We acquired through laser-assisted APT data from 7 specimens yielding at least 30 million atoms each. Stable measurement conditions, with a homogeneous detector pattern and a steady smoothly increasing voltage curve over time, were obtained with a detection rate of 3 ions per 1000 laser pulses, at a repetition rate of 100 kHz and a pulse energy between 40 and 80 nJ. Chemical information is derived from the measured time of flight (ToF). The ToF measurement is continuously restarted by the emission of a new laser pulse, defining the maximum opening time of the ToF measurement window. While the maximum detectable mass for a flight length of 120 mm at 6 kV and a repetition rate of 200 kHz accounts to 200 u e-1, the range can be extended at 100 kHz to about 800 u e-1. Such large masses are normally of limited interest for APT, but at 100 kHz we could detect significant signals stemming from large molecules up to a mass of 350 u e-1. For high laser repetition rates these large fragments will have not enough time to reach the detector before a new laser pulse will be initiated. Besides, the decreased repetition rate enables samples with low thermal conductivity to cool down between laser pulses manifesting in an improved signal to noise ratio 16.
The mass spectrum of the saturated glucose solution (Fig. 1) reveals more than 140 mass peaks, a clear increase compared to the pure water spectra 15. Peak identification is ambiguous due to the large number of possible combinations of charge states and their elemental combinations. We generally favoured the simplest explanation for a specific mass signal, using the lowest possible charge state option to assign a molecular identity to each signal, since the effective evaporation field for water is low 15,16 and thus lower charge states are more likely to be observed. Different approaches to assign individual peaks will be discussed below and compared to the expected ratio of water to glucose molecules.
Mass spectra comparison of glucose solution to pure water
Since water is the majority compound in the saturated glucose solution (470 g L-1 at 20°C), it is reasonable to expect a mass spectrum with significant similarity to pure water 15. We observe the same protonated water-containing ions (H2O)nH+ with n = 1-5, with peaks at m/q = 19, 37, 55, 73 and 91 u e-1, as for pure water. Comparing the peak shapes of the signals match to the previous measurement of water with regard to their peak width, relative intensity and the pronounced tailing15. Furthermore, higher charged signals corresponding to the composition (H2O)n(OH)m2+ and their satellite peaks (Δm=+1) match as well. Distinct differences become visible for larger atomic masses. Periodic signals at masses larger than m/q = 100 u e-1 are readily visible in Fig. 2. These high-mass signals have a distinct mass difference of 18 u e-1. All signals stemming from m/q ratios above 91 u e-1 could in principle be explained by large protonated water clusters (H2O)nH+ with n >5, which, however, are not observed in this quantity in earlier measurements of pure water (Fig 2).
The glucose molecule has a mass of 180 u e-1. A reasonably strong signal appears at m/q = 181 u e-1 and can be also interpreted as a protonated glucose molecule. Glucose contains seven hydrogen atoms and five OH-groups attached to different carbon atoms. The periodic peaks with lower masses than 181 u e-1 can be explained by the simultaneous removal of an OH group and one H-atom from the carbon atoms forming the pyranose ring. The removal of (HO+H)n with n = 0 – 5 would result in the distinct spacing of mass peaks less than 181 u e-1 with a mass difference of Δm/q = 18 u e-1 (H2O+). This periodicity stops once all OH groups are removed (Fig. 2b), at m/q = 91 u e-1. To complete the chain of evidence, relative peak intensities are determined for protonated molecules (Fig. 3 a). The relative intensities of the water cluster signal at m/q = 37, 55, 73, and 91 u e-1 agree with the intensity distribution determined for pure water, implying a similar effective evaporation field strength for both liquids. Beyond m/q = 91 u e-1 the relative intensities increase again in the case of glucose solution (m/q = 91, 109, 127, 145, 163, 181, u e-1). Since measurement conditions are comparable and such large clusters of water molecules were absent in the case of pure water, all signals with high masses above 91 u e-1 are therefore attributed to glucose.
Molecular ions consideration
DFT calculations have been performed to calculate the structure and the stability of the formed glucose fragments. The molecular ions smaller than the glucose molecule are depicted in Figure 4a. In each case, the equivalent of n water molecules n = 1 - 5 has been removed compared to the structure at m/q = 181 u . At the mass-to-charge state ratios of m/q = 127 u e-1 and m/q = 109 u e-1 isomers with planar 6-membered rings were found. These 6-membered pyrylium rings are aromatic, which renders these isomers particularly stable. The last molecule at m/q = 91 u e-1 has a linear structure.
