greatest effects on the S/N ratio were optimized through the CCD. The results showed that for the 2 6-2 fractional factorial design with the 532-1064 nm laser sequence, the LE for the 1064 nm laser did not influence the S/N ratio for any element, while the LE for the 532 nm pulse explained very little of the data variability.

Therefore, these two factors were fixed at their lowest values (34 and 35 mJ for the 1064 and 532 nm lasers, respectively) for implementation of the CCD. Higher values of AP resulted in maximization of the S/N ratio for all the elements influenced by this factor (with the exception of Ca, for which the RI value was only 2%). In addition, it was observed that for the SP LIBS system operating with the 1064 and 532 nm lasers, the highest S/N ratio also occurred at the maximum AP value. Therefore, this factor was fixed at its highest value (10 accumulated pulses) for implementation of the CCD. Since the factors GW, ID, and DT had the greatest effects on the S/N ratio, they were selected for refining the optimal conditions.

In the CCD experiment, Sr presented little variation of the S/N ratio, with CV of only 2% (Table 4). Consequently, no factor affected the response of this element. GW only affected the S/N ratio for Cr and Zn (Table 4), both with RI of 9%, so the lowest value of this factor corresponded to its optimized value. ID influenced 13 elements (Table 4), most of which showed a maximum response at the minimum ID value, except Ca, Fe, and Mg, for which the intermediate value represented the best condition (Figure 4). DT affected 8 elements (Table 4), of which 5 elements (N, Co, Ni, P, and Zn) presented a maximum response at the minimum DT value (Figure 4). For Ca and Mg, the best condition was at the maximum DT value, while for Fe it was at an intermediate As in the case of SP LIBS, LE in the range studied had little or no influence on the S/N ratio for the elements evaluated, while the highest AP value maximized the S/N ratio. Different to SP LIBS, the lowest GW value maximized the response. The optimized DT for DP LIBS was the same as that for SP LIBS with the 1064 nm laser (0.2 μs, GW = s). The maximization of the S/N ratio at the lowest DT value was due to the higher excitation temperature and electron density at the beginning of plasma formation [START_REF] Nicolodelli | Signal enhancement in collinear double-pulse laser-induced breakdown spectroscopy applied to different soils[END_REF]. For the elements influenced by ID, most presented a maximum response at ID of 0.2 μs, GW = s, because the plasma absorbed the energy from the 1064 nm laser that reheated the plasma (second pulse), consequently increasing the temperature of the plasma formed by the 532 nm laser [START_REF] Gautier | Quantification of the intensity enhancements for the double-pulse laser-induced breakdown spectroscopy in the orthogonal beam geometry[END_REF].

Conclusions

The parameters that influence the qualitative multi-elemental analysis of a sediment sample from the Piracicaba River by SP LIBS (1064 nm and 532 nm lasers)

were optimized using a central composite design (CCD) for each system, preserving the multi-element advantage of this technique. In the data range evaluated, the laser energy (LE) had little or no influence on the S/N ratio for the elements studied, using both SP LIBS. Regardless of the system, the maximum accumulated pulses (AP) and gate width (GW) values maximized the responses for most of the elements affected by these factors. However, for SP LIBS at 1064 nm laser, the use of the delay time (DT) at its lowest value maximized the S/N ratio for most elements, while for SP LIBS at 532 nm, the highest value of this factor maximized the response for most elements. The 2 6-2 fractional factorial design for DP LIBS showed that the 532-1064 nm laser sequence provided the best performance, so this system was optimized using a CCD. According to the results obtained by 26-2 fractional factorial design with the 532-1064 nm laser sequence, the factors GW, ID, and DT had the greatest effects on the S/N ratio, they were selected for refining the optimal conditions. Unlike SP LIBS, the response was maximized at the lowest GW value. The optimized DT for DP LIBS was the same as for SP LIBS with the 1064 nm laser. For the elements affected by ID, most presented a maximum response at the lowest ID value.

The DOE allowed describing the combined effects of the factors in the response using a smaller number of experiments and then saving time and costs, when compared to the optimization of a factor at a time. The CCD combined with the LIBS technique proved to be an excellent tool for optimizing the parameters that affect the LIBS analysis, and the fractional factorial design proved to be very efficient for screening and deciding which factors deserve further study.

Figure 1 .Fig. 1 .

