Hamaker Software

Hamaker.ab Program

For Calculating London Dispersion Spectra and Hamaker Constants for the London Dispersion Forces for 3 and 5 layer configurations, in both the Nonretarded and the Retarded cases.

For more information on the fundamentals and applications of London Dispersion Forces and Hamaker Constants Download a recent review Article or look at the Dispersion Page of this Website.

Full Spectral Database

Figure 1. The Hamaker Program Interface.

Hamaker contains a database of interband transition strength spectra and their London dispersion (LD) spectra. Since the calculation of the LD spectra is time consuming, these spectra are databased, and available for rapid calculation of the Hamaker constant for different configurations, Figure 1.

Calculation of the London Dispersion Spectrum

The London dispersion spectrum is calculated from the interband transition strenght spectra (Re[Jcv] is proportional to E² Im[epsilon] ) as shown in Figure 2 and the result stored in the Hamaker database. Low and high energy wings are attached to the experimental data so as to extrapolate the results over a sufficiently large energy range. The Jcv spectra can be acquired from VUV spectroscopy, Valence EELS spectroscopy or from first principles LDA band structure calculations.

Figure 1.

Nonretarded Three Layer, A(1-2-1) Hamaker Constants

Figure 3.

To Calculate the Nonretarded Hamaker constant for Al2O3 separated from Al2O3 by Vacuum, one just labels the Al2O3 spectra as Layer 1 and the Vacuum spectra as Layer 2. Then push N 1-2-1 and the results are presented in the dialog box, Figure 3.

The Nonretarded Hamaker constant is calculated presented for three temperatures, 0 K, Room Temperature and 2000 K. If one wants the temperature dependence of the Hamaker constant presented explicitly, then just hit A vs. T and the Hamaker Constant result is presented as a function of temperature as shown in Figure 4. The Temperature dependence effect is typically small.

Figure 4.

If instead SiO2 replaces Vacuum, then the Hamaker constant is reduced as shown in Figure 5.

Figure 5.

Nonretarded A(1-2-3) Hamaker Constants

Non-Wetting Case, A>0

If one calculates the Nonretarded Hamaker constant for a surficial film of Al2O3, coating an SiO2 substrate, the Hamaker constant, Figure 6 is postive, representing a non-wetting condition.

Figure 6.

Wetting Case, A<0

If instead a surficial film of SiO2 is coating an Al2O3 substrate, then the Non-Retarded Hamaker Constant is negative corresponding to a wetting condition, Figure 7.

Figure 7.

LD Contribution to Contact Angles and Surface Energies

For systems in which London Dispersion forces dominate, (as is not the case for most ionic ceramic materials, but is a reasonable assumption for most polymers), one can calculate the Contact angles and surface energies, assuming a value of d0, the effect interatomic spacing that is typically assumed to be 0.165nm. For example, a droplet of water on polyester has a calculated contact angle of 53.5 degrees and the surface and interface energies are also listed in Figure 8.

Figure 8.

Retarded Hamaker Constants

As an interlayer increases in thickness, then the effects of optical retardation come into play and reduce the magnitude of the Hamaker constant and the London disperion force. It is important to take into account these retardation effects for thick layers, and we fully calculate the Retarded Hamaker constant, London Dispersion Energy and Forces as a function of layer thickness. For the example of an SiO2 surficial layer on an Al2O3 substrate, the Retarded results are shown in Figure 9, with the Retarded Hamaker constant shown in Red.

Figure 9.

For more information on the fundamentals and applications of London Dispersion Forces and Hamaker Constants Download a recent review Article or look at the Dispersion Page of this Website.