# For which energetic reasons are ions blocked by cell membranes?

The permeability of cell membranes is given by the following diagram from the book "Biochemistry":

The reason that ions get blocked can be explained chemically: The ions favor interactions with the polar parts, but cannot undergo favorable interactions with the non-polar parts of the membrane.

However, in my biophysics lecture, the reason for this phenomena was explained by the different relative permittivities $$\epsilon_r$$ in the Coloumb-Potential:

$$\Phi (r) = \frac{q}{4\pi\epsilon_0\epsilon_rr}$$

Outside of the cell, water has a relative permittivity of 80, inside the cell, $$\epsilon_r$$ is around 4 or 5. I'm not sure how to understand this energetic considerations, but I would formulate it in the following way:

I calculate the electric potentials of an ion with respect to the polar components outside of the cell membrane. Because of the difference in the relative permittivities, the potential outside of the membrane will be much less than the potential on the inside of the cell. The work the ion would have to do to overcome this energy barrier is too high, thus the ion gets blocked.

Do you think my formulation is correct?