Water activity in polyol/water systems: new UNIFAC parameterization

International audienceWater activities of a series of polyol/water systems were measured with an AquaLab dew point water activity meter at 298K. The investigated polyols with carbon numbers from n=2-7 are all in liquid state at room temperature and miscible at any molar ratio with water. In aqueous solutions with the same molar concentration, the diols with lower molecular weight lead to lower water activities than those with higher molecular weights. For diols with four or more carbon atoms, the hydrophilicity shows considerable differences between isomers: The 1,2-isomers - consisting of a hydrophilic and a hydrophobic part - bind less strongly to water than isomers with a more balanced distribution of the hydroxyl groups. The experimental water activities were compared with the predictions of the group contribution method UNIFAC: the model predictions overestimate the water activity of water/polyol systems of substances with two or more hydroxyl groups and can not describe the decreased binding to water of isomers with hydrophobic tails. To account for the differences between isomers, a modified UNIFAC parameterization was developed, that allows to discriminate between three types of alkyl groups depending on their position in the molecule. These new group interaction parameters were calculated using water activities of alcohol/water mixtures. This leads to a distinctly improved agreement of model predictions with experimental results while largely keeping the simplicity of the functional group approach

Computation of liquid-liquid equilibria and phase stabilities: implications for RH-dependent gas/particle partitioning of organic-inorganic aerosols

Semivolatile organic and inorganic aerosol species partition between the gas and aerosol particle phases to maintain thermodynamic equilibrium. Liquid-liquid phase separation into an organic-rich and an aqueous electrolyte phase can occur in the aerosol as a result of the salting-out effect. Such liquid-liquid equilibria (LLE) affect the gas/particle partitioning of the different semivolatile compounds and might significantly alter both particle mass and composition as compared to a one-phase particle. We present a new liquid-liquid equilibrium and gas/particle partitioning model, using as a basis the group-contribution model AIOMFAC (Zuend et al., 2008). This model allows the reliable computation of the liquid-liquid coexistence curve (binodal), corresponding tie-lines, the limit of stability/metastability (spinodal), and further thermodynamic properties of multicomponent systems. Calculations for ternary and multicomponent alcohol/polyol-water-salt mixtures suggest that LLE are a prevalent feature of organic-inorganic aerosol systems. A six-component polyol-water-ammonium sulphate system is used to simulate effects of relative humidity (RH) and the presence of liquid-liquid phase separation on the gas/particle partitioning. RH, salt concentration, and hydrophilicity (water-solubility) are identified as key features in defining the region of a miscibility gap and govern the extent to which compound partitioning is affected by changes in RH. The model predicts that liquid-liquid phase separation can lead to either an increase or decrease in total particulate mass, depending on the overall composition of a system and the particle water content, which is related to the hydrophilicity of the different organic and inorganic compounds. Neglecting non-ideality and liquid-liquid phase separations by assuming an ideal mixture leads to an overestimation of the total particulate mass by up to 30% for the composition and RH range considered in the six-component system simulation. For simplified partitioning parametrizations, we suggest a modified definition of the effective saturation concentration, C_j^*, by including water and other inorganics in the absorbing phase. Such a C_j^* definition reduces the RH-dependency of the gas/particle partitioning of semivolatile organics in organic-inorganic aerosols by an order of magnitude as compared to the currently accepted definition, which considers the organic species only

Liquid-liquid phase separation and morphology of internally mixed dicarboxylic acids/ammonium sulfate/water particles

Knowledge of the physical state and morphology of internally mixed organic/inorganic aerosol particles is still largely uncertain. To obtain more detailed information on liquid-liquid phase separation (LLPS) and morphology of the particles, we investigated complex mixtures of atmospherically relevant dicarboxylic acids containing 5, 6, and 7 carbon atoms (C5, C6 and C7) having oxygen-to-carbon atomic ratios (O:C) of 0.80, 0.67, and 0.57, respectively, mixed with ammonium sulfate (AS). With micrometer-sized particles of C5/AS/H_2O, C6/AS/H_2O and C7/AS/H_2O as model systems deposited on a hydrophobically coated substrate, laboratory experiments were conducted for various organic-to-inorganic dry mass ratios (OIR) using optical microscopy and Raman spectroscopy. When exposed to cycles of relative humidity (RH), each system showed significantly different phase transitions. While the C5/AS/H_2O particles showed no LLPS with OIR = 2:1, 1:1 and 1:4 down to 20% RH, the C6/AS/H_2O and C7/AS/H_2O particles exhibit LLPS upon drying at RH 50 to 85% and ~90%, respectively, via spinodal decomposition, growth of a second phase from the particle surface or nucleation-and-growth mechanisms depending on the OIR. This suggests that LLPS commonly occurs within the range of O:C < 0.7 in tropospheric organic/inorganic aerosols. To support the comparison and interpretation of the experimentally observed phase transitions, thermodynamic equilibrium calculations were performed with the AIOMFAC model. For the C7/AS/H_2O and C6/AS/H_2O systems, the calculated phase diagrams agree well with the observations while for the C5/AS/H_2O system LLPS is predicted by the model at RH below 60% and higher AS concentration, but was not observed in the experiments. Both core-shell structures and partially engulfed structures were observed for the investigated particles, suggesting that such morphologies might also exist in tropospheric aerosols