After removal of OH+H the remainder of the glucose molecule undergoes a molecular rearrangement. Due to their inherent mobility, the remaining hydrogen atoms relocate and bind to a different carbon atom. In the case of C6O6H13+ (m/q = 181 u e-1), it is possible to remove an H2O from one carbon atom. H2O is removed from C2 and subsequently one hydrogen relocates from C1 to C2 resulting in the structure shown in Figure 4a. It is unknown which OH molecule and which hydrogen atom are removed in the smaller fragments.
Each of the structures has been found to be stable against the abstraction of the equivalence of one H2O from the ring structure except for the clusters at m/q = 181 u e-1 and m/q = 163 u e-1, which are therefore metastable. However, in those cases the calculated dissociation energy is rather small, 1.5 kJ mol-1 for m/q = 181 u e-1 and 8 kJ mol-1 for m/q = 163 u e-1 (table 1).
Molecular structures with alternative compositions were found for m/q = 145, 127 and 109 u e-1 (see Figure 4a marked with *). In contrast to the structures shown in Figure 4a and 4b they contain only 5 instead of 6 carbon atoms. The formation of these structures is, however, considered unlikely as it would require a fragmentation of the carbon skeleton of the molecule, followed by the simultaneous removal of one carbon, one oxygen and several hydrogen atoms. A direct comparison of the energy to those structures shown in Figure 4b is impossible due to the different composition.
The reaction energies listed in table 1 are calculated using
Where E(x) denotes the electronic energy + Zero-point correction from the DFT calculations and x is equal to the respective mass to charge state ratio m/q. E(n) = E(x=18) being either E(H2O) or E(H+OH).
Molecules with a mass-to-charge state ratio higher than m/q = 181 u e-1 following with a Δm/q = 18 u e-1 are detected in considerable quantity and most likely correspond to a glucose molecule with one or more additional cations (H+, H3O+ and H5O2+, depicted in Figure 4b) bound via hydrogen bonds to the glucose ring. An analysis of the partial charges shows how the charges are distributed within the molecule. Oxygen is more electronegative than carbon and accumulates negative charge. The most weakly-charged oxygen atom, with -0.6 e, is located within the closed ring structure, while the oxygen in the hydroxyl groups is more strongly charged with - 0.7 e and the oxygen atoms in H3O+ or H5O2+ carry between -0.9 and -0.8 e. All carbon atoms on the other hand only carry small charges (-0.09 to + 0.4 e). For this reason, the hydrogen atoms have different amounts of positive charge depending on their binding partner: around 0.5 e for hydrogen attached to oxygen and 0.2 – 0.3 e for hydrogen attached to carbon. In the case of the molecular cluster at the mass-to-charge ratio of m/q = 217 u e-1, H5O2+, also known as Zundel cation, is bound to the cluster via hydrogen bonds. 79% of the overall charge of the cluster is located in the H5O2 group. Most of the molecule’s positive charge is therefore located in the water component of the cluster and this portion increases with the size of the molecule. For the biggest cluster depicted in Figure 4b, the percentage increases to 97 % in the water component.
In a saturated glucose solution, there are 21 water molecules available to solvate each glucose molecule. Further investigations of molecules at higher mass-to-charge ratio with more than two additional water molecules with the formula C6O6H12+(H2O)nH+ with n = 2 – 9 could also be observed (see supplementary material Fig. A 5). The respective stabilities and the arrangement of larger water cluster around the glucose molecule were also computed. The DFT calculations show that it is energetically favourable to build compact water cluster bound via hydrogen bonds to the glucose molecule instead of arranging water molecules around the glucose molecule as a hydration shell (Fig. 4 b).
The apparent distribution of relative intensities above m/q = 91 u e-1, assumed to stem from glucose molecules show a distribution with the maximum centred at m/q = 127 u e-1 (Fig. 3b). From the analysis of multi-hit events 36 on the detector no preferential co-evaporation of HO, H2O, H3O with a large glucose cluster could be observed. Even in the spectra for the single, double, triple etc. events, no significant difference in the detected species is observed (see supplementary part Fig. A 1-4). The loss of HO+H does not occur simultaneously. A way to explain the observed distribution is to assume a step-by-step evaporation process with certain evaporation probabilities influenced by the remaining molecular fragment. Mass 181 is assumed to be generated in the first evaporation attempt k = 1.
