What frequencies are important to the interaction of real materials? It is best to learn from example. If we can develop an intuition to know the significant frequencies of fluctuation, our partial ignorance of absorption spectra need not daunt us in computation or, better, this intuition might give us some idea about the accuracy of computation. Differences in dielectric response create the force; sampling-frequency density weights the contribution from higher frequencies; retardation snuffs out the highest frequencies first. These general features show up in specific examples. Water, hydrocarbon (liquid tetradecane), gold, and mica are not only popular materials in van der Waals force measurement but, as a group, they also display a wide variety of dielectric response. (See, e.g., tables in SubSection L2.4.D).

Their detailed energy-absorption spectra as functions of radial frequency ωR translate into smooth functions ε(iξ) of imaginary frequency. This blurring of details in ε(iξ) is one reason why it is often possible to compute van der Waals interactions to good accuracy without full knowledge of spectra (see Fig. L1.21).

To see how these different ε(iξ) functions combine to create an interaction, consider the case of two hydrocarbon half-spaces A = B = H across water medium m = W. First plot εH(iξ) and εW(iξ) as continuous functions [see Fig. L1.22(a)].