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Yang XD, Chen W, Ren Y, Chu LY. Exploration of the Adsorption Kinetics of Surfactants at the Water-Oil Interface via Grand-Canonical Molecular Dynamics Simulations. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:1277-1286. [PMID: 35015552 DOI: 10.1021/acs.langmuir.1c03205] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
It is well-known that surfactants tend to aggregate into clusters or micelles in aqueous solutions due to their special structures, and it is difficult for the surfactant molecules involved in the aggregation to move spontaneously to the oil-water interface. In this article, we developed a new grand-canonical molecular dynamics (GCMD) model to predict the saturated adsorption amount of surfactant with constant concentration of surfactant molecules in the bulk phase, which can prevent surfactants aggregating in the bulk phase and get the atomic details of the interfacial structural change with increase of the adsorption amount through a single GCMD run. The adsorption of anionic surfactant sodium dodecyl sulfate (SDS) at the heptane-water interface was studied to validate the model. The saturated adsorption amount obtained from the GCMD simulation is consistent with the experimental results. The adsorption kinetics of SDS molecules during the simulation can be divided into three stages: linear adsorption stage, transition adsorption stage, and dynamic equilibrium stage. We also carried out equilibrium molecular dynamics (EMD) simulations to compare with GCMD simulation. This GCMD model can effectively reduce the simulation time with correct prediction of the interfacial saturation adsorption. We believe the GCMD method could be especially helpful for the computational study of surfactant adsorption under complex environments or emulsion systems with the adsorption of multiple types of surfactants.
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Affiliation(s)
- Xue-Dan Yang
- School of Chemical Engineering, Sichuan University, Chengdu, Sichuan 610065, China
- State Key Laboratory of Polymer Materials Engineering, Sichuan University, Chengdu, Sichuan 610065, China
- State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
| | - Wei Chen
- State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049,China
- Dalian National Laboratory for Clean Energy, Chinese Academy of Sciences, Dalian, Liaoning 116023, China
| | - Ying Ren
- State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049,China
- Innovation Academy for Green Manufacture, Chinese Academy of Sciences, Beijing 100190, China
| | - Liang-Yin Chu
- School of Chemical Engineering, Sichuan University, Chengdu, Sichuan 610065, China
- State Key Laboratory of Polymer Materials Engineering, Sichuan University, Chengdu, Sichuan 610065, China
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2
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Role of the Counterions in the Surface Tension of Aqueous Surfactant Solutions. A Computer Simulation Study of Alkali Dodecyl Sulfate Systems. COLLOIDS AND INTERFACES 2020. [DOI: 10.3390/colloids4020015] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We have investigated the surface tension contributions of the counterions, surfactant headgroups and tails, and water molecules in aqueous alkali dodecyl sulfate (DS) solutions close to the saturated surface concentration by analyzing the lateral pressure profile contribution of these components using molecular dynamics simulations. For this purpose, we have used the combination of two popular force fields, namely KBFF for the counterions and GROMOS96 for the surfactant, which are both parameterized for the SPC/E water model. Except for the system containing Na+ counterions, the surface tension of the surfactant solutions has turned out to be larger rather than smaller than that of neat water, showing a severe shortcoming of the combination of the two force fields. We have traced back this failure of the potential model combination to the unphysically strong attraction of the KBFF counterions, except for Na+, to the anionic head of the surfactants. Despite this failure of the model, we have observed a clear relation between the soft/hard character (in the sense of the Hofmeister series) and the surface tension contribution of the counterions, which, given the above limitations of the model, can only be regarded as an indicative result. We emphasize that the obtained results, although in a twisted way, clearly stress the crucial role the counterions of ionic surfactants play in determining the surface tension of the aqueous surfactant solutions.
