id
stringlengths 24
24
| idx
int64 0
402
| paragraph
stringlengths 106
17.2k
|
---|---|---|
639371ca44ccbcf7271541a3
| 3 |
Figure : Phenyl group geometric outliers and unexplained electron density for original (1a) and revised (1b) structures of BU72. Colors: fitted structures (black); ideal structures (grey); geometric outliers in the phenyl group (Z scores, red); 2Fo-Fc density (2.5σ, violet); Fo-Fc omit density (2σ, green). Adapted from The original proposed configuration of 1a was based on unpublished nuclear Overhauser effect (nOe) data, and the basis for the necessary NMR assignments was not stated . Thus, no published data support the original assignment, and the structure of BU72 should be revised to 1b. The authors of the crystal structure, including the lead author of the original synthesis, accepted this revision in a correction notice . However, the revised structure was not shown. Protein Data Bank entry Figure ) should also be revised, since they differ only in the N-substituent ; their synthetic routes diverge after establishment of the phenyl configuration, and the benzylic hydrogen is not exchangeable.
|
639371ca44ccbcf7271541a3
| 4 |
However, a second puzzling feature of the crystal structure remains unexplained after this revision. The truncated N-terminus of the receptor, which is highly disordered and hence unresolved in other opioid receptor structures, unexpectedly intrudes into the binding pocket . The third residue, His54, clashes with BU72. The overlapping atoms also contact a pocket of strong, unexplained electron density (Figure ). The atom responsible for this density could not be identified; experiments testing for an alternative ligand structure or a coordinated heavy metal were unsuccessful . The atom was ultimately omitted from the model altogether. The revised model with 1b
|
639371ca44ccbcf7271541a3
| 5 |
2) reduced the clash between ligand and receptor, but did not account for the unexplained density. All results in this paper are based on revised structure 1b. Other authors later proposed that the missing atom is a magnesium ion . This fitted the unexplained density well, while lithium, sodium, nickel, and zinc ions did not .
|
639371ca44ccbcf7271541a3
| 6 |
The missing atom is not magnesium I first refined a complex with the previous candidate, Mg 2+ . Consistent with the earlier reports , this gave a good fit, with no excess or unexplained density above 2.5σ (Figure ; data in Additional files 1 and 2). However, contrary to the prior reports, the 4σ 6σ BU72 (1a)
|
639371ca44ccbcf7271541a3
| 7 |
N-Mg bonds were unrealistically short (1.9 and 1.7 Å). Compare the N-Mg bond lengths in structures of subatomic resolution: 2.19 ± 0.06 Å . These bonds are thus extreme outliers, with Z scores of -5 and -9, respectively. The high resolution of the structure (2.1 Å) allows strong conclusions about bond lengths, with a diffraction precision index (DPI) of 0.22 Å for the Mg 2+ ion . Note also that the ion is not centered in the density even with these unrealistically short distances, suggesting that the actual bonds must be shorter still (Figure ). This resulted in a poor real-space R value (RSR) of 0.32 for the Mg 2+ ion, despite good values for His54 (0.11) and BU72 (0.08).
|
639371ca44ccbcf7271541a3
| 8 |
A later report from the same group added a third bond to the model , from Mg 2+ to Tyr148 3x33 (using GPCRdb numbering ) (Figure ). However, this would require an O-Mg bond length of 3.1 Å; compared with high-resolution structures (2.10 ± 0.04 Å), this is untenable (Z = 25) . It is instead suggestive of a hydrogen bond to another element. Note also the large gap in the electron density along this proposed bond, unlike the strong and uninterrupted density for the bonds to BU72 and His54 (Figure ). Additionally, note the highly asymmetrical geometry required, with a bond angle of 105°, compared to 90° for the N atoms; magnesium complexes are symmetrical . Other evidence against Mg 2+ was revealed by CheckMyMetal . The values of five of the eight parameters evaluated were classed as dubious, including three that strongly suggest a misidentified element:
|
639371ca44ccbcf7271541a3
| 9 |
While the element is evidently misidentified, the fit of the Mg 2+ ion to the density does firmly establish a non-hydrogen atom in this approximate position. As noted above, this missing atom is likely nearer to both His54 and BU72 than the modelled position of Mg 2+ ; that is, < 1.9 Å from each (Figure ). This is much too close for non-covalent interactions (≥ 2.4 Å) , which would also not result in strong, uninterrupted electron density connecting the three atoms. For instance, the protonated tertiary amine of BU72 forms a charge-assisted hydrogen bond (salt bridge) to aspartate Asp147 3x32 (Figure ); these are among the shortest of all noncovalent interactions .
|
639371ca44ccbcf7271541a3
| 10 |
However, each of these also gave multiple outliers when validated. Also, of these metals, only nickel was present during preparation of the crystals (in the affinity column used for purification) . The bond lengths are more plausible than for magnesium, since N-Ni bonds are short (1.88 ± 0.03 Å) . However, as noted above, nickel did not fit the electron density, leaving a substantial excess ; further evidence against 2σ BU72 (1b)
|
639371ca44ccbcf7271541a3
| 11 |
The only metal in the buffer solution, sodium, also gave five CheckMyMetal outliers, including even more extreme outliers from typical N-Na bond lengths (2.46 ± 0.02 Å, Z = -29 and -40) , and a much worse fit to the density than magnesium . Indeed, no metal forms coordination bonds to N shorter than 1.76 Å . It is thus extremely implausible that the missing atom is a metal.
|
639371ca44ccbcf7271541a3
| 12 |
Given the above, it appears that the missing atom is a non-metal approximately isoelectronic with magnesium, but that forms shorter bonds. The element must also be at least divalent, and can probably form hydrogen bonds given its distance to Tyr148 3x33 (~3.1 Å). One candidate meeting these criteria is oxygen; based on electron density alone, water molecules are frequently misidentified as magnesium .
|
639371ca44ccbcf7271541a3
| 13 |
Formation of an oxygen-bridged adduct between the secondary amine of BU72 and the imidazole ring of His54 would require harsh conditions. Reactive oxygen species (ROS), for instance, can oxidize secondary amines and histidine . But how might these arise? Surprisingly, several potential sources of ROS were present. The BU72-μOR complex was purified and crystallized in HEPES buffer, which generates hydrogen peroxide on exposure to light . HEPES has also been reported to enhance metal-catalyzed generation of other ROS from hydrogen peroxide . A further potential source is the N-terminus, which contains a sequence motif known to generate ROS. The N-terminus used was truncated, leaving glycine as the first residue and histidine as the third . This sequence motif (Gly-Xaa-His) forms redox-active nickel coordination complexes . Moreover, a nickel affinity column was used for purification , and the Gly-Xaa-His motif can capture Ni 2+ ions from these columns . The resulting square planar nickel complexes catalyze the decomposition of hydrogen peroxide to other ROS such as hydroxyl radicals . Thus, the conditions used were sufficient to generate ROS immediately adjacent to His54, potentially oxidizing both the residue itself and BU72.
|
639371ca44ccbcf7271541a3
| 14 |
3UM9 , and 3ZUC . Intriguingly, in 1JVN the electron density was not consistent with the expected ligand structure; no density supported several of the atoms, suggesting partial decomposition . The buffer used, PIPES, is an analog of HEPES that also generates hydrogen peroxide and other ROS . This provides a plausible explanation for the decomposition of the ligand.
|
639371ca44ccbcf7271541a3
| 15 |
Two previous reports of adduct formation between aminoxyl radicals and imidazole rings are shown in Figure 7a . These suggested potential structure 6 for an adduct between BU72 and His54 (Figure ). The stereochemistry of the bond to the modified histidine residue was dictated by the observed density. A possible intermediate aminoxyl radical is also shown; these can form from oxidation of secondary amines by ROS . proposed here, with the nickel complex and a possible aminoxyl intermediate
|
639371ca44ccbcf7271541a3
| 16 |
Substituting adduct 6 for His54 and BU72 gave an excellent fit, with no excess or unexplained density even at 2σ (Figure ; data in Additional files 3-6). Both bonds to oxygen were of typical length (1.5 Å), and were resolved up to 4.2σ -that is, higher density than most of the ligand itself and surrounding side-chains. Unlike Mg 2+ , the oxygen atom was well centered in the density. Oxygen also gave a superior B-factor to Mg 2+ , both lower and consistent with its bonding partners, making this a much more plausible candidate element (Figure ) . The lower B-factor for oxygen results in a more precise fit (DPI 0.14 vs 0.22 Å). Indeed, it is among the most precisely-resolved atoms in the entire structure, which is itself the highest-resolution structure of μOR to date. The bridging oxygen and modified histidine moiety make favorable polar contacts with Tyr148 3x33 , which are close to the length of a weak hydrogen bond. The adduct is highly strained
|
639371ca44ccbcf7271541a3
| 17 |
The bound geometry of adduct 6 gave acceptable validation metrics, which were superior to the original model of BU72, 1a (Table ; data in Additional file 7). The only severe outlier was the bond angle at the bridging oxygen (131° vs the ideal, 109°: Z = 7.2). There are several indications that this is real strain rather than a fitting artefact, however. The angle is clearly resolved at high density, and is consistent with tension from the tethered N-terminus. The phenyl group is bent 11° out of plane, consistent with being pulled against the adjacent residue Ile144 3x29 by the same tension (Figure ). This bend is also clearly resolved, and is comparable to those seen in severely strained aromatic residues at subatomic resolution . It also yields a more complementary fit to Ile144 3x29 than the original model, as well as eliminating another small pocket of unexplained density (Figure ). Despite the very strong interactions apparent between BU72 and His54, removal of the side chain of His54 by receptor mutagenesis had no detectable effect on the affinity or potency of BU72 . This seeming paradox, however, is consistent with the mechanism proposed here. Since the full-length receptor was used for the assays, the Gly-Xaa-His motif was not at the N-terminus, and therefore nickel complexation and adduct formation could not occur. Thus, binding would be unaffected by the presence or absence of His54.
