Weak Interactions in Dimethyl Sulfoxide (DMSO)–Tertiary Amide Solutions: The Versatility of DMSO as a Solvent

The structures of equimolar mixtures of the commonly used polar aprotic solvents dimethylformamide (DMF) and dimethylacetamide (DMAc) in dimethyl sulfoxide (DMSO) have been investigated via neutron diffraction augmented by extensive hydrogen/deuterium isotopic substitution. Detailed 3-dimensional structural models of these solutions have been derived from the neutron data via Empirical Potential Structure Refinement (EPSR). The intermolecular center-of-mass (CoM) distributions show that the first coordination shell of the amides comprises ∼13–14 neighbors, of which approximately half are DMSO. In spite of this near ideal coordination shell mixing, the changes to the amide–amide structure are found to be relatively subtle when compared to the pure liquids. Analysis of specific intermolecular atom–atom correlations allows quantitative interpretation of the competition between weak interactions in the solution. We find a hierarchy of formic and methyl C–H···O hydrogen bonds forms the dominant local motifs, with peak positions in the range of 2.5–3.0 Å. We also observe a rich variety of steric and dispersion interactions, including those involving the O=C–N amide π-backbones. This detailed insight into the structural landscape of these important liquids demonstrates the versatility of DMSO as a solvent and the remarkable sensitivity of neutron diffraction, which is critical for understanding weak intermolecular interactions at the nanoscale and thereby tailoring solvent properties to specific applications.


