J. Am. Soc. Mass Spectrom. (2014) 25:310Y318 DOI: 10.1007/s13361-013-0792-9

RESEARCH ARTICLE

Thermal Proton Transfer Reactions in Ultraviolet Matrix-Assisted Laser Desorption/Ionization Kuan Yu Chu,1 Sheng Lee,1 Ming-Tsang Tsai,1 I-Chung Lu,1 Yuri A. Dyakov,1 Yin Hung Lai,1 Yuan-Tseh Lee,1,2 Chi-Kung Ni1,3 1

Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan 3 Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan 2

Abstract. One of the reasons that thermally induced reactions are not considered a crucial mechanism in ultraviolet matrix-assisted laser desorption ionization (UV–4 MALDI) is the low ion-to-neutral ratios. Large ion-to-neutral ratios (10 ) have been used to justify the unimportance of thermally induced reactions in UVMALDI. Recent experimental measurements have shown that the upper limit of –7 the total ion-to-neutral ratio is approximately 10 at a high laser fluence and less –7 than 10 at a low laser fluence. Therefore, reexamining the possible contributions of thermally induced reactions in MALDI may be worthwhile. In this study, the concept of polar fluid was employed to explain the generation of primary ions in MALDI. A simple model, namely thermal proton transfer, was used to estimate the ion-to-neutral ratios in MALDI. We demonstrated that the theoretical calculations of ion-to-neutral ratios exhibit the same trend and similar orders of magnitude compared with those of experimental measurements. Although thermal proton transfer may not generate all of the ions observed in MALDI, the calculations demonstrated that thermally induced reactions play a crucial role in UV-MALDI. Key words: Thermal proton transfer, MALDI, Ion-to-neutral ratio, Ionization mechanism Received: 2 June 2013/Revised: 24 November 2013/Accepted: 25 November 2013/Published o nline: 7 January 2014

Introduction

M

atrix-assisted laser desorption/ionization (MALDI), introduced by Tanaka [1] and Karas and Hillenkamp [2], has become one of the most widely used techniques for performing mass analysis of biomolecules. In MALDI, the analyte is mixed with a suitable matrix and then placed onto a sample holder. Ultraviolet (UV) laser pulses strike the target, releasing large numbers of analyte and matrix molecules. The desorbed molecules include ions and neutrals, and the ions are subsequently analyzed in a mass spectrometer. Although MALDI was invented more than two decades ago, the ionization mechanism remains unclear. The generation of primary ions in MALDI remains the most controversial component of the MALDI mechanism. Several theoretical models have been presented to explain

Electronic supplementary material The online version of this article (doi:10.1007/s13361-013-0792-9) contains supplementary material, which is available to authorized users. Correspondence to: Chi-Kung Ni; e-mail: [email protected]

the ion-generation phenomena that occur in MALDI. Hillenkamp et al. proposed a photoionization and photochemical model, which emphasizes the role of the highly electronically excited matrix in ion generation [3]. Knochenmuss suggested that the primary ions are generated by exciton hopping followed by energy pooling. The subsequent gas-phase ion-molecule reactions generate the ions observed in the mass spectrum [4]. In the cluster ionization (CI) model proposed by Karas and Kruger [5], MALDI ions are generated after sample preparation as solvated counterions in the solid state. Laser pulses caused these ions to transition from the solid state to the gas phase. Allwood et al. proposed the thermal ionization of a photoexcited matrix model. Ionization is assumed to occur through the thermal ionization of electronically excited matrix molecules [6, 7]. Chait et al. [8] and Beavis et al. [9] proposed a polar fluid model to explain the generation of MALDI ions. In this model, matrix molecules in a dense gas plume behave similarly to a bulk polar solvent, which enables ion generation. However, no quantitative description was given. Recently, Wang et al. proposed a model based on the thermal proton transfer reactions that occur on a solid-

K. Y. Chu et al.: Thermal Proton Transfer in UV-MALDI

311

state surface [10]. Kim and co-workers [11, 12] suggested that ion generation in MALDI is caused by thermal reactions, however, no specific thermal reaction and quantitative description were proposed. The ion-to-neutral ratio (or ion yields, or degree of ionization) is one crucial parameter in characterizing the properties of MALDI, and has been frequently used to justify the theoretical models of MALDI. The ion-to-neutral ratio is defined as the number of desorbed ions divided by the number of desorbed neutrals. Typical MALDI samples contain both matrix and analyte molecules; therefore, the ion-to-neutral ratio can be classified into three categories, which include the ion-to-neutral ratio of the matrix

In this study, the concept of a polar fluid was employed to explain the primary ions generated in MALDI. A simple model, namely thermal proton transfer, was used to estimate the ion-to-neutral ratios in MALDI. We demonstrate that the theoretical calculations of the ion-to-neutral ratios exhibit the same trend and similar orders of magnitude compared with those of the experimental measurements. Although thermal proton transfer may not generate all of the ions observed in MALDI, the calculations demonstrate that thermally induced reactions must play a vital role in UV-MALDI.

¼

desorbed matrix ions ; ion‐to‐neutral ratio of the analyte desorbed matrix neutrals desorbed analyte ions ; and ion‐to‐neutral ratio of the total species ¼ desorbed analyte neutrals desorbed total ions : ¼ desorbed total neutrals

Ion-to-neutral ratios have been measured by numerous research groups [12–17]. The ratios measured in these studies range from 5 × 10−4 to less than 10−7. Experiments involving the use of short laser wavelengths (193 nm at 230 J/m2) produce a large value for the ion-to-neutral ratio of the matrix, 1.4 × 10−4 [16]. For such a short wavelength, two-photon ionization may provide an additional ionization pathway in the generation of ions. Conversely, 10−7 or less than 10−7 was obtained for the ionto-neutral ratio of the matrix under typical MALDI conditions (337 nm or 355 nm, 100–300 J/m2) [12, 15, 17]. For the matrix and analyte mixture, ion-to-neutral ratios of the analyte as large as 10−3–10−4 were determined for analytes with large proton affinities, and less than 10−8 for analytes with small proton affinities, but the ion-to-neutral ratios for the matrix and ion-toneutral ratios for the total species remain at 10−7 or less than 10−7 [17]. These experimental results indicate that the ion-to-neutral ratios of the matrix and analyte are extremely dissimilar. However, values of 10−3–10−4 (or 10−3–10−5) that were not specified for the ion-to-neutral ratios of the analyte or matrix were cited in numerous recently published articles or used in theoretical simulations [4, 18–26]. A recent report [17] emphasized that the confusion of ion-to-neutral ratios of the analyte and matrix may cause the inaccurate determination of the MALDI mechanism. For example, thermally induced reactions were not considered to be crucial in the MALDI ionization mechanism because large (10−4) ion-to-neutral ratios of the matrix and total species were used to justify the contribution of thermally induced reactions in MALDI [18]. Because recent measurements have indicated that the upper limit of the ion-toneutral ratios of the matrix and total species is approximately 10 −7 at a high laser fluence and less than 10−7 at a low laser fluence [17], reexamining the possible contribution of thermally induced reactions in MALDI might be worthwhile.

Thermal Proton Transfer Model Most matrices have large UV absorption cross sections and low fluorescence quantum yields at desorption laser wavelengths, indicating that ultrafast nonradiative processes play a critical role for energy relaxation in these molecules. A nonradiative process changes the electronic energy produced by photoexcitation to vibrational energy. These highly vibrationally excited molecules transfer energy to surrounding molecules through intermolecular vibrational energy transfer. Consequently, photon energy becomes thermal energy and the temperature in the laser-irradiated volume increases rapidly. The increase in temperature causes (1) the sample to melt before desorption occurs; (2) thermally induced chemical reactions to occur in liquid; and (3) the matrix and analyte molecules (both neutrals and ions) to desorb from the liquid phase to the gas phase. Proton transfer reactions typically have small heats of reaction. For example, the heat of reaction of a proton transfer reaction (Reaction (16) in text below) and a charge transfer reaction in the gas phase are 521 and 745 kJ/mol, respectively, for 2,5dihydroxy benzoic acid (25DHB). Therefore, proton transfer reactions can be enhanced efficiently by high temperatures. These thermally induced proton transfer reactions include the following: M þ M→ðM‐HÞ− þ ðM þ HÞþ

ð1Þ

M þ A→ðM‐HÞ− þ ðA þ HÞþ

ð2Þ

ðM þ HÞþ þ A→M þ ðA þ HÞþ

ð3Þ

M þ A→ðM þ HÞþ þ ðA‐HÞ−

ð4Þ

ðM ‐ HÞ− þ A→M þ ðA ‐ HÞ−

ð5Þ

M and A represent the matrix and analyte, respectively. Reactions 2 and 3 occur when the proton affinity of the

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analyte exceeds that of the matrix. By contrast, Reactions 4 and 5 occur when the reverse order is true. These reactions occur when the molecular density is large (in the liquid phase), and reach equilibrium because of the low reaction barriers and high collision frequencies in the liquid phase. The concentrations of these chemical species decrease and the reactions slow down when desorption into the gas phase occurs. Eventually, no reactions occur after extensive expansion in the gas phase. To simplify this study, only a sample of a pure matrix was examined. The samples containing matrix-analyte mixtures will be described in a subsequent paper. For pure matrix compounds, only Reaction 1 occurs. The equilibrium constant K for Reaction 1 in the liquid phase can be written as follows:

irradiated volume during the desorption process and that κ/ρ 0 c p ∇ 2 T = 0 can be considered to be a suitable approximation (the verification of this approximation is described in Supplementary Material). Therefore, Equation 8 can be simplified:

K¼

ΔG1 ½M − H − ½M þ H þ ¼ e− RT 2 M

ð6Þ

ρ 0 cp

The solution of Equation 9 is Z Z tf ρ0 F≡ Idt ¼ αð1− ΦÞ ti

pﬃﬃﬃﬃ ΔG1 cation anion ¼ ¼ K ¼ e− 2RT neutral neutral

ð7Þ

Therefore, the cation-to-neutral ratio and anion-to-neutral ratio can be predicted if the Gibbs free energy and the temperature are known. In this study, 2,5-DHB was used to demonstrate that the ion-to-neutral ratios can be calculated in accordance with the thermal proton transfer model. The temperature and the Gibbs free energy used in Equation 7 are calculated in the following two sections.

Temperature Because the laser pulse duration (approximately 7 ns) is far shorter than the time required for desorption (in sub-μs [27, 28]), to simplify the process we assumed that desorption is absent during the laser pulse. The temperature T in the irradiated volume as a function of time t, prior to desorption, can be described using heat equation [29]: ρ0 cp

∂T ¼ κ∇2 T þ αð1− ΦÞI ∂t

ð8Þ

where ρ0, cp, κ, α, Φ, and I denote the mass density before laser irradiation, specific heat capacity, thermal conductivity, the absorption coefficient, fluorescence quantum yield of the solid matrix, and the laser intensity, respectively. The heat diffusivity (κ/ρ0cp) for organic solids is in the range of 10−5– 10−6 m2⋅s−1 [30]. A small value for the heat diffusivity implies that the thermal energy is confined within the

T

ð9Þ

cp ðT ÞdT

ð10Þ

T0

where T0 and F represent the initial temperature and laser fluence, respectively, and ti and tf are the start and stop times for the laser pulse, respectively. Equation 10 can be further modified by adding the latent heat of fusion L. Z

The Gibbs free energy for Reaction 1 is ΔG1. In accordance with the charge balance, [M − H]– = [M + H]+, Equation 7 can be derived from the square root of Equation 6:

∂T ¼ αð1− ΦÞI ∂t

F≡

tf ti

Idt ¼

ρ0 αð1− ΦÞ

Z

T

cp ðT ÞdT þ Δmð F Þ L

ð11Þ

T0

Molecular desorption per unit area is given by Δm, which depends on the laser fluence. We incorporated previous experimental measurements of Δm [17] into the following calculations. The number of desorbed molecules per unit area is 1.2 × 1017 m−2 (or 2 × 10−7 mole/m2) at a laser fluence of 50 J/m2 and 2.5 × 1018 m−2 (or 4 × 10−6 mol/m2) at a laser fluence of 200 J/m2. Typical latent heats of fusion for organic molecules exhibiting intermolecular hydrogen bonding are in the range of 10–30 kJ/mol [30]. In Equation 11, the value of the second term on the right-hand side is less than 0.1 % of the laser fluence F. Therefore, Equation 10 can be used to achieve a suitable approximation. The temperature can be calculated once the absorption coefficient, fluorescence quantum yield, mass density, and heat capacity are known. The absorption coefficient for 2,5-DHB is 8.7 × 104 cm−1 [31], the mass density is 1.43 ± 0.05 g⋅cm−3, which was measured from the volume change of saturated 25DHB aqueous solution by adding a given weight of 25DHB powder into the solution. The fluorescence quantum yield is 0.06 ± 0.02, which was measured using a commercial integrating sphere (Fluorescence Spectrometer, model: FLS 920 Edinburgh Photonics, Edinburgh Instrument Ltd.). We calculated the temperature dependent heat capacity using a modification of Einstein’s heat capacity model. According to this model [32], the constant volume molar heat capacity Cv (J mole−1 K−1) of an atomic crystal is given by 2 hv hv e kT C v ¼ 3R ð12Þ 2 hv kT kT 1− e where h is Planck’s constant, R is the gas constant, and v is the oscillator frequency. We calculated the molar heat capacity of the solid matrix using Equation 13:

K. Y. Chu et al.: Thermal Proton Transfer in UV-MALDI

hv kT

2

3N−6−m hv X 3 e kT i 2 R 2 þ R þ hvi 2 hv 2 kT i 1− e kT 1− e kT hvi

hv

e kT

ð13Þ The first term represents the molecular oscillation relative to neighboring molecules within the solid. The second and third terms represent the contribution from molecular rotation and vibration, respectively. Because only temperatures greater than room temperature are relevant to this study, the first term approaches 3R. When the temperature is below the melting point, molecular rotation is restricted. Therefore, the second term is not included in the calculations for temperatures below the melting point. The third term includes all possible molecular vibrations. Vibrational frequencies from ab initio calculations using Gaussian-09 were used in the calculation of heat capacity. Only vibrational modes with low vibrational frequencies make substantial contributions in Equation 13. Vibrational modes possessing large amplitudes of motion (e.g., internal rotation) typically have low vibrational frequencies. However, the vibrational motions of these modes are restricted in the solid state and they are not completely free to undergo vibrational motion in the liquid phase. The number of restricted vibrational motions at low temperature was from the fit of calculated heat capacity to experimental measurements. In the calculations of heat capacity, no rotation occurs and the number of restricted motions with a low vibrational frequency is 7 at low temperatures; rotation is included in the calculations and the number of restricted motions with a low vibrational frequency gradually decreases to 3 at high temperatures. The detailed calculations are described in Supplementary Material. The relationship between molar heat capacities (i.e., Cv and Cp) is given by the following equation: C p ¼ C v þ VT

a2 b

ð14Þ

where a is the coefficient of thermal expansion and b is the isothermal compressibility. The volumetric thermal expansion for common liquids ranges from 2 × 10−4 to 1.5 × 10−3 (K−1) [33]. The isothermal compressibility for common organic liquid is from 0.5 × 10−4 to 1.5 × 10−4 atm−1 [34]. Both isothermal compressibility and volumetric thermal expansion of 2,5-DHB are not available now. The values a = 8.5 × 10−4 (K−1) and b = 4.5 × 10−5 atm−1 (similar to the values of aniline and phenol) in Equation 14 were used for the calculation of Cp. The specific heat capacity cp (Jg−1 K−1), used in Equation 10, was determined according to the relationship, cp = Cp/Mw, where Mw is the molecular weight. The results of the heat capacity calculations for 2,5-DHB are illustrated in Supplementary Material. The surface temperature T, resulting from laser irradiation, can be calculated using Equation 10. The findings are shown in Figure 1 and represent

Temperature (K)

C v ¼ 3R

313

1000

500

0

50

100

150

200

250

300

2

Fluence (J/m ) Figure 1. Calculated surface temperature (black line) for 2,5DHB before desorption occurs. Effect of decomposition on temperature was included in calculations. In the uncertainty estimation, thermal conductivity, range of the numbers of restricted vibrational modes in the solid state and the liquid phase, and ranges of thermal expansion coefficient and isothermal compressibility were taken into consideration. The effects of these factors on temperature are presented in details in Supplementary Material. The gray curves represent the maximum and minimum of temperature attributable to the total uncertainty of these factors

the temperature in the condensed phase (including the solid and liquid phases) before desorption occurs. In the MALDI process, surface temperature increases rapidly when laser irradiation occurs and reaches the maximal value prior to molecular desorption. Because energy is consumed during desorption, the temperature decreases as molecules desorb from the surface to form a dense gas plume. Additional decreases in temperature are caused by the adiabatic expansion of the dense plume. These temperatures have been estimated based on the internal energy of peptides after desorption occurs, or based on the survival yields of thermometer ions [20, 35–38]. The measured temperatures in these previous studies represent the average temperature during the entire desorption process. The temperature prior to desorption, which was used in this study, was not presented in these previous studies. The measured temperature derived from the timeresolved blackbody radiation represents the temperature evolution that occurs during the MALDI processes [39]. The temperature illustrated in Figure 1 represents the temperature before desorption occurs, which corresponds to the peak value of the measured temperature derived from the time-resolved blackbody radiation. The calculated temperature for 2,5-DHB was similar to the experimental measurement [39]. The high temperature derived from calculations can also be justified by the decomposition of the matrix itself. The dissociation channel of 2,5-DHB at the ground state, C6H3(OH)2COOH → C6H3(OH)OCO + H2O has a barrier height of 42 kcal/mol. This dissociation channel was observed in molecules placed under collisionless conditions [40], and in molecules produced from laser desorption of

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K. Y. Chu et al.: Thermal Proton Transfer in UV-MALDI

solid sample [40, 41]. Although high temperatures can cause 2,5-DHB molecules to dissociate into fragments, the dissociation rate is not sufficiently fast and, therefore, only a fraction of the 2,5-DHB molecules dissociate into fragments [41]. Once desorption occurs, the desorption energy and adiabatic expansion of the gas plume in a vacuum causes the temperature to decrease rapidly (within 30 ns [39]) and eventually the dissociation process stops. The dissociation rate of this channel was calculated using Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The temperature dependence of the dissociation rate constants were determined to be 4.0 × 10−4 s−1 (550 K), 8.5 × 102 s−1 (750 K), 9.7 × 105 s−1 (1000 K), 5.5 × 107 s−1 (1250 K), and 7.3 × 108 s−1 (1500 K). The experimental data of this study indicate that approximately 10 % of 2,5-DHB dissociates into fragments at a laser fluence of 180 J/m2 (Supplementary Material), which corresponds to the temperature of 900 K. This is extremely similar to the temperature calculated in this study. Because a portion of the photon energy is used in decomposition, the temperature increase caused by the photon energy is expected to be reduced when the decomposition of molecules is taken into consideration. The reduction of the temperature increase was estimated based on the dissociation rate and bond energy. The reductions were approximately 0 % (550 K), 0.05 % (750 K), and 1.5 % (1000 K). Effect of decomposition on temperature was included in calculations of Figure 1. The detailed calculations are presented in Supplementary material.

package [43]. The results are presented in Supplementary Material. Reaction 16 depicts the proton transfer for isolated molecules. The respective heat of reaction ΔH16 calculated using ab initio methods was 521.7 kJ/mol. In the ab initio calculations, the geometries of the reactants and products were fully optimized using the hybrid density functional B3LYP method [44–47] with the 6-31G* basis set [48]. The energies of the reactants and products at B3LYP/6-31G* optimized geometries were calculated using the G3-type computational scheme [49], specifically the G3(MP2,CCSD)//B3LYP modification [50, 51]. Zero point energy (ZPE) corrections were taken into account by using B3LYP/6-31G* frequencies without scaling. All of the ab initio calculations were performed using the Gaussian 09 package [43]. The optimized structures show that proton attaches to carboxyl group to form protonated 2,5-DHB, and detaches from carboxyl group to form deprotonated 2,5-DHB. By using the respective vibrational frequencies and moments of inertia, the entropy for each molecular species in Equation 16 was calculated. The change in entropy was small. Values for TΔS were less than 2 kJ/mol, even at temperatures as high as 2000 K, which is only 0.5 % of ΔH16. Consequently, using ΔG16 ≈ ΔH16 for this reaction is appropriate. In the calculations using the PCM, dielectric constant ε played an essential role. Because the dielectric constant generally decreases as the temperature increases, the Gibbs free energy for Reaction 15 is expected to decrease accordingly. By contrast, the Gibbs free energy for Reaction 17 increases as the temperature increases. The dielectric constant for polar liquids as a function of temperature was calculated using the Kirkwood-Froehlich equation [52, 53].

Gibbs Free Energy The Gibbs free energy for Reaction 1 in the liquid phase, ΔG1, can be derived using the Gibbs free energies of the following three reactions: 2Ml →2Mg

Mg þ Mg →ðM ‐ HÞ g − þ ðM þ HÞ g þ

ð15Þ

ð16Þ

ðM ‐ HÞ g ‐ þ ðM þ HÞ g þ →ðM ‐ HÞ l ‐ þ ðM þ HÞ l þ ð17Þ

Subscripts g and l represent the gas and liquid phases, respectively. The Gibbs free energy relationship for these reactions is ΔG1 = ΔG15 + ΔG16 + ΔG17. Reaction 15 represents the transition from the liquid phase to isolated molecules. Reaction 17 depicts the solvation of ions. The corresponding Gibbs free energies were calculated using the polarizable continuum model (PCM) [42] included in the Gaussian 09 computational

gμ2 ¼

9kT ðε − ε∞ Þð2ε þ ε∞ Þ 4πρN εðε∞ þ 2Þ2

ð18Þ

The Kirkwood correlation factor g is greater than 1 when molecules tend to direct themselves using parallel dipole moments. For molecules that prefer to order using antiparallel dipoles, g is less than 1. If no specific correlation exists, g is equal to 1. At high temperatures, g approaches 1. The approximation g = 1 was used in the calculations because only the high temperature region is relevant to this study. The high-frequency dielectric constant ε∞ is related to the molecular polarizability α' through the Clausius-Mossotti equation: ε∞ − 1 4π ¼ α0 ρN ε∞ þ 2 3

ð19Þ

The respective polarizability and dipole moment (calculated using the Gaussian 09 MP2/6-31 + G** method) for 2,5-DHB were α' = 1.84 × 10−23 cm3 and μ = 2.8 D, respectively. The computed polarizability value includes the

K. Y. Chu et al.: Thermal Proton Transfer in UV-MALDI

315

electronic and vibrational polarizabilities. The density as a function of temperature in Equations 18 and 19 was calculated using Equation 20:

calculations of solvation energy (ΔG15 and ΔG17), the hydrogen bond is not taken into consideration in the PCM. Fortunately, the solvation energies affected by the hydrogen bond in ΔG15 and ΔG17 have a similar order of magnitude but exhibit opposite signs. Therefore, they are likely to cancel each other out and the uncertainty of the PCM calculations caused by not considering the hydrogen bond is small. The uncertainties of dielectric constant from Equations 18–20 and solvation energy from PCM are not well studied. We used ± 8 kJ/mol to represent the uncertainties due to dielectric constant and solvation energy.

ρ N ðT Þ ¼

ρN ðT ¼ 300K Þ ð1 þ 0:0008 ΔT Þ

ð20Þ

where the room temperature density was derived from the experimental measurement and coefficient of the volumetric thermal expansion, 8 × 10−4 (K−1), which was derived from the average volumetric expansion coefficient of common liquids [33]. The temperature-dependent dielectric constant calculated using Equations 18–20 is presented in Supplementary Material. The Gibbs free energy of Reaction 1 in the liquid phase is shown in Figure 2a. Based on the temperature values shown in Figure 1 and the Gibbs free energy values shown in Figure 2a, the theoretical predictions for the ion-to-neutral ratios in the liquid phase were determined using Equation 7 and are given in Figure 2b. The ion-to-neutral ratio calculated using previous experimental measurements [17] is also shown in Figure 2b for comparison. The Gibbs free energy of Reaction 1 is dominated by ΔH16 and ΔG17. The uncertainty of ΔH16 derived from an ab initio calculation was approximately ± 6 kJ/mol. In the

(a)

G1 (kJ/mol)

-250

Effects of Reactions in the Gas Plume After molecules desorb from the surface, they generate a dense gas plume, and the collisions in the dense plume cause Reaction 1 to occur. However, the collision frequency decreases rapidly as the plume expands and the reaction eventually stops. We estimated the generation and loss of ions in the gas phase by separately calculating the forward reaction of Reaction 1, M + M → MH+ + (M-H)–, and the backward reaction of Reaction 1, MH+ + (M-H)– → M + M. The generation of ions in the forward reaction and the loss of cations and anions caused by the ion-ion recombination that occurs in the backward reaction in the gas phase were calculated using Equations 21 and 22, separately. d ½M H þ d ½ðM − H Þ− ΔE ¼ ¼ k f ½M 2 ¼ σ f < v > e− RT ½M 2 dt dt ð21Þ

-300

-350 400

600

800

1000

1200

Temperature (K)

−

d ½M H þ d ½ðM − H Þ− ¼− ¼ k b ½M H þ ½ðM − H Þ− ð22Þ dt dt ¼ σ b < v > ½M H þ ½ðM − H Þ−

1E-6

ion-neutral ratio

(b) 1E-7

1E-8 Theory Experiment 1E-9

0

50

100

150

200

250

2

Fluence (J/m ) Figure 2. (a) Gibbs free energies as a function of temperature for Reaction 1 in the liquid phase. (b) Ion-to-neutral ratios derived from the thermal proton transfer model and the values derived from experimental measurements. Dotted lines represent the maximum and minimum of ion-to-neutral ratios attributable to the uncertainties of temperature and Gibbs free energy

The rate constant of the forward reaction (an endothermic reaction) was estimated using simple collision theory [54]. σf, Gv9, and ΔE represent the reaction cross section, relative velocity, and activation energy (which is equal to heat of reaction), respectively. The rate constant of the backward reaction was estimated using the hard sphere model because it is an exothermic reaction and no reaction barrier exists. In the calculations of both the forward and backward reactions, the initial concentration of the neutrals and ions are the corresponding concentrations in the liquid phase before desorption occurs. As the molecules desorb from the surface, the volume increases rapidly. The change in volume as a function of time was estimated based on the relative velocity and angular distributions of the desorbed molecules. The relative velocity and angular distributions were measured in a previous study [41] and portions of the data are

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K. Y. Chu et al.: Thermal Proton Transfer in UV-MALDI

presented in Supplementary Material. The relative velocities normal to the surface were approximately 1400 m/s. The relative velocity parallel to the surface was calculated using the angular distribution, which was 500 m/s. The heat of reaction, ΔE, depends on the dielectric constant of the gas plume. The dielectric constant was calculated using Equations 18 and 19. The dielectric constant decreases rapidly as the plume expands in the gas phase. Consequently, the solvation energy decreases rapidly and the heat of reaction approaches the heat of reaction in a vacuum (512 kJ/mol). Few ions can be generated in the gas plume because of the large heat of reaction that occurs in the forward reaction. The total number of ions generated in the gas phase is less than 0.1 % times that of the initial ions generated in the liquid phase. In the calculations for the backward reaction, several distinct mechanisms may contribute to the ion-ion recombination, including the charge transfer caused by direct contact of counterions following electron hopping, and electron and proton tunneling. To simplify the calculations, a reaction cross section was used to include all of the various recombination mechanisms. A large cross section, σb = π(10−7 cm)2, was used to ensure that we did not underestimate the ion-ion recombination reaction. The loss of ions caused by recombination (backward reaction) was determined to be less than 0.05 % of the initial ions generated in the liquid phase. The detailed calculations for both the forward and backward reactions are presented in Supplementary Material. Ion–ion recombination was demonstrated to be a crucial process in the simulation conducted by Knochenmuss [25] because the initial ion concentration was extremely large (ion yields: 10−3–10−4). In the calculations performed in this study, the initial ion concentration was too low (ion yields: 10−7 or less than 10−7) to cause substantial ion–ion recombination. Consequently, the reaction in the gas plume does not cause the ion-to-neutral ratio to change substantially. The ratio measured in the gas phase is extremely similar to the ratio generated in the liquid phase. Although Reaction 1 does not reach equilibrium in the gas plume, this does not signify that the other reactions do not reach equilibrium in the gas plume. For example, Reaction 3, (M + H)+ + A →M + (A + H)+, can reach near equilibrium in the gas plume. The rates of the forward and backward reactions of Reaction 3, calculated using equations analogous to Equations 22 and 21, respectively, were approximately 104 to 106 times faster than the forward and backward reaction rates of Reaction 1 obtained using Equations 22 and 21. This is because the concentrations of M and A were large, and the heat of reaction of the backward reaction of Reaction 3 was small.

