We examine the microscopic origin of the pronounced x-ray scattering pre-peaks observed in water-rich aqueous alkylamine mixtures. While neat amines display weak pre-peaks compared to alcohols, and aqueous alcohols generally exhibit none, aqueous amines display a striking and unexpected signal. Molecular dynamics simulations of primary amines from propylamine to octylamine show that nitrogen head groups preferentially saturate the surfaces of water-rich domains, stabilizing both water and amine regions through water-nitrogen donor hydrogen bonding. This interfacial anchoring prevents macroscopic demixing except at high water contents, where too few amines remain to cover the interfaces. The resulting disordered bilayer-like arrangement generates long-ranged domain oscillations that appear as positive like-like species and negative cross species correlations, whose partial cancellation produces the experimental pre-peak. Model comparisons further show that the effect is highly sensitive to both solute and water force fields, with the CHARMM-AA/SPC/E combination offering the most consistent description. These results establish aqueous amines as prototypical systems in which stable micro-heterogeneity and supramolecular topology directly give rise to scattering pre-peaks, providing a concrete bridge between molecular liquids and micro-emulsions.

Aqueous alkylamine mixtures reveal an unexpected form of molecular self-assembly analogous to more complex soft matter systems. Using X-ray scattering, we uncover exceptionally intense structural prepeaks, sometimes surpassing the first sharp diffraction peak, which indicate stable microheterogeneity over nanometer scales. Temperature- and concentration-dependent measurements across the single-liquid, lamellar, and two-liquid regimes demonstrate that alkylamine headgroups stabilize extended water domains through bilayer-like arrangements. This molecular architecture persists in a macroscopically homogeneous solution, a behavior in strong contrast with aqueous alcohol solutions. Molecular dynamics simulations corroborate the experimental findings, showing that amine headgroups saturate water interfaces and prevent demixing. The aqueous amines represent a new class of molecular emulsions, where bilayer-stabilized domains account for both the unusual scattering signatures and the remarkable miscibility. Beyond rationalizing the prepeak anomaly in X-ray diffraction, these results call for a general theoretical framework to understand how molecular-scale amphiphilicity can mimic soft-matter architectures.

Binary mixtures of two dimensional, site-based models of alcohols are investigated by computer simulations, with a focus on ideal mixing, local clustering and miscibility trends. Four representative systems are considered: methanol/ethanol, butanol/pentanol, methanol/pentanol, and methanol/octanol. The models retain chemical specificity, while allowing to investigate dimensional constraints and uncover non/trivial micro/structurations. Two unexpected results are observed. First, mixtures of short and long alcohols are well mixed, instead of the macroscopic phase separation found in their three-dimensional counterparts. Second, ideality and micro phase separation compete within the chain like polar head aggregates. These behaviors cannot be explained solely by enhanced fluctuations in two dimensions, and instead point to a key role of charge ordering in shaping the local structure. The resulting interplay between concentration fluctuations and micro heterogeneous aggregation is analyzed through snapshots, site/site distribution functions, structure factors and Kirkwood Buff integrals. In particular, the analysis reveals that the domain correlations in the long range part of the correlations have an intriguing non self averaging behaviour, similar to that found in the real systems, indicating that mixtures of associating molecules are not ruled by conventional fluctuations.

Understanding how molecular correlations give rise to mesoscale organization is central to the physics of complex fluids such as hydrogen-bonded mixtures. In this work, we develop a mesoscale bridge formalism that connects the site-site Ornstein-Zernike (SSOZ) framework to the field theoretical Teubner-Strey (TS) approach. This bridge highlights how local orientational correlations, typically lost in the SSOZ closure, reemerge as effective long-range components at the mesoscale. The resulting theory provides a unified description of density fluctuations spanning molecular to mesoscopic length scales. The approach is illustrated using x-ray scattering spectra from simulated and experimental hydrogen-bonded fluids, showing that the TS representation captures the essential features of the mesoscale structure. Beyond this specific application, the proposed formalism offers a general route to interpret the structural crossover between microscopic interactions and collective mesoscale organization in complex fluids, including aqueous and amphiphilic systems. Application to aqueous amine mixtures illustrates how the TS expression agrees well with the experimental x-ray scattering data.

