This treatment requires complete knowledge of the transmittance as a function of frequency for all components in the relevant suspension. According to the DLVO theory, the total interaction potential was calculated by summing the repulsive and attractive potentials of each suspension (a total of 84 suspensions) as a function of separation distance.
INTRODUCTION
Van der Waals Attractive Potential
Therefore, if the separation distance between the two atoms/molecules is greater than the wavelength of the characteristic radiation, the charge. Furthermore, the Hamaker constant must be calculated knowing the dielectric spectra (of each component) as a function of frequency.
Repulsive Potential
From equation 41, the Debye length can be defined as a measure of the double layer thickness. Knowing the diffuse double-layer electrostatic potential allows the calculation of the diffuse double-layer interaction potential.
Total Interaction Potential
Curve A is represented by a positive primary maximum potential and no primary or secondary minimum potentials. The predicted stability of the colloidal suspension in curve C is dependent on two variables – the magnitude of the energy barrier (difference between the primary maximum and the secondary minimum) and the separation distance associated with the secondary minimum.
List of Variables
CIR – Characteristic oscillator strength for the infrared frequency range CUV – Characteristic oscillator strength for the ultraviolet frequency range. ULondon – Interaction potential due to the London scattering effect Um – Free energy in the midpoint plane between interacting particles U∞ – Free energy of the bulk suspension.
Landau, “A theory of the stability of strongly charged lyophobic sols and the adhesion of strongly charged particles in electrolyte solutions,” Acta Physicochim. Parsegian, "Van der Waals forces: special features in lipid-water systems and a general calculation method based on Lifshitz theory". Pashley, "Van der Waals Interaction for Liquid Water: Comparison of the Oscillator Model Approximation and Application of the Kramers-Kronig Equation to Full Spectral Data," J.
Hsia, "Van der Waals calculation of the force between laminated media as applied to the magnetic memory head-disk interface", J.
PAPER #1
Title
Keywords
Abstract
Introduction
The Hamaker constant (A) includes all material specific terms; the other terms in equation 70 describe the geometry of the system. The resulting Van der Waals force is calculated by correlating the changes in the electromagnetic field between two bodies, causing the interacting fields to be in phase. The role of the suspending medium is to further modify the interacting electromagnetic field between colloidal particles.
The band gap energy is determined by the amount of energy required for an electron in the valence band to move to the conduction band.10-12 Therefore the material will absorb light corresponding to that energy resulting in a dielectric relaxation.
Determination of Spectral Parameters
Obtaining this information requires knowledge of the entire complex permittivity on a real frequency axis from zero to infinity. This knowledge is then used to calculate ε(iξn) via Kramers-Kronig relations.4 The required information is not readily available for many materials. but by treating the permittivity as damped oscillators the characteristic absorption frequencies and strengths can be derived.13 This treatment, developed by Ninham and Parsegian, models the complex permittivity using a Debye relaxation for the microwave region and a Lorentz electron dispersion term for infrared by by means of radiation. ultraviolet areas:13. The dielectric dispersion parameters for each colloid and medium were characterized within the microwave, infrared, visible, and ultraviolet ranges of the electromagnetic spectrum for use in the Ninham-Parsegian model (Table V). Therefore, at frequencies higher than that of the final ultraviolet relaxation, the relative static permittivity is equal to unity.
The spectroscopic dispersion parameters used for water were derived from Bergström.3 A scheme was prepared to help facilitate the understanding of the dispersion properties required for the analysis (Figure 4).
Previous Approach to Approximate non-Retarded Hamaker Constant
Characterization of the Mediums
Since the relative permittivity of a material at frequencies higher than that of the ultraviolet relaxation frequency is unity, εr(ω) →1 as ω → ∞ (demonstrated in Equation 78) the total characteristic strength of the infrared oscillator can be calculated. Non-delayed Hamaker constant as a function of the refractive index of the medium, showing that for some materials there is a correlation between the two. If the square root of the refractive index is approximately equal to the relative static permittivity, the contribution from the frequencies lower than the ultraviolet frequencies is negligible.
Therefore, studying the correlation between the Hamaker constant and the refractive index of the medium will allow the determination of the relative influence that the electron dispersion properties have on the colloid in question.
Characterization of Colloids
Correlation of the approximate Hamaker constant with the Hamaker constant using the accepted value of ωUV without non-oxide materials. Correlation of the approximate Hamaker constant with the Hamaker constant using the accepted value of ωUV. A negative value indicates a decrease in the non-retarded Hamaker constant when microwave relaxation is not included in the calculation.).
Comparison of non-disabled Hamaker Constant (at 298K) in water with the ionic character of the bond.
Hamaker Constant Calculations
The band gap method described in this work uses the band gap of a particle to approximate the UV/visible spectroscopic properties. Determining the band gap energy is a relatively simple process and for most materials values are published. The Pugh approximation is the simplest of the three non-retarded methods of calculating the Hamaker constant, requiring only the knowledge of the static dielectric conditions of the particles and the suspending medium.
For all media the Cauchy method was used except for sec-butanol in which the first ionization potential was used due to the lack of available refractive index data (Table V).
Conclusions
The range of the Hamaker constant values for a single particle type in the different suspending media (excluding vacuum) is 2.70 x 10-20J, while the range of the Hamaker constant for a single suspending medium with different particles is 33.4 x 10 is -20J. Based on the Hamaker constants, it appears that silica (both glassy and quartz) generates a weak van der Waals attraction between particles, while Co3O4 generates the largest van der Waals force.
List of Variables
Maryott, “Tables of dielectric dispersion data for pure liquids and dilute solutions,” National Bureau of Standards Circular 589 (USA), 1958. Cáceres, “Refractive index temperature and wavelength dependencies of normal saturated fatty acids in the liquid state,” Exp. Riedle, “Direct measurement of the group velocity mismatch and derivation of the refractive index dispersion for a variety of solvents in the.