 11 Fig. 1. Means of the S/N ratio outside the 95% CI for each analyte, as a function of the number of spectra for each measurement.

  (i) LE (1064 nm) = 34, 37, 40, 43, and 46 mJ; (ii) DT = 0.2, 0.5, 0.9, 1.2, and 1.5 µs; (iii) GW = 1, 5, 11, 16, and 20 µs; and (iv) AP = 1, 3, 6, 8, and 10. The same DT, GW, and AP values used in the CCD experiment for SP LIBS with the 1064 nm laser were used for SP LIBS with the 532 nm laser, with only the LE (532 nm) values being different: 35, 47, 59, 71, and 83 mJ. For each experimental run, different regions of the sediment sample pellet were used to acquire the minimum number of spectra that ensured sample representativeness.

  . The values of the lower, intermediate, and upper levels for the factors were as follows: (i) LE (1064 nm) = 34, 40, and 46 mJ; (ii) LE (532 nm) = 35, 47, and 59 mJ; (iii) AP = 5, 18, and 10; (iv) GW = 5, 13, and 20 µs; (v) ID = 0.2, 1.6, and 3.0 µs; and (vi) DT = 0.2, 0.7, and 1.2 µs. For each experimental run, different regions of the sediment sample pellet were used to acquire the minimum number of spectra that ensured representativeness. The 2 6-2 fractional factorial design performed for the DP LIBS in crossed beam configuration with the best laser sequence was optimized using CCD. The three independent factors (GW, ID, and DT) were optimized to obtain information about the linear, interaction, and quadratic effects, identifying a condition suitable for most of the elements. The number of runs was 17, including 2 runs at the central point. According to equation (2), the distance from the axial points to the central point, α, was 1.68. The values of the critical factors were calculated and varied between the upper and lower levels, as follows: GW = 5, 8, 11, 17, and 20 µs; ID = 0.2, 0.8, 1.6, 2.4, and 3.0 µs; and DT = 0.2, 0.4, 0.7, 1.0, and 1.2 µs. For each experimental run, different regions of the sediment sample pellet were used to acquire the minimum number of spectra that ensured sample representativeness.

Fig. 2 .

 2 Fig. 2. S/N ratio contour graphs of the CCD model for SP LIBS with the 1064 nm laser.

  3), the optimized factors were LE = 35 mJ, DT = 1.5 μs, GW = s, GW = 20 μs, GW = s, and AP = 10.

Fig. 3 .

 3 Fig. 3. S/N ratio contour graphs of the CCD model for SP LIBS with the 532 nm laser.

  value. However, the CV values for Ca and Fe were below 15%. The sum of the interactions between the factors corresponded to less than 10% for most elements, except B and Fe, for which the ID*DT interaction corresponded to 2 and 16%, respectively. Therefore, the optimized factors for DP LIBS in crossed beam configuration with the 532-1064 nm laser sequence were as follows: LE (1064 nm) = 34 mJ; LE (532 nm) = 35 mJ; AP = 10; GW = 5 μs, GW = s; ID = 0.2 μs, GW = s; and DT = 0.2 μs, GW = s.

Fig. 4 .

 4 Fig. 4. S/N ratio contour graphs of the CCD model for DP LIBS.

Table 1 .

 1 Spectroscopic atomic emission lines evaluated.

	Element	Wavelength (nm)
	B I	249.77
	Ca I	422.67
	Co I	252.13
	Cr I	359.35
	Cu I	324.75
	Fe I	259.93
	Mg I	383.82
	Mn I	403.44
	Na I	588.99
	Ni I	232.00
	P I	214.91
	Sr II	407.77
	V I	437.92
	Zn I	213.85

Table 2 .

 2 Coefficient of variation (CV), coefficient of determination (R 2 ), and relative importance (RI) for the linear and quadratic effects in the CCD final models for SP LIBS with the 1064 and 532 nm lasers.

