Intersection local times of fractional Brownian motions with H∈(0,1)H\in(0,1) as generalized white noise functionals

In $\R^d$, for any dimension $d\geq 1$, expansions of self-intersection local times of fractional Brownian motions with arbitrary Hurst coefficients in $(0,1)$ are presented. The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals.Comment: 17 page

Influence of Nanosegregation on the Surface Tension of Fluorinated Ionic Liquids

We have investigated, both theoretically and experimentally, the balance between the presence of alkyl and perfluoroalkyl side chains on the surface organization and surface tension of fluorinated ionic liquids (FILs). A series of ionic liquids (ILs) composed of 1-alkyl-3-methylimidazolium cations ([C_<i>n</i>C₁im] with <i>n</i> = 2, 4, 6, 8, 10, or 12) combined with the perfluorobutanesulfonate anion was used. The surface tensions of the investigated liquid salts are considerably lower than those reported for non-fluorinated ionic liquids. The most surprising and striking feature is the identification, for the first time, of a minimum at <i>n</i> = 8 in the surface tension versus the length of the IL cation alkyl side chain. Supported by molecular dynamics (MD) simulations, it was found that this trend is a result of the competition between the two nonpolar domains (perfluorinated and aliphatic) pointing toward the gas–liquid interface, a phenomenon which occurs in ILs with perfluorinated anions. Furthermore, these ILs present the lowest surface entropy reported to date

Cation Alkyl Side Chain Length and Symmetry Effects on the Surface Tension of Ionic Liquids

Aiming at providing a comprehensive study of the influence of the cation symmetry and alkyl side chain length on the surface tension and surface organization of ionic liquids (ILs), this work addresses the experimental measurements of the surface tension of two extended series of ILs, namely R,R′-dialkylimidazolium bis­[(trifluoromethyl)­sulfonyl]­imide ([C_<i>n</i>C_<i>n</i>im]­[NTf₂]) and R-alkyl-3-methylimidazolium bis­[(trifluoromethyl)­sulfonyl]­imide ([C_<i>n</i>C₁im]­[NTf₂]), and their dependence with temperature (from 298 to 343 K). For both series of ILs the surface tension decreases with an increase in the cation side alkyl chain length up to aliphatic chains no longer than hexyl, here labeled as critical alkyl chain length (CACL). For ILs with aliphatic moieties longer than CACL the surface tension displays an almost constant value up to [C₁₂C₁₂im]­[NTf₂] or [C₁₆C₁im]­[NTf₂]. These constant values further converge to the surface tension of long chain <i>n</i>-alkanes, indicating that, for sufficiently long alkyl side chains, the surface ordering is strongly dominated by the aliphatic tails present in the IL. The enthalpies and entropies of surface were also derived and the critical temperatures were estimated from the experimental data. The trend of the derived thermodynamic properties highlights the effect of the structural organization of the IL at the surface with visible trend shifts occurring at a well-defined CACL in both symmetric and asymmetric series of ILs. Finally, the structure of a long-alkyl side chain IL at the vacuum-liquid interface was also explored using Molecular Dynamics simulations. In general, it was found that for the symmetric series of ILs, at the outermost polar layers, more cations point one of their aliphatic tails outward and the other inward, relative to the surface, than cations pointing both tails outward. The number of the former, while being the preferred conformation, exceeds the latter by around 75%

Effect of the Methylation and N–H Acidic Group on the Physicochemical Properties of Imidazolium-Based Ionic Liquids

This work presents and highlights the differentiation of the physicochemical properties of the [C₁Him]­[NTf₂], [C₂Him]­[NTf₂], [¹C₁²C₁Him]­[NTf₂], and [¹C₄²C₁³C₁im]­[NTf₂] that is related with the strong bulk interaction potential, which highlights the differentiation on the physicochemical arising from the presence of the acidic group (N–H) as well as the methylation in position 2, C(2), of the imidazolium ring. Densities, viscosities, refractive indices, and surface tensions in a wide range of temperatures, as well as isobaric heat capacities at 298.15 K, for this IL series are presented and discussed. It was found that the volumetric properties are barely affected by the geometric and structural isomerization, following a quite regular trend. A linear correlation between the glass transition temperature, <i>T</i>_g, and the alkyl chain size was found; however, ILs with the acidic N–H group present a significant higher <i>T</i>_g than the [¹C_<i>N</i>‑1³C₁im]­[NTf₂] and [¹C_<i>N</i>³C_<i>N</i>im]­[NTf₂] series. It was found that the most viscous ILs, ([¹C₁Him]­[NTf₂], [¹C₂Him]­[NTf₂], and [¹C₁²C₁Him]­[NTf₂]) have an acidic N–H group in the imidazolium ring in agreement with the observed increase of energy barrier of flow. The methylation in position 2, C(2), as well as the N–H acidic group in the imidazolium ring contribute to a significant variation in the cation–anion interactions and their dynamics, which is reflected in their charge distribution and polarizability leading to a significant differentiation of the refractive indices, surface tension, and heat capacities. The observed differentiation of the physicochemical properties of the [¹C₁Him]­[NTf₂], [¹C₂Him]­[NTf₂], [¹C₁²C₁Him]­[NTf₂], and [¹C₄²C₁³C₁im]­[NTf₂] are an indication of the stronger bulk interaction potential, which highlights the effect that arises from the presence of the acidic group (N–H) as well as the methylation in position 2 of the imidazolium ring