The document summarizes research conducted by Alejandro Gil Villegas of the University of Guanajuato's Department of Physical Engineering on predicting phase diagrams of fluids using thermodynamic perturbation theory and Monte Carlo simulations. Some key points:
- The research combines thermodynamic perturbation theory and Monte Carlo simulations to predict phase diagrams of mixtures of fluids.
- Gil Villegas' department offers degrees in physics, physical engineering, chemical engineering, and biomedical engineering at both the undergraduate and postgraduate levels.
- The research focuses on associating fluids, using theories like SAFT (Statistical Associating Fluid Theory) to model interactions.
- Applications include modeling asphaltene precipitation and predicting phase equ
Some reactions seem to obvious to fail, so what happens when they do? Quantum calculations yield invaluable insight to the nature of a reaction mechanism.
Presented at the Virtual Conference on Computational Chemistry VCCC 2014
Credit due to Guillermo Caballero on whose BSc thesis this presentation is based.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Some reactions seem to obvious to fail, so what happens when they do? Quantum calculations yield invaluable insight to the nature of a reaction mechanism.
Presented at the Virtual Conference on Computational Chemistry VCCC 2014
Credit due to Guillermo Caballero on whose BSc thesis this presentation is based.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
A quantitative structure-activity relationship
(QSAR) correlates measurable or calculable
physical or molecular properties to some
specific biological activity in terms of an
equation.
The manipulation and analysis of chemical structural information is made possible through the use of molecular descriptors.
These are numerical values that characterise properties of molecules.
For example, they may represent the physicochemical properties of a molecule or they may be values that are derived by applying algorithmic techniques to the molecular structures.
Many different molecular descriptors have been described and used for a wide variety of purposes.
They vary in the complexity of the information they encode and in the time required to calculate them.
In general, the computational requirements increase with the level of discrimination that is achieved. For For example, the molecular weight does not convey much about a molecule’s properties but it is very rapid to compute.
By contrast, descriptors that are based on quantum mechanics may provide accurate representations of properties, but they are much more time consuming to compute.
Some descriptors have an experimental counterpart (e.g.the octanol–water partition coefficient), whereas others are purely algorithmic constructs (e.g. 2D fingerprints).
The screening of chemical libraries with traditional methods, such as high-throughput screening (HTS), is expensive and time consuming. Quantitative structure–activity relation (QSAR) modeling is an alternative method that can assist in the selection of lead molecules by using the information from
reference active and inactive compounds. This approach requires good molecular descriptors that are representative of the molecular features responsible for the relevant molecular activity.
Thermodynamic Assessment (Suggestions) Of the Gold-Rubidium SystemIRJESJOURNAL
Abstract: Thermodynamic modellings of the Au–Rb system was carried out by means of the CALPHAD (calculation of phase diagrams) method. The liquid phase and the intermetallic compounds Au5Rb, Au2Rb, AuRb and Au7Rb3 and Au3Rb2 (new compounds) in addition to the compound AuRb2 (suspected compound) are taken into consideration in this optimization. The substitutional solution model was used to describe the liquid phase. The six compounds are treated as stoichiometric phases. The enthalpies of formation used in these optimizations were calculated within ab-initio method in precedent work
This is a PRESENTATION just to help students to easily understand one of the method of drug designing i.e. QSAR.. this is a combination of many slides and books..this is not my personal.
la importancia y la funcion ademas de lso tipos de iimplantes hacen parte de la estetica y rehabilitacion de la persona , devolviendole su aspecto emocional social y mas que todo funcional , ademas de comodidad y ventajas como la oseointegracion , teniendo en cuenta las desventajas como precio
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
A quantitative structure-activity relationship
(QSAR) correlates measurable or calculable
physical or molecular properties to some
specific biological activity in terms of an
equation.
The manipulation and analysis of chemical structural information is made possible through the use of molecular descriptors.
These are numerical values that characterise properties of molecules.
For example, they may represent the physicochemical properties of a molecule or they may be values that are derived by applying algorithmic techniques to the molecular structures.
Many different molecular descriptors have been described and used for a wide variety of purposes.
They vary in the complexity of the information they encode and in the time required to calculate them.
In general, the computational requirements increase with the level of discrimination that is achieved. For For example, the molecular weight does not convey much about a molecule’s properties but it is very rapid to compute.