			SP LIBS 1064 nm			SP LIBS 532 nm
	Elements	CV (%)	R 2 (%)	RI (%) of factors* LE DT GW AP	CV (%)	R 2 (%)	RI (%) of factors* LE D T GW AP
	B	51	94		70		17	25	92 10	4	70
	Ca	21	90		21 40 29	29	83		15 54 14
	Co	52	94		75		11	21	82 11	9	4	45
	Cr	27	93	2	15 14 54	50	80		28 45	7
	Cu	17	50				50	32	69	3	9	17	8
	Fe	21	57	4	39			64	89	8	58	1	19
	Mg	34	91		20 10 61	43	95		8	53 31
	Mn	37	94	3	4	9	75	51	87		15 45 24
	Na	35	93		5	36 52	53	86		14 51 16
	Ni	32	90		16		74	45	88		46 10 32
	P	27	66		13		53	28	72		49	6	17
	Sr	22	45	5	11 20		9	62		10 32 20
	V	33	95 10	5	7	69	50	88		16 60 12
	Zn	30	63		4		38	29	86 13 14	59
	* Linear and quadratic effects.

2 fractional factorial design with the 1064-532 nm laser sequence 2 6-2 fractional factorial design with the 532- 1064 nm laser sequence

  10 elements: B, Ca, Co, Cr, Mg, Na, Ni, P, V, and Zn).

	Element s	2 6-CV (%)	R 2 (%)	1064 nm LE	RI (%) of factors* 532 nm LE A P G W ID DT	CV (%)	R 2 (% )	1064 nm LE	RI (%) of factors* 532 nm LE AP G W ID DT
	B	52	85		5	7	16 57	59	76			15	18 43
	Ca	50	43			43		39	96			2	85 9
	Co	64	90		3	8	24 55	62	82		8	15	16 43
	Cu	27	42				42	28	28			28
	Cr	30	47			18 29		24	60			20 18	22
	Fe	47	66		10		56	48	32			32
	Mg	37	76			34 12 23 7	23	74			37 12 14 11
	Mn	40	58			26 19	13	26	58			42 16
	Na	65	68			43 25		29	51			29 22
	Ni	42	74				66 8	38	53		14 16	23
	P	43	74			8	47 19	47	35			19	16
	Sr	39	58				58	7	41			41
	V	27	18			18		10	41			15	26
	Zn	52	88		9	18	46 15	41	63		20 13	30
	*Linear effect.

Table 3 .

 3 Coefficient

	378
	379	of variation (CV), coefficient of determination (R 2 ), and relative
	380	importance (RI) for linear effects in the fractional factorial design final models for DP
	381	LIBS.
	382
	39	20

Table 4 .

 4 Coefficient of variation (CV), coefficient of determination (R 2 ), and relative importance (RI) for the linear and quadratic effects in the CCD final models for DP LIBS.

	Element	CV (%)	R² (%)	RI (%) of factors*
				GW	ID	DT
	B	97	99		72	25
	Ca	14	95		73	22
	Co	113	92		81	11
	Cu	16	67		67
	Cr	14	72	9	63
	Fe	14	72		42	14
	Mg	22	83		54	29
	Mn	23	80		80
	Na	13	42		42
	Ni	108	92		72	20
	P	67	99		69	30
	Sr	2
	V	16	83		83
	Zn	56	57	9	15	33
	* Linear and quadratic effects.

Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) Finance Code 001, grant number -88882.331025/2019-01 for providing a fellowship to Carla Pereira de Morais, FAPESP grant numbers (2013/07276-1 and 16/14227-5), CNPq grant number (403405/2013-0), and EMBRAPA Instrumentation.


Carla Pereira De Morais

Gustavo Nicolodelli

Milene Corso Mitsuyuki

Kleydson Stênio

Gaioso Da Silva

Frederico Fábio Mauad

Stéphane Mounier

Marcondes Débora

Pereira Bastos

Milori

Total phosphorus determination in Eutrophic Tropical River Sediments by Laser-Induced Breakdown Spectroscopy techniques

Total phosphorus (TP) in sediments is an important chemical variable in the study of the extent of eutrophication in water bodies. Two methods, based on Single Pulse (SP) and Double Pulse (DP) Laser-Induced Breakdown Spectroscopy (LIBS), were developed for determining TP in the sediment cores of Brazilian rivers upstream from the Barra Bonita reservoir. TP concentration in the sediments was determined by inductively coupled plasma optical emission spectrometry (ICP OES) on digested samples. Besides, a LIBS system operating in SP and DP mode was used to develop methods for the TP quantification in sediment pellets. In LIBS, the most appropriate wavelength to measure P was at 214.91 nm. The calibration curves showed correlation coefficients of 0.93 and 0.92, limits of detection of 709 mg kg-1 and 349 mg kg-1 for SP and DP LIBS, respectively. The two proposed methods were validated and presented an average percentage error of 14% and 10% for SP and DP LIBS, respectively. The ICP OES, SP and DP LIBS data showed that the most superficial layers of the Piracicaba river, all the sedimentary layers of the Tietê river, and the confluence region present a high concentration of TP, according to Brazilian sediment quality criterion. In conclusion, SP and DP LIBS were confirmed as promising alternative tools to traditional analytical methods for monitoring the TP content in the sediments that come from different hydrographic units. The proposed method using DP LIBS proved more sensitive than SP LIBS, but the SP LIBS method demonstrated enough precision for determining TP in eutrophic river sediments.

