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Langmuir, 2002
A method for calculating activity coefficients at infinite dilution from surface tension data is ... more A method for calculating activity coefficients at infinite dilution from surface tension data is derived from the conditions for equilibrium between surface and bulk phases rather than from the conditions for liquid-vapor or liquid-liquid equilibrium, as is more usual. Specifically, the method combines the Volmer surface equation of state and the Gibbs adsorption equation to derive an expression for the surface chemical potential. The key operation of this treatment is the choice of the same reference state for both bulk and surface phases. The γ ∞ values calculated for systems for which suitable data are available in the literature agree well with values obtained by other methods.
Educación Química, 2018
La ecuación de Young-Laplace establece la relación entre curvatura, tensión superficial y la dife... more La ecuación de Young-Laplace establece la relación entre curvatura, tensión superficial y la diferencia de presiones en fases fluidas, resultado de la competencia entre los trabajos volumétrico y superficial. La forma de una superficie depende de la diferencia de presiones entre las fases que la conforman. La descripción de una superficie curva requiere al menos de dos radios de curvatura, de aquí el requisito de los conceptos de curvatura, radio de curvatura y radio máximo de curvatura, que constituyen los elementos indispensables para construir la ecuación de Young-Laplace en sus formas ordinaria y diferencial.
HTS Religion & Society Series, 2021
The Circle of Concerned African Women Theologians (hereafter Circle) has benefited from various c... more The Circle of Concerned African Women Theologians (hereafter Circle) has benefited from various contributions of its members over the years, both in kind and cash. For this, the authors are truly grateful to our Circle member, Musimbi Kanyoro, who has supported various fund-raising opportunities and also made substantial personal contributions. At the time of the All Africa 5th Circle Conference in Botswana (July 2019), Musimbi was wrapping up her responsibilities as the President and CEO of the Global Fund for Women, and therefore, was unable to attend the conference in person. Keeping her commitment as one of the founders of the Circle, she decided to take a step of faith and contributed to the Circle 30th anniversary celebration through a significant amount of money which included her end of service bonus and some funds raised through the Global Fund for Women. For this, the authors are grateful to Musimbi Kanyoro and to the Global Fund for Women. They are also grateful to the University of Botswana, Global Challenges Research Fund, Kerk in Actie, Holland and the World Council of Churches Ecumenical HIV and AIDS Initiatives and Advocacy (WCC-EHAIA) for their contributions towards the conference. Special thanks are extended to the University of Pretoria Department of Theology and Religion for the inclusion of this volume in the research project of Yolanda Dreyer titled: 'Gender Studies and Practical Theological Theory Formation'. The authors especially thank the Dean of the Faculty of Theology and Religion for the seed funding and Professor Andries G. van Aarde, Commissioning Editor AOSIS Books, for facilitating this process. The authors are also grateful to the Botswana Circle Chapter for successfully organising and hosting a splendid conference. Special thanks are also extended to Musa W. Dube for the important role played in conceptualising the conference theme. The authors thank Johanna Stiebert and Katie Edwards for their contributions and are grateful to all the contributors and peer reviewers who made this project a success by devoting their time and expertise. Last, but not least, the authors thank AOSIS Book Publishers for the publication of the volume.
Journal of Colloid and Interface Science, 2005
The Young-Laplace equation differential form can be solved under the elliptic representation for ... more The Young-Laplace equation differential form can be solved under the elliptic representation for a fluid-fluid interface in the range 0 </= phi </= 90 degrees . For a characteristic point (X(max), Y = 90 degrees ) we find a simple analytical relation between the curvature radius and the elliptic parameters that yields the surface tension in the range 0.125 < beta < 100. The solution to the differential equation gives an error lower than 2.5% for published normalized data. The origin of the coordinates of the profile drop is the maximum diameter and the distance from the equator to the drop apex. Through this mechanism, the need for numerical methods and published algorithms prior to this work is eliminated. To challenge the method, the procedure is used with published data of numerical solutions. The dimensions of the parameters used are invariant with respect to the coordinate system. For practical applications, this useful equation can be used in pendant drop, sessile drop, rising bubble, spinning drop, and capillary methods. Finally, to increase the sensitivity of the procedure, the elliptic segment data under the maximum diameter can be treated with a linear regression (y2 vs x2) to obtain the elliptic parameters (a and b) in order to apply the final equation.
