Graph Theoretical Description of Phase Transitions in Complex Multiscale Phases with Supramolecular Assemblies.

Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high-contrast phases with large structural differences. However, the identification of phases with high complexity, multiscale organization and of complex patterns during the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases, is challenging for those traditional analyses. Here, it is shown that for two model systems- thermotropic liquid crystals and a lyotropic water/surfactant mixtures-graph theoretical (GT) descriptors can successfully identify complex phases combining molecular and nanoscale levels of organization that are hard to characterize with traditional methodologies. Furthermore, the GT descriptors also reveal the pathways between the different phases. Specifically, centrality parameters and node-based fractal dimension quantify the system behavior preceding the transitions, capturing fluctuation-induced breakup of aggregates and their long-range cooperative interactions. GT parameterization can be generalized for a wide range of chemical systems and be instrumental for the growth mechanisms of complex nanostructures.

Counter-ion adsorption and electrostatic potential in sodium and choline dodecyl sulfate micelles - a molecular dynamics simulation study.

CONTEXT: Choline-based surfactants are interesting both from the practical point of view to obtaining environmental-friendly surfactants as well as from the theoretical side since the interactions between the choline and surfactants can help to understand self-assembly phenomena in deep eutectic solvents. Although no significant change was noticed in the micelle size and shape due to the exchange of the sodium counter-ion by choline in our simulations, the adsorption of the choline cation over the micelle surface is stronger than the adsorption of the sodium, which leads to a reduction of the exposed surface area of the micelle and remarkable effects over the electrostatic potential. The choline neutralizes the surface charge of the surfactant better than sodium; however, this is partially compensated by a stronger water orientation around the SDS micelle. The balance between the contributions from the surfactant, the counter-ion, and water to the electrostatic potential leads to a complex pattern with alternate regions of positive and negative potential at the micelle/water interface which can be important to the incorporation of other charged species at the micelle surface as well as for the interaction between micelles in solution. METHODS: To evaluate the effects of the counter-ion substitution, micelles of sodium dodecyl sulfate (SDS) and choline dodecyl sulfate (ChDS) were studied and compared by means of molecular dynamics simulations in aqueous solution. In both cases, the simulations started from pre-assembled micelles with 60 dodecyl sulfate ions and 240-ns simulations were performed at NPT ensemble at T = 323.15 K and P = 1 bar using the Gromacs software with the OPLS-AA force field to describe dodecyl sulfate and choline, Åqvist parameters for sodium, and SPC model for water molecules.

Confined ionic liquids films under shear: The importance of the chemical nature of the solid surface.

Ionic liquids have generated interest in applications as lubricants and as additives to conventional lubricants due to their unique physical properties. In these applications, the liquid thin film can be subjected simultaneously to extremely high shear and loads in addition to nanoconfinement effects. Here, we use molecular dynamics simulations with a coarse-grained model to study a nanometric film of an ionic liquid confined between two planar solid surfaces both at equilibrium and at several shear rates. The strength of the interaction between the solid surface and the ions was changed by simulating three different surfaces with enhanced interactions with different ions. The increase in the interaction with either the cation or the anion leads to the formation of a solid-like layer that moves alongside the substrates; however, this layer can exhibit different structures and stability. An increase in the interaction with the high symmetry anion produces a more regular structure that is more resistant to the effects of shear and viscous heating. Two definitions were proposed and used for the calculation of the viscosity: a local definition based on the microscopic characteristics of the liquid and an engineering definition based on the forces measured at the solid surfaces, with the former displaying a correlation with the layered structure induced by the surfaces. Because of the shear thinning behavior of the ionic liquids as well as the temperature rise brought on by viscous heating, both the engineering and the local viscosities decrease as the shear rate increases.

Role of density and electrostatic interactions in the viscosity and non-newtonian behavior of ionic liquids - a molecular dynamics study.

Strong ionic interactions, as well as the consequent correlations between cation and anion dynamics, give ionic liquids various physical features that set them apart from ordinary organic solvents. In particular, they result in larger viscosities and larger densities than mixtures of neutral compounds with similar molecular structures. However, both the direct effect of electrostatic interactions and the increase of liquid density contribute to the high viscosity and so far no experimental or computational work enabled a clear quantification of those effects. Also, the effects over the shear thinning behavior, which may have important consequences for application as lubricants, were not considered yet. Here, these questions were tackled by performing non-equilibrium molecular dynamics (NEMD) simulations changing both the strength of ionic interactions and liquid density at several shear rates using a coarse grained model. The relative dielectric constant was adjusted to reproduce viscosity data from all-atoms simulations on both zero shear and high shear conditions. Elimination of ionic interactions results in a reduction of density and zero shear viscosity and also delays the beginning of shear thinning to higher shear rates. Restoring density to the ionic liquid's value only partially reverses the alterations. Correlations of the non-newtonian behavior and changes in the intermolecular structure and contact lifetimes were also explored.

Relating the structure and dynamics of ionic liquids under shear by means of reverse non-equilibrium molecular dynamics simulations.

The effect of the shear rate on the viscosity and the structure of 1-ethyl-3-methylimidazolium based ionic liquids with three different anions (tetrafluoroborate, dicyanamide, and bis(trifluoromethylsulfonyl)imide) was studied by means of reverse non-equilibrium molecular dynamics (RNEMD) simulations using a polarizable force field. The three liquids display a Newtonian plateau followed by a shear thinning regime at shear rates of the order of GHz. Even though the main features of the liquid structure remains under shear, systematic changes were noticed at the GHz rates, with coordination shells becoming more diffuse as noticed by the reduction in the difference between consecutive maxima and minima in the radial distribution function. Interestingly, these structural changes with the shear rate can be precisely fitted using the Carreau equation, which is a well-known expression for the shear rate dependence of the viscosity. The fitting parameters for different distributions can be used to explain qualitatively the shear thinning behavior of these liquids. In the GHz range, the cations and, in a minor extension, some anions, tend to assume preferentially a parallel orientation with the flux, which contributes to the shear thinning behavior and may have consequences for adhesion in applications as lubricants.

Enhanced optical asymmetry in supramolecular chiroplasmonic assemblies with long-range order.

Chiral assemblies of plasmonic nanoparticles are known for strong circular dichroism but not for high optical asymmetry, which is limited by the unfavorable combination of electrical and magnetic field components compounded by strong scattering. Here, we show that these limitations can be overcome by the long-range organization of nanoparticles in a manner similar to the liquid crystals and found in helical assemblies of gold nanorods with human islet amyloid polypeptides. A strong, polarization-dependent spectral shift and the reduced scattering of energy states with antiparallel orientation of dipoles activated in assembled helices increased optical asymmetry g-factors by a factor of more than 4600. The liquid crystal-like color variations and the nanorod-accelerated fibrillation enable drug screening in complex biological media. Improvement of long-range order can also provide structural guidance for the design of materials with high optical asymmetry.

Effect of alkyl-group flexibility on the melting point of imidazolium-based ionic liquids.

The low melting point of room temperature ionic liquids is usually explained in terms of the presence of bulky, low-symmetry, and flexible ions, with the first two factors related to the lattice energy while an entropic effect is attributed to the latter. By means of molecular dynamics simulations, the melting points of 1-ethyl-3-methyl-imidazolium hexafluorophosphate and 1-decyl-3-methyl-imidazolium hexafluorophosphate were determined, and the effect of the molecular flexibility over the melting point was explicitly computed by restraining the rotation of dihedral angles in both the solid and the liquid phases. The rotational flexibility over the bond between the ring and the alkyl chain affects the relative ordering of the anions around the cations and results in substantial effects over both the enthalpy and the entropy of melting. For the other dihedral angles of the alkyl group, the contributions are predominantly entropic and an alternating behavior was found. The flexibility of some dihedral angles has negligible effects on the melting point, while others can lead to differences in the melting point as large as 20 K. This alternating behavior is rationalized by the different probabilities of conformation defects in the crystal.

Emergence of complexity in hierarchically organized chiral particles.

The structural complexity of composite biomaterials and biomineralized particles arises from the hierarchical ordering of inorganic building blocks over multiple scales. Although empirical observations of complex nanoassemblies are abundant, the physicochemical mechanisms leading to their geometrical complexity are still puzzling, especially for nonuniformly sized components. We report the self-assembly of hierarchically organized particles (HOPs) from polydisperse gold thiolate nanoplatelets with cysteine surface ligands. Graph theory methods indicate that these HOPs, which feature twisted spikes and other morphologies, display higher complexity than their biological counterparts. Their intricate organization emerges from competing chirality-dependent assembly restrictions that render assembly pathways primarily dependent on nanoparticle symmetry rather than size. These findings and HOP phase diagrams open a pathway to a large family of colloids with complex architectures and unusual chiroptical and chemical properties.

Ion pair free energy surface as a probe of ionic liquid structure.