|
639371ca44ccbcf7271541a3
| 18 |
The largest movement during activation of G protein-coupled receptors (GPCRs) involves TM6. Viewed from the intracellular end, TM6 pivots outwards and rotates clockwise; this 'macroswitch' occurs in all GPCRs studied to date . This shift is markedly different in the BU72-μOR-Nb39 structure than in later structures of active μOR bound to Gi protein (Figure and Table ). Although these 13 later structures feature diverse µ opioids bound to mouse or human μOR, they cluster very tightly in this key region. The BU72-bound structure is a clear outlier, with TM6 much closer to TM5, and rotated in the opposite direction. As a result, intracellular loop 3 (ICL3) bunches outwards in a disordered loop, rather than being pulled into a helix as in the Gi-bound structures. These differences appear to be largely due to Nb39, since the structure of the κ opioid receptor (κOR) bound to the same nanobody is similar (Figure ).
|
639371ca44ccbcf7271541a3
| 19 |
Another conspicuous discrepancy between the BU72-bound structure and the others is in helix 8 (H8). Activation of class A GPCRs, such as opioid receptors, involves an inward shift of H8, making and breaking contacts at its base (see Figures and in ). Relative to the inactive structure, the base of H8 shifts noticeably more in BU72-μOR-Nb39 than in the μOR-Gi structures or κOR-Nb39, which again cluster tightly (Figure ). This suggests that the nanobody itself is not responsible for the discrepancy, but rather some other factor, such as distortion due to strain in the adduct.
|
639371ca44ccbcf7271541a3
| 20 |
Figure : Overlay of H8 (inactive, Nb39-bound, and Gi-bound). See Table for PDB identifiers and other details Whether due to the influence of the adduct, the nanobody or both, these differences from the μOR-Gi structures are experimental artefacts, and the consistency between the Gi-bound structures establishes them as superior templates for modeling the active conformation.
|
639371ca44ccbcf7271541a3
| 21 |
In the original study, a search for alternative ligands to account for the unexplained density was unsuccessful. The mass spectrum of the crystallization mixture revealed a molecular ion consistent with BU72, but no others of similar mass . However, the intact adduct would not be detectable in solution, and one decomposition product per binding site would yield negligible concentrations relative to saturating BU72. An alternative test would be for modification of His54: proteolysis of the receptor and mass spectrometry of the fragments should reveal either the adduct or decomposition products. A simpler alternative would be to substitute a short Gly-Xaa-His-containing peptide for the receptor, although this might also result in side-reactions. The initial nickel complex itself should be detectable spectroscopically, and may indeed give a noticeable yellow color to the solution .
|
639371ca44ccbcf7271541a3
| 22 |
An obstacle to isolation of the adduct may be instability. Previously-reported adducts 4 and 5 were not isolated, but detected only by mass spectrometry as reaction intermediates . However, the tethered conformation of the N-terminus separates Gly52 from His54, rendering a nickel complex between the two residues impossible (Figure ). Thus, adduct formation would liberate the ion and end the catalytic cycle. Moreover, the 'lid' formed by the N-terminus almost entirely occludes the binding pocket , leaving only a narrow tunnel filled with structured water molecules. Thus, the adduct bonds are sterically shielded, which may inhibit further reactions.
|
639371ca44ccbcf7271541a3
| 23 |
The risk of unexpected complexes and oxidations like this is not specific to the structures discussed here. The conditions that led to these reactions, in both this case and previously , are widely used. Many common methods for the cleavage of fusion proteins (thrombin, factor Xa, tobacco etch virus protease, and rhinovirus 3C protease) leave glycine as the N-terminal residue . Unsurprisingly then, the N-terminal Gly-Xaa-His motif is common in the Protein Data Bank, appearing in >7,000 sequences (~4% of the total). Nickel affinity columns are also widely used. Many of these proteins would therefore be expected to form Gly-Xaa-His-Ni 2+ complexes. However, the first few residues of the N-terminus are almost invariably disordered: 97% of human proteins have disordered terminal residues , and 42% of all disordered residues are in the N-terminus . Thus, these complexes are very unlikely to be resolved, and are therefore likely to go undetected. Peroxide-generating buffers such as HEPES are also ubiquitous; thus, quite common procedures for protein preparation inadvertently generate ROS. Oxidation by ROS can have many undesirable effects on proteins, from modifying side chains (which may influence the overall conformation) to cleaving the amide backbone .
|
639371ca44ccbcf7271541a3
| 24 |
In summary, the density observed between BU72 and His54 is not consistent with noncovalent interactions or a metal coordination complex, and must instead represent covalent bonds to a non-metal atom, approximately isoelectronic with Mg 2+ . The density firmly establishes the presence of this atom and two covalent bonds, and suggests a polar contact with Tyr148. While this evidence does not unambiguously identify the atom, it does establish that the published model is incorrect. The use of conditions known to generate ROS, along with adducts reportedly previously in the presence of ROS, suggest a tentative structure and mechanism for the formation of an oxygen-bridged adduct. All features examined are consistent with this proposal.
|
639371ca44ccbcf7271541a3
| 25 |
The structure differs in several respects from subsequent structures of μOR bound to Gi protein, likely due to the use of a nanobody, severe strain within the N-terminus, and its contacts with surrounding residues. These subsequent μOR-Gi structures are likely to be more accurate templates of the active receptor for docking and simulations of molecular dynamics. Oxidative artefacts like this can be prevented by careful choice of truncation sites and purification conditions.
|
639371ca44ccbcf7271541a3
| 26 |
Starting from the previously reported model of μOR with 1b, Mg 2+ was added to the center of the unexplained density with sphere refinement using Coot in CCP4i2 , and uploaded with the original structure factors to PDB-REDO server for automated refinement. The resulting complex was submitted to CheckMyMetal for validation; all suggested alternative metals were also resubmitted for validation.
|
639371ca44ccbcf7271541a3
| 27 |
was mutated to the adduct, and the model fitted and refined as above. Because the PDB validation report did not evaluate the geometry of adduct 6, ligand distortions in the bound ligands were tabulated in Coot and used to calculate Z scores, comparing ideal values and standard deviations from GRADE with modeled values for 1a, 1b and 6 (Additional file 7). Diffraction precision indexes were calculated using Online_DPI . Protein structures were aligned and illustrated using Pymol , and annotated
|
66e1358e12ff75c3a1012401
| 0 |
As atomic layer deposition (ALD) processes continue to be developed, the necessity for investigating reaction mechanisms remains important to understand both new reaction chemistries and existing processes. Thus, studying reaction mechanisms is crucial for identifying appropriate reactions to achieve desired materials and material combinations, especially as thin films in device structures reach thicknesses achievable within just a few ALD cycles. The trend towards shrinking device dimensions necessitates, for example, the deposition of thinner films within higher aspect ratio holes and vias. In this context, ALD is an ideal method for growing depositing conformal films as it operates through two consecutive self-limiting reactions that take place between a gaseous precursor and the solid substrate, depositing a thin film through iteratively executing these surface reactions.
|
66e1358e12ff75c3a1012401
| 1 |
Aluminum nitride (AlN) is a wide-gap semiconductor known for its wide bandgap of around 6.2 eV 2 , a thermal conductivity comparable to that of metals of 285 Wm -1 K -1 , a high melting point of 2750 °C, and electrical resistance of 10 Ωcm, making it a highly promising material for utilization in micro-and optoelectronic applications. ALD of AlN typically relies on trimethyl aluminum (TMA) and ammonia (NH3) as precursors. The deposition of AlN from TMA, with aluminum-carbon bonds, often suffers from carbon impurities and an efficient carbon-cleaning surface chemistry is needed. Precursors with aluminum-nitrogen bonds could possibly reduce this problem when depositing AlN. The homoleptic amide precursor tris(dimethylamido)aluminum(III) (Al(NMe2)3, TDMAA), is therefore an interesting alternative, but it is less explored for ALD. TDMAA has been used for AlN in thermal- and in plasma ALD with NH3 as a co-reactant but neither theoretical nor experimental surface reaction studies for ALD of AlN from TDMAA have been reported to date.
|
66e1358e12ff75c3a1012401
| 2 |
The dimethylamido ligand has been extensively used for ALD of titanium nitride (TiN) in the tetrakis(dimethylamido)titanium(IV) (Ti(NMe2)4, TDMAT) precursor. TiN is a commonly employed diffusion barrier material known for its hardness, refractory properties, and boasts a bulk resistivity of 20 µΩcm. The decomposition and reaction mechanisms of TDMAT have been extensively studied. Another study on gas phase decomposition and reactions of different tris(dimethylamido) precursors, utilizing Fourier transform infrared spectroscopy and molecular beam mass spectrometry found that gas-phase decomposition of tris(dimethylamido)stibine (TDMASb) leads to the production of several stable products including methylmethyleneimine (MMI), dimethylamine (DMA), and methane (CH4). These species are analogous to the pyrolysis of tris(dimethylamido)arsine (TDMAAs) and tris(dimethylamido)phosphine (TDMAP). Therefore, one could hypothesize that TDMAA could have a similar gas phase chemistry to these precursors.
|
66e1358e12ff75c3a1012401
| 3 |
To the best of our knowledge, no earlier study has investigated or described a detailed reaction mechanism for TDMAA, making its surface chemistry less understood. Studies of other dimethylamido precursor can provide insights into the TDMAA surface chemistry. Hence, in this study, the surface chemistry of TDMAA for ALD of AlN was investigated for both plasma and thermal ALD, with NH3 as the co-reactant, using mass spectrometry. Comparisons between TDMAA and TDMAT was also done to probe similarities between the possible reaction pathways of the two dimethylamido precursors.
