arXiv subjects

Simon Müller

Publications and source records attributed to Simon Müller.

53 records · Page 3Linked to original sources

arXiv2023

Calculation of Thermodynamic Equilibria with the Predictive Electrolyte Model COSMO-RS-ES: Improvements for Low Permittivity Systems

The predictive electrolyte model COSMO-RS-ES is refined to improve the description of systems at 25°C in which strong ion pairing is expected due to a low static permittivity of the liquid phase. Furthermore, the short-range ion energy interaction equations have been modified to better describe the misfit and energy interaction terms between ions and solvent molecules. In addition, the salt solubility database is extended with additional non-aqueous systems containing solvents that have a low (ε_s<15) dielectric constant and promote near to full ion association. Throughout this work it is demonstrated that liquid-liquid equilibrium calculations and solid-liquid equilibrium predictions for electrolyte systems can be markedly improved with the inclusion of Bjerrum treatment based phenomenological considerations while introducing only one general additional parameter. Our modified approach reinforces the capabilities of COSMO-RS ES as a powerful predictive tool for the calculation of phase equilibria in systems with scarce experimental data.

physics.chem-ph↗

arXiv2023

Impact of extended long-range electrostatics on the correlation of liquid-liquid equilibria in aqueous ionic liquid systems

Recently an improved long-range model for electrolyte solutions was developed that is applicable from infinite dilution to pure salt. This paper tests this claim for the first time applying it to the calculation of liquid-liquid equilibria for mixtures of different ionic liquids (ILs) and water. The conventional Pitzer-Debye-Hückel (PDH) equation is compared to two of its new, thermodynamically consistent extensions. Both development stages, the extended PDH term and the modified-extended PDH, account for concentration dependent mixture properties instead of using solvent properties. The latter one additionally introduces a modified parameter of closest approach which improves the overall performance of the model for high electrolyte concentrations in systems with variable or low permittivities. To account for the short-range interactions, these long-range models are coupled with the UNIversal QUAsi-Chemical (UNIQUAC) model. Three modeling strategies were tested for the short-range contribution. First, the UNIQUAC parameters were adjusted to each system individually, then the binary interaction parameters were the same for each binary interaction type for all the systems and lastly a linear function of the carbon number was used where possible. For all systems and all modeling strategies tested, the predictive performance increased from PDH to E-PDH and then to ME-PDH. Overall, an introduction of concentration dependent properties and the modification added to ME-PDH enhanced modeling performance when describing these systems, showing the general applicability of this novel long-range term.

cond-mat.soft↗

arXiv2023

On the analogy between the restricted primitive model and capacitor circuits: Semi-empirical alternatives for over- and underscreening in the calculation of mean ionic activity coefficients

The analogy between the restricted primitive model and capacitor circuits, originally described decades ago for the Mean Spherical Approximation, is explored to demonstrate its transferability in linearized electrolyte theories. On this basis, we offer an explanation of why treating the salt diameter as a free adjustable parameter blurs differences between electrolyte theories in the calculation of mean ionic activity coefficients. Furthermore, a capacitor circuit analogy with an approximation of the Dressed Ion Theory is applied to develop a modified closest approach parameter "b" for the Pitzer-Debye-Hückel term. This modification is able to account for the qualitative effects of over- and underscreening in the calculation of mean ionic activity coefficients. This is achieved by defining "b" as a semi-empirical function that allows close resemblance with the multiple decay-length extension of the Debye-Hückel theory for high dielectric constant values and that lies close to recommended literature values of "b" for low dielectric constant values. Finally, as proof of principle, this modified semi-empirical Pitzer-Debye-Hückel term is implemented in the predictive COSMO-RS-ES model, an own reimplementation of the COSMO-RS theory developed for thermodynamic property calculations of electrolyte systems. It is shown that the modified semi-empirical Pitzer-Debye-Hückel term is an effective replacement for the recently published version of COSMO-RS-ES with explicit considerations for ion pairing. This reduces the modelling complexity by implicitly considering ion pairing and improves overall qualitative performance for the prediction of salt solubilities in mixed-solvent systems and even mean ionic activity coefficients in non-aqueous media.

physics.chem-ph↗

arXiv2023

On the analogy between the restricted primitive model and capacitor circuits. Part II: A generalized Gibbs-Duhem consistent extension of the Pitzer-Debye-Hückel term with corrections for low and variable relative permittivity