Introduction

The origin of P in sediments can be natural, coming from outside the aquatic system (allochthonous) or from within the system (autochthonous), and anthropogenic 1 Depending on the concentrations, P can be harmful to the aquatic system, accelerating the eutrophication process of rivers. 2,3 The most severe environmental consequence is the decrease in dissolved oxygen in the water, causing the death of plant and animal species. Also, it changes the taste and smell of water. 4 Total phosphorus (TP) is an important chemical variable in the study of sediment quality, as it assesses the nutrient load and the extent of the degree of eutrophication of water bodies. The chemical analysis of sediment cores is used to evaluate the distribution of the elements in-depth and correlate the profile obtained with the history of land use and occupation and, consequently, with potential anthropic contributions. These conditions are not always detectable using water variables. The official method for determining TP in sediments is the USEPA 6010C Method. [START_REF]Method 6010C (SW-846): Inductively Coupled Plasma -Atomic Emission Spectrometry[END_REF] This method uses inductively coupled plasma optical emission spectrometry (ICP OES) for determination and requires treatment of samples, such as wet decomposition using high volumes of oxidizing mixtures. 4,[START_REF] De | [END_REF]7 Thus, generating considerable amounts of chemical residues, disagreeing with the principles of Green Chemistry. 8 Laser-Induced Breakdown Spectroscopy (LIBS) is an alternative to the disadvantages associated with sample preparation, as it provides direct analysis, thus eliminating or reducing the use of chemical reagents. Besides, the LIBS technique has other advantages, such as relatively low analyses cost when compared to conventional analytical methods, and fast real-time analysis. LIBS is an optical emission spectroscopy technique that uses a laser-generated plasma to vaporize, atomize and excite analytes. When excited species return to a lower energy state, they emit discrete emission lines that are characteristic of each element. [START_REF] Cremers | Handbook of Laser-Induced Breakdown Spectroscopy[END_REF] This emission spectrum contains qualitative and quantitative information on the sample composition. [START_REF] Senesi | [END_REF] Due to the matrix effect, quantitative analysis and increased sensitivity are still analytical challenges to be overcome. 11 The Double Pulse (DP) LIBS approach has demonstrated a significant increase in sensitivity when compared with the Single Pulse (SP) LIBS. [12][13][14] Although the LIBS technique has shown potential for elementary analysis in marine 15,16 and river sediments, 17 there is no study on the application of SP and DP LIBS techniques combined with ICP OES to assess the quality of river sediments concerning the TP concentration. This lack of LIBS work in the literature is due to the challenge of constructing calibration models for samples with significant variation in their physic-chemical characteristics, as can be seen in sediments that receive sewage runoff, and industrial activities. 18 This work aims to develop methods using SP and DP LIBS techniques to assess the quality of river sediments from different hydrographic units, which receive different effluent loads, concerning the TP distribution in different sediment core depths.

Experimental

Collection and preparation of samples

Sediment samples were collected in the Tietê and Piracicaba rivers, from their input compartments in the Barra Bonita reservoir, São Paulo state, Brazil (Fig. 1), 19 on the 25th of July of 2017, from three points on the Tietê river, three points on the Piracicaba river, and one point in the confluence region.