|
66e1358e12ff75c3a1012401
| 4 |
A hot-wall Picosun R-200 Advanced ALD reactor, equipped with a Litmas remote inductively coupled plasma (ICP) source, was used for deposition. The reactor operated at 4 mbar with a continuous flow of 400 sccm high-purity N2 (99.999 % with further drying using a getter filter) into the chamber, which was also used as the purge gas. TDMAA and TDMAT from Sigma-Aldrich (both ≤ 100 %) were sublimed at 120 °C and 60 °C respectively, and vapor was drawn by opening a valve to the low-pressure reactor. The thermal processes used NH3 (AGA/Linde, 99.999 % and further purified by a getter filter) as the nitrogen precursor whereas the plasma ALD processes used a plasma discharge in a mixture of 75 sccm NH3 and 100 sccm Ar (99.999 % and further purified by a getter filter). The ICP plasma source was located approximately 75 cm above the substrate and ignited the plasma with a 2800 W plasma power. Prior to deposition, approximately 2 cm x 2 cm Si(100) substrates were cleaned with acetone and isopropanol for 10 minutes each to remove surface contaminants before blow-drying them with N2 gas. To avoid unwanted effects, the reactor was conditioned by doing long passivation runs for at least 24 hours while maintaining it at 4 mbar operating pressure and 150 °C on both substrate and wall temperature.
|
66e1358e12ff75c3a1012401
| 5 |
In-situ quadrupole mass spectrometry (QMS) for gaseous species measurements was conducted using a Hiden Analytical HPR-30 residual gas analysis (RGA) vacuum process sampling system that includes a HAL 201 RC mass spectrometer in multiple ion detection (MID) mode and Bar Scan mode with the Faraday detector (source voltage for electron impact ionization set at 70 eV to ensure efficient reactant molecule fragmentation). The mass spectrometer is placed approximately 80 cm from the main reaction zone (substrate stage). It is important to acknowledge that the surface-generated species detected in the QMS analysis may arise from all surfaces in the reactor. Given that the reactor wall surfaces are relatively much larger than the substrate size, species originating from the walls can significantly impact the measured signal. To guarantee that all identified reaction products stem from reactions occurring at a consistent temperature, it is essential to maintain uniform temperatures across both the walls and substrate. In this study, temperatures were standardized at 150 °C to ensure that the measured reaction products were representative of reactions taking place.
|
66e1358e12ff75c3a1012401
| 6 |
The system was differentially pumped and the operating pressure during typical measurements is kept in the order of 10 -6 mbar to enable mean free paths that allow collisionless particle transport of the ions from the orifice to the detector. The Bar Scan measurements covered a mass range of 1 to 50 atomic mass units (amu), which was suitable for detecting all relevant masses while maintaining a high scanning speed. To analyze the formation of reaction products and the utilization of reactant species, a series of MID measurements were carried out. The MID-scan involved five complete ALD cycles (both precursor and reactant pulses).
|
66e1358e12ff75c3a1012401
| 7 |
The measurement procedure for the process involved monitoring mass-to-charge (m/z) values in the same pressure ranges simultaneously. This monitoring encompassed three distinct sets of measurements: five 'background' ALD cycles with no precursor, co-reactant or plasma power turned on; five 'normal' plasma ALD cycles with both precursor and co-reactant and five 'normal' thermal ALD cycles. Selected m/z values were chosen from the Bar Scans to make up MID scans based on similar pressure ranges for easy comparison e.g. grouping them as m/z = 15 and 16; m/z = 29 and m/z = 42, 43, 44 and 45. By structuring the measurement procedure in this manner, all sets of cycles were designed to induce similar pressure fluctuations as those experienced during a standard ALD cycle. This approach aimed to minimize any potential impact of pressure variations on the measured signal, ensuring a more accurate assessment of the process dynamics and reaction products. The obtained data was analysed using MASsoft 10 (Hiden Analytical) software.
|
66e1358e12ff75c3a1012401
| 8 |
Fig. and Fig. show that the TDMAA and NH3 surface reactions are self-limiting, suggesting that reactions should produce atomic layer controlled growth of AlN films. The strong increase in growth per cycle (GPC) at temperatures above the temperature window for both plasma and thermal processes indicates that the deposition in those temperature regions is governed by a decomposition chemistry with a significant gas phase component, i.e., decomposition of the TDMAA precursor. TDMAA is a dialkylamide precursor and since the thermal stability of dialkylamides is generally limited, substrate temperatures must be kept below the decomposition temperature . For TDMAA, the decomposition temperature is at least 250 °C, if we consider data points outside of the temperature window where 'CVD-like' growth starts to occur (Fig. and Fig. ). The growth rate of the AlN films was slightly above 1 Å/cycle for the plasma process and approximately 0.8 Å/cycle for the thermal process. Fig. ) shows that the thermal process, just like the plasma process, has a low temperature window which is, however, slightly narrower. The linear trend lines show that no incubation cycles are required before nucleation begins from ALD cycles versus film thickness in both processes (Fig. and Fig. ). The fact that the fitted curve intersects the thickness axis above the origin suggests that the TDMAA based processes have substrate-enhanced growth. This can occur if the number of reactive sites on the substrate is higher than on the ALD grown film. The GPC is then high at the very start of the deposition.
|
66e1358e12ff75c3a1012401
| 9 |
Several species, summarized in Table , were detected during the ALD process as illustrated in It should be noted that nitride processes with NH3 adds uncertainties to the interpretation of the m/z = 16 signal, as it can also be NH2 from NH3 decomposition/ fragmentation in the QMS. Mass spectrometry species from an electron impact energy of 70 eV show that the detected ions primarily consisted of fragments from the effluent molecules, with no portion of the spectrum representing parent molecular ions. This is illustrated in Fig. for both the plasma and thermal processes in comparison to the background where no parent precursor is pulsed. DMA is characterized by known peaks at m/z = 45, 44, 30 (HNCH3 + ), and 15 (CH3 + ). The presence of peaks at m/z = 28 (N=CH2 + ), 27, and 26 is indicative of N-methylmethaneimine (MMI, CH₃N=CH₂). MMI can also be identified by the peak at m/z = 43 or 42 (CH2=N-CH2 + ). Additionally, a fraction of the peak at m/z = 15 (CH3 + ) may result from the fragmentation of MMI, a common byproduct from the decomposition of dimethylamido-metal precursors.
|
66e1358e12ff75c3a1012401
| 10 |
Therefore, in low-temperature ALD utilizing TDMAA, it is important to consider possible reactions in the gas phase or on the surface that could result in the formation of MMI since MMI should be reactive towards the surface. The signal at m/z = 18 is assigned to H2O + , residual water vapor could be present in the reactor chamber given its background pressure of 4 hPa or introduced with the TDMAA precursor which was loaded in a stainless-steel container in a glove box but inserted in the ALD reactor in air. This handling could expose the TDMAA briefly to air. Although mass spectrometry data predominantly show DMA as a major product from the ligand, distinguishing between gas phase decomposition reactions and surface reactions poses a challenge.
|
66e1358e12ff75c3a1012401
| 11 |
Competitive reactions could also result in the formation of additional byproducts such as MMI and CH4 as will be explained later. Additionally, another species, hydrogen cyanide (HCN), was detected at m/z = 27 during the process, while cyanide (CN), reported as a decomposition product in ALD of TiN from TDMAT, 20 was not detected.
|
66e1358e12ff75c3a1012401
| 12 |
TDMAT is a well-studied precursor and has been used extensively for TiN deposition. The suggested main decomposition mechanisms for TDMAT shown in Fig. can be summarized as: i) β-hydride elimination, where a hydrogen atom located on the β-carbon (adjacent to the Ti metal center) is eliminated. Subsequently, a double bond between the β-carbon and the adjacent is formed, resulting in the creation of hydride species and N-methyl methyleneimine (CH3N=CH2); ii) an intramolecular insertion metallacycle generation reaction which results in the formation of a metallacycle Ti-C-N ring, that can participate in consecutive reactions and iii) the transfer of a proton (transamination and hydrogenation) to a dimethylamido group, leading to the formation of dimethylamine.
|
66e1358e12ff75c3a1012401
| 13 |
These species are formed as intermediates during the decomposition and reaction processes involving TDMAT on Si. Generation of methane (CH4) during the gas phase decomposition of TDMAT at elevated temperatures (>350 °C) was proposed to be a gaseous radical disproportion reaction. We carried out a mass spectrometric survey scan to see the residual reaction species and byproducts leaving the ALD reactor during TDMAT-NH3 processes (Fig. and Fig. ). The main residual species from the reactor (other than co-reactant NH3, carrier gases N and Ar, and residual
|
66e1358e12ff75c3a1012401
| 14 |
AlN growth from TDMAA and NH3, is likely similar to the much more researched TDMAT and NH3 for ALD of TiN. We therefore did thermal-and plasma ALD experiments with TDMAT for comparisons to TDMAA. From the mass spectra in Fig. ) and Fig. ), we note prominent peaks around m/z = 44 signalling DMA as well as m/z = 16, 27, 29 and 30 which we also identified in the TDMAA-NH3 process. Looking at how TDMAT and TDMAA compare in the mass spectra, we believe that the reaction mechanisms for TDMAA are the same or at least very similar to the ones for TDMAT. In literature , TDMAT has been suggested to decompose and react through an insertion-elimination reaction or a hydrogenation reaction leading to a transamination exchange, consisting of an attack on the Ti centre of TDMAT by the N lone electron pair of ammonia (H2N-H). This reaction is characterized by elimination of -N(CH3)2 ligands at m/z = 44 or 45 (as dimethylamine) and insertion of ammonia (as NH2) where a proton is transferred to a dimethylamido group, which leaves as dimethylamine. As was observed in TDMAA, complex surface reactions and intermediates do take place in TDMAT-NH3 process as well, including the release of methane (m/z = 16) and signals at m/z = 27 and 30. However, the outstanding question at this point is the source of nitrogen in the deposited AlN films. There are two possible sources: TDMAA and NH3. It is also important to note that results of TiN deposition with TDMAT and NH3 as precursors, from isotopic labelling studies have concluded that all of the N in a 'clean' TiN thin film is derived from NH3 via an intermolecular process which facilitates transamination. We believe this could be the case as well for the TDMAA-NH3 process, even though mass spectrometric results alone cannot drive us towards that same conclusion.
