Sven
Heiles‡
,
Richard J.
Cooper
,
Matthew J.
DiTucci
and
Evan R.
Williams
*
Department of Chemistry, University of California, Berkeley B42 Hildebrand Hall, Berkeley, California 94720-1460, USA. E-mail: erw@berkeley.edu; Tel: +1-510-643-7161
First published on 26th January 2017
Sequential water molecule binding enthalpies, ΔHn,n−1, are important for a detailed understanding of competitive interactions between ions, water and solute molecules, and how these interactions affect physical properties of ion-containing nanodrops that are important in aerosol chemistry. Water molecule binding enthalpies have been measured for small clusters of many different ions, but these values for ion-containing nanodrops containing more than 20 water molecules are scarce. Here, ΔHn,n−1 values are deduced from high-precision ultraviolet photodissociation (UVPD) measurements as a function of ion identity, charge state and cluster size between 20–500 water molecules and for ions with +1, +2 and +3 charges. The ΔHn,n−1 values are obtained from the number of water molecules lost upon photoexcitation at a known wavelength, and modeling of the release of energy into the translational, rotational and vibrational motions of the products. The ΔHn,n−1 values range from 36.82 to 50.21 kJ mol−1. For clusters containing more than ∼250 water molecules, the binding enthalpies are between the bulk heat of vaporization (44.8 kJ mol−1) and the sublimation enthalpy of bulk ice (51.0 kJ mol−1). These values depend on ion charge state for clusters with fewer than 150 water molecules, but there is a negligible dependence at larger size. There is a minimum in the ΔHn,n−1 values that depends on the cluster size and ion charge state, which can be attributed to the competing effects of ion solvation and surface energy. The experimental ΔHn,n−1 values can be fit to the Thomson liquid drop model (TLDM) using bulk ice parameters. By optimizing the surface tension and temperature change of the logarithmic partial pressure for the TLDM, the experimental sequential water molecule binding enthalpies can be fit with an accuracy of ±3.3 kJ mol−1 over the entire range of cluster sizes.
One way to obtain detailed information about ion–solvent interactions is to study hydrated ions in a well-defined environment, i.e., clusters of water molecules containing a single ion.9–27 In this way, any effects of impurities or counter ions are eliminated. By investigating size selected clusters, it is possible to monitor how thermodynamic quantities, such as water molecule binding enthalpies, evolve with cluster size.13,28–45 Several methods have been used to measure the sequential water molecule binding energies of hydrated ions with up to 14 water molecules attached.28–45 The most commonly used approaches are high-pressure ion source mass spectrometry (HPMS),28–34 threshold collision induced dissociation (TCID)35–42 and blackbody infrared radiative dissociation (BIRD).43–45 Singly and doubly charged hydrated ions have been studied with these methods. The results reveal that especially for the first hydration shell, the ion identity and charge state significantly influence water molecule binding enthalpies. As the result of increasing ion solvation, the influence of the sequential water binding enthalpies on the specific ion–water interactions diminishes with increasing cluster size. For example, the sequential water molecule binding enthalpies for hydrated Li+ decrease from 134 to 63 kJ mol−1 for one to six water molecules attached.37
Ultraviolet photodissociation (UVPD) experiments have been used to deduce water molecule binding enthalpies at larger cluster sizes and these measurements can be made with high precision. The sequential water binding enthalpies for hydrated aniline, protonated proflavine, protonated tryptophan, rhodamine 590 and rhodamine 640 ions have been studied by UVPD.46,47 In these experiments, the sequential water molecule binding enthalpy is deduced from the number of water molecules that are lost from the cluster upon photoexcitation with a photon of known energy. For aniline+·(H2O)n with n = 5–20 (where n is the number of water molecules) for example, the energy removed per water molecule decreases from 74.5 kJ mol−1 at n = 5 to an average value of ∼40.2 kJ mol−1 between n = 10–20.46 A very similar trend but slightly higher sequential water molecule binding enthalpies were measured for hydrated doubly charged atomic ions and paraquat.47,48 These UVPD studies indicate that for larger cluster sizes, the sequential water molecule binding enthalpies are close to the bulk water vaporization enthalpy (43.1 kJ mol−1 (ref. 49)) and depend only slightly on the cluster size. These results and recent velocity map imaging experiments50 are consistent with the idea that the absorbed photon energy is fully redistributed into the internal modes of the entire cluster for n > 10, resulting in sequential water molecule evaporation, although ion fluorescence resulting in fewer water molecules that are lost can also occur.47,51
Despite the progress in obtaining thermodynamic reference data for larger hydrated ions, only limited data for sequential water binding enthalpies over a broad range of cluster sizes and for different charge states is available. These data are especially important to accurately model ion-induced water nucleation6,7 in the atmosphere and for ion nanocalorimetry.9–13 In the latter method, hydrated ions are irradiated, for example, with slow electrons that can lead to a one-electron reduction of the ion.9 The recombination energy (RE), which corresponds to the energy released due to the ion-electron recombination, leads to the evaporation of water molecules from the hydrated ion. The RE can be obtained from the number of water molecules that are lost by modeling of this thermochemical process for water evaporation, which is based on the sequential water molecule binding energies as well as energy that partitions into translational, rotational and vibrational modes of the departing water molecules. By extrapolating REs measured as a function of cluster size to “infinite dilution”, absolute reduction potentials of metal ions can be measured and ultimately related to an absolute reduction potential of the standard hydrogen electrode (SHE).10,11,13 Due to the lack of thermochemical reference data for sequential water binding enthalpies of large ion-containing water clusters, the RE modeling currently uses values from the Thomson liquid drop model (TLDM).52–58 The TLDM combines the self-energy of solvating a charged particle in the Born solvation model with the increased energy due to the droplet surface area and the bulk vaporization energy to give sequential binding enthalpies of water molecules as a function of cluster size. Any systematic error in the TLDM will result in an error for the absolute SHE value obtained from the ion nanocalorimetry measurements, and this error increases with increasing number of water molecules that are lost as a result of ion-electron recombination.
In this work, we present an extensive study of sequential water binding enthalpies as a function of charge state (z = +1–3), ion identity, and cluster size (n = 20–500) derived from high-precision UVPD measurements. A newly developed program is used to deduce ΔHn,n−1 from experimental precursor and product cluster distributions. The various ions studied for every charge state, the different types of electronic transitions ranging from atomic transitions to electronic excitations in aromatic systems to charge transfer transitions, and the diverse chemical nature of the formed atomic, organic and inorganic ions, make the herein presented binding enthalpy trends important for many chemically relevant systems. The sequential water molecule binding enthalpies show a clear dependence on the ionic charge and cluster size and depend less on ion identity. The results are compared to binding enthalpy predictions from the TLDM. A better agreement between theory and experiment is obtained for the TLDM model employing water ice parameters at 133 K, indicating that the clusters may largely solidify under these experimental conditions.
Results of UVPD of (Phe + H)+, Cu2+ and [Ru(NH3)6]3+ with 193.0 ± 0.5 nm laser light, 250 Hz repetition rate and 0.5 s irradiation time for isolated ensembles with n = 198–202 water molecules are shown in Fig. 1b–d, respectively. In addition to the isolated precursors at n = 198–202, new clusters with n = 195–197, which are formed by BIRD, appear. The mean cluster size, 〈n〉, for the precursor distributions shown in Fig. 1b–d containing (Phe + H)+, Cu2+ and [Ru(NH3)6]3+ ions is 198.73, 198.09 and 198.60, respectively. There are also product ion distributions at lower mass that are generated due to UVPD (Fig. 1b–d). The average cluster size of the highest mass product ion distribution that is separated from the precursor is 185.24, 184.66 and 185.17 for (Phe + H)+, Cu2+ and [Ru(NH3)6]3+. This product ion distribution has 〈x〉 = 13.50, 13.43 and 13.43 fewer water molecules than the corresponding precursor ion. Both the precursor and fragment distributions include contributions from BIRD, which should effect both populations similarly for large clusters.48 The difference in the average number of water molecules for these populations should reflect just UV absorption consistent with 〈x〉 being independent of the laser irradiation time (see ESI†). For (Phe + H)+·(H2O)198–202 and Cu2+·(H2O)198–202, additional product ion distributions are formed at even lower mass (Fig. 1b and c). For the second and third product ion distribution of (Phe + H)+ and Cu2+ containing water clusters, an average of 26.46 (26.83) and 40.77 (40.31) water molecules are lost from the precursor ion distribution. For the UVPD mass spectra shown in Fig. 1b and c, the consecutive product ion distributions differ by 13.4–13.5 water molecules. Thus, the absorption of one 193 nm UV photon by ions solvated by ∼200 water molecules results in the loss of about 13.4 water molecules and the formation of product ion distributions with similar hydration state width as the precursor distribution, namely 5–7 hydration states for the precursor and 5–8 for product ion distributions. These multiple product ion distributions (Fig. 1b and c) are due to sequential UV photon absorption, i.e., one, two and three 193 nm UV photons are absorbed sequentially to form the first, second and third product ion distribution, respectively, and not to multiphoton processes. A detailed discussion of sequential UV photon absorption on experimental UVPD results is provided in ref. 48.
Whereas 〈x〉 for (Phe + H)+·(H2O)198–202, Cu2+·(H2O)198–202 and [Ru(NH3)6]3+·(H2O)198–202 do not significantly differ (Fig. 1b–d), the photofragment yield is affected by ion identity. The UVPD yields vary from 51% for (Phe + H)+·(H2O)198–202 to 31% and 12% for Cu2+·(H2O)198–202 and [Ru(NH3)6]3+·(H2O)198–202, respectively. (Phe + H)+ in aqueous solution has a strong absorption band between 190–210 nm as a result of the phenyl group.59 The UV absorption at 193 nm for [Ru(NH3)6]3+ is due to a ligand-to-metal charge transfer transition.60 The molar extinction coefficient for (Phe + H)+ in the water at 193 nm is about six times larger than that for [Ru(NH3)6]3+,60 consistent with the higher photoproduct yield for (Phe + H)+·(H2O)198–202 compared to [Ru(NH3)6]3+·(H2O)198–202. No solution phase reference data is available for Cu2+ ions (nor other divalent transition metal ions) at 193 nm precluding a comparison to this ion. However, the photoproduct yield for Cu2+·(H2O)198–202 and other divalent transition metal ions used in this study (Scheme 1) are similar to previously reported results on hydrated divalent ions with n ≤ 124.48
