We consider the irreversible random sequential adsorption of particles taking k sites at a time, on a one‐dimensional lattice. We present an exact expansion for the coverage, θ(t,k)=A0(t)+A1(t)k−1+A2(t)k−2+..., for times, 0≤t≤O(k), and at saturation t=∞. The former is new and the latter extends Mackenzie’s results [J. Chem. Phys. 37, 723 (1962)]. For these expansions, we note that the coefficients Ai≥1(∞) are not obtained as large‐t limits of the Ai≥1(t). Finally, we comment on the Laurent expansions for general O(k)<t<∞, which reveal the occurrence of additional kn terms, with n≳0.
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Apart from simple rearrangements of terms, this follows from evaluating the derivative of Eq. (1) with respect to T, and then applying the variable changes: and
10.
The coefficients of positive and negative powers of z in the expansion of f are obtained as appropriate contour integrals around For the powers with the original contour is joined by a cut line to a circle at infinity, whose contribution vanishes [cf. the evaluation of the Bernoulli numbers in G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1985), p. 413] .
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© 1993 American Institute of Physics.
1993
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