A simple extension of the commonly used fitting equation for oscillatory structural forces in case of silica nanoparticle suspensions

Abstract

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.

Screening Lengths in Ionic Fluids

“…Our theory explains recent ex-perimental findings concerning a jump of the wavelength of the structural force in ionic fluids [14], and it sheds new light on the screening in dense electrolytes and the fitting of structural forces [19]. Our results are important for the interpretation of measurements and effective interactions [19,[40][41][42], because they show that species correlation functions can be superpositions of charge contributions and density contributions of the same order of magnitude. A fit using the asymptotic form (12) hence cannot be expected to be accurate on intermediate length scales.…”

“…However, in technological applications, ions are usually mixed with a solvent in order to enhance conductivity and reduce viscosity [15][16][17]. This raises the important question of how the presence of solvents influences ion-ion correlations.Recent surface force balance experiments show that the disjoining force between charged surfaces across ionic liquid-solvent mixtures decays in an oscillatory manner * andreas.haertel@physik.uni-freiburg.de with an exponentially decaying envelope [14,18,19]. However, as the ion concentration is increased, the oscillation frequency undergoes a steplike transition [14] -at low ion concentration, it is comparable to the size of the solvent molecule, whereas for concentrated electrolytes it is comparable to the size of an ion pair.…”

The Influence of Mechanical Deformations on Surface Force Measurements

“…gives a decay of ∼1 nm and an amplitude of ∼4 mN, respectively, one order of magnitude smaller and two orders of magnitude larger than for long-range electrostatic force reported for this system [18,26]. In fact, the exponentially decaying harmonic oscillation given by Equation (2) can be predicted theoretically in the asymptotic limit of large distances (far-field term), and an additional (non-oscillating) exponentially decay has been proposed as a correction at small distances (short-field term, with two additional fitting parameters) [68,73,74]. This second term, which is intrinsic to the liquid for infinitely stiff surfaces, could contribute to the asymmetry of the measured force profile.…”

Atomic Force Microscopy Meets Biophysics, Bioengineering, Chemistry, and Materials Science

“…High-resolution images can be obtained by using af eedback loop that keeps the amplitude of the cantilever oscillation at ac onstant level during scanning. [26][27][28] Second, contact of the cantilever with the sample (the dwell time can be defined by the researcher) permits mechanical properties (e.g., the Young modulus, relaxation time, and viscosity) to be investigated. [16,17] Representative( biological) samples measured with these imaging modes include nanotubes, lipids,p roteins, molecular self-assemblies, or cells.…”

“…[25] The force-distance curvesc an be divided into three parts (see Figure 1, right).F irst, the approachingc urve delivers information about repulsive or attractive forces (e.g.,e lectrostatic,v an der Waals, hydration, or entropic forces). [26][27][28] Second, contact of the cantilever with the sample (the dwell time can be defined by the researcher) permits mechanical properties (e.g., the Young modulus, relaxation time, and viscosity) to be investigated. [29][30][31] Finally Af lexible cantilever (in this case, with as harp tip) interactsw ith the sample (through attractive/repulsive forces),a nd therefore, is the AFMsensing element.…”