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Laser Pulse Width Dependence and Ionization Mechanism of Matrix-Assisted Laser Desorption/Ionization

  • Sheng-Ping Liang
  • I-Chung Lu
  • Shang-Ting Tsai
  • Jien-Lian Chen
  • Yuan Tseh Lee
  • Chi-Kung Ni
Research Article

Abstract

Ultraviolet laser pulses at 355 nm with variable pulse widths in the region from 170 ps to 1.5 ns were used to investigate the ionization mechanism of matrix-assisted laser desorption/ionization (MALDI) for matrices 2,5-dihydroxybenzoic acid (DHB), α-cyano-4-hydroxycinnamic acid (CHCA), and sinapinic acid (SA). The mass spectra of desorbed ions and the intensity and velocity distribution of desorbed neutrals were measured simultaneously for each laser shot. These quantities were found to be independent of the laser pulse width. A comparison of the experimental measurements and numerical simulations according to the multiphoton ionization, coupled photophysical and chemical dynamics (CPCD), and thermally induced proton transfer models showed that the predictions of thermally induced proton transfer model were in agreement with the experimental data, but those of the multiphoton ionization model were not. Moreover, the predictions of the CPCD model based on singlet–singlet energy pooling were inconsistent with the experimental data of CHCA and SA, but were consistent with the experimental data of DHB only when some parameters used in the model were adjusted to extreme values.

Graphical Abstract

Keywords

MALDI Ionization mechanism Laser pulse width Ion-to-neutral ratio Thermal model CPCD model Multiphoton ionization 

Introduction

Although matrix-assisted laser desorption/ionization (MALDI) was invented more than 25 years ago [1, 2], its ionization mechanisms are still under investigation. Numerous models have been proposed for MALDI ionization processes. The models can be classified into two categories: the excited state-driven model (e.g., multiphoton ionization model and coupled photophysical and chemical dynamics (CPCD) model) [3, 4] and the ground state-driven model (e.g., polar fluid model [5, 6] and thermally induced proton transfer model) [7, 8, 9, 10, 11, 12]. According to the excited state-driven model, ions are produced from the excitation of the molecules in the electronically excited state. The ion generation efficiency must depend strongly on the excited state properties. According to the ground state-driven model, ions are produced from the reactions in the ground state. The ion generation efficiency must depend on the properties of the ground state if most electronically excited molecules rapidly relax to the ground state.

Most MALDI processes involve an ultraviolet (UV) laser pulse at a wavelength of 337 or 355 nm, and the pulse width ranges from 10 ns down to picoseconds. Previous studies of laser pulse width dependence on UV-MALDI have demonstrated that the thresholds of desorbed ions and neutrals depend on fluence, but not on irradiance [13, 14]. Identical laser fluence but different irradiance (i.e., identical laser pulse energy, but different pulse widths) results in varying rates of pumping molecules from the ground state to the S1 state, giving rise to various excitation efficiencies of molecules from S1 to the higher states. In principle, research on laser pulse width dependence should be able to elucidate the contributions of the excited state-driven mechanism versus the ground state-driven mechanism when the excited state and ground state properties are known. However, previous studies have not compared the theoretical models and experimental results or determined the ionization mechanism. This is likely because most properties of the electronically excited state were previously unknown, and the numerical values from theoretical calculations were not available for comparison with experimental data.

Although photoionization was considered to be involved in the ionization process of MALDI in an earlier study [15] multiphoton ionization has not been considered as the major ionization mechanism until recently. The frequently used argument for excluding the contribution of multiphoton ionization is that “the ionization potentials of free UV matrix molecules are too high for two-photon ionization, but typical MALDI laser intensities are too low for efficient three-photon excitation” [16]. The efficiency of three-photon excitation depends not only on the laser intensity but also on the absorption cross-section and excited state lifetime. The absorption cross-sections include the excitation from S0 to S1, S1 to Sn, and Sn to ion. The lifetimes include those of S1 and Sn. Because most lifetimes and absorption cross-sections were unknown before, the claim that laser intensities are too low for efficient three-photon excitation could not be verified. Therefore, it is too early to exclude the contribution of multiphoton ionization in MALDI without further investigation. The lifetimes of solid matrices in the S1 state were measured recently [17] and we suggest that the role of multiphoton ionization in MALDI must be reinvestigated.

Another model that depends strongly on the properties of the excited state is the CPCD model (also known as the two-step model or two-step energy pooling model) [3, 4]. This model suggests that ions are produced by a two-step energy pooling (exciton annihilation) of matrix. The S1–S1 energy pooling, M(S1) + M(S1) → M(S0) + M(Sn), and S1–Sn energy pooling M(S1) + M(Sn) → M(S0) + M+ + e, were included, where M represents a matrix molecule. The ion generation efficiency depends on the lifetimes of S1 and Sn and the energy pooling rate constants.

A recent study investigated the time-resolved fluorescence spectra of 12 commonly used matrices [17]. No S1–S1 energy pooling was observed in six of these matrices: 3-hydroxy-picolinic acid, 6-aza-2-thiothymine, 2,4-dihydroxy-acetophenone, 2,6-dihydroxy-acetophenone, 2,4,6-trihydroxyacetophenone, and ferulic acid. The study excluded the role of S1–S1 energy pooling in the ion generation of these matrices. The same study also eliminated the S1–S1 energy pooling as a general ionization mechanism in MALDI. The excited state lifetime of sinapinic acid (SA) is too short to determine whether S1–S1 energy pooling occurs. Two molecules reacting in an electronically excited state (S1) were observed in five of these matrices, 2,5-dihydroxybenzoic acid (DHB), α-cyano-4-hydroxycinnamic acid (CHCA), 2,5-dihydroxy-acetophenone, 2,3-dihydroxybenzoic acid, and 2,6-dihydroxybenzoic acid, and S1–S1 energy pooling is a possible reaction. The S1–S1 energy pooling rate constants were obtained by assuming that two molecules reacting in the S1 state were completely attributable to the S1–S1 energy pooling. This yields the maximum S1–S1 energy pooling rate constants, which is favorable for the CPCD model. The observation of S1–S1 energy pooling does not necessarily indicate that ions are generated by energy pooling for these matrices because no S1–Sn energy pooling has been observed for any matrices. The lifetimes and S1–S1 energy pooling rate constants obtained from the time-resolved fluorescence spectra facilitated research on the laser pulse width dependence of the CPCD model for these matrices, suggesting that the role of CPCD model in MALDI can be re-investigated.

Previous studies have proposed the concept of ion generated from the reaction of molecules in the ground state because of the high temperature in MALDI [5, 6]. However, quantitative description of ion generation efficiency by thermal process has been provided only in recent studies [7, 8, 9, 10, 11, 12]. The quantitative description of ion generation facilitates a comparison of the prediction by a thermal model with that obtained from experimental measurements.

In this study, UV laser pulses at 355 nm with variable pulse width in the region from 170 ps to 1.5 ns were used to investigate the MAIDI ionization mechanism. We investigated three matrices: DHB, CHCA, and SA. We selected these three matrices because the absolute UV absorption cross-sections and lifetimes of the S1 state in the solid state were measured. The absorption cross-section and lifetimes are two necessary parameters for numerical simulations. Two of these three matrices (DHB and CHCA) exhibited the reaction of two molecules in the electronically excited state (S1), and the maximum values of S1–S1 energy pooling rate constants were determined. Energy pooling is a potential reaction for generating ions for these matrices. Although the excited state lifetime of SA is too short to determine whether S1–S1 energy pooling occurs, energy pooling as a potential ionization mechanism for SA was not yet completely excluded. A comparison of predictions by the CPCD model and experimental measurements facilitates the investigation of the role of energy pooling in the ion generation of these matrices. We measured the mass spectra of desorbed ions and the intensity and velocity distribution of desorbed neutrals simultaneously for each laser shot. The experimental results were then compared with the numerical simulation results according to the multiphoton ionization, CPCD, and thermal models to determine the contributions of various ionization processes in MALDI.

Experimental

MALDI-grade materials purchased from Sigma Aldrich (St. Louis, MO, USA) were used in this study. All the chemicals are used without further purification. Matrix stock solutions were prepared by dissolving the corresponding compounds separately in a 50% acetonitrile aqueous solution. The solution was vacuum-dried evenly on the sample holder. The thickness of the sample after being vacuum-dried was approximately 500 μm.

The experimental apparatus consisted of a Nd:YAG laser, a rotatable sample holder, an electrostatic quadrupole ion beam deflector, a time-of-flight mass spectrometer, and a differentially pumped quadrupole mass spectrometer. A schematic of the apparatus is shown in Figure 1. The laser irradiation spot on the sample surface was located at the axis of the quadrupole mass spectrometer at 0°. The rotation axis of the sample holder (12 mm in diameter) was offset by 4 mm from the axis of neutral detection. This enabled us to use a new sample surface for laser desorption by rotating the sample holder without breaking the vacuum. Four quantities were measured simultaneously for each laser pulse, namely the intensity and velocity of desorbed neutrals, the mass spectra of desorbed ions, and the laser pulse energy.
Figure 1

Schematic of the experimental apparatus. Relative dimensions of each component are not drawn in scale. Thin dot line represents the axis of the quadrupole mass spectrometer at 0°, and thick dot line represents the rotation axis of the sample holder

Neutral Detection

The desorbed neutral molecules were detected using a modified crossed molecular beam apparatus. Most of the details concerning the main chamber and detector chamber have been reported in previous studies [18, 19]. The details of the apparatus and the modifications made specifically for laser desorption studies have been described in previous reports [20].

The sample was located in a source chamber (1.4 m × 1.51 m × 0.7 m), which was pumped by two turbomolecular pumps (2000 L/s, TG2000M; Osaka Vacuum Ltd., Osaka, Japan) to 3.8 × 10–7 Torr. The detection chamber included three differently pumped chambers. Each differently pumped chamber was pumped by a turbomolecular pump (4440 L/s, STP 451; Edwards, West Sussex, UK). In the differently pumped chamber III, where the quadrupole mass spectrometer was located, the chamber was cooled by liquid nitrogen to further reduce the pressure. The pressure of the differently pumped chamber III was 6 × 10–10 Torr.

Neutrals desorbed from the sample surface flew through their desorbed velocity to the region of electron impact ionizator and were ionized by a home-made electron impact ionizer. The distance between the sample surface and the ionization region of the mass spectrometer was 35 cm. The ions, which were generated by the ionization of neutrals, passed through the quadrupole mass filter (Max-500; Extrel CMS, LLC, Pittsburgh, PA, USA) and were detected using the Daly detector. In this study, the DC voltage of the quadrupole was set to zero to enable the quadrupole mass filter to become an ion guide and to enable all ions to pass through the filter. The arrival time of each ion was recorded. The velocity of each desorbed neutral molecule was obtained according to the formula v = 0.35/t, where v is the velocity in meters per s, t is the arrival time (equal to the time duration from laser pulse irradiated on the sample surface to the neutral arrived at the ionizator).

Electrostatic Quadrupole Ion Beam Deflector and Ion Detection

The stainless steel sample holder was connected to a high DC voltage power supply set at 2.5 kV. Ions desorbed from sample surface through laser irradiation were accelerated by an electric field of 3846 V/cm. The ions passed through a fine metal mesh (transmission efficiency, 88.6%; BM-0117-01; Industrial Netting, Minneapolis, MN, USA), which was 6.5 mm above the sample surface and electronically grounded, and entered a home-made electrostatic quadrupole ion beam deflector. The traveling direction of the desorbed ions was bent 90° by the deflector. After exiting the ion deflector, ions entered a homemade time-of-flight mass spectrometer. The mass spectrometer included an Einzel lens, field-free tube, and ion detector (double-stage Chevron MCP assemblies). The details of the quadrupole ion beam deflector and the simulation of ion trajectories are shown in Figures S1 and S2 of Supplementary Material.

Laser

The third harmonic of a Nd:YAG laser (SL 230; EKSPLA, Vilnius, Lithuania, pulse width adjustable from 150 ps to 1.5 ns) was used in this study. The Nd:YAG laser includes an oscillator, a stimulated Brillouin scattering (SBS) cell, an amplifier, and a harmonic generator. The SBS cell is widely used as a phase conjugate mirror to correct aberration in oscillator and amplifier [21], reduce the amplified spontaneous emission [22, 23], and compress the laser pulse duration [23, 24, 25]. The 1064 nm laser beam generated from the oscillator was focused in the SBS cell, which compressed the laser pulse duration. The pulse duration from the output of the SBS cell can be varied by changing the focus condition in the SBS cell. The output of the SBS cell was then amplified by an amplifier. A laser beam profiler (LBP2; Newport Corporation, Irvine, CA, USA) was used to measure the laser beam profiles of various pulse widths. It was found that the laser beam profiles remained the same for various pulse widths. The shot-to-shot energy fluctuation of 1064 nm was less than 8%, and pulse duration fluctuation was less than 5%. The 355 nm laser beam generated from the third harmonic of the amplified laser beam was used in this study.

The optical breakdown in the SBS cell occurred in 1–3 out of 100 laser shots. When optical breakdown occurred, the laser pulse energy and temporal profile of laser pulse did not follow the desired settings. We recorded the laser pulse energy of 355 nm laser beam, ion time-of-flight mass spectra, and the intensity and velocity of desorbed neutrals of every laser shot by a digital oscilloscope (Wave Runner 610Zi, LeCroy, NY, USA). After recording a number of laser shots, the data were downloaded to a computer for data analysis. We checked the energy of every laser shot before analyzing the data. The signals from the laser pulses in which optical breakdown occurred were not taken into average in data analysis.

It is well known that the ion intensities of DHB have large fluctuations between different sample positions. Previous study showed that ion intensities of CHCA and SA decreased significantly within 100 laser shots from the same sample position, but no clear change was observed in DHB [26, 27]. As a result, the experimental procedures for these matrices were different. For CHCA and SA, the first sample spot was irradiated by 39 laser shots of 200 ps pulse width. Then the sample holder was rotated to the second sample spot, and the second spot was irradiated by another 39 laser shots of 400 ps pulse width, followed by the third sample spot irradiated by 39 laser shots of 600 ps pulse width and the fourth sample spot irradiated by 39 laser shots of 1.5 ns pulse width. The entire procedure was repeated 40 times for CHCA and 41 times for SA. For DHB, the first 5, 6th–10th, 11th–15th, and 15th–20th laser shots of a given sample spot was irradiated by laser with 200 ns, 400 ns, 600 ns, and 1.5 ns pulse widths, respectively. The same procedure was repeated for the 21th–1260th laser shots on the same sample spot.

After rejection of the laser shots for which the laser pulse energy was outside the setting values (see text below), the final data analysis was the calculations of standard deviations (SD), average of signals, and dividing the average ion signal by average neutral signal. It was carried out by using package program Origin 9.1.

Results

Experimental Measurements

All the desorbed ions were collected and sent to TOF mass spectrometer for detection, as shown by the trajectory simulation in the Supplementary Material. In contrast, only a small fraction of neutrals (normal to the surface) were detected. However, our previous study [20] shows that same velocity and intensity measured at the angle normal to the surface indicates the same angular distribution of desorbed neutrals. The same intensity and velocity of desorbed neutrals for different laser pulse widths observed in this study suggest that the total desorbed neutrals (integration of desorbed neutral in all angles) are the same.

The signals for which the laser pulses energies were within the setting region (one SD of energy fluctuation, CHCA: 84 ± 6 J/m2, SA: 162 ± 11 J/m2, DHB: 243 ± 20 J/m2), were taken for data analysis. Most of the SD of ion counts and neutral intensities from these laser pulses are less than ±20%. Details of the values are listed in the Table S1 of Supplementary Material. The intensity and velocity distribution of desorbed CHCA neutrals, as illustrated in Figure 2a, show that they do not vary with the laser pulse width. In addition, Figure 2b shows that the ion intensity and mass spectra do not vary with the laser pulse width. Similar results were observed for DHB and SA, as illustrated in Figures S3 and S4 of Supplementary Material.
Figure 2

(a) Intensity and velocity distribution of desorbed CHCA neutrals. (b) Ion intensity and mass spectra of desorbed CHCA ions. Laser fluence was 84 ± 6 J/m2; m/z = 379, 190, 172, and 146 represent [2M + H]+, MH+, [M – H2O]+, [M – CO2]+, respectively, where M is CHCA

The relative ion-to-neutral ratios of each matrix for the various laser pulse widths are shown in Figure 3. These ratios were obtained by dividing the total ion intensity of the mass spectra (the sum of the area of the peaks in the mass spectra) by the desorbed neutral intensity. No clear change (decrease or increase) of the ratio with the change in the laser pulse width was observed.
Figure 3

Relative ion-to-neutral ratios for various laser pulse widths. (a) CHCA (gray), (b) SA (orange), and (c) DHB (olive). The ratios among the different matrices were scaled using arbitrary numbers to enable clear display. Error bars represent the SD of relative ion-to-neutral ratio

Numerical Simulation

The ion-to-neutral ratio (also called ion yield or ion generation efficiency) [28] is a frequently used parameter for justifying the theoretical models of ionization mechanisms in MALDI. Ion-to-neutral ratio is defined as the ratio of desorbed ions to desorbed neutrals. In contrast to the comparison of the desorbed ion intensity, the comparison of the ion-to-neutral ratio avoids the bias of different desorption capabilities for various samples and/or experimental conditions. The experimental results, as illustrated in Figure 2a, show that the desorbed neutrals did not vary with the laser pulse width from 170 ps to 1.5 ns. Because the desorbed neutrals were identical for various laser pulse widths in this study, the comparison of ion-to-neutral ratio of various pulse widths can be simply represented by the comparison of the desorbed ion intensity.

In the following paragraphs, we calculate the ion intensity as a function of the laser pulse width according to the multiphoton ionization models, CPCD model, and thermal model, followed by a comparison of the calculated results and experimental measurements to justify the importance of various ionization processes in MALDI.

Multiphoton Ionization

Multiphoton ionization results from the simultaneous absorption of several photons in a matrix molecule. A matrix cation is generated when the absorbed photon energy is higher than the ionization threshold of the matrix molecule. The ejected electrons may attach to other neutral molecules and produce anions. The adiabatic (and vertical) ionization potentials of the matrices DHB, CHCA, and SA in the gas phase are 7.9 (8.2), 8.3 (8.5), and 7.3 (7.6) eV, respectively [29]. They are higher than the two-photon energy of 355 nm; therefore, absorption of three photons is necessary to produce cations in gas phase. However, the ionization thresholds of these matrices in the solid state can be reduced by the interaction of molecules in the solid state (analogous to the solvation effect in a solution). Consequently, the energy of two photons might be higher than the ionization threshold. In the following paragraphs, we discuss the ion generation by two- and three-photon absorption separately.

Ionization by Two-Photon Absorption

The ionization by two-photon absorption can be described as follows:
$$ \mathrm{M}\left({\mathrm{S}}_0\right) + \mathrm{h} v\to \mathrm{M}\left({\mathrm{S}}_1\right) $$
(1)
$$ \mathrm{M}\left({\mathrm{S}}_1\right) + \mathrm{h} v\to {\mathrm{M}}^{+} + {\mathrm{e}}^{-} $$
(2)
where M(S0) and M(S1) represent the matrix molecules in the electronic ground state and singlet excited state S1, respectively. M+ represents the matrix cation. We used the following rate equations to calculate the ion generation as a function of the laser pulse width.
$$ \frac{\mathrm{d}\left[{\mathrm{S}}_0\left(\mathrm{t}\right)\right]}{\mathrm{d}\mathrm{t}}=-\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{01}\left[{\mathrm{S}}_0\left(\mathrm{t}\right)\right]+\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{10}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]+{\mathrm{k}}_1\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right] $$
(3)
$$ \frac{\mathrm{d}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]}{\mathrm{d}\mathrm{t}}=\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{01}\left[{\mathrm{S}}_0\left(\mathrm{t}\right)\right]-\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{10}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]-{\mathrm{k}}_1\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]-\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{1\mathrm{i}}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right] $$
(4)
$$ \frac{\mathrm{d}\left[{\mathrm{S}}_{\mathrm{i}}\left(\mathrm{t}\right)\right]}{\mathrm{d}\mathrm{t}}=\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{1\mathrm{i}}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right] $$
(5)

where [S0(t)], [S1(t)], and [Si(t)] represent time-dependent population of the matrix molecules in the electronic ground state, singlet excited state, and matrix ion, respectively. The photon absorption cross-sections of matrix molecule from S0 to S1, and from S1 to ion are represented by α01 and α1i, respectively. The cross-section of the stimulated emission from S1 to S0 is α10. The lifetime of the S1 state is t1 = 1/k1 = 1/(kr + knonr), where kr and knonr represent the rate constants of radiative decay and non-radiative decay, respectively. The term I(t) represents the time-dependent laser intensity.

Ion intensity as a function of laser width was calculated through numerical simulations by using Equations 35. Because the ions were generated not only from the surface but also from deeper regions in the crystal where laser fluence was decreased because of the absorption, the sample was divided into 20-nm thick layers for the calculations. The depth of each layer was sufficiently low to avoid much change in the laser fluence from the top to the end of the layer. The temporal profile of the laser pulse intensity was described using a Gaussian function. Numerical simulations for each layer were calculated at 1-ps time increments. For DHB, CHCA, and SA, values of 1.6 × 10−17, 6.8 × 10−17, and 2.3 × 10−17 cm2 were reported for α01 in one study [30], and values of 1.6 × 109, 1.7 × 1010, and 9.5 × 1010 s−1 were reported for k1 in another study [17]. We used these values in the numerical simulation. However, the α10 and α1i values were unknown. We observed that the absolute ion intensity depended on the α10 and α1i values (in addition to the α01 and k1 values), but the relative ion intensities for various laser pulse widths did not vary considerably for various α10 and α1i values. Figure 4 shows the relative ion intensities for DHB, CHCA, and SA as a function of the laser pulse width. In this calculation, α10 = 1 × 10−18 cm2 and α1i = 1 × 10−17cm2 were used. The calculated results for other α10 and α1i values are presented in Figure S6 of the Supplementary Material. They are similar to Figure 4.
Figure 4

Predicted relative ion intensity as a function of the laser pulse width according to the ionization by two-photon absorption. (a) DHB, assuming the lifetime of the S1 state is 2 ns (red), 620 ps (green, experimental value), and 62 ps (black). (b) CHCA, (c) SA. Only the experimental S1 lifetime values were used for CHCA and SA. The values of the parameters used in the calculations are as follows: (a) DHB: α01 = 1.6 × 10−17 cm2, α1n = 1 × 10−17 cm2, α10 = 1 × 10−18 cm2, k1 = 5 × 108 s−1 (red), k1 = 1.6 × 109 s−1 (green), and k1 = 1.6 × 109 s−1 (black). (b) CHCA: α01 = 6.8 × 10−17 cm2, α1n = 1 × 10−17 cm2, α10 = 1 × 10−18 cm2, and k1 = 1.7 × 1010 s−1. (c) SA: α01 = 2.3 × 10−17 cm2, α1n = 1 × 10−17 cm2, α10 = 1 × 10−18 cm2, and k1 = 9.5 × 1010 s−1

The relative ion intensities for various laser pulse widths strongly depended on the k1 value. The lifetime of DHB in the singlet excited state is 625 ps [17], which is close to the longest laser pulse width used in this study. The ratio of ion intensities for the laser pulse widths of 170 and 1500 ps was 2.2:1 [Figure 4a]. To reveal the dependence of relative ion intensity on the lifetime, we calculated the relative ion intensities for various lifetimes. If the lifetime of DHB were 62 ps, the ion intensity ratio for the laser pulse widths of 170 and 1500 ps would be 8.1:1. However, if the lifetime were 2 ns, the ion intensity ratio would be 1.16:1. The calculations showed that relative ion intensities varied substantially for different laser pulse widths only when the lifetime was markedly shorter than the laser pulse width.

Figure 4b and c show the relative ion intensity as a function of the laser pulse width for CHCA and SA. Because the lifetimes of CHCA (57.8 ps) and SA (10.5 ps) were considerably shorter than the laser pulse width used in this study, the relative ion intensities varied substantially with the pulse width. The ratios of the ion intensity for laser pulse widths of 170 and 1500 ps were 8.7:1 (CHCA) and 11:1 (SA), respectively.

The calculations showed that the ion intensity varied substantially with the laser pulse width when ions were generated by the ionization of two-photon absorption. Because the experimental data showed that the ion intensity did not vary with the laser pulse width, we can conclude that the ions of DHB, CHCA, and SA generated in MALDI were not produced by the ionization of two-photon absorption.

Ionization by Three-Photon Absorption

The ionization by three-photon absorption can be described as follows:
$$ \mathrm{M}\left({\mathrm{S}}_0\right) + \mathrm{h} v\to \mathrm{M}\left({\mathrm{S}}_1\right) $$
(6)
$$ \mathrm{M}\left({\mathrm{S}}_1\right) + \mathrm{h} v\to \mathrm{M}\left({\mathrm{S}}_{\mathrm{n}}\right) $$
(7)
$$ \mathrm{M}\left({\mathrm{S}}_{\mathrm{n}}\right) + \mathrm{h} v\to {\mathrm{M}}^{+} + {\mathrm{e}}^{-} $$
(8)
The ion intensity as a function of the laser pulse width for three-photon absorption was calculated using the following equations.
$$ \frac{\mathrm{d}\left[{\mathrm{S}}_0\left(\mathrm{t}\right)\right]}{\mathrm{d}\mathrm{t}}=-\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{01}\left[{\mathrm{S}}_0\left(\mathrm{t}\right)\right]+\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{10}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]+{\mathrm{k}}_1\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right] $$
(9)
$$ \frac{\mathrm{d}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]}{\mathrm{d}\mathrm{t}}=\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{01}\left[{\mathrm{S}}_0\left(\mathrm{t}\right)\right]-\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{10}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]-{\mathrm{k}}_1\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]-\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{1\mathrm{n}}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]+\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{\mathrm{n}1}\left[{\mathrm{S}}_{\mathrm{n}}\left(\mathrm{t}\right)\right]+{\mathrm{k}}_{\mathrm{n}}\left[{\mathrm{S}}_{\mathrm{n}}\left(\mathrm{t}\right)\right] $$
(10)
$$ \frac{\mathrm{d}\left[{\mathrm{S}}_{\mathrm{n}}\left(\mathrm{t}\right)\right]}{\mathrm{d}\mathrm{t}}=\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{1\mathrm{n}}\left[{\mathrm{S}}_1\left(\mathrm{t}\right)\right]-\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{\mathrm{n}1}\left[{\mathrm{S}}_{\mathrm{n}}\left(\mathrm{t}\right)\right]-{\mathrm{k}}_{\mathrm{n}}\left[{\mathrm{S}}_{\mathrm{n}}\left(\mathrm{t}\right)\right]-\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{\mathrm{n}\mathrm{i}}\left[{\mathrm{S}}_{\mathrm{n}}\left(\mathrm{t}\right)\right] $$
(11)
$$ \frac{\mathrm{d}\left[{\mathrm{S}}_{\mathrm{i}}\left(\mathrm{t}\right)\right]}{\mathrm{d}\mathrm{t}}=\mathrm{I}\left(\mathrm{t}\right){\upalpha}_{\mathrm{n}\mathrm{i}}\left[{\mathrm{S}}_{\mathrm{n}}\left(\mathrm{t}\right)\right] $$
(12)

where [Sn(t)] represents the time-dependent population of the matrix molecules in the electronic Sn state. The photon absorption cross sections of the matrix molecule from S1 to Sn and from Sn to ion are represented by α1n and αni, respectively. The cross-section of the stimulated emission from Sn to S1 is αn1, and the lifetime of the Sn state is tn = 1/kn. The definitions of the other parameters are identical to those of two-photon absorption.

Among the various parameters in Equations 912, the α01 and k1 values were known, but the values of all other parameters were unknown. Similar to the two-photon absorption, the numerical simulation of three-photon absorption by using Equation 912 showed that the absolute values of ion intensity varied for the values of k1, kn, α10, α1n, αn1, and αni. However, the relative ion intensities for the various laser pulse widths did not vary considerably for various values of α10, α1n, αn1, and αni. Details are presented in Table S2 of the Supplementary Material. The relative ion intensities depended strongly only on the k1 and kn values. The k1 values reported in a previous study [17] were used in the present study. Because the kn values were unknown, we calculated the relative ion intensities for various kn (or tn) values, as illustrated in Figure 5.
Figure 5

Predicted relative ion intensity as a function of the laser pulse width according to the ionization by three-photon absorption. Because the lifetime of the Sn state was unknown, we calculated the ion intensity for two Sn lifetimes (i.e., tn = ∞ and tn = 0.06 ns). The values of the other parameters used in calculations are as follows: (a) DHB: α01 = 1.6 × 10−17 cm2, α1n = αn = 1 × 10−17 cm2, α10 = αn1 = 1 × 10−18 cm2, and k1 = 1.6 × 109 s−1. (b) CHCA: α01 = 6.8 × 10−17 cm2, α1n = αn = 1 × 10−17 cm2, α10 = αn1 = 1 × 10−18 cm2, and k1 = 1.7 × 1010 s−1. (c) SA: α01 = 2.3 × 10−17 cm2, α1n = αn = 1 × 10−17 cm2, α10 = αn1 = 1 × 10−18 cm2, and k1 = 9.5 × 1010 s−1

Our results showed that the relative ion intensities of three-photon absorption were similar to those of two-photon absorption when kn was very low (i.e., long lifetime of the Sn state). When kn was high (short lifetime of the Sn state), the relative ion intensity varied more rapidly with the change in the laser pulse width than that of two-photon absorption. The relative ion intensities of DHB at 170 and 1500 ps were 2:1 (when tn = ∞) and 14.3:1 (when tn = 60 ps), 7.3:1 (when tn = ∞) and 53.8:1 (when tn = 60 ps) for CHCA, and 10:1 (when tn = ∞) and 77:1 (when tn = 60 ps) for SA, respectively. The ratio of ion intensities according to the ionization by three-photon absorption was distinct from the experimental measurements, indicating that ions of DHB, CHCA, and SA generated in MALDI were not produced by the ionization of three-photon absorption.

Coupled Photophysical and Chemical Dynamics (CPCD) Model

The CPCD model suggests that matrix exciton in the highly electronically excited state, M(Sn), are generated from exciton hopping followed by S1–S1 energy pooling (or exciton annihilation). Ions, M+, are produced by the subsequent S1–Sn energy pooling, or thermal ionization from the Sn state.
$$ \mathrm{M}\left({\mathrm{S}}_0\right) + \mathrm{h}\nu \to \mathrm{M}\left({\mathrm{S}}_1\right)\ \left(\mathrm{photoexcitation}\right) $$
(13)
$$ \mathrm{M}\left({\mathrm{S}}_1\right) + \mathrm{M}\left({\mathrm{S}}_1\right)\to \left({\mathrm{S}}_0\right) + \mathrm{M}\left({\mathrm{S}}_{\mathrm{n}}\right)\ \left({\mathrm{S}}_1\hbox{--} {\mathrm{S}}_1\mathrm{energy}\ \mathrm{pooling}\right) $$
(14)
$$ \mathrm{M}\left({\mathrm{S}}_1\right) + \mathrm{M}\left({\mathrm{S}}_{\mathrm{n}}\right)\to \mathrm{M}\left({\mathrm{S}}_0\right) + {\mathrm{M}}^{+} + {\mathrm{e}}^{-}\kern1.25em \left({\mathrm{S}}_1\hbox{--} {\mathrm{S}}_{\mathrm{n}}\mathrm{energy}\ \mathrm{pooling}\right) $$
(15)
$$ \mathrm{M}\left({\mathrm{S}}_{\mathrm{n}}\right) + \mathrm{heat}\to {\mathrm{M}}^{+} + {\mathrm{e}}^{-}\kern1.25em \left(\mathrm{thermal}\ \mathrm{ionization}\right) $$
(16)
Equations 1720 were used to calculate the ion intensity as a function of the laser pulse width according to the energy pooling model.
$$ \frac{d\left[{S}_0(t)\right]}{ d t}=- I(t){\alpha}_{01}\left[{S}_0(t)\right]+ I(t){\alpha}_{10}\left[{S}_1(t)\right]+{k}_1\left[{S}_1(t)\right]+{k}_p{\left[{S}_1(t)\right]}^2+{k}_{p n}\left[{S}_1(t)\right]\left[{S}_n(t)\right] $$
(17)
$$ \begin{array}{l}\frac{d\left[{S}_1(t)\right]}{ d t}= I(t){\alpha}_{01}\left[{S}_0(t)\right]- I(t){\alpha}_{10}\left[{S}_1(t)\right]- I(t){\alpha}_{1 n}\left[{S}_1(t)\right]+ I(t){\alpha}_{n1}\left[{S}_n(t)\right]-{k}_1\left[{S}_1(t)\right]+{k}_n\left[{S}_n(t)\right]\\ {}-2{k}_p{\left[{S}_1(t)\right]}^2-{k}_{p n}\left[{S}_1(t)\right]\left[{S}_n(t)\right]\end{array} $$
(18)
$$ \frac{d\left[{S}_n(t)\right]}{ d t}= I(t){\alpha}_{1 n}\left[{S}_1(t)\right]- I(t){\alpha}_{n1}\left[{S}_n(t)\right]-{k}_n\left[{S}_n(t)\right]+{k}_p{\left[{S}_1(t)\right]}^2-{k}_{p n}\left[{S}_1(t)\right]\left[{S}_n(t)\right]-{k}_{thm}\left[{S}_n(t)\right] $$
(19)
$$ \frac{d\left[{S}_i(t)\right]}{ d t}={k}_{thm}\left[{S}_n(t)\right]+{k}_{pn}\left[{S}_1(t)\right]\left[{S}_n(t)\right] $$
(20)

The rate constants of Reactions 14 and 15 are represented by kp and kpn. The decay rate constant of the Sn state is represented by kn, and the thermal ionization rate constant is represented by kthm. The definitions of all other parameters are identical to those of three-photon absorption (described previously).

Among these parameters, only the α01, k1, and kp values have been measured in previous studies [17, 30]. The values of other parameters were unknown. Numerical simulation showed that the absolute number of ions generated from MALDI depended on the values of all parameters; however, the relative ion intensities for various pulse widths were sensitive only to the k1, kn, kpn, and kthm values. Details are presented in Table S3 of the Supplementary Material.

S1–S1 energy pooling is the first step toward ionization. High concentrations of S1(t) can substantially increase the S1–S1 energy pooling reaction rate. Because a short laser pulse width can excite molecules from the S0 state to the S1 state within a short duration, it creates a high concentration of S1(t). In principle, the reaction rate can be increased by decreasing the laser pulse width. However, the magnitude of the increase depends on the ratio of the pulse width and the lifetime of the S1 state. If the lifetime of the S1 state is comparable to or longer than the laser pulse widths, the change in the laser pulse width does not substantially change the reaction rate of S1–S1 energy pooling. This is because the long S1 lifetime ensures that the molecules excited to S1 stay in S1 until they all undergo S1–S1 energy pooling before S1 → S0 decay. Because the accumulated number of molecules in the S1 state is identical for identical pulse energies, the various accumulation rates, because of the various pulse widths, has only a small difference in energy pooling reaction for a long S1 lifetime. This is what was observed for DHB. The lifetime of DHB is 625 ps, which is close to the largest laser pulse width used in this study. On the other hand, because the S1 lifetimes of CHCA (58 ps) and SA (10 ps) are considerably shorter than the laser pulse width, the reaction rate of S1–S1 energy pooling varies substantially with the change in the laser pulse width for these two matrices. The different S1 lifetimes of DHB, CHCA, and SA make the ion generation efficiency of DHB insensitive to the laser pulse width; however, the ion generation efficiency of CHCA and SA are sensitive to laser pulse width in the first step of energy pooling.