The average water depth upstream of the reservoir is 10.2 m. The sediment cores were taken at different depths using core sampling. The collection points were georeferenced using the Trimble Navigator GPS (Table S1). Each river belongs to a water resource management unit, with different types of land use and occupation. The Tietê river is the most polluted in Brazil and practically crosses Please do not adjust margins Please do not adjust margins Please do not adjust margins the entire state of São Paulo passing through the Metropolitan Region of São Paulo City. The Piracicaba river is the largest tributary in terms of the water volume of the Tietê river. 20 The transversal slicing was done in different sizes (Table S2) along the seven cores without removing interstitial water-sediment, totaling 69 sample layers. All samples collected were placed in plastic containers and stored in a thermal box during transport to the laboratory. The samples were freeze-dried (L101, Liotop), ground using a mortar grinder (RM 200, Retsch), and sieved through a 100-mesh sieve. For SP and DP LIBS analyses, an aliquot of 500 mg of each sample was converted into pellets by applying 5 tons of pressure for 1 min in a hydraulic press.

Emission spectrometry analyses

ICP OES was the reference technique for determining the P concentration for all the samples. It used an iCAP 6000 ICP OES (Thermo Fisher Scientific) with an axial view, radio frequency (RF) generator of 1.55 kW, echelle polychromator with continuous wavelength coverage in the range of 166.4 nm to 847.0 nm, and a high-performance solid-state detector with CID86 chip. Argon gas (99.996%, White Martins-Praxair) was used in all the measurements. The P line at 178.2 nm was monitored in optimized plasma operating conditions (Table 1).

Spray chamber Cyclonic

The ICP OES analyses were conducted on digested samples. The decomposition procedure is described below: 200 mg of each homogenized sample was accurately weighed and transferred to the Perfluoro alkoxy (PFA) decomposition flasks with 10.0 mL of HNO3 (Synth) purified in a sub-boiling distillation system Distillacid™ BSB-939-IR (Berghof, Eningen). Then, this solution was digested using a microwave oven (Speedwave four, Berghof, Eningen) in triplicate. The microwave oven heating program used consisted of (i) 5 min to reach 120 °C, (ii) remained at that temperature for 5 min, (iii) 5 min to reach 175 °C, and (iv) remained at that temperature for 10 min. The maximum temperature of the flasks was approximately 175 °C, and the time for complete digestion was 25 minutes. The tubes were cooled to room temperature in a fume hood. An analytical blank accompanied all procedures. After digesting and cooling, the samples and analytical blanks were transferred to 50.0 mL volumetric flasks, and the volume was completed with deionized water. Subsequently, the digests were diluted 2.5 times with deionized water so that the acid concentration would remain in the equipment's standards. The accuracy of the reference method was evaluated using certified reference materials (CRMs) Montana II Soil (SRM 2711a), and San Joaquin Soil (SRM 2709a).

LIBS setup

A cross beam double pulse LIBS system was developed to analyze sediments. It was composed of two Nd:YAG pulsed lasers operating at different wavelengths, 1064 nm and 532 nm (Fig. 2). A delay generator pulse was used for the temporal control between the two lasers and the data acquisition system. An echelle spectrometer equipped with an intensified coupled charge device (ICCD) with 1024 x 1024 pixels was used to obtain the spectra. The spectrometer operated in two spectral bands, 175-330 nm, and 275-750 nm, with a resolution of 13-24 pm, and 29-80 pm, respectively. The laser that emits in 1064 nm (Q-switched Ultra, Quantel) operates at a maximum pulse energy of 50 mJ, pulse duration of 8 ns, and a repetition rate of 20 Hz. The other one (Brilliant, Quantel) operates at a maximum pulse energy of 180 mJ, pulse duration of 4 ns, and a repetition rate of 10 Hz. The laser beams were directed to the sample surface using the minimum number of optical components to avoid loss of power from the lasers. The plasma emission was collected using a telescope system composed of two Si plano-convex spherical lenses. An optical fiber was placed just before the focal point of the telescope to ensure the maximum efficiency of collected light. For optical alignment, the optical fiber was put in XYZ positioning stages, allowing an adjustment with the precision of 1 μm.m. Sediment samples were analyzed in triplicate using two different LIBS setups. The first setup was the SP LIBS system using the laser at 1064 nm. The laser energy was fixed in 34 mJ, the delay time was at 200 ns, and the acquisition gate width was 20 µs.

The second setup was the DP LIBS with crossed beam configuration. The first pulse was at 532 nm, and the second was at 1064 nm. The energy of the infrared laser (1064 nm) was 34 mJ, and the other laser (532 nm) was 35 mJ. The delay time between pulses was 200 ns, the delay time between the last pulse and acquisition was 200 ns, and the acquisition gate width was 5 µs. In both setups, for each sample, 45 spectra were acquired from different regions of the pellet with the 10 pulses accumulation.

