Functional-segment activity coefficient equation of state : F-SAC-Phi

COSMO-RS refinements and applications have been the focus of numerous works, mainly due to their great predictive capacity. However, these models do not directly include pressure effects. In this work, a methodology for the inclusion of pressure effects in the functional-segment activity coefficient model, F-SAC (a COSMO-based group-contribution method), is proposed. This is accomplished by the combination of F-SAC and lattice-fluid ideas by the inclusion of free volume in the form of holes, generating the F-SAC-Phi model. The computational cost when computing the pressure (given temperature, volume, and molar volume) with the proposed model is similar to the cost for computing activity coefficients with any COSMO-type implementation. For a given pressure, the computational cost increases since an iterative method is needed. The concept is tested for representative substances and mixtures, ranging from light gases to molecules with up to 10 carbons. The proposed model is able to correlate experimental data of saturation pressure and saturated liquid volume of pure substances with deviations of 1.7 and 1.1%, respectively. In the prediction of mixture vapor−liquid equilibria, the resulting model is superior to COSMO-SAC-Phi, SRK-MC (Soave−Redlich−Kwong with the Mathias−Copeman α-function) with the classic van der Waals mixing rule, and PSRK in almost all tested cases, from low pressures to over 100 bar

Prediction of Solubility of Active Pharmaceutical Ingredients in Single Solvents and Their Mixtures — Solvent Screening

In this chapter, the applicability of two predictive activity coefficient-based models will be examined. The experimental data from five different types of VLE (vapor-liquid equilibrium) and VLLE (vapor-liquid-liquid equilibrium) systems that are common in industry are used for the evaluation. The nonrandom two-liquid segment activity coefficient (NRTL-SAC) and universal functional activity coefficient (UNIFAC) were selected to model the systems. The various thermodynamic relations existing in the open literature will be discussed and used to predict the solubility of active pharmaceutical ingredients and other small organic molecules in a single or a mixture of solvents. Equations of states, the activity coefficient, and predictive models will be discussed and used for this purpose. We shall also present some of our results on solvent screening using a single and a mixture of solvents

An evaluation of thermodynamic models for the prediction of drug and drug-like molecule solubility in organic solvents

Prediction of solubility of active pharmaceutical ingredients (API) in different solvents is one of the main issue for crystallization process design. Experimental determination is not always possible because of the small amount of product available in the early stages of a drug development. Thus, one interesting perspective is the use of thermodynamic models, which are usually employed for predicting the activity coefficients in case of Vapour–Liquid equilibria or Liquid–Liquid equilibria (VLE or LLE). The choice of the best thermodynamic model for Solid–Liquid equilibria (SLE) is not an easy task as most of them are not meant particularly for this. In this paper, several models are tested for the solubility prediction of five drugs or drug-like molecules: Ibuprofen, Acetaminophen, Benzoic acid, Salicylic acid and 4-aminobenzoic acid, and another molecule, anthracene, a rather simple molecule. The performance of predictive (UNIFAC, UNIFAC mod., COSMO-SAC) and semi-predictive (NRTL-SAC) models are compared and discussed according to the functional groups of the molecules and the selected solvents. Moreover, the model errors caused by solid state property uncertainties are taken into account. These errors are indeed not negligible when accurate quantitative predictions want to be performed. It was found that UNIFAC models give the best results and could be an useful method for rapid solubility estimations of an API in various solvents. This model achieves the order of magnitude of the experimental solubility and can predict in which solvents the drug will be very soluble, soluble or not soluble. In addition, predictions obtained with NRTL-SAC model are also in good agreement with the experiments, but in that case the relevance of the results is strongly dependent on the model parameters regressed from solubility data in single and mixed solvents. However, this is a very interesting model for quick estimations like UNIFAC models. Finally, COSMO-SAC needs more developments to increase its accuracy especially when hydrogen bonding is involved. In that case, the predicted solubility is always overestimated from two to three orders of magnitude. Considering the use of the most accurate equilibrium equation involving the ΔCp term, no benefits were found for drug predictions as the models are still too inaccurate. However, in function of the molecules and their solid thermodynamic properties, the ΔCp term can be neglected and will not have a great impact on the results

A universal segment approach for the prediction of the activity coefficient.

Doctor of Philosophy in Chemical Engineering. University of KwaZulu-Natal, Durban 2016.This study comprised an investigation into solid-liquid equilibrium prediction, measurement and modelling for active pharmaceutical ingredients, and solvents, employed in the pharmaceutical industry. Available experimental data, new experimental data, and novel measuring techniques, as well as existing predictive thermodynamic activity coefficient model revisions, were investigated. Thereafter, and more centrally, a novel model for the prediction of activity coefficients, at solid-liquid equilibrium, which incorporates global optimization strategies in its training, is presented. The model draws from the segment interaction (via segment surface area), approach in solidliquid equilibrium modelling for molecules, and extends this concept to interactions between functional groups. Ultimately, a group-interaction predictive method is proposed that is based on the popular UNIFAC-type method (Fredenslund et al. 1975). The model is termed the Universal Segment Activity Coefficient (UNISAC) model. A detailed literature review was conducted, with respect to the application of the popular predictive models to solid-liquid phase equilibrium (SLE) problems, involving structurally complex solutes, using experimental data available in the literature (Moodley et al., 2016 (a)). This was undertaken to identify any practical and theoretical limitations in the available models. Activity coefficient predictions by the NRTL-SAC ((Chen and Song 2004), Chen and Crafts, 2006), UNIFAC (Fredenslund et al., 1975), modified UNIFAC (Dortmund) (Weidlich and Gmehling, 1987), COSMO-RS (OL) (Grensemann and Gmehling, 2005), and COSMOSAC (Lin and Sandler, 2002), were carried out, based on available group constants and sigma profiles, in order to evaluate the predictive capabilities of these models. The quality of the models is assessed, based on the percentage deviation between experimental data and model predictions. The NRTL-SAC model is found to provide the best replication of solubility rank, for the cases tested. It, however, was not as widely applicable as the majority of the other models tested, due to the lack of available model parameters in the literature. These results correspond to a comprehensive comparison conducted by Diedrichs and Gmehling (2011). After identifying the limitations of the existing predictive methods, the UNISAC model is proposed (Moodley et al, 2015 (b)). The predictive model was initially applied to solid-liquid systems containing a set of 18 structurally diverse, complex pharmaceuticals, in a variety of solvents, and compared to popular qualitative solubility prediction methods, such as NRTLSAC and the UNIFAC based methods. Furthermore, the Akaike Information Criterion (AIC) (Akaike, 1974) and Focused Information Criterion (FIC) (Claeskens and Hjort, 2003) were used to establish the relative quality of the solubility predictions. The AIC scores recommend the UNISAC model for over 90% of the test cases, while the FIC scores recommend UNISAC in over 75% of the test cases. The sensitivity of the UNISAC model parameters was highlighted during the initial testing phase, which indicated the need to employ a more rigorous method of determining parameters of the model, by optimization to the global minimum. It was decided that the Krill Herd algorithm optimization technique (Gandomi and Alavi, 2012), be employed to accomplish this. To verify the suitability of this decision, the algorithm was applied to phase stability (PS) and phase equilibrium calculations in non-reactive (PE) and reactive (rPE) systems, where global minimization of the total Gibbs energy is necessary. The results were compared to other methods from the literature (Moodley et al., 2015 (c)). The Krill Herd algorithm was found to reliably determine the desired global optima in PS, PE and rPE problems. The algorithm outperformed or matched all other methods considered for comparison, including swarm intelligence and genetic algorithms, with an average success rate of 89.5 %, and with an average number of function evaluations of 1406. The UNISAC model was then reviewed, and extended, to incorporate the significantly more detailed group fragmentation scheme of Moller et al. (2008), to improve the range of application of the model. New UNISAC segment group area parameters that were obtained by data fitting, using the Krill Herd Algorithm as an optimization tool, were calculated. This Extended UNISAC model was then used to predict SLE compositions, or temperatures, of a large volume of experimental binary and ternary system data, available in the literature, (over 4000 data points), and was compared to predictions by the UNIFAC-based and COSMO-based models (Moodley et al., 2016 (d)). The AIC scores suggest that the Extended UNISAC model is superior to the original UNIFAC, modified UNIFAC (Dortmund) (2013), COSMO-RS(OL), and COSMO-SAC models, with relative AIC scores of 1.95, 4.17, 2.17 and 2.09. In terms of percentage deviations alone between experimental and predicted values, the modified UNIFAC (Dortmund) model, and original UNIFAC models, proved superior at 21.03% and 29.03% respectively; however, the Extended UNISAC model was a close third at 32.99%. As a conservative measure to ensure that inter-correlation of the training set did not occur, previously unmeasured data was desired as a test set, to verify the ability of the Extended UNISAC model to estimate data outside of the training set. To accomplish this, SLE measurements were conducted for the systems diosgenin/ estriol/ prednisolone/ hydrocortisone/ betulin and estrone. These measurements were undertaken in over 10 diverse organic solvents, and water, at atmospheric pressure, within the temperature range 293.2-328.2 K, by employing combined digital thermal analysis and thermal gravimetric analysis, to determine compositions at saturation (Moodley et al., 2016 (e), Moodley et al., 2016 (f), Moodley et al., 2016 (g)). This previously unmeasured test set data was compared to predictions by the Extended UNISAC, UNIFAC-based and COSMO-based methods. It was found that the Extended UNISAC model can qualitatively predict the solubility in the systems measured (where applicable), comparably to the other popular methods tested. The desirable advantage is that the number of model parameters required to describe mixture activities is far lower than for the group contribution and COSMO-based methods. Future developments of the Extended UNISAC model were then considered, which included the preliminary testing of alternate combinatorial expressions, to better account for size-shape effects on the activity coefficient. The limitations of the Extended UNISAC model are also discussed

Spot activity of the RS CVn star {\sigma} Geminorum

We model the photometry of RS CVn star $\sigma$ Geminorum to obtain new information on the changes of the surface starspot distribution, i.e., activity cycles, differential rotation and active longitudes. We use the previously published Continuous Periods Search-method (CPS) to analyse V-band differential photometry obtained between the years 1987 and 2010 with the T3 0.4 m Automated Telescope at the Fairborn Observatory. The CPS-method divides data into short subsets and then models the light curves with Fourier-models of variable orders and provides estimates of the mean magnitude, amplitude, period and light curve minima. These light curve parameters are then analysed for signs of activity cycles, differential rotation and active longitudes. We confirm the presence of two previously found stable active longitudes, synchronised with the orbital period $P_{\rm{orb}}=19.60$d and find eight events where the active longitudes are disrupted. The epochs of the primary light curve minima rotate with a shorter period $P_{\rm{min,1}}=19.47$d than the orbital motion. If the variations in the photometric rotation period were to be caused by differential rotation, this would give a differential rotation coefficient of $\alpha \ge 0.103$. The presence of two slightly different periods of active regions may indicate a superposition of two dynamo modes, one stationary in the orbital frame and the other one propagating in the azimuthal direction. Our estimate of the differential rotation is much higher than previous results. However, simulations show that this can be caused by insufficient sampling in our data.Comment: 10 pages, 6 figures. Submitted to A&

Trading activity and price impact in parallel markets: SETS vs. off-book market at the London Stock Exchange

We empirically study the trading activity in the electronic on-book segment and in the dealership off-book segment of the London Stock Exchange, investigating separately the trading of active market members and of other market participants which are non-members. We find that (i) the volume distribution of off-book transactions has a significantly fatter tail than the one of on-book transactions, (ii) groups of members and non-members can be classified in categories according to their trading profile (iii) there is a strong anticorrelation between the daily inventory variation of a market member due to the on-book market transactions and inventory variation due to the off-book market transactions with non-members, and (iv) the autocorrelation of the sign of the orders of non-members in the off-book market is slowly decaying. We also analyze the on-book price impact function over time, both for positive and negative lags, of the electronic trades and of the off-book trades. The unconditional impact curves are very different for the electronic trades and the off-book trades. Moreover there is a small dependence of impact on the volume for the on-book electronic trades, while the shape and magnitude of impact function of off-book transactions strongly depend on volume.Comment: 16 pages, 9 figure

Using an audit tool (MAPS Global) to assess the characteristics of the physical environment related to walking for transport in youth : reliability of Belgian data

Background: The aim was to examine inter-rater and alternate-form reliability of the Microscale Audit of Pedestrian Streetscapes (MAPS) Global tool to assess the physical environment along likely walking routes in Belgium. Methods: For 65 children participating in the BEPAS-children study, routes between their individual homes and the nearest pre-defined destination were defined. Using MAPS Global, physical environmental characteristics of the routes were audited by 4 trained auditors (2 on-site, 2 online using Google Street View). Inter-rater reliability was studied for on-site and online ratings separately. Alternate-form reliability was examined by comparing on-site with online ratings. Results: Inter-rater reliability for on-site ratings was acceptable for 68% of items (kappa range 0.03–1.00) and for online ratings for 60% of items (kappa range −0.03 to 1.00). Acceptable alternate-form reliability was reported for 60% of items (kappa range −0.01 to 1.00/r range 0.31–1.00). Conclusions: MAPS Global can be used to assess the physical environment of potential walking routes. For areas where Google Street View imagery is widely covered and often updated, MAPS Global can be completed online