By contrast, descriptors that are based on quantum mechanics may provide accurate representations of properties, but they are much more time consuming to compute.
Some descriptors have an experimental counterpart (e.g.the octanol–water partition coefficient), whereas others are purely algorithmic constructs (e.g. 2D fingerprints).
The screening of chemical libraries with traditional methods, such as high-throughput screening (HTS), is expensive and time consuming. Quantitative structure–activity relation (QSAR) modeling is an alternative method that can assist in the selection of lead molecules by using the information from
reference active and inactive compounds. This approach requires good molecular descriptors that are representative of the molecular features responsible for the relevant molecular activity.
Thermodynamic Assessment (Suggestions) Of the Gold-Rubidium SystemIRJESJOURNAL
Abstract: Thermodynamic modellings of the Au–Rb system was carried out by means of the CALPHAD (calculation of phase diagrams) method. The liquid phase and the intermetallic compounds Au5Rb, Au2Rb, AuRb and Au7Rb3 and Au3Rb2 (new compounds) in addition to the compound AuRb2 (suspected compound) are taken into consideration in this optimization. The substitutional solution model was used to describe the liquid phase. The six compounds are treated as stoichiometric phases. The enthalpies of formation used in these optimizations were calculated within ab-initio method in precedent work
This is a PRESENTATION just to help students to easily understand one of the method of drug designing i.e. QSAR.. this is a combination of many slides and books..this is not my personal.
la importancia y la funcion ademas de lso tipos de iimplantes hacen parte de la estetica y rehabilitacion de la persona , devolviendole su aspecto emocional social y mas que todo funcional , ademas de comodidad y ventajas como la oseointegracion , teniendo en cuenta las desventajas como precio
Presentación SRI Proyecto de Ley solidaria y de corresponsabilidad ciudadana ...Rocío Albán Torres
La Comisión de Régimen Económico y Tributario, su Regulación y Control en sesión Nª095 recibió en comisión generel al Econ. Leonardo Orlando representante máximo del SRI. Compartimos la presentación realizada.
Proyecto de ley solidaria y de corresponsabilidad ciudadana por las afectacio...Rocío Albán Torres
Se designó a la Comisión de Régimen Económico Tributario, su Regulación y Control para el tratamiento de este proyecto de ley calificado como URGENTE en materia económica.
5353The Molecular Structures and Thermodynamic Functions.docxtroutmanboris
5353
The Molecular Structures and Thermodynamic Functions
of 2-Methylbutane and 2,3-Dimethylbutane
Richard H. Boyd
Contribution from the Department of Chemical Engineering and the
Department of Materials Science and Engineering,
University of Utah, Salt Lake City, Utah 84112. Received September 16, 1974
Abstract: Previous values of the stabilities of the conformational isomers of 2-methylbutane and 2,3-dimethylbutane as in-
ferred from the Raman spectra and the thermodynamic functions of these compounds have not been in accord with confor-
mational concepts as expressed by the number of gauche (skew methyl) interactions. Recent Raman studies have removed
some previous ambiguities and have resulted in improved values of the conformational isomer stabilities which show that
they cannot be accounted for in terms of numbers of gauche interactions alone. Further, the redetermined stability of the 2-
methylbutane conformers is not in accord with previous interpretation of the thermodynamic functions. In the present work,
we show that the isomer stabilities, the thermodynamic functions, and the conformational energy minimization calculations
are all in reasonable mutual accord. It is emphasized that valence angle distortion is important in reducing gauche strain and
accounts for the lack of correlation with the number of gauche interactions.
Interest in the interpretation and prediction of the con-
formational properties of complex organic molecules and
polymers has focused a great deal of attention on the prop-
erties of those relatively few simple molecules whose prop-
erties have been studied thoroughly experimentally. Ob-
viously, methods for property prediction must work well on
these “test” molecules if we are to have confidence in pre-
dictions on more complex molecules. Two examples of the
apparent failure of current qualitative concepts of hydro-
carbon structure have been the properties of 2-methylbu-
tane and 2,3-dimethylbutane. The series «-butane, 2-meth-
ylbutane, and 2,3-dimethylbutane each should have two
conformational isomers. The conformers of each molecule
differ by one gauche (skew methyl) interaction (see Table I
and Figures 1, 2, and 3). Hence, the difference in energy
between each isomer pair should, on this basis, be nearly the
same. In the case of «-butane, it has been known for some
time that both the intensity of the Raman vibrational
bands1 and the thermodynamic functions2 (S° and Cp°) are
in accord with the gauche isomer being ~800 cal more en-
ergetic than the trans. This value along with values3 from
«-pentane and «-hexane forms the basis of much of the cur-
rent interpretation of hydrocarbon conformational proper-
ties. However, the situation with respect to 2-methylbutane
and 2,3-dimethylbutane has been perplexing. In earlier
work, the Raman spectrum of 2-methylbutane indicated an
energy difference of ~100 cal between conformers.4 How-
ever, from analysis of the thermodynamic functions (S°,
Cp°) Scott et al.5 con.
Shortcut Design Method for Multistage Binary Distillation via MS-ExceIJERA Editor
Multistage distillation is most widely used industrial method for separating chemical mixtures with high energy consumptions especially when relative volatility of key components is lower than 1.5. The McCabe Thiele is considered to be the simplest and perhaps most instructive method for the conceptual design of binary distillation column which is still widely used, mainly for quick preliminary calculations. In this present work, we provide a numerical solution to a McCabe-Thiele method to find out theoretical number of stages for ideal and non-ideal binary system, reflux ratio, condenser duty, reboiler duty, each plate composition inside the column. Each and every point related to McCabe-Thiele in MS-Excel to give quick column dimensions are discussed in details
We show that for MS/MS analysis using quadrupole collision cells, tuning the collision cell RF amplitude for each SRM (or MRM) transition can increase, sometimes by greater than 2X, the signal at the detector.
AN IMPLEMENTATION FOR FRAMEWORK FOR CHEMICAL STRUCTURE USING GRAPH GRAMMAR | ...Journal For Research
Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach to modeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like merging, splitting, and isomerisation of molecules. In this paper a generic approach for composing graph grammar rules to define a chemically useful rule compositions. We iteratively apply these rule compositions to elementary transformations in order to automatically infer complex transformation patterns.
The Futures of the Physic-Chemical and Thermoelectric Properties of the InTe-...theijes
By the methods of the physic-chemical analysis as well the measurements of microhadness and picknomentric density the semiconducting system InTe-Cu2ZnSnS4 has been investigated and its state diagram has been plotted. Guazibinarity of the system with restricted homogeneous fields has established on the basis of both initial components. The boundaries of solid solutions at 300K reach on side of InTe ~ 2mol% and on side of Cu2ZnSnS4 ~ 13mol%. The coordinates of the system eutectic correspond to the composition ~23mol% Cu2ZnSnS4 and temperature ~813K. A study of thermoelectric and galvanomagnetic parameters of solid solutions (InTe)1-x(Cu2ZnSnS4)x showed dispersion of electrons from the ionized admixture at low temperatures, and at higher temperatures from thermal vibrations of crystalline lattice. Heat transfer takes place according to one-phonon mechanism. The alloy of solid solution (InTe)0,98(Cu2ZnSnS4)0,02 possesses a high value of thermoelectric efficiency.
This is the plenary talk given by Prof Shyue Ping Ong at the 57th Sanibel Symposium held on St Simon's Island in Georgia, USA.
Abstract: Powered by methodological breakthroughs and computing advances, electronic structure methods have today become an indispensable toolkit in the materials designer’s arsenal. In this talk, I will discuss two emerging trends that holds the promise to continue to push the envelope in computational design of materials. The first trend is the development of robust software and data frameworks for the automatic generation, storage and analysis of materials data sets. The second is the advent of reliable central materials data repositories, such as the Materials Project, which provides the research community with efficient access to large quantities of property information that can be mined for trends or new materials. I will show how we have leveraged on these new tools to accelerate discovery and design in energy and structural materials as well as our efforts in contributing back to the community through further tool or data development. I will also provide my perspective on future challenges in high-throughput computational materials design.
Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...
TYC
1. Predicting phase diagrams of fluids combining
Thermodynamic Perturbation Theory
and
Monte Carlo computer simulations.