Introduction
[3] In this context, their relevant physicochemical properties include high dipole moments, high relative permittivities, and high boiling points, along with broad electrochemical stability windows when compared to their protic analogues. 46][7][8][9] For example, in electrochemistry their inertness and ability to solvate both metal ions and polymeric co-electrolytes under highly reducing conditions is critical for battery function and stability. 2,3,10In addition, polar aprotic liquids provide are the simplest aprotic amides, in which the proton donor (protic) N-H groups present in formamide (FA, H 2 NC(= O)H), N-methylformamide (NMF, MeHNC(= O)H), and Nmethylacetamide (NMAc, MeHNC(= O)Me) are replaced by N-Me (Figure 1).The aprotic nature and the high dipolar character of these amides make them the ideal candidate for studying weak competitive interactions in the liquid state.Both DMF and DMAc are planar acyclic amides, where partial double bond character in the N-C=O framework arises from π electron delocalisation that enforces the planarity of the molecule. 11DMF and DMAc have similar dipole moments (µ = 3.86 D and 3.72 D respectively) and relative permittivities ( r = 36.8and 37.8 at 20 °C respectively, Table 1) which lead to strong dipole-dipole interactions and relative orientational effects in the liquid structure. 12Both molecules are regarded as weak Lewis bases, with donor numbers (DN) of 26.6 kcal mol −1 and 27.8 kcal mol −1 and acceptor numbers (AN) of 16.0 kcal mol −1 and 13.6 kcal mol −1 respectively for DMF and DMAc, Table 1. 13 Furthermore, the presence of a C(=O)-H group in DMF raises the possibility of hydrogen bonding by a weakly donating formic H atom. On a practical level, this functionality also means that while DMF is one of the most heavily used solvents for chemical synthesis, it can react under highly basic conditions and with strong reducing and chlorinating agents.DMAc is usually more inert, and so has complementary applications for example in the production of pharmaceuticals and polymers. 11utron diffraction studies of liquid DMF and DMAc have shown well-defined local structures. 12For both cases, the coordination number of molecules in the first solvation shell is found to be around 13, with a clear second shell also present.In DMF, weak C(=O)-H • • • O hydrogen bonds are observed that are thought to be electrostatic in nature.In DMF the first solvation shell shows the expected preference for anti-parallel dipole orientation between molecules, while in DMAc parallel dipoles maximise dispersion forces between the π-delocalised O=C-N backbones and methyl groups. 12[16][17][18][19] Dimethylsulfoxide (DMSO, Me 2 S = O) is a pyramidal molecule with high dipole moment (µ = 3.96 D), weak Lewis base character (DN = 29.8kcal mol −1 and AN = 19.3kcal mol −1 ), and a remarkably high permittivity for an aprotic solvent ( r = 47.2 at 20 °C).Its unique properties are due to the combination of a soft lone pair on the sulfur atom and the strong polarisation of the S=O bond.DMSO, like DMF and DMAc, is miscible with water and many organic solvents, and has an unique ability to solvate a wide range of chemical species from apolar hydrocarbons to entirely dissociated salts.DMSO is therefore extremely important in processing and technology. 20Moreover, DMSO is able to penetrate human skin with a non-destructive effect on tissues and is a keystone protectant in cryobiology. 213][24] Structural studies of liquid DMSO by X-ray and neutron diffraction have reported nearest neighbour coordination numbers in the range 11.5 -13.8 and have provided evidence for short-range antiparallel alignment of dipoles, with head-to-tail ordering at longer distances.[27][28] While the bulk physicochemical properties of DMF, DMAc and DMSO are therefore similar (Table 1), the pure liquids exhibit contrasting local structures.This latter point immediately raises the question as to which interactions will dominate in mixtures of these molecules, and in particular how, and to what extent, DMSO is accommodated within the local solvation environments of DMF and DMAc (and vice versa).
Previous studies of mixtures the polar protic solvent NMF in DMSO by neutron diffraction point to the formation of a strong N-H • • • O=S hydrogen bond between the protic amine group of NMF and the oxygen of DMSO at 1.6 Å. 29 The latter distance is considerably shorter than the typical strong hydrogen bonding in the liquid state: taking the interaction between water molecules as an example, the first O-H • • • O contact is found at 1.85 Å at ambient conditions. 30,31NMF-DMSO hydrogen bonding is more similar in length to liquid HF, one of the shortest hydrogen bonds reported in a liquid. 32As a consequence, NMF and DMSO molecules form very stable dimers in the mixtures.4][35][36] NMF, though, is a protic, highly polar solvent (µ = 3.86 D), with extremely high relative permittivity ( r = 181 at 25 °C) and the ability to act as both proton donor and acceptor via its N-H and C=O groups.In clear contrast to NMF, DMF and DMAc are aprotic solvents that only form weak hydrogen bonds via the C-H and methyl groups.As such, they will pose a very different conundrum for DMSO as a co-solvent when they are compared with NMF.
In this study we have used neutron diffraction in conjunction with isotopic substitution of hydrogen (H) by deuterium (D) to study both the pure liquid amides DMF and DMAc and equimolar 50 : 50 mixtures of these with DMSO to understand the role of weak intermolecular interactions, such as weak hydrogen bonding and dispersion forces, on a molecular level and to reveal the role of DMSO as co-solvent in a aprotic environment.The use of the Empirical Potential Structure Refinement (EPSR) computations has allowed us to uncover the 3-dimensional site-site correlations in these systems. 37

