Determination of Diffusion Coefficients through a Polymer Membrane Using a Rotating Disc Electrode
Authors: Reynolds Marissa Kayle , Paul David W 
Published: February 2020

Sensocompatibility is the loss of sensor function caused by intereferents preventing the analyte from getting to the surface of the sensor so that a signal can be produced. Problems can occur because of membrane biofouling, electrode fouling, and sensor to sensor variability. The confinement of small molecules in the pores of the membrane can amplify the signal. The perfect membrane would be one that would not become biofouled, that would transfer the analyte to the sensor rapidly, that would not interfere with the analyte being transported, and that would be biocompatible with the physiological system of the body. After a thirty year search, this “perfect membrane” remains elusive. Instead, the best alternative seems to be the characterization of the membranes currently in use. Because the sensitivity of an amperometric sensor is determined by the diffusion rate of the analyte, discovering the changes in the diffusion through the membrane would be one of the more useful endeavors in the characterization of the membrane. Diffusion coefficients in bulk solution have traditionally been measured using a rotating disc electrode (RDE). To a lesser extent, the RDE technique has been used to determine the diffusion coefficients of an analyte through a membrane.
Figure 1 shows the traditional use of the RDE to determine diffusion coefficients. (A) shows the cyclic voltammogram (CV) of a 50:50 mixture of 5mM ferri- and ferrocyanide in 0.1M KCl on a bare gold RDE (against Ag/AgCl in saturated KCl) with a series of rotations and (B) shows the resulting Levich Plot. Using the determined kinematic viscosity of 9.913x10-3 (cm2/s), the diffusion coefficient for ferricyanide was determined to be 5.66x10-5 (cm2/s).
Nafion® (DuPont™) is the most widely used membrane electrolyte polymer. The electrolyte solution and the casting technique of the polymer onto the electrode both have a significant effect on the membrane characteristics. Figure 2 shows five different membranes. Two of the membranes, shown in red, were cast by dip-coating and the other three, shown in blue, were cast by spin-coating. All of these membranes were cast onto a working gold RDE and then a CV from 0.5V to -0.1V was taken without rotation of the RDE gold electrode against a Ag/AgCl in saturated KCl reference electrode and platinum flag counter electrode. The electrolyte used, 5mM ferricyanide in 0.1M KCl, remained constant for each CV. The large variability seen in the dip-coated polymers shows the irreproducibility of the membrane employing that type of casting due to both an incomplete covering of the electrode by the membrane and entrapment of ferricyanide into the membrane. A better consistency in signal is seen among the spin-coated polymers.
Even though Nafion® is a negatively charged polymer, there have been reports of using a negatively charged molecule as a probe molecule for electron charge transfer. Diffusion of ferricyanide through Nafion® membranes has been reported with diffusion coefficients in the membrane of 2.8x10-12 cm2/s. From this we can conclude that Nafion® does in fact enter into the membrane, albeit very slowly. Figure 3 shows a CV of ferricyanide at 1600 RPM through a spin-coated Nafion® membrane. The black curve is a CV taken immediately after being exposed to the 5mM ferricyanide in 0.1M KCl solution. The other curves show the same procedure with the only difference being the amount of time the membrane was exposed to the ferricyanide solution before the CV was performed. The green curve shows the ferricyanide signal through the membrane after exposure to the ferricyanide solution for one hour, the blue for two hours, the purple for three hours, and the red was exposed overnight. This shows that the charge transfer resistance decreases after the membrane is exposed to the solution for over time. However, the signal retreats after the three hour and overnight solution exposure leading us to conclude that there might be multiple mechanisms affecting the charge transfer and one begins to take precedence during the longer exposure time.
With Figure 1A as a comparison, the charge transfer resistance through a membrane is clear from the lack of a limiting current in Figure 3. Therefore, we can conclude that the RDE is not a suitable technique to determine the diffusion coefficients of negatively charged molecules through the Nafion® membrane when there is a difference of more than six orders of magnitude between diffusion coefficients in the membrane and over the bulk solution. Our future molecule of interest is oxygen. Its small size and neutrality should allow us to use the RDE technique to determine its diffusion rate through Nafion®.

Figure 1