Data analysis

The simple linear regression was performed between TP concentration determined by ICP OES and the depth of the sediment core at each collection station to evaluate the P distribution along the sediment core. The spectra obtained with SP and DP LIBS were processed with software developed using Python programming language. Outliers were excluded using a scalar product between the average and each measured spectrum. The correlation coefficient between the intensity at each wavelength of the spectra and the P concentration determined by ICP OES was calculated. This evaluation helps to identify the best lines for modeling. The analytical calibration was constructed with 70% of the samples and validation with the 30% remaining. The samples from the calibration and validation sets were chosen at random. For the chosen P lines, a baseline correction was done. 21 The area under the best wavelength emission line, obtained using the correlation graph, was integrated using the Lorentz function. The average area was calculated for each sample (n=3). The limit of detection (LOD) was calculated according to Currie. 22

Results and discussion

LIBS

Fig. 3 shows two typical plasma emission spectra from 175 to 341 nm from sediment samples obtained with the SP (Fig. 3a) and DP (Fig. 3b) LIBS systems.

Fig. 2 Scheme of the LIBS setup.

The P atomic emission line at 214.91 nm presented the most significant correlation with the reference values for both configurations, 0.75 and 0.76 for non-treated data of SP and DP LIBS, respectively (Fig. 4). The average signal-to-noise (S/N) ratio for P I 214.91 nm was 15.1 and 27.9, for SP and DP LIBS, respectively, so DP LIBS increased the S/N ratio 1.8 times. Thus, the 214.91 nm line was chosen for the construction of the calibration models. Calibration models were constructed for the direct correlation between peak area fitted by Lorentz function and reference values obtained with ICP OES (Fig. 5a,b) for SP and DP LIBS. The P analytical calibration curves showed the existence of a strong linear correlation, in which Pearson's correlation coefficients of 0.93 and 0.92 were obtained for SP and DP LIBS, respectively, and a linear working range of 802 -5770 mg kg -1 of P for both curves. The LOD of 709 mg kg -1 and 349 mg kg -1 for SP and DP LIBS, respectively, were calculated according to Currie. 22 The two proposed methods were validated using the validation set (Fig. 5c,d). In this kind of validation, graphs were constructed using correlation of the P concentration predicted by the calibration models with the P concentration determined by ICP OES.

To better interpret the RMSEC (root mean squares error of calibration) and RMSEV (root mean squared error of validation) values, the average percentage error was calculated for the calibration and validation set in both methods. The percentage of average error for the calibration curves was 12% and 11% for SP and DP LIBS, respectively. For the validation curves, it was 14% and 10% for SP and DP LIBS, respectively. The mean errors in the quantification of TP by SP and DP LIBS is acceptable for measurements of samples without preparation, 21 and although the matrix effect is common in the LIBS technique 31 , the models developed using the PI 214.91 nm line proved to be independent of the matrix and did not present non-linear effects. Additionally, in the chosen emission line, there is no interference from other elements present in the matrix, thus, allowing the construction of univariate calibration models for different types of samples 32 . The two methods developed for P quantification in river sediments have LODs below the maximum natural level value (750 mg kg -1 ) defined by Brazilian laws 29 and can be used to determine TP in the replacement of ICP OES. The method developed using DP LIBS is more sensitive and presented LOD two times smaller than the method using SP LIBS. However, to analyze the trophic level of eutrophic rivers, SP LIBS is sufficient and preferable, because it uses only one laser, therefore, being a cheaper system.

Phosphorus distribution inside the sediment cores

The P concentration determined by ICP OES, SP and, DP LIBS was correlated with the depth of the sediment cores (Fig. 6). The P distribution in the sediment cores according to the developed LIBS methods showed the same behavior in all stations when compared with ICP OES. Therefore, both methods are very efficient to assess the degree of eutrophication and to obtain information about the anthropic contributions with regard to the P content in sediment cores.