The second step toward ionization is (1) S1–Sn energy pooling or (2) thermal ionization. For S1–Sn energy pooling, the reaction rate depends on the concentration of S1 and Sn. If the lifetimes of both S1 and Sn are markedly longer than the laser pulse width, the reaction rate of S1–Sn energy pooling does not vary substantially with the laser pulse width. The reason is similar to the S1–S1 energy pooling described in the previous paragraph. For thermal ionization, molecules produced in the Sn state are ionized by thermal ionization before the Sn → S1 decay if the rate constant of kthm is much higher than the decay rate constant kn. Because S1–Sn energy pooling has not been observed for any matrix and the kn and kthm values are unknown, we calculated the relative ion intensity as a function of the laser pulse width for various kn and kthm values. The long lifetime of Sn and high kthm value render the relative ion intensity less sensitive to the laser pulse width. One boundary of the relative ion intensity as a function of the laser pulse width (small ratio of relative ion intensity for various laser pulse widths) is presented in Figure 6. By contrast, the short lifetime of the Sn, low kthm values, and high kpn value provide the other boundary of relative ion intensity as a function of the laser pulse width (large ratio of relative ion intensity for various laser pulse widths in Figure 6).
Figure 6

Relative ion intensity as a function of the laser pulse width according to CPCD model. Because the values of many parameters in these equations were unknown, these values were adjusted to enable the relative ion intensity to be less sensitive to the pulse width (orange line or blue line) or very sensitive to the pulse width (green line). The adjusted values became the upper and lower limits of the relative ion intensity. See details in the text. The parameter values used in calculations are as follows: (a) DHB: α01 = 1.6 × 10−17 cm2, α10 = α1n = αn1 = 2 × 10−18 cm2, k1 = 1.6 × 109 s−1, kn = 7.5 × 1010 s−1 (green, red, blue) and 2 × 108 s−1 (orange), kthm = 1 × 108 s−1 (green, orange), 1 × 1010 s−1 (red), and 1 × 1011s−1 (blue), and kp = kpn = 1.6 × 10−10 cm3 molec−1 s−1. (b) CHCA: α01 = 6.7 × 10−17 cm2, α10 = α1n = αn1 = 2 × 10−18 cm2, k1 = 1.7 × 1010 s−1, kn = 1 × 1011 s−1 (green) and 2 × 108 s−1 (orange), kthm = 1 × 108 s−1 (green) and 1 × 1011 s−1 (orange), and kp = kpn = 1.7 × 10−10 cm3 molec−1 s−1. (c) SA: α01 = 2.3 × 10−17 cm2, α10 = α1n = αn1 = 2 × 10−18 cm2, k1 = 9.5 × 1010 s−1, kn = 1 × 1011 s−1 (green) and 2 × 108 s−1 (orange), kthm = 1 × 108 s−1 (green) and 1 × 1011 s−1 (orange), and kp = kpn = 1.7 × 10−10 cm3 molec−1 s−1

Figure 6a shows the relative ion intensity of DHB as a function of the laser pulse width. When the thermal ionization rate constant, kthm, changes from 1 × 108 to 1 × 1010 and 1 × 1011 s−1, the relative ion intensity changes from rapidly changing with the pulse width to being almost independent of the pulse width, as illustrated by the green, red, and blue lines in Figure 6a. In addition, the long lifetime of the Sn state makes the relative ion intensity nearly independent of the pulse width, as shown by the orange line in Figure 6a. The relative ion intensity of DHB for pulse widths of 170 ps and 1.5 ns were 2:1 (for the scenario of high kn, 7.5 × 1010 s−1 and low kthm, 1 × 108 s−1) or 1.1:1 (for the scenario of low kn, 7.5 × 108 s−1 and high kthm, 1 × 1011 s−1). Because (1) the kn and kthm values for DHB were unknown, (2) one ratio (2:1) was different from experimental data, and (3) another ratio (1.1:1) was consistent with experimental data, the comparison of the experimental data and numerical simulation could not be used to support or refute the CPCD model for the matrix DHB.

In contrast to DHB, both CHCA and SA have very short S1 lifetimes. Although the long Sn lifetime and high kthm value can render the S1–Sn energy pooling slightly less sensitive to the laser pulse width, the short S1 lifetimes of CHCA and SA ensure that the relative ion intensity varies rapidly with the laser pulse width for all possible kn and kthm values, as illustrated in Figure 6b and c. The relative ion intensities for pulse widths of 170 ps and 1.5 ns were 2:1 (CHCA) and 6:1 (SA) (for a low kn, 2 × 108 s−1 and high kthm, 1 × 1011 s−1), or 6:1 (CHCA) and 57: 1 (SA) (for a high kn, 1 × 1011 s−1 and low kthm, 1 × 108 s−1), respectively. These relative ion intensities differed markedly from those of the experimental measurements. The results suggest that the ions of CHCA and SA in MALDI are not produced by the ionization process according to the CPCD model based on S1–S1 energy pooling.

In our previous study [17, 31], we have shown that THAP does not undergo S1–S1 energy pooling. Knochenmuss proposed an alternative energy pooling mechanism to replace the S1–S1 energy pooling for THAP [32]. They stated that ions can be produced from the proton transfer by triplet-triplet reactions,
$$ {\mathrm{S}}_0+\mathrm{h}\nu \to {\mathrm{S}}_1\to {\mathrm{T}}_1 $$
$$ {\mathrm{T}}_1+{\mathrm{T}}_1\to {\mathrm{X}}_1{\mathrm{H}}^{+}+{\left({\mathrm{X}}_1-\mathrm{H}\right)}^{-} $$
where X denotes a triplet or a singlet. The lifetime of triplet T1 is long, such that the ion generation efficiency does not depend on the laser pulse width. The current study excludes the S1–S1 energy pooling mechanism for CHCA and SA, but it cannot exclude the possible T1–T1 energy pooling mechanism if CHCA and SA in the S1 state undergo intersystem crossing. However, no intersystem and triplet–triplet reactions have been observed for CHCA and SA.

