Concentration Fluctuation/Microheterogeneity Duality Illustrated with Aqueous 1,4-Dioxane Mixtures.

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.

The influence of charge ordering in the microscopic structure of monohydroxy alcohols.

While radiation scattering data provides insight inside the microstructure of liquids, the Debye relation relating the scattering intensityI(k) to the atom-atom structure factorsSab(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 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 underlying 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 functiongab(r)affect that of the structure factorsSab(k), and reveal that the micro-structure is ultimately the result of the charge ordering between different atoms in the system.

On the dual behaviour of water in octanol-rich aqueous n-octanol mixtures: an X-ray scattering and computer simulation study.

Aqueous n-octanol (n = 1, 2, 3, and 4) mixtures from the octanol rich side are studied by X-ray scattering and computer simulation, with a 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 in the chain formations in a different manner for 1-octanol and the branched octanols. The hydration of the octanol hydroxyl chains is confirmed by the shifting of the scattering pre-peak position kPP to smaller values, both from measured and simulated X-ray scattering intensities, which corresponds to an increased size of the clusters. Experimental pre-peak 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 the branching number. Conjecturing that the amplitudes of pre-peaks are related to the density of the corresponding aggregates, these results are 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. The analysis of the cluster distributions from computer simulations provide more details on the role of water. For cluster sizes smaller than dc = 2π/kPP, water is found to always play the role of a structure enforcer for all n-octanols, while for clusters of size dc water is always a destructor. For cluster sizes larger than dc, the role of water differs from 1-octanol and the branched ones: it 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).

Reply to the 'Comment on "Universal features in the lifetime distribution of clusters in hydrogen-bonding liquids"' by J. Grelska, Phys. Chem. Chem. Phys., 2024, 26, https://doi.org/10.1039/D3CP05269A.

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.

Role of Charge Ordering in the Dynamics of Cluster Formation in Associated Liquids.

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.

Lifetime distribution of clusters in binary mixtures involving hydrogen bonding liquids.

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.

Camel back shaped Kirkwood-Buff integrals.

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.

Isomeric effects in structure formation and dielectric dynamics of different octanols.

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.

Universal features in the lifetime distribution of clusters in hydrogen-bonding liquids.

Hydrogen-bonding liquids, typically water and alcohols, are known to form labile structures (network, chains, etc.); hence, the lifetime of these structures is an important microscopic parameter, which can be calculated via computer simulations. Since these cluster entities are mostly statistical in nature, one would expect that, in the short-timescale regime, their lifetime distribution would be a broad Gaussian-like function of time, with a single maximum representing their mean lifetime, and be weakly dependent on criteria such as the bonding distance and angle, much similar to non-hydrogen-bonding simple liquids, while the long-timescale regime is known to have some power law dependence. Unexpectedly, all the hydrogen-bonding liquids studied herein, namely water and alcohols, display three highly hierarchical specific lifetimes, in the sub-picosecond range 0-0.5 ps. The dominant lifetime depends very strongly on the bonding-distance criterion and is related to hydrogen-bonded pairs. This mode is absent in non-H-bonding simple liquids. The secondary and tertiary mean lifetimes are related to clusters and are nearly independent of the bonding criterion. Of these two lifetimes, only the first one can be related to that of simple liquids, which poses the question of the nature of the third lifetime. The study of alcohols reveals that this third lifetime is related to the topology of the H-bonded clusters and that its distribution may also be affected by the alkyl tail surrounding the "bath". This study shows that hydrogen-bonding liquids have a universal hierarchy of hydrogen-bonding lifetimes with a timescale regularity across very different types, and which depend on the topology of the cluster structures.

On the X-ray Scattering Pre-peak of Linear Mono-ols and the Related Microstructure from Computer Simulations.

The X-ray scattering intensities (I(k)) of linear alkanols OH(CH2)n-1CH3 obtained from experiments (methanol to 1-undecanol) and computer simulations (methanol to 1-nonanol) of different force field models are comparatively studied particularly in order to explain the origin and the properties of the scattering pre-peak in the k-vector range 0.3-1 Å-1. The experimental I(k) values show two apparent features: the pre-peak position kP decreases with increasing n, and more intriguingly, the amplitude AP goes through a maximum at 1-butanol (n = 4). The first feature is well reproduced by all force-field models, while the second shows strong model dependence. The simulations reveal various shapes of clusters of the hydroxyl head-group from n>2. kP is directly related to the size of the meta-objects corresponding to such clusters surrounded by their alkyl tails. The explanation of the AP turnover at n = 4 is more involved in terms of cancellations of atom-atom structure factor S(k) contributions related to domain ordering. The flexibility of the alkyl tails tends to reduce the cross contributions, thus revealing the crucial importance of this parameter in the models. Force fields with all-atom representation are less successful in reproducing the pre-peak features for smaller alkanols, n<6, possibly because they blur the charge ordering process since all atoms bear partial charges. The analysis clearly shows that it is not possible to obtain a model-free explanation of the features of I(k).

Structural behavior of aqueous t-butanol solutions from large-scale molecular dynamics simulations.

Large-scale molecular dynamics simulations are reported for aqueous t-butanol (TBA) solutions. The CHARMM generalized force field (CGenFF) for TBA is combined with the TIP4P/2005 model for water. Unlike many other common TBA models, the CGenFF model is miscible with water in all proportions at 300 K. The main purpose of this work is to investigate the existence and nature of a microheterogeneous structure in aqueous TBA solutions. Our simulations of large systems (128 000 and 256 000 particles) at TBA mole fractions of 0.06 and 0.1 clearly reveal the existence of long-range correlations (>10 nm) that show significant variations on long time scales (∼50 ns). We associate these long-range slowly varying correlations with the existence of supramolecular domainlike structures that consist of TBA-rich and water-rich regions. This structure is always present but continually changing in time, giving rise to long-range slowly varying pair correlation functions. We find that this behavior appears to have little influence on the single particle dynamics; the diffusion coefficients of both TBA and water molecules lie in the usual liquid state regime, and mean square displacements provide no indication of anomalous diffusion. Using our large system simulations, we are able to reliably calculate small angle x-ray scattering and small angle neutron scattering spectra, except at a very low wave vector, and the results agree well with recent experiments. However, this paper shows that simulation of the relatively simple TBA/water system remains challenging. This is particularly true if one wishes to obtain properties such as Kirkwood-Buff factors, or scattering functions at a low wave vector, which strongly depend on the long-range behavior of the pair correlations.

Microscopic origin of the scattering pre-peak in aqueous propylamine mixtures: X-ray and neutron experiments versus simulations.

The structure of aqueous propylamine mixtures is investigated through X-ray and neutron scattering experiments, and the scattered intensities compared with computer simulation data. Both sets of data show a prominent scattering pre-peak, which first appears at propylamine mole fraction x ≥ 0.1 around scattering vector k ≈ 0.2 Å-1, and evolves towards k ≈ 0.8 Å-1 for neat propylamine x = 1. The existence of a scattering pre-peak in this mixture is unexpected, specifically in view of its absence in aqueous 1-propanol or aqueous DMSO mixtures. The detailed analysis of the various atom-atom structure factors and snapshots indicates that significant micro-structures exist, which produces correlation pre-peaks in the atom-atom structure factors, positive for like species atom correlations and negative for cross species correlations. The scattering pre-peak depends on how these two contributions cancel out or not. The way the amine group bonds with water produces a pre-peak through an imbalance of the positive and negative scattering contributions, unlike 1-propanol and DMSO, where these 2 contributions compensate exactly. Hence molecular simulations demonstrate how chemical details influence the microscopic segregation in different types of molecular emulsions and can be detected or not by scattering experiments.

Modeling micro-heterogeneity in mixtures: The role of many body correlations.

A two-component interaction model is introduced herein, which allows us to describe macroscopic miscibility with various modes of tunable micro-segregation, ranging from phase separation to micro-segregation, and is in excellent agreement with structural quantities obtained from simulations and the liquid state hypernetted-chain like integral equation theory. The model is based on the conjecture that the many-body correlation bridge function term in the closure relation can be divided into one part representing the segregation effects, which are modeled herein, and the usual part representing random many body fluctuations. Furthermore, the model allows us to fully neglect these second contributions, thus increasing the agreement between the simulations and the theory. The analysis of the retained part of the many body correlations gives important clues about how to model the many body bridge functions for more realistic systems exhibiting micro-segregation, such as aqueous mixtures.

Molecular emulsions: from charge order to domain order.

Aqueous mixtures of small molecules, such as lower n-alkanols for example, are known to be micro-segregated, with domains in the nano-meter range. One consequence of this micro-segregation would be the existence of long range domain-domain oscillatory correlations in the various atom-atom pair correlation functions, and subsequent pre-peaks in the corresponding atom-atom structure factors, in the q-vector range corresponding to nano-sized domains. However, no such pre-peak have ever been observed in the large corpus of radiation scattering data published so far on aqueous mixtures of small n-alkanols. By using large scale simulations of aqueous-1propanol mixtures, it is shown herein that the origin for the absence of scattering pre-peak resides in the exact cancellation of the contributions of the various atom-atom correlation pre-peaks to the total scattered intensity. The mechanism for this cancellation is due to the differences in the long range oscillatory behaviour of the correlations (beyond 1 nm), which are exactly out-of-phase between same species and cross species. This is similar to the charge order observed in ionic melts, but differs from room temperature ionic liquids, where the segregation is between charged and neutral groups, instead of species segregation. The consequences of such cancellation in the experimental scattering data are examined, in relation to the possibility of detecting micro-segregation through such methods. In the particular case of aqueous-1propanol mixtures, it is shown the X-ray scattering leads an exact cancellation, while this cancellation in neutron scattering is seen to depend on the deuteration ratio between solvent and solute.

Lifshitz phase: the microscopic structure of aqueous and ethanol mixtures of 1,n-diols.

We study binary mixtures of ethylene glycol and 1,3-propandiol with water or ethanol using computer simulations. Despite strong hydrogen bonding tendencies between all these molecules, we find that these mixtures are surprisingly homogeneous, in contrast to the strong micro-heterogeneity found in aqueous ethanol mixtures. The aqueous diol mixtures are found to be close to ideal mixtures, with near-ideal Kirkwood-Buff integrals. Ethanol-diol mixtures show weak non-ideality. The origin of this unexpected randomness is due to the fact that the two hydrogen bonding hydroxyl groups of the 1,n-diol are bound by the neutral alkyl bond, which prevents the micro-segregation of the different types of hydroxyl groups. These findings suggest that random disorder can arise in the presence of strong interactions - in contrast to the usual picture of random disorder due to weak interactions between the components. They point to the important role of molecular topology in tuning concentration fluctuations in complex liquids. We propose and justify herein the name of Lifshitz phases to designate such types of disordered systems.

Charge ordering and scattering pre-peaks in ionic liquids and alcohols.

The structural properties of ionic liquids and alcohols are viewed under the charge ordering process as a common basis to explain the peculiarity of their radiation scattering properties, namely the presence, or absence, of a scattering pre-peak. Through the analysis of models, it is shown that the presence, or absence, of a radiation scattering pre-peak is principally related to the symmetry breaking, or not, of the global charge order, induced by the peculiarities of the molecular shapes. This symmetry breaking is achieved, in practice, by the emergence of specific types of clusters, which manifests how the global charge order has changed into a local form. Various atom-atom correlations witness the symmetry breaking induced by this re organization, and this is manifested into a pre-peak in the structure factor. This approach explains why associated liquids such as water do not show a scattering pre-peak. It also explains under which conditions core-soft models can mimic associating liquids.

The microscopic structure of cold aqueous methanol mixtures.

The evolution of the micro-segregated structure of aqueous methanol mixtures, in the temperature range 300 K-120 K, is studied with computer simulations, from the static structural point of view. The structural heterogeneity of water is reinforced at lower temperatures, as witnessed by a pre-peak in the oxygen-oxygen structure factor. Water tends to form predominantly chain-like clusters at lower temperatures and smaller concentrations. Methanol domains have essentially the same chain-like cluster structure as the pure liquid at high concentrations and becomes monomeric at smaller ones. Concentration fluctuations decrease with temperature, leading to quasi-ideal Kirkwood-Buff integrals, despite the enhanced molecular interactions, which we interpret as the signature of non-interacting segregated water and methanol clusters. This study throws a new light on the nature of the micro-heterogeneous structure of this mixture: the domain segregation is essentially based on the appearance of linear water clusters, unlike other alcohol aqueous mixtures, such as with propanol or butanol, where the water domains are more bulky.