The average concentration of TP in the sediments of the Tietê and Piracicaba rivers is high when compared with similar studies for eutrophic aquatic ecosystems. [23][24][25] The highest P concentration is at the top of the sediment core of station 4 (5770 mg kg -1 ), this result is because the region of confluence between the rivers causes the immobilization of P in the surface sediments. 26 The collection points on the Piracicaba river (stations 1, 2, and 3) and the confluence region (station 4) showed a significant decreasing linear trend of P content with depth, with levels in the surface layers of 1846, 2174, 3506, and 5770 mg kg -1 of P, respectively. The values for the decrease rates of the P content per centimeter were: -14.9, -53.6, -66.4, and -66.7 mg kg -1 cm -1 with r² values corresponding to 0.87, 0.98, 0.99, and 0.91 for stations 1, 2, 3, and 4, respectively. The increase in the TP content from the bottom to the top of the sediment core indicates that the deposition of P is increasing, and this is due to the intensification of anthropogenic activities in the region 27 . Stations 5, 6, and 7, in the Tietê river, do not show a significant linear trend, their average levels and corresponding standard deviations of P content were: 4072 ± 643, 3629 ± 1293, and 5178 ± 498 mg kg -1 of P, respectively. The difference in the behavior of the TP distribution along the profile in the Tiete (stations 5, 6, and 7), and Piracicaba rivers (stations 1, 2, and 3), may be linked to the supply and resuspension of P in the sediments. The main sources of P at the sampled points are discharges from domestic sewage, with a large amount of fecal organic matter and detergents, water drained in agricultural areas, and some industrial effluents. 28 According to Brazilian sediment quality criterion concerning the TP content, the deepest sediment layers of the Piracicaba river (stations 1, 2, and 3) are at the level that impacts the water body (TP concentration between 750 to 1500 mg kg -1 ), and the most superficial layers of the Piracicaba, all the sedimentary layers of the Tietê river (stations 5, 6, and 7), and the confluence region are at the level that causes a high impact on the water body (TP concentration above 1500 mg kg -1 ). 29 . These results indicate that the variability of TP in the vertical distribution is high for the Piracicaba river, while low in the Tietê river. The results presented in the Tietê river corroborate with those observed by Baran et. al in the Dunajec river, where there was no high P variability in the vertical distribution, this means that the intensely suspended matter transported by theses rivers have been homogeneous. 30

Conclusions

SP and DP LIBS techniques proved to be a potential tool to determine TP in river sediments. The developed methods show a strong correlation (> 0.91) with the reference values, using univariate linear calibration. The method developed using DP LIBS is more sensitive, but the method using SP LIBS also demonstrated enough sensitivity for TP determination in eutrophic river sediments. The methods developed have the potential to be used by agencies responsible for preserving and restoring the quality of aquatic ecosystems by monitoring the TP content in sediment in these environments. Considering a high number of sampled points, the LIBS technique can be indicated, because it eliminates the use of reagents for sample preparation, reduces the time and cost of the analysis, and there is no generation of chemical residues. Therefore, we propose the use of LIBS techniques for monitoring of the large areas of rivers, in order to help the development of technologies, to avoid the entrance of P in water bodies, for remediation of these ecosystems.

From ICP OES, SP and DP LIBS analysis a significant difference can be observed in the TP content of the sediment cores of the Piracicaba and Tietê rivers. The variability of TP in vertical distribution is greater in the Piracicaba river. These results suggest that the intensely suspended matter transported by the Piracicaba river was heterogeneous, while for the Tietê river it was homogeneous.

Fig.

  Fig. Emission spectrum of a sediment sample, from 175 to 341 nm obtained with the SP (a) and DP (a) LIBS systems.

Table 1

 1 Operating conditions for ICP OES determinations.

	Instrument parameter	Operating condition
	Integration time (s)	15.0
	Sample introduction flow rate (mL min -1 )	1.00
	Pump stabilization time (s)	5
	RF applied power (kW)	1.25
	Auxiliary gas flow rate (L min -1 )	0.50
	Carrier gas flow rate (L min -1 )	0.50
	Plasma gas flow rate (L min -1 )	12
	Nebulizer	V-Goove

Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brazil (CAPES) Finance Code 001. The authors thank CAPES (Grant 88882.331025/2019-01) for providing a fellowship to Carla Pereira de Morais, EMBRAPA Instrumentation and CEPOF (2013/07276-1) for financial support of this work, EMBRAPA Southeast Livestock and GAIA for the preparation and analysis of samples by ICP OES, and Bruno Ricardo Silva Costa for making the map with the geographical coordinates.

Conflicts of interest

There are no conflicts to declare.