Theoretical Basis
The function of interest which can be extracted from a neutron diffraction measurement is know as the total structure factor, F (Q), which can be written as: where c α and c β , b α and b β are respectively the fractional concentrations of the atomic species α and β and the (isotope dependent) coherent neutron scattering lengths, Q = 4π sin θ λ is the magnitude of the neutron scattering vector, and S αβ (Q) the Faber-Ziman partial structure factor for any two types of atoms.There is, therefore, a unique F(Q) for each isotopic composition (isotopologue) of a sample.In particular, we can exploit the difference in sign and magnitude between the coherent neutron scattering lengths of hydrogen (b H = -3.74fm) and deuterium (b D = 6.72 fm) to distinguish between specific sites in a molecule and thereby measure multiple distinct F (Q)s.[40] The partial structure factors are related to the partial radial distribution functions (RDFs), g αβ (r), via Fourier transformation: where ρ is the atomic number density and r is the distance between two species α and β.The g αβ (r)s represent the probability density of finding, by spherical averaging, an atom of species β at distance r from an atom of species α chosen as origin of the reference system.These functions therefore contain important site-specific structural information of the sample. 40In a liquid system, g αβ (r) tends to 1 at large values of r.
In order to quantify the average coordination number, N αβ (r 0 ), of sites of type β in proximity to a site of type α up to a maximum distance r 0 , one can integrate the partial radial distribution function g αβ (r) over separation distance, r : where ρ β is the number density of species β and r 0 is the maximum distance of integration.
By definition, the first coordination number gives the average number of sites of species β present in a sphere of radius r 0 centred on a site of species α.Traditionally, the upper limit of the integral in Equation 3 is the position of the first minimum of the partial g αβ (r).
Alternatively, the cumulative coordination numbers can be plotted as a function of the distance r from the central species.
Beyond a one-dimensional analysis, the Spatial Density Functions (SDFs) are a three-  2. The samples were inserted into flat-plate null coherent scattering titanium/zirconium cells, with 1 mm sample and wall thicknesses.Each composition was run for a minimum of 2 hours at 298 K. Data for the pure liquid DMF and DMAc have been reanalysed using the same methods and protocols as the mixture to allow for a more rigorous comparison. 12To allow data correction and calibration, scattering data were also collected from the empty instrument, empty sample cells, and an incoherent scattering vanadium-niobium reference slab of thickness 3 mm.Reduction of the experimental data, including absolute normalisation, background subtraction, and multiple and inelastic scattering corrections, has been conducted using standard procedures as implemented within the Gudrun package. 44

Computational Details
The EPSR method consists of a classical Monte Carlo molecular simulation which takes initial seed potentials for modelling pairwise interactions, and subsequently refines these through the incorporation of an empirical potential.This empirical potential is calculated with reference to any mismatch between the experimental and simulated data, until a satisfactory agreement between the calculated structure factors and the measured neutron scattering data is reached.In this manner, a three-dimensional structural model of the system can be obtained which is consistent with the experimental data.
The inter-molecular potential between two atomic sites α and β is modelled in EPSR via a Lennard-Jones 12-6 function plus a Coulombic term: where q α,β are the atomic partial charges, αβ and σ αβ are the well depth parameter and the range parameter respectively and are given by the Lorentz-Berthelot mixing rules in terms of their values of the individual atoms. 45All the molecules were generated in Avogadro and their geometry is optimised for 500 steps using the MMFF94 force field. 46,479][50][51] The cubic EPSR boxes of side-length 44.