Numerous combinations of cations and anions are possible for the production of ionic liquids with fine-tuned properties once the correlation with the molecular structure is known. In this sense, computer simulations are useful tools to explain and even predict the properties of ionic liquids. However, quantum mechanical methods are usually restricted to either small clusters or short time scales so that parameterized force fields are required to study the bulk liquids. In this work, a method is proposed to enable a comparison between the quantum mechanical system and both polarizable and nonpolarizable force fields by means of the calculation of free energy surfaces for the translational motion of the anion around the cation in gas phase. This method was tested for imidazolium-based cations with 3 different anions, [BF4]-, [N(CN)2]-, and [NTf2]-. Better agreement was found with the density functional theory calculations when polarizability is introduced in the force field. In addition, the ion pair free energy surfaces reproduced the main structural patterns observed in the first coordination shell in molecular dynamics simulations of the bulk liquid, proving to be useful probes for the liquid phase structure that can be computed with higher level methods and the comparison with forcefields can indicate further improvements in their parameterization.

Low-Temperature Phase Transitions of the Ionic Liquid 1-Ethyl-3-methylimidazolium Dicyanamide.

Several calorimetric measurements have shown that 1-ethyl-3-methylimidazolium dicyanamide, [C2C1im][N(CN)2], is a glass-forming liquid, even though it is a low-viscous liquid at room temperature. Here, we found slow crystallization during cooling of [C2C1im][N(CN)2] along Raman spectroscopy measurements. The low-frequency range of the Raman spectrum shows that the same crystalline phase is obtained at 210 K either by cooling or by reheating the glass (cold-crystallization). Another crystalline phase is formed at ca. 260 K just prior the melting at 270 K. X-ray diffraction and calorimetric measurements confirm that there are two crystalline phases of [C2C1im][N(CN)2]. The Raman spectra indicate that polymorphism is related to [C2C1im]+ with the ethyl chain on the plane of the imidazolium ring (the low-temperature crystal) or nonplanar (the high-temperature crystal). The structural reason for the glass-forming ability of [C2C1im][N(CN)2], despite the relatively simple molecular structures of the ions, was pursued by quantum chemistry calculations and molecular dynamics (MD) simulations. Density functional theory calculations were performed for ionic pairs in order to draw free-energy surfaces of the anion around the cation. The MD simulations using a polarizable model provided maps of occurrence of anions around cations. Both the quantum and classical calculations suggest that the delocalization of preferred positions of the anion around the cation, which adopts different conformations of the ethyl chain, is on the origin of the crystallization being hampered during cooling and the resulting glass-forming ability of [C2C1im][N(CN)2].

Electrostatic potential and counterion partition between flat and spherical interfaces.

While the electrostatic potential and the counterion distribution produced by interfaces with idealized geometries can be well-described by analytical models, the same does not hold true for the interaction between surfaces with different and arbitrary geometries. Besides, the geometry of a charged interface may also affect the counterion adsorption, potentially modulating the electrostatic potential and the solvent organization close to the interfaces, demanding molecular details to be taken into account. The complex electrostatics of a sodium dodecyl sulfate micelle in the presence of monolayers of the same surfactant at the water-vapor interface was assessed by a set of molecular dynamics simulations. The electrostatic potential was evaluated numerically, and its total magnitude was decomposed into contributions arising from each species comprising the system. The counterion adsorption was stronger at the flat interfaces due to the more favorable formation of sodium bridges, where the same counterion is bounded to two or more anionic heads, while water reorientation was more pronounced near the micelle. These opposing effects counteracted each other so that the overall electrostatic potential changes were similar for both interfaces. The increase in the counterion concentration between the micelle and the interface originates a double layer mediated repulsion amounting to a free energy barrier of at least 14 kJ/mol, preventing the micelle to get closer to the monolayers. It is noteworthy that the hydrophobic regions had electrostatic potential contributions as large as those arising from the hydrophilic regions, mostly due to the orderly orientation of the terminal methyl groups.

Two different pathways for assembling bis-urea in benzene and toluene.

The thermodynamic stability of assemblies formed by a bis-urea-based supramolecular polymer, 2,4-bis(2-ethylhexylureido)toluene (EHUT), was investigated in solutions using either benzene or toluene as the solvent. Starting from a higher temperature in which EHUT was soluble in both solvents, molecules spontaneously self-organized into tubular assemblies upon cooling and these assemblies were stable in a wide range of temperatures. However, the systems followed different paths below a specific temperature: while the supramolecular polymer remained stable in toluene, EHUT molecules underwent precipitation in benzene. The causes for these different behaviors were explored by molecular dynamics simulations, which provided support for stronger enthalpic stabilization of the tubular assemblies in toluene as compared to benzene. This stabilization was due mainly to the better interaction energy of trapped toluene molecules instead of benzene ones. For both cases, lowering the temperature makes the solvent penetration inside the tubes less favorable, which reduces the stability of supramolecular structures upon cooling. Graphical abstract Different EHUT solubilities.

Optical anisotropy and sign reversal in layer-by-layer assembled films from chiral nanoparticles.

Chiral anisotropy and related optical effects at the nanoscale represent some of the most dynamic areas of nanomaterials today. Translation of optical activity of chiral semiconductor and metallic nanoparticles (NPs) into optoelectronic devices requires preparation of thin films from chiral NPs on both flat and curved surfaces. In this paper we demonstrate that chiral NP films can be made via layer-by-layer assembly (LBL) using negatively charged chiral CdS NPs, stabilized by d- and l-cysteine and positively charged polyelectrolytes, as building blocks. LBL coatings from NPs combine simplicity of preparation and strong optical activity. Circular extinction measurements using circular dichroism instruments indicate that the film possess four chiroptical bands at 280, 320, 350, and 390 nm. The latter two bands at 390 and 350 nm are associated with the band gap transitions (chiral excitons), while the former two are attributed to transitions involving surface ligands. When NPs are assembled in LBL films, the rotatory activity and the sign for circular extinction associated with the electronic transition in the inorganic core of the NPs is conserved. However, this is not true for circular extinction bands at short wavelengths: the sign of the rotatory optical activity is reversed. This effect is attributed to the change of the conformation of surface ligands in the polyelectrolyte matrix, which was confirmed both by semi-empirical and density functional (DFT) quantum mechanical calculations. Circular dichroism spectra calculated using a DFT algorithm closely match the experimental spectra of CdS NPs. These findings indicate that the spectroscopic methods sensitive to chirality of the surface ligands can be used to investigate fine structural changes in the surface layer of nanocolloids. Strong rotatory optical activity of nanostructured semiconductor films opens the possibilities for new polarization-based optical devices.

Surface Electrostatic Potential and Water Orientation in the presence of Sodium Octanoate Dilute Monolayers Studied by Means of Molecular Dynamics Simulations.

A series of atomistic molecular dynamics simulations were performed in the present investigation to assess the spontaneous formation of surfactant monolayers of sodium octanoate at the water-vacuum interface. The surfactant surface coverage increased until a saturation threshold was achieved, after which any further surfactant addition led to the formation of micellar aggregates within the solution. The saturated films were not densely packed, as might be expected for short-chained surfactants, and all films regardless of the surface coverage presented surfactant molecules with the same ordering pattern, namely, with the ionic heads toward the aqueous solution and the tails lying nearly parallel to the interface. The major contributions to the electrostatic surface potential came from the charged heads and the counterion distribution, which nearly canceled out each other. The balance between the oppositely charged ions rendered the electrostatic contributions from water meaningful, amounting to ca. 10% of the contributions arising from the ionic species. And even the aliphatic tails, whose atoms bear relatively small partial atomic charges as compared to the polar molecules and molecular fragments, contributed with ca. 20% of the total electrostatic surface potential of the systems under investigation. Although the aliphatic tails were not so orderly arranged as in a compact film, the C-H bonds assumed a preferential orientation, leading to an increased contribution to the electrostatic properties of the interface. The most prominent feature arising from the partitioning of the electrostatic potential into individual contributions was the long-range ordering of the water molecules. This ordering of the water molecules produced a repulsive dipole-dipole interaction between the two interfaces, which increased with the surface coverage. Only for a water layer wider than 10 nm was true bulk behavior observed, and the repulsive dipole-dipole interaction faded away.

Thermodynamic insights into the self-assembly of capped nanoparticles using molecular dynamic simulations.

Although the molecular modeling of self-assembling processes stands as a challenging research issue, there have been a number of breakthroughs in recent years. This report describes the use of large-scale molecular dynamics simulations with coarse grained models to study the spontaneous self-assembling of capped nanoparticles in chloroform suspension. A model system comprising 125 nanoparticles in chloroform evolved spontaneously from a regular array of independent nanoparticles to a single thread-like, ramified superstructure spanning the whole simulation box. The aggregation process proceeded by means of two complementary mechanisms, the first characterized by reactive collisions between monomers and oligomers, which were permanently trapped into the growing superstructure, and the second a slow structural reorganization of the nanoparticle packing. Altogether, these aggregation processes were over after ca. 0.6 µs and the system remained structurally and energetically stable until 1 µs. The thread-like structure closely resembles the TEM images of capped ZrO2, but a better comparison with experimental results was obtained by the deposition of the suspension over a graphene solid substrate, followed by the complete solvent evaporation. The agreement between the main structural features from this simulation and those from the TEM experiment was excellent and validated the model system. In order to shed further light on the origins of the stable aggregation of the nanoparticles, the Gibbs energy of aggregation was computed, along with its enthalpy and entropy contributions, both in chloroform and in a vacuum. The thermodynamic parameters arising from the modeling are consistent with larger nanoparticles in chloroform due to the solvent-swelled organic layer and the overall effect of the solvent was the partial destabilization of the aggregated state as compared to the vacuum system. The modeling strategy has been proved effective and reliable to describe the self-assembling of capped nanoparticles, but we must acknowledge the fact that larger model systems and longer timescales will be necessary in future investigations in order to assess structural and dynamical information approaching the behavior of macroscopic systems.

Aggregation thermodynamics of sodium octanoate micelles studied by means of molecular dynamics simulations.

The present work is aimed at studying the computation of the thermodynamic potentials that describe the stability of anionic surfactant molecules in micellar aggregates. We report a set of molecular dynamics simulations of a sodium octanoate micelle in aqueous solution using the umbrella sampling method along with the Jarzynski equality in order to compute the potential of mean force for the dissociation process of one surfactant molecule from a previously assembled micellar aggregate. The Jarzynski average was computed at several different temperatures in order to estimate the Gibbs energy of association for the octanoate anion, which was split into its enthalpic and entropic contributions. We also estimated the contributions arising from the polar head and the apolar tail for each thermodynamic potential, and a detailed picture emerged from these simulations. The aggregation is driven mostly by the Gibbs energy contribution arising from the hydrophobic tail, which was large enough to cancel out the unfavorable contribution from the polar head. Although the association process may be ascribed mostly to the transfer of the apolar tail to the micellar core, it should be noted that the polar head also contributed with a favorable entropic term to the overall Gibbs energy. These findings were rationalized by comparing the energetic and structural patterns of the hydration process of a free monomer in solution to an aggregated molecule. The interaction energy distributions presented at least two discernible populations and each population was related to a different structural pattern, as characterized by the radial distribution functions. Altogether, the changes in both the energy and structure of the hydration layer are consistent with the entropy-driven association of the surfactant into the micellar aggregate.

Solvation of sodium octanoate micelles in concentrated urea solution studied by means of molecular dynamics simulations.

The effects of urea on self-assembling remains a challenging topic on surface chemistry, and computational modeling may have a role on the unraveling of the molecular mechanisms underlying these effects. Bearing that in mind, we performed a set of molecular dynamics simulations to assess the effects of urea on the self-assembling properties of sodium octanoate, an anionic surfactant, as compared to the aggregation of the same surfactant in pure water as the solvent. The concentration of free monomers increased 3-fold in the presence of urea, in agreement with the accepted view that urea should increase monomer solubility. Regarding the size distribution of micellar aggregates, the urea solution favored smaller micelles and a narrower distribution. Preferential solvation by either water or urea changed along the surfactant molecules, from urea-rich shells around apolar atoms at the end of the hydrophobic tails to nearly no urea at the polar headgroups. This solvation profile is consistent with two different hypotheses from the literature: on one hand, urea molecules interact directly with apolar atoms from the hydrophobic tails, acting as a surfactant, and on the other hand the presence of urea molecules increases the hydration of polar sites. Another important observation regards the solvent structure, which exhibits a complex composition profile around both water and urea molecules. Although the solvent structure was appreciably different in each case, the free energy calculations for the dissociation of a pair of octanoate molecules pointed to a purely enthalpic free energy loss in urea solution, a finding that does not lend support to the third hypothesis that is often claimed as accounting for the urea effects, namely, that urea disrupts water structure and that this structural change decreases the hydrophobic effect due to an entropy change. The presence of urea had no significant effect on the molecular structure of the surfactant molecules, although it caused chain dynamics to become slower. The overall picture arising from the molecular-scale data extracted from our computational models is somewhat different from the traditional views about the structural and dynamical features of self-assembled surfactant systems, pointing out the need for more studies on other self-organized systems using a realistic model system as a way to achieve a more detailed picture.