Mathematical Gnostics Research Articles

Heat capacity measurements by a Setaram μDSC3 evo microcalorimeter: estimation of deviation in the measurement, advanced data analysis by mathematical gnostics, and prediction by the artificial neural network

AbstractThe aim of the work is to study the variation in the isobaric heat capacity measurement due to changes in the amount of sample and the calibration standard using a Setaram $$\mu$$ μ DSC3 evo microcalorimeter batch cells to provide a guideline toward the selection of the sample amount to minimize heat capacity measurement error in $$\mu$$ μ DSC. Moreover, overall variation, variation due to the sample amount, and variation due to the calibration standard (reference) amount in heat capacity measurement were estimated for different amounts of the sample or/and the calibration standard material. In the present work, heat capacity measurements were taken for [C4mim][Tf2N] (1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide) ionic liquid as a sample material and 1-butanol as a calibration standard. A novel non-statistical approach, mathematical gnostics (MG), was used for data analysis of measured heat capacities data. Moreover, the artificial neural network (ANN) model was developed to predict the deviation in the heat capacity measurement with 99.83% accuracy and 0.9939 R2 score. The Python package PyCpep based on the trained ANN model was developed to predict the deviation in the heat capacity measurement.

Aqueous solutions of chiral ionic liquids based on (–)-menthol: An experimental and computational study of volumetric and transport properties

Aqueous solutions of ionic liquids remain at the focus of the physico-chemical and chemical-engineering research due to their interesting behaviour in the bulk and on the molecular level as well as thanks to their possible application potential. Indeed, the molecular structure of the aqueous solutions of ionic liquids is still poorly understood. In this work, imidazolium-based chiral ionic liquids with a (–)-menthol substituent on the cation 1-alkyl-3-[(1R,2S,5R)-(–)-menthoxymethyl]imidazolium chlorides were studied in aqueous solutions. Their volumetric properties and electrical conductivity were measured to better understand their hydration and dissociation. The bulk experimental data were interpreted in the light of MD simulations that enabled us to obtain spatial and radial distribution functions and to estimate the volumetric and transport properties of the studied systems. Experimental data of density and conductivity were analyzed by methods of mathematical gnostics which is naturally robust, is valid for small data set (no coverage factor needed), and does not require prior knowledge of the distribution of the measurement errors. It is therefore applicable in cases where tests of data normality are statistically insignificant or even fail.

Thermochemical Properties of Menthol and Terpineol

The work continues the project of physicochemical characterization of terpenic substances that are present in plants and after emission to the atmosphere play an important role in the formation of cloud condensation nuclei. Two substances, which are solid at room temperature, were studied in this work, namely both enantiomers of menthol and (–)- $$\upalpha$$ -terpineol. Temperatures and enthalpies of fusion were measured, isobaric heat capacities were measured in the temperature range 326.15–348.15 K and vapor pressures were measured in the temperature range 400–430 K. The experimental values were compared with predictions by COSMO-RS. Modern nonstatistical algorithms based on mathematical gnostics were used for data analysis.

Thermochemical Properties of Selected Terpenes

This work is a continuation of our project of physico-chemical characterization of terpenic compounds participating as a source of secondary organic aerosols. In this work, S-(–)-limonene, terpinolene, (1R)-(–)-myrtenal, and α-terpinyl acetate were studied. Their densities, sound velocities, and isobaric heat capacities were measured in the temperature range (290–343) K, vapor pressures were measured in temperature range where stable boiling was achieved. The previous work was supplemented by measurement of isobaric heat capacities of α-pinene and β-pinene. Experimental values of vapor pressures were compared with prediction by COSMO-RS. Modern nonstatistical algorithms based on mathematical gnostics were used for data analysis.

Comparison of prediction methods of heat capacity of ionic liquids with selected experimental data by means of advanced data analysis

Heat capacity of selected series of ionic liquids was predicted by means of several group contribution models of ionic liquid and compared with available experimental data. The examined series of ionic liquids were with methylimidazolium, menthoxymethyl imidazolium and ethoxyethoxyethyl imidazolium cations with different alkyl substituents, while the anions were the saccharinate or bistriflate. All data, experimental and predicted, were analyzed by means of mathematical gnostics and critically evaluated. Based on the thermodynamics of data and theory of measurement, mathematical gnostics is a novel non-statistical approach towards data uncertainty.

Thermal properties of novel oligoether-substituted ionic liquids and the influence of alkyl-substituent isomery

This paper is a continuation of a study focused on thermodynamic properties of isomeric and quasi-isomeric ionic liquids. In this work 5 novel ionic liquids were synthesized, namely 1-(2-(2-ethoxyethoxy)ethyl)-3-alkylimidazolium bis(trifluoromethylsulfonyl)imides, where alkyl stands for different C5 substituents. These species were characterized as to their isobaric molar heat capacity and thermal stability. The results are discussed with respect to different substituent isomerism and compared with data from our previous work (Rotrekl, Fluid Phase Equilib. 2017) that reported on a similar group of isomeric ionic liquids, namely 1-butyl-3-alkylimidazolium bis(trifluoromethylsulfonyl)imides. Data analysis of the experimental heat capacites was carried out using a non-statistical approach of the mathematical gnostics. The conclusions drawn from the present work bring an insight into the fine structure-property relationship which is useful in the development of predictive tools as well as it direct applications such as in energy storage or thermal fluids development.

Heat capacity of 1-hexadecyl-3-methylimidazolium based ionic liquids in solid and liquid phase

In this work, two ionic liquids with a 1-hexadecyl-3-methylimidazolium cation were synthesized with different anions; chloride and saccharinate, respectively, both of them showing melting points above room temperature, ranging between (324.15 and 338.15) K and enthalpies of fusion close to or higher than 100 J/g, making them potentially suitable phase-change materials (PCMs) for latent heat storage. This application potential can be enhanced by a suitably large heat capacity and thermal conductivity of the material both in the liquid and solid phase. Heat capacity was therefore measured in this work as a function of temperature using the differential scanning calorimetry (DSC) to determine how it is affected by the anion structure. Care has been taken to evaluate the influence of the phase change on the measured data. The experimental data have then been analyzed by means of methods based on mathematical gnostics (MG). As a non-statistical approach towards data uncertainty, MG enabled us to analyze the underlying phenomena that affect the value of the experimental heat capacity. • Heat capacity for two 1-hexadecyl-3-methylimidazolium based ILs was measured in liquid and solid phase by DSC. • Two anions, chloride and saccharinate, respectively, were studied. • The influence of the sample volume and phase change was assessed by means of mathematical gnostics.

Phase transitions in higher-melting imidazolium-based ionic liquids: Experiments and advanced data analysis

As thermal energy storage becomes an increasingly important topic, good knowledge of properties of phase-change materials (PCM) is essential. Among other properties, a good PCM should show a large enthalpy of melting, reproducible melting/solidification cycles, and long-term thermal stability. Temperatures and enthalpies of fusion should be determined at a possibly large range of conditions to allow for a critical evaluation of the experimental data and assessment of the material application potential.In this work, imidazolium-based ionic liquids (ILs) with long alkyl chain substituents 1-hexadecyl-3-methylimidazolium chloride and 1-hexadecyl-3-methyl-imidazolium saccharinate were studied in view of their possible use as phase-change materials. Differential scanning calorimetry (DSC) and the heat-leak modulus (HLM) methods were used to determine the temperatures and the enthalpies of phase transitions in the studied ILs, enabling us to study the influence of the heating and cooling rates on the measured properties. Enthalpies of fusion near to or larger than 100 J·g−1 were found in the studied ionic liquids, making them promising candidates for thermal energy storage. Peaks corresponding to possible liquid crystalline phases in the DSC traces of 1-hexadecyl-3-methylimidazolium saccharinate were observed, pointing to more complex phase behaviour of the studied ionic liquids.Finally, to critically evaluate the experimental data measured in this work, methods based on mathematical gnostics were used. Repeatability of measurements and the degree of mutual agreement between the methods used in this work could thus be determined.

Densities, Vapor Pressures, and Surface Tensions of Selected Terpenes

The knowledge of physico-chemical properties of terpenes and terpenoids are necessary for understanding of formation of cloud condensation nuclei. In this work properties of $$\upalpha$$ -pinene and $$\upbeta$$ -pinene, namely liquid densities, saturated vapor pressure, surface tension and interfacial tension in mixtures with water were measured in the temperature range between 300 and 370 K. Saturated vapor pressures were also modelled by COSMO-RS and compared both with our mesurements and literature values measured at lower temperatures. A modern nonstatistical technique based on mathematical gnostics was used for data analysis.

