Hamaker's constant

The Hamaker constant A is a quantity for the force between two particles between which Van der Waals forces act. The Hamaker constant depends on the substances of the two particles (which may be different) and the medium in between. The Hamaker constant is named after the Dutch physicist Hugo Christiaan Hamaker (1905–1993). The Hamaker constant is independent of the geometry of the particles.

definition

The Hamaker constant is defined by:

${\displaystyle A=\pi ^{2}\cdot C\cdot \rho _{1}\cdot \rho _{2}}$

Here and stand for the number of atoms per unit volume in two interacting bodies. is a parameter for the particle-particle interaction. The SI unit of the Hamaker constant is the joule . The values ​​of the constants are exceptionally small and range from 10 ⁻¹⁹ to 10 ⁻²⁰ joules. The value can be determined either from the dielectric constant or the ionization potential . ${\displaystyle \rho _{1}}$ ${\displaystyle \rho _{2}}$ ${\displaystyle C}$

The Hamaker constant offers the possibility of determining the interaction coefficient from the van der Waals interaction potential, which has the following form for small molecules or atoms (for more macroscopic bodies the van der Waals potential has other forms, see Van- der Waals forces ): ${\displaystyle C}$

${\displaystyle w(r)=-C/r^{6}}$

For example , the Hamaker constant plays an important role in the description of dispersions . If its value decreases, this leads to a decrease in the Van der Waals interaction energy, which in turn leads to a relative increase in the repulsive interaction of the particles in the suspension, making the system more stable. The constant itself can be influenced by the solvent used. The potential for attraction is also dependent on the substance.

The Hamaker method and constant of the same name neglect matrix effects between the interacting particles. In the 1950s, Jewgeni Lifschitz developed a descriptive model of Van der Waals energy that also takes into account the dielectric interaction of the matrix. It is a macroscopic description of the optical properties of the interacting bodies.

In addition, the Hamaker constant can be estimated from the surface energy : ${\displaystyle \gamma }$

${\displaystyle A=24\pi \gamma d_{0}^{2}}$

${\displaystyle d_{0}}$is defined as the intermolecular equilibrium distance between the molecules. If, on the other hand, the surface energy is only determined by the dispersive part, the Fowkes equation can be used:

${\displaystyle A=6\pi \gamma ^{d}d_{0}^{2}}$

The van der Waals forces have a short range of a few hundred angstroms .

Typical values ​​for some materials

material	A in 10 −20 years
acetone	04.2
water	04.35
toluene	05.4
Polystyrene	07.8 ... 09.8
Alumina	15.4
Metals	16 , 0… 45
silver	39.8
gold	45.3

Dielectrics

The following applies to dielectric media :

${\displaystyle A={\frac {3}{4}}k_{B}T{\frac {\epsilon _{1}-\epsilon _{3}}{\epsilon _{1}+\epsilon _{3}}}{\frac {\epsilon _{2}-\epsilon _{3}}{\epsilon _{2}+\epsilon _{3}}}+{\frac {3h\nu _{e}}{8{\sqrt {2}}}}{\frac {(n_{1}^{2}-n_{3}^{2})(n_{2}^{2}-n_{3}^{2})}{{\sqrt {n_{1}^{2}+n_{3}^{2}}}\left({\sqrt {n_{1}^{2}+n_{3}^{2}}}+{\sqrt {n_{2}^{2}+n_{3}^{2}}}\right)}},}$

with the dielectric constants and the refractive indices of the media involved (where 3 is the intermediate medium), the absorption frequency (which must be similar for all media involved), the Planck constant and the Boltzmann constant . The first term in the above formula takes into account the Debye and Keesom interaction, while the second term in the above formula takes into account the London dispersion interaction. ${\displaystyle \epsilon _{i}}$ ${\displaystyle n_{i}}$ ${\displaystyle \nu _{e}}$ ${\displaystyle h}$ ${\displaystyle k_{B}}$

Individual evidence

1. ↑ HC Hamaker: The London - van der Waals attraction between spherical particles. In: Physica IV, 10, 1937, pp. 1058-1072. doi : 10.1016 / S0031-8914 (37) 80203-7
2. ↑ L. Seung-woo Lee and WM Sigmund: AFM study of repulsive van der Waals forces between Teflon AF thin film and silica or alumina. In: Colloids and Surfaces A: Physicochemical and Engineering Aspects 204, 2002, pp. 43-50.
3. ↑ L. Bergstrom: Hamaker constants of inorganic materials. In: Advances in Colloid and Interface Science 70, 1997. pp. 125-169.
4. ↑ ^{a b} S. Dünisch: Investigation of the mode of action of nanomaterials Dissertation, Julius Maximilians University of Würzburg, 2005
5. ↑ D. Tabor and FRS Winterton: The direct measurement of normal and retarded van der Waals forces. In: Proc. Roy. Soc. 312, 1969, pp. 435-450.
6. ^ University of Magdeburg: Lecture on processing technology and recycling Prof. Dr. J. Tomas (PDF; 564 kB) of September 21, 2008 p. 31.
7. ^ J. Visser: Van der Waals and other cohesive forces affecting powder fluidization. In: Powder Technology 58, 1989, pp. 1-10.
8. ^ EM Lifshitz, Soviet Phys. JETP 2, 1956, p. 73.
9. ↑ DC Prieve and WB Russel: Simplified predictions of Hamaker Constants from Lifshitz Theory. In: Journal of Colloid and Interface Science 125, 1987, pp. 1-13.
10. ↑ PC Hiemenz and R. Rajagopalan, Principles of Colloid and Surface Chemistry, Vol. 14. CRC press, 1997.
11. ↑ PC Hiemenz and R. Rajagopalan, Principles of Colloid and Surface Chemistry, Vol. 14. CRC press, 1997.
12. ↑ PC Hiemenz and R. Rajagopalan, Principles of Colloid and Surface Chemistry, Vol. 14. CRC press, 1997.
13. ^ ^{A b} Fabio L. Leite, et al .: Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy. In: International Journal of Molecular Sciences . 13, 2012, p. 12773, doi : 10.3390 / ijms131012773 .

literature

• C. Schlumbohm: Stability and structural modifications in catalyst dispersions of the direct methanol fuel cell. In: Writings from Forschungszentrum Jülich, Energietechnik 48 series , 2005, ISBN 3-89336-429-3
• A. Mersmann et al .: Thermal process engineering. Springer-Verlag, 2005, pp. 81–82. ISBN 3-540-23648-1
• J. Laven and JPC Vissers: The Hamaker and the Lifshitz approaches for the Van der Waals interaction between particles of composite materials dispersed in a medium. In: Colloids and Surfaces A: Physicochemical and Engineering Aspects 152, 1999, pp. 345-355.
• HY Xie: Hamaker theory for atom-tip interactions of non-reactive surface in noncontact AFM. In: Applied Surface Science 239, 2005, pp. 129-131.