Letters to the Editor with the low temperature spectra shows that there are two lines remaining constant at different water contents, at 1534 and 1633 cm- I • In between one finds a broadband increas- ing in intensity and splitting into two lines at 1575 and 1591 cm -I at higher water content. (vi) At room temperature two broad lines arise at 3300 (assigned to v NH, r NH, and 'T' CN ll ) and 3103 cm- I (assigned to v NH, 'T' CN II ). The question concerning the nature of these lines is not easy to answer. For such low concentrations of water (in NMA) one could first consider the vibrational lines of the isolated molecule, but not all possible lines (1595,3151, and 3652 cm -I) 16 fit to our observed ones. The problem seems to be more complicated as the water molecule will be bound in some way to the hydrogen bonds of the NMA crystal. One might even speculate that there are at least two different sites that are accessible to different numbers of water molecules. This could cause the different sensitivities of the two lines in the amide 1111 region at room temperature. Further investi- gations on deuteration effects may lead to the necessary new assignments although the two factors of deuterating the amide group in NMA and water can only be switched at the same time because of the fast HID exchange between NMA and the added water. We would like to thank A. Breitschwert for the oper- ation of the spectrometer. a) Present address: Robert Bosch GmbH, Werk Schwieberdingen, Postfach 300240, 7000 Stuttgart 30, West Germany. b) On leave from the Department of Chemistry, University of Oregon, Eu- gene, Oregon 97403. IS. J. Mizushima, T. Shimanouchi, S. Nagakura. K. Kuratani, M. Tsuboi, H. Baba, and O. Fujioka, J. Am. Chem. Soc. 72, 3490 (1950). 2T. Miyazawa, T. Shimanouchi, and S. J. Mizushima, J. Chem. Phys. 24, 408 (1956); 29, 611 (1958). Miyazawa, J. Mol. Spectrosc. 4, 168 (1960). 4E. M. Bradbury and A. Elliott, Spectrochim. 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Fractal behavior of correlated random walk on percolating clusters Panos Argyrakis Department 0/ Physics, University 0/ Crete, Iraklion, Crete, Greece Raoul Kopelman Department o/Chemistry, University 0/ Michigan, Ann Arbor, Michigan 48109 (Received 2 May 1985; accepted 2 October 1985) Correlation in diffusional motion has been shown in the past to be a necessary idea for the explanation of experimen- tal data ranging from the diffusion of hydrogen in metals I and models of diffusion in concentrated lattice gases, 2 to the relaxation mechanism of low-lying excited states of organic molecules at low temperatures 3 as studied by the use of ran- dom walk hopping models. 4 Recently a new model was in- troduced 6 • 7 that incorporates the effects of correlation in the usual s random walk models, first on perfect lattices, 6 and then on mixed binary lattices. 7 Also of interestS has been the application of the simple stochastic random walk on the fractal structures of percolating clusters around the critical threshold point. In the present paper we study the behavior of correlated random walks on such fractal structures, we test the possible universality of these phenomena, and also their crossover to the classical limit of a perfect crystal. Percolating clusters are generated by a Monte-Carlo simulation method, using the cluster growth technique. 9 The only prescribed parameter is the concentration (relative fraction) of the open (allowed) lattice sites C, ranging from the critical value C c = 0.593, to the limit of perfect lattice C = 1.00. Correlation is the retention of the directional memory over a certain number of lattice spacings. This is quantitatively described by the fraction PI' which is the probability of a forward jump, and it is in the range: a-I <PI < 1.00, where a is the lattice coordination number. The well-known relations connecting S N' the number of distinct sites visited in an N -step walk, with N ( time) is SN_N d • 12 which has been shown 9 to hold true for a variety of lattices for stochastic random walks with a d. value: d: = 1.30, for J. Chern. Phys. 84 (2), 15 January 1986 . 0021-9606/96/021047-02$02.10 @ 1986 American Institute of Physics 1047