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Siegfried Dietrich - One of the best experts on this subject based on the ideXlab platform.
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Effective pair interaction of patchy particles in critical fluids
The Journal of chemical physics, 2020Co-Authors: N. Farahmand Bafi, Piotr Nowakowski, Siegfried DietrichAbstract:We study the critical Casimir interaction between two spherical colloids immersed in a binary liquid mixture close to its critical demixing point. The surface of each colloid prefers one species of the mixture with the exception of a circular patch of arbitrary size, where the other species is preferred. For such objects, we calculate, within the Derjaguin Approximation, the scaling function describing the critical Casimir potential, and we use it to derive the scaling functions for all components of the forces and torques acting on both colloids. The results are compared with available experimental data. Moreover, the general relation between the scaling function for the potential and the scaling functions for the force and the torque is derived.
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Electrostatic interaction of particles trapped at fluid interfaces: effects of geometry and wetting properties.
Soft matter, 2018Co-Authors: Arghya Majee, Markus Bier, Siegfried DietrichAbstract:The electrostatic interaction between pairs of spherical or macroscopically long, parallel cylindrical colloids trapped at fluid interfaces is studied theoretically for the case of small inter-particle separations. Starting from the effective interaction between two planar walls and by using the Derjaguin Approximation, we address the issue of how the electrostatic interaction between such particles is influenced by their curvatures and by the wetting contact angle at their surfaces. Regarding the influence of curvature, our findings suggest that the discrepancies between linear and nonlinear Poisson-Boltzmann theory, which have been noticed before for planar walls, also occur for spheres and macroscopically long, parallel cylinders, though their magnitude depends on the wetting contact angle. Concerning the influence of the wetting contact angle θ simple relations are obtained for equally sized particles which indicate that the inter-particle force varies significantly with θ only within an interval around 90°. This interval depends on the Debye length of the fluids and on the size of the particles but not on their shape. For unequally sized particles, a more complicated relation is obtained for the variation of the inter-particle force with the wetting contact angle.
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Critical Casimir interactions between Janus particles.
Soft matter, 2016Co-Authors: M. Labbé-laurent, Siegfried DietrichAbstract:Recently there has been strong experimental and theoretical interest in studying the self-assembly and the phase behavior of patchy and Janus particles, which form colloidal suspensions. Although in this quest a variety of effective interactions have been proposed and used in order to achieve a directed assembly, the critical Casimir effect stands out as being particularly suitable in this respect because it provides both attractive and repulsive interactions as well as the potential of a sensitive temperature control of their strength. Specifically, we have calculated the critical Casimir force between a single Janus particle and a laterally homogeneous substrate as well as a substrate with a chemical step. We have used the Derjaguin Approximation and compared it with results from full mean field theory. A modification of the Derjaguin Approximation turns out to be generally reliable. Based on this approach we have derived the effective force and the effective potential between two Janus cylinders as well as between two Janus spheres.
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Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques
Soft matter, 2014Co-Authors: M. Labbé-laurent, M. Tröndle, Ludger Harnau, Siegfried DietrichAbstract:Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basis of the Derjaguin Approximation. The range of validity of the latter is assessed via mean-field theory. This assessment shows that the Derjaguin Approximation is reliable in experimentally relevant regimes, so that we extend it to Janus particles endowed with opposing adsorption preferences. Our analysis indicates that critical Casimir interactions are capable of achieving well-defined, reversible alignments both of chemically homogeneous and of Janus cylinders.
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Critical Casimir effect for colloids close to chemically patterned substrates
The Journal of chemical physics, 2010Co-Authors: M. Tröndle, Ludger Harnau, Svyatoslav Kondrat, Andrea Gambassi, Siegfried DietrichAbstract:Colloids immersed in a critical or near-critical binary liquid mixture and close to a chemically patterned substrate are subject to normal and lateral critical Casimir forces of dominating strength. For a single colloid we calculate these attractive or repulsive forces and the corresponding critical Casimir potentials within mean-field theory. Within this approach we also discuss the quality of the Derjaguin Approximation and apply it to Monte Carlo simulation data available for the system under study. We find that the range of validity of the Derjaguin Approximation is rather large and that it fails only for surface structures which are very small compared to the geometric mean of the size of the colloid and its distance from the substrate. For certain chemical structures of the substrate the critical Casimir force acting on the colloid can change sign as a function of the distance between the particle and the substrate; this provides a mechanism for stable levitation at a certain distance which can be strongly tuned by temperature, i.e., with a sensitivity of more than 200nm/K.
Mark W. Matsen - One of the best experts on this subject based on the ideXlab platform.
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Repulsion Exerted on a Spherical Particle by a Polymer Brush
Macromolecules, 2008Co-Authors: Jaeup U. Kim, Mark W. MatsenAbstract:The steric repulsion exerted on spherical particles by a semidilute polymer brush is evaluated using numerical self-consistent field theory (SCFT) in cylindrical coordinates. This accurate treatment provides the opportunity to test the conventional analytical approach, where the strong-stretching theory (SST) of Milner, Witten, and Cates for uniform compression can be adapted to particles of any shape using the Derjaguin Approximation. While the Derjaguin Approximation works well, at least, for the interaction energy, the SST proves to be seriously inaccurate for realistic grafting densities. Nevertheless, an efficient and accurate treatment for arbitrarily shaped particles remains possible if the uniform compression in the Derjaguin Approximation is supplied by SCFT.
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Interaction between Polymer-Grafted Particles
Macromolecules, 2008Co-Authors: Jaeup U. Kim, Mark W. MatsenAbstract:Previous self-consistent field theory (SCFT) calculations have predicted that the steric interaction between two polymer-grafted particles in good solvent can become attractive, but this conclusion has since been questioned. Here we reexamine the problem with a new numerical scheme using multiple coordinate systems, and find that the interaction remains repulsive regardless of the particle size, brush thickness, or particle separation. The erroneous attraction in the earlier calculations can be attributed to numerical inaccuracy and a subtle issue with how the chains were grafted to the particles. Using our corrected SCFT solution, we also investigate the accuracy of a previous calculation based on strong-stretching theory (SST) and the applicability of the Derjaguin Approximation, where the interaction between large particles is estimated from the one-dimensional uniform compression of polymer brushes.
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Effect of Chain Tilt on the Interaction between Brush-Coated Colloids
Macromolecules, 2005Co-Authors: Mark W. MatsenAbstract:The interaction between two spherical particles coated by end-grafted polymers immersed in a good solvent is examined using the strong-stretching theory of Milner, Witten, and Cates. Our calculation allows the polymer chains to tilt outward from the axis of closest approach, where the separation between the substrates is a minimum. This transfers the stress toward the extremity of the contact region, but to such a degree that the central chains can experience a reduction in free energy relative to the unperturbed brush. Nevertheless, the chain tilt has a small effect on the overall free energy, and thus the traditional Derjaguin Approximation predicts a reasonably accurate interaction potential, provided the particles are large relative to the height of their brushes. Better yet, we propose an improved version that performs well for particles not much larger than the brushes.
Phil Attard - One of the best experts on this subject based on the ideXlab platform.
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ENTROPIC FORCES IN BINARY HARD SPHERE MIXTURES: THEORY AND SIMULATION
The Journal of Chemical Physics, 1997Co-Authors: Ronald Dickman, Phil Attard, Veronika SimonianAbstract:We perform extensive Monte Carlo simulations of binary hard-sphere mixtures (with diameter ratios of 5 and 10), to determine the entropic force between (1) a macrosphere and a hard wall, and (2) a pair of macrospheres. The microsphere background fluid (at volume fractions ranging from 0.1 to 0.34) induces an entropic force on the macrosphere(s); the latter component is at infinite dilution. We find good overall agreement, in both cases, with the predictions of a hypernetted chain-based theory for the entropic force. Our results also argue for the validity of the Derjaguin Approximation relating the force between convex bodies to that between planar surfaces. The earlier Asakura-Oosawa theory, based on a simple geometric argument, is only accurate in the low-density limit.
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bubbles cavities and the long ranged attraction between hydrophobic surfaces
The Journal of Physical Chemistry, 1994Co-Authors: John L. Parker, Per M Claesson, Phil AttardAbstract:Measurements of the forces in water between neutral hydrophobic surfaces prepared by covalent modification of glass are presented. The surfaces are stable under a variety of conditions including high temperature, high salt concentrations and with added ethanol. The forces between these surfaces have been studied under all of these different conditions. In water the force is attractive at very large surface separations, and discontinuities or steps are present in the force curves. It is suggested that the steps at the onset of the force are due to the bridging of submicroscopic bubbles or cavities between the surfaces and that it is their consequent growth with decreasing separation that causes the long-range attraction between hydrophobic surfaces. Electrolyte has a negligible effect on the range and strength of the measured forces, except at very high salt concentrations where the strength of the attractive forces and the adhesion between the surfaces increases slightly. The addition of ethanol reduces both the strength of the long range forces and the adhesion between the surfaces. On the basis of the comparison between these results and earlier measurements, it appears that the attraction does not obey the Derjaguin Approximation. Forces were also measured in the presence of a microscopic vapor cavity created by first bringing the surfaces into contact.
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Oscillatory solvation forces: a comparison of theory and experiment
The Journal of Physical Chemistry, 1992Co-Authors: Phil Attard, John L. ParkerAbstract:Measurements are reported for the oscillatory force between mica surfaces in octamethyltetracyclosiloxane (OMCTS). Improved experimental resolution is achieved by solid-state distance control and force measurement and by an automated data acquisition system. The period of the oscillations is measured to be 0.82±0.02 nm. Theoretical calculations are shown to quantitatively describe the magnitude of the force in the case of hard-sphere and Lennard-Jones models of the OMCTS molecule, with the period being 0.74 and 0.78 nm, respectively. A rigorous proof of the Derjaguin Approximation is also given
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interaction free energy between planar walls in dense fluids an ornstein zernike approach with results for hard sphere lennard jones and dipolar systems
Physical Review A, 1991Co-Authors: Phil Attard, D R Berard, C P Ursenbach, G N PateyAbstract:The interaction free energy per unit area between planar walls is given as a convolution of wall-solvent pair-correlation functions. This result, derived from the large radius limit of the macrosphere-solvent Ornstein-Zernike equations, and from the hypernetted-chain closure, provides a statistical-mechanical basis for the Derjaguin Approximation, and is both generally applicable and computationally tractable. It is found that the interaction between hard walls in a hard-sphere fluid is oscillatory, and in good agreement with simulations. The van der Waals attraction emerges from asymptotic analyses of Lennard-Jones and dipolar fluids, and the full expression allows calculation of this quantity down to molecular separations. This is demonstrated by numerical results for dipolar fluids.
M. Labbé-laurent - One of the best experts on this subject based on the ideXlab platform.
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Critical Casimir interactions between Janus particles.
Soft matter, 2016Co-Authors: M. Labbé-laurent, Siegfried DietrichAbstract:Recently there has been strong experimental and theoretical interest in studying the self-assembly and the phase behavior of patchy and Janus particles, which form colloidal suspensions. Although in this quest a variety of effective interactions have been proposed and used in order to achieve a directed assembly, the critical Casimir effect stands out as being particularly suitable in this respect because it provides both attractive and repulsive interactions as well as the potential of a sensitive temperature control of their strength. Specifically, we have calculated the critical Casimir force between a single Janus particle and a laterally homogeneous substrate as well as a substrate with a chemical step. We have used the Derjaguin Approximation and compared it with results from full mean field theory. A modification of the Derjaguin Approximation turns out to be generally reliable. Based on this approach we have derived the effective force and the effective potential between two Janus cylinders as well as between two Janus spheres.
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Critical Casimir interactions between Janus particles
Soft Matter, 2016Co-Authors: M. Labbé-laurent, Sven DietrichAbstract:Recently there is strong experimental and theoretical interest in studying the self-assembly and the phase behavior of patchy and of Janus particles, which form colloidal suspensions. Although in this quest a variety of effective interactions have been proposed and used in order to achieve directed assembly, the critical Casimir effect stands out as being particularly suitable in this respect because it provides both attractive and repulsive interactions as well as the potential of a sensitive temperature control of their strength. Specifically, we have calculated the critical Casimir force between a single Janus particle and a laterally homogeneous substrate as well as a substrate with a chemical step. We have used the Derjaguin Approximation and compared it with results from full mean field theory. A modification of the Derjaguin Approximation turns out to be generally reliable. Based on this approach we have derived the effective force and the effective potential between two Janus cylinders as well as between two Janus spheres.
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Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques
Soft matter, 2014Co-Authors: M. Labbé-laurent, M. Tröndle, Ludger Harnau, Siegfried DietrichAbstract:Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basis of the Derjaguin Approximation. The range of validity of the latter is assessed via mean-field theory. This assessment shows that the Derjaguin Approximation is reliable in experimentally relevant regimes, so that we extend it to Janus particles endowed with opposing adsorption preferences. Our analysis indicates that critical Casimir interactions are capable of achieving well-defined, reversible alignments both of chemically homogeneous and of Janus cylinders.
S. Dietrich - One of the best experts on this subject based on the ideXlab platform.
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Depletion potential in colloidal mixtures of hard spheres and platelets.
Physical review. E Statistical nonlinear and soft matter physics, 2004Co-Authors: L Harnau, S. DietrichAbstract:The depletion potential between two hard spheres in a solvent of thin hard disclike platelets is investigated by using either the Derjaguin Approximation or density functional theory. Particular attention is paid to the density dependence of the depletion potential. A second-order virial Approximation is applied, which yields nearly exact results for the bulk properties of the hard-platelet fluid at densities two times smaller than the density of the isotropic fluid at isotropic-nematic phase coexistence. As the platelet density increases, the attractive primary minimum of the depletion potential deepens and an additional small repulsive barrier at larger sphere separations develops. Upon decreasing the ratio of the radius of the spheres and the platelets, the primary minimum diminishes and the position of the small repulsive barrier shifts to smaller values of the sphere separation.
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DEPLETION FORCES IN FLUIDS
Physical Review E, 1998Co-Authors: B. Gotzelmann, Robert Evans, S. DietrichAbstract:We investigate the entropic depletion force that arises between two big hard spheres of radius ${R}_{b},$ mimicking colloidal particles, immersed in a fluid of small hard spheres of radius ${R}_{s}.$ Within the framework of the Derjaguin Approximation, which becomes exact as ${s=R}_{s}{/R}_{b}\ensuremath{\rightarrow}0$, we examine an exact expression for the depletion force and the corresponding potential for the range $0lhl{2R}_{s},$ where $h$ is the separation between the big spheres. These expressions, which depend only on the bulk pressure and the corresponding planar wall-fluid interfacial tension, are valid for all fluid number densities ${\ensuremath{\rho}}_{s}.$ In the limit ${\ensuremath{\rho}}_{s}\ensuremath{\rightarrow}0$ we recover the results of earlier low density theories. Comparison with recent computer simulations shows that the Derjaguin Approximation is not reliable for $s=0.1$ and packing fractions ${\ensuremath{\eta}}_{s}=4\ensuremath{\pi}{\ensuremath{\rho}}_{s}{R}_{s}^{3}/3\ensuremath{\gtrsim}0.3$. We propose two new Approximations, one based on treating the fluid as if it were confined to a wedge and the other based on the limit ${s=R}_{s}{/R}_{b}\ensuremath{\rightarrow}1$. Both improve upon the Derjaguin Approximation for $s=0.1$ and high packing fractions. We discuss the extent to which our results remain valid for more general fluids, e.g., nonadsorbing polymers near colloidal particles, and their implications for fluid-fluid phase separation in a binary hard-sphere mixture.
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DENSITY PROFILES AND PAIR CORRELATION FUNCTIONS OF HARD SPHERES IN NARROW SLITS
Physical Review E, 1997Co-Authors: B. Gotzelmann, S. DietrichAbstract:A hard-sphere fluid confined by hard, structureless, and parallel walls is investigated using a certain version of the weighted density-functional theory. The density profile, the excess coverage, the finite-size contribution to the free energy, the solvation force, and the total correlation function are determined as functions of the slit width L for various bulk number densities ${\mathrm{\ensuremath{\rho}}}_{\mathrm{b}}$. In quantitative agreement with rigorous results, the present version of density-functional theory yields a constant and large but finite number density profile for the limiting case that L is reduced to the diameter of the hard spheres. Within the Derjaguin Approximation, the results for the slit geometry allows us to obtain the solvation force between two large hard spheres immersed in a fluid of much smaller hard spheres.
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Density profiles and pair correlation functions of hard spheres in narrow slits
arXiv: Statistical Mechanics, 1996Co-Authors: B. Gotzelmann, S. DietrichAbstract:A hard sphere fluid confined by hard, structureless, and parallel walls is investigated using a certain version of weighted density functional theory. The density profile, the excess coverage, the finite size contribution to the free energy, the solvation force, and the total correlation function are determined as function of the slit width $L$ for various bulk number densities $\rho_b$. In quantitative agreement with rigorous results the present version of density functional theory yields a constant and large but finite number density profile for the limiting case that $L$ is reduced to the diameter of the hard spheres. Within the Derjaguin Approximation the results for the slit geometry allows us to obtain the solvation force between two large hard spheres immersed into a fluid of much smaller hard spheres.