|
66e1358e12ff75c3a1012401
| 15 |
Based on the main reaction product intensities monitored at 150 °C in Fig. , we propose that HN(CH3)2 is liberated both during the TDMAA pulse, and during the NH3 pulse. This is supported by analogous results regarding the reaction mechanism in the plasma-assisted ALD process of TaNx using similar ligand precursors, Ta(NMe2)5 and H2 plasma and thermal ALD of TiN from Ti(NMe2)4 and NH3 and can be illustrated through transamination exchange reactions:
|
66e1358e12ff75c3a1012401
| 16 |
Additionally, it has previously been suggested that the N-C bond on the ligand can only be broken at elevated temperatures, or by using plasma, leading to loss of the entire intact ligand. The combination of a weak metal-N bond and high volatility in metal alkylamides generally facilitates effective deposition at lower temperatures. Our results are in line with this as we only detect the assumed ligand decomposition product, NCH3 + , with m/z = 29, during the NH3 plasma pulse (Fig. ). This activation process is occasionally achieved using plasma containing hydrogen, or nitrogen radicals (NH3 plasma in this case). Presumably, NH3 undergoes oxidation during the reaction process to produce molecular nitrogen as a byproduct, reaction (2). The oxidation of the reducing agent is a key step in the overall reaction mechanism, where it plays a role in facilitating the reaction with the metal center and the formation of AlN.
|
66e1358e12ff75c3a1012401
| 17 |
Because HN(CH3)2 is detected during both TDMAA and NH3 pulses, (Fig. and Fig. ) while CH4 is only detected during the NH3 pulse (Fig. ), it is reasonable to assume that CH4 evolves as either a ligand decomposition (illustrated later in reaction ( )), or a reductive elimination product, that has possibly undergone hydrogenation reactions upon interaction with NH3, which acts as an atomic H source and this reaction pathway can be illustrated as follows:
|
66e1358e12ff75c3a1012401
| 18 |
It is important to acknowledge that the presence of plasma necessitates consideration of dissociation and recombination reactions, as they may have a significant impact on the deposition process. Furthermore, dimethylamine radicals can participate in reductive coupling and elimination reactions leading to the formation of tetramethylhydrazine, highlighting their further potential role in the complex gas phase chemistry.
|
66e1358e12ff75c3a1012401
| 19 |
However, tetramethylhydrazine was not detected as a product in our study. We assume that the formation of a hydrazine from the reductive coupling of two amido ligands in the TDMAA molecule is hindered when NH3 is introduced into the reaction mixture. Instead, the presence of NH3 promotes the reductive elimination by hydrogenation of the dimethylamido ligands , leading to the production of the corresponding amine, which in this case is DMA. This phenomenon can be explained by NH3 acting as a competing reactant or coordinator in the reaction system. NH3 may interact with the Al metal center or the ligands, altering the reaction pathway and favoring the hydrogenation process over the reductive coupling to form hydrazine. As a result, the formation of hydrazine is suppressed, and more dimethylamine is produced due to the increased hydrogenation of the amido ligands. In a way, the presence of NH3 influences the reaction selectivity by shifting the equilibrium towards the hydrogenation pathway, thereby affecting the overall product distribution in the decomposition and reactivity of TDMAA.
|
679f540b81d2151a02e748e6
| 0 |
The conformational spaces of active pharmaceutical ingredients (APIs) are of great interest. Many clinically and economically relevant drug molecules are highly flexible, capable of changing shape readily in biological environments, as well as displaying conformational polymorphism in the solid state . This polymorphism is particularly important to the drug design and manufacturing process, as the pharmacological properties of APIs can depend very strongly on the crystal's polymorphism . That the environment of a molecule impacts its conformational landscape is accepted ; however, a systematic method for the mapping and understanding of the conformational spaces of APIs is lacking , partly due to the inherent high-dimensionality of these spaces . Thus, a general mechanistic understanding of the impact of conformational states on crystallization does not exist. Here, we present a workflow that combines enhanced sampling molecular dynamics techniques with densitybased clustering methods to systematically explore the conformational free energy surface (FES) of a small, organic API. A molecule's conformation can be defined using the values of the molecule's freely rotatable dihedral angles (henceforth referred to as torsions). The conformation space is, therefore, always bounded and periodic in all dimensions. Veber's rules , a set of heuristics initially designed to predict whether a molecular structure would possess pharmacological properties, can be used to identify the relevant torsions in any given molecular structure. Characterizing conformers through the values of a set of torsions is not without precedent, and several approaches are based on this definition. For example, Torsiflex 10 is a software package that aims to explore a single molecule's potential energy surface utilizing a semirandom exploration of conformational spaces defined by torsions.
|
679f540b81d2151a02e748e6
| 1 |
Molecular dynamics (MD) simulations can be used to sample the conformational space and map out the conformational FES of a given molecule. Figure shows different extents of MD sampling of the same collective variable (CV) space. Sampling the probability distribution with MD offers several key advantages; MD sampling is inherently physics-inspired and allows for the analysis of the molecule in various environments and conditions. The physics-based nature of the sampling means the distribution sampled in conformational space by the MD simulation can be converted into a FES through the relationship:
|
679f540b81d2151a02e748e6
| 2 |
where S represents the dihedral angle space S = [γ 1 , γ 2 , ..., γ D ], where γ i is one of the D torsional angles of a given molecule. p(S) is the probability distribution in the conformational space, F (S) is therefore the FES in conformational space S, k B is Boltzmann's constant, and T is the temperature.
|
679f540b81d2151a02e748e6
| 3 |
However, for the exhaustive sampling of a conformation space, this approach is limited by the computational feasibility of storing the bias values on a grid of the same dimensionality as the conformation space, which is the same issue faced with the conventional method of FES construction. For this reason, in practical applications, conventional metadynamics biases constructed in dimensionalities higher than three are very rare.
|
679f540b81d2151a02e748e6
| 4 |
Figure shows a FES for alanine dipeptide computed from a non-concurrent WTMetaD simulation using what will be referred to as the conventional method . The WTMetaD biases are deposited in the 2D conformational space, defined by two torsions, ϕ and ψ (as illustrated in Figure ), ensuring that the entire space is fully sampled over the course of the simulation. The space is split into a 100 × 100 bins histogram. The distribution of MD configurations throughout the histogram follows the system's natural probability distribution as distorted by the metadynamic bias. The total bias deposited in each bin is known, allowing this distortion of the probability distribution to be reweighted. The resulting FES has a resolution equal to the fineness of the grid, in this case (2π)/100 rad. This methodology is robust but scales poorly to higher dimensional FESes. Both the bias deposition during the simulation and the estimate of the probability distribution require the construction of a grid with the same dimensionality as the conformation space. If the same resolution is desired, increasing the number of torsions incurs an exponential cost on computational resources, rapidly becoming unfeasible. In the scientific literature, this issue is addressed by employing dimensionality reduction methods such as SketchMap . In these methods, the conformational probability density is obtained by histogramming sampled configurations in a lowdimensional space of unphysical coordinates. While this approach can be effective for relatively small systems , its ability to resolve degeneracies and identify conformers when the conformational spaces are defined by a large number of torsional degrees of freedom is not straightforward.
|
679f540b81d2151a02e748e6
| 5 |
Grid-less Probabilities with Density Peaks Advanced Density-based clustering techniques form a family of unsupervised machine learning algorithms that group data points within spatial datasets into clusters based on the distance between data points within the data space. Algorithms in this family include DBSCAN and Fast Search and Find of Density Peaks (FSFDP) . There is precedent for the use of FSFDP in molecular conformation spaces, Marinova et al. used it to study the conformation space of Sildenafil 8 . Here, Density Peaks Advanced (DPA) , a successor to FSFDP, is used. DPA, developed by d'Errico et al., splits a set of data points distributed in space into clusters by grouping points within density peaks, a term referring to regions of high data density (N.B. In this work, the term 'density' refers to the density of data points in S, unless otherwise noted). It does this partly by calculating the local density of every region centered on every single point in the dataset. This calculation is a function of the Euclidean distances between the point and its nearest neighbors. Here, the process is applied to a sample of N configurations in conformation space sampled by the MD simulation. These local density calculations are extremely powerful in this context for two key reasons: firstly, each additional dimension in S adds a single term to the Euclidean distance calculation, so the cost with increasing dimensionality scales linearly, and secondly these local densities map a distribution in much the same way as the previously described histogram, so the same reweighing and inversion procedure may be applied to calculate the free energy. These free energies, unlike in the above histogram, are not associated with a defined region of conformation space. Rather, they are associated with a specific configuration sampled by the simulation. Thus, this per point FES has no fixed spatial resolution; data is rich in regions that have been heavily sampled and sparse in regions that have not been frequented. This is advantageous as it means that while data in the local minima remains highly dense due to the frequent sampling, little cost is incurred considering data from the rarely visited, largely irrelevant high-energy regions. This contrasts with the grid-based approach, where these high-energy regions are modeled in as high a resolution as the more relevant local minima. The results of applying this approach to alanine dipeptide can be seen in Figure .
|
679f540b81d2151a02e748e6
| 6 |
This entails simultaneously depositing a single one-dimensional bias for each torsion in the molecule, thus promoting exploration of the rotation of that torsion. . The cost of this approach scales linearly with dimensionality (shown in Figure ), as one additional monodimensional grid is needed for each additional torsion considered. The cost savings of this approach come with a trade-off; conventional metadynamics promotes the exploration of the entire conformational phase space and guarantees that previously visited configurations will be penalized accordingly.
|
679f540b81d2151a02e748e6
| 7 |
Concurrent metadynamics does not explicitly bias the combinations of any torsion values. Instead, it promotes the escaping from local free energy wells by driving the rotation of individual torsions. This can be seen in the use of this technique on alanine dipeptide in Figure . This work will demonstrate that DPA analysis of datasets generated using concurrent WTmetaD can be used to model the probability distribution of a flexible molecule's conformational state and create a 'per-point' FES, where the data points themselves are configurations sampled by the simulation. This approach will be shown to recreate the well-studied 2D FES of alanine dipeptide before being demonstrated on 4 and 11-dimensional conformation spaces.