Two dimensional site interaction models of water and alcohols are mixed in various proportions and studied by Monte Carlo simulations, with the purpose to clarify problems related to simulation of real micro-heterogeneous systems. Three alcohols are considered, methanol, pentanol and octanol. The main finding is that, while real alcohols demix with water from butanol onward, their 2D analogs are always fully miscible, while developing increasingly pronounced micro-segregation as the alcohol tail length increases. This is not a consequence of the intrinsically higher fluctuations in 2D, but rather a reorganization of these fluctuations under the charge ordering mechanism. The second finding is that water drives the micro-segregation through strong self-aggregation, but this is not enough to achieve full phase separation because of the water-alcohol contact at the outer rim of the water domains. In this work we examine how this local heterogeneity develops with increasing alcohol alkyl tails, monitored with the study of pair correlation functions, structure factors and Kirkwood-Buff integrals. The absence of clear local self-averaging of the latter provides an illustration of the tension between energy driven maintaining of local structures and entropy driven global homogeneity. In that, the 2D modelisation of real hydrogen bonding mixtures allows to better capture and reveal the physics behind the chemistry of these liquids.

An interaction site-based model of two-dimension alcohols is proposed as a follow up of the recent SSMB site-site model for 2D water in Baré et al. (2023) [13]. Computer simulation studies indicate that the model exhibits hbond-type clustering based on the same charge order feature observed in real alcohols. Hence, the equivalent of 2D mono-ols ranging from methanol to octanol are studied for their clustering properties, focusing on how the micro-structure affects the shape of the site-site pair correlation functions and structure factors, as well as the combination of the latter into the radiation scattering intensities. The major finding is the apparent contradiction between the existence of large pre-peaks in the structure factors, usually associated to the existence of clusters, and the exponential decay of the cluster distribution indicating the absence of specific clusters, contrary to the 3D case. This is resolved by realizing that the pair correlation function is an observable of the local density fluctuations, hence the pre-peak witnesses fluctuations around clustering tendencies, which are the result of charge ordering of the polar groups, and visible in the snapshots. The scattering pre-peak witnesses only fluctuations due to charge ordering, and not the clusters themselves, underlining the fact that these are labile entities. The study highlights how charge order through atomic sites is an universal feature behind the micro-structure of organized liquids, and, in the particular case of 2D liquids, a more realistic alternative to orientation based models such as the Mercedes-Benz model, for instance.

Aqueous alkylamine mixtures are studied by computer simulations in order to understand the microscopic origin of the water rich side prominent x-ray scattering pre-peaks reported in a recent study. These pre-peaks are puzzling in view of the apparently contradicting facts that neat amines show pre-peaks much weaker than neat alkanols, while water-rich aqueous alcohols do not. These observations can be intuitively rationalized by noting that the amine head group have two hydrogen atoms when the hydroxyl group have only one, but they oppose the following two facts: i) computer simulations show micro-heterogeneity for both systems; ii) amines mix with water better than alcohols, both over larger concentrations and alkyl tails lengths. The study of the atom-atom pair correlation functions and related structure factors allows to understand the microscopic molecular details. The most interesting observation is that the amine head groups accumulate preferentially at the surface of the water domains, and increasingly better with longer alkyl tail, thus allowing to stabilize both the water and alkylamine domains, hence avoiding macroscopic demixing, except at high water concentrations when amines are scarce to achieve efficient surface saturation. The amine domains appear as disordered bilayers. Hence, aqueous amines are analogous to an inverse micelle melt and as precursor micro-emulsion. This stable micro-segregation produces large domain oscillations in the long range part of the correlation functions, translating into positive pre-peaks and negative anti-peaks in the related structure factors, the latter which contribute destructively to produce the prominent scattering pre-peak observed in the x-ray experiments. The model dependence is shown to be quite important, both for water and solute models. The CHARMM-AA model associated with the SPC/E model seems to be a good compromise.

Liquids in equilibrium exhibit two types of disorder, simple and complex. Typical simple disorder liquid is liquid nitrogen, or weakly polar liquids. Complex liquids concern those who can form long lived local assemblies, and cover a large range from water to some soft matter and biological liquids. The existence of such structures leaves characteric features upon the atom-atom correlation functions, concerning both atoms which directly participate to these structures and those who do not. The question we ask here is: do these features have also characteristic dynamical aspects, which could be tracked through dynamical correlation functions? Herein, we compare the van Hove function, intermediate scattering function and the dynamical structure factor, for both types of liquids, using force field models and computer simulations. The calculations reveal the paradoxical fact that neighbouring atom correlations for simple disorder liquids relax slower than that for complex disorder liquids, while prepeak features typical of complex disorder liquids relax even slower. This is an indication of the existence of fast kinetic self-assembly processes in complex disorder liquids, while the lifetime of such assemblies itself is quite slow. This is further confirmed by the existence of a very low -k dynamical pre-peak uncovered in the case of water and ethanol.