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3
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Investigation of oil-in-water emulsion stability with relevant interfacial characteristics simulated by dissipative particle dynamics. Colloids Surf A Physicochem Eng Asp 2018. [DOI: 10.1016/j.colsurfa.2018.02.063] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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4
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Abrankó-Rideg N, Darvas M, Horvai G, Jedlovszky P. Immersion Depth of Surfactants at the Free Water Surface: A Computer Simulation and ITIM Analysis Study. J Phys Chem B 2013; 117:8733-46. [DOI: 10.1021/jp401749r] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Nóra Abrankó-Rideg
- Laboratory of Interfaces and
Nanosize Systems, Institute of Chemistry, Eötvös Loránd University, Pázmány P. Stny
1/A, H-1117 Budapest, Hungary
| | - Mária Darvas
- SISSA, Department of Biological and Statistical
Physics, 265 via Bonomea,
I-34136 Trieste, Italy
| | - George Horvai
- MTA-BME Research Group of Technical Analytical Chemistry, Szt. Gellért
tér 4, H-1111 Budapest, Hungary
- Department of Inorganic and
Analytical Chemistry, Budapest University of Technology and Economics, Szt. Gellért tér 4, H-1111
Budapest, Hungary
| | - Pál Jedlovszky
- Laboratory of Interfaces and
Nanosize Systems, Institute of Chemistry, Eötvös Loránd University, Pázmány P. Stny
1/A, H-1117 Budapest, Hungary
- MTA-BME Research Group of Technical Analytical Chemistry, Szt. Gellért
tér 4, H-1111 Budapest, Hungary
- EKF Department of Chemistry, Leányka u. 6, H-3300 Eger, Hungary
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5
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Kovalchuk K, Landman M, Masalova I. A Computational Study of the Succinimide Derivative Surfactant. J DISPER SCI TECHNOL 2013. [DOI: 10.1080/01932691.2012.695955] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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6
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Burlatsky SF, Atrazhev VV, Dmitriev DV, Sultanov VI, Timokhina EN, Ugolkova EA, Tulyani S, Vincitore A. Surface tension model for surfactant solutions at the critical micelle concentration. J Colloid Interface Sci 2013; 393:151-60. [DOI: 10.1016/j.jcis.2012.10.020] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2012] [Revised: 10/09/2012] [Accepted: 10/10/2012] [Indexed: 10/27/2022]
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7
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Physicochemical characterization of a monorhamnolipid secreted by Pseudomonas aeruginosa MA01 in aqueous media. An experimental and molecular dynamics study. Colloids Surf B Biointerfaces 2013; 101:256-65. [DOI: 10.1016/j.colsurfb.2012.06.035] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2011] [Revised: 06/26/2012] [Accepted: 06/29/2012] [Indexed: 11/19/2022]
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8
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Feng S, Bummer PM. Competition of hydrophobic steroids with sodium dodecyl sulfate, dodecyltrimethylammonium bromide, or dodecyl β-D-maltoside for the dodecane/water interface. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2012; 28:16927-16932. [PMID: 23151278 DOI: 10.1021/la303751e] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The surface tension lowering abilities of insoluble steroids, progesterone and testosterone, were examined at the dodecane/water interface in the presence and absence of surfactants, sodium dodecyl sulfate, dodecyltrimethylammonium bromide, and dodecyl maltoside. In the absence of these surfactants, the steroids significantly lowered the interfacial tension while exhibiting no activity at the air/water and air/dodecane surfaces. Further, in mixtures of surfactants and steroids, significant enhancement of interfacial tension lowering was observed. At a sufficiently high concentration of surfactant, no further lowering of tension was observed in the presence of the steroids. The synergistic effects on interfacial tension of steroids and surfactants were characterized by the free energy of transfer to the interface of each solute based on a two-dimensional solution equation of state. Assuming no significant interaction between the steroids and the surfactants in the interface, predictions of interfacial tensions were made based on the calculated free energies of transfer and interfacial area occupied. Good agreement was found between the predicted values and experimental values for interfacial tension. The results of these studies show that progesterone and testosterone, molecules not normally thought of as surface active, exhibit significant interfacial activity and can successfully compete with surfactants for the dodecane/water interface.