We present a novel, thermodynamically consistent modification of the Pitzer-Debye-Hückel term and its extension for concentration dependent density, molar mass and relative permittivity. This extension is validated for ionic liquids by comparison with a reference model from the literature and, in contrast to similar extensions, also applied to conventional salts with small spherical ions in aqueous, mixed and non-aqueous solvents. The central novelty is the inclusion of a modified parameter of closest approach, which improves the overall qualitative performance of the Pitzer-Debye-Hückel term over the complete relative permittivity range. Gibbs-Duhem consistency is retained in the modified extension and sample calculations for aqueous [BMIM][BF4] and aqueous NaCl are provided. The novel, modified and extended term with concentration dependent properties is combined with the predictive COSMO-RS-ES model for the calculation of phase equilibria and activity coefficients in electrolytes with conventional salts. The performance of the COSMO-RS-ES model for predictions of salt solubility in fully non-aqueous media improves significantly upon introduction of concentration dependent properties within the long-range electrostatics. Modelling performance with the modified extended Pitzer-Debye-Hückel term outperforms modelling with the unmodified extension as well as with the conventional term with no extension. The correlated relative permittivity of the mixture is overestimated with respect to experimental values and kinetic depolarization effects provide a plausible explanation for this observation. Overall, our results support the consistent introduction of concentration dependent properties within the electrostatic theory in order to improve the modelling of electrolytes with particular emphasis on non-aqueous electrolytes.

cond-mat.soft↗

arXiv2023

Thermodynamic and Transport Properties Modeling of Deep Eutectic Solvents: A review on gE-models, equations of state and molecular dynamics

Deep eutectic solvents (DESs) have gained attention in recent years as attractive alternatives to traditional solvents. There is a growing number of publications dealing with the thermodynamic modeling of DESs highlighting the importance of modeling the solutions' properties. In this review, we summarize the state-of-the-art in DES modeling as well as its current challenges. We also summarize the various modeling approaches to phase equilibria and properties of DESs with gE-models, EOS and molecular dynamics (MD) simulations. The current gE-model and EOS-based approaches handle DESs as pseudo-components in order to simplify the parameterizations and calculation strategies. However, for the models to become more transferable and predictive, it would be preferable to model the individual DES constituents instead of using the pseudo-components. This implies that validation with more detailed experimental data that includes the distribution of the DES components is also required. MD simulations, in contrast to gE-models and EOS, are capable of providing information about the liquid structure and can predict dynamic properties although, the latter quantities still show some imprecisions. Therefore, insights into the liquid structure of DES systems from MD could also aid in improving present modeling strategies in addition to a better understanding. Finally, the latest developments for DES force fields are discussed as the quality of the applied force fields determine the results of MD simulations.

physics.chem-ph↗

arXiv2022

A simple recipe to create three-dimensional reciprocal space maps

Combinations of advanced X-ray sources and zero-noise detector of enormous dynamic range have significantly increased the opportunity of mapping the reciprocal space of crystal lattices. It is particularly important in the design of new devices based on epitaxial thin films. In this work, we present a simple approach to the three-dimensional geometry involved in plotting reciprocal space maps, along with an example of computer codes to allow X-ray users to write their own codes. Experimental data used to illustrate an application of the codes are from antimony telluride epitaxial film on barium difluoride substrate.

cond-mat.mtrl-sci↗

arXiv2021

Synthetic Evolution Tracks of Giant Planets

Giant planet evolution models play a crucial role in interpreting observations and constraining formation pathways. However, the simulations can be slow or prohibitively difficult. To address this issue, we calculate a large suite of giant planet evolution models using a state-of-the-art planetary evolution code. Using these data, we create the python program planetsynth that generates synthetic cooling tracks by interpolation. Given the planetary mass, bulk & atmospheric metallicity, and incident stellar irradiation, the program calculates how the planetary radius, luminosity, effective temperature, and surface gravity evolve with time. We demonstrate the capabilities of our models by inferring time-dependent mass-radius diagrams, estimating the metallicities from mass-radius measurements, and by showing how atmospheric measurements can further constrain the planetary bulk composition. We also estimate the mass and metallicity of the young giant planet 51 Eri b from its observed luminosity. Synthetic evolution tracks have many applications, and we suggest that they are valuable for both theoretical and observational investigations into the nature of giant planets.