Educación Química
Las combinaciones de n elementos tomados de dos en dos, cuantifican el número total de pares posi... more Las combinaciones de n elementos tomados de dos en dos, cuantifican el número total de pares posibles formados a partir de los n elementos. Si a cada uno de estos pares se le asigna un potencial atractivo, entonces se puede calcular la magnitud atractiva total entre pares de una misma especie y la magnitud atractiva entre pares diferentes. Este tratamiento puede extenderse a un número mayor de primeros vecinos y entonces responder a la pregunta sobre la solubilidad total o parcial entre líquidos diferentes a través de la construcción de la función de energía libre de Gibbs de mezclado correspondiente.
Colloids and Surfaces A-physicochemical and Engineering Aspects, 2004
Acrysol TT-935 R&H is an associative alkali soluble polymer with applications to the paper and co... more Acrysol TT-935 R&H is an associative alkali soluble polymer with applications to the paper and coating industry. For hydrophobic modified polymers there is a lack of fundamental understanding on their surface properties in aqueous solutions. The aim of this work is to report surface properties of the Acrysol TT-935 obtained from the equilibrium surface tension (EST) (by the du Noüy
Educación Química
El estudio del comportamiento de solutos con actividad superficial (abatimiento de la tensión sup... more El estudio del comportamiento de solutos con actividad superficial (abatimiento de la tensión superficial del disolvente) o tensoactivos, permite conocer la relación entre las propiedades de la superficie y las propiedades del disolvente. La Ecuación de Adsorción de Gibbs es la expresión termodinámica fundamental en el estudio de tensoactivos, que cuantifica la adsorción o concentración de solutos en la superficie de contacto entre fases (interfase líquido/gas o líquido/ líquido), mediante la variación de la tensión superficial con respecto a la concentración de soluto...
Educación Química
En la ecuación 8, el término 2a/Vc 3 tiene signo negativo (−) y debe ser positivo (+).
Educación Química
Dilution, emulsification, continuous and semi-continuous chemical reactions, assessment of equili... more Dilution, emulsification, continuous and semi-continuous chemical reactions, assessment of equilibrium diagrams and in general, formulation procedures, require the addition of pure liquids or binary mixtures to other mixtures or pure compounds. These processes follow defined ternary diagrams paths. The path tracking and the corresponding balance material allow the determination of both the composition and the process tendency at each discreet or differential addition of one or more components. The graphical representation justifies the balance material and the position within the equilibrium diagram provides a clear idea of the experimental trajectory, which is an aspect not often addressed in the common literature on equilibrium and process design.
Open Journal of Physical Chemistry, 2012
The Gibbs elasticity modulus represents an important tool to predict the foamability for transien... more The Gibbs elasticity modulus represents an important tool to predict the foamability for transient and permanent foams like polyurethane flexible systems. Elasticity is related to foamability and so is used as a synonymous for the purpose of this paper. In this article we propose a method and a thermodynamic model to analyze the espumability of silicone surfactants in polyol binary mixtures using surface tension data. The present work describes foamability through the Gibbs elasticity modulus expressed in terms of first and second derivatives of surface pressure vs bulk composition. Furthermore, the Gibbs adsorption equation and the corresponding novel surface equation of state based on a modification of the Langmuir isotherm resulted in an elasticity equation with analytical solution. It is shown that according to foam model systems of surfactant solution in polyol used at commercial processes, optimum concentration level of surfactant obtained at this article by Gibbs adsorption equation and maximus on elasticity modulus finally match.
Journal of the Electrochemical Society, 2013
The synthesis and characterization of bimetallic catalysts with Pt and W as active phases, suppor... more The synthesis and characterization of bimetallic catalysts with Pt and W as active phases, supported on carbon, were carried out. A synthesis method based on the thermolysis of metal precursors was developed with systems in which an aqueous phase, an organic one and solid carbon are present. The Pt loading in the synthesized catalysts was kept constant and the amounts of W and carbon changed. It was found that the Pt phase forms hemispherical particles with average diameter of 3 nm. The W is predominantly in the form of hexagonal WO 3 crystals with average dimensions 35 by 15 nm. No evidence of alloy formation is found. The electrochemical characterization of ethanol oxidation includes cyclic voltammetry and current-sampled voltammetry techniques. Tungsten exerts a promoting role in the activity of the catalysts, revealed by considerably increased current densities with respect to carbon-supported Pt. Details of this enhanced activity are revealed by cyclic voltammetry with different operating conditions and electrolyte formulations. These experiments allowed to identify the oxidation of adsorbed organic intermediates influenced by the tungsten phase. WO 3 appears as well to cause the decrease in the rate at which Pt oxides reduce, leading to higher surface coverage of OH• species.
