All-atom molecular dynamics analysis of kinetic and structural properties of ionic micellar solutions

All-atom molecular dynamics simulation results regarding aqueous sodium dodecyl sulfate (SDS) solutions have been presented. Both salt-free solutions with different SDS concentrations and those containing calcium chloride additives have been studied. The simulation has shown that surface-active SDS ions form stable premicellar aggregates. The obtained molecular dynamics trajectories have been used to describe both the kinetic and structural properties of solutions containing SDS molecular aggregates and the properties of individual aggregates. Aggregation kinetics has been investigated, and the characteristic sizes of the aggregates have been calculated by different methods. It has been found that the size of a premicellar aggregate with aggregation number n = 16 in a salt-free solution virtually does not depend on surfactant concentration. Radial distribution functions (RDFs) of hydrogen and oxygen atoms of water molecules relative to the center of mass of an aggregate have no local maxima near the aggregate surface; i.e., the surface is incompletely wetted with water. Corresponding RDFs of carbon atoms have one, two or three maxima depending on the surfactant concentration and the serial number of a carbon atom in the hydrocarbon radical of the surface- active ion. The study of the potentials of mean force for the interaction of sodium and calcium ions with an aggregate having aggregation number n = 32 shows that only calcium ions can be strongly bound to such an aggregate.     

Computer investigation of physical properties of water clusters. 1. Stability

The method of molecular dynamics is applied to investigate the stability of water clusters containing up to 90 molecules. With increasing size of aggregates, (H₂O)_n≥10 10, their thermal stability strengthens. Mechanical stability of great clusters keeps the quickly reached level, and the coefficient of dielectric stability passes through the maximum at n = 50.     

Halogen aggregation in chlorobenzene-<Emphasis Type="Italic">o</Emphasis>-dichlorobenzene solutions

The chlorobenzene (CB)–o-dichlorobenzene (o-DCB) liquid system has been studied by classical molecular dynamics simulation over the entire range of concentrations. The structure of the solutions is characterized by using radial angular distribution functions for the distances between the planes of benzene rings and the angle between them, using radial distribution functions for the distances between chlorine atoms, and by calculating the self-diffusion coefficients and local dipole moments. Halogen aggregation in the pure components and solutions is analyzed. It is found that in pure CB, chlorine aggregates consisting of four to ten molecules are most likely to form. The sizes of chlorine aggregates increase with increasing o-DCB concentration, and at a o-DCB concentration of 0.50-1.00 ppm, an extended system of chlorine–chlorine contacts is formed. In pure o-DCB, the chlorine aggregation system includes 99% of the molecules of the simulated system. The agglomeration of solute molecules in the range of dilute solutions (x < 0.1 ppm) is investigated.     

When does a diblock copolymer probe the interfacial rheological effect?

Lateral diffusion of diblock copolymer residing on the interfaces between two immiscible liquids is investigated at single molecular level. Fluorescence correlation spectroscopy was used to study the diffusion of fluorescence-labeled diblock copolymer, polystyrene-b-polyisoprene, at the interface formed between two immiscible liquids. The interfaces are formed between N,N-dimethylformamide (DMF) and a few immiscible liquids, n-alkane and polyisoprene. Interfacial diffusion coefficient of the diblock copolymer probe is found to decrease monotonously with the increase of the molecular length of the interface constituting liquids. The decrease of diffusion coefficient follows the prediction by Einstein relation using the viscosity of the constituting liquids as the variables only for interfaces between DMF and very small n-alkanes. For interfaces formed between DMF and bigger alkanes and especially between DMF and polyisoprene, the diffusion coefficient is much higher than the calculated value, indicating that the probe molecule starts to probe the much less viscous interfacial region because the interfacial width gets larger, whose thickness is comparable to the molecule size of the liquids.     

