Non-retarded Hamaker Constants Research Articles

Hamaker functions for kaolinite and montmorillonite

An oscillator representation for the calculation of van der Waals forces/energies is presented for kaolinite and montmorillonite. The non-retarded Hamaker constants across water (air) are 5.1 (59.2) zJ and 7.3 (75.4) zJ for montmorillonite and kaolinite, respectively. The combined effect of retardation and geometrical peculiarities of the monmorillonite system are discussed briefly. It is shown that the van der Waals free energy between two montmorillonite layers of finite thickness, immersed in water, changes from attractive to repulsive at a separation distance primarily determined by their thickness.

Lifshitz calculations of Hamaker constants for fusion relevant materials

The determination of the Hamaker constant is necessary for the quantification of the van der Waals force and thus of dust-wall adhesion. Here Lifshitz theory is employed for the calculation of the non-retarded Hamaker constants of ten common dust-wall material combinations. Extended-in-frequency reliable dielectric data are employed and two independent computational methods are considered for the calculation of the dielectric function at the imaginary Matsubara frequencies. The Hamaker constant for tungsten-on-tungsten is the largest calculated, which implies the strongest adhesion. The Hamaker constant for graphite-on-graphite is much smaller than tungsten-on-tungsten and even beryllium-on-beryllium. Copper, chromium and especially aluminium are identified to be proper adhesive proxies of beryllium.

Dielectric properties of lignin and glucomannan as determined by spectroscopic ellipsometry and Lifshitz estimates of non-retarded Hamaker constants

We present in this study a quantitative estimate of the dispersive interactions between lignin, hemicellulose and cellulose, which are the dominating components in wood and also extensively used to ...

Hamaker Constants of Iron Oxide Nanoparticles

The Hamaker constants for iron oxide nanoparticles in various media have been calculated using Lifshitz theory. Expressions for the dielectric responses of three iron oxide phases (magnetite, maghemite, and hematite) were derived from recently published optical data. The nonretarded Hamaker constants for the iron oxide nanoparticles interacting across water, A(1w1) = 33 - 39 zJ, correlate relatively well with previous reports, whereas the calculated values in nonpolar solvents (hexane and toluene), A(131) = 9 - 29 zJ, are much lower than the previous estimates, particularly for magnetite. The magnitude of van der Waals interactions varies significantly between the studied phases (magnetite < maghemite < hematite), which highlights the importance of a thorough characterization of the particles. The contribution of magnetic dispersion interactions for particle sizes in the superparamagnetic regime was found to be negligible. Previous conjectures related to colloidal stability and self-assembly have been revisited on the basis of the new Lifshitz values of the Hamaker constants.

Computation of Nonretarded London Dispersion Coefficients and Hamaker Constants of Copper Phthalocyanine.

A time-dependent density functional theory (TDDFT) scheme has been validated for predictions of the dispersion coefficients of five molecules (H2O, NH3, CO2, C6H6, and pentane) and for predictions of the static dipole polarizabilities of three organometallic compounds (TiCl4, OsO4, and Ge(CH3)4). The convergence of grid spacing has been examined, and two types of pseudopotentials and 13 density functionals have been tested. The nonretarded Hamaker constants A11 are calculated by employing a semiempirical parameter a along with the standard Hamaker constant equation. The parameter a is optimized against six accurate Hamaker constants obtained from the full Lifshitz theory. The dispersion coefficients of copper phthalocyanine CuPc and CuPc-SO3H are then computed. Using the theoretical densities of ρ1 = 1.63 and 1.62 g/cm(3), the Hamaker constants A11 of crystalline α-CuPc and β-CuPc are found to be 14.73 × 10(-20) and 14.66 × 10(-20) J, respectively. Using the experimentally derived density of ρ1 = 1.56 g/cm(3) for a commercially available β-CuPc (nanoparticles of ∼90 nm hydrodynamic diameter), A11 = 13.52 × 10(-20) J is found. Its corresponding effective Hamaker constant in water (A121) is calculated to be 3.07 × 10(-20) J. All computed A11 values for CuPc are noted to be higher than those reported previously.

