Abstract:The equivalence of the asymptotic expression for the interaction energy between a pair of large hard spheres in a fluid of small hard spheres that has been obtained by Roth et al. [Phys. Rev. E, 2000, vol. 62, p. 5360] using Fourier transforms and an expression that we have obtained [J. Colloid Int. Sci., 1999, vol. 210, p. 320] using Laplace transforms is pointed out and commented upon.
“…Particularly, as we can see from Figure , beyond the depletion region, defined by the position of the main repulsive maxima in the energy profile, both results are practically indistinguishable. This is an expected result, because, as we already noted, , both equations have common roots. 2 Energy of interaction between the macrosphere and the flat wall in a monodisperse fluid of hard-sphere particles calculated from the present approach (solid lines) and computed according to the DFT approach proposed by Roth et al (symbols).…”
Section: Sphere−wall Interaction Mediated By a
Bidisperse Fluidsupporting
The interaction between the macrosphere and the flat wall immersed in a binary fluid comprising small and large (size ratio around 1:10) hard spheres has been investigated. We find that the presence of the highly size-asymmetric particles qualitatively modifies the induced excluded-volume interaction between the macrosphere and the flat wall compared to that observed in a single-component suspending fluid comprised of only large or only small species. The role in the interaction between a macrosphere and a flat wall played by species of the fine component that usually is approximated by a continuum medium (primitive description of a bidisperse fluid) is emphasized. Particularly, we show that taking into account the smaller component of a bidisperse suspending fluid modifies significantly the macrosphere-wall depletion attraction that is predicted when only large particles are taken into account. The depletion attraction force created by the presence of small fluid particles enhances the adsorption of large particles and their structuring on the wall.
“…Particularly, as we can see from Figure , beyond the depletion region, defined by the position of the main repulsive maxima in the energy profile, both results are practically indistinguishable. This is an expected result, because, as we already noted, , both equations have common roots. 2 Energy of interaction between the macrosphere and the flat wall in a monodisperse fluid of hard-sphere particles calculated from the present approach (solid lines) and computed according to the DFT approach proposed by Roth et al (symbols).…”
Section: Sphere−wall Interaction Mediated By a
Bidisperse Fluidsupporting
The interaction between the macrosphere and the flat wall immersed in a binary fluid comprising small and large (size ratio around 1:10) hard spheres has been investigated. We find that the presence of the highly size-asymmetric particles qualitatively modifies the induced excluded-volume interaction between the macrosphere and the flat wall compared to that observed in a single-component suspending fluid comprised of only large or only small species. The role in the interaction between a macrosphere and a flat wall played by species of the fine component that usually is approximated by a continuum medium (primitive description of a bidisperse fluid) is emphasized. Particularly, we show that taking into account the smaller component of a bidisperse suspending fluid modifies significantly the macrosphere-wall depletion attraction that is predicted when only large particles are taken into account. The depletion attraction force created by the presence of small fluid particles enhances the adsorption of large particles and their structuring on the wall.
“…Oscillatory structural forces can be described either theoretically via the solutions of numerical simulations [ 34 , 40 – 42 ] or statistical mechanics equations [ 43 – 50 ] or with a semi empirical approach [ 51 – 53 ]. A common example for the latter is an exponentially decreasing harmonic oscillation:…”
Section: Introductionmentioning
confidence: 99%
“…The theoretical descriptions and the semi-empirical approach have in common that they were designed for diluted samples and large separations. Despite this it has been proven that their validity extends towards medium separations [ 35 , 48 , 50 , 54 ]. Trying to fit data at small separations, such as the first and second layer, especially at higher concentrations of particles, remains a challenge.…”
Background: The ordering of molecules or particles in the vicinity of a confining surface leads to the formation of an interfacial region with layers of decreasing order normal to the confining surfaces. The overlap of two interfacial regions gives rise to the well-known phenomenon of oscillatory structural forces. These forces are commonly fitted with an exponentially decaying harmonic oscillation as introduced by Israelachvili (Israelachvili, J. N. Intermolecular & surface forces; Academic Press: San Diego, CA, USA, 1985). From the fit three important parameters are obtained, namely wavelength, amplitude and decay length, which are related to the period, the strength and the correlation length of the oscillatory structural forces, respectively. The paper addresses structural forces between a silica microsphere and a silicon wafer across silica nanoparticle suspensions measured with a colloidal probe AFM. Using the simple fitting procedure with three parameters often leads to underestimation of actually measured forces. The deviation of the fit from the experimental data is especially pronounced at small distances of the confining surfaces and at high concentrations of silica nanoparticles. As a consequence, the parameters of the common fit equation vary with the starting point of the fit. Although the wavelength is least affected and seems to be quite robust against the starting point of the fit, all three parameters show distinct oscillations, with a period similar to the wavelength of the oscillatory structural forces themselves. The oscillations of amplitude and decay length, which are of much higher magnitude, show a phase shift of 180° implying not only a dependence on the starting point of the fit but also on each other. The range affected by this systematic deviation of the fit parameters is much larger than the optically perceived mismatch between fit and experimental data, giving a false impression of robustness of the fit.
Results: By introducing an additional term of exponentially decaying nature the data can be fitted accurately down to very small separations and even for high silica nanoparticle concentrations (10 wt %). Furthermore wavelength, amplitude and decay length become independent of the starting point of the fit and in case of the latter two of each other. The larger forces at small separations indicate a more pronounced ordering behavior of the particles in the final two layers before the wall. This behavior is described by the proposed extension of the common fit equation.
Conclusion: Thus, the extension increases the accessible data range in terms of separation and concentration and strongly increases the accuracy for all fitting parameters in the system studied here.
“…The approaches have also been varied ranging from experiment, 2 density functional theory, [3][4][5][6][7][8][9][10] computer simulations, [11][12][13][14][15][16][17] virial expansions, 18 the Derjaguin approximation, [19][20][21][22] or the integral equation formulation of liquid state theory. 7,[23][24][25][26][27][28][29][30][31][32][33][34] Very recently we have addressed the problem of deriving the density profiles of multicomponent hard-sphere mixtures near a planar hard wall 35 using an alternative approach to the integral equation theory for the structural properties of the system. 36,37 The main aim of this paper is to complement our former results with the study of the depletion potential for various systems involving hard-sphere mixtures.…”
The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the rational function approximation method for the structural properties of hard-sphere mixtures [S. B. Yuste, A. Santos, and M. Lopez de Haro, J. Chem. Phys. 108, 3683 (1998)]. The cases of equal solute particles and of one big particle and a hard planar wall in a background monodisperse hard-sphere fluid are explicitly analyzed. An improvement over the performance of the Percus-Yevick theory and good agreement with available simulation results are found.
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