Results and Discussion
The isotopically distinct experimental neutron diffraction structure factors, F (Q), are plotted for the pure liquid amides and their DMSO mixtures against the EPSR model in Figure 3.
Excellent agreement between the experimental data and model has been achieved for each data-set; the small discrepancies at low-Q in fully hydrogenated samples such as h-DMF and h-DMAc are attributed to a residual presence of inelastic and multiple scattering events. 44,52e rise in low-Q scattering for samples such as hd-DMF and hd-DMAc can then be attributed to the fact that these liquids are comprised of a mixture of fully hydrogenated and fully deuterated molecules, Table 2.This isotopic partitioning on individual molecules leads to a genuine rise in elastic scattering that is well captured by the EPSR model.These neutron diffraction data (Figure 3     Our CoM-CoM RDF data do reveal subtle structural differences in peak features and positions, for example a small shortening of the heteromolecular amide-DMSO first peak relative to that of the amide-amide (Table 4) and concomitant slightly enhanced definition of the second and third peaks in the mixtures.In both systems, the first peak of the CoM-CoM RDF, associated to the homomolecular first solvation shell of DMF (Figure 4, left) and DMAc (Figure 4, right) shifts to marginally longer distances in the presence of DMSO.
However, when interpreting these rather nuanced effects, we must bear in mind that the CoM for each molecule (Figure 1) is in a different position relative to the C=O group, and that they possess different, albeit comparable, molecular volumes (Table 1).The N CoM −CoM (r) for the pure liquids show that at the distance of the first minimum of g CoM −CoM (r) DMF and DMAc are surrounded by an average of 13.4 and 13.0 neighbours respectively.When in a 50 : 50 mixture the composite coordination shells are made up of ∼ 7 amide molecules, and ∼ 6.5 DMSO, giving total coordination numbers of 13.7 and 13.9 for DMF and DMAc respectively.Our data therefore indicate that the total coordination shells in the mixtures are remarkably similar to those in the pure amides, and that DMF and DMAc are almost equally solvated by other molecules of the same species as by DMSO.This contrasts with NMF/DMSO mixtures, where there was a strong preference for NMF-DMSO contacts due to N-H • • • O hydrogen bonding. 29e CoM-CoM RDFs and cumulative coordination numbers reflect the radially averaged packing structure of the solutions.By interrogating the EPSR model, we are also able to extract the 3-dimensional CoM-CoM spatial density functions (SDFs).These typically reveal whether there is any directional preference within the local coordination environments.
With this in mind, Figure 5 presents the CoM-CoM SDFs for the pure liquids and mixtures.These functions show that the first coordination shell is distributed broadly over the molecular spheroid, particularly over the C=O groups and the O=C-N backbone.As one might expect, lacunae occur over the methyl groups (H A , H Z and H E ).However, we see no clear preference for DMSO over DMF/DMAc, except in the region of the C=O groups.We will examine this effect in detail by analysing the atomic site specific RDFs, coordination numbers and SDFs.
To understand the inter-molecular amide-amide interactions between two specific atomic sites, we can extract the relevant partial radial distribution g αβ (r). Figure 6 reports selected g αβ (r)s for DMF (left) and DMAc (right) in both the pure liquid (solid-line) and the mixture with DMSO (dashed-line).The corresponding intermolecular partial structure factors, S αβ (Q), are presented in Supporting Information Figure S6.Table 5 provides the peak positions and coordination numbers, along with the integration limits.Note that in Table 5, we have used the same integration limit in the pure and mixed systems for the H-O correlations.
Further pairs are given in Supporting Information Figure S3 and S4.
First, we focus on the amide-amide interactions between the various protons and the O(=C) site, g H−O (r).In DMF, the H F -to-oxygen distribution shows a peak at ∼ 2.5 Å, which is consistent with a weak hydrogen bond of electrostatic nature. 53The coordination numbers for this pair of sites in the pure and mixed systems are 1.3 and 0.6 respectively, in line with the overall mole fraction of DMF and indicative of no preference for/against DMSO.In both pure DMF and DMAc, the methyl protons H A , H Z and H E show maxima in the RDF at around 2.7 Å.This again is indicative of weak hydrogen bonding.Changes to the RDFs on mixing are subtle, but in the case of DMF we observe peak shifts to ∼ 2.9 Å (H Z ) and ∼ 3.0 Å (H E ) in the presence of DMSO.
Turning now to the amide-amide O=C-N backbone correlations, in Figure 6   .06/4.17 0.9/0.3* The integration limit is set to the first minimum of the mix to allow more direct comparison between the corresponding H-bonding coordination numbers.hydrogen bond.From Figure 6 and Table 5 we see that nearest neighbour DMAc-DMAc backbone interactions have peak positions in the range 3.3 -3.8 Å, slightly shorter than their DMF-DMF counterparts.This confirms the importance of dispersion forces and the steric hindrance of the acetic methyl in pure DMAc. 12In contrast to the case of DMF, DMAc-DMAc backbone interactions are significantly displaced to longer distances in the presence of DMSO.We can investigate the origins of this effect by turning to the heteromolecular amide-DMSO interactions.
Selected amide-DMSO g αβ (r) partial RDFs are shown in Figure 7 for DMF/DMSO (left) and DMAc/DMSO (right) respectively, along with the corresponding peak positions and coordination numbers in Table 6.Further pairs are given in supporting information Figure S5.Regarding the heteromolecular hydrogen bonding, we note that for DMF, the formic proton H F to DMSO oxygen distribution shows a peak at ∼ 2.5 Å.This is an indication of a weak, electrostatic hydrogen bond, with C(=O)-H • • • O=S distance almost identical to that observed for C(=O)-H • • • O=C between two DMF molecules (Table 5).Weak hydrogen bonds are also observed between amide methyl protons (H A , H Z and H E ) and DMSO oxygen, and DMSO methyl protons and amide oxygen, at distances between ∼ 2.6 and 2.8 Å.This    We see that in the mixture, DMSO sulfonyl oxygen and sulfur mimic the closest approach of DMAc carbonyl oxygen and carbon in the pure liquid.We conclude that DMSO prefers to approach DMAc from above and below the plane of the O=C-N backbone, or axially around Me A and Me E .In doing this, DMSO molecules displaces some of the DMAc-DMAc interactions observed in the pure liquid, thereby displacing the DMAc-DMAc density in the mixture towards Me Z and Me E .This is entirely consistent with the shifts observed in the DMAc-DMAc backbone RDFs (Figure 6).As with DMF, the most likely location for DMSO methyl carbons is a band centred around the amide oxygen, but broadened and cleft due to the presence of Me A .