To match the observed frequency distribution with this simple concept, the probability for evaporation has to increase continuously after each removal of an HO+H fragment ( k > 1) . Or in other word, the further removal of another HO+H event becomes harder (see Table 1). Once all OH groups have been released, the molecule opens into a linear structure (Fig. 4a) as this structure is energetically more stable. Fragments smaller than C6 can be explained by the splitting of the C6H3O+ chain. To derive these probabilities, the number of occurring complete molecules in the range between 91 – 181 u e-1 are normalized. The relative number of occurring complete molecules at m/q = 181 u e-1 is equal to the probability of evaporating the respective molecule. The detected relative distribution is used to match the respective probabilities in each step according to:
Being a model, this simplified approach has limitations, but the decrease in split-off-probability is supported by DFT calculations and correlates with experiments (see Fig. 3c), since the remaining fragment become more stable against further dissociation with every water or HO + H molecule removed (see Table 2).
Between the main peaks at m/q = 109 and 217 u e-1, small peaks appear that are separated by a distance of 1 u e-1, corresponding to a single additional hydrogen atom. There are always three very prominent peaks between the two main peaks, with a distance of Δm/q = 5, 7, 12 u e-1 from the previous peak. The peaks between the mass-to-charge state ratio of m/q = 109-181 u e-1 can be associated to C4-6OxHy. However, the intermediate peaks from m/q = 181-217 u e-1 can only correspond to the molecular ions C5O5H11-14 + (H2O)xHy+ with x = 2 - 3.
The identification of an ion only by its mass, of course, does not tell anything about the internal structure of the detected species. In this specific case, the structure and the identity of the injected molecules are a priori known But it would not be possible to differentiate common monosaccharides like galactose and fructose based on the molecular mass. Since current detectors used for APT have an efficiency around 80%, it is still doubtful, whether current reconstruction algorithms could assign the original molecule even when it evaporated atomically. This would require a more sophisticated analysis of the data, and likely statistical comparison with a database of fragments, as is done in proteomics44 . Whether the observed frequency distribution of fragments as described in table 2 is unique for glucose and allows a clear distinction from other monosaccharides is unknown and must be evaluated in the future. Typically, the respective evaporation field scales with the sublimation energy, which is increasing with the melting temperature of the substance 2,45. The monosaccharides at least differ in their melting temperatures (glucose 146°C, fructose 106°C, galactose 164°C). In a first view, one may speculate that the melting point mostly affects the probability to evaporate the complete molecule, while the probability to split OH or H in both cases covalently bond might be less influenced. Thus, the relative fractions of the high-mass peaks would change, which may result in a distinguishable pattern.
The exact identification of fragments for lower masses is even more complicated. For all lower mass peaks combinations of different CxHy / CxOyHz permutations in various charge state modifications can be found. A full interpretation list can be found in Table A 1 of the supplementary part.
Comparison of a saturated glucose solution to bulk glucose
In the measurements presented before, water is the majority component. Thus the situation becomes less transparent, as signals stemming from water claim the same positions within the spectrum than the sugar molecules. To avoid such superposition, we also investigated pure bulk glucose sample to identify peak positions of probably highest overlap. Still, the ionization field strength of frozen water is rather low (2 – 6 V/nm) 17,28,46 while we can expect for solid sugar field strengths of some tens of V/nm which may hinder a direct comparison.
Samples were prepared from pure solid bulk glucose by FIB lift-out (see Materials and Methods section) 47. Comparing the mass spectrum of bulk glucose plotted in Fig. 5 with that of glucose in aqueous solution (Fig. 1), significant differences are readily visible. First, for bulk glucose no signals above m/q = 80 u e-1 are detected, indicating that the average field condition is sufficient to split the pyranose rings from the glucose molecule. Focusing on lower mass signals, most peaks pertain to molecular ions, although small but significant C (12 u e-1) and H (1 and 2 u e-1) atomic signals are present as reported for other carbon-based system with varying finger prints 48–51
Nevertheless, series of peaks appear that are spaced by 1 u e-1 up to a mass-to-charge state ratio of m/q = 80 u e-1. A full interpretation list can be found in Table A2 of the supplementary part. The most intense peaks are at m/q = 15 u e-1, corresponding to CH3+, m/q = 29 u e-1 attributed to C2H5+ or COH+, and at m/q = 44 u e-1 giving multiple identification options (C3H8+, C2OH4+ or COO+).
