Capillary Condensation and Interface Structure of a Model Colloid-Polymer Mixture in a Porous Medium

We consider the Asakura-Oosawa model of hard sphere colloids and ideal polymers in contact with a porous matrix modeled by immobilized configurations of hard spheres. For this ternary mixture a fundamental measure density functional theory is employed, where the matrix particles are quenched and the colloids and polymers are annealed, i.e. allowed to equilibrate. We study capillary condensation of the mixture in a tiny sample of matrix as well as demixing and the fluid-fluid interface inside a bulk matrix. Density profiles normal to the interface and surface tensions are calculated and compared to the case without matrix. Two kinds of matrices are considered: (i) colloid-sized matrix particles at low packing fractions and (ii) large matrix particles at high packing fractions. These two cases show fundamentally different behavior and should both be experimentally realizable. Furthermore, we argue that capillary condensation of a colloidal suspension could be experimentally accessible. We find that in case (ii), even at high packing fractions, the main effect of the matrix is to exclude volume and, to high accuracy, the results can be mapped onto those of the same system without matrix via a simple rescaling.Comment: 12 pages, 9 figures, submitted to PR

Research data supporting "Toward automatic analysis of random monolayers: The effect of pair correlation"-B-spline representations of total correlation function

The files contain knots and coefficients of fourth order (cubic) B-spline representations approximating total correlation functions. We calculated the functions for the classical 2D RSA systems at five values of surface coverage. First, using the model, we produced hard disk monolayers at surface coverage: 0.1, 0.2, 0.3, 0.4, and 0.5. For each coverage, we generated 20 replicas of a big system with the square simulation area As = 1E8 Ap, where Ap is the disk surface area. For each replica, we first calculated the pair-correlation function g(r) by counting disk pairs in narrow distance intervals of width dr = 0.01 a, where a is the disk radius. For each coverage, we calculated 20 replicas of the function g(r) in the range from r = 2a to r = 10a, i.e., in 800 narrow intervals. Next, we calculated replicas of the total correlation function h(r) = g(r) - 1. After ensemble averaging we got 800 discrete, arithmetic mean values of correlation function and standard deviations of the means, for each coverage. We identified and compared the maximum values of the standard deviation for each of the five coverages. The maximum standard deviations decreased with the increase in coverage from 6E-3 at coverage 0.1 to 7E-4 at coverage 0.5. Finally, we fitted fourth order (cubic) B-spline representations to the mean total correlation functions. For that, we used the procedure DFC of SLATEC library. To calculate the total correlation function with the B-splines, you can use the procedure DBVALU of SLATEC library. Knot vectors in the attached files begin and end with three improper knots, in accordance with requirements of the procedure. For details, see the paper: P. Weronski & K. Palka, "Toward automatic analysis of random monolayers: The effect of pair correlation", Measurement 179 (2021) 109536

Research data supporting "Toward automatic analysis of random monolayers: The effect of pair correlation". B-spline representations of total correlation function.

The files contain knots and coefficients of fourth order (cubic) B-spline representations approximating total correlation functions.We calculated the functions for the classical 2D RSA systems at five values of surface coverage. First, using the model, we produced hard-disk monolayers of surface coverage: 0.1, 0.2, 0.3, 0.4, and 0.5. For each coverage, we generated 20 replicas of a big system with the square simulation area As = 1E8 Ap, where Ap is the disk surface area. For each replica, we first calculated the pair-correlation function g(r) by counting disk pairs in narrow distance intervals of width dr = 0.01 a, where a is the disk radius. For each coverage, we calculated 20 replicas of the function g(r) in the range from r = 2a to r = 10a, i.e., in 800 narrow intervals. Next, we calculated replicas of the total correlation function h(r) = g(r) - 1. After ensemble averaging we got 800 discrete, arithmetic mean values of correlation function and standard deviations of the means, for each coverage. We identified and compared the maximum values of the standard deviation for each of the five coverages. The maximum standard deviations decreased with the increase in coverage from 6E-3 at coverage 0.1 to 7E-4 at coverage 0.5. Finally, we fit fourth order (cubic) B-spline representations to the mean total correlation functions. For that, we used the procedure DFC of SLATEC library.To calculate the total correlation function with the B-splines, you can use the procedure DBVALU of SLATEC library. Knot vectors in the attached files begin and end with three improper knots, in accordance with requirements of the procedure. For details, see the paper: P. Weroński & K. Pałka, "Toward automatic analysis of random monolayers: The effect of pair correlation", Measurement 179 (2021) 109536.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

Research data supporting "Toward automatic analysis of random monolayers: The effect of pair correlation". B-spline representations of integral Ic(q).