Refining of nonionic surfactant micellization theory based on the law of mass action

Two approaches to determining critical micelle concentration (CMC) are assessed, i.e., from the inflection point in the curve for the concentration dependence of the degree of micellization and as K^1/(1–n), where K is the constant of the law of mass action and n is the aggregation number. The latter approach makes the theory simpler, while the former explicitly expresses the critical degree of micellization via the aggregation number. The concentrations of monomers and micelles are analyzed as functions of the overall concentration of a surfactant in a micellar solution. These functions look much simpler in the graphical form as compared with their complex exact analytical representation. This has resulted in derivation of simple analytical approximations for these functions, with these approximations being useful for calculations. The concentration dependence of the surfactant diffusion coefficient has been considered based on these approximations. It turned out that this dependence not only provides the known method for determining the diffusion coefficient of micelles, but also gives the possibility in principle to determine the aggregation number from the slope of the dependence of the diffusion coefficient on the inverse concentration (counted from the CMC in the CMC units). This new method for determining the aggregation number has been tested using the literature data on the diffusion coefficient of penta(ethylene glycol)-1-hexyl ether in an aqueous solution.     

Investigation of aggregation behavior using computational methods and absorption spectra for trisazo direct dyes

Direct dyes are likely to self-associate in aqueous solutions. Here, we present the aggregation characteristics of three trisazo direct dyes investigated using a procedure, which combines computational and experimental approaches. The geometric features of the molecules and their aggregates were elucidated by molecular modeling and optimization. The relative energies specific for the aggregation process yielded the optimum number of molecules forming an aggregate: two for AHDS dye and three for SDH and AIDS dyes. The results were further confirmed by using spectrometric determination and mathematical analysis. Accordingly, molecular aggregation was studied in aqueous solutions as a function of dye concentration (10^?6–10^?3 mol/l) and solution pH (4–10). As the dye concentration increased, shifts in absorption spectra were observed, suggesting the formation of aggregates. The pH variation produced a change in the spectral maximum, confirming the aggregation. The mathematical processing of the absorption spectrum data confirmed the number of chemical species of each aggregate as resulted from computational calculations.     

Premicellar aggregation in water–salt solutions of sodium alkyl sulfonates and dodecyl sulfate

The features of premicellar aggregation in aqueous solutions of sodium n-octyl, n-nonyl, and n-decyl sulfonate, as well as sodium n-dodecyl sulfate, at a constant ionic strength maintained by adding NaCl are studied by potentiometry using modified ion-selective electrodes reversible with respect to the ions of these surfactants. For the studied surfactants, the critical micelle concentrations are refined, the compositions of the products of premicellar aggregation are determined, and the stability constants of aggregates are evaluated.     

Structure,Stability, and Fragmentation of Sodium bis(2-ethylhexyl)Sulfosuccinate Negatively Charged Aggregates In Vacuo by MD Simulations

Negatively charged supramolecular aggregates formed in vacuo by n bis(2-ethylhexyl)sulfosuccinate (AOT^–) anions and n + n _c sodium counterions (i.e., [AOT _n Na _n+nc ] ^nc ) have been investigated by molecular dynamics (MD) simulations for n = 1 to 20 and n _c = –1 to –5. By comparing the maximum excess charge values of negatively and positively charged AOTNa aggregates, it is found that the charge storage capability is higher for the latter systems, the difference decreasing as the aggregation number increases. Statistical analysis of physical properties like gyration radii and moment of inertia tensors of aggregates provides detailed information on their structural properties. Even for n _c = –5, all stable aggregates show a reverse micelle-like structure with an internal core, including sodium counterions and surfactant polar heads, surrounded by an external layer consisting of the surfactant alkyl chains. Interestingly, the reverse micelle-like structure is retained also in proximity of fragmentation. Moreover, the aggregate shapes may be approximated by elongated ellipsoids whose longer axis increases with n and |n _c |. The fragmentation patterns of a number of these aggregates have also been examined and have been found to markedly depend on the aggregate charge state. The simulated fragmentation patterns of a representative aggregate show good agreement with experimental data obtained using low collision voltages. Figure

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Molecular dynamics study of micellization thermodynamics in AOT/hexane system

The thermodynamics of reverse micelle formation from an ionic surfactant, sodium bis(2-ethylhexyl) sulfosuccinate (Aerosol OT, AOT), in hexane is studied by molecular dynamics simulation. A change in the Gibbs free energy upon the addition of one AOT molecule to a reverse micelle is calculated as depending on aggregation number N by the thermodynamic integration method. This dependence has a minimum at N ≈ 20 and maximum at N ≈ 35 and predetermines the monotonically decreasing character of the standard chemical potential of AOT in a micelle with the increase of the aggregation number. The simulation results predict the formation of reverse AOT micelles with an average aggregation number of ≈30, which is in good agreement with experimental data.     

