Can I write to the reviewer directly to expedite the review of my paper?
My target journal specifies that the cover letter should include four experts in the field as potential reviewers for the manuscript. I have asked some professors to have their permission to include their name as reviewers and have found four. I have sent their details to the journal but I did not hear from the journal even after 8 months. Then I sent an email asking about the status of my manuscript and they said that they have received one review and are waiting for the second. Now almost one year has passed for my manuscript, and the journal is still waiting for the second review. My question is should I send an email to the reviewers to ask them to read my manuscript? Thank you.
No, you should definitely not write to the reviewers. Direct interaction between the author and the reviewers is not appreciated by journals as it goes against the confidