Alfred Pennyworth has also provided first aid up to and including suturing wounds and removing bullets, as well as occasional tactical support. He is also able to perform arthroscopy and other advanced medical procedures, thus limiting, if not eliminating, the need for hospital medical treatment even in the face of grievous injuries, helping to maintain Batman's secret identity by ensuring that Bruce Wayne has no need to visit hospitals for wounds inflicted as Batman. Nevertheless, Batman still requires professional medical treatment when Bane breaks his back ("") and Hush's machinations result in his suffering a skull fracture (""). On these occasions, Alfred
Butler–Volmer equation the surface is equal to that in the bulk. There are two limiting cases of the Butler–Volmer equation: where formula_21 and formula_22 are constants (for a given reaction and temperature) and are called the Tafel equation constants. The theoretical values of the Tafel equation constants are different for the cathodic and anodic processes. However, the Tafel slope formula_22 can be defined as: where formula_25 is the faradaic current, expressed as formula_26, being formula_27 and formula_28 the cathodic and anodic partial currents, respectively. Butler–Volmer equation The Butler–Volmer equation (named after John Alfred Valentine Butler and Max Volmer), also known as Erdey-Grúz–Volmer