Aqueous n-octanol (n=1,2,3,4) mixtures from the octanol rich side are studied by x-ray scattering and computer simulation, with focus on structural changes, particularly in what concerns the hydration of the hydroxyl-group aggregated chain-like structures, under the influence of various branching of the alkyl tails. Previous studies have indicated that hydroxyl-group chain-cluster formation is hindered in proportion to the branching number. Here, water mole-fractions up to x=0.2 are examined, i.e. up to the miscibility limit. It is found that water molecules within the hydroxyl-chain domains, participate to the chain formations in different manner for the 1-octanol and the branched octanols. The hydration of the octanol hydroxyl chains is confirmed by the shifting of the scattering pre-peak to low momentum transfer both from measured and simulated x-ray scattering intensities, which corresponds to an increased size of the clusters. Experimental x-ray scattering amplitudes are seen to increase with increasing water content for 1-octanol, while this trend is reversed in all branched octanols, with the amplitudes decreasing with the increase of branching number n. Conjecturing that amplitude of pre-peaks are related to the density of corresponding aggregates, these results interpreted as water breaking large OH hydroxyl chains in 1-octanol, hence increasing the density of aggregates, while enhancing hydroxyl aggregates in branched alcohols by inserting itself into the OH chains. Hence, water acts as a structure maker or breaker in inverse proportion to the hindering of OH hydroxyl chain structures arising from the topology of the alkyl tails (branched or not)

Linear amines, from propylamine to nonylamine, are studied under ambient conditions by X-ray scattering and molecular dynamics simulations of various force field models. The major finding is that the prepeak in alkylamines is about 1 order of magnitude weaker than that in alkanols, hence suggesting much weaker hydrogen bonding-induced clustering of the amine groups than for the hydroxyl groups. Computer simulation studies reveal that the OPLS-UA model reproduces the prepeak, but with larger amplitudes, while the GROMOS-UA and CHARMM-AA force fields show almost no prepeak. Simulations of all models show the existence of hydrogen-bonded clusters, equally confirmed by the prominent prepeak of the structure factor between the nitrogen atoms. The hydrogen bond strength, as modeled by the Coulomb association in classical force field models, is about the same order of magnitude for both systems. Then, one may ask what is the origin of the weaker prepeak in alkylamines? Simulation data reveal that the existence of the prepeak is controlled through the cancellation of the positive contributions from the charged group correlations by the negative contributions from the cross charged-uncharged correlations. The C2v symmetry of the amine headgroup hinders clustering, which favors cross correlations with the tail atoms. This is opposite to alkanols where the symmetry of the hydroxyl headgroup favors clustering and hinders cross correlations with the alkyl tail. This competition between charged and uncharged atomic groups appears as a general mechanism to explain the existence of scattering prepeaks, including their position and amplitude.

While radiation scattering data provides insight inside the microstructure of liquids, the Debye relation relating the scattering intensity $I(k)$ to the atom-atom structure factors $S_{ab}(k)$ shows that, ultimately, it is these individual structure correlation functions which contain the relevant information about the micro-structure. However, these quantities are not observables, except in few cases where one can invert the Debye relation in order to obtain the structure functions. In the majority of other cases, the need for model dependent computer simulations is unavoidable. The resulting calculations reveal that the scattering pre-peak is the result of cancellations between positive pre-peaks and negative anti-peaks contributions from the atom-atom structure factors. What of systems where this cancellation is such that it entirely suppresses the scattering pre-peak? One would be tempted to falsely conclude that there is no uderlying micro-heterogeneity. Hence, the structure functions appear as hidden variables, and it is important to understand the relation between their features and the micro-structure of the system. Through the computer simulation study of various mono-ols, ranging from methanol to 1-nonanol, as well as the branched octanols, we show how the features of the atom-atom pair correlation function $g_{ab}(r)$ affect that of the structure factors $S_{ab}(k)$, and reveal that the micro-structure is ultimately the result of the charge ordering between different atoms in the system.