Alejandro Gil Villegas
Department of Physical Engineering
University of Guanajuato
México
Thomas Young Centre
November 2015
5. Associating Fluids
Ludwig Boltzmann, Lectures in gas theory (1895)
Modelos de sistemas asociativos
Michael Wertheim, “Fluids with highly directional attractive forces”
J. Stat. Phys. 35, 19 (1984)
6. Conclusiones
To exclude all knowledge but that which has already been applied
to immediate utility, would be to reduce our faculties to a state of
servitude, and to frustrate the very purposes which we are laboring
to accomplish. No discovery, however remote in its nature from the
subjects of daily observation, can with reason be declared wholly
inapplicable to the benefit of mankind.
Thomas Young
A course of lectures on Natural Philosophy and the Mechanical Arts (1807).
RIFUG 2013 Hooke,Young & Gibbs
7. W. Chapman, K. Gubbins, G. Jackson, M. Radosz, Fluid Phase Equil. 52, 31 (1989)
W. Chapman, K. Gubbins, G. Jackson, M. Radosz, Ind. Eng. Chem. Res. 29, 1709 (1990)
SAFT: Statistical Associating Fluid Theory
Fluidos Asociativ
Michael Wertheim:
Fluids with highly directional attractive
J. Stat. Phys. (1984-1986)
A
NkT
=
Aideal
NkT
Amonomers
NkT
Achain
NkT
Aassoc
NkT
Yukawa:Yukawa:
SAFT-VRSAFT-VR
11. OH
σ
Buenrostro, Lira, Gil-Villegas & WuBuenrostro, Lira, Gil-Villegas & Wu
AIChE JAIChE J 50, 255250, 2552 (2004)(2004)
SAFT-VR prediction for asphaltene precipitationSAFT-VR prediction for asphaltene precipitation
from titration data of oil Y3 with n-heptane. Values of the new
parameters are AA/k ϭ 2062.21 K and AR/k ϭ 2359.43 K. No
other assumptions or parameter modifications were used.
The predicted precipitation curves for oil Y3 resulted within
10% error of the experimental data for precipitant/oil ratios Ն 10.
However, for lower ratios, there are larger deviations from the
experimental values, even though the model reproduces the de-
crease of the precipitation as the carbon number of the precipitant
increases. As mentioned earlier, for the prediction of the precipi-
tation in oil Y3, it was not necessary to refit the parameters related
to the mean-attractive energy (the Hamaker constants and the
range of the mean-force potentials). These results can be explained
in terms of the similar properties and composition of C1 and Y3
crude oils and the use of the same values for the asphaltene and
resin properties (Table 1), considering that both oils are produced
To model asphaltene precipitation in
certain T and P conditions, the vapor–liqu
culation of the reservoir fluid is first perfo
equation of state, to obtain the composition
of the liquid phase at equilibrium. Then, us
resin–oil model system described before,
analysis is applied to find out the onset of
tation. When asphaltene precipitation appe
precipitated material is calculated by solvi
equilibrium equations.
Calculation of Medium Properties. F
(2000), the volume-shifted Peng–Robinson
al., 1982; Peng and Robinson, 1976) was
vapor–liquid–equilibrium to obtain the de
tion of the liquid phase. Recommended va
Figure 10. Comparison between experimental and predicted APE for live oil C1.E. Buenrostro, C. Lira, A. Gil-Villegas and J. Wu, AIChE J 50, 2552 (2004).
effective spherical potential given by the following
expression:16
where r is the distance between the centers of mass
(CM) of each molecule with facing parallel aromatic
regions, and Z1, Z2 are the number of atoms in each
molecule. The parameters C1, C2, R, β, and γ were
obtained by fitting eq 1 to the corresponding MM
numerical values (T ) 0 K, in vacuum). Figure 2
displays the A-A, A-R, and R-R intermolecular po-
tentials generated according to the previous discus-
sion.16 The symbols correspond to the MM numerical
values and the continuous curves to the best over-all
fit found with eq 1. Note that within this spherical
approximation for the interactions, asphaltenes and
resins are considered as entities without internal struc-
ture in the MD simulations described further below.
Thus we shall be only concerned with the A-A, A-R,
and R-R spatial distributions in terms of the molecular
CM positions.
The embedding medium is accounted for through a
mean field approximation given by its dielectric con-
stant, ϵ, affecting only the Coulomb and London con-
tributions. The use of an effective medium through its
dielectric constant is known to be questionable for
intermolecular distances of the order of the molecular
size, mainly because it is at these distances where
atomic detail becomes important.18 However, it is still
a valuable first exploratory means to account for the
screening of Coulomb and London interactions due to
the embedding medium for intermediate to large inter-
molecular distances. It is deemed that the initial stages
of aggregation will correlate strongly with the long-
range interactions. As the interacting molecules become
closer to each other the molecular structure of the
solvent is more apparent and local effects become
important. These local interactions may be dominant
in defining the structure of an aggregate, solvation free
energies, possible chemical reactions, etc. Hence, the use
of an effective medium in our case has its aim in looking
at the evolution of aggregation from its initial stages
and extrapolating the behavior of the system in its final
“gross” equilibration (see further below).
Molecular Dynamics Simulations. The intermo-
lecular potentials described in the previous section were
used in a canonical molecular dynamics (MD) simula-
tion for mixtures of asphaltene/resin in different host
media. Our model system consists of NAs and NRe
(18) Smith, P. E.; Pettitt, M. B. J. Phys. Chem. 1994, 98, 9700.
Figure 1. Molecular models used in this work. (a) 3D diagram
of the MM-optimized asphaltene structure (C57H63N1S1) re-
ported in ref 7 showing an aromatic region (continuous lines)
and its aliphatic chain (dashed lines). (b) Transverse view of
the asphaltene structure showing the aromatic region in more
detail. (c) Diagram showing the resin structure (C13H10S1)
reported in ref 5.
V(r) )
Z1Z2
ϵr
(e-Rr
+ C1ϵre-βr
) -
C2
ϵ2
r6
e-γ/r4
(1)
Figure 2. Intermolecular potential curves in a vacuum for
the most favorable relative orientation (see text) between
asphaltene-asphaltene (A-A), asphaltene-resin (A-R), and
resin-resin (R-R). Symbols correspond to MM calculations.
Continuous curve: best fit using eq 1 according to ref 16.
12. Lauric Acid
+ Methanol + Water
Methy Laureate
F. Perdomo, B. Millán, G. Mendoza & A. Gil-VillegasF. Perdomo, B. Millán, G. Mendoza & A. Gil-Villegas
J. Mol. Liq.J. Mol. Liq. 185, 8 (2013).185, 8 (2013).
F. Perdomo, B. Millan, G. Mendoza, A. Gil-Villegas, J. Mol. Liq. 185, 8 (2013)
respect to the theoretical predictions a
with water, since integrals are inaccurate.
compounds: circles for lauric acid, square
for methyl laurate. From Figs. 2B and 3A w
reacting method is consistent with the exp
viations are noted for the biodiesel compo
tailed study, both experimental and the
case. With exception of this point, the agr
experiment is very good.
An expanded version of Fig. 2B is give
retical predictions are given for higher va
this figure, the molar fraction for lauric
R=6. The production of methyl laurate
that enable us to determine the optimal r
tive compositions. This information is of g
of an esterification reactor, and these re
tage of a molecular thermodynamic theor
predictions for compositions that maxim
6. Conclusions
We have presented in this article a the
proach for the prediction of reactive equ
compounds, that was applied to the est
order to test the predictions, experimenta
tion were measured from an experiment
an esterification batch reactor. The molar
Lauric Acid Methanol
Methyl Laurate
Methanol
Lauric Acid
Methyl Laurate
B
Fig. 2. Predicted chemical equilibrium manifold for the esterification of lauric acid with
methanol to produce methyl laureate and water, for atmospheric pressure at experimen-
tal conditions (0.83 atm) and temperature T=338.4 K. Experimental chemical reactions
correspond to reactive relation values R=0.125, 0.166, 0.250 and 1.0 (square, triangle,
circle and rhombus, respectively). Theoretical predictions are given by a dotted and
solid lines in (A) and (B), respectively. Figure (A) corresponds to the four-vertex chemical
equilibrium manifold whereas (B) is the projection onto the lauric acid-methanol-methyl
Fig. 3. Molar fraction of reactants and products (χ) a
(R). In figure (A) dotted, dashed and solid lines corr
acid, methanol and methyl laurate, respectively, wh
noted by circles, squares and triangles, respectively
for lauric acid; in the case of the other two species t
the symbol size. Theoretical predictions are given f
SAFT-VR Reactive System
13. Niels Bohr (1885-1962)
On the Constitution of Atoms and Molecules
Phil. Mag. 26, 1 (1913); 26, 476 (1913); 26, 857 (1913)
17. Eugene Wigner (1902-1995)
Symmetry properties in Quantum Mechanics
Wigner-D matrix
Wigner-Seitz cell
Metallic phase of hydrogen
The Unreasonable Effectiveness of Mathematics
in the Natural Sciences (1960).
18. Wigner-Kirkwood first-order QLJ potential
uLJ r( )= 4ε
σ
r
⎛
⎝⎜
⎞
⎠⎟
12
−
σ
r
⎛
⎝⎜
⎞
⎠⎟
6
⎡
⎣
⎢
⎤
⎦
⎥ u r( )= uLJ r( )+
Λ2
48π2
T *
∇2
uLJ r( )
Λ =
h
σ mε
λB =
Λσ
2πT *
r σ
u r( )
ρ*
T*
WK-1 pair potential for Ne, D2, H2 and He-IV
T* = 0.60
GEMC simulations and Wegner’s expansion
for the LV coexistence curves (WK-1 systems)
V.M. Trejos, A. Martínez, A. Gil-Villegas, J. Chem. Phys. 139, 184505 (2013)
19. Confined fluids
Classical Lennard-Jones system
V.M. Trejos, A. Martínez, A. Gil-Villegas, J. Chem. Phys. 139, 184505 (2013)
Y. Liu, A. Z. Panagiotopoulos, P. Debenedetti, J. Chem. Phys. 132, 144107 (2010)
A. Trokhymchuk, J. Alejandre, J. Chem. Phys. 111, 8510 (1999)
21. i!
∂ψ
∂t
= ˆHψ t → i!β
∂ ˆρ
∂β
= − ˆH ˆρ
x
t
Path Integral Method
R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948)
S. F. Edwards, Proc. Phys. Soc. 85, 613 (1965)
D. Chandler, P. G. Wolynes, J. Chem. Phys. 74, 4078 (1981)
27. βWNP =
πP
λB
2
ri
t
− ri
t+1
( )
2
t
P
∑
i
N
∑ + βWI
Crude propagator
Kinetic contribution = Diffraction term
Corrected propagators
pair interactions contribution
Improving kinetic term
Modelling diffraction of thermal waves
36. Aads
NkT
= a2D − ln
λwallσ
λB
⎛
⎝⎜
⎞
⎠⎟ + βuwall
Abulk
NkT
= a3D
µads = µbulk
Adsorption of CO2 + CH4 and Asphalte
CO2 + CH4/
activated carbon
Asphaltenes/
Dolomite Rock
M. Castro, A. Mart´ınez, A. Gil-Villegas, AST 29, 59 (2011).
M. Castro, J.L. Mendoza, E. Buenrostro-Gonz´alez, S. L´opez-Rodr´ıguez, A. Gil-Villegas, Fluid Pha
M. Sudibandriyo, Z. Pan, J.E. Fitzgerald, R.L. Robinson Jr., K.A.M. Gasem, Langmuir 19, 5323
Thermodynamics 2013 Confined fluids with quantu
SAFT-VR
Experimental data
C/mg/L
AmountAdsorbed/mg/m2
Adsorption Theory
CH4 + CO2 / activated carbon Asphaltenes /Dolomite Rock
bulk phase
adsorbed phase
M. Castro, A. Martínez, A. Gil-Villegas, Ads. Sci. & Techn. 29, 59 (2011)
M. Castro, J. L. Mendoza, E. Buenrostro, S. López, A. Gil-Villegas, Fluid Phase Equil. 286, 113 (2009)
F. del Río, A. Gil-Villegas, J. Phys. Chem. 95, 787 (1991)
40. Exchange Contribution
Indistinguishability
of identical particles
e
−βAQ
=
1
N!
drN
rN
e−β ˆH
rN
∫
Ρ12 rN
= Ρ12 r1 r2 ... rN = ± r2 r1 ... rN
Exchange effects are equivalent to associating ring polymers
D. Chandler & P. G. Wolynes, J. Chem. Phys. 74, 4078 (1981)
41. Felipe Perdomo
Guadalupe Jiménez
Joel
Tavera
César Serna
Jonatan
Suaste
Eduardo Buenrostro,
Mexican Institute of Petroleum
Carlos Ariel Cardona,
National University of Colombia
Gerardo Gutiérrez,
University of Guanajuato
Gerardo
Campos
Mario
Becerra
Victor Manuel Trejos
Francisco
Espinosa
Job
Lino