The Weil proof and the geometry of the adèles class space

This paper explores analogies between the Weil proof of the Riemann hypothesis for function fields and the geometry of the adèles class space, which is the noncommutative space underlying Connes' spectral realization of the zeros of the Riemann zeta function. We consider the cyclic homology of the cokernel (in the abelian category of cyclic modules) of the “restriction map” defined by the inclusion of the idèles class group of a global field in the noncommutative adèles class space. Weil's explicit formula can then be formulated as a Lefschetz trace formula for the induced action of the idèles class group on this cohomology. In this formulation the Riemann hypothesis becomes equivalent to the positivity of the relevant trace pairing. This result suggests a possible dictionary between the steps in the Weil proof and corresponding notions involving the noncommutative geometry of the adèles class space, with good working notions of correspondences, degree, and codegree etc. In particular, we construct an analog for number fields of the algebraic points of the curve for function fields, realized here as classical points (low temperature KMS states) of quantum statistical mechanical systems naturally associated to the periodic orbits of the action of the idèles class group, that is, to the noncommutative spaces on which the geometric side of the trace formula is supported

Old and New Minimalism: a Hopf algebra comparison

In this paper we compare some old formulations of Minimalism, in particular Stabler's computational minimalism, and Chomsky's new formulation of Merge and Minimalism, from the point of view of their mathematical description in terms of Hopf algebras. We show that the newer formulation has a clear advantage purely in terms of the underlying mathematical structure. More precisely, in the case of Stabler's computational minimalism, External Merge can be described in terms of a partially defined operated algebra with binary operation, while Internal Merge determines a system of right-ideal coideals of the Loday-Ronco Hopf algebra and corresponding right-module coalgebra quotients. This mathematical structure shows that Internal and External Merge have significantly different roles in the old formulations of Minimalism, and they are more difficult to reconcile as facets of a single algebraic operation, as desirable linguistically. On the other hand, we show that the newer formulation of Minimalism naturally carries a Hopf algebra structure where Internal and External Merge directly arise from the same operation. We also compare, at the level of algebraic properties, the externalization model of the new Minimalism with proposals for assignments of planar embeddings based on heads of trees.Comment: 27 pages, LaTeX, 3 figure

Syntax-semantics interface: an algebraic model

We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface. We show that methods adopted in the formulation of renormalization (extraction of meaningful physical values) in theoretical physics are relevant to describe the extraction of meaning from syntactic expressions. We show how this formulation relates to computational models of semantics and we answer some recent controversies about implications for generative linguistics of the current functioning of large language models.Comment: LaTeX, 75 pages, 19 figure

Efficiency of immersion mode ice nucleation on surrogates of mineral dust

A differential scanning calorimeter (DSC) was used to explore heterogeneous ice nucleation of emulsified aqueous suspensions of two Arizona test dust (ATD) samples with particle diameters of nominally 0&amp;ndash;3 and 0&amp;ndash;7 μm, respectively. Aqueous suspensions with ATD concentrations of 0.01&amp;ndash;20 wt% have been investigated. The DSC thermograms exhibit a homogeneous and a heterogeneous freezing peak whose intensity ratios vary with the ATD concentration in the aqueous suspensions. Homogeneous freezing temperatures are in good agreement with recent measurements by other techniques. Depending on ATD concentration, heterogeneous ice nucleation occurred at temperatures as high as 256 K or down to the onset of homogeneous ice nucleation (237 K). For ATD-induced ice formation Classical Nucleation Theory (CNT) offers a suitable framework to parameterize nucleation rates as a function of temperature, experimentally determined ATD size, and emulsion droplet volume distributions. The latter two quantities serve to estimate the total heterogeneous surface area present in a droplet, whereas the suitability of an individual heterogeneous site to trigger nucleation is described by the compatibility function (or contact angle) in CNT. The intensity ratio of homogeneous to heterogeneous freezing peaks is in good agreement with the assumption that the ATD particles are randomly distributed amongst the emulsion droplets. The observed dependence of the heterogeneous freezing temperatures on ATD concentrations cannot be described by assuming a constant contact angle for all ATD particles, but requires the ice nucleation efficiency of ATD particles to be (log)normally distributed amongst the particles. Best quantitative agreement is reached when explicitly assuming that high-compatibility sites are rare and that therefore larger particles have on average more and better active sites than smaller ones. This analysis suggests that a particle has to have a diameter of at least 0.1 μm to exhibit on average one active site