The structural properties of aqueous 1-4 dioxane mixtures are studied by computer simulations of different water and dioxane force field models, from the perspective of illustrating the link between structural properties at the molecular level and measurable properties such as radiation scattering intensities and Kirkwood-Buff integrals (KBIs). A strategy to consistently correct the KBI obtained from simulations is proposed, which allows us to obtain the genuine KBI corresponding to a given pair of molecular species, in the entire concentration range, and without necessitating excessively large system sizes. The application of this method to the aqueous dioxane mixtures, with an all-atom CHARMM dioxane model and 2 water models, namely, SPC/E and TIP3P, allows one to understand the differences in the structure of the corresponding mixtures at the molecular level, particularly concerning the role of the water aggregates and its model dependence. This study allows us to characterize the dual role played by the concentration fluctuations and the domain segregation, particularly in what concerns the calculated X-ray spectra.

In this reply, we discuss some aspects of the comments in Phys. Chem. Chem. Phys., 2024, 26, https://doi.org/10.1039/D3CP05269A, by Grelska, about our work Phys. Chem. Chem. Phys., 2021, 23, 19537. In this latter work, we have shown for the first time that, at short times below the picosecond range, the uninterrupted hydrogen lifetime probability L(t) is composed of 3 peaks that are universal across many hydrogen bonding systems. By definition, L(t) concerns pairs (dimers) of hydrogen bonded atoms, typically oxygen atoms. The first peak concerns the lifetime of strictly dimers, the second concerns the influence of chain clusters on dimers and the third the influence of their topology. The comment by Grelska contains a confirmation of our findings through similar calculations for other hydrogen bonding liquids. However, this author claims that it is the (first) dimer peak which concerns the topology of clusters, instead of the 3rd as we reported. Our response is that the 3rd peak reflects topology in the sense of branching, hence the presence of trimer bonding in the cluster, while the first peak shows clear species dependence at long times.

In this reply, we discuss some aspects of the comments in Phys. Chem. Chem. Phys., 2024, 26, https://doi.org/10.1039/D3CP05269A, by Grelska, about our work Phys. Chem. Chem. Phys., 2021, 23, 19537. In this latter work, we have shown for the first time that, at short times below the picosecond range, the uninterrupted hydrogen lifetime probability L(t) is composed of 3 peaks that are universal across many hydrogen bonding systems. By definition, L(t) concerns pairs (dimers) of hydrogen bonded atoms, typically oxygen atoms. The first peak concerns the lifetime of strictly dimers, the second concerns the influence of chain clusters on dimers and the third the influence of their topology. The comment by Grelska contains a confirmation of our findings through similar calculations for other hydrogen bonding liquids. However, this author claims that it is the (first) dimer peak which concerns the topology of clusters, instead of the 3rd as we reported. Our response is that the 3rd peak reflects topology in the sense of branching, hence the presence of trimer bonding in the cluster, while the first peak shows clear species dependence at long times.

A site-site interaction model is proposed for water in two-dimension, as an alternative to the traditional Mercedes-Benz model. In MB model, water molecules are modelled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz logo. The MB model qualitatively predicts both the anomalous properties of pure water and the anomalous solvation thermodynamics of non-polar molecules. One of the features of this earlier model was to have a pair correlation function with first peak for the Lennard-Jones contact distinct of that corresponding to the hydrogen bonding, which is very different from real water which has a single first peak, but a dual peak for the structure factor. The site-site model proposed here reproduces this typical feature of real water, both in real and reciprocal space. It also reproduces several of the known anomalies of real water, such as the density maximum. In addition, because of the screened Coulomb interaction between the sites, the new model appear to exhibit more homogeneity that the MB models and their variants, the latter which is highlighted by a k=0 increase of their structure factors. The new model transfers the usual bond order paradigm into a charge order paradigm, enforcing atom-atom interactions over orientational interactions.