(Phe + H)+·(H2O)198–202, Cu2+·(H2O)198–202 and [Ru(NH3)6]3+·(H2O)198–202 lose ∼13.5 water molecules upon UVPD at 193 nm. Previously reported sequential water molecule binding energies, En,n−1, are ∼0.45 eV per water molecule for clusters with n = 10–124.46,48 Assuming that water molecules are lost sequentially as a result of full internal conversion from an excited electronic state to the ground electronic state, the number of water molecules that are lost is estimated to be 14.2 for a 6.41 eV photon. This is ∼0.7 water molecules higher than the experimental value of ∼13.5. Because this simple calculation does not take into account energy partitioned into the degrees of freedom of the water molecules that evaporated, this calculation overestimates the number of water molecules that are lost. Hence, our experimental results are consistent with water loss due to full internal conversion of the absorbed photon. Further evidence for sequential water molecule loss and full internal conversion producing the product distributions at about 〈x〉 = hν/En,n−1 below the precursor distribution in UVPD experiments of hydrated ions comes from the wavelength-dependent UVPD measurements of anilinium·(H2O)69–71 shown in Fig. 2b and c. In the 193 nm UVPD experiment shown in Fig. 2b, there are two product ion distributions. The distribution corresponding to the most extensive water loss is shifted by 〈x〉 = 13.47 water molecules compared to the precursor ion distribution whereas the other distribution is shifted by 〈xf〉 = 7.22. The product distribution with the highest water loss is consistent with the expected loss of ∼13.5 water molecules due to full internal conversion of a 193 nm photon, and the additional product ion distribution is due to partial internal conversion followed by fluorescence with an emitted photon wavelength of ∼2.80 eV.47 The fluorescence quantum yield, obtained from the relative ion abundances of the two product ion distributions, is 0.11. UVPD of anilinium·(H2O)69–71 at 248 nm results in only a single product ion distribution corresponding to 〈x〉 = 10.68 (Fig. 2c). For the photon energy of 5.0 eV (248 nm), an estimated water loss of 〈n〉 = 11.11 is expected from full internal conversion, consistent with the experimental result. These measurements show that the fluorescent quantum yield varies significantly with excitation photon wavelength.
Because the number of water molecules lost from precursor ion distributions to product ion distributions at ∼hν/En,n−1 are consistent with a full internal conversion process and additional ion product distributions are identified for partial internal conversion/fluorescence processes, we conclude that full internal conversion and sequential water loss are the major processes leading to product ion distributions at 〈x〉 ≈ hν/En,n−1 in UVPD.
In addition to cluster size, the charge state of the hydrated ion affects the average number of water molecules that are lost (Fig. 4). For clusters of the same median size, 〈x〉 for monovalent ions is bigger than that for divalent ions which is bigger than that for trivalent ions up to a cluster size ∼150. This is consistent with the TLDM model that predicts this charge-dependent ordering of En,n−1.52 The differences in the number of water molecules that are lost deceases significantly for clusters with more than ∼150 water molecules (Fig. 4). This indicates a vanishing influence of the charge state on the binding energies of water molecules to the large clusters.
The identity of the ion of a given charge state and at the same cluster size has only a small effect on the number of water molecules lost (Fig. 4). For example, [Ru(NH3)6]3+ and [Co(NH3)6]3+ with 100 water molecules or [Ru(NH3)6]3+ and [Cr(NH3)6]3+ with 350 water molecules lose 13.21 ± 0.03 and 13.16 ± 0.03 or 13.21 and 13.26 water molecules at 193 nm excitation wavelength. Similarly, 〈x〉 differs only by 0.02 for 248 nm UVPD of (Phe + H)+ and anilinium with 120 water molecules attached. Although the number of water molecules lost following photoabsorption is minimally affected by ion identity for the majority of the ions investigated, 〈x〉 at 193 nm for hydrated Mn2+ and Fe2+ ions differs significantly from that for Cu2+ and Co2+ at precursor sizes with n > 130. At a precursor ensemble size of 220, 〈x〉 is 13.38 ± 0.04 and 12.94 ± 0.19 for Cu2+ and Fe2+, respectively. More water molecules can be lost from a cluster either as a result of lower water molecule binding energies or competition between water molecule loss and internal energy conversion. If internal conversion is not instantaneous, ions are not heated to as high of an effective temperature compared to when internal conversion is instantaneous because water molecules that evaporate during internal conversion take away energy. Thus, less energy partitions into translational, rotational and vibration energy of evaporated water molecules. There is evidence for a long-lived excited state for Cu2+ in smaller nanodrops for which competition between water loss and internal conversion could be relevant, but this effect should be negligible for the larger clusters investigated here owing to a slower water molecule evaporation rate.10,62 Thus, the different number of water molecules lost for Cu2+/Co2+ compared to Fe2+/Mn2+ likely reflect a difference in water molecule binding enthalpy. A comparison between the divalent ions at 248 nm is not possible because UVPD products are only observed for Fe2+. However, the decrease of 〈x〉 for hydrated Fe2+ at 248 nm with increasing cluster size, even below 〈x〉 for trivalent ions, is also consistent with an increasing binding enthalpy with increasing cluster size (Fig. 4). This is unexpected because the influence of ion identity should decrease with increasing cluster size.47,48 A possible explanation for this effect is an ion specific water patterning effect, so that Fe2+/Mn2+ containing water clusters form water clusters differing in shape or water phase from Cu2+/Co2+·(H2O)n. Evidence for the influence of ions on the water phase in large water clusters comes from a recent study that showed that La3+ ions can affect the onset of crystallinity in clusters as large as 375 water molecules.63
Fig. 6 The average sequential water molecule binding enthalpy, ΔHn,n−1, in kJ mol−1 deduced from UVPD measurements for hydrated PTMA, (Phe + H)+, anilinium (); Cu2+, Co2+ (); Fe2+, Mn2+ (); [Co(NH3)6]3+, [Cr(NH3)6]3+, [Ru(NH3)6]3+ () ions upon 193 nm photon absorption and (Phe + H)+, anilinium (); Fe2+ (); [Ru(NH3)6]3+ () upon 248 nm photon absorption as a function of 〈n〉 − 〈x〉/2. The sublimation enthalpy ΔHsub = 51.0 kJ mol−1 of bulk water ice at 133 K and the vaporization enthalpy ΔHvap = 44.8 kJ mol−1 of bulk water at 273 K are depicted as dashed and solid black horizontal lines, respectively. The TLDM at 133 K and the fitted TLDM are shown as dashed and solid red, blue and green lines for mono-, di-, and trivalent ions, respectively. Literature binding enthalpies for clusters with 〈n〉 − 〈x〉/2 ≤ 12 monovalent () and divalent () ions are included in the figure.32–45 |
Also shown in Fig. 6 (dashed colored lines) are the average binding enthalpies calculated with the TLDM (see ESI†) using 133 K bulk ice parameters (Table 1). The mean deviation of the TLDM at 133 K with ice parameters for mono-, di- and trivalent ions is lower than the mean deviations (root-mean-square-deviation; RMSD) of the TLDM at 273 K, 298 K and 313 K using liquid water parameters (see ESI†). Namely, the RMSD for monovalent ions is 4.69 kJ mol−1, 2.47 kJ mol−1, 2.01 kJ mol−1 and 1.38 kJ mol−1 at 313 K, 298 K, 273 K and 133 K, respectively. The use of ice parameters for the TLDM calculations is consistent with recent results, which indicate that large clusters are “ice-like” at low temperature.63–66 It is still debated at what cluster size the thermodynamic concept of phase is applicable to nanodrops and it has been shown that spectroscopic features for amorphous and crystalline ice can coexist for clusters with up to 550 water molecules,63 hence, we use the phrase “ice-like” in what follows as a synonym for the presence of amorphous or crystalline ice phases.
Parameters | 133 K |
---|---|
a ref. 52. b ref. 49. c ref. 69. d ref. 70. e Not known; 273 K parameter used; value only marginally effect the results. | |
M/g mol−1 | 18.015 |
ρ/kg m−1 | 931.7b |
∂ρ/∂T/kg m−3 K−1 | −0.065b |
ε | 197.4c |
∂ε/∂T/K−1 | −1.5300c |
γ/mN m−1 | 109d |
∂γ/∂T/mN m−1 K−1 | −0.1407e |
ln(p/p0) | −28.6471b |
∂ln(p/p0)/∂T/K−1 | 0.3185b |
Although the TLDM using 133 K bulk ice parameters provides binding enthalpies that are more similar to the experimental values for small clusters compared to those using liquid water parameters, the model does not accurately account for the increase of ΔHn,n−1 with cluster size above 〈n〉 − 〈x〉/2 ≈ 175. In order to improve the agreement between values from the TLDM and the experiment at large cluster size changing the least number of parameters in the model, a sensitivity analysis was performed. The surface energy, γ, and the change of the logarithmic partial pressure with temperature, ∂ln(p/p0)/∂T (p0 is the standard pressure), have the biggest effect on the TLDM at large cluster size. For mono-, di- and trivalent ions, these two parameters were optimized and the resulting fits are shown in Fig. 6 (solid colored lines). The corresponding charge-dependent parameters are shown in Table 2. The RMSD values improve from 1.25 kJ mol−1, 1.92 kJ mol−1 and 2.05 kJ mol−1 for the 133 K TLDM to 0.92 kJ mol−1, 1.17 kJ mol−1 and 0.67 kJ mol−1 for the corresponding fits for mono-, di- and trivalent ions, respectively. The surface energy and ∂ln(p/p0)/∂T increase for all charge states compared to bulk 133 K parameters and the extent of the increase depends on charge. For example, the surface tension for divalent ions is 215 mN m−1, which is nearly double the corresponding bulk value. Excluding the Fe2+/Mn2+ data for the fit of the TLDM for divalent ions, i.e., only using ΔHn,n−1 values for Cu2+ and Co2+ (Table 2 values in parentheses), results in a value of 180 mN m−1 for γ (Fig. S10†). The higher value of γ compared to bulk parameters of pure water ice and the increase in this value with charge state is consistent with the influence of ions on surface energy in electrolyte solutions.67 In bulk solutions, the relative surface energy increase of dilute electrolyte solutions compared to pure water is between 0–15% for salts such as K2SO4 and up to 100–160% for LaCl3 or K4[Fe(CN)6].67 Even though these clusters contain only one isolated cation and up to 500 water molecules, solution data provide support for the use of a higher surface energy in the TLDM that should be charge dependent. This indicates that hydrated ions can influence the properties of water, such as surface energy, in clusters containing up to 500 water molecules. The higher ∂ln(p/p0)/∂T for clusters compared to bulk water is in qualitative agreement with the Kelvin equation, which predicts an increase of droplet partial pressure compared to bulk water.68
Although optimization of the 133 K TLDM results in an improved fit to the experimental data, it is difficult to interpret the physical relevance of the extracted parameters. The values of γ and ∂ln(p/p0)/∂T are averaged over all cluster sizes between n = 20–500 so there is no explicit size dependence of these parameters. The TLDM also has difficulties in accurately reproducing ΔHn,n−1 for small hydrated ions because specific bonding in the first and second solvation shells is not taken into account by the TLDM.52 Finally, large and hydrophobic ions like (Phe + H)+ or PTMA may not be fully solvated or the nanodrop may not be spherical at small cluster sizes. Despite these factors, the close agreement with experimental data justifies the use of the modified TLDM. Additionally, the relatively close correspondence of the optimized parameters to the bulk ice parameters at 133 K, considering the discussed uncertainties, is consistent with isolated ions in larger nanodrops as “ice-like” particles in the gas phase.
Footnotes |
† Electronic supplementary information (ESI) available: Detailed description of the experimental and computational modeling methods. Isolation, BIRD and UVPD sequence for [Ru(NH3)6]3+·(H2O)169–171, nanoESI spectra for 2+ and 3+ ions. Detailed description of the isotope distribution simulation program. Comparison between experimental and simulated 1+, 2+ and 3+ ion isotope distributions. Wavelength dependence of the deduced sequential binding enthalpies. Comparison of experimental UVPD binding enthalpies to the liquid drop model at different temperatures. Complete list of binding enthalpies and average number of water molecules lost upon UVPD. See DOI: 10.1039/c6sc04957e |
‡ Current address: Institute of Inorganic and Analytical Chemistry, Justus Liebig University Giessen, 35392 Giessen, Germany. |
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