|
679f540b81d2151a02e748e6
| 8 |
To discuss the approach developed in this work in detail, it is helpful to begin by introducing how DPA allows the estimation of an FES from unbiased MDgenerated data. Density Peaks Advanced (DPA) is run on a subset of configurations sampled from an MD trajectory. The size of this subset is the limiting factor in the cost of this approach as each point has a local density determined by the distance to its neighbors, so the process depends on constructing a complete distance matrix between all configuration pairs. We, therefore, expect the cost of this approach to scale with the square of the dataset size, as demonstrated in Figure . Because the thermodynamics of the system directs the MD trajectory's sampling, the local density of each configuration is proportional to the relative probability of encountering this configuration. It thus can be directly inverted to the free energy of the configuration using Equation .
|
679f540b81d2151a02e748e6
| 9 |
DPA estimates the probability associated with the ensemble of configurations projected in a given point i of the configuration space S, using the PAk density esitmator , based on the Euclidean distances between point i and its k nearest neighbors. An underpinning assumption of this method is that the density is constant in the neighborhood of the point i. Hence, the parameter k is selected to be as large as possible to maximize the data used in calculating the local density while still representing a hypervolume of constant density. Each neighbor l can be said to occupy the volume v l of the hyperspherical shell enclosed between hyperspheres of radii r l and r l-1 . The sum of these volumes up to neighbor k is equal to volume V k of a hypersphere with radius r k . DPA leverages the fact that for a region of constant density, the volumes will be drawn from an exponential distribution with a rate of this density ρ and that thus the log-likelihood function of ρ given a set of k neighbors is given by
|
679f540b81d2151a02e748e6
| 10 |
which increases as the two models differ. If D k grows over a threshold D thr (D thr = 23.928 according to Ref. ) then the densities of i and j cannot be considered constant. As such, PAk selects an appropriate k value by iteratively calculating D k to increasing values of k until the threshold is passed.
|
679f540b81d2151a02e748e6
| 11 |
In practice, we generate conformational datasets using WTmetaD simulations. Using PAk on configurations sampled from a WTmetaD simulation produces densities that reflect a probability distribution perturbed by the Cluster centers generated from smaller amounts of data (shown in red) are paired to the nearest cluster center in the reference set, allowing comparison of distances and energy differences between cluster centers. It is expected that as dataset size grow, the positions and energies of the cluster centers will converge, as seen in Fig. .
|
679f540b81d2151a02e748e6
| 12 |
where ρ * is the reweighed density, β is equal to 1/k B T , V t i is the bias in torsion t, D t=1 V t i represents the sum of the concurrent biases acting on the D torsions, for configuration i. Practically, we evaluate ρ, the biased density, from configurations generated in a quasistatic bias regime, as the bulk of the bias is deposited during the early stages of the simulation and the bulk of sampled configurations are visited when bias deposition is negligible. We therefore apply the final bias approximation to obtain a time-independent value of V t i acting on configuration i. To mitigate the noise introduced by exponential reweighting , the density of each point is then averaged over hyperspherical domains of radius 0.1 rad. This step generates a new smoothed set of densities ρ * i , at the cost of a small controllable loss in spatial resolution. The free energy F i , associated with configuration i (thus termed per point), is computed as
|
679f540b81d2151a02e748e6
| 13 |
In the classification step, DPA identifies peaks in the density as cluster centers, i.e., distinct conformers. This operation is equivalent to identifying local minima in the D-dimensional free energy surface. For this step, we use the set of reweighted, smoothed densities ρ * i . Moreover, to avoid every fluctuation in density from being identified as a distinct peak, the DPA classifier is set to merge clusters separated by a saddle point between the free energy basins (a conformational transition state) with free energy less than 1 kT higher than one of the cluster centers it connects. Once cluster centers have been determined, all remaining configurations are assigned membership to the same cluster as their nearest neighbor of higher density . With all configurations classified, clusters with a population smaller than 1% of the total sample are discarded to avoid spurious clusters identified from anomalously isolated configurations.
|
679f540b81d2151a02e748e6
| 14 |
Where simulation time t runs from [0, τ ], F (t) is a monodimensional FES obtained with data gathered up to time t, F (τ ) is the same quantity computed with all the data available. This quantity represents the average free energy difference per histogram bin in any of the D monodimensional free energy surfaces. Figure displays an example of δF M (t) computed for ϕ and ψ torsional angles of alanine dipeptide during concurrent metadynamics. The flattening of these differences as the fraction of utilized trajectory increases indicates that the simulation has been run for long enough that these torsions have been ergodically sampled.
|
679f540b81d2151a02e748e6
| 15 |
This check is computationally inexpensive and offers a first qualitative check on the quality of the configurational exploration obtained with concurrent WTmetaD. If the marginal FES associated with a torsion is still evolving rapidly at time τ , i.e., when the simulation ends, the sampling has not yet reached the ergodic limit with respect to the configurations discovered.
|
679f540b81d2151a02e748e6
| 16 |
For this purpose, a consistency check has been devised, which offers a similarity score between two cluster sets generated from different configurations. A cluster set generated from a dataset of size N , C N can be compared with a reference cluster set C ref , which is generated with the largest number of configurations feasible. Each cluster center C N i is matched with the nearest center in the reference set C ref i , according to the Euclidean distances in S between members of the two cluster sets. This matching process is demonstrated in Fig. . Differences in free energy ∆F i and position ∆d i are determined and averaged across all matched pairs as ∆F
|
679f540b81d2151a02e748e6
| 17 |
N and ∆d N . This comparison to C ref can be repeated for cluster-sets generated from datasets of increasing N , and evolution of ∆F N and ∆d N with growing N can thus be assessed. Once datasets are large enough, the positions and relative free energies of minima would be expected to be independent of dataset size. The results of this analysis on the case of alanine dipeptide are shown in Figure ,g,h.
|
679f540b81d2151a02e748e6
| 18 |
Unless otherwise specified, all simulations carried out for this work consisted of a single molecule in vacuum, simulated with a 2 fs timestep. GAFF 28 forcefield parameters were used, and GROMACS was the MD engine used. WTMetaD was carried out using the Plumed 30 plugin for GROMACS. The simulations were carried out in the NVT ensemble, at a temperature of 300K, maintained using the velocity-rescaling thermostat developed by Bussi et al. For the determination of WTMetaD parameters, a short 10 ns unbiased simulation was run. The marginal FES in each torsion was computed. A Gaussian Mixture Model was fitted to the resulting FES, and the smallest width parameter of the GMM, corresponding to the narrowest local minimum in the marginal FES, was considered as the minimum reference width for the marginal under consideration. The width of the Gaussian terms used to update the metadynamics bias was set to a quarter of the minimum reference width. Following the end of the WTMetaD simulation, configurations from the simulation were paired with the total deposited bias at the corresponding position in conformation space, which was in line with the final bias approximation.
|
679f540b81d2151a02e748e6
| 19 |
The workflow outlined in this work was first tested on the Ramachandran plot 32 of alanine dipeptide. This system was chosen for several reasons: the Ramachandran plot of alanine dipeptide is a commonly used model system in the field of molecular dynamics and enhanced sampling techniques, making it one of the best-studied conformational FESes available. Additionally, its low dimensionality allows for both the visualization of the FES and access to more conventional methods of exploring this conformational space. The principal results of this are shown in Figure . The structure of alanine dipeptide, with ϕ and ψ, indicated, is shown in Figure . The conventional FES of alanine dipeptide, obtained through histogramming and reweighing of a trajectory generated through a WTMetaD MD simulation , is shown in Figure . A per point FES, generated from the same simulation but with free energies calculated using the local densities of the sampled configurations, as discussed in the Methods section, is shown in Figure . From a visual comparison, it clearly appears that the two FESes are in agreement, demonstrating that the reweighted-DPA density estimate leads to results virtually indistinguishable from standard histogramming-based approaches. Figure shows a per point FES generated using a trajectory from a concurrent metadynamics simulation where ϕ and ψ are biased independently. Besides demonstrating the consistency of the free energies obtained by concurrent biasing, the comparison between Figure and Figure illustrates the trade-offs entailed using concurrent metadynamics. As detailed in the Methods section, concurrent metadynamics promotes the sampling of metastable states without guaranteeing an exhaustive sampling of the joint configurational probability density. Nevertheless, all relevant free energy minima are adequately sampled, and their positions and free energies agree with those obtained by standard, two-dimensional metadynamics (Fig. ). The results of the consistency analysis techniques outlined in the Methods section on the per-point FES outlined in Figure are shown on Figure . Figure shows the evolution of δF (t) for ϕ and ψ. The flattening of the curves shows that the sampling of the two torsions is indeed ergodic over the timescale of the simulation.
|
679f540b81d2151a02e748e6
| 20 |
Figure shows mean conformer free energy difference ∆F N (defined in the Methods section) obtained from clustering datasets of increasing N and a reference dataset at N =50,000 configurations. Figure shows a similar plot displaying the mean separation of the cluster centers, ∆d. Figure shows the number of minima identified by DPA for each reduced-size dataset. The plot shows that all reduced datasets agreed that there were 3 conformers, with the exception of the 10,000 configuration dataset. In all other datasets, there is very good agreement on the position and free energies of the local minima, with energy differences well within 1 kJ mol -1 and mean separations hovering around 0.1 rad.
|
679f540b81d2151a02e748e6
| 21 |
Having demonstrated the workflow developed here on the two-dimensional case of Alanine Dipeptide, higher dimensional cases are now explored, where visualization of the entire conformation space is not possible and conventional grid-based methods become unfeasible. Sulfadiazine, with a 4-dimensional conformational space, and Candidate XXXII, from the CSP Blind Test , with an 11-dimensional conformational space, serve as a test for the ability of the workflow to handle conformational complexity. Sketch-map 17 is used in these cases to project a 2D representation of the high dimensional perpoint FES for human interpretation.
|
679f540b81d2151a02e748e6
| 22 |
Sulfadiazine is an antibiotic molecule with a 4dimensional conformational space; its clinical relevance and intermediate complexity make it an ideal next step for the method outlined here. A 4-dimensional space is too high to allow a FES to be fully visualized while still being low enough that reasonable data density can be obtained (50,000 data points in a periodic 4D space results in an average density of roughly 32 configurations per rad 4 ).
