Do you want bigger biceps?
Instead of trying to grow the biceps directly, target the brachialis instead.
The brachialis is an elbow flexor that lies underneath both the bicep heads and is often forgotten by many.
Working the brachialis will push the biceps up, creating the illusion of bigger biceps/arms. In order to target the brachialis, have your hands in a neutral position (hammer curl is a great exercise for the brachialis).
The grip-width you use on barbell curls can make all the difference on your biceps growth. Using a standard, shoulder-width grip uses both the long (outer) head and short (inner) head of the biceps fairly evenly. The wider you go from there, the more short head emphasis and the narrower you go, the more long head emphasis.
Be sure to include in addition to shoulder-width grip curls, some wider-than-shoulder-width-grip curls to place extra stress on the short head (building the bicep width)
and close-grip curls to place extra stress on the long head (building bicep peak). This will help you bring up the size of each biceps head, which together will create larger biceps.