  We develop a set of numerical schemes for the Poisson--Nernst--Planck
equations. We prove that our schemes are mass conservative, uniquely solvable
and keep positivity unconditionally. Furthermore, the first-order scheme is
proven to be unconditionally energy dissipative. These properties hold for
various spatial discretizations. Numerical results are presented to validate
these properties. Moreover, numerical results indicate that the second-order
scheme is also energy dissipative, and both the first- and second-order schemes
preserve the maximum principle for cases where the equation satisfies the
maximum principle.
