392
W. W. KITTELBERGER
T H E DTFFUSIO?: O F ELECTROLYTES THROUGH ORGANIC MEMBRANES
I. AN EQUATION FOR CALCULATING DIFFUSION RATES 11. EXPERIMENTAL VERIFICATION OF CALCULATED RATES‘ W . W. K I T T E L B E R G E R Research Diuision, Y’echnical Department, The New Jersey Zinc Company (of Pennsylvania), Palmerton, Pennsylvania Received May 11, 1948 INTRODUCTION
The primary function of metal-protective paints is to provide protection from corrosioii. The extent to which a coating fulfills this purpose is to a large degree determined by the effectivenesswith which it isolates the metal surface or object from its environment. Since no known organic coating of practical thickness will completely exclude materials such as water, salts, oxygen, acids, etc., which are nebessary for or accelerate corrosion, any broad fundamental study of metalprotective coatings must include their permeability to such corrosive agents. The permeability of organic coatings to water can be quite readily measured and, as a result, extensive studies during the last fifteen or twenty years have done much to elucidate the mechanism of the absorption and transfer of water. The permeability of organic coatings or membranes to materials such as sodium chloride, hydrochloric acid, etc., which can greatly accelerate the corrosion of metals, has received scant attention by paint technologists, although considerable wadi on this subject will be found in the various journals of physiology (4, 9, 10, 11, 12, 13, 14, 18, 19). The usual method of determining the permeability of membranes to salts employs some form of diffusion cell in which the test film separates known volumes of two solutions of different concentration. The changes in solute concentration that occur as diffusion proceeds are then determined by analysis or other suitable means. Some preliminary measurements with orthodox paint coatings indicated that this method would be much too slow for use in a routine study of the influence of the composition of the coating or membrane upon its permeability to various salts. The first objective of this investigation was therefore to devise a means of determining diffusion rates rapidly, that is, without waiting until measurable changes occurred in the concentrations of the test solutions. This was accomplished, and the first part of the paper is devoted t o the derivation of the diffusion equations. The second part describes a number of experiments that were carried out to test the validity of this method of determining diffusion rates. 1 Presented before the Division of Paint, Varnish, and Plastics Chemistry a t the 113th Meeting of t h e American Chemical Society, which was held in Chicago, Illinois, April,
1918.
DIFFUSION O F ELECTROLYTES THROGGH ORGANIC MEMBRANES
393
I. BN EQUATION FOR CALCULATING DIFFUSION RATES
The equations that were used in this investigation to compute diffusion rates are simply modifications of those which apply to the migration of ions under the influence of a potential gradient. Their application is based on the assumption that the electrolytic resistance of a membrane, which is a restrictive force retarding the migration of ions, will oppose the diffusion of the same ions with equal force. Before proceeding with the derivation of the diffusion equations, the various symbols to be employed will be defined. &+, Q-,Q = millimoles of cation, anion, and salt, respectively I = electric current, in milliamperes E = c .M.F., electromotive force E, = liquid-junction potential E, = membrane c oncentra tion potential E,+ = the potential difference that is equivalent to a given difference in cation concentration2 E,- = the potential difference that is equivalent to a given difference in anion concentration2 E+ = the net effecti1.e potential difference acting on the cations E- = the net effective potential difference acting- on the anions For the sake of convenience only, all potentials are in millivolts. C+, Z+,ti, antl 21 are the cation concentration, valency, transference number, and mobility, respectiyely. C-, 2-,t-, antl 1' are the corresponding anion properties. C1 and Cz are the salt concentrations of the diffusion solutions. All concentrations are in grani-equivalents per liter of solution (normality). f r and f 2 are the molar activity coefficients of the concentrated and dilute diffusion solutions, respectively. t = the difYusion time in seconds T -- the absolute temperature R = the gas constant F = 96,500 coulombs, the faraday R, = solution resistance in ohms R, = electrolytic resistance of the membrane in ohms (D.c. resistance) d = solution density The well-known laws of electrolysis provide the following equations for the migration of the ions in an aqueous solution;
tIt+ rF
Q+
=
Q-
= __
tIt-
z-F
2 These are the potential differerices t h a t would arise in concentration chains with electrodes reversible t o the cat.ions arid anions, respectively, in the absence of liquid-junction potentials,
394
W. W. KITTELBERGER
where Q+ and Q- represent the millimoles of cation and anion, respectively, which must migrate in t seconds in order t o carry the current I . Substituting E / R , for I in equations 1 and l a and differentiating with yespect to t yields equations for the migration rate: d+ Q dt
=
E+ t+ Z+ FR,
(2)
~
and
If a membrane is placed in the solution in such a way as to restrict the movement of the ions, equations 2 and 2a still give the migration rates, but t+ and tare now the transference numbers of the ions in the membrane rather than in the free solution, and R , is substituted for R,. I n migration, the force causing movement, of the ions is an electrical potential difference; in diffusion it is a concentration difference. But since a solute concentration difference can be expressed as an equivalent potential difference, their effect on the movement of the ions is the same. It was assumed that equations 2 and 2a could be directly applied to the di$usion of ions provided the proper values of the potentials and the ion transference numbers mere employed. Tyansference numbers The equation for the potential that is set up a t the junction of two solutions containing different concentrations of the same salt is
v\
l u
The derivation of equation 3 need not be given here because it is usually discussed in some detail in textbooks on electrochemistry, for example, that of MacInnes (6). The assumption is made that equation 3 gives, a t least with reasonable accuracy, the potential (E,) which is set up when the two solutions are separated by a membrane through which the movement of ions can take place. Therefore, E,,, may be substituted for E , in equation 3.
E,,, = RT F
(" + ;I) -
1L
In fiC, -
u
$le2
By definition t+ =
e+z+u + c-z-v
C+Z+U
and t-
=
c- ze+z+ + c-z-v 2)
11
DIFFUSION O F ELECTROLYTES THROUGH ORGANIC MEMBRANES
395
But for our experimental conditions, where the test solutions contain different concentrations of a single salt, C+Z+ = C-Z-; hence t+ =
U
~
11
U
and
+v
+
t- = 11
2’
and 1L
Since t+
+ t-
=
2,
1 the ionic mobility term in equation 3a becomes
t+ - 1 - t+ t+@+ -or
z+
z-
+ 2-1 - z+ z+z-
Substituting in equation 3a and solving for t+ yields equation 4, which gives the transference number of the cation in the membrane in terms of the solution concentrations, the membrane potential] and the ion valencies.
( 2;) EmF
RTln
t+ = (%%)
-
+
z+ z++ z-
(4)
T h e concentration di
