1
|
Jadrich RB, Lindquist BA, Truskett TM. Treating random sequential addition via the replica method. J Chem Phys 2022; 157:084116. [DOI: 10.1063/5.0096276] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.
Collapse
Affiliation(s)
| | | | - Thomas M. Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, United States of America
| |
Collapse
|
2
|
Stadik A, Kahl G. Deformable hard particles confined in a disordered porous matrix. J Chem Phys 2021; 155:244507. [PMID: 34972368 DOI: 10.1063/5.0068680] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
With suitably designed Monte Carlo simulations, we have investigated the properties of mobile, impenetrable, yet deformable particles that are immersed into a porous matrix, the latter one realized by a frozen configuration of spherical particles. By virtue of a model put forward by Batista and Miller [Phys. Rev. Lett. 105, 088305 (2010)], the fluid particles can change in their surroundings, formed by other fluid particles or the matrix particles, their shape within the class of ellipsoids of revolution; such a change in shape is related to a change in energy, which is fed into suitably defined selection rules in the deformation "moves" of the Monte Carlo simulations. This concept represents a simple yet powerful model of realistic, deformable molecules with complex internal structures (such as dendrimers or polymers). For the evaluation of the properties of the system, we have used the well-known quenched-annealed protocol (with its characteristic double average prescription) and have analyzed the simulation data in terms of static properties (the radial distribution function and aspect ratio distribution of the ellipsoids) and dynamic features (notably the mean squared displacement). Our data provide evidence that the degree of deformability of the fluid particles has a distinct impact on the aforementioned properties of the system.
Collapse
Affiliation(s)
- Alexander Stadik
- Institute for Theoretical Physics and Center for Computational Materials Science (CMS), Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
| | - Gerhard Kahl
- Institute for Theoretical Physics and Center for Computational Materials Science (CMS), Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
| |
Collapse
|
3
|
Patsahan O, Patsahan T, Holovko M. Vapour-liquid critical parameters of a 2:1 primitive model of ionic fluids confined in disordered porous media. J Mol Liq 2018. [DOI: 10.1016/j.molliq.2017.12.033] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
4
|
Qiao CZ, Zhao SL, Liu HL, Dong W. Fluids in porous media. IV. Quench effect on chemical potential. J Chem Phys 2017. [PMID: 28641429 DOI: 10.1063/1.4984773] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
It appears to be a common sense to measure the crowdedness of a fluid system by the densities of the species constituting it. In the present work, we show that this ceases to be valid for confined fluids under some conditions. A quite thorough investigation is made for a hard sphere (HS) fluid adsorbed in a hard sphere matrix (a quench-annealed system) and its corresponding equilibrium binary mixture. When fluid particles are larger than matrix particles, the quench-annealed system can appear much more crowded than its corresponding equilibrium binary mixture, i.e., having a much higher fluid chemical potential, even when the density of each species is strictly the same in both systems, respectively. We believe that the insight gained from this study should be useful for the design of functionalized porous materials.
Collapse
Affiliation(s)
- C Z Qiao
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Chimie, UMR 5182, 46, Allée d'Italie, 69364 Lyon Cedex 07, France
| | - S L Zhao
- School of Chemical Engineering and State Key Laboratory of Chemical Engineering, East China University of Science and Technology, 130 Meilong Road, 200237 Shanghai, China
| | - H L Liu
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, 130 Meilong Road, 200237 Shanghai, China
| | - W Dong
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Chimie, UMR 5182, 46, Allée d'Italie, 69364 Lyon Cedex 07, France
| |
Collapse
|
5
|
Ciach A, Hall CK, Kahl G, Lomba E. Fifty years of liquid state physics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:410301. [PMID: 27545863 DOI: 10.1088/0953-8984/28/41/410301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
|
6
|
Holovko MF, Patsahan O, Patsahan T. Vapour-liquid phase diagram for an ionic fluid in a random porous medium. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:414003. [PMID: 27548356 DOI: 10.1088/0953-8984/28/41/414003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the vapour-liquid phase behaviour of an ionic fluid confined in a random porous matrix formed by uncharged hard sphere particles. The ionic fluid is modelled as an equimolar binary mixture of oppositely charged equisized hard spheres, the so-called restricted primitive model (RPM). Considering the matrix-fluid system as a partly-quenched model, we develop a theoretical approach which combines the method of collective variables with the extension of the scaled-particle theory (SPT) for a hard-sphere fluid confined in a disordered hard-sphere matrix. The approach allows us to formulate the perturbation theory using the SPT for the description of the thermodynamics of the reference system. The phase diagrams of the RPM in matrices of different porosities and for different size ratios of matrix and fluid particles are calculated in the random-phase approximation and also when the effects of higher-order correlations between ions are taken into account. Both approximations correctly reproduce the basic effects of porous media on the vapour-liquid phase diagram, i.e. with a decrease of porosity the critical point shifts towards lower fluid densities and lower temperatures and the coexistence region gets narrower. For the fixed matrix porosity, both the critical temperature and the critical density increase with an increase of size of matrix particles and tend to the critical values of the bulk RPM.
Collapse
Affiliation(s)
- M F Holovko
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine
| | | | | |
Collapse
|
7
|
Multiscale modeling of solvation in chemical and biological nanosystems and in nanoporous materials. PURE APPL CHEM 2013. [DOI: 10.1351/pac-con-12-06-03] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Statistical–mechanical, 3D-RISM-KH molecular theory of solvation (3D reference interaction site model with the Kovalenko–Hirata closure) is promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. 3D-RISM-KH explains the molecular mechanisms of self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), aggregation of prion proteins and β-sheet amyloid oligomers, protein-ligand binding, and function-related solvation properties of complexes as large as the Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) and GroEL/ES chaperone. Molecular mechanics/Poisson–Boltzmann (generalized Born) surface area [MM/PB(GB)SA] post-processing of molecular dynamics (MD) trajectories involving SA empirical nonpolar terms is replaced with MM/3D-RISM-KH statistical–mechanical evaluation of the solvation thermodynamics. 3D-RISM-KH has been coupled with multiple time-step (MTS) MD of the solute biomolecule driven by effective solvation forces, which are obtained analytically by converging the 3D-RISM-KH integral equations at outer time-steps and are calculated in between by using solvation force coordinate extrapolation (SFCE) in the subspace of previous solutions to 3D-RISM-KH. The procedure is stabilized by the optimized isokinetic Nosé–Hoover (OIN) chain thermostatting, which enables gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties. The multiscale OIN/SFCE/3D-RISM-KH algorithm is implemented in the Amber package and illustrated on a fully flexible model of alanine dipeptide in aqueous solution, exhibiting the computational rate of solvent sampling 20 times faster than standard MD with explicit solvent. Further substantial acceleration can be achieved with 3D-RISM-KH efficiently sampling essential events with rare statistics such as exchange and localization of solvent, ions, and ligands at binding sites and pockets of the biomolecule. 3D-RISM-KH was coupled with ab initio complete active space self-consistent field (CASSCF) and orbital-free embedding (OFE) Kohn–Sham (KS) density functional theory (DFT) quantum chemistry methods in an SCF description of electronic structure, optimized geometry, and chemical reactions in solution. The (OFE)KS-DFT/3D-RISM-KH multi-scale method is implemented in the Amsterdam Density Functional (ADF) package and extensively validated against experiment for solvation thermochemistry, photochemistry, conformational equilibria, and activation barriers of various nanosystems in solvents and ionic liquids (ILs). Finally, the replica RISM-KH-VM molecular theory for the solvation structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous materials reveals the molecular mechanisms of sorption and supercapacitance in nanoporous carbon electrodes, which is drastically different from a planar electrical double layer.