|
679f540b81d2151a02e748e6
| 23 |
The inset in Figure shows the 4 torsions considered in sulfadiazine. Using the same approach outlined above for alanine dipeptide, sulfadiazine's conformational FES was studied by analyzing the configurations sampled within a 1 µs single-molecule WTmetaD simulation. The resulting per-point FES cannot be fully visualized without dimensionality reduction, so the relative free energies and coordinates of each minimum are presented in Tab. I. Figure shows a 2D projection of the 4D perpoint FES created using SketchMap. This representation preserves the short-distance connectivity between data points, allowing the visualization of distinct free energy basins and the transition states between them, though the two axes of the new 2D projection are not physically meaningful themselves. It should be emphasized that the estimation of densities and the determination of the number and coordinates of the free energy minima are determined in the full 4-dimensional conformation space and that the projection in Figure serves only to assist in the visualization of the relationships between different conformers. It is possible to combine the 4dimensional information presented in Table with the 2-dimensional intuition provided by Figure . For example, the FES in Figure appears to be bisected by a diagonal channel, and indeed, by inspecting the torsion values of the conformer pairs 17 and 2, 10 and 6, 21 and 15, and 7 and 8, it can be determined that these conformers pairs are identical, and differ from each other in a symmetric rotation of π radians of γ 3 . This example serves to show how these 2D projections may be manually interpreted and to demonstrate how symmetry elements in the molecule's conformation space can be preserved in the 2D projection.
|
679f540b81d2151a02e748e6
| 24 |
The plots of δF (t) for the four torsions show that the four marginals in Figure converge rapidly, providing evidence of ergodicity. Figure shows that, with the exception of the 5000-point dataset, repeated analyses achieve a consistent number of 24 conformers. Figure ,e shows the evolution of ∆F and ∆d respectively, as N increases to a reference value of 50,000. Here, the differences between alanine dipeptide and sulfadiazine become apparent. The mean free energy deviation jumps from being nearly negligible to a range between 0.5 and 2 kJ mol -1 , and positional deviation increases from approximately 0.1 rad to between 0.3 and 0.4 rad. Sulfadiazine's energy deviation is still within 1 k B T, and the positional deviations still correspond to very small changes in the molecular structure. However, the abrupt change following an increase in dimensionality highlights the importance of carrying out consistency checks when working with highly unintuitive results that are difficult to inspect visually. Due to the number of equivalent conformers related to one another by symmetric transformations in sulfadiazine, it is possible to compare the free energies of equivalent conformers as an assessment of the reproducibility of the free energy calculation. This is not recommended as a standard practice, as the presence of symmetrically related conformers is system-dependent and not guaranteed. However, in this case, comparing the differences between equivalent conformers reveals deviations of the same order as the mean free energy deviations calculated in the smaller datasets (Figure .
|
679f540b81d2151a02e748e6
| 25 |
The final conformational FES explored here is that of Molecule XXXII, a target from the 7th CSP Blind Test . As a highly flexible drug-like molecule with a conformation space defined by 11 torsions (shown inset in Figure ), it is chosen here to test the limits of our method. To facilitate comparison with results collected for alanine dipeptide and sulfadiazine, the results presented here were generated using consistent simulation and analysis parameters. Using 50,000 data points in this high dimensional space results in an average data density of approximately 8×10 -5 configurations per rad . Despite the extremely low data density, which is inherently linked to the complexity of the conformational space, we show that meaningful results are achievable. Figure shows the projected 11-dimensional perpoint FES, with cluster centers corresponding to 11dimensional coordinates presented in Tab. II. When comparing this FES to sulfadiazine's in Figure , the features of XXXII can be seen reflected in its own FES. The relative lack of symmetrical torsions results in a less symmetrical FES, and the higher-dimensional FES is much sparser, illustrating that the computational savings arise from a more efficient, rather than more exhaustive, sampling of conformational space.
|
679f540b81d2151a02e748e6
| 26 |
The consistency metrics in Figure -e are, however, less reliable than those obtained for sulfadiazine. Figure shows well-converged marginal free energies, but Figure shows that the number of conformers identified is less consistent than in lower-dimensional cases. The number of metastable states identified as distinct conformers hovers between 22 and 25 for datasets sized 10000 and upwards. Along with a fluctuating number of conformers, Larger deviations in free energies and positions are now observed, with ∆F between cluster sets now varying by up to 5 kJmol -1 , and ∆d drifting by as much one full radian, even at large dataset sizes. Despite this drop in the quality of the results, we believe it is still remarkable that a reasonably intuitive understanding of such a high-dimensional conformational FES can be derived from a limited amount of data in a computationally accessible way, even if its value in this instance is chiefly qualitative. To further explore the consistency of the FES in Figure , Figures S2-S10 contain the FES projection for each of the smaller datasets used in the consistency analysis, allowing the evolution of this per-point FES to be observed. Inspection of this evolution in the FES seems to reveal that the majority of the fluctuations in ∆F and ∆d observed arise in higher energy conformers, with the low energy regions converging at lower N values. While we do not rigorously prove that here, it is a reasonable expectation, as lower energy regions have a high data density, resulting in free energy estimates based on a greater amount of data.
|
679f540b81d2151a02e748e6
| 27 |
A new analysis method, based on the use of DPA clustering, allows for creating high-dimensional conformational free energy surfaces in a gridless, computationally accessible way, allowing the conformational ensembles of highly flexible molecules to be characterized in a systematic and efficient way which scales better than the conventional grid-based approach. Pairing DPA's density estimation tool with a dataset of configurations generated through concurrent well-tempered metadynamics simulations allows for quantitative per-point FES generation through a simple Zwanzig-based reweighing scheme. DPA's classification approach further allows for automatic, high-dimensional interpretation of these FESes. This approach has been demonstrated for systems with 2, 4, and 11-dimensional conformation spaces, and the performance of this method was tracked using a set of consistency metrics that enable its application in realistic cases. The approach is entirely simulation agnostic, operating solely on the coordinates of configurations in conformation space and their corresponding biases. We thus envision applications for simulations performed at a broad range of theory levels and across various physical environments. The code developed here is fully open source and available from .
|
63aedbf204902ad473148fa4
| 0 |
Evaporation from a porous medium can induce the precipitation of salt, thus leading to the formation of a porous salt crust. Depending on the topology of the system, the precipitated salt crust can either enhance or hinder evaporation . A better understanding of the water transport properties near aqueous/solid salt interfaces is necessary to predict the formation and impact of precipitated salt crusts, which is vital for arid regions where soil salinisation due to irrigation is a critical problem .
|
63aedbf204902ad473148fa4
| 1 |
Fast-Field-Cycling (FFC) NMR relaxometry is a powerful tool to analyse water properties in disordered porous media such as salt crusts. It probes the return of the macroscopic nuclear magnetization to its equilibrium state along an external magnetic field after a perturbation . The return to equilibrium of the magnetization, quantified by the so-called spin-lattice relaxation time T 1 , is induced by fluctuations in local magnetic fields, which in fluids occur primarily due to two effects: the rotational tumbling of individual molecules, which is responsible for intramolecular relaxation, and (2) the relative translational motion of molecules, which is responsible for intermolecular relaxation. For fluids confined in nanoporous media, a decrease in T 1 for increasing surface-to-volume ratio S/V is generally observed . For a slit pore of size h = V /S, one expects 1
|
63aedbf204902ad473148fa4
| 2 |
where λ is the size of the surface layer, which is typically a a) Electronic mail: schlaich@icp.uni-stuttgart.de few molecular sizes, and T bulk 1 and T surf 1 are the bulk and surface relaxation times, respectively. Therefore, NMR relaxometry can be used to probe the effect of confinementinduced phenomenona on the dynamical properties of the fluid .
|
63aedbf204902ad473148fa4
| 3 |
Atomistic Molecular Dynamics (MD) simulations can provide an accurate picture of the nanoscale thermodynamics and dynamics of fluids confined in nanochannels . For typical systems sizes of a few nanometers, simulations can be performed for hundreds of nanoseconds, corresponding to frequencies of tens of MHz and thus allowing for direct comparison with experiments in this frequency range, which is at about the upper limit of typical FFC measurements.
|
63aedbf204902ad473148fa4
| 4 |
Here, we combine FFC experiments and MD simulations to study the dynamics of water confined within two specific salt crusts, namely NaCl and Na 2 SO 4 . Experimental results reveal significant differences for the water dynamics for the two salts, which we reproduce with our MD simulations. To further explore how the presence of salt crusts affects this behavior, we then explore the dynamics of water in nanoslits composed of either NaCl or Na 2 SO 4 via MD simulations. For these systems, NMR relaxation times T 1 of pure water and salt solutions with different concentrations are computed, and the results are discussed in terms of the state of the water-salt interface, including the average orientation of the water molecules and adsorption of ions at the wall.
|
63aedbf204902ad473148fa4
| 5 |
Relaxometric Magnetic Resonance Imaging (MRI) was used to extract the relaxation time T 1 from bulk salt solutions. NaCl and Na 2 SO 4 solutions were prepared at the concentrations of 1, 2, and 4 mol/kg and 0.2, 0.5, and 1 mol/kg, respectively (Supplemental Material, Table ) and filled in 10 mm diameter NMR glass tubes. All measurements were done at room temperature (20 • C). Dissolved oxygen was removed by stripping the samples with a helium gas stream for 5 minutes, and tubes were immediately closed to prevent re-diffusion of air. The glass tubes were arranged in a bundle so that T 1 could be determined simultaneously for all different concentrations using an imaging pulse sequence. MRI images of the salt solutions were recorded using a Bruker Ultra-Shield super-wide bore magnet, with a magnetic field B 0 = 4.7 T (200 MHz) equipped with a wide-bore gradient system and a GREAT60 gradient amplifier, operated by a Bruker Avance III console. A multi-slice multi-echo (MSME) pulse sequence with inversion recovery (IR) preparation at intervals t inv = 0.2 to 8 s (logarithmically sampled) was used. A reference scan without IR preparation was performed at the end of the image series. Other pulse sequence parameter settings: the slice thickness was equal to 3 mm, the field of view was 30 mm × 30 mm, the matrix size was 128 × 128 points, the echo time t E was 5 ms and the recycle delay time t R was set to 10 s. The first step of the evaluation was performed by complex division of the images with IR preparation by the reference image to eliminate the dependence of the signal intensity on the transverse relaxation time. A value of T 1 was obtained for each voxel by fitting a single exponential function to the data. Finally, a single value of T 1 was obtained for each sample by averaging the values over a region of interest defined by the entire cross section of the tubes (Supplemental Material, Table ).
|
63aedbf204902ad473148fa4
| 6 |
FFC relaxometry was used to generate nuclear magnetic resonance dispersion (NMRD) curves , i.e., a plot of the relaxation time T 1 as a function of the Larmor frequency ν. Salt crusts of NaCl and Na 2 SO 4 were prepared by evaporation from a column filled with fine quartz sand F32 (Quarzwerke Frechen, Germany) and a porous glass plate of pore size class P2 (40 -100 µm, Robu GmbH, Germany), respectively. The columns were connected to a storage vessel via a tube ensuring that evaporation took place under wicking conditions (i.e., constant hydraulic and near-saturated conditions). The concentration of the solutions was 4 M for NaCl and 1 M for Na 2 SO 4 , just below the respective saturation concentrations of the two salts. The evaporation was stopped after several days. In the case of NaCl, small granules made of pure efflorescent crust were collected and placed in a 10 mm NMR tube. In the case of Na 2 SO 4 , the crust was carefully removed from the porous support plate and glass walls and transferred to a 10 mm NMR tube at constant relative humidity near saturation to prevent dehydrated thenadite species from forming . FFC experiments were performed with a Stelar Spinmaster II (Stelar s.r.l., Mede, Italy) operating with a magnetic field for relaxation B rlx corresponding to a Proton Larmor frequency ranging from 10 kHz to 20 MHz. In a first step, the raw data, i.e., the free induction decay curves as a function of time period τ and magnetic field B rlx were analyzed with the Stelar software, thus yielding the magnetization in the z-direction, M z , at time zero. In a second step, the relaxation curves (i.e., M z versus time τ ) were analyzed by fitting a mono-exponential function to the data yielding the relaxation time T 1 . We found that in all cases such a fit was a sufficient representation of the data. Finally, the NMRD profiles were obtained by plotting the T 1 relaxation times as a function of the Larmor frequency ν. All measurements were done at room temperature (20 • C).
|
63aedbf204902ad473148fa4
| 7 |
Scanning Electron Microscopy (SEM) measurements were performed on dry salt samples using a FEI Quanta 200F electron microscope, equipped with an Apollo X silicon drift Detector (EDS) from EDAX. Measurements were undertaken using a back scattered electron (BSE) detector in low vacuum mode (60 Pa) at an accelerating voltage of 20 kV and a working distance of 11.5 mm for the Na 2 SO 4 and 9.4 mm for the NaCl (Fig. ). SEM images were then used for estimating the pore size distribution using ImageJ . First, the local contrast was adjusted using the CLAHE tool. Then the data was binarized and filtered using a morph open operation. On this basis, distance maps were calculated and quantified by frequency distributions of pore radii.
|
63aedbf204902ad473148fa4
| 8 |
Molecular dynamics simulations of both bulk salt solutions and 2D nanoslit systems were performed using the GROMACS simulation package . The transferable force field developed by Loche et al. was used for the sodium (Na + ) and chloride (Cl -) ions, the TIP4P/ force field was used for water, and the parameters for the sulfate (SO -2 4 ) ion were recalibrated for this study as explained in the Supplemental Material. Cross parameters were calculated using the Lorentz-Berthelot mixing rule. Parameters used for this study are summarized in Supplementary Table . The temperature T was imposed using the CSVR thermostat with a default time constant of t CSVR = 0.5 ps, and the pressure P was imposed using a Berendsen barostat with a time constant of 1 ps. Long range electrostatic interactions were handled using the smooth particle mesh Ewald method (SPME) . The LINCS algorithm with the highest order of expansion N LINCS = 4 and one iteration step was used to constrain the geometry of water molecules . Careful analysis of the influence of the Lennard-Jones cutoff discussed in the Supplemental Material reveals convergence for the value employed for production, r LJ = 1.4 nm. The realspace contributions to the electrostatic interaction were cutoff at r C = r LJ and an integration timestep of 1 fs was employed for all simulations. In all simulations, periodic boundary conditions in all directions were employed.
|
63aedbf204902ad473148fa4
| 9 |
A total number of N = 2000 water molecules and ions were initially disposed on a simple cubic lattice. The ratio of ions-to-water molecules was set by the salt concentration c s , which was varied from 0 to 5 mol/kg for NaCl solutions, and from 0 to 1.25 mol/kg for Na 2 SO 4 solutions. The system was first relaxed at a temperature T = 20 • C in the NVT ensemble during 50 ps, and then at a pressure P = 1 bar and temperature T = 20 • C in the isotropic NPT ensemble during 250 ps. Finally, production runs in the NPT ensemble were performed for 2 ns, after which all observables are well converged. During the production runs, configurations were saved every 0.05 ps for analysis. Simulation input scripts are available in the DaRUS repository .
|
63aedbf204902ad473148fa4
| 10 |
Slit nanopore systems were constructed out of a salt crystal of approximate lateral dimensions 4 × 4 nm 2 and approximate thickness 1.2 nm to create a slit geometry. The slab was filled with fluid composed either of pure water, or of a salt solutions of given concentration c s . The system was first relaxed at a temperature T = 20 • C in the NVT ensemble for 50 ps. Then, the system was compressed in the anisotropic NPT ensemble with an imposed pressure P z = 1000 bar along the z axis, an imposed pressure P xy = 1 bar along the x and y axis, and a temperature T = 20 • C for 100 ps , thus ensuring the contact between liquid/solid interfaces. The system was then equilibrated for 5 ns in the anisotropic NPT ensemble with P xy = P z = 1 bar at T = 20 • C. Finally, production runs with high temporal resolution of the saved configurations of 0.05 ps were performed in the NVT ensemble for 2 ns, as well as a low resolution production run of 200 ns length during which configurations were saved every 5 ps. Simulation input scripts are available in the DaRUS repository .
|
63aedbf204902ad473148fa4
| 11 |
The NMR relaxation time T 1 was calculated using our freely available analysis package NMRforMD . For brevity, only essential details are given here, more information about the method can be found in the original paper by Bloembergen, Purcell, and Pound , as well as in Refs. . In essence, T 1 can be related to autocorrelation functions of fluctuating magnetic dipole-dipole interactions of the form
|
63aedbf204902ad473148fa4
| 12 |
where the order m corresponds to the three position coordinates defining the dipoles in the lab frame, namely the nuclear spin separation r ij (t) and the polar and azimuthal angles θ ij (t) and ϕ ij (t) with respect to the applied static magnetic field that is parallel to e z . N R and N T are the number of intramolecular and intermolecular degrees of freedom, respectively, where R denotes the rotational and T the translational relaxation modes, see Ref. for more details. A typical assumption is the stochastic independence of rotational and translational molecular diffusion, where the first corresponds to fast molecular reorientations while the latter is due to molecular translations over distances much longer than the molecular sizes . The ensemble average is performed by a double summation over spin pair i and j with i = j. The functions F (m) ij (t) are dependent on the vector r ij which specifies the position of spin j with respect to spin i, and read
|
63aedbf204902ad473148fa4
| 13 |
In order to validate the numerical procedure, the NMR relaxation time T 1 was calculated for a bulk water solution having five different temperatures ranging from 10 to 30 • C. Our results show an increase of T 1 with increasing temperature, in good agreement with experimental results from Refs. (Fig. ). The increasing relaxation time results from the comparatively faster molecular motion (i.e., lower viscosity) at higher temperatures. Our MD results show a slightly slower increase of T 1 with T than experimental data, resulting in a value of T 1 that is underestimated by about 5 % compared to the experimental values at T = 30 • C. This slight underestimation cam be attributed to the known small discrepancy between the viscous behavior of the employed TIP4P/ water model and experiments . We also performed MRI measurements at T = 20 • C shown as red data in Fig. . The value of T 1 measured using MRI is slightly larger than the results from Refs. , and differs by about 5 % from our MD result. From the MD simulations we also evaluate the translational diffusion coefficient D T = 4r 2 Stokes /(5τ T ), where r Stokes = 1 Å is the Stokes radius of a water molecules and τ T the correlation time calculated as . The corresponding simulation results for D T are in good agreement with experimental data from Refs. , as well as with simulation results from Refs. (Fig. ). Note, that D T values agree well with the diffusion coefficient calculated from the mean square displacement, D MSD , shown in Fig. , while being slightly larger at the lower temperatures, where the difference for the lowest temperature considered here is about 20 %.
|
63aedbf204902ad473148fa4
| 14 |
The value of T 1 was then determined for bulk solutions of NaCl and Na 2 SO 4 at varying salt concentration c s . Both MD simulations and MRI experiments show a decrease of T 1 upon increasing the concentration of either salt (Fig. ). In the case of NaCl, our simulations underestimate T 1 for all salt concentrations c s , with a maximum difference of ≈ 14 % for c s = 4 mol/kg. For Na 2 SO 4 , the value of T 1 from experiments was found to decrease faster with c s as compared with the MD value, with T 1 value at c s = 1 mol/kg being overestimated by the simulations, while the T 1 value at c s = 0 mol/kg is being underestimated. These slight differences in T 1 between experiments and simulations for both NaCl and Na 2 SO 4 salt solutions could be the consequence of the parametrization of the ion force fields that are based solely on thermodynamics quantities: the ion solvation energy as well as the ionic activity are matched to their respective experimental counterparts (see Ref. as well as the Supplemental Material), whereas T 1 is a dynamic property that is sensitive to the molecular motions (i.e., to the viscosity of the fluid).