a
unique arena in which to study and tune the fundamental nature of weak inter-molecular interactions, including C-H • • • O and C-H • • • π hydrogen bonds and both cyclic and acyclic ππ effects.Dimethylformamide (DMF, Me 2 NC(= O)H) and dimethylacetamide (DMAc, Me 2 NC(= O)Me)

Figure 1 :
Figure 1: DMF, DMAc and DMSO molecular models.The arrow indicates the direction of the molecular dipole, while the circle through which it passes highlights the centre of mass (CoM) for each species.
map of the density of neighbouring molecules around a central molecule as a function of angular distance, r, and angular position θ.The SDFs therefore represent regions of space around a central molecule that are most likely to be occupied by a molecule of the same or another species at a given distance. 41,42Experimental Details Experimental data have been acquired at the Near and InterMediate Range Order Diffractometer (NIMROD) at the ISIS Neutron and Muon Source (Didcot, UK) across a Q range of 0.05 Å −1 − 50 Å −1 . 43DMF, DMAc and DMSO and their isotopes were purchased from Sigma Aldrich with purities ≥ 99.5% and handled under inert atmosphere.For pure DMF and DMAc, fully hydrogenated, fully deuterated and a 50:50 mixture of hydrogenated and deuterated liquids were loaded into Ti 0.68 Zr 0.32 null scattering cells to give a total of 3 isotopically distinct samples for each liquid amide.To produce 50 : 50 amide/DMSO mixtures, the anhydrous liquids were mixed to obtain 7 isotopically distinct samples for DMF/DMSO and 5 for DMAc/DMSO, as summarised in Table 80 Å and 47.58 Å contain 700 molecules for pure liquid DMF and DMAc while cubic boxes of side 49.77Å and 51.63 Å containing 1000 molecules of which 500 are DMF/DMAc and 500 are DMSO.The atomic number densities for the four systems are 0.0934 atoms/Å 3 and 0.0975 atoms/Å 3 for the DMF and DMAc pure liquid and 0.08925 atoms/Å 3 and 0.09080 atoms/Å 3 for DMF/DMSO and DMAc/DMSO mixtures.These values are obtained from a weighted average of the relevant bulk densities of the pure liquids and are verified by reference to the overall scattering levels of the experimental data.The labels assigned to atomic sites of the DMF, DMAc and DMSO molecules are shown for clarity in Figure 2.

Figure 2 :
Figure 2: DMF, DMAc and DMSO molecular models with relevant atomic sites labelled.
solid-line) show clearly that the liquid amides are fully miscible with DMSO at this concentration, as there is an absence of any residual low-Q signal that would indicate the presence of homomolecular clustering.This observation can be confirmed by examining the molecular Centre-of-Mass (CoM) radial distribution functions, g CoM −CoM (r) obtained from the EPSR model.

Figure 4 :
Figure 4: CoM-CoM inter-molecular partial radial distribution functions, g CoM −CoM (r), and cumulative coordination numbers, N CoM −CoM (r), for DMF (left) and DMAc (right).Note that the RDFs for the pure liquids and the mixtures are very similar, showing that DMSO does not disrupt the amide-amide correlations as it infiltrates the local coordination.In addition, we observe clear second and third solvation shells which, if anything, become more ordered in the presence of DMSO.

