Freundlich and Langmuir Isotherms as Models for the Adsorption of Toxicants on Activated Charcoal

Cooney, 1980, 24 Levy, 1982, N. Engl. J. Med., 307, 676, 10.1056/NEJM198209093071109 Israili, 1984, Drug Metab. Rev., 15, 1123, 10.3109/03602538409033559 Spyker, 1985, Arch. Int. Med., 145, 43, 10.1001/archinte.1985.00360010063005 Kulig, 1985, Ann. Emerg. Med., 14, 562, 10.1016/S0196-0644(85)80780-0 Park, 1986, Arch. Intern. Med., 146, 969, 10.1001/archinte.1986.00360170207027 Berg, 1982, N. Eng. J. Med., 307, 642, 10.1056/NEJM198209093071102 Lake, 1984, Pharmacotherapy, 4, 161, 10.1002/j.1875-9114.1984.tb03343.x Lalonde, 1985, Clin. Pharmacol. Thera., 37, 367, 10.1038/clpt.1985.55 Hillman, 1985, Br. Med. J., 297, 1472, 10.1136/bmj.291.6507.1472 Laufen, 1986, Int. J. Clin. Pharmacol., 24, 48 Winchester, 1977, Trans. Am. Soc. Artif. Intern. Organs, 23, 762, 10.1097/00002480-197700230-00204 Tsuchiya, 1972, J. Pharm. Sci., 61, 587 Bainbridge, 1977, J. Pharm. Sci., 66, 480, 10.1002/jps.2600660405 Hincal, 1979, J. Pharm. Sci., 68, 472, 10.1002/jps.2600680421 Van de Graaf, 1982, J. Pharmacol. Exp. Ther., 221, 656 Javaid, 1983, J. Pharm. Sci., 72, 82, 10.1002/jps.2600720120 Neuvonen, 1983, Clin. Tox., 21, 333 Kannisto, 1984, J. Pharm. Sci., 73, 253, 10.1002/jps.2600730228 Lehmann, 1984, Clin. Tox., 22, 331 Dedrick, 1967, Trans. Amer. Soc. Artif. Int. Organs, 13, 236 Manes, 1974, Clin. Tox., 7, 355, 10.3109/15563657408987998 Cooney, 1977, Clin. Tox., 11, 387, 10.3109/15563657708988201 Ganjian, 1980, J. Pharm. Sci., 69, 352, 10.1002/jps.2600690329 Skalsky, 1978, Artif. Org., 3, 258, 10.1111/j.1525-1594.1979.tb01060.x Freundlich, 1922 Kipling, 1955, 24 Traditionally, the exponent P has been written as 1/n (to underscore that its value is always less than unity); it is a usage which complicates matters unnecessarily. Goldstein, 1949, Pharm. Rev., 1, 102 Henry, 1922, Phil. Mag., S6, 44 Langmuir, 1918, J. Am. Chem. Soc., 1361, 10.1021/ja02242a004 Andersen, 1946, Acta Pharmacol., 2, 69, 10.1111/j.1600-0773.1946.tb02599.x Andersen, 1947, Acta Pharmacol., 3, 199, 10.1111/j.1600-0773.1947.tb02649.x Andersen, 1948, Acta Pharmacol., 4, 275, 10.1111/j.1600-0773.1948.tb03349.x Holt, 1963, J. Pediat., 63, 306, 10.1016/S0022-3476(63)80344-3 Gosselin, 1966, Clin. Pharmacol. Therap., 7, 279, 10.1002/cpt196673279 Mann, 1970, Pediatr. Clin. N. A., 17, 617, 10.1016/S0031-3955(16)32455-5 Cooney, 1980, 32 Sorby, 1960 Sorby, 1961, J. Pharm. Sci., 50, 355, 10.1002/jps.2600500419 Sorby, 1965, J. Pharm. Sci., 54, 677, 10.1002/jps.2600540504 Sorby, 1966, J. Pharm. Sci., 55, 785, 10.1002/jps.2600550807 Snedecor, 1957, 199 Marquardt, 1964 Marquardt, 1963, J. Soc. Ind. Appl. Math., 11, 431, 10.1137/0111030 Cabana, 1970, J. Pharmacol. Exp. Ther., 174, 260 Atkins, 1983, Biochim. Biophys. Acta, 732, 455, 10.1016/0005-2736(83)90062-7 Matyska, 1985, Biochem. J., 271, 171, 10.1042/bj2310171 Tommasini, 1985, Can. J. Biochem. Cell Biol., 63, 225, 10.1139/o85-032 Acton, 1959, 129 Since eq 2 is that of a logarithmic relationship, analyses of variance were performed using logarithmic transforms of the values of x/m and C in Tables I and II. The parameter K is a logarithmic parameter in eq 2; its 95% confidence limits are, accordingly, geometrically symmetrical. Draper, 1981, 484 Endrenyi, 1972, 219 Specifically: logx/m=log[−(k1q+mk1k2+1)+(k1q+mk1k2+1)2−4k12k2mq−2k1m] Draper, 1981, 141 Jeng, 1985, J. Pharm. Sci., 74, 1053, 10.1002/jps.2600741006 Godfrey, 1985, N. Eng. J. Med., 313, 1629, 10.1056/NEJM198512263132604 Monot, 1983, J. Pharm. Sci., 72, 35, 10.1002/jps.2600720109 Riggs, 1963, 51 Wilkinson, 1961, Biochem. J., 80, 324, 10.1042/bj0800324 The maximum likelihood solution of eq 6 is that which gives the smallest value for the sum-of-squares of deviations of „observed” values of C/(x/m) from those predicted. However, log x/m rather than C/x(/m) is the true dependent variable of the Langmuir relationship. Accordingly, to allow direct comparison with the sum-of-squares obtained for the solution of the logarithmic form of eq 3 and the transform of eq 4,50 the sum-of-squares of log x/m for the parameters generated by the solution of eq 6 was calculated by insertion of these parameters into the logarithmic form of eq 3. Dowd, 1965, J. Biol. Chem., 240, 863, 10.1016/S0021-9258(17)45254-9 Atkins, 1975, Biochem. J., 149, 775, 10.1042/bj1490775 Scatchard, 1949, Ann. N.Y. Acad. Sci., 51, 660, 10.1111/j.1749-6632.1949.tb27297.x Riggs, 1963, 57 Scholtan, 1978, Arzneim.-Forsch., 28, 1037