With regard to Mme. Defarge, the word duty does not seem appropriate. For, hers is no patriotic or altuistic cause for which she devotes herself. Instead, it seems more a personal devotion to her personal idee fixe.
Madame Defarge's devotion is her all-consuming dedication to revenge. She is of this single, fatal idea; her entire life is devoted to the death of as many of the French aristocrats as can. She watches as a cat watches its prey, knitting into her work the names of those to be executed. Above all, the entire Evremonde [which is derived from every in English and monde, meaning the world in French] family is etched into her being as sentenced to death. For, in her venomous revenge she is not satisfied that Charles Darnay die; his entire family must be eradicated. When her husband suggests that she goes too far with her revenge, Madame Defarge responds, "Tell the wind and fire where to stop; not me."
Dissolute and phlegmatically going through life, Sydney Carton finds his raison d'etre in his love for Lucie. After he perceives his flaws, set in sharp contrast to his foil, Charles Darnay, Carton is moved to devote his life to Lucie in order to give meaning to his existence. His love and devotion regarding Lucie prompts him to promise that he will do anything to protect her. When the occasion arrives for him to make good on his promise, Carton does not waiver in his duty: He switches places with the condemned Darnay. Nonetheless Carton also performs a duty to himself in mounting the stairs to the guillotine: "It is a far, far better thing than I have ever done before...." For,by redeeming himself through his self-sacrifice Sydney Carton can imagine that his name will have respect attached to it ,
I see that child who lay upon her bosom and who bore my name, a man, winning his way up in that path of life which once was mine. I see him winning it so well, that my name is made illustrious there by the light of his.