Collapse
|
8
|
Dourado EMA, Herdes C, van Tassel PR, Sarkisov L. Molecular recognition effects in atomistic models of imprinted polymers. Int J Mol Sci 2011; 12:4781-804. [PMID: 21954325 PMCID: PMC3179132 DOI: 10.3390/ijms12084781] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2011] [Revised: 07/08/2011] [Accepted: 07/25/2011] [Indexed: 12/02/2022] Open
Abstract
In this article we present a model for molecularly imprinted polymers, which considers both complexation processes in the pre-polymerization mixture and adsorption in the imprinted structures within a single consistent framework. As a case study we investigate MAA/EGDMA polymers imprinted with pyrazine and pyrimidine. A polymer imprinted with pyrazine shows substantial selectivity towards pyrazine over pyrimidine, thus exhibiting molecular recognition, whereas the pyrimidine imprinted structure shows no preferential adsorption of the template. Binding sites responsible for the molecular recognition of pyrazine involve one MAA molecule and one EGDMA molecule, forming associations with the two functional groups of the pyrazine molecule. Presence of these specific sites in the pyrazine imprinted system and lack of the analogous sites in the pyrimidine imprinted system is directly linked to the complexation processes in the pre-polymerization solution. These processes are quite different for pyrazine and pyrimidine as a result of both enthalpic and entropic effects.
Collapse
Affiliation(s)
- Eduardo M. A. Dourado
- Institute for Materials and Processes, School of Engineering, University of Edinburgh, Edinburgh, Midlothian EH9 3JL, UK; E-Mail:
| | - Carmelo Herdes
- Centro de Química de Évora, Universidade de Évora, Rua Romão Romalho 59, 7000 Évora, Portugal; E-Mail:
| | - Paul R. van Tassel
- Department of Chemical and Environmental Engineering, Yale University, New Haven, CT 06520-8286, USA; E-Mail:
| | - Lev Sarkisov
- Institute for Materials and Processes, School of Engineering, University of Edinburgh, Edinburgh, Midlothian EH9 3JL, UK; E-Mail:
- Author to whom correspondence should be addressed; E-Mail: ; Tel.: +44-131-650-4862
| |
Collapse
|
9
|
Kurzidim J, Coslovich D, Kahl G. Dynamic arrest of colloids in porous environments: disentangling crowding and confinement. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:234122. [PMID: 21613709 DOI: 10.1088/0953-8984/23/23/234122] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Using numerical simulations we study the slow dynamics of a colloidal hard-sphere fluid adsorbed in a matrix of disordered hard-sphere obstacles. We calculate separately the contributions to the single-particle dynamic correlation functions due to free and trapped particles. The separation is based on a Delaunay tessellation to partition the space accessible to the centres of fluid particles into percolating and disconnected voids. We find that the trapping of particles into disconnected voids of the matrix is responsible for the appearance of a nonzero long-time plateau in the single-particle intermediate scattering functions of the full fluid. The subdiffusive exponent z, obtained from the logarithmic derivative of the mean squared displacement, is essentially unaffected by the motion of trapped particles: close to the percolation transition, we determined z approximately = 0.5 for both the full fluid and the particles moving in the percolating void. Notably, the same value of z is found in single-file diffusion and is also predicted by mode-coupling theory along the diffusion-localization line. We also reveal subtle effects of dynamic heterogeneity in both the free and the trapped component of the fluid particles, and discuss microscopic mechanisms that contribute to this phenomenon.
Collapse
Affiliation(s)
- Jan Kurzidim
- Institut für Theoretische Physik and Center for Computational Materials Science, Technische Universität Wien, Wien, Austria.
| | | | | |
Collapse
|
10
|
Kurzidim J, Coslovich D, Kahl G. Impact of random obstacles on the dynamics of a dense colloidal fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041505. [PMID: 21230280 DOI: 10.1103/physreve.82.041505] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2010] [Indexed: 05/30/2023]
Abstract
Using molecular dynamics simulations we study the slow dynamics of a colloidal fluid annealed within a matrix of obstacles quenched from an equilibrated colloidal fluid. We choose all particles to be of the same size and to interact as hard spheres, thus retaining all features of the porous confinement while limiting the control parameters to the packing fraction of the matrix, φ(m), and that of the fluid, φ(f). We conduct detailed investigations on several dynamic properties, including the tagged-particle and collective intermediate scattering functions, the mean-squared displacement, and the van Hove function. We show the confining obstacles to profoundly impact the relaxation pattern of various quantifiers pertinent to the fluid. Varying the type of quantifier (tagged-particle or collective) as well as φ(m) and φ(f), we unveil both discontinuous and continuous arrest scenarios. Furthermore, we discover subdiffusive behavior and demonstrate its close connection to the matrix structure. Our findings partly confirm the various predictions of a recent extension of mode-coupling theory to the quenched-annealed protocol.
Collapse
Affiliation(s)
- Jan Kurzidim
- Institut für Theoretische Physik and CMS, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
| | | | | |
Collapse
|
11
|
ZHANG LINGHUI, VAN TASSEL PAULR. Configurational effects of templating on the adsorption isotherms of templated porous materials. Mol Phys 2009. [DOI: 10.1080/00268970009483357] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- LINGHUI ZHANG
- a Department of Chemical Engineering and Materials Science , Wayne State University , 5050 Anthony Wayne Drive, Detroit , MI , 48202 , USA
| | - PAUL R. VAN TASSEL
- a Department of Chemical Engineering and Materials Science , Wayne State University , 5050 Anthony Wayne Drive, Detroit , MI , 48202 , USA
| |
Collapse
|
12
|
KIERLIK E, ROSINBERG ML, TARJUS G, PITARD E. Mean-spherical approximation for a lattice model of a fluid in a disordered matrix. Mol Phys 2009. [DOI: 10.1080/00268979809483166] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
13
|
Pellicane G, Vink RLC, Caccamo C, Löwen H. Colloid-polymer mixtures in the presence of quenched disorder: a theoretical and computer simulation study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:115101. [PMID: 21694215 DOI: 10.1088/0953-8984/20/11/115101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We use theory and computer simulation to study the structure and phase behavior of colloid-polymer mixtures in the presence of quenched disorder. The Asakura-Oosawa model (AO) (Asakura and Oosawa 1954 J. Chem. Phys. 22 1255) is used to describe the colloid-colloid, colloid-polymer, and polymer-polymer pair interactions. We then investigate the behavior of this model in the presence of frozen-in (quenched) obstacles. The obstacles will be placed according to two different scenarios, both of which are experimentally feasible. In the first scenario, polymers are distributed at positions drawn from an ideal gas configuration. In the second scenario, colloidal particles are distributed at positions drawn from an equilibrium hard sphere configuration. We investigate how the unmixing transition of the AO model is affected by the type of quenched disorder. The theoretical formalism is based on the replica method of Given and Stell (1994 Physica A 209 495). Our foremost aim is to test the accuracy of three common closures to the replica Ornstein-Zernike equations, namely the hypernetted chain, the Percus-Yevick, and the Martinov-Sarkisov equations. The accuracy is determined by comparison with grand canonical Monte Carlo simulations. We find that, for quenched polymer disorder, all three closures perform remarkably well. However, when quenched colloid disorder is considered, i.e. the second mentioned scenario, the predictions of all three closures worsen dramatically.
Collapse
Affiliation(s)
- Giuseppe Pellicane
- Dipartimento di Fisica Contrada Papardo, Università degli Studi di Messina, 98166 Messina, Italy
| | | | | | | |
Collapse
|
14
|
Sarkisov L. Theory of pair connectedness in templated quenched-annealed systems. J Chem Phys 2008; 128:044707. [DOI: 10.1063/1.2823734] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
15
|
Abstract
The liquid-liquid phase behavior of binary mixtures in random pores is investigated with non-additive hard spheres using both ROZ (Replica Ornstein-Zernike) integral equations and cavity biased grand canonical Monte Carlo simulations. The critical densities of the coexistence phase envelopes are determined as function of the non-additivity parameter Delta, varying from Delta = 0.2, 0.4, 0.6, up to 0.8. The matrix is made of quenched hard spheres. Its porosity is varied to ascertain the effects of confinement, with packing densities rho(0) ranging from 0.1, 0.3, to 0.5. To obtain fiduciary results from ROZ, we use the accurate ZSEP closure relation proposed earlier with and without thermodynamic consistency. The ZSEP closure is known to enforce the zero-separation theorems via special adjustable parameters in the bridge function. Two versions of this closure are used to assess their accuracies (vis-à-vis the Monte Carlo data): first ZSEP-T, namely, the ZSEP closure with added thermodynamic consistency (the Gibbs-Duhem relation); and second purely ZSEP without adding thermodynamic consistency. It is found that both closures give correct qualitative trend, with errors of ZSEP falling within 8-9%, while ZSEP-T, being more accurate, to within 1-2%. As non-additivity is increased, both versions become more accurate. The critical density rho(c) is found to decrease with decreasing porosity. In addition, rho(c) also decreases with increasing Delta, in a non-monotone fashion.
Collapse
Affiliation(s)
- Giuseppe Pellicane
- Dipartimento di Fisica, Università di Messina, Contrada Papardo, 98166 Messina (Me), Italy.
| | | |
Collapse
|
16
|
Lafuente L, Cuesta JA. First-principles derivation of density-functional formalism for quenched-annealed systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041502. [PMID: 17155060 DOI: 10.1103/physreve.74.041502] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2006] [Indexed: 05/12/2023]
Abstract
We derive from first principles (without resorting to the replica trick) a density-functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the average density profile of the fluid as well as the pair correlation of the fluid and matrix particles. For practical reasons it is preferable to use another functional: the disorder-averaged free energy plus the fluid-matrix interaction energy, which, for fixed fluid-matrix interaction potential, is a functional only of the average density profile of the fluid. When the matrix is created as a quenched configuration of another fluid, the functional can be regarded as depending on the density profile of the matrix fluid as well. In this situation, the replica Ornstein-Zernike equations which do not contain the blocking parts of the correlations can be obtained as functional identities in this formalism, provided the second derivative of this functional is interpreted as the connected part of the direct correlation function. The blocking correlations are totally absent from QA-DFT, but nevertheless the thermodynamics can be entirely obtained from the functional. We apply the formalism to obtain the exact functional for an ideal fluid in an arbitrary matrix, and discuss possible approximations for nonideal fluids.
Collapse
Affiliation(s)
- Luis Lafuente
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Madrid, Spain.
| | | |
Collapse
|
17
|
Jiang J, Sandler SI. Capillary phase transitions of linear and branched alkanes in carbon nanotubes from molecular simulation. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2006; 22:7391-9. [PMID: 16893243 DOI: 10.1021/la0608720] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
Capillary phase transitions of linear (from C(1) to C(12)) and branched (C(5) isomers) alkanes in single-walled carbon nanotubes have been investigated using the gauge-cell Monte Carlo simulation. The isotherm at a supercritical temperature increases monotonically with chemical potential and coincides with that from the traditional grand canonical Monte Carlo simulation, whereas the isotherm at a subcritical temperature exhibits a sigmoid van der Waals loop including stable, metastable, and unstable regions. Along this loop, the coexisting phases are determined using an Maxwell equal-area construction. A generic confinement effect is found that reduces the saturation chemical potential, lowers the critical temperature, increases the critical density, and shrinks the phase envelope. The effect is greater in a smaller diameter nanotube and is greater in a nanotube than in a nanoslit.
Collapse
Affiliation(s)
- Jianwen Jiang
- Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576.
| | | |
Collapse
|
18
|
Sarkisov L, Van Tassel PR. Replica Ornstein-Zernike theory of adsorption in a templated porous material: Interaction site systems. J Chem Phys 2005; 123:164706. [PMID: 16268721 DOI: 10.1063/1.2049247] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular templating offers the possibility of porous materials whose selectivity rivals the molecular recognition observed in nature. The design of templated materials requires a molecular understanding of the templating effect on the material structure and performance. We present here a theoretical description of adsorption in a model templated porous material. Our model material is a quenched, equilibrated mixture of template and matrix molecular species where the template component has been subsequently removed. We propose a set of site-site [i.e., reference interaction site model (RISM)] replica Ornstein-Zernike equations relating the correlation functions of template, matrix, and adsorbing fluid molecules. To test this approach, we focus here on systems interacting via hard-sphere site-site potentials and employ a Percus-Yevick closure. We consider chain and cluster species composed of up to five spheres and observe a range of effects associated with template structure, including higher affinity toward, and enhanced templating by, compact cluster molecules. We assess these effects by grand canonical Monte Carlo simulation and discuss their implication to the design of templated molecular recognition materials.
Collapse
Affiliation(s)
- Lev Sarkisov
- Department of Chemical Engineering, Yale University, New Haven, Connecticut 06520-8286, USA
| | | |
Collapse
|
19
|
Sung BJ, Yethiraj A. Monte Carlo simulation and self-consistent integral equation theory for polymers in quenched random media. J Chem Phys 2005; 123:074909. [PMID: 16229622 DOI: 10.1063/1.2008232] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction.
Collapse
Affiliation(s)
- Bong June Sung
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, USA
| | | |
Collapse
|
20
|
Manciu M, Ruckenstein E. Estimation of the available surface and the jamming coverage in the Random Sequential Adsorption of a binary mixture of disks. Colloids Surf A Physicochem Eng Asp 2004. [DOI: 10.1016/j.colsurfa.2003.10.001] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
21
|
Matubayasi N, Nakahara M. Theory of solutions in the energy representation. III. Treatment of the molecular flexibility. J Chem Phys 2003. [DOI: 10.1063/1.1613938] [Citation(s) in RCA: 111] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
22
|
JORGE S, SCHÖLL-PASCHINGER ELISABETH, KAHL GERHARD, FERNAUD MARÍAJOSÉ. Structure and thermodynamic properties of a polydisperse fluid in contact with a polydisperse matrix. Mol Phys 2003. [DOI: 10.1080/0026897031000085128] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
23
|
RESZKO-ZYGMUNT JOANNA, PATRYKIEJEW ANDRZEJ, SOKOŁOWSKI STEFAN, SOKOŁOWSKA ZOFIA. Phase coexistence and interface structure of a two-component Lennard-Jones fluid in porous media: application of Born—Green—Yvon equation. Mol Phys 2002. [DOI: 10.1080/00268970210126600] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
|
24
|
|
25
|
Rżysko W, Sokołowski S, Pizio O. Theory of adsorption in a polydisperse templated porous material: Hard sphere systems. J Chem Phys 2002. [DOI: 10.1063/1.1450556] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
26
|
Kovalenko A, Hirata F. A replica reference interaction site model theory for a polar molecular liquid sorbed in a disordered microporous material with polar chemical groups. J Chem Phys 2001. [DOI: 10.1063/1.1409954] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
27
|
Zhang L, Cheng S, Van Tassel PR. Effect of templated quenched disorder on fluid phase equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:042101. [PMID: 11690064 DOI: 10.1103/physreve.64.042101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2001] [Indexed: 05/23/2023]
Abstract
Templating offers a means to direct the structure of quenched disorder. We show here that changes in phase equilibrium due to the presence of quenched disorder can themselves be altered by templating. We calculate the phase diagram of a fluid in a collection of template-directed, quenched particles by solving a set of replica Ornstein-Zernike equations within the mean spherical approximation and show templating to enhance phase behavior, that is, shift the phase envelope upward from its location for a nontemplated system of identical available volume. This enhancement is due to an augmented number of fluid-fluid interactions.
