Long-range attraction, plates

J.H. De Boer and H.C. Hamaker computed the London interaction between a pair of semi-infinite plates and between spherical particles. They showed that, despite the relatively long-range attractive nature of the force between molecular pairs, the total attractive force between the bodies decays much less rapidly. 

It has been shown [21j that the dispersion interaction between pairs of atoms is additive. Calculations show [22] that a large long-range attractive interaction may result from the simultaneous dispersion interaction of many atoms. For example, the attractive potential energy of interaction between two flat plates F in vacuum, due to the summation of the pairwise dispersion forces, varies inversely with the square of the distance F oc r" . 

Also, in the 1930 s London (9) indicated the quantum mechanical origin of dispersion forces between apolar molecules and in subsequent work extended these ideas to interaction between particles (10). It was shown that whereas the force between molecules varied inversely as the seventh power of the separation distance, that between thick flat plates varied inversely as the third power of the distance of surface separation. These ideas lead directly to the concept of a "long range van der Waals attractive force. A similar relationship was found for interaction between spheres (10). 

Since the Hamaker constant for proteins in a physiological solution is of the order of 10 20 J, Eq. (18) provides a concentration of approximately 2 M even for the large value of /(=31 X10 50 Jm3 corresponding to Cl- ions [14]. This corresponds to an ideal gas pressure of approximately 50 atm. Consequently, the long-range repulsion or attraction between plates due to the van der Waals interactions between a gas of neutral particles and the plates is expected to be negligible in most cases. 

Klein (1980) has recently measured directly the forces between two mica plates coated by polystyrene in cyclohexane at a temperature (24 °C) below the 0t/-temperature (35 °C). These measurements showed clearly the existence of a long-range force of attraction that is in part attributable to the mutual attraction between the polystyrene segments under worse than 0-conditions. This experiment will be discussed more fully in Section 13.4.1.2. 

Photographic plates used in early instruments have now been abandoned because they are slow, non-reproducible and their response is nonlinear with ion intensity (low dynamic range). However, the principle of simultaneous detection is very attractive. Spark source Mattauch-Herzog spectrographs have long used this detection system. 

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