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Affiliation(s)
- Shaoxin Feng
- College of Pharmacy, University of Kentucky, Lexington, Kentucky 40536, USA
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9
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Emborsky CP, Cox KR, Chapman WG. Exploring parameter space effects on structure-property relationships of surfactants at liquid-liquid interfaces. J Chem Phys 2011; 135:084708. [DOI: 10.1063/1.3628452] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
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10
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Darvas M, Gilányi T, Jedlovszky P. Competitive Adsorption of Surfactants and Polymers at the Free Water Surface. A Computer Simulation Study of the Sodium Dodecyl Sulfate−Poly(ethylene oxide) System. J Phys Chem B 2011; 115:933-44. [DOI: 10.1021/jp110270c] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mária Darvas
- Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eötvös Loránd University, Pázmány P. Stny 1/A, H-1117 Budapest, Hungary
- Institut UTINAM—UMR CNRS 6213, Faculté des Sciences, Université de Franche-Comté, F-25030 Besançon Cedex, France
| | - Tibor Gilányi
- Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eötvös Loránd University, Pázmány P. Stny 1/A, H-1117 Budapest, Hungary
| | - Pál Jedlovszky
- Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eötvös Loránd University, Pázmány P. Stny 1/A, H-1117 Budapest, Hungary
- HAS Research Group of Technical Analytical Chemistry, Szt. Gellért tér 4, H-1111 Budapest, Hungary
- EKF Department of Chemistry, Leányka utca 6, H-3300 Eger, Hungary
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11
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Cheng T, Chen Q, Li F, Sun H. Classic Force Field for Predicting Surface Tension and Interfacial Properties of Sodium Dodecyl Sulfate. J Phys Chem B 2010; 114:13736-44. [DOI: 10.1021/jp107002x] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Tao Cheng
- School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Qing Chen
- School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Feng Li
- School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Huai Sun
- School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
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12
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Li Y, He X, Cao X, Zhao G, Tian X, Cui X. Molecular behavior and synergistic effects between sodium dodecylbenzene sulfonate and Triton X-100 at oil/water interface. J Colloid Interface Sci 2007; 307:215-20. [PMID: 17188285 DOI: 10.1016/j.jcis.2006.11.026] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2006] [Revised: 11/17/2006] [Accepted: 11/19/2006] [Indexed: 11/17/2022]
Abstract
Significant synergistic effects between sodium dodecylbenzene sulfonate (SDBS) and nonionic nonylphenol polyethylene oxyether, Triton X-100 (TX-100), at the oil/water interface have been investigated by experimental methods and computer simulation. The influences of surfactant concentration, salinity, and the ratio of the two surfactants on the interfacial tension were investigated by conventional interfacial tension methods. A dissipative particle dynamics (DPD) method was used to simulate the adsorption properties of SDBS and TX-100 at the oil/water interface. The experiment and simulation results indicate that ultralow (lower than 10(-3) mN m(-1)) interfacial tension can be obtained at high salinity and very low surfactant concentration. Different distributions of surfactants in the interface and the bulk solution corresponding to the change of salinity have been demonstrated by simulation. Also by computer simulation, we have observed that either SDBS or TX-100 is not distributed uniformly over the interface. Rather, the interfacial layer contains large cavities between SDBS clusters filled with TX-100 clusters. This inhomogeneous distribution helps to enhancing our understanding of the synergistic interaction of the different surfactants. The simulation conclusions are consistent with the experimental results.
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Affiliation(s)
- Ying Li
- Key Lab for Colloid and Interface Chemistry of State Education Ministry, Shandong University, Jinan 250100, People's Republic of China
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13
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López-Díaz D, García-Mateos I, Velázquez MM. Surface properties of mixed monolayers of sulfobetaines and ionic surfactants. J Colloid Interface Sci 2006; 299:858-66. [PMID: 16563413 DOI: 10.1016/j.jcis.2006.02.030] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2005] [Revised: 02/10/2006] [Accepted: 02/14/2006] [Indexed: 10/24/2022]
Abstract
To study the influence of the head group in the properties of the mixed monolayers adsorbed at the air-water interface, the surface tension and surface potential of binary mixtures of surfactant have been determined as a function of the surfactant composition. Experiments were carried out with anionic-zwitterionic sodium dodecyl sulfate and dodecyl dimethyl ammoniopropane sulfonate (SDS/DDPS), and cationic-zwitterionic dodecyl trimethylammonium bromide and dodecyl dimethyl ammoniopropane sulfonate (DTAB/DDPS), and dodecyl trimethylammonium bromide and tetradecyl dimethyl ammoniopropane sulfonate (DTAB/TDPS). It was shown that mixed monolayers of cationic-zwitterionic surfactant exhibit small negative deviations of ideal behavior, whereas for SDS/DDPS monolayers show strong negative deviation from the ideality. Deviations of ideal behavior are interpreted by regular solution theory. The surface potential values agree very well with the concentration of the ionic component at the interface. The dynamic surface tension values show that the adsorption kinetics on the interface is a diffusion-controlled process. In monolayers with significant deviation of the ideal behavior, anionic-zwitterionic, there is some evidence of intermolecular attractions after diffusion of both surfactants at the interface.
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Affiliation(s)
- David López-Díaz
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad de Salamanca, Plaza de los Caídos s/n, 37008 Salamanca, Spain
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14
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Domínguez H. Computer Studies on the Effects of Long Chain Alcohols on Sodium Dodecyl Sulfate (SDS) Molecules in SDS/Dodecanol and SDS/Hexadecanol Monolayers at the Air/Water Interface. J Phys Chem B 2006; 110:13151-7. [PMID: 16805627 DOI: 10.1021/jp062018n] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Molecular dynamics simulations of sodium dodecyl sulfate (SDS)/dodecanol and SDS/hexadecanol monolayers at the air/water interface were investigated where the monolayer mixtures were prepared by two different configurations. In the first configuration, all of the dodecanol (or hexadecanol) molecules were placed together and also the SDS molecules were placed together in the surface area. In the second configuration, the dodecanol (or hexadecanol) molecules were uniformly distributed with the SDS molecules, forming a homogeneous mixture. The results showed that the alcohol tails are more ordered and thicker than the SDS tails in monolayers where the alcohol molecules are close to each other and separated from the SDS. However, the reverse trend is observed in monolayers where the SDS and alcohol molecules are well mixed; that is, the alcohol tails seem to have less order. Studies of how the SDS tails are affected by the presence of long chain alcohols are also discussed. Basically, by increasing the alcohol chain length, the order and the thickness of the SDS tails increased when those molecules were placed all together in a region of the surface area. When both surfactants were well mixed, the order and thickness of the SDS chains decreased as the alcohol chain length increased. Comparisons of the present results with actual experiments of similar systems were performed, and they showed similar tendencies.
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Affiliation(s)
- Héctor Domínguez
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México (UNAM), México, D.F. 04510.
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15
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Sodium dodecyl sulfate-modified carbon paste electrodes for selective determination of dopamine in the presence of ascorbic acid. Bioelectrochemistry 2006; 70:408-15. [PMID: 16843072 DOI: 10.1016/j.bioelechem.2006.05.011] [Citation(s) in RCA: 114] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2006] [Revised: 04/05/2006] [Accepted: 05/29/2006] [Indexed: 11/21/2022]
Abstract
A carbon paste electrode (CPE) modified by a monolayer film of sodium dodecyl sulfate (SDS) was used for detection of dopamine (DA). Cyclic voltammetry demonstrated improved response of the DA sensor. This suggests the effectivity of surface modification of CPE by SDS. Impedance spectroscopy was used for the characterization of CPE surface properties. The effect of SDS concentration on the electrode quality also reveals that SDS formed a monolayer on CPE surface with a high density of negative-charged end directed outside the electrode. As a result, the carbon paste electrode modified with SDS (SDS/CPE) exerted discrimination against ascorbic acid in physiological circumstance. Thus, it can selectively determine dopamine even in the presence of 220-fold AA combined with differential pulse stripping voltammetry. In pH 7.40 phosphate buffer solution, the oxidation peak current on differential pulse voltammograms increases linearly with the concentration of DA in the range of 5.0 x 10(-7) to 8.0 x 10(-4) mol . L(-1) with a detection limit of 5.0 x 10(-8) mol . L(-1). Satisfying results are achieved when detecting the DA in injection and simulated biology sample.
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16
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Dominguez H, Goicochea AG, Mendoza N, Alejandre J. Computer simulations of surfactant monolayers at solid walls. J Colloid Interface Sci 2006; 297:370-3. [PMID: 16289187 DOI: 10.1016/j.jcis.2005.10.020] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2005] [Revised: 10/12/2005] [Accepted: 10/16/2005] [Indexed: 10/25/2022]
Abstract
A series of molecular dynamics simulations to study the structure of a surfactant monolayer near real surfaces was carried out. A comparison of two different surfaces, TiO2 and SiO2, with the same monolayer was performed. Moreover, each surface was modeled by two different approaches, the first model considers the complete structure of a TiO2 (or SiO2) wall, whereas the second model is a continuous solid wall with an effective potential. Both wall models give essentially the same monolayer configuration suggesting that the explicit form of the wall does not play a relevant role to study the structure of surfactant monolayers close to planar surfaces.
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Affiliation(s)
- Hector Dominguez
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, UNAM, Ciudad Universitaria, Coyoacan México, DF 04510, Mexico.
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Li Y, Zhang P, Dong FL, Cao XL, Song XW, Cui XH. The array and interfacial activity of sodium dodecyl benzene sulfonate and sodium oleate at the oil/water interface. J Colloid Interface Sci 2005; 290:275-80. [PMID: 15927196 DOI: 10.1016/j.jcis.2005.04.035] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2005] [Revised: 04/07/2005] [Accepted: 04/09/2005] [Indexed: 10/25/2022]
Abstract
There is a close correlation between the interfacial activity and the adsorption of the surfactant at the interface, but the detailed molecular standard information was scarce. The interfacial activity of two traditional anionic surfactants sodium dodecyl benzene sulfonate (SDBS) and sodium oleate (OAS) were studied by experimental and computer simulation methods. With the spinning drop method and the suspension drop method, the interfacial tension of oil/aqueous surfactant systems was measured, and the influence of surfactant concentration and salinity on the interfacial tension was investigated. The dissipative particle dynamics (DPD) method was used to simulate the adsorption of SDBS and OAS at the oil/water interface. It was shown that it is beneficial to decrease interfacial tension if the hydrophobic chains of the surfactant and the oil have similar structure. The accession of inorganic salts causes surfactant molecules to form more compact and ordered arrangements and helps to decrease the interfacial tension. There is an osculation relation between interfacial density and interfacial activity. The interfacial density calculated by molecular simulation is an effective parameter to exhibit the interfacial activity.
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Affiliation(s)
- Ying Li
- School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, People's Republic of China
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18
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Domínguez H, Rivera M. Mixtures of sodium dodecyl sulfate/dodecanol at the air/water interface by computer simulations. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2005; 21:7257-62. [PMID: 16042450 DOI: 10.1021/la046926s] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Molecular dynamics simulations of monolayers of surfactant mixtures at the air/water interface were performed where the binary mixture was composed of sodium dodecyl sulfate (SDS) and dodecanol molecules. At the same ratio of SDS and dodecanol molecules, two monolayer mixtures were prepared. In the first monolayer, all the dodecanol molecules were placed together in the center of the simulation box, whereas in the second monolayer, those molecules were uniformly distributed in the surface area in such a way that they were far from each other. Simulations of both systems indicate that the dodecanol tails in the first monolayer are straighter and more ordered than those in the second monolayer. From the present results, we observed new insights of how the different molecules should array or distribute at the interface in real systems. Finally, studies of the interfacial water around the different surfactants were also analyzed, showing that they are closer to the polar headgroups of dodecanol than to the SDS headgroups.
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Affiliation(s)
- Hector Domínguez
- Instituto de Investigaciones en Materiales, UNAM, Universidad Nacional Autónoma de México, México, D.F. 04510.
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