fluence) to 1000 K (corresponding to a laser fluence of 200 J/m2) for Reaction 1. The considerable increase in concentration caused by the increase in temperature suggests that any preformed ions at room temperature were negligible. Temperature plays a vital role in MALDI. Large UV absorption cross sections and low fluorescence quantum yields are necessary to generate high surface temperatures. One argument against the importance of thermally induced reactions in UV-MALDI is that the ion intensity resulting from infrared MALDI (IR-MALDI) is approximately 1000 times lower than that resulting from UV-MALDI. Because no electronically excited states are involved in IR-MALDI, thermally induced reactions are more likely to occur than other types of reaction. In a previous study, the weak ion intensities resulting from IR-MALDI compared with those resulting from UV-MALDI were considered to indicate that thermally induced reactions are not crucial in UV-MALDI [23]. However, the low ion intensities resulting from IRMALDI can readily be explained by the thermal model used in this study. The respective absorption cross sections in the infrared region are typically 10–100 times smaller than those in the ultraviolet region. According to the thermal proton transfer model used in this study, small absorption cross sections cause lower temperatures, as shown in Equation 10. Consequently, the ion intensity is greatly reduced in IRMALDI. Large IR laser fluence is necessary for IR-MALDI to generate an ion intensity similar to that generated in UVMALDI. For example, the threshold fluence of IR-MALDI was determined to be within 4000–12000 J/m2 [55], which is approximately 20–60 times larger than the threshold fluence of UV-MALDI. We used several approximations in the thermal proton transfer model, which might account for the differences we observed between the calculation and experimental results. For example, using the harmonic oscillator approximation when we calculated the molar heat capacity (Equation 13) for the solid matrix might have caused differences between the calculated temperatures and the actual temperatures. Accurate temperature calculations also depend on accurate absorption cross section measurements for the solid-state matrix. The homogeneity of the thin film and a precise measure of its thickness may be critical in determining the absolute absorption coefficient. The absorption coefficient used in Equation 9 indicates that the saturation of absorption does not occur. However, saturation is likely to occur in the high laser fluence region. In the calculations of solvation energy (ΔG15 and ΔG17), the dielectric constant plays a critical role. The accuracy of the dielectric constant calculations, according to Equations 18 and 19, at high temperatures is uncertain. No experimental measurement of the dielectric constants of 2,5-DHB or similar organic molecules at high temperatures is currently available for comparison. Although we demonstrated that thermal proton transfer must play a crucial role in UV-MALDI, this does not signify

Discussion In the thermal proton transfer model used in this study, the ion concentration greatly increased as the temperature increased. For example, Figure 2b shows that the ion-toneutral ratios increased by a factor of more than 1000 as the temperature increased from 300 K (corresponding to zero

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that all of the ions observed in MALDI resulted from the thermal proton transfer reaction. For example, in addition to protonated cations and deprotonated anions, radical cations and anions of 2,5-DHB were also observed. Radical cations and anions must be produced by other reactions. However, the fraction of radical cations and anions in the total ion intensity of the 2,5-DHB mass spectrum is small. Radical cations and anions were not observed in the other MALDI matrices. For example, no radical cations and anions were observed for 2,3-dihydroxybenzoic acid (2,3-DHB), 2,4-dihydroxybenzoic acid (2,4-DHB), 2,3dihydroxybenzoic acid (2,3-DHB), 2,4,6-trihydroxyacetophenone (THAP), and α-cyano-4-hydroxycinnamic acid (CHCA). Electrons observed in MALDI experiments and the difference in positive and negative ion intensities in MALDI experiments are the other examples that suggest that thermal proton transfer reactions do not generate all of the observed ions. However, the difference between positive and negative ion intensities is small. A previous study [56] indicated that positive and negative ion intensities exhibit similar intensities in a laser fluence of 180–280 J/m2 for 2,5-DHB deposited on stainless steel substrates. These are typical laser fluences used in MALDI. Outside this laser fluence range, positive ion intensity is larger than negative ion intensity, but the difference between them is smaller than a factor of 2. The difference becomes less than 20 % if 2,5-DHB is deposited on glass substrates. These studies suggest that other mechanisms, for example photoelectrons generated from the metal surface, contribute to the generation of MALDI ions, but they are not the dominant mechanisms.

exclude the possibility that other mechanisms contribute to these processes.

Conclusions We demonstrated that the ion-to-neutral ratios of 2,5-DHB calculated using a thermal proton transfer model indicate an analogous trend and exhibit orders of magnitude that are similar to those derived from experimental measurements. The calculations were performed without using any fitting parameters, and the results provide only an estimated order of magnitude of the ion-to-neutral ratio of the matrix. Although the calculated values derived from this model differed by approximately one order of magnitude from those derived from the experimental measurements, the difference between the values derived from this model and the experimental measurements is much smaller than the difference between the values derived from the other models and the experimental measurements. For example, ion-toneutral ratios derived from the energy pooling model and the thermal ionization of photoexcited matrix model differed by approximately four orders of magnitude from those derived from the experimental measurements [4, 6, 7]. The findings of this study indicate that thermally induced proton transfer must play a critical role in MALDI processes, but we do not

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