Triplet correlations in two-dimensional colloidal model liquids

Ruß, C.; Zahn, Klaus; Grünberg, Hans-Hennig von

doi:10.1088/0953-8984/15/48/011

Cited by 18 publications

(17 citation statements)

References 41 publications

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“…The difference between the two-body pair force and the effective pair force calculated for a three-body system is mostly referred to as the three-body effect. The three-body effect widely exists in other systems besides paramagnetic colloid suspension in a rotational field, such as charged colloidal suspension with the Yukawa potential [29,30] and paramagnetic colloid suspension in a uniform vertical field [31]. Here a significant three-body effect of 20% is observed for LES results when r/D = 1.06, indicating the pair magnetic force from LES is not sufficient to describe the magnetic force for oligomer aggregates.…”

Section: Force Between Particles In a Rotational Magnetic Fieldmentioning

confidence: 93%

Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Toffoletto

Biswal

2014

Phys. Rev. E

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Typically the force between paramagnetic particles in a uniform magnetic field is described using the dipolar model, which is inaccurate when particles are in close proximity to each other. Instead, the exact force between paramagnetic particles can be determined by solving a three-dimensional Laplace's equation for magnetostatics under specified boundary conditions and calculating the Maxwell stress tensor. The analytical solution to this multi-boundary-condition Laplace's equation can be obtained by using a solid harmonics expansion in conjunction with the Hobson formula. However, for a multibody system, finite truncation of the Hobson formula does not lead to convergence of the expansion at all points, which makes the approximation physically unrealistic. Here we present a numerical method for solving this Laplace's equation for magnetostatics. This method uses a smoothed representation to replace all the boundary conditions. A two-step propagation is used to dramatically accelerate the calculation without losing accuracy. Using this method, we calculate the force between two paramagnetic particles in a uniform and a rotational external field and compare our results with other models. Furthermore, the many-body effects for three-particle, ten-particle, and 24-particle systems are examined using the same method. We also calculate the interaction between particles with different magnetic susceptibilities and particle diameters. The Laplace's equation solver method described in this article that is used to determine the force between paramagnetic particles is shown to be very useful for dynamic simulations for both two-particle systems and a large cluster of particles.

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Section: Force Between Particles In a Rotational Magnetic Fieldmentioning

confidence: 93%

Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Toffoletto

Biswal

2014

Phys. Rev. E

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“…The colloid density was varied by means of optical line traps realized with a sophisticated system of computer-driven mirrors which control a scanned optical laser tweezer. We have investigated six different colloid densities, collected for each density about 1000 colloidal configurations (with up to 1700 particles), and evaluated these data to extract in [12,13] the colloid pair potentials, to compute in [14] the triplet correlation functions and in [15] the equation of state. In all of these papers, we have found at higher densities marked deviations from the expected behavior of a simple Yukawa liquid, in which particles interact via a screened Coulomb potential u (2) (r) = A exp[−κr]/r.…”

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confidence: 99%

“…-We now apply our method to the experimental data of [12,13]. Typical triplet correlation functions as produced from these data are plotted in [14]. In fig.…”

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confidence: 99%

Three-body forces at work: Three-body potentials derived from triplet correlations in colloidal suspensions

et al. 2005

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Abstract. -Two-and three-particle correlation functions are computed from video-microscopy data of two-dimensional suspensions of charged colloids and inverted to derive the pair and three-body interaction potentials between the colloidal particles. Our method allows to resolve the full spatial dependence of the three-body potentials. Examining colloidal systems at different colloid densities, we find density-independent, attractive three-body potentials, with a minimum of a few kT that is most pronounced in the equilateral triangle configuration.A simple liquid is a liquid consisting of particles which interact with pair potentials only dependent on the particle separations. A charge-stabilized colloidal suspension, by contrast, is a complex fluid: here the inter-particle interaction is governed by the inhomogeneous distribution of electrolyte ions between the highly charged colloids. Only in certain limiting cases, is it possible to integrate out the ionic degrees of freedom, leading to an effective colloid-colloid potential of the Yukawa form. This pair potential is an essential element of the classic DerjaguinLandau-Verwey-Overbeek (DLVO) theory of interactions in charge-stabilized colloids [1,2]. In general, however, the interaction between colloids in a charge-stabilized suspension may not be expected to be pairwise additive: many-body interactions among the colloids can be important, primarily under low salt conditions and for highly charged colloids. A good example is the three-body interaction potential which has received some attention recently: it has been theoretically predicted [3][4][5], and also experimentally observed [6,7]. In [6, 7] a video-microscopy experiment is described, examining in what way the presence of a third charged colloid in the neighborhood of a pair of colloids affects their mutual interaction. By decomposing the measured total interaction potential in an appropriate way, the three-particle interaction potentials could be extracted and successfully compared to theoretical Poisson-Boltzmann calculations.Examining only three isolated particles remains a somewhat artificial situation, considering that, in reality, colloids live together in a suspension of finite density. Therefore, in order to prove that three-body potentials are present also in concentrated colloidal suspensions, one has to observe three-body forces "at work", that is, one has to infer the shape and magnitude of the three-body potential from analyzing the particle coordinates of a large number of colloids which are together in a concentrated suspension. In this letter, we compute correlation functions and extract from these functions the whole three-body interaction potentials among the colloids. Since from two-particle correlations one obtains microscopic information only on the level of pair interactions, we have to analyze pair and, in addition, triplet correlation Letters (EPL) ; 69 (2005), 3. -S. 468-474 https://dx

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“…, N, of the N molecules in the system at various separation radii. 8,[43][44][45][46][47][48][49][50] These relative probabilities are trivial for n = 1, g (1) α = 1, and obtainable for n = 2, g (2) α β , for monatomic liquids as described above. For molecular systems, a complete description of the structure would additionally require knowledge of the relative probability of finding triplets, etc., of the molecules' constituent atoms at various separation radii and the angular relative probability distributions that describe the molecular orientations.…”

Section: -38mentioning

confidence: 72%

Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids

Ploetz

Karunaweera

Smith

2015

The Journal of Chemical Physics

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Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined. C 2015 AIP Publishing LLC. [http://dx

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Triplet correlations in two-dimensional colloidal model liquids

Cited by 18 publications

References 41 publications

Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Three-body forces at work: Three-body potentials derived from triplet correlations in colloidal suspensions

Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids

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