Langmuir, 2002
A method for calculating activity coefficients at infinite dilution from surface tension data is ... more A method for calculating activity coefficients at infinite dilution from surface tension data is derived from the conditions for equilibrium between surface and bulk phases rather than from the conditions for liquid-vapor or liquid-liquid equilibrium, as is more usual. Specifically, the method combines the Volmer surface equation of state and the Gibbs adsorption equation to derive an expression for the surface chemical potential. The key operation of this treatment is the choice of the same reference state for both bulk and surface phases. The γ ∞ values calculated for systems for which suitable data are available in the literature agree well with values obtained by other methods.
Educación Química, 2018
La ecuación de Young-Laplace establece la relación entre curvatura, tensión superficial y la dife... more La ecuación de Young-Laplace establece la relación entre curvatura, tensión superficial y la diferencia de presiones en fases fluidas, resultado de la competencia entre los trabajos volumétrico y superficial. La forma de una superficie depende de la diferencia de presiones entre las fases que la conforman. La descripción de una superficie curva requiere al menos de dos radios de curvatura, de aquí el requisito de los conceptos de curvatura, radio de curvatura y radio máximo de curvatura, que constituyen los elementos indispensables para construir la ecuación de Young-Laplace en sus formas ordinaria y diferencial.
HTS Religion & Society Series, 2021
The Circle of Concerned African Women Theologians (hereafter Circle) has benefited from various c... more The Circle of Concerned African Women Theologians (hereafter Circle) has benefited from various contributions of its members over the years, both in kind and cash. For this, the authors are truly grateful to our Circle member, Musimbi Kanyoro, who has supported various fund-raising opportunities and also made substantial personal contributions. At the time of the All Africa 5th Circle Conference in Botswana (July 2019), Musimbi was wrapping up her responsibilities as the President and CEO of the Global Fund for Women, and therefore, was unable to attend the conference in person. Keeping her commitment as one of the founders of the Circle, she decided to take a step of faith and contributed to the Circle 30th anniversary celebration through a significant amount of money which included her end of service bonus and some funds raised through the Global Fund for Women. For this, the authors are grateful to Musimbi Kanyoro and to the Global Fund for Women. They are also grateful to the University of Botswana, Global Challenges Research Fund, Kerk in Actie, Holland and the World Council of Churches Ecumenical HIV and AIDS Initiatives and Advocacy (WCC-EHAIA) for their contributions towards the conference. Special thanks are extended to the University of Pretoria Department of Theology and Religion for the inclusion of this volume in the research project of Yolanda Dreyer titled: 'Gender Studies and Practical Theological Theory Formation'. The authors especially thank the Dean of the Faculty of Theology and Religion for the seed funding and Professor Andries G. van Aarde, Commissioning Editor AOSIS Books, for facilitating this process. The authors are also grateful to the Botswana Circle Chapter for successfully organising and hosting a splendid conference. Special thanks are also extended to Musa W. Dube for the important role played in conceptualising the conference theme. The authors thank Johanna Stiebert and Katie Edwards for their contributions and are grateful to all the contributors and peer reviewers who made this project a success by devoting their time and expertise. Last, but not least, the authors thank AOSIS Book Publishers for the publication of the volume.
Journal of Colloid and Interface Science, 2005
The Young-Laplace equation differential form can be solved under the elliptic representation for ... more The Young-Laplace equation differential form can be solved under the elliptic representation for a fluid-fluid interface in the range 0 </= phi </= 90 degrees . For a characteristic point (X(max), Y = 90 degrees ) we find a simple analytical relation between the curvature radius and the elliptic parameters that yields the surface tension in the range 0.125 < beta < 100. The solution to the differential equation gives an error lower than 2.5% for published normalized data. The origin of the coordinates of the profile drop is the maximum diameter and the distance from the equator to the drop apex. Through this mechanism, the need for numerical methods and published algorithms prior to this work is eliminated. To challenge the method, the procedure is used with published data of numerical solutions. The dimensions of the parameters used are invariant with respect to the coordinate system. For practical applications, this useful equation can be used in pendant drop, sessile drop, rising bubble, spinning drop, and capillary methods. Finally, to increase the sensitivity of the procedure, the elliptic segment data under the maximum diameter can be treated with a linear regression (y2 vs x2) to obtain the elliptic parameters (a and b) in order to apply the final equation.
Educación Química
Las combinaciones de n elementos tomados de dos en dos, cuantifican el número total de pares posi... more Las combinaciones de n elementos tomados de dos en dos, cuantifican el número total de pares posibles formados a partir de los n elementos. Si a cada uno de estos pares se le asigna un potencial atractivo, entonces se puede calcular la magnitud atractiva total entre pares de una misma especie y la magnitud atractiva entre pares diferentes. Este tratamiento puede extenderse a un número mayor de primeros vecinos y entonces responder a la pregunta sobre la solubilidad total o parcial entre líquidos diferentes a través de la construcción de la función de energía libre de Gibbs de mezclado correspondiente.
Colloids and Surfaces A-physicochemical and Engineering Aspects, 2004
Acrysol TT-935 R&H is an associative alkali soluble polymer with applications to the paper and co... more Acrysol TT-935 R&H is an associative alkali soluble polymer with applications to the paper and coating industry. For hydrophobic modified polymers there is a lack of fundamental understanding on their surface properties in aqueous solutions. The aim of this work is to report surface properties of the Acrysol TT-935 obtained from the equilibrium surface tension (EST) (by the du Noüy
Educación Química
El estudio del comportamiento de solutos con actividad superficial (abatimiento de la tensión sup... more El estudio del comportamiento de solutos con actividad superficial (abatimiento de la tensión superficial del disolvente) o tensoactivos, permite conocer la relación entre las propiedades de la superficie y las propiedades del disolvente. La Ecuación de Adsorción de Gibbs es la expresión termodinámica fundamental en el estudio de tensoactivos, que cuantifica la adsorción o concentración de solutos en la superficie de contacto entre fases (interfase líquido/gas o líquido/ líquido), mediante la variación de la tensión superficial con respecto a la concentración de soluto...
Educación Química
En la ecuación 8, el término 2a/Vc 3 tiene signo negativo (−) y debe ser positivo (+).
Educación Química
Dilution, emulsification, continuous and semi-continuous chemical reactions, assessment of equili... more Dilution, emulsification, continuous and semi-continuous chemical reactions, assessment of equilibrium diagrams and in general, formulation procedures, require the addition of pure liquids or binary mixtures to other mixtures or pure compounds. These processes follow defined ternary diagrams paths. The path tracking and the corresponding balance material allow the determination of both the composition and the process tendency at each discreet or differential addition of one or more components. The graphical representation justifies the balance material and the position within the equilibrium diagram provides a clear idea of the experimental trajectory, which is an aspect not often addressed in the common literature on equilibrium and process design.
Open Journal of Physical Chemistry, 2012
The Gibbs elasticity modulus represents an important tool to predict the foamability for transien... more The Gibbs elasticity modulus represents an important tool to predict the foamability for transient and permanent foams like polyurethane flexible systems. Elasticity is related to foamability and so is used as a synonymous for the purpose of this paper. In this article we propose a method and a thermodynamic model to analyze the espumability of silicone surfactants in polyol binary mixtures using surface tension data. The present work describes foamability through the Gibbs elasticity modulus expressed in terms of first and second derivatives of surface pressure vs bulk composition. Furthermore, the Gibbs adsorption equation and the corresponding novel surface equation of state based on a modification of the Langmuir isotherm resulted in an elasticity equation with analytical solution. It is shown that according to foam model systems of surfactant solution in polyol used at commercial processes, optimum concentration level of surfactant obtained at this article by Gibbs adsorption equation and maximus on elasticity modulus finally match.
Journal of the Electrochemical Society, 2013
The synthesis and characterization of bimetallic catalysts with Pt and W as active phases, suppor... more The synthesis and characterization of bimetallic catalysts with Pt and W as active phases, supported on carbon, were carried out. A synthesis method based on the thermolysis of metal precursors was developed with systems in which an aqueous phase, an organic one and solid carbon are present. The Pt loading in the synthesized catalysts was kept constant and the amounts of W and carbon changed. It was found that the Pt phase forms hemispherical particles with average diameter of 3 nm. The W is predominantly in the form of hexagonal WO 3 crystals with average dimensions 35 by 15 nm. No evidence of alloy formation is found. The electrochemical characterization of ethanol oxidation includes cyclic voltammetry and current-sampled voltammetry techniques. Tungsten exerts a promoting role in the activity of the catalysts, revealed by considerably increased current densities with respect to carbon-supported Pt. Details of this enhanced activity are revealed by cyclic voltammetry with different operating conditions and electrolyte formulations. These experiments allowed to identify the oxidation of adsorbed organic intermediates influenced by the tungsten phase. WO 3 appears as well to cause the decrease in the rate at which Pt oxides reduce, leading to higher surface coverage of OH• species.