The files contain knots and coefficients of third order (quadratic) B-spline representations approximating the integral Ic(q) appearing in the equation for power spectral density of particle or cavity monolayer.The integral depends on the total correlation function of objects forming the monolayer. We used B-spline representations of the correlation functions computed for the classical RSA systems at five values of surface coverage: 0.1, 0.2, 0.3, 0.4, and 0.5. For each coverage, we generated 20 replicas of the correlation function, as described at http://dx.doi.org/10.17632/s4k84ccxww.2. Next, for each replica, we numerically computed the integral using the procedure DBFQAD of SLATEC library. This way we got 1E5 values of the integral at equidistant wavenumbers in the interval from 1E-3 to 1E2. After ensemble averaging we got 1E5 arithmetic mean values of the integral and standard deviations of the means, for each coverage. We identified and compared the maximum values of the standard deviation for each of the five coverages. The maximum standard deviations decreased with the increase in coverage from 1E-3 at coverage 0.1 to 8E-5 at coverage 0.5. Finally, we fit B-spline representations to the averaged integrals. For that, we used the B-spline fitting procedure splrep of the package SciPy.interpolate included in the Python-based open-source library SciPy. Considering the very small values of maximum standard deviations of the means, we used third order (quadratic) B-splines with the default knot vector generated by the procedure splrep, i.e., with the knot separation distance equal about 1E-3.To calculate the integral with the B-splines you can use the procedures splev or BSpline of the module SciPy.interpolate of SciPy library v. 1.1.0. Knot vectors in the attached files begin and end with two improper knots, in accordance with the requirements of the procedures. For details, see the paper: P. Weroński & K. Pałka, "Toward automatic analysis of random monolayers: The effect of pair correlation", Measurement 179 (2021) 109536.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

Research data supporting "Toward automatic analysis of random monolayers: The effect of pair correlation"-B-spline representations of integral Ic(q)

The files contain knots and coefficients of third order (quadratic) B-spline representations approximating the integral Ic(q) appearing in the equation for power spectral density of particle or cavity monolayer. The integral depends on the total correlation function of objects forming the monolayer. We used B-spline representations of the correlation functions computed for the classical RSA systems at five values of surface coverage: 0.1, 0.2, 0.3, 0.4, and 0.5. For each coverage, we generated 20 replicas of the correlation function, as described at http://dx.doi.org/10.17632/s4k84ccxww.1. Next, for each replica, we numerically computed the integral using the procedure DBFQAD of SLATEC library. This way we got 1E5 values of the integral at equidistant wavenumbers in the interval from 1E-3 to 1E2. After ensemble averaging we got 1E5 arithmetic mean values of the integral and standard deviations of the means, for each coverage. We identified and compared the maximum values of the standard deviation for each of the five coverages. The maximum standard deviations decreased with the increase in coverage from 1E-3 at coverage 0.1 to 8E-5 at coverage 0.5. Finally, we fitted B-spline representations to the averaged integrals. For that, we used the B-spline fitting procedure splrep of the package SciPy.interpolate included in the Python-based open-source library SciPy. Considering the very small values of maximum standard deviations of the means, we used third order (quadratic) B-splines with the default knot vector generated by the procedure splrep, i.e., with the knot separation distance equal about 1E-3. To calculate the integral with the B-splines you can use the procedures splev or BSpline of the module SciPy.interpolate of SciPy library v. 1.1.0. Knot vectors in the attached files begin and end with two improper knots, in accordance with the requirements of the procedures. For details, see the paper: P. Weronski & K. Palka, "Toward automatic analysis of random monolayers: The effect of pair correlation", Measurement 179 (2021) 109536

Research data supporting "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image". Replicas of small system.