Liquids are archetypes of disordered systems, yet liquids of polar molecules are locally more ordered than nonpolar molecules, due to the Coulomb interaction based charge ordering phenomenon. Hydrogen bonded liquids, such as water or alcohols, for example, represent a special type of polar liquids, in that they form labile clustered local structures. For water, in particular, hydrogen bonding and the related local tetrahedrality, play an important role in the various attempts to understand this liquid. However, labile structures imply dynamics, and it is not clear how it affects the understanding of this type of liquids from purely static point of view. Herein, we propose to reconsider hydrogen bonding as a charge ordering process. This concept allows us to demonstrate the insufficiency of the analysis of the microscopic structure based solely on static pair correlation functions, and the need for dynamical correlation functions, both in real and reciprocal space. The subsequent analysis allows to recover several aspects of our understanding of hydrogen bonded liquids, but from the charge order perspective. For water, it confirms the jump rotation picture found recently, and it allows to rationalize the contradicting pictures that arise when following the interpretations based on hydrogen bonding. For alcohols, it allows to understand the dynamical origin of the scattering prepeak, which does not exist for water, despite the fact that both these liquids have very similar hydroxyl group chain clusters. The concept of charge ordering complemented by the analysis of dynamical correlation functions appear as a promising way to understand microheterogeneity in complex liquids and mixtures from kinetics point of view.

Some binary mixtures, such as specific alcohol-alkane mixtures or even water-tbutanol, exhibit two humps "camel back" shaped Kirkwood-Buff integrals (KBIs). This is in sharp contrast with the usual KBIs of binary mixtures having a single extremum. This extremum is interpreted as the region of maximum concentration fluctuations, usually occurs in binary mixtures presenting appreciable micro-segregation, and corresponds to where the mixture exhibits a percolation of the two species domains. In this paper, it is shown that two extrema occur in binary mixtures when one species forms "meta-particle" aggregates, the latter acts as a meta-species, and they have their own concentration fluctuations, hence their own KBI extremum. This "meta-extremum" occurs at a low concentration of the aggregate-forming species (such as alcohol in alkane) and is independent of the other usual extremum observed at mid-volume fraction occupancy. These systems are a good illustration of the concept of the duality between concentration fluctuations and micro-segregation.

Hydrogen bonded liquids are associated liquids and tend to exhibit local inhomogeneity in the form of clusters and segregated sub-nano domains. It is an open question as to whether Hbonded clusters in pure water have common features with the water segregated pockets observed in various aqueous binary mixtures, such as water-alcohol mixtures, for example. In the present study, we demonstrate through classical molecular dynamics studies of the lifetime distributions of the hydrogen bonds in different types of binary mixtures, that these lifetimes exhibit the same universal features in the case of the pure liquids, independently of the species concentrations. The same types of three distinct lifetimes are observed, all of them in the sub picosecond regime. The primary lifetime concerns that of Hbonded dimers, and strongly depends on Hbonding criteria such as the bonding distance. The two others are independent of bonding criteria and appear as universal accross many liquids and mixtures. The secondary lifetime ([Formula: see text] fs) concerns Hbonded cluster lifetimes, while the tertiary lifetime ([Formula: see text] fs) concerns the topology of these clusters, such as chains or globules, for example. This surprizing separation in three distinct lifetimes suggests the existence of associated three distinct kinetic mechanisms in the very short sub-picosecond time scales, with, in addition, an appealing connection to the concepts of local energy and entropy.

The understanding of the microstructure of associated liquids promoted by hydrogen-bonding and constrained by steric hindrance is highly relevant in chemistry, physics, biology and for many aspects of daily life. In this study we use a combination of X-ray diffraction, dielectric spectroscopy and molecular dynamics simulations to reveal temperature induced changes in the microstructure of different octanol isomers, i.e., linear 1-octanol and branched 2-, 3- and 4-octanol. In all octanols, the hydroxyl groups form the basis of chain-, cyclic- or loop-like bonded structures that are separated by outwardly directed alkyl chains. This clustering is analyzed through the scattering pre-peaks observed from X-ray scattering and simulations. The charge ordering which pilots OH aggregation can be linked to the strength of the Debye process observed in dielectric spectroscopy. Interestingly, all methods used here converge to the same interpretation: as one moves from 1-octanol to the branched octanols, the cluster structure evolves from loose large aggregates to a larger number of smaller, tighter aggregates. All alcohols exhibit a peculiar temperature dependence of both the pre-peak and Debye process, which can be understood as a change in microstructure promoted by chain association with increased chain length possibly assisted by ring-opening effects. All these results tend to support the intuitive picture of the entropic constraint provided by branching through the alkyl tails and highlight its capital entropic role in supramolecular assembly.