242 H. K. SCHACHMAN AND R, C. WILLIAMS 



result of the net movement of particles mider the influence of an impressed 

 electric or centrifugal field. The latter two situations are considered separ- 

 ately in later sections. Here the discussion is restricted to experiments in 

 which no external field is imposed. 



Measurement of diffusion coefiicients requires an apparatus in which a 

 solution of some solute at a given concentration can be brought into contact 

 with another solution that is identical except for a difference in concentra- 

 tion. Generally one of the two solutions contains no solute, i.e., it is pure 

 solvent, although there are occasions when it is necessary to study the 

 diffusion of a solute from one concentration region to another, 



Basic to all diffusion measurements, and at the same time providing a 

 definition of the diffusion coefficient, is the statement now laiown as Fick's 

 first law of diffusion (Fick, 1855). Fick projaosed a transport equation which 

 can be written 



dm= — BA — dt (10) 



where dm is the mass of material transported in the time, dt; A is the cross- 

 sectional area of the diffusion cell; and {'bcf'bx) is the concentration gradient 

 representing the change in concentration between two levels in the apparatus 

 separated by a very small distance. The negative sign is present in this 

 equation because the transport of solute is in the direction of decreasing 

 concentration. Thus, if we think of a vertical cell in which the bottom 

 solution is more concentrated and the positive direction is downward, mass 

 is transported in the negative direction. This equation provides a definition 

 of the diffusion coefficient, D, as a measure of the mass of solute transported 

 across a plane of known cross section in a given period of time under the 

 influence of a known driving force. The driving force arises from the differ- 

 ence in chemical potential of the solute in the two solutions. For many 

 macromolecules in dilute solutions the driving force can be related directly 

 to the concentration gradient. Dimensional analysis of the various terms in 

 the flow equation presented above shows that the diffusion coefiicient has 

 the units, square centimeters per second. Since the flow of solute is measured 

 relative to the ceU walls the return flow of solvent must be considered, but 

 it can be shown that a single diffusion coefficient can be used to describe 

 the transport of either solute or solvent (Gosting, 1956). 



Diffusion coefficients can be measured by direct application of Equation 

 (10) to the determination of the amount of material diffusing across a porous 

 membrane separating a pure solvent from a solution containing solute. 

 Such diffusion studies, referred to as diffusion through a porous disk, are 

 particidarly useful, as shown below, for biological materials for which a 

 specific bioassay is available. Though the method by itself does not give 