|
63aedbf204902ad473148fa4
| 15 |
After having assessed the performance of comparing experimental and numerical values of T 1 obtained in bulk systems, we now turn to FFC experiments performed both for NaCl and Na 2 SO 4 salt crusts. In the low frequency regime (ν ≤ 1 MHz), our results reveal a stronger dispersion for T 1 with the frequency ν in the case of Na 2 SO 4 as compared to the NaCl salt crusts (Fig. ). For NaCl, the T 1 spectrum is almost flat for ν ≤ 1 MHz, with T 1 ≈ 1.25 s, i.e., about half of its value in the bulk solution. For Na 2 SO 4 , T 1 has lower values, as compared to NaCl, and reaches value as low as T 1 ≈ 0.15 s for the lowest frequency available. Pore size distributions evaluated from SEM images show that smaller pores are more prevalent in Na 2 SO 4 crusts as compared to NaCl salt crusts (Figs. ). The predominance of smaller pores in the case of the Na 2 SO 4 salt crust could explain, at least in part, the stronger dispersion of T 1 with ν as compared to the NaCl salt crust. However, the smallest pores that can be observed with SEM imaging correspond to a radius of 1 µm, leaving room for further investigation that goes beyond the present paper.
|
63aedbf204902ad473148fa4
| 16 |
Since the NaCl and Na 2 SO 4 crusts have different pore size distributions, as indicated by SEM measurements (Fig. ), their respective surface-to-volume ratios and the corresponding relative amount of 'small' pores is expected to be different, which will affect the frequency dependence of T 1 . NaCl and Na 2 SO 4 solid surfaces also have different surface chemistry, SO 2- 4 ions bear a -2e charge, compared to the -1e charge of the Cl -ions. Differences in surface chemistry are likely to impact the water structure, as well as the characteristic residence time of the molecules at the solid walls. In order to obtain results from NaCl and Na 2 SO 4 systems with a controlled surface-to-volume ratio, MD simulations of pure water confined within slit nanopores were performed (results obtained with salt solutions with finite concentration are presented in the next subsection). The surface area of the nanopore was chosen as A ≈ 16 nm 2 , and the distance between the wall was varied from h ≈ 0.4 nm (about one water layer thickness) to h ≈ 7 nm (Fig. ). Although such nanometersized slit pores might not be representative for salt crusts, they allow to systematically study the effect of the liquidsolid interface on the relaxation time T 1 .
|
63aedbf204902ad473148fa4
| 17 |
For NaCl slit pores, T 1 extracted from MD is found to be quasi-independent from the frequency for ν ≤ 500 MHz, and to be very close to its bulk value T 1 ≈ 3.1 s (Fig. ). In contrast, for Na 2 SO 4 slit pores, T 1 increases from ≈ 2 s to ≈ 3 s as ν increases from 1.5 to 500 MHz. Therefore, the value of T 1 at the lowest accessible frequency in the simulations, ν = 1.5 MHz, is lower in the case of Na 2 SO 4 as compared to NaCl (Fig. ). For frequencies larger than ≈ 500 MHz, which corresponds to events whose duration is below ≈ 100 ps, T 1 strongly increases with ν for both NaCl and Na 2 SO 4 slit pores (Fig. ). This significant increase of T 1 for frequencies larger than ≈ 500 MHz is related to the molecular motion, and is also observed for bulk systems (see for instance Fig. ).
|
63aedbf204902ad473148fa4
| 18 |
The distinct values for T 1 measured in slit pores with identical surface-to-volume ratio suggest differences in the properties of the water near solid Na 2 SO 4 and NaCl surfaces. Density profiles computed along the z-axis normal to the pore surface using MDAnalysis together with the MAICoS Python toolkit show that the maximum density within the first molecular layer is almost twice as large in the case of NaCl as compared to Na 2 SO 4 (Fig. ). The apparent weaker structuring of the water in the case of the Na 2 SO 4 as compared to NaCl could be the consequence of the different atomic roughness of the two solid surfaces: the NaCl block remains perfectly crystalline and its surface along the (100)-plane remains atomically smooth in contact with water (as has been previously observed for example in Refs. ), while the Na 2 SO 4 block is slightly disorganized and its surface is atomically rough in contact with water (Fig. ).
|
63aedbf204902ad473148fa4
| 19 |
where θ(z) is the angle between the dipole moment of a water molecule and the normal to the solid surface at the position z. The bracket • θ denotes the ensemble average over all angles θ. The parameter S is equal to 1 when the molecules are perfectly aligned normally to the surface, S = -0.5 when the molecules are perfectly aligned horizontally to the surface, and S = 0 when the molecules are randomly aligned. For a translationally invariant, isotropic bulk system one thus expects S = 0. Calculations of S(z) for both NaCl and Na 2 SO 4 pores indicate that the water molecules within the first molecular layer are dominantly aligned with their dipole being parallel to the solid surface in the case of NaCl, and with their dipole pointing normal to the surface in the case of Na 2 SO 4 (Fig. ). The 'amount' of oriented water follows from the product of the density (ρ) and the orientation (S) shown in Fig. , which highlights even more pronounced differences between the two surfaces: water molecules of the first density layer are strongly polarized only in the case of Na 2 SO 4 .
|
63aedbf204902ad473148fa4
| 20 |
A two-dimensional mapping of salt density and water orientation within the first density layer reveals that water molecules are particularly strongly aligned in front of the divalent SO 2- 4 ions (Fig. ). This strong alignment of water molecules induced by the SO 2- 4 ions can be rationalized due to sulfate partial charges and the corresponding strong quadrupole moment: the sulfur atom has a charge of +2 e, and the four oxygen atoms each bear a charge of -1 e, for a total charge for the SO 2- 4 ions of -2 e. The alignment could also be interpreted in terms of hydrogen bonds that form between the water molecules and the oxygen atoms of the SO 2- 4 ions. In contrast, hydrogen bonds are quasi absent between water and the NaCl surface: water molecules sometimes form hydrogen bonds with chlorine atoms, but the typical number of hydrogen bonds per water molecule between the water and the solid surface is two orders of magnitude lower in the case of NaCl, as compared to Na 2 SO 4 (Fig. ).
|
63aedbf204902ad473148fa4
| 21 |
In addition to the different water structures near NaCl and Na 2 SO 4 solid surfaces, which are not probed directly by relaxation measurements, there exist remarkable differences in terms of the water dynamical properties. We determine the average residence time of a water molecule within the first density layer (i.e., the typical duration a water molecule remains adsorbed at the solid wall), according to the mean first passage time
|
63aedbf204902ad473148fa4
| 22 |
where F (t)dt is the probability that a molecule leaves the first density layer for the first time between t and t + dt. We find the residence time to be larger in the case of Na 2 SO 4 than in the case of NaCl, respectively τ A ≈ 85 ps vs. τ A ≈ 52 ps (Fig. ). These longer surface residence times reveal a higher affinity between water and Na 2 SO 4 surface as compared to water and NaCl. The typical rotation time of a water molecule within the first density layer, which was calculated as
|
63aedbf204902ad473148fa4
| 23 |
is also much larger in the case of Na 2 SO 4 as compared to NaCl: τ R ≈ 15 ps instead of τ R ≈ 6 ps, respectively (for bulk water, τ R = 2.7 ps) (Fig. ). Such as slower molecular dynamics is consistent with the lower values of T 1 measured (Fig. ).
|
63aedbf204902ad473148fa4
| 24 |
Results obtained for decreasing pore size systematically reveal lower values of T 1 in the case of Na 2 SO 4 solid surfaces, as compared with NaCl (insert in Fig. ). Moreover, for both NaCl and Na 2 SO 4 slit pores, 1/T 1 decreases for decreasing pore size h, as is expected from the increase in surface-to-volume ratio (Eq. ( )). For both salts, the scaling of 1/T 1 with the pore size h is in between 1/h (surface-limited regime) and 1/h 2 (diffusion-limited regime) . For the smallest pore size considered here (h ≈ 0.3-0.4 nm), for which the water film has a thickness similar to a single molecular layer, T 1 is about one order of magnitude larger than in bulk in the case of NaCl, and about 2 orders of magnitudes larger than in bulk in the case of Na 2 SO 4 . For such narrow pores, the value of T 1 is likely affected by the exotic effects displayed by fluids confined within sub-nanometer pores that can be linked to the breakdown of the continuum Navier-Stokes formulation . Similar trends have been reported from previous MD studies. of Lennard-Jones liquids confined in slit pores , and Mutisya et al. showed a decrease in the spin-spin relaxation time T 2 as the pore size decreases for water confined in calcite pores .
|
63aedbf204902ad473148fa4
| 25 |
All MD results discussed so far have been obtained in the limit of zero added salt concentration, c s = 0. However, the salt concentration within porous salt crusts is expected significantly different from 0. Indeed, prior to evaporation, the experimental concentrations of the NaCl and Na 2 SO 4 solutions were chosen as 4 M and 1 M, respectively (see Methods section), and during evaporation, the concentration is expected to reach saturation within the pores (at least locally). The salt concentration within nanopores can even reach supersaturation, as has been observed for NaCl solutions confined in silica nanopores . To evaluate the effect of finite salt concentration c s on T 1 in the case of confined liquids, simulations were performed for slit pore systems with size h ≈ 7 nm and c s up to 5 mol/kg in the case of NaCl, and up to 1.5 mol/kg in the case of Na 2 SO 4 (Fig. ).
|
63aedbf204902ad473148fa4
| 26 |
Our results show that, for both NaCl and Na 2 SO 4 solutions, T 1 decreases upon increasing the salt concentration c s (Fig. ). In slits, T 1 decreases faster with c s than in bulk (compare full and open symbols in Fig. ), which suggests the presence of additional interfacial effects that are induced by the presence of the salt in the confined solutions. For a given salt concentration, T 1 is always lower for Na 2 SO 4 than for NaCl in the slit pores. For the highest salt concentrations considered here (6 mol/kg for NaCl, and 1.5 mol/kg for Na 2 SO 4 ), the values of T 1 are of similar magnitude for the two salts: T 1 ≈ 0.6 s for Na 2 SO 4 , and T 1 ≈ 0.4 s for NaCl, respectively, which is about a factor 5 smaller than pure water confined within a slit pore of same size.
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.