Ionic Liquids as Thermal Energy Storage Materials: On the Importance of Reliable Data Analysis in Assessing Thermodynamic Data

In spite of many statements on the application potential of ionic liquids, these organic salts present both advantages and drawbacks for their possible use in real processes. Nevertheless, they are still an undeniably fascinating class of compounds, both from the fundamental point of view and as promising task-specific materials. For instance, reliable thermal property data seem to be significantly lacking for pure ionic liquids. In addition, to assess the application potential of any material or process, a reliable analysis of experimental data is of key importance, not only to obtain recommended data, but also to be able to identify patterns in structure–property relationships, even if those may not seem evident at first sight. The aim of this work is to assess the potential application of a series of 1-alkyl-3-methylimidazolium saccharinate ionic liquids (alkyl standing for butyl, hexyl, octyl, and decyl) in thermal energy storage. To this end, heat capacity and energy density were determined experimentally by means of differential scanning calorimetry (DSC) and oscillating-tube densitometry. The experimental data were then analyzed by means of advanced data analysis methods based on mathematical gnostics. Based on the thermodynamic data and theory of measurement, mathematical gnostics is a novel non-statistical approach towards data uncertainty. As such it enables us to evaluate measurement uncertainty of statistically non-significant data sets containing as few as four data points. Also, using robust regression algorithms along a gnostic influence function, functional dependencies and structure–property patterns can be reliably determined.

Advanced Analysis of Isobaric Heat Capacities by Mathematical Gnostics

Two novel imidazolium based ether-functionalized room temperature ionic liquids were synthesized to study the temperature dependence of the isobaric heat capacity in the temperature range 298.15–348.15 K. In-house synthesized ionic liquids are often available in small amounts only, owing to the high cost of the precursors and difficulties during the synthesis itself. It is therefore impossible to repeat measurement many times so that a statistically significant data sample can be obtained. In addition, to obtain at least several values of the measured property, the ionic liquid must be recycled and reused. In this work two recycling techniques were used and their influence on the values of the experimental isobaric heat capacity was analyzed. Advantages of a modern nonstatistical data analysis technique, namely mathematical gnostics, were demonstrated.

Influence of the alkyl side chain length on the thermophysical properties of chiral ionic liquids with a (1R,2S,5R)-(–)-menthol substituent and data analysis by means of mathematical gnostics

A comprehensive physico-chemical characterization of the chiral ionic liquids of a 3-alkyl-1-[(1R,2S,5R)-(–)-menthoxymethyl]imidazolium bis(trifluoromethylsulfonyl)imides homologous series with a linear alkyl substituent ranging from the methyl up to the dodecyl group was carried out experimentally to investigate the way in which the measured thermophysical properties were influenced by the alkyl chain length on the cation. Refractive index, density, speed of sound, and isobaric heat capacity were measured as a function of temperature at atmospheric pressure and analyzed by methods based on mathematical gnostics. A robust linear regression along a gnostic influence function was used to optimize parameters of the relationships used in this work and to estimate the changing nanosegregation in the studied ionic liquid series by finding the Critical Alkyl Length Size (CALS) from heat capacity data. In addition, we propose the use of the marginal analysis to assess the quality of the measured data as an alternative to the estimate of the measurement uncertainty.

Group Contribution Method for Evaluation of Volumetric Properties of Ionic Liquids Using Experimental Data Recommended by Mathematical Gnostics

The volumetric properties of 81 different ionic liquids (ILs) have been modeled as a function of temperature and pressure using an extended version of the group contribution method previously reported by our group (Jacquemin et al. J. Chem. Eng. Data 2008, 53, 716–726). Prior to correlating collected data from the literature using this model, the mathematical gnostics was used to critically analyze experimental density data sets as a function of temperature (from 217–473 K) and pressure (from 0.1–207 MPa) to be then able to recommend one data set for each IL. In addition, recommended density data sets were then fitted as a function of temperature and pressure using a series of mathematical equations reported in the literature. These fitting equations were then assessed through the comparison of the calculated mechanical coefficients with the limited directly measured experimental data reported in the literature. Among these recommended data sets, 5399 density data points for 54 different ILs were then used as the training data set to determine the temperature and pressure dependences on the effective molar volume of 31 different cations and 24 different anions. Then 2522 density data points for 27 other ILs were used as a test data set to determine the accuracy of this method. In light of this analysis, excellent agreement was observed between calculated and recommended literature data within the whole temperature and pressure ranges investigated herein as stated by the overall relative average absolute deviation (RAAD) for each volumetric property, which was lower than 0.31% and 3.5% in the case of the density and isobaric thermal expansion coefficient of pure ILs, respectively. Finally, this model was further assessed with other methods reported in the literature in the case of the evaluation of the density of binary mixtures of two ILs as a function of temperature at atmospheric pressure. This analysis demonstrates that the proposed method shows a good ability to evaluate the density even in the case of mixture of ILs with a RAAD lower than 0.25%.

