The electrophoretic mobility of a cylindrical particle is calculated by combining the solution of the complete Poisson-Boltzmann equation in cylindrical coordinates with the equations of Henry. Results are obtained for pointlike counterions (Gouy-Chapman picture) and for counterions having a finite diameter (Stern layer model). The deformation of the ionic atmosphere under the influence of the external field (relaxation effect) is not taken into account. In application to actual data a correction procedure for the relaxation effect, such as the semiempirical method proposed by W. J. H. M. Mfller, G. A. J. van Os, and J. Th. G. Overbeek (Trans. Faraday Soc. 57, 312,325, 1961), should be combined with the present treatment. Results can be applied to stiff (e.g., DNA) and to flexible (e.g., vinylic polyacids) polyelectrolytes.

It has been derived, that the electraphoretic mobility of a randomIy oriented charged cylinder is obtiinec? by adding onethird of the mobility of a cylinder parallel to the fieId to tw&hirds of its mobility perpendicular to the field, when the relaxation effect is nedectedThe calculation of the electrophoretic mobility of randomly oriented charged cylinders is of special interest, because it may bc applied in an approximate way to molecules of biological importance such as DNA and to other Iiaear poly-electrolytes. The average electrophoretic mobility of randomly oriented cylinders is found by taking a suitable average of the mobtities of a cylinder with its axis perpendicular to the electric field, (U/X), and of one parallel to the field, (U/X),,.Remarkably enough, even in the recent literature two different metiads of averaging can be found, one method averaging mobilities [l-3], the other one averaging reciprocal mobilities [4,5] _ it is the purpose of this paper to prove that, when the relaxation effect is neglected, the correct result is obttied by averaging mobilities.For nonconducting cylinders, Henry 161 has given the following equations:

Electric mobilities of polyions, bromide ions, and alkali ions have been determined in solutions of Li, Na, and K salts of polymethacrylic acid (PMA) in aqueous solutions of the corresponding bromide of concentrations varying from 0.001 to 0.1 M. The Hittorf method was used for the determination of the mobilities of the PMA ion and of the Br-ion. The mobilities of the alkali ions followed from these two mobilities and the conductivity. A few moving boundary experiments have been carried out with tetramethylammonium PMA. The mobility of PMA was independent of the PMA concentration and of the kinds of cations and changed only slowly with the degree of neutralization. The bromide mobility decreased slowly with increasing PMA concentration. The interpretation was based upon a separation of the contributions from the polyelectrolyte salt and those of the supporting electrolytes. The mobilities of the counterions that neutralized the polyions were very low and in several cases even negative. Electrophoretic retardations varied from about 20 to 70 12 -~ cmz eq -~. By using the relaxation correction as found from conductivity data we could interpret the mobility of the PMA ion as that of a cylinder of 0.35-nm radius surrounded by a solvation layer of 0.2-to 0.3-nm thickness. For bromide concentrations up to 0.03 M the agreement was excellent; at a 0.1 M bromide concentration binding of about 25% of the counterions to the polyions had to be assumed to reconcile the model calculations with the experiments. Intrinsic viscosities of NaPMA in NaBr solutions have been used to obtain an estimate of the overall size of the polyelectrolyte coil and to justify the cylinder model.

= 238 nm, E , , ,~~ = 13.800. N M R : 6 1.02 (s) and 1.04 (s) 18-CH3 and IY-CH,, 1.49 (s) h,,, = 314 nm, E, , , = 20.900; shoulders at 302 and 238 nm. 21-CH3 and 3-OAc, 5.48 (m) and 5.60 (m) 16-CH2, 5.64 (m) 6-CH and 7-CH. 5.80 (d) 4-CH. 2.22 (s) 21-CH,, 3.10 (m) 16-CH3, 5.22 (m) 7-CH, 5.80 (t) 4-CH. N M R : 6 0.63 ( s ) 18-CH3, 0.89 ( s ) 19-CH3, 2.09 ( s ) 17-OAc, 2.14 ( s ) 7a-Dihydroxy-16-methylene-9~,IOa-pregna-3.5,7-trien-20-one 3,17-diaceiate (11)To a solution of 3.17 g of 10 in 90 ml of dry toluene were added 55 mg of p-toluenesulphonic acid and 11 ml of acetic anhydride. The reaction mixture was boiled and allowed to distil very slowly. After 4 h another 20 mg of p-toluenesulphonic acid and 6 ml of acetic anhydride were added and distillation was continued. After a total reaction time of h the mixture was cooled to room temperature and 50 ml of water and 15 ml of pyridine were added.After stirring for 30 min the organic phase was separated and washed first with a sodium bicarbonate solution and then with water. After drying and removal of the solvent the residue was chromatographed on silica gel to yield 2.2 g (56 04,) of the pure trienol acetate 11. I 72-Hydro.xyy-l6-methy1ene-9P,I Or-pregna-4,6-diene-3, ZO-dionc 17-acetate (12)