Besides the Liebig condenser design, there are multiple variations - which I will try to outline.
A Graham condenser has a spiral coil running the length of the condenser. There are two possible configurations for a Graham condenser. In the first, the spiral contains the coolant, and the condensation takes place on the outside of the spiral. This configuration maximizes flow capacity since vapors can flow over and around the spiral. In the second configuration, the jacket tube contains the coolant, and the condensation takes place inside the spiral. This configuration maximizes collected condensate, since all the vapors must flow through the entire length of the spiral, thus having prolonged contact with the coolant.
A Dimroth condenser, named after Otto Dimroth, is somewhat similar to the Graham condenser. It has an internal double spiral for the cooling medium so that both the coolant inlet and outlet is at the top. The vapors travel through the jacket from bottom to top. Dimroth condensers are more effective than conventional coil condensers. They are often found in rotary evaporators.
The Allihn condenser or bulb condenser or simply reflux condenser is named after Felix Richard Allihn. The Allihn condenser consists of a long glass tube with a water jacket. A series of large and small constrictions on the inside tube increases the surface area upon which the vapor constituents may condense. Ideally suited for laboratory-scale refluxing. Again, a liebig readily substitutes, taking care to enter coolant at the cooler point to maintain a correct thermal gradient; i.e., the HIGHER fitting in this case.
A Friedrichs condenser (sometimes Friedrich condenser), also known as a spiraled finger condenser, consists of a large, spiraled internal cold finger-type capillary tube disposed within a wide cylindrical housing. Coolant flows through the internal cold finger; accordingly, vapors rising up through the housing may condense on the cold finger as it is cooled. Compared to a Graham condenser of similar dimension, which also includes a spiral internal tube, the Friedrich condenser often provides more efficient condensing because the Friedrich condenser provides greater effective surface area for cooling. That is, vapors may be cooled not only by the coolant flowing through the internal cold finger, but also by the interior wall of the cylindrical housing. The spiral cold finger-type apparatus now known as the Friedrichs condenser was invented by Fritz Walter Paul Friedrichs, who published a design for this type of condenser in 1912.
Overview of the designs