4 research outputs found
Intersection local times of fractional Brownian motions with as generalized white noise functionals
In , for any dimension , expansions of self-intersection local
times of fractional Brownian motions with arbitrary Hurst coefficients in
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<sub><i>n</i></sub>C<sub>1</sub>im] 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 gasāliquid
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,Rā²-dialkylimidazolium bisĀ[(trifluoromethyl)Āsulfonyl]Āimide
([C<sub><i>n</i></sub>C<sub><i>n</i></sub>im]Ā[NTf<sub>2</sub>]) and R-alkyl-3-methylimidazolium bisĀ[(trifluoromethyl)Āsulfonyl]Āimide
([C<sub><i>n</i></sub>C<sub>1</sub>im]Ā[NTf<sub>2</sub>]),
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 [C<sub>12</sub>C<sub>12</sub>im]Ā[NTf<sub>2</sub>] or [C<sub>16</sub>C<sub>1</sub>im]Ā[NTf<sub>2</sub>]. 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 NāH Acidic Group on the Physicochemical Properties of Imidazolium-Based Ionic Liquids
This work presents and highlights
the differentiation of the physicochemical properties of the [C<sub>1</sub>Him]Ā[NTf<sub>2</sub>], [C<sub>2</sub>Him]Ā[NTf<sub>2</sub>],
[<sup>1</sup>C<sub>1</sub><sup>2</sup>C<sub>1</sub>Him]Ā[NTf<sub>2</sub>], and [<sup>1</sup>C<sub>4</sub><sup>2</sup>C<sub>1</sub><sup>3</sup>C<sub>1</sub>im]Ā[NTf<sub>2</sub>] that is related with the strong
bulk interaction potential, which highlights the differentiation on
the physicochemical arising from the presence of the acidic group
(NāH) 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><sub>g</sub>, and the alkyl chain size
was found; however, ILs with the acidic NāH group present a
significant higher <i>T</i><sub>g</sub> than the [<sup>1</sup>C<sub><i>N</i>ā1</sub><sup>3</sup>C<sub>1</sub>im]Ā[NTf<sub>2</sub>] and [<sup>1</sup>C<sub><i>N</i></sub><sup>3</sup>C<sub><i>N</i></sub>im]Ā[NTf<sub>2</sub>] series. It was
found that the most viscous ILs, ([<sup>1</sup>C<sub>1</sub>Him]Ā[NTf<sub>2</sub>], [<sup>1</sup>C<sub>2</sub>Him]Ā[NTf<sub>2</sub>], and [<sup>1</sup>C<sub>1</sub><sup>2</sup>C<sub>1</sub>Him]Ā[NTf<sub>2</sub>]) have an acidic NāH 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 NāH acidic group in the
imidazolium ring contribute to a significant variation in the cationāanion
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
[<sup>1</sup>C<sub>1</sub>Him]Ā[NTf<sub>2</sub>], [<sup>1</sup>C<sub>2</sub>Him]Ā[NTf<sub>2</sub>], [<sup>1</sup>C<sub>1</sub><sup>2</sup>C<sub>1</sub>Him]Ā[NTf<sub>2</sub>], and [<sup>1</sup>C<sub>4</sub><sup>2</sup>C<sub>1</sub><sup>3</sup>C<sub>1</sub>im]Ā[NTf<sub>2</sub>] are an indication of the stronger bulk interaction potential, which
highlights the effect that arises from the presence of the acidic
group (NāH) as well as the methylation in position 2 of the
imidazolium ring