Micro-heterogeneity versus clustering in binary mixtures of ethanol with water or alkanes.

Ethanol is a hydrogen bonding liquid. When mixed in small concentrations with water or alkanes, it forms aggregate structures reminiscent of, respectively, the direct and inverse micellar aggregates found in emulsions, albeit at much smaller sizes. At higher concentrations, micro-heterogeneous mixing with segregated domains is found. We examine how different statistical methods, namely correlation function analysis, structure factor analysis and cluster distribution analysis, can describe efficiently these morphological changes in these mixtures. In particular, we explain how the neat alcohol pre-peak of the structure factor evolves into the domain pre-peak under mixing conditions, and how this evolution differs whether the co-solvent is water or alkane. This study clearly establishes the heuristic superiority of the correlation function/structure factor analysis to study the micro-heterogeneity, since cluster distribution analysis is insensitive to domain segregation. Correlation functions detect the domains, with a clear structure factor pre-peak signature, while the cluster techniques detect the cluster hierarchy within domains. The main conclusion is that, in micro-segregated mixtures, the domain structure is a more fundamental statistical entity than the underlying cluster structures. These findings could help better understand comparatively the radiation scattering experiments, which are sensitive to domains, versus the spectroscopy-NMR experiments, which are sensitive to clusters.

On the nature of the molecular ordering of water in aqueous DMSO mixtures.

Computer simulation studies of aqueous dimethyl sulfoxyde (DMSO) mixtures show micro-heterogeneous structures, just like aqueous alcohol mixtures. However, there is a marked difference in the aggregate structure of water between the two types of systems. While water molecules form multiconnected globular clusters in alcohols, we report herein that the typical water aggregates in aqueous DMSO mixtures are linear, favouring a 2 hydrogen bond structure per water molecule, and for all DMSO mole fractions ranging from 0.1 to 0.9. This linear-aggregate structure produces a particular signature in the water site-site structure factors, in the form of a pre-peak at k ≈ 0.2-0.8 Å(-1), depending on DMSO concentration. This pre-peak is either absent in other aqueous mixtures, such as aqueous methanol mixtures, or very difficult to see through computer simulations, such as in aqueous-t-butanol mixtures. This difference in the topology of the aggregates explains why the Kirkwood-Buff integrals of aqueous-DMSO mixture look nearly ideal, in contrast with those of aqueous alcohol mixtures, suggesting a connection between the shape of the water aggregates, its fluctuations, and the concentration fluctuations. In order to further study this discrepancy between aqueous DMSO and aqueous alcohol mixture, two models of pseudo-DMSO are introduced, where the size of the sulfur atom is increased by a factor 1.6 and 1.7, respectively, hence increasing the hydrophobicity of the molecule. The study shows that these mixtures become closer to the emulsion type seen in aqueous alcohol mixtures, with more globular clustering of the water molecules, long range domain oscillations in the water-water correlations and increased water-water Kirkwood-Buff integrals. It demonstrates that the local ordering of the water molecules is influenced by the nature of the solute molecules, with very different consequences for structural properties and related thermodynamic quantities. This study illustrates the unique plasticity of water in presence of different types of solutes.

Pattern formation in binary fluid mixtures induced by short-range competing interactions.

Molecular dynamics simulations and integral equation calculations of a simple equimolar mixture of diatomic molecules and monomers interacting via attractive and repulsive short-range potentials show the existence of pattern formation (microheterogeneity), mostly due to depletion forces away from the demixing region. Effective site-site potentials extracted from the pair correlation functions using an inverse Monte Carlo approach and an integral equation inversion procedure exhibit the features characteristic of a short-range attractive and a long-range repulsive potential. When charges are incorporated into the model, this becomes a coarse grained representation of a room temperature ionic liquid, and as expected, intermediate range order becomes more pronounced and stable.