## Ygw

This electrostatic potential difference occurs only over a few nanometers at the interface between the two phases; the bulk phases are electrically neutral and at the same potential. Nonetheless, the interface potential difference can be measured by electrodes inserted into the bulk phases.

### Example

What is the electric potential difference between the dextran-rich and PEG-rich phases for points on the tie line of the phase diagram in Fig. 11.19 if the total NaCl concentration is 0.5 M? The difference between the PEG (B) concentrations between points m and n is 15 mM. Using this value and bS = -2.6 M-1 in Eq (11.67) yields an electric potential difference of -2.4 mV.

### 12.8.3 Protein distribution

This section aims to calculate the distribution coefficient of a protein in a two-polymer, two-phase aqueous system with added electrolyte. The chemical potentials of the protein in the two phases are (see Eq (11.53):

m p = m P + RT ln a p + ZFf , and m P = mP + RT ln a p + ZFf,, (11.68)

Z is the charge on the protein and is assumed to be the same in both aqueous phases. Equating these chemical potentials and replacing the activity by the product of the activity coefficient and the molar concentration leads to:

gP is the "chemical" activity coefficient of the protein in the aqueous solution. It is also expressed in terms of osmotic second virial coefficients (B) reflecting the interactions between the three solutes:

where b = Bvw. The effect of the electric potential difference on KP can be important because proteins in aqueous solution are almost always charged.

Example

If Z = 10 and the electric potential difference is - 2.4 mV, the exponential term in Eq (11.69) is

I.5, which constitutes a 50% increase in KP.