def _bridge_dangling_Os(self, oh_density, thickness):
        """Form Si-O-Si bridges to yield desired density of reactive surface sites.

        References
        ----------
        .. [1] Hartkamp, R., Siboulet, B., Dufreche, J.-F., Boasne, B.
               "Ion-specific adsorption and electroosmosis in charged
               amorphous porous silica." (2015) Phys. Chem. Chem. Phys.
               17, 24683-24695
        """

        area = self.periodicity[0] * self.periodicity[1]
        target = int(oh_density * area)

        dangling_Os = [atom for atom in self.particles()
                       if atom.name == 'O' and
                       atom.pos[2] > thickness and
                       len(self.bond_graph.neighbors(atom)) == 1]

        n_bridges = int((len(dangling_Os) - target) / 2)

        for _ in range(n_bridges):
            bridged = False
            while not bridged:
                O1 = random.choice(dangling_Os)
                Si1 = self.bond_graph.neighbors(O1)[0]
                for O2 in dangling_Os:
                    if O2 == O1:
                        continue
                    Si2 = self.bond_graph.neighbors(O2)[0]
                    if Si1 == Si2:
                        continue
                    if any(neigh in self.bond_graph.neighbors(Si2)
                           for neigh in self.bond_graph.neighbors(Si1)):
                        continue
                    r = self.min_periodic_distance(Si1.pos, Si2.pos)
                    if r < 0.45:
                        bridged = True
                        self.add_bond((O1, Si2))
                        dangling_Os.remove(O1)
                        dangling_Os.remove(O2)
                        self.remove(O2)
                        break
Form Si-O-Si bridges to yield desired density of reactive surface sites.

        References
        ----------
        .. [1] Hartkamp, R., Siboulet, B., Dufreche, J.-F., Boasne, B.
               "Ion-specific adsorption and electroosmosis in charged
               amorphous porous silica." (2015) Phys. Chem. Chem. Phys.
               17, 24683-24695