Search results for "THERMODYNAMICS"

Modified Gaussian models applied to the description and deconvolution of peaks in chiral liquid chromatography.

2020

Abstract The description of the profiles of chromatographic peaks has been studied extensively, with a large number of proposed mathematical functions. Among them, the accuracy achieved with modified Gaussian models that describe the deviation of an ideal Gaussian peak as a change in the peak variance or standard deviation over time, has been highlighted. These models are, in fact, a family of functions of different complexity with great flexibility to adjust chromatographic peaks over a wide range of asymmetries and shapes. However, an uncontrolled behaviour of the signal may occur outside the region being fitted, forcing the use of different strategies to overcome this problem. In this wo…

Estimation of peak capacity based on peak simulation.

2018

Peak capacity (PC) is a key concept in chromatographic analysis, nowadays of great importance for characterising complex separations as a criterion to find the most promising conditions. A theoretical expression for PC estimation can be easily deduced in isocratic elution, provided that the column plate count is assumed constant for all analytes. In gradient elution, the complex dependence of peak width with the gradient program implies that an integral equation has to be solved, which is only possible in a limited number of situations. In 2005, Uwe Neue developed a comprehensive theory for the calculation of PC in gradient elution, which is only valid for certain situations: single linear …

The Fractal Approach to Secondary Mechanisms in SEC

2007

Abstract Size‐exclusion chromatography (SEC) is one of the most used experimental techniques to characterize polymers in solution; it has been applied to interpret the elution behaviour of many polymer‐solvent systems in five types of column packings. The experimental data have revealed that the classical universal calibration is not accomplished. Deviations from a unique curve are a consequence of two effects: entropic (exclusion by size) and enthalpic (binary and ternary interactions between solvent, polymer, and gel), which results in secondary mechanisms accompanying the main “ideal” SEC separation mechanism. Therefore, three approaches of building a calibration curve have been compared…

Extension of the linear solvent strength retention model including a parameter that describes the elution strength changes in liquid chromatography.

2020

Modelling the retention behaviour of solutes in liquid chromatography, based on the composition of the mobile phase is a common task in the chromatographic practice. Along the development of liquid chromatography (LC), several models have been proposed to help in understanding the retention mechanisms, and especially, allow the prediction of retention times with optimisation purposes. Particular models are used for different LC modes, such as normal phase (NPLC), reversed phase (RPLC), hydrophilic interaction (HILIC), and micellar (MLC). In this work, a general equation is proposed that includes a parameter (the elution degree, g), which characterises the way the elution strength varies wit…

Enhancement in the computation of gradient retention times in liquid chromatography using root-finding methods.

2019

Abstract Gradient elution may provide adequate separations within acceptably short times in a single run, by gradually increasing the elution speed. Similarly to isocratic elution, chromatograms can be predicted under any experimental condition, through strategies based on retention models. The most usual approach implies solving an integral equation (i.e., the fundamental equation of gradient elution), which has an analytical solution only for certain combinations of retention model and gradient programme. This limitation can be overcome by using numerical integration, which is a universal approach although at the cost of longer computation times. In this work, several alternatives to impr…

Enhanced calculation of optimal gradient programs in reversed-phase liquid chromatography

2003

Abstract The resolution of a mixture of 16 β-blockers under gradient elution was optimised using both isocratic and gradient training sets, with a reversed-phase column and acetonitrile–water eluents. Error theory was applied to measure the information extracted from different gradient experimental designs. This allows checking the expected accuracy when gradient predictions exceed the initial solvent concentrations tested in the training set. This work applies the results on modelling found in a previous study [J. Chromatogr. A 1018 (2003) 169] where the performance of several retention models was compared. Enhanced retention predictions were applied to the optimisation of gradient program…

Applications of mathematical modelling to the simulation of binary perfusion chromatography

1993

Abstract A mathematical model of binary (competitive adsorption involving two components) perfusion chromatography is used to simulate and study the behavior of a binary adsorption system. The dynamic behavior of column systems (frontal analysis) is examined for different particles sizes, column fluid superficial velocities, Vf, and intraparticle fluid velocities, νp. Column systems with perfusive (νp > 0) and purely diffusive (νp = 0) adsorbent particles are studied. The results obtained from the binary system studied in this work suggest that the times at which breakthrough begins for components 1 and 2, and the dynamic (unsteady state) relative separation between components 1 and 2 obtai…

Variances as order parameter and complexity measure for random Boolean networks

2005

Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it with the results of numerical experiments. Finally, we propose a complexity measure based on the compromise between temporal and spatial variances. This new order parameter and its related complexity measure can be easily applied to other complex systems.

Theoretical study of oligomeric alumatranes present in the chemistry of materials from micro to mesoporous molecular sieves and alumina composites

2008

Quantum chemical calculations using density functional theory have been carried out to investigate molecular precursors based on alumatranes which are one of the components with silatranes for the preparation of mesoporous aluminosilicate materials. In the same way, some oligomeric alumatranes of this study take part in chemical syntheses related to materials such as zeolites and alumina composite. Gas phase and solution equilibrium geometries of the alumatrane precursors were fully optimized at B3LYP level, modeling solvent effects using a self-consistent reaction field (SCRF). From these optimized geometries, calculations of the 1 H, 13 C and 27 Al NMR chemical shifts at GIAO/B3LYP/6-31G(…

2019

Abstract The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalised to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be o…