Scholar Robert Cate explains what Second Isaiah is in Mercer Dictionary of the Bible.
Robert L. Cate, "Isaiah, Book of," in Mercer Dictionary of the Bible, ed. Watson E. Mills (United States: Mercer University Press, 1990), 414
Divisions of Isaiah. (1) The issues regarding unity can generally all be found, with only minor exceptions, in Isa 40-66. Those supporting the disunity point out that nowhere in these chapters is Isaiah ever identified as the author. Further, the attitude changes radically, with the first part of the book, i.e., Isa 1-39, being concerned with confrontation and rebuke, while the latter half deals with comfort and assurance. The mood of the first part is gloom while the mood of the second part of the book is hope and light. In addition, in the latter part of the book the destruction of Jerusalem is presupposed as an accomplished fact. Yet, this catastrophe is merely anticipated in the first part. Further, in the latter part both the prophet and his people are in Exile, while the Exile is far in the future in the first part.