astro-ph.EP↗

arXiv2020

Theoretical vs. observational uncertainties: composition of giant exoplanets

In order to characterize giant exoplanets and better understand their origin, knowledge of how the planet's composition depends on its mass and stellar environment is required. In this work, we simulate the thermal evolution of gaseous planets and explore how various common model assumptions such as different equations of state, opacities, and heavy-element distributions affect the inferred radius and metallicity. We examine how the theoretical uncertainties translate into uncertainties in the inferred planetary radius and bulk metallicity. While we confirm the mass-metallicity trend previously reported in the literature, this correlation disappears when removing a 20 $M_{\oplus}$ heavy-element core from all the planets. We also show that using an updated hydrogen-helium equation of state leads to more compact planets. As a result, we present six planets that should be classified as inflated warm Jupiters. We next demonstrate that including the opacity-enhancement due to metal-rich envelopes of irradiated planets changes the planetary radius significantly, which can have large effects on the inferred metallicity. Even though there are other model assumptions that have not been considered in this work, we could show that the calculated theoretical uncertainties can already be comparable or even larger than the observational ones. Therefore, theoretical uncertainties are likely to be even larger. We therefore conclude that progress in theoretical models of giant planets is essential in order to take full advantage of current and future exoplanetary data.

astro-ph.EP↗

arXiv2020

Quantifier elimination for quasi-real closed fields

We prove quantifier elimination for the theory of quasi-real closed fields with a compatible valuation. This unifies the same known results for algebraically closed valued fields and real closed valued fields.

math.LO↗

arXiv2020

The Formation of Jupiter's Diluted Core by a Giant Impact

The Juno mission has provided an accurate determination of Jupiter's gravitational field, which has been used to obtain information about the planet's composition and internal structure. Several models of Jupiter's structure that fit the probe's data suggest that the planet has a diluted core, with a total heavy-element mass ranging from ten to a few tens of Earth masses (~5-15 % of the Jovian mass), and that heavy elements (elements other than H and He) are distributed within a region extending to nearly half of Jupiter's radius. Planet-formation models indicate that most heavy elements are accreted during the early stages of a planet's formation to create a relatively compact core and that almost no solids are accreted during subsequent runaway gas accretion. Jupiter's diluted core, combined with its possible high heavy-element enrichment, thus challenges standard planet-formation theory. A possible explanation is erosion of the initially compact heavy-element core, but the efficiency of such erosion is uncertain and depends on both the immiscibility of heavy materials in metallic hydrogen and on convective mixing as the planet evolves. Another mechanism that can explain this structure is planetesimal enrichment and vaporization during the formation process, although relevant models typically cannot produce an extended diluted core. Here we show that a sufficiently energetic head-on collision (giant impact) between a large planetary embryo and the proto-Jupiter could have shattered its primordial compact core and mixed the heavy elements with the inner envelope. Models of such a scenario lead to an internal structure that is consistent with a diluted core, persisting over billions of years. We suggest that collisions were common in the young Solar system and that a similar event may have also occurred for Saturn, contributing to the structural differences between Jupiter and Saturn.

astro-ph.EP↗

arXiv2020

The Challenge of Forming a Fuzzy Core in Jupiter

Recent structure models of Jupiter that match Juno gravity data suggest that the planet harbours an extended region in its deep interior that is enriched in heavy elements, a so-called dilute/fuzzy core. This finding raises the question of what possible formation pathways would lead to such a structure. We model Jupiter's formation and long-term evolution, starting at late-stage formation before runaway gas accretion. The formation scenarios we consider include both primordial composition gradients, as well as gradients that are built as proto-Jupiter rapidly acquires its gaseous envelope. We then follow Jupiter's evolution as it cools down and contracts, with a particular focus on the energy and material transport in the interior. We find that none of the scenarios we consider lead to a fuzzy core that is compatible with interior structure models. In all the cases, most of Jupiter's envelope becomes convective and fully mixed after at most a few million years. This is true even when we consider a case where the gas accretion leads to a cold planet, and large amounts of heavy elements are accreted. It is therefore concluded that it is very challenging to explain Jupiter's dilute core from standard formation models. We suggest that future work should consider more complex formation pathways as well as the modelling of additional physical processes that could lead to Jupiter's current-state internal structure.

astro-ph.EP↗

arXiv2020

On the Tree Structure of Orderings and Valuations on Rings

Let $R$ be a not necessarily commutative ring with $1.$ In the present paper we first introduce a notion of quasi-orderings, which axiomatically subsumes all the orderings and valuations on $R$. We proceed by uniformly defining a coarsening relation $\leq$ on the set $\mathcal{Q}(R)$ of all quasi-orderings on $R.$ One of our main results states that $(\mathcal{Q}(R),\leq')$ is a rooted tree for some slight modification $\leq'$ of $\leq,$ i.e. a partially ordered set admitting a maximum such that for any element there is a unique chain to that maximum. As an application of this theorem we obtain that $(\mathcal{Q}(R),\leq')$ is a spectral set, i.e. order-isomorphic to the spectrum of some commutative ring with $1.$ We conclude this paper by studying $\mathcal{Q}(R)$ as a topological space.

math.RA↗

arXiv2018

Compatibility of quasi-orderings and valuations; A Baer-Krull Theorem for quasi-ordered Rings

In his work of 1969, Merle E. Manis introduced valuations on commutative rings. Recently, the class of totally quasi-ordered rings was developped by the second author. In the present paper, we establish the notion of compatibility between valuations and quasi-orders on rings, leading to a definition of the rank of a quasi-ordered ring. Moreover, we prove a Baer-Krull Theorem for quasi-ordered rings: fixing a Manis valuation v on R, we characterize all v-compatible quasi-orders of R by lifting the quasi-orders from the residue class ring to R itself.

math.AC↗

arXiv2018

Topological and Network Analysis of Lithium Ion Battery Components: The Importance of Pore Space Connectivity for Cell Operation

The structure of lithium ion battery components, such as electrodes and separators, are commonly characterised in terms of their porosity and tortuosity. The ratio of these values gives the effective transport of lithium ions in the electrolyte-filled pore spaces, which can be used to determine the ionic resistivity and corresponding voltage losses. Here, we show that these microstructural characteristics are not sufficient. Analysis of tomographic data of commercial separators reveals that different polyolefin separators have similar porosity and through-plane tortuosity, which, in the homogenised picture of lithium ion cell operation, would imply that these different separators exhibit similar performance. However, numerical diffusion simulations indicate that this is not the case. We demonstrate that the extent to which lithium ion concentration gradients are induced or smoothed by the separator structure is linked to pore space connectivity, a parameter that can be determined by topological or network based analysis of separators. These findings enable us to propose how to design separator microstructures that are safer and accommodate fast charge and discharge.

physics.app-ph↗

arXiv2018

On the diversity in mass and orbital radius of giant planets formed via disk instability

We present a semi-analytical population synthesis model of protoplanetary clumps formed by disk instability at radial distances of 80 - 120 AU. Various clump density profiles, initial mass functions, protoplanetary disk models, stellar masses, and gap opening criteria are considered. When we use more realistic gap opening criteria, we find that gaps open only rarely which strongly affects clump survival rates and their physical properties (mass, radius and radial distance). The inferred surviving population is then shifted towards less massive clumps at smaller radial distances. We also find that populations of surviving clumps are very sensitive to the model assumptions and used parameters. Depending on the chosen parameters, the protoplanets occupy a mass range between 0.01 and 16 $M_{\text{J}}$ and may either orbit close to the central star or as far out as 75 AU, with a sweet spot at 10-30 AU for the massive ones. However, in all the cases we consider we find that massive giant planets at very large radial distances are rare in qualitative agreement with current direct imaging surveys. We conclude that caution should be taken in deriving population synthesis models as well as when comparing the models' results with observations.

astro-ph.EP↗

arXiv2017

Quasi-ordered Rings

A quasi-order is a binary, reflexive and transitive relation. In the Journal of Pure and Applied Algebra 45 (1987), S.M. Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered field or else a valued field. Hence, quasi-ordered fields are very well suited to treat ordered and valued fields simultaneously. In this note, we will prove that the same dichotomy holds for commutative rings with 1 as well. For that purpose we first develop an appropriate notion of (totally) quasi-ordered rings. Our proof of the dichotomy then exploits Fakhruddin's result that was mentioned above.

math.AC↗

arXiv2017

Leveraging Large Amounts of Weakly Supervised Data for Multi-Language Sentiment Classification

This paper presents a novel approach for multi-lingual sentiment classification in short texts. This is a challenging task as the amount of training data in languages other than English is very limited. Previously proposed multi-lingual approaches typically require to establish a correspondence to English for which powerful classifiers are already available. In contrast, our method does not require such supervision. We leverage large amounts of weakly-supervised data in various languages to train a multi-layer convolutional network and demonstrate the importance of using pre-training of such networks. We thoroughly evaluate our approach on various multi-lingual datasets, including the recent SemEval-2016 sentiment prediction benchmark (Task 4), where we achieved state-of-the-art performance. We also compare the performance of our model trained individually for each language to a variant trained for all languages at once. We show that the latter model reaches slightly worse - but still acceptable - performance when compared to the single language model, while benefiting from better generalization properties across languages.

cs.CL↗