The 10 files attached are output packing files obtained with 2D event-driven molecular dynamics for hard-disk monolayers of surface coverage 0.85. Specifically, to produce the hard disk systems, we used the program PackLSD.64.x by Aleksandar Donev, available at https://cims.nyu.edu/~donev/Packing/PackLSD/Instructions.html. We started the simulations of 2138 disks at the initial surface coverage of 0.1 to gradually increase their size. In the nml parameter file, we set the disk expansion rate parameter expansions_=0.001. Once the surface coverage achieved 0.85, we stopped the simulation.The output file format is described on the web page https://cims.nyu.edu/~donev/Packing/PackLSD/Instructions.html. On this website, you can also find programs for numerical analysis or visualization of the systems. The files mostly contain hard disk coordinates on the area of a square of unit side. Because of the simple, two-column ASCII format of the files, they can serve as input files for many other programs. See, e.g., the calculations of power spectral density of the systems, described in the paper: P. Weroński & K. Pałka, "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image", Measurement 196 (2022) 111263.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

Research data supporting "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image". B-spline representation of radial distribution function.

The files contain knots and coefficients of third order (quadratic) B-spline representation approximating a radial distribution function (RDF).We calculated the function for a hard-disk monolayer generated with event-driven molecular dynamics, of surface coverage 0.85. Specifically, to produce the monolayer, we used the program PackLSD.64.x by Aleksandar Donev, available at https://cims.nyu.edu/~donev/Packing/PackLSD/Instructions.html. We started the simulation of 8.5E7 disks at the initial surface coverage of 0.1 to gradually increase their size. In the nml parameter file, we set the disk expansion rate parameter expansions_=0.001. Once the surface coverage achieved 0.85, we stopped the simulation.We generated 26 replicas of the big system with a constant area of square simulation box. For each replica, we first calculated the discrete RDF g(r) by counting disk pairs in narrow distance intervals of width dr = 1E-3 a, where a is the disk radius. In the narrow interval 3.9900 ≤ r ≤ 4.0020, where the slope of the RDF changes extremely rapidly, we used the ring thickness 1E-4. For each replica of the system, we calculated the mean distance and RDF over the 88108 narrow intervals, averaging over the central particles. We calculated 26 replicas of the function g(r) in the range from r = 2a to r = 90a. Averaging over them, we got 88108 discrete, arithmetic mean values of RDF and standard deviations of the means. We identified the maximum value of the RDF standard deviation to be 0.009. Finally, we fit a third order (quadratic) B-spline representation to the mean RDF. For that, we used the procedure DFC of SLATEC library, with 3786 proper knots.To calculate the RDF with the B-spline, you can use the procedure DBVALU of SLATEC library. The knot vector in the attached file begins and ends with two improper knots, in accordance with requirements of the procedure. For details, see the paper: P. Weroński & K. Pałka, "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image", Measurement 196 (2022) 111263.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

Research data supporting "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image". B-spline representation of static structure factor.

The files contain knots and coefficients of third order (quadratic) B-spline representation approximating the structure factor S(q) appearing in the equation for power spectral density of particle or cavity monolayer.The structure factor depends on the radial distribution function (RDF) of objects forming the monolayer. In our computations, we used a B-spline representation of the RDF computed for a hard disk system of surface coverage 0.85. The representation, averaged over 26 replicas of RDF, was calculated as described at http://dx.doi.org/10.17632/3csw4wmjnr.1. With the RDF representation, we numerically computed the structure factor using the procedure DBFQAD of SLATEC library. This way we got 1E5 values of the structure factor at equidistant wavenumbers in the interval from 1E-3 to 1E2. Finally, we fit a B-spline representation to the discrete function S(q). For that, we used the B-spline fitting procedure splrep of the package SciPy.interpolate included in the Python-based open-source library SciPy. We used a forth order (cubic) B-spline with the default knot vector generated by the procedure splrep, i.e., with the knot separation distance equal about 1E-3.To calculate the structure factor with the B-spline you can use the procedures splev or BSpline of the module SciPy.interpolate of SciPy library v. 1.7.1. The knot vector in the attached files begins and ends with three improper knots, in accordance with the requirements of the procedures. For details, see the paper: P. Weroński & K. Pałka, "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image", Measurement 196 (2022) 111263.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV