ON DIFFUSION; OSMOSIS 211 



by AF\ the energy of binding within the shroud of neighboring molecules 

 through which the jumping species must penetrate if it is to move success- 

 fully to the next position of rest. 



Two innovations have been introduced into discussions of diffusion in 

 recent years, one for theoretical reasons and the other for practical reasons. 

 Firstly, it is more proper to consider activities (effective concentrations) than 

 measured concentrations, and more proper still to consider as the "force," 

 the gradient of the chemical potential which drives the diffusion process; and 

 therefore dc/dx is replaced by dn/dx, in the more esoteric discussions, if not 

 in practice. 



Secondly, the thickness of the interface, at a cell wall for instance, is really 

 a matter of definition rather than of position of chemicals. Who can say 

 where the water phase stops and the heavily hydrated protein of the wall 

 begins? Therefore dc/dx is hard to measure for living membranes, and re- 

 course is made to a phenomenological trick: dx is taken into the diffusion 

 constant, and the rate of flow is expressed as the difference between the flows 

 in the two directions through the membrane. Thus 



j =(P,A Cl -(P 2 Ac 2 



where 1 and 2 represent diffusions in the forward and back reactions, and 

 c, and c 2 represent concentrations on the two sides; the (P's then have units 

 cm sec -1 (velocity) and are called permeability constants. A few of these are 

 collected in Table 8-7 for monovalent cations penetrating through living 

 membranes. These permeability constants can be compared with values de- 

 termined for synthetic interfaces also given in the table. 



TABLE 8-7. Some Permeability Constants ( § ) for Synthetic and Biological Membranes.* 



, _._ . Permeability Constant x 10 



Intertace Diffusion ' _i. 



(cm sec ) 



K + into erythrocyte of: man 5.0 



dog 1 .0 



rat 10 

 KC1, KBr, KI into nitrobenzene 0.007, 0.075, 1 .4 



Na + into erythrocyte of: rabbit 3.0 



dog 0.5 



Na + through frog skin 5.0 



Na + (as iodide) into nitrobenzene 0.2 



Alcohols into erythrocyte 10,000 to 100,000 



Water into erythrocyte ~ 1 0,000 



♦Collected by J. T. Davies, J. Rhys. Coll. Chem., 54,185(1950). See also Ref. 17. 



For ionic flow the values in the table can be transformed very easily into 

 electrical resistance units. Thus if the concentration of the salt at the mem- 



