= Solution
Let $\Phi(x)$ be the <electrostatic potential> in volts, relative to the bulk value, and $x$ the distance normal to the surface. The positive quantity $e$ is the elementary charge; the monovalent ions carry $\pm e$. The bulk number density $n_0$ refers to each ionic species in a symmetric electrolyte, so the total bulk ion density is $2n_0$. $\epsilon_0$ is vacuum <permittivity>, $\epsilon_r$ relative <permittivity>, $k_B$ the Boltzmann constant and $T$ absolute <temperature>. The hyperbolic sine acts on the dimensionless potential $u=e\Phi/(k_BT)$.
\b[The printed sign is inconsistent with physical Poisson–Boltzmann screening under these usual definitions.] Indeed,
$$
n_\pm=n_0e^{\mp u},\qquad
\rho=e(n_+-n_-)=-2en_0\sinh u,
$$
and <Poisson's equation> gives $\Phi''=-\rho/(\epsilon_0\epsilon_r)=+2en_0\sinh u/(\epsilon_0\epsilon_r)$, with a plus sign. The literal printed equation and the physical screened solution must therefore be distinguished.
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