Structure and dynamics of surfaces of thin films and water microdroplets

Systems containing 3456 water molecules in a periodic rectangular cell are studied by molecular dynamics simulation. The cell parameter along the z axis noticeably exceeds parameters along the x and y axes. Thin film with a thickness of about 30 Å is formed in a cell. Some molecules are transferred into the vapor phase; however, due to the periodicity along the z axis, they are poured into periodic images of the simulated layer above or below this layer. The width of the transition surface layer is about 6–7 Å in density upon passage from the liquid to vapor phases is generally related to the roughness of the surface rather than to a decrease in a local density. The self-diffusion coefficient of molecules in the surface layer is greatly larger than inside the film. Noticeable anisotropy in the diffusion motion of molecules in the surface layer is not revealed. As all of the cell parameters increase, the film is transformed into nearly spherical micro-droplet with a strongly roughed surface. The self-diffusion coefficient of surface molecules of microdroplet is also larger than for molecules inside the droplet.     

Molecular Dynamics Study on Carbon Dioxide Absorbed Potassium Glycinate Aqueous Solution

Molecular dynamics (MD) simulations have been performed to investigate the effects on structure, transport properties, and dynamical properties in the potassium glycinate aqueous solution caused by carbon dioxide (CO₂) absorption. The optimized structure and charges of constituents of the solution, such as the glycine zwitterion, have been determined by Gaussian09 using the density functional theory. The obtained pair distribution functions, g _ij (r)’s, show the significant distribution difference of bicarbonate ion, \({\text{HCO}}_{3}^{ - }\), around the glycine anion and glycine zwitterion. The shear viscosity and diffusion coefficient obtained by MD show different CO₂ concentration dependences. The frequency dependent diffusion coefficient D _i (ν) for N and C in glycine ions are mainly influenced by the cage effect of surrounding water molecules, whereas D _i (ν) for H show the characteristic vibration due to the structure difference of the glycine ions.     

Inclusion of the concentration dependence of the diffusion coefficient in the sand equation

The applications of the Sand equation in potentiometry of electrode and membrane systems for precise measurements of the transition time (τ) have been determined. An approach was suggested for choosing the diffusion coefficient of electrolyte (D) in the case when the concentration changes from its value in the agitated solution (where D = D_b) to the nearly zero value at the surface (D = D₀ corresponds to an infinitely dilute solution), D_b and D₀ being substantially different. The Nernst–Planck–Poisson nonstationary equations were numerically solved in a one-dimensional system including an ion-exchange membrane and two adjacent diffusion layers (for the electrode–solution system, the result is a particular case). An effective value D_ef was found, whose substitution in the Sand equation gave τ identical to that obtained by numerical solution. The neglect of the concentration dependence D(с) can lead to a nonadequate determination of the ion transport numbers in the membrane.     

Investigation on the self-association of an inorganic coordination compound with biological activity (Casiopeína III-ia) in aqueous solution

From studies using different experimental techniques employed to determine the presence of aggregates e.g. isothermal titration calorimetry, surface tension, electrical conductivity, UV–Vis spectrophotometry, dynamic and static light scattering, it is clearly demonstrated that the compound [Cu(4, 4′-dimethyl-2, 2′-bipyridine)(acetylacetonato)H₂O]NO₃ (Casiopeína III-ia), promising member of a family of new generation compounds for cancer treatment, is able to auto associate in aqueous media. Physicochemical properties associated with the formation of the aggregates were determined in pure water and in phosphate buffer media in order to simulate physiological conditions. From isothermal titration calorimetry and electrical conductivity measurements we calculated the dissociation constant of the aggregates, K _D . For pure water the values obtained in both techniques are 2.73 × 10^?4 and 5.93 × 10^?4 M respectively while for the buffer media we obtained 4.61 × 10^?4 and 1.57 × 10^?3 M. The enthalpy of dissociation, ?H _D , calculated from the calorimetric data shows that the presence of the phosphate ions has an energetic effect on the aggregate stability since in pure water a value of 18.79 kJ mol^?1 was obtained in comparison with the buffer media where a value 4 times bigger was found (70.48 kJ mol^?1). With the data collected from these techniques the number of monomers calculated which participate in the formation of the aggregates is around two. From our surface tension, electrical conductivity and UV–Vis spectrophotometry measurements the critical aggregate concentration, cac, was determined. For each technique specific concentration ranges were obtained but we can summarize that the cac in pure water is between 3 and 3.5 mM and for the buffer media is between 3.5 and 4 mM. Dynamic light scattering measurements provide us with the hydrodynamic diameter of the aggregates and from static light scattering measurements we determined the molecular weight of the Casiopeína III-ia aggregates to be of 1000.015 g mol^?1 which is two times the molecular weight of the Casiopeína III-ia molecule. This value is in agreement with the number of monomers which participate in the formation of the aggregates obtained from isothermal titration calorimetry and electrical conductivity data analysis.     

Prediction of transport properties of new functional materials based on lanthanum-strontium cuprates: Molecular mechanics calculations

The method of molecular dynamics is used for prediction of properties of new functional materials based on lanthanum-strontium cuprates La_{2 ? x} Sr _x CuO_{4 ? δ} as new materials of the solid state ionics. The most interesting phases are synthesized to test the obtained calculation data and their electrophysical and thermomechanical characteristics are studied. It is shown that the high values of the oxygen diffusion coefficients are obtained in the La_{2 ? x} Sr _x CuO_{4 ? δ} solid solutions with a high replacement degree of Sr → La (up to x = 1). The calculated values of lattice cell parameters, thermal expansion coefficients and oxygen diffusion coefficients agree with the experimental data. The observed anisotropy of anionic transport for all the studied compositions corresponds to the regularities of crystal structure of complex oxides. Using the molecular dynamics method allows tracing the contribution of separate types of oxygen ions (equatorial and apical) into ionic transport at the microscopic level and also confirming directly that oxygen diffusion occurs according to the usual jump mechanism, mainly in (CuO₂) layers.     

Molecular dynamics simulation of the structure and thermodynamic properties of liquid rubidium at pressures of up to 10 GPa and temperatures of up to 3500 K

The models of rubidium at temperatures of up to 3500 K, degrees of compression of up to Y = V/V₀ = 0.3, and pressures of up to 32 GPa were constructed by molecular dynamics (MD) using the interparticle potential ЕАМ. The thermodynamic properties of the MD models agree satisfactorily with experiment in the range of parameters under study at rubidium densities higher than 0.86 g/cm³. The behavior of the models in the range of the van der Waals loop was analyzed; the calculated critical temperature of rubidium T_c is ～2250 ± 25 K, density ～0.41 g/cm³, pressure ～0.019 GPa, and compressibility factor Z = pV/RT ≈ 0.137. The states with the unity factor Z = 1 were observed at pressures of up to 0.30 GPa (at ～3000 K); the temperature dependence of the density of the models with Z = 1 is nearly linear, and the Boyle temperature is T_B ≈ 10160 K. The ratio T_c/T_B = 0.221 is close to this value for cesium (0.23) and mercury (0.276). In the temperature and pressure ranges under study, the inversion of the Joule–Thomson coefficient did not take place, but should be observed at pressures of ?0.3 GPa and elevated temperatures. It was found that the diffusion coefficient D(T) dependences do not straighten in the usually used coordinates within wide temperature ranges. It was concluded that the structure of the liquid smoothly changes when the rubidium models are compressed and this reveals in the change of the degree of asymmetry of the first peak of the radial distribution function.     

Deformation Behavior of Three-Dimensional Carbon Structures Under Hydrostatic Compression

The paper presents the results of numerical simulation aimed at studying the deformation behavior of carbon structures containing carbon atoms with various coordination numbers and, consequently, various electronic configurations and properties. Namely, the method of molecular dynamics was used to study the deformation behavior of two different structures of crumpled graphene (sp²-material formed by graphene flakes bonded by Van der Waals forces) and carbon diamond-like phases (rigid sp³-structures) under hydrostatic compression. Stress-strain curves have been obtained, structural features have been shown to affect mechanical properties of three-dimensional carbon structures.     

A density functional study on the aggregation of alumina clusters

A calculation has been performed to explore the mechanism of aggregation reaction between two small molecular clusters [(Al₂O₃) _n1 and (Al₂O₃) _n2] by the density functional theory method. Five pathways of aggregation reactions between two different (Al₂O₃)₁ clusters isomers were identified. The detailed process of (Al₂O₃)₁ interaction with (Al₂O₃)₂ were also obtained. All the products of the aggregation reactions between two cage structures are cage-dimer structures. We calculated the thermodynamic properties of all the aggregate clusters. The Gibbs free energy changes of aggregation reactions in 0–1000 K were negative and increased with the temperature increase. The energy changes of enthalpy and entropy were also obtained.     

Supramolecular systems based on polyethyleneimines and octa-2-hydroxyethylated calix[4]resorcinarenes. Aggregation and catalytic activity

The aggregation of octa-2-hydroxyethylated calix[₄]resorcines (CR) with different alkyl chain length (R = Et, n-C₅H₁₁, n-C₁₁H₂₃), hydrophobically modified polyethyleneimine (HPEI) and their mixed systems was investigated by the tensiometry and dynamic light scattering in water and water-organic solvents at different temperatures. The critical aggregation concentration (CAC) and the size of aggregates were determined. It was established that the temperature affects significantly the surface and aggregation properties of the CR. The hydrolysis of 4-nitrophenyl-О-butylchloromethyl phosphonate was investigated in the presence of CR, HPEI, and their mixed systems by spectrophotometry. The parameters of the reaction (rate constant in the micellar phase, binding constant of the substrate with aggregates, and CAC) testify that the catalytic activity of the HPEI system in the presence of СR with undecyl radicals is the highest.     

The equilibrium structures of the Li[C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>]<Subscript>1</Subscript> (<Emphasis Type="Italic">n</Emphasis> = 7–12) complexes and their alternation depending on <Emphasis Type="Italic">n</Emphasis>

The equilibrium geometric configurations of the Li[C _n ]₁ (n = 7–12) complexes, where [C _n ]₁ is a cylindrical hydrocarbon containing the simplest zigzag nanotube fragment, were determined by the density functional theory method with the PBE0 exchange-correlation functional. Analytic molecular orbital (MO) estimates were obtained for isolated [C _n ]₁ hydrocarbons in the Hückel approximation. The appearance of nonbonding MOs for hydrocarbons with even n was demonstrated. Equilibrium structure types were found to alternate as n increased. This alternation correlated with the behavior of the frontier orbitals of the [C _n ]₁ hydrocarbon. At odd n, the Li atom was situated near the boundary of the π electron density of the bracelet, and the complex had C _s symmetry. Complexes with even n had the C _2v point group, and lithium was situated in the inner cylinder cavity above the center of one of benzene rings.     

Molecular dynamic studies of amyloid-beta interactions with curcumin and Cu<Superscript>2+</Superscript> ions

Amyloid-beta (Aβ) peptide readily forms aggregates that are associated with Alzheimer’s disease. Transition metals play a key role in this process. Recently, it has been shown that curcumin (CUA), a polyphenolic phytochemical, inhibits the aggregation of Aβ peptide. However, interactions of Aβ peptide with metal ions or CUA are not entirely clear. In this work, molecular dynamics (MD) simulations were carried out to clear the nature of interactions between the 42-residue Aβ peptide (Aβ-42) and Cu²⁺ ions and CUA. Altogether nine different models were investigated, and more than 2 µs of the simulation data were analyzed. The models represent the possible modes of arrangement between Aβ-42 and Cu²⁺ ions and CUA, respectively, and were used to shed light on the Aβ-42 conformational behavior in the presence of Cu²⁺ ions and CUA molecules. Obtained data clearly showed that the presence of a CUA molecule or a higher concentration of copper ions significantly affect the conformational behavior of Aβ-42. Calculations showed that the change of the His13 protonation state (Aβ(H13δ)-Cu²⁺, Aβ(H13δ)-Cu²⁺ -CUA models) leads to higher occurrence of the Asp23-Lys28 salt bridge. Analyzes of trajectories revealed that C-terminal β-sheet structures occurred significantly less frequently, and CUA promoted the stabilization of the α-helical structure. Further, calculations of the Aβ-42 complex with CUA and Cu²⁺ ions showed that CUA can chelate the Cu²⁺ ion and directly interact with Aβ, which may explain why CUA acts as an inhibitor of Aβ aggregation.