Thermal Model

Most matrices have large UV absorption cross-sections at desorption laser wavelengths and low quantum yields of photon emission. Therefore, most of the photon energy absorbed by the matrix molecules is converted into thermal energy, and the temperature in the laser-irradiated volume increases rapidly after laser irradiation. The thermal model suggests that the increase in temperature causes the sample to melt, and subsequently, thermally induced chemical reactions occur in the liquid before desorption occurs. Thermally induced proton transfer (Reaction 21) occurs in the pure matrix sample (without analyte or salt) and reaches thermal equilibrium before desorption occurs,
$$ {\mathrm{M}}_l + {\mathrm{M}}_l\to {{\left(\mathrm{M}-\mathrm{H}\right)}^{-}}_l + {{\left(\mathrm{M}+\mathrm{H}\right)}^{+}}_l $$
(21)
where subscript l represents the liquid phase, and M, (M − H), and (M + H)+ represent the neutral matrix molecule, deprotonated matrix molecule, and protonated matrix molecule, respectively. The equilibrium constant K of Reaction 21 in the liquid phase can be expressed in terms of Gibbs free energy of Reaction 21, ΔG, and temperature T,
$$ K=\frac{{\left[ M- H\right]}^{-}\times {\left[ M+ H\right]}^{+}}{M^2}={e}^{-\frac{\varDelta G}{RT}} $$
(22)
Because of the charge balance, [M − H] = [M + H]+, Equation 23 can be derived from the square root of Equation 22:
$$ \frac{cation}{neutral}=\frac{anion}{neutral}=\sqrt{K}={e}^{-\frac{\varDelta G}{2 RT}} $$
(23)

For a given matrix (therefore, a given ΔG), Equation 23 suggests that the ion-to-neutral ratio remains unchanged if the temperature is constant. Although we did not measure the temperature of the sample irradiated with various laser pulse widths in this study, the desorbed neutrals reveal information regarding the relative temperature. A previous study showed that the increase in laser fluence increases the temperature, and the increase in temperature increases the intensity and velocity of the desorbed neutrals [20]. That study indicated that the intensity and velocity of desorbed neutrals were indicators of the relative temperature. We further confirmed the correlation between the temperature and the intensity and velocity of desorbed neutrals by a separate experiment. In this separate experiment, laser pulse width and pulse energy remained the same, but the initial temperature of the matrix changed. Figure S5 in Supplementary Material shows that the intensity and velocity of desorbed neutrals changed with the initial temperature, suggesting that the intensity and velocity of desorbed neutrals can be used as indicators of the relative temperature. Figure 2a shows that the intensity and velocity of the desorbed neutrals did not vary when the samples were irradiated using a laser pulse with various pulse widths (but same pulse energy).

Degrees of fragmentation observed in ion TOF mass spectra also can be used as the indicator of relative temperatures for different laser pulse widths. High temperature tends to have a large degree of fragmentation and vice versa. Figure 2b shows that the degrees of fragmentation of desorbed ions are the same for different laser pulse widths.

Both the velocity of neutrals and fragmentation of ions indicate that the sample irradiated using various laser pulse widths reached the same temperature. This phenomenon occurred because (1) the laser pulse widths used in this study were short, (2) desorption occurred after the laser pulse irradiation on the sample and energy transfer from excited molecules to the surrounding molecules were complete. Because the temperatures are the same, we can conclude that the ion-to-neutral ratio of a given matrix does not vary with the laser pulse width according to the Equation 23 of thermal model. The prediction of the thermal model was consistent with the experimental observations.

Conclusions

Our experimental measurements demonstrated that the mass spectra of desorbed ions as well as the intensity and velocity distribution of desorbed neutrals were found to be independent of the laser pulse width in the range from 170–1500 ps for DHB, CHCA, and SA.

Ionization by two- or three-photon absorption predicted that the ion-to-neutral ratios varied substantially when the laser pulse width was varied from 170 to 1500 ps. These results are inconsistent with the experimental data, indicating that multiphoton ionization is not the major ionization process in MALDI for the matrices DHB, CHCA, and SA.

The CPCD model, based on S1–S1 energy pooling, predicted that the ion-to-neutral ratios of CHCA and SA, which have short S1 lifetimes, varied rapidly with the laser pulse width. These results are inconsistent with the experimental data, suggesting that the ionization mechanism of the CPCD model is not the major ionization process in MALDI for matrices CHCA and SA.

For DHB, which has a long S1 lifetime, the CPCD model predicted that the ion-to-neutral ratios vary rapidly with laser pulse width for a low thermal ionization rate constant, short Sn lifetime, and high S1–Sn energy pooling rate constant. By contrast, the predicted ratios by the CPCD model do not change very much with laser pulse width for a high thermal ionization rate constant or long Sn lifetime. Because the values of these parameters were unknown, neither the experimental data nor numerical simulations could be used to support or refute the CPCD model for DHB.

The ion-to-neutral ratios of DHB, CHCA, and SA predicted by the thermal model were in agreement with the experimental measurements, indicating that thermal reaction in the ground state is the major ionization mechanism in MALDI.

Notes

Acknowledgements

The authors acknowledge the support of the Thematic Research Program, Academia Sinica, Taiwan (AS-102-TP-A08) and the Ministry of Science and Technology, Taiwan (NSC 100-2113-M-001-026-MY3).

Supplementary material

13361_2017_1734_MOESM1_ESM.docx (582 kb)
ESM 1 (DOCX 582 kb)

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Copyright information

© American Society for Mass Spectrometry 2017

Authors and Affiliations

  1. 1.Institute of Atomic and Molecular SciencesAcademia SinicaTaipeiTaiwan
  2. 2.Department of ChemistryWayne State UniversityDetroitUSA
  3. 3.Department of ChemistryNational Taiwan UniversityTaipeiTaiwan
  4. 4.Department of ChemistryNational Tsing Hua UniversityHsinchuTaiwan

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