Singularities in the coverage dependence of the chemical diffusion coef5cient near the critical points corresponding to transitions from one phase to another are studied by employing two different latticegas models. (i) For the hard hexagon model, the chemical diffusion coeScient is shown to be exactly equal to zero at the critical coverage and its behavior near this point is in agreement with the predictions of the scaling theory provided that one takes into account the Fisher renormalization of the specific-heat exponent. (ii) For a square lattice with repulsive interactions between nearest-neighbor particles, the detailed transfer-matrix and Monte Carlo data indicate that the chemical diffusion coefficient has a minimum at critical coverages and its value at these points decreases with increasing lattice size (there is even evidence that D -+0 at L -+~)l

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