Collapse
Affiliation(s)
- L Zhang
- Department of Chemical Engineering and Materials Science, Wayne State University, Detroit, Michigan 48202, USA
| | | | | |
Collapse
|
28
|
Schöll-Paschinger E, Levesque D, Weis JJ, Kahl G. Phase diagram of a symmetric binary fluid in a porous matrix. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:011502. [PMID: 11461257 DOI: 10.1103/physreve.64.011502] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2000] [Revised: 11/27/2000] [Indexed: 05/23/2023]
Abstract
The phase behavior of a binary symmetric fluid in thermal equilibrium with a porous matrix has been studied with the optimized random phase approximation and grand canonical Monte Carlo simulations. Depending on the matrix properties and the matrix-fluid and fluid-fluid interactions we find three types of phase diagram characterized by a tricritical point, a tricritical point with a triple point, or a critical end point. Small changes in the properties of the matrix or in the interactions are demonstrated to lead to drastic modifications of the phase diagram of the fluid, in qualitative agreement with observations in experimental studies. We show, in particular, that the change between the different types of phase diagram is triggered not only by the fluid-fluid interactions (internal parameters) but also by the properties of the matrix and of the matrix-fluid potentials (external parameters).
Collapse
Affiliation(s)
- E Schöll-Paschinger
- Institut für Theoretische Physik and Center for Computational Materials Science, TU Wien, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
| | | | | | | |
Collapse
|
29
|
Cheng S, Van Tassel PR. Theory and simulation of the available volume for adsorption in a chain molecule templated porous material. J Chem Phys 2001. [DOI: 10.1063/1.1350442] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
30
|
|
31
|
Talbot J, Tarjus G, Van Tassel P, Viot P. From car parking to protein adsorption: an overview of sequential adsorption processes. Colloids Surf A Physicochem Eng Asp 2000. [DOI: 10.1016/s0927-7757(99)00409-4] [Citation(s) in RCA: 259] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
|
32
|
Senger B, Voegel JC, Schaaf P. Irreversible adsorption of colloidal particles on solid substrates. Colloids Surf A Physicochem Eng Asp 2000. [DOI: 10.1016/s0927-7757(99)00413-6] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
|
33
|
Paschinger E, Kahl G. Structure and thermodynamic properties of a binary liquid in a porous matrix: the formalism. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:5330-5338. [PMID: 11031581 DOI: 10.1103/physreve.61.5330] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2000] [Indexed: 05/23/2023]
Abstract
Using the replica trick we derive a formalism to describe the structure and the thermodynamic properties of a binary liquid in equilibrium with a porous medium. We present the replica Ornstein-Zernike equations for the general case of a k-component liquid inside a porous matrix; besides the usual liquid-state closure relations, we consider in particular the optimized random phase approximation (ORPA) restricting ourselves at present to hard-core potentials exclusively. We present furthermore several thermodynamic relations: the Gibbs-Duhem equation, the compressibility, and the viral equation. Within the framework of the ORPA (mean spherical approximation), closed expressions for the perturbation contribution to the free energy and the chemical potentials can be presented. Finally, we offer suggestions for numerical implementations.
Collapse
Affiliation(s)
- E Paschinger
- Institut fur Theoretische Physik, TU Wien, Austria
| | | |
Collapse
|
34
|
Series expansion and computer simulation studies of random sequential adsorption. Colloids Surf A Physicochem Eng Asp 2000. [DOI: 10.1016/s0927-7757(99)00444-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
35
|
Wang Q, Danwanichakul P, Glandt ED. Sequential addition of particles: Integral equations. J Chem Phys 2000. [DOI: 10.1063/1.481240] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
36
|
Zhang L, Van Tassel PR. Theory and simulation of adsorption in a templated porous material: Hard sphere systems. J Chem Phys 2000. [DOI: 10.1063/1.480874] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
37
|
Alvarez M, Levesque D, Weis JJ. Monte Carlo approach to the gas-liquid transition in porous materials. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:5495-504. [PMID: 11970424 DOI: 10.1103/physreve.60.5495] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/1999] [Indexed: 04/18/2023]
Abstract
The gas-liquid transition of a "quenched-annealed"(QA) system is studied by grand-canonical Monte Carlo simulation. The "quenched" particles are hard spheres within configurations chosen randomly from those of an equilibrium hard-sphere system at given density. The fluid particles interact with the matrix particles by a hard-core potential and with each other by a hard-core potential and an additional potential of a Lennard-Jones type. Our results are in good qualitative agreement with various theoretical approaches. With increasing matrix density the critical temperature is lowered compared to that of the bulk system and the gap between the gas and liquid densities narrowed. Our simulations confirm, for this QA system, the possibility of two fluid-fluid transitions substituting for the unique gas-liquid transition of the bulk system. They demonstrate the necessity to average over a significant number of matrix realizations in order to obtain a quantitative location of the phase coexistence lines.
Collapse
Affiliation(s)
- M Alvarez
- Laboratoire de Physique Théorique, Bâtiment 210, Université de Paris-Sud, 91405 Orsay Cedex, France
| | | | | |
Collapse
|
38
|
Cardenas M, Franz S, Parisi G. Glass transition and effective potential in the hypernetted chain approximation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/31/9/001] [Citation(s) in RCA: 73] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
39
|
Trokhymchuk A, Sokołowski S. Phase coexistence and interface structure of a Lennard-Jones fluid in porous media. Application of Born–Green–Yvon equation. J Chem Phys 1998. [DOI: 10.1063/1.477117] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
40
|
|
41
|
Kierlik E, Rosinberg ML, Tarjus G, Monson PA. Phase diagrams of single-component fluids in disordered porous materials: Predictions from integral-equation theory. J Chem Phys 1997. [DOI: 10.1063/1.474134] [Citation(s) in RCA: 100] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
42
|
Pitard E, Rosinberg ML, Tarjus G. Thermodynamics of Fluids in Disordered Porous Materials. MOLECULAR SIMULATION 1996. [DOI: 10.1080/08927029608024118] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
43
|
|
44
|
Kierlik E, Rosinberg ML, Tarjus G, Monson P. The pressure of a fluid confined in a disordered porous material. J Chem Phys 1995. [DOI: 10.1063/1.470663] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
45
|
Boyer D, Tarjus G, Viot P, Talbot J. Percus–Yevick‐like integral equation for random sequential addition. J Chem Phys 1995. [DOI: 10.1063/1.469783] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
46
|
Dong W. Mechanical route to the pressure of a fluid adsorbed in a random porous medium. J Chem Phys 1995. [DOI: 10.1063/1.469372] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
47
|
|
48
|
Dong W, Kierlik E, Rosinberg ML. Integral equations for a fluid near a random substrate. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:4750-4753. [PMID: 9962554 DOI: 10.1103/physreve.50.4750] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
49
|
Samaj L, Percus JK. Inhomogeneous random sequential adsorption with equilibrium initial conditions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:5149-5157. [PMID: 9961838 DOI: 10.1103/physreve.49.5149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
50
|
Tarjus G, Viot P, Choi HS, Talbot J. Restructuring effects in irreversible deposition of spheres on a plane. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:3239-3252. [PMID: 9961592 DOI: 10.1103/physreve.49.3239] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|