Colloidal dispersion stability of unilamellar DPPC vesicles in aqueous electrolyte solutions and comparisons to predictions of the DLVO theory

The colloidal dispersion stability at 25 °C of aqueous dispersions of sonicated DPPC (dipalmitoylphosphatidylcholine) vesicles was quantitatively evaluated from the Fuchs–Smoluchowski stability ratio W. Data of average particle size vs. time were obtained with dynamic light scattering measurements. Dispersions in water, 1, 10, or 150 mM aqueous sodium chloride, and phosphate buffer saline (PBS) solutions were tested. The W-values ranged from about 8 × 10 6 to 6 × 10 8. The dispersed particles had small but significant zeta-potentials ζ, implying that the vesicles had some significant charge due to preferential adsorption of negative hydroxyl ions over hydronium ions in water, and chloride ions over sodium ions in the electrolyte solutions. Hence, there was some contribution of the double-layer electrostatic forces to the dispersion stability. The initial values of ζ ranged from −30 to 8 mV. The vesicle non-retarded Hamaker constants were estimated from the published values of the Hamaker constants of DPPC and water in vacuum, and they varied with the vesicle size. A new dimensionless model of the DLVO theory for spherical particles was formulated, focusing on the conditions for the existence of a positive interaction potential energy maximum, Φ max, which is linked to W. The dimensionless number N, which is defined as the ratio of the electric double layer energy to the Hamaker constant A, was found to be the key determinant of Φ max and W. DLVO calculations of Φ max, and W with error analysis show that the charged DPPC vesicles tested are quite more stable than predicted. This discrepancy highlights some significant weaknesses in the premises and approximations of the DLVO theory, and the need for improved theories, possibly considering other repulsive forces.

Coalescence of a bubble at a fluid–fluid interface: Comparison of theory and experiment

Coalescence times for air bubbles rising through hexadecane to an air-hexadecane interface are measured and compared with an analysis based upon our previous extension of continuum mechanics to the nanoscale [J.C. Slattery, E.-S. Oh, K. Fu, Chem. Eng. Sci. 59 (2004) 4621-4635] with the assumption of retarded dispersion forces. The relation between the retarded and non-retarded Hamaker constants proposed by Görner and Pich [J. Aerosol Sci. 20 (7) (1989) 735-747] is tested for the first time.

Determination of contact angles: Consistency between experiment and theory

The Lifshitz–van der Waals theory has been used to calculate the contact angles of dispersive liquids and solids: diiodomethane, α-bromonaphtalene, methylnaphtalene, benzene, and n-octane, liquids on polytetrafluoroethylene, polystyrene, polyisobutene, polyvinylchloride, and polyethylene. The theoretical calculation of the contact angles was based on the nonretarded Hamaker constants which have been calculated from the dielectric properties of the materials and application of the Lifshitz theory. These theoretical contact angles were compared with the experimental contact angles measured by the Wilhelmy plate method. Closely related values have been found for the theoretical and experimental contact angles.

Hydrophobic radiofrequency plasma-deposited polymer films: dielectric properties and surface forces

Advancing and receding contact angles for various liquids placed on the surface of thin n-hexane plasma polymer films have confirmed that the surface is hydrophobic; comparable to polyethylene. A waveguide technique has been employed to determine the refractive indices of the plasma polymer films in the visible and near infrared regions of the dielectric spectrum. Along with ESCA data that provide polymer group functionality, this information has been used to estimate the n-hexane plasma polymer density and to construct a simple dielectric permeability function (ϵ(iξ), the dielectric constant at imaginary frequency iξ) for the polymer. The dielectric permeability function and Lifshitz theory have been used to calculate the Hamaker function (including non-retarded Hamaker constants) which should characterise the van der Waals interaction in systems that contain n-hexane plasma polymers. The atomic force microscope (AFM) has been employed to measure the force of interaction between n-hexane plasma polymer films deposited on muscovite mica flat plates and either uncoated silicon nitride AFM tips or n-hexane plasma polymer coated glass spheres. The force versus separation curves have been compared with DLVO theory. The homointeraction between n-hexane plasma polymer coatings in water initially displays a long-range attraction additional to van der Waals interaction. There is evidence that after prolonged immersion in water the thin n-hexane plasma polymer films swell.

Van der Waals Interaction, Surface Free Energies, and Contact Angles: Dispersive Polymers and Liquids