Thermal properties of 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids with linear, branched and cyclic alkyl substituents

The present study is focused on four isomeric and quasi-isomeric ionic liquids, namely 1-alkyl-3-butylimidazolium bis{(trifluoromethyl)sulfonyl}imides, where alkyl stands for pentyl, isopentyl, 3-pentyl, or cyclopentyl. This series of ionic liquids has formerly been studied as to their densities and transport properties and has shown interesting behaviour with respect to their chemical structure [1]. This work extends our knowledge of the thermal properties of these ionic liquids. The isobaric heat capacity and the thermal stability were measured and put into relationships with the different chemical structures studied. Because of recycling of ionic liquids used, density was measured as a benchmark of the quality of material. Newly, the density data from this work were corrected for their viscosity using experimental viscosity data. Together with measurements of velocity of sound, these data provided basis for calculation of coefficients of isobaric thermal expansivity and isentropic compressibility, quantities that are related to heat capacity. Similarly to previous work, the isomerization was found to have a pronounced effect on studied properties and the present fundamental physico-chemical data are therefore useful both in the design of new ionic liquids as well in theoretical studies and molecular modeling. The data analysis and correlation were carried out using robust non-statistical methods based on mathematical gnostics.

New Method Based on the UNIFAC–VISCO Model for the Estimation of Ionic Liquids Viscosity Using the Experimental Data Recommended by Mathematical Gnostics

The viscosity of ionic liquids (ILs) has been modeled as a function of temperature and at atmospheric pressure using a new method based on the UNIFAC–VISCO method. This model extends the calculations previously reported by our group (see Zhao et al. J. Chem. Eng. Data 2016, 61, 2160–2169) which used 154 experimental viscosity data points of 25 ionic liquids for regression of a set of binary interaction parameters and ion Vogel–Fulcher–Tammann (VFT) parameters. Discrepancies in the experimental data of the same IL affect the quality of the correlation and thus the development of the predictive method. In this work, mathematical gnostics was used to analyze the experimental data from different sources and recommend one set of reliable data for each IL. These recommended data (totally 819 data points) for 70 ILs were correlated using this model to obtain an extended set of binary interaction parameters and ion VFT parameters, with a regression accuracy of 1.4%. In addition, 966 experimental viscosity data po...

Intravesical instillation of onabotulinum toxin A embedded in inert hydrogel in the treatment of idiopathic overactive bladder: A double-blind randomized pilot study

Objective. It was hypothesized that increasing the time for which onabotulinum toxin A (OnabotA) is exposed to the urothelium following intravesical instillation will augment its effect. TC-3 is an inert heat-sensitive hydrogel, which creates an intravesical bulk providing a slow release of the embedded drug after instillation. The aim of this study was to evaluate the effect of OnabotA, embedded in inert TC-3 hydrogel, in patients with idiopathic overactive bladder (OAB).Methods. In total, 39 female patients (age 30–65, average 53.8 years) with OAB symptoms were randomized for the study into four groups, each receiving 50 ml of the following intravesical instillations: Group A, 0.9% NaCl (placebo, n = 11); Group B, TC-3 gel + 200 U OnabotA (n = 9); Group C, TC-3 gel + 200 U OnabotA + dimethyl sulfoxide (DMSO) (n = 10); and Group D, DMSO (n = 9). The parameters were compared before and 1 month after treatment.Results. When comparing parameters using conventional statistical methods (Kruskal–Wallis test), no statistically significant changes were observed within the groups. Comparison of the medians using an analysis based on the mathematical gnostics showed the superiority of the method used in Group B over the other groups in the following parameters: number of urgency grade 3 + 4 episodes/72 h, number of leakage episodes/72 h, Overactive Bladder Questionnaire total score and Patient Perception of Bladder Condition total score. Group D showed its superiority over the other groups in respect to the number of nocturia episodes/72 h.Conclusions. The results indicate that intravesical instillation of OnabotA, embedded in TC-3 gel, could become an alternative to intramural injection for a well-selected subgroup of patients.