White, “The calculation of Hamaker constants from Lifshitz theory with applications to wetting phenomena,” Adv.
PAPER #2
Experimental
The Co sample was degassed but not heated due to the flammable nature of the powder. The advantage of the laser method is that it allows the direct observation of particle mobility in an applied electric field. Before each measurement, the instrument was returned to the zero velocity plane within the sample holder.
The location of the zero-velocity plane was determined by the thickness of the sample holder and the magnification power of the objective lens.
Results and Discussion
The thickness of the double layer is an important aspect regarding the repulsive potential. The diffuse double layer electrostatic potential has been calculated for each powder type in each solvent as a function of distance. In all samples tested, water was observed to have the lowest diffuse double layer electrostatic potential gradient.
From equation 93, the diffuse double-layer interaction potential at the midpoint plane can be calculated as a function of the particle separation distance.
Conclusions
Isopropanol, sec-Butanol, acetone and 2-butanone also have good dispersion characteristics based on repulsion potential data. Suspensions made using heptane, toluene, or octanoic acid as the suspending medium showed that, according to rejection potential data, most colloids tested would aggregate. All colloids suspended in acetone, methanol or ethanol exhibit a significant rejection potential and are therefore hypothesized as universal media - allowing the dispersion of any studied colloidal system.
Possible candidate systems for dispersion are identified by observing the generation of the rejection potential.
List of Variables
In contrast, colloids that developed a smaller double layer (non-polar media) had a lower charge density and therefore a large charge gradient (charge decreased rapidly from the colloidal surface). Heptane and toluene are not expected to result in a stable suspension without the use of a surfactant, while each colloid tested in acetone, methanol, and ethanol developed a large repulsion potential that can be translated into suspension stability without the need for use of surfactant. Um – Free energy on the mid-plane between interacting particles U∞ – Free energy of the underlying suspension.
Mills, “Electrokinetic studies of colloidal silica particles dispersed in nonaqueous media in the presence of a nonionic surfactant, dodecyl hexaethylene glycol monoether (C12E6),” Colloids Surf., A.
PAPER #3
Rheology of the Suspensions
The viscosity of the suspension medium was taken into account by using the specific viscosity (Equation 102) to describe the suspension viscosity instead of the measured viscosity. The stability of the suspension was defined by the viscosity at a shear rate of 1.0s-1, which corresponds to the y-intercept in equation 101. The specific viscosity for each suspension at a shear rate of 1.0s-1 is summarized in Table XVII.
Suspensions below the specific viscosity limit of 1.1 x 104 have the specific viscosity value in italics and bold.
Determination of Stability Mechanism
Since these points are located just outside the electrostatic band, it proves that non-electrostatic effects are not the primary mechanism, although they are important. By comparing the shear thinning exponent with the specific viscosity at a shear rate of 1.0 s-1, it is shown that a trend develops for suspensions in which the only significant dispersion mechanism is the electrostatic mechanism. Using the master curve, the primary dispersion mechanism of methanol, ethanol, isopropanol, sec-butanol, acetone, 2-butanone, toluene and water was found to be an electrostatic mechanism.
It was also found that the primary dispersion mechanism of heptane and octanoic acid is an electrostatic mechanism; however, since the points did not fall within the 95% confidence interval of the trend line, other dispersion mechanisms, although not the primary mechanism, were found to be important and influence particle interactions.
PAPER #4
Repulsive Potential
From the ζ-potential measurements, the repulsion potential between particles due to double layer overlap can be calculated. The Debye length is inversely proportional to the double layer thickness and is a function of the static permittivity of the suspension medium. The larger the double layer, the less a charge decays from the particle surface to the bulk.
Because charge decay is much less in polar media, the double layers of colloids will interact at greater separation distances than when a nonpolar medium is used.
Attractive Potential
Repulsive potential generated in vitreous silica as a function of separation distance for different suspending media. The attractive potential versus particle separation distance curves have the same shape, unlike the repulsive potential curves. Total van der Waals attractive potential as a function of separation distance and calculated non-delayed Hamaker constants (x 10-20J) for parenthesized vitreous silica near the identified environment.
Total Interaction Potential
Where η1.0 is the viscosity of the suspension at a shear rate of 1.0s-1 and n is the shear thinning exponent. Conversely, if the colloids form agglomerates and subsequently settle out of the suspension, the suspension is described as unstable (flocculated). The isoelectric point corresponds to the pH at which the shear plane of the colloids has no net charge.
For each of the suspensions, the thermal limit and the separation of the secondary minimum if present were recorded. If the thermal boundary is greater than the internal thermal energy of the colloids, the colloids will move to the secondary minimum and act independently or as a weakly flocculated suspension depending on the separation distance to the secondary minimum. To determine the internal thermal energy of the colloids at 298K, the calculated thermal limits were compared with viscosity measurements.
CONCLUSIONS
It was observed that the ionic character had an indirect relationship with the ionic character of the bonds in the colloid for oxide particles. The basis for this observation is believed to be due to the increased strength of the dipoles as the ionic character increases. The correlation between ζ-potential and suspension stability is inaccurate because it does not account for the decay of charge away from the colloid.
The charge breakdown is indirectly proportional to the thickness of the bilayer formed: the larger the bilayer, the less the charge of the colloid in the bulk suspension is broken down.
APPENDIX A: ELLIPTICAL INTEGRAL PROGRAM
Program
1 Function EllipInt2(ByVal phi As Double, ByVal .k As Double) As Double ' 2nd order elliptic integral – k in Rad, phi in Rad. Example of If Then statements to determine the value of the elliptic integral from Table A-IV.