The Lifshitz theory of van der Waals interaction has been employed to calculate the contact angles of diiodomethane, 1-bromonaphthalene, 1-methylnaphthalene, bromobenzene, 1-tert-butylnaphthalene, liquid paraffin, and hexadecane on poly(dimethylsiloxane), poly(4-methyl-1-pentene), polyethylene, natural rubber, and polystyrene surfaces. The theoretical treatment is based on the equation cos θ = [(2APVL/ALVL)(HoLVL/HoPVL)2] − 1, where θ is the contact angle and APVL and ALVL are the non-retarded Hamaker constants for the heterointeraction between polymer and liquid across vacuum and the homo interaction of the liquid across vacuum, respectively. Nonretarded Hamaker constants have been determined from the dielectric properties of the materials and application of the Lifshitz theory. HoLVL and HoPVL are the equilibrium “contact” surface separations associated with the liquid−liquid homointeraction and polymer−liquid heterointeraction across vacuum, respectively. HoLVL values, and the analogous HoPVP values associated with polymer homointeraction, have been estimated from the surface free energies of the dispersive liquids and polymers. Four different approaches, each with a different assumption regarding the heterointeraction between polymer and liquid, have been used to obtain HoPVL values: (i) HoPVL = HoLVL, (ii) HoPVL = HoPVP, (iii) a geometric mean relationship, HoPVL = (HoPVPHoLVL)1/2, and (iv) an arithmetic mean relationship, HoPVL = (HoPVP + HoLVL)/2. Theoretical contact angles obtained with the four approaches have been compared with experimental contact angles. In general, the approaches which employ the combining rules, whether geometric or arithmetic, provide the best agreement between theory and experiment. Previous work that has dealt with the contact angles of n-alkanes on poly(tetrafluoroethylene) has also been re-examined. For the perfluorocarbon−hydrocarbon system none of the approaches are able to reconcile theory and experiment.

Surface chemistry and tip-sample interactions in atomic force microscopy

Microfabricated silicon nitride cantilevers with integral tips are commonly employed in atomic force microscopy. The link between surface chemistry, including surface group acid-base dissociation and counterion complexation, and tip-sample interaction in aqueous electrolyte solution is examined. Silicon nitride tip interaction with “flat plate” samples of both muscovite mica and silicon nitride as a function of aqueous solution pH and electrolyte concentration is investigated. The long-range component of the interaction is normalized with respect to an effective tip radius, and as a result electrical double layer and van der Waals interactions can be discussed quantitatively. Microfracture and tribochemical tip wear is also discussed with reference to atomic force microscope contact mode imaging. Non-retarded Hamaker constants are reported for a range of silicon nitride, silica, silicon and muscovite mica systems.

Full spectral calculation of non-retarded Hamaker constants for ceramic systems from interband transition strengths

The van der Waals (vdW) interaction is one of the key terms in the force balances dictating wetting behavior and intergranular film thicknesses. The characteristics of thin intergranular or surficial glass films are of increasing importance due to their role in determining the properties of polycrystalline ceramics. The Hamaker constant scales the London dispersion force part of the vdW interaction for a particular configuration of grains and films and is a direct function of the interband optical properties of the interatomic bonds of the materials. For ceramics, much previous work focused on simplified models, such as the Tabor-Winterton approximation (TWA), to determine Hamaker constants based on refractive indices. Herein we develop full spectral calculations of the Hamaker constants for various ceramic systems using experimentally determined interband transition strengths (ĵcv(ω)) to directly derive the London dispersion spectra (ε2(ξ)) from which spectral difference functions lead to direct determination of the Hamaker constants. The results affirm the expectation that transitions involving valence electrons provide the predominant contribution to the dispersion forces for the compounds examined. Calculations have been done for the planar case of a gap between two semi-infinite bodies containing either vacuum or an intervening glassy layer. The results indicate that the TWA is useful for oxides with relatively low refractive indices, i.e., n ~ 1.4–;1.8. However, when any of the materials have larger indices, this approximation becomes inexact, and no obvious, simple correction to the TWA gives uniformly good results, as the behavior differs for simple covalent materials and for oxides with partially filled d-shells but having similar refractive indices. An important consequence is that Hamaker constants are smaller for such high index materials, especially oxides, with intervening glassy films than might be expected from approximations. Calculations have also been done for two other geometries, i.e., for an intervening film with a layer of a third material at both interfaces and for glass coated free surfaces. The former of these provides first insights regarding the behavior with nonuniform films which often differs markedly from that expected for homogeneous films of the same average composition.

Simplified predictions of Hamaker constants from Lifshitz theory

Approximations to Lifshitz theory are developed to estimate the van der Waals interaction of coated and uncoated nonmetallic half spaces as a function of separation distance. Using a three-parameter representation of the dielectric spectrum of each material, based only on refractive index data from the visible part of the spectrum and the static dielectric constant, the approximations yield nonretarded Hamaker constants within an average error of 4% of corresponding values computed from rigorous evaluation of Lifshitz theory with the complete dielectric spectra. The effects of retardation and a coating on one of the half-spaces can also be estimated from the approximations but with less accuracy. These approximations should be useful in semiquantitative applications requiring a very large number of such evaluations but not a high level of precision (e.g., to screen materials to be used as a coating or to assess stability to flocculation).