Exponential growth in the number of scientific publications yields the need for effective automatic analysis of rhetorical aspects of scientific writing. Acknowledging the argumentative nature of scientific text, in this work we investigate the link between the argumentative structure of scientific publications and rhetorical aspects such as discourse categories or citation contexts. To this end, we (1) augment a corpus of scientific publications annotated with four layers of rhetoric annotations with argumentation annotations and (2) investigate neural multi-task learning architectures combining argument extraction with a set of rhetorical classification tasks. By coupling rhetorical classifiers with the extraction of argumentative components in a joint multi-task learning setting, we obtain significant performance gains for different rhetorical analysis tasks.