I understand that free haptens, by definition, are not immunogenic. However, once produced against a protein-bound hapten, can the antibody always bind the hapten in its free form as well? Is there a general rule, or does it depend on each antibody?
Normally, to get a good immune response, you need both T-cell and B-cell epitopes in your Immunogen. You may get a T-cell independent immune response if your immunogen is highly polymeric, but in this case the response will not progress beyond IgM. By coupling a hapten to a suitable carrier protein you both provide T-cell epitopes and multimerization of the hapten. The response will usually consist of a mixture of B-cells/antibodies with different specificity: some only recognizing the hapten in the context of the peptide sequence it is coupled to, others may also recognize the free hapten. Since you randomly couple the hapten to different sites of the carrier, those that recognize the hapten independent of the sequence context have an advantage, since they "see" a larger antigen concentration. On the other hand, since the binding affinity of an antibody is limited by the contact area, antibodies recognizing more than just the hapten may achieve higher affinities. In consequence, the antiserum generated will most likely contain both antibodies against the hapten alone and antibodies only recognizing the hapten in the context of the carrier protein sequence it was coupled to. The proportion of the two types of antibodies in the serum may vary between different animals injected with the same immunogen as well as in the course of the immune response. If you generate monoclonal antibodies, you can screen for clones that fit your requirement.