Figure 4 and
Figure 4 and Table 4 present the radial distribution functions (RDFs) for the CoM amideamide interactions, g CoM −CoM (r), and the cumulative coordination number, N CoM −CoM (r), as a function of the separation distance r.These RDFs generated by EPSR are compared with those obtained by classical Monte Carlo simulation in Supporting Information Section S5.We see immediately from these functions that the local structure of liquid DMF and DMAc, as depicted by the CoM-CoM RDFs, is almost unaltered by the presence of DMSO in the mixtures.Moreover, the plotted and tabulated cumulative coordination numbers confirm that approximately half of the ∼ 13 -14 first shell amide molecules in the pure liquids are replaced by DMSO in the mixtures.This corresponds to near ideal coordination shell mixing at the molecular level.In addition, the RDFs provide clear evidence for a second and third solvation shell.

Figure 5 :
Figure 5: CoM-CoM spatial density functions (SDFs) representing the 25% most likely configuration of: (a,b) the DMF molecule CoM around another DMF up to 7.5 Å from the DMF Centre-of-Mass (CoM) in bulk liquid amide (left) and in the mixture with DMSO (right); (d,e) the DMAc molecule CoM around another DMAc up to 7.9 Å from the DMAc CoM in bulk liquid amide (left) and in the mixture with DMSO (right); (c,f) the DMSO molecule CoM around a DMF and a DMAc up to 7.5 Å and 7.9 Å distance from the DMF and DMAc CoM respectively.

Figure 6 :
Figure 6: Amide-Amide inter-molecular partial radial distribution functions, g αβ (r), for DMF (left) and DMAc (right): pure liquids (solid-lines) compared to the structure of DMF and DMAc in the equimolar mixtures with DMSO (dashed-lines).Note the remarkable similarity between the pure and mixture functions for DMF-DMF, and the slight outward shift on mixing for the N-O, O-O and C-O distributions in the DMAc system.
we plot the N-O, O-O and C-O RDFs for both the pure and mixed DMF and DMAc systems.In the case of DMF-DMF, we observe N-O and O-O correlations with peak positions in the range 4.1 -4.6 Å, with relatively mild perturbations when comparing the RDFs for the pure and mixed systems.As a general point, however, we note that such discrepancies between specific site-site correlations are not captured by the CoM-CoM RDF shown in Figure 4.The DMF-DMF g C−O (r)s have a first peak at ∼ 3.4 Å, consistent with the observed H(-C) • • • O

Figure 7 :
Figure 7: Amide-DMSO inter-molecular partial radial distribution functions, g αβ (r), for DMF/DMSO (left) and DMAc/DMSO (right).Note that the approaches between DMF and DMAc with DMSO are very similar, the main differences lie in the shorter inter-atomic distances in case of DMF and is linked to the ability of the formic proton H F to interact via C-H • • • O hydrogen bonding.
methyl C-H • • • O interaction is extremely weak for sp 3 carbon 54 and in this case is facilitated by the high molecular dipoles of DMF, DMAc and DMSO.The partial RDFs relative to the amide O=C-N backbone and the O, S, and C sites of DMSO are presented in Fig- of DMF-DMSO, the N-O, O-O, C-O and O-C partial RDFs show only subtle differences when compared with their amide-amide counterparts.This is consistent with our observation that DMF-DMF backbone RDFs are very similar in the bulk and mixed liquids.We attribute this relative insensitivity to the presence of a formic proton, H F , and consequent C(=O)-H • • • O hydrogen bond as a dominant structural motif in DMF-DMSO mixtures.This C(=O)-H • • • O interaction is absent in DMAc, where we observe only very weak Me-H • • • O hydrogen bonds and dispersion interactions.In this case, DMAc-DMAc backbone interactions were displaced to longer distances in the mixture.We see faint indications in the DMAc-DMSO RDFs that DMSO may compensate for this effect.Specifically, we point to the lower separation shoulders in g N −O (r) and g C−O (r) occuring at around 3.4 Å.To obtain more detailed insight into the solvation shells, we need to look beyond the radially averaged representations of g αβ (r) and N αβ (r) and we therefore turn again to the 3-dimensional spatial density functions (SDFs).

Figure 8 :
Figure 8: Amide-amide and amide-DMSO spatial density functions (SDFs) representing: (a,b) the 7% most likely configuration of the DMF C (black) = O (pink) group up to 7.5 Å from the DMF CoM in bulk liquid amide (left) and in the mixture with DMSO (right); (c,d) the 7% most likely configuration of the DMAc C (black) = O (pink) group up to 7.9 Å from the DMAc CoM in bulk liquid amide (left) and in the mixture with DMSO (right).(e,f) the 5% most likely position of the DMSO S (orange) = O (pink) group up to 7.35 Å and 7.6 Å distance from the DMF and DMAc CoM respectively; (g,h) the 5% most likely position of the DMSO methyl carbons (black) up to 7.35 and 7.6 Å distance from the DMF and DMAc CoM respectively.Note that Figures (f,h) have been rotated for clarity.
Neutron diffraction augmented by isotopic substitution of hydrogen (H) for deuterium(D)   has been used to study pure DMF and DMAc, and equimolar mixtures of DMF in DMSO and DMAc in DMSO in the liquid state.The atomistic resolution provided by neutron diffraction is critical for understanding weak inter-molecular interactions on a molecular level, as these bonding motifs are elusive and often invisible to many experimental techniques.Empirical Potential Structure Refinement (EPSR) has been used to generate 3-dimensional atomistic models that are consistent with the experimental data.This approach has enabled us to uncover individual site-site interactions, and to conduct detailed comparison between the pure and mixed systems.Our scattering data show that the amides and DMSO are mixed on the nanoscale.Analysis of the EPSR Centre-of-Mass (CoM) correlations shows that in all of our systems the coordination shell contains ∼ 13 -14 molecules, and that in the mixed systems there is, on average, near ideal solvation shell sharing between amide and DMSO.Examination of site-specific correlations reveals a rich structural landscape, in which replacement of the formic proton H F in DMF by the methyl group Me A in DMAc leads to fundamentally different solvation environments for these amides in both the pure liquids and mixtures.Weak C-H • • • O hydrogen bonds are formed by formic (DMF) and methyl (DMF, DMAc) protons, with distances around 2.5 Å and 3.0 Å.In addition, we observe dispersion interactions above and below the plane of the O=C-N amide π-backbones, particularly in the DMAc systems in which dispersive forces are expected to be predominant.By comparing pure amides with the liquid mixtures, we show that DMSO has a noteworthy ability to share in hydrogen bonding to both formic and methyl groups, matching the bond distances observed in the pure amides leading to similar solvation motifs and perfect mixing.As a result, DMSO is able to penetrate the amide-amide solvation shells while causing only subtle disruption to the amide-amide interactions.The new knowledge provided by our study is particularly important to tailor electrolytes in confined geometries such as battery electrodes and supercapacitors, since molecular mixing and local interactions are likely to impact on performance.•Intermolecular Partial Structure Factors• Classical Monte Carlo Simulations

Table 1 :
Selected physicochemical properties of the liquids DMF, DMAc and DMSO.

Table 2 :
List of the isotopically distinct samples run in the neutron experiments * .

Table 3 :
Lennard-Jones parameters and charges for DMF, 48 DMAc 49 and DMSO 50,51 from top to bottom.Atomic sites correspond to the labelling of Figure 2.

Table 4 :
CoM-CoM first and second peak positions, integration limits and coordination numbers in the pure liquid amides and the 50 : 50 mixtures with DMSO.The integration limit is set to the first minimum of the mix to allow more direct comparison between the corresponding coordination numbers.

Table 5 :
Amide-amide peak positions, integration limits and coordination numbers for interactions between the main sites of interest for DMF and DMAc in the pure liquids and the 50 : 50 mixture with DMSO.

Table 6 :
Amide-DMSO peak positions, integration limits, and coordination numbers with reference to the main sites of interest on DMF and DMAc and DMSO.

Table 6 .
In the case