Sentiment is a way of viewing the world complementary to that of comedy. It is based on the recognition that certain situations are not reducible to comedy; the frustration and imprisonment of a good man, for example. It then tries to make literary capital of poignant situations. As comedy tries to draw laughter, sentiment tries to draw tears. In the eighteenth century these two modes were frequently mixed, and Dickens combined them in Pickwick Papers. Sentiment is not at all close to tragedy, however, since it depicts sad situations more or less for their own sake.
Comedy is by far the dominant mode of the novel, but sentiment crops up at frequent intervals. The interpolated tales tend to exploit the pathos of innocent victims of evil. In the tale about Prince Bladud, Dickens goes further and treats sentiment in a jocular way, but this is unsuccessful. In fact, Dickens generally fails when he tries to exploit sentiment in these tales, not merely because their style is so wretched, but because the situations themselves are obviously artificial.
However, Dickens is more successful with sentiment when he deals with Mr. Pickwick's stay in prison. Here the sentiment is integrated into its context; it fits the prison environment. The deathbed pathos of the Chancery prisoner is exactly what one might expect under the circumstances. Moreover, Dickens balances his bitter sadness with other points of view about prison, so it is not really obtrusive.