Various peaks can be explained by combinations of carbon, oxygen and hydrogen (CxOyHz). For example, in the range of m/q = 28 - 31 u e-1 COHz combinations can fit. The interpretation is not univocal, many possibilities exist for each peak (see table A 2 supplementary part), and because of the electric field conditions, only singly charged molecules are considered. However, a comparison of all shown measurements reveals a very different fragmentation behaviour of the glucose depending on whether it is dissolved in water or evaporated as bulk material. Bulk glucose shows a high fragmentation rate, whereas glucose dissolved in water has a lower fragmentation rate and frequently evaporates as a complete molecule. This observation must be traced back to the different bonding conditions in the solid and dissolved state and the respective electrical field strength necessary to cause field evaporation.
A further difference can be observed regarding the intensities of the detected molecules H2O+ and H3O+. In the aqueous medium the molecule H3O+ is dominant, but in the solid state the molecule H2O+ is much more present, which could be due to a cleaving effect of the HO and H parts of the pyranose ring.
This significant difference in the ratio of H2O+ to H3O+ seems to be a reasonable marker in between the discussed measurements. Generally, the mass signals stemming from the solid samples display sharper peaks and less tailing compared to the aqueous solution samples. A simple explanation by a difference in heat conductivity λ is not feasible, since the reported values for a saturated aqueous glucose solution and glucose crystals are both in the range of 0.5 ± 0.1 Wm-1K-1 52,53 while the reported value for ice are about 5 -10 times higher depending on the crystal structure with the lower limit given by low-density amorphous ice to be 0.6 Wm-1K-1 54. The increased tailing has to be attributed to a more direct influence of the ice 15.
It is insightful to discuss and interpret the correct determination of the oxygen content. The interpretation of all signals stemming from pure bulk glucose as carbohydrates CxHz results in an extreme underestimation of oxygen (Table 3), which cannot be simply explained by the loss of neutral oxygen during the APT measurement.
Instead, one may favour the interpretation of the mass signals as CxOyHz molecules. In this case the amount of available oxygen is overestimated by 18.31 %. Thus, the reality seems to be a convolution between both possibilities. Further experiments are needed to resolve the sources of uncertainty.
Determination of compositional information for the aqueous solution
In general, compositional information is of tremendous interest. Identification of compositions, and therefrom phases, diffusion coefficients, segregations factors are important cornerstones to identify processes and underlying mechanisms. In our case, the initial composition of the solution is well known. Since glucose and other sugars act as cryoprotectants and form glasses for highly concentrated solutions55 it can be used to judge the peak identification and to identify open questions and problems to be addressed in the future.
A bijective identification of the retrieved mass information is difficult due to the already discussed overlapping mass signals and the large number of possible explanations. Various combinations of (H2O)nH, CxHy, CxOyHz molecules would deliver reasonable explanations. Though a combination of all sources is highly likely and increases the complexity and leads to uncertainty and loss of local spatial resolution.
For stoichiometry calculations, all peaks are identified, and the resulting number of individual events counted. Different interpretation approaches are used, and the unfolding molecule was split into its atomic components carbon (C), oxygen (O) and hydrogen (H). In addition, a baseline correction was performed to obtain an accurate determination of the atomic ratios.
All obtained carbon atoms are assumed to be originating from glucose molecules. By dividing the total number of carbon atoms by a factor of six, the total amount of glucose molecules is calculated. In a next step the total number of glucose molecules is multiplied by six and subtracted from the total number of oxygen atoms. The remaining oxygen atoms are assumed to stem from water molecules. The saturated glucose solution should exhibit a mass fraction of glucose to water of 0.47, which corresponds to 21.27 water molecules per glucose molecule for a saturated solution. For the calculation of the stoichiometry different peak interpretation approaches were used (Table A 3,4 supplementary part) and the results are listed in Table 4.
Interpreting the signals at m/q = 17, 18 and 19 u e-1 as HO, H2O and H3O, respectively, and all other peaks as molecules by various combinations of CxHy results in a glucose to water mass-ratio of 519.94. The ratio deviates massively from the theoretical value by a factor of 1100.
Using our earlier measurements of pure water 15 as a footprint, all peaks visible in the water spectrum are attributed to water, while large molecules are assumed to be large glucose molecules. Signals at masses below 91 u e-1 which were not visible in the water measurements are assumed to be hydrocarbons with the formula CxHy. The mass-ratio of glucose to water is calculated to be 1.40. In this case, this corresponds to 7.17 water molecules per glucose molecule. The ratio still deviates from the theoretical value by a factor of 3. However, it shows that the ratio has improved by a factor of 366 with only the pure re-interpretation of the water molecules. Nevertheless, there is also an underestimation of oxygen, which is caused by the overlapping of peaks or by wrong interpretation of the carbon chains.
As already mentioned, various signals can also be explained by CxOyHz. Using this interpretation only for signals not stemming from water leads to a ratio of 0.61, which deviates by a factor of only 1.3 from the theoretical value of 0.47. This corresponds to 16.36 water molecules for each glucose molecule.
Since we observe the evaporation of large and mostly intact glucose rings, it seems unlikely from previous considerations and DFT calculations, that the pyranose ring is cracked and fragments of CxOyHz are observed. However, DFT calculation for the fragment with mass m/q = 91 u e-1 reveal a chain like structure with unsaturated carbon atoms. The bond energy between a C-O bond 56 is slightly higher than that of a C-C bond 56. HxO molecules of water can possibly recombine with the adjacent glucose fragment and therefore CxOyHz fragments would allow to explain the observed mass signals.
To achieve a result close to the correct stoichiometry, the results from bulk glucose (Fig. 5) are considered. Especially in the mass range from m/q = 27 to 36 u e-1 and m/q = 41 to 48 u e-1 significant overlap with water signals occurs. By assigning 33% of the signals to CxOYHz fragments and 67% to water clusters the mass-ratio of 0.48 is achieved. This is very close to the theoretical value, but demonstrates the ambiguity of the correct determination of the stoichiometry at the moment. The excess of hydrogen is reduced by a factor of 1.3 if only the reinterpretation of the protonated water clusters was considered. However, the hydrogen content of still 25.15% is clearly too high, which is due to a wrong interpretation. Only with the assumption of CxOyHz molecules and protonated water cluster the proportion is reduced by a factor of 5.2 and is about 4.28%. This overestimation of hydrogen can be attributed to residual hydrogen from the stainless-steel chamber and cannot be quantified exactly, but it is a very likely reason for the overestimation of the hydrogen content in APT measurements.
Correlative information sources have to be used to support the APT analysis.
Three-dimensional structural analysis
The unique feature of APT is the reconstruction of the measured volume in 3D with a near atomic resolution. With the dominating evaporation of molecular species, the principal resolution limit is controlled by the size of the individual fragments. Desorption maps for selected molecules are depicted in Figure 6. While the distribution especially for larger protonated water clusters and glucose molecules is homogenous, local density changes for H3O+ molecules are apparent. The occurrence of line features seems to be related to the laser incidence direction, as reported for pure water 15.
In order to investigate the distribution of the solvated glucose molecules inside the water matrix the measurement data are reconstructed (see materials and methods section for more details) (Fig. 7). As majority component the signal from water and related water clusters is dominating. Small local density imperfections become visible which are related to the line structures in the desorption maps. Their origin has to be further investigated.
The distribution of HO, H2O and H3O molecules is probed by a cylinder, dimension of 20 x 100 nm, along the tip axis (Fig. 7a) and perpendicular to the axis (10 x 50 nm) (Fig. 7b). While the relative ratio of the water signals is relatively constant in tip direction, a change of relative abundance from H3O+ to H2O+ is recorded perpendicular to the tip axis. Since asymmetric with respect to the tip symmetry axis, again, the laser incidence direction can be made responsible. A suggested explanation would refer to the local heating of the sample due to the laser matter interaction leading to local change in tip curvature. As a result, the effective field at the impact side of the laser is usually less than at the opposite. A lower field, appears to favour H2O molecules evaporating.
The glucose fragments show a homogeneous distribution in the 3D volume as observed in the desorption maps, which can be attributed to a very fast cooling of the sample, therefore no segregation zone is observed, caused by recrystallization of the water (Fig. 8).
By determining the radius of a sphere around an identified glucose molecule (masses m/q = 109 -181 u e-1) that includes a given number of nearest neighbouring (NN) glucose molecules, the distribution of the glucose inside the solution can be investigated. The number of included nearest neighbours’ scales with the radius to the power 3.
Here ρ denotes the glucose density and is determined to 0.5 ± 0.1 molecules nm-3. As initially described, about 1.57 glucose molecules are expected per cubic nanometre. Taking the detection efficiency of 50% into account a partial fragmentation of a distinct number of molecules into smaller fragments, the value represents quite well the expected density distribution (Fig. 9).
In a saturated glucose solution, there are 21 water molecules available to solvate each glucose molecule. In order to visualize the hydrate shell around a solvated glucose molecule, two isosurfaces in a small volume of 5 x 5 nm, 2 x 3 nm, and 2 x 2 nm are plotted (Fig. 10 a-c). The position of evaporated glucose molecules is indicated by a second iso-surface. The surrounding water molecules/clusters are represented by the blue iso-surface with a water concentration around 67% (Fig. 10 a-c). The glucose molecules are surrounded by water molecules and homogenously distributed inside the volume. The structural information of the individual molecules is of course not directly retrievable from the APT data. In Fig. 10c the DFT calculated structure is placed at the position of a detected glucose molecule implying a higher resolution than technically achieved. More advanced reconstruction algorithms combined with suitable simulation packages and DFT calculations might be able to derive the likely structure on an atomic scale from the purely molecular data sets, if of course other problematic sources of error are excluded. Any alteration of the sample structure by the freezing process has to be excluded. This is a necessary precondition like for all characterisation methods.
Equipped with the knowledge for pure water, we now have provided field evaporation measurements for a saturated glucose solution. Due to the low evaporation field of water the glucose molecules evaporated as large, partially intact, molecules. Smaller fragments overlap with the signals related to water. However, overlap and ambiguity of mass peaks leaves room for various approaches of chemical interpretation. The APT data of pure bulk glucose differ strongly from the data of the glucose solution. The solid bulk material exhibits a higher fragmentation rate of the molecule rings as compared to the solution, probably caused by a high evaporation field of bulk glucose. Other causes may be different absorption coefficients and/or different binding conditions between bulk glucose and the solution. Nevertheless, with comparison of both measurements and the a-priori knowledge of the overall composition, a suitable interpretation of the mask peaks could be suggested.
A reasonable matching of the measured stoichiometry with the known one can be achieved by interpreting the overlap in the range m/q = 27-36 u e-1 and m/q = 41-48 u e-1 as a ratio of 33% of CxOyHz to 67% (H2O)1-5H+. Resulting in a total mass fraction about 0.48, which agrees reasonably with the theoretical value of 0.47. However, there is also a certain overlap with many other peaks, which makes it exceedingly difficult to calculate them exactly, since the exact fractions are not yet known. A significant loss of oxygen or hydrogen cannot be excluded. The identification of glucose molecules within the matrix is only possible by the existence of nearly complete ionic molecules. These allow an unambiguous identification also locally in the volume space. The effective detection efficiency of the solute molecules results in only one molecule out of three identified with certainty.
What sounds like a disadvantage in comparison to the analysis of metals and semiconductors enables APT to retrieve distinguishable information’s of solutes in aqueous solutions, if a sample modification by the freezing process can be excluded. A breakdown of the solutes into smaller molecular parts would render them invisible against the background of the matrix signals.
A better understanding of the measurement conditions is necessary with regard to the solutes, laser power, field strength, temperature. The change of molecular fragmentation in dependence of the local environment has to be understood. Furthermore, the influence of the evaporation of large clusters on the accuracy of the reconstruction is not known and must be examined and in the best case attributed by an improved reconstruction algorithm. Nevertheless, the possibility to detect certain molecules within an aqueous solution, opens the opportunity to inject suitable markers and biological molecules, to study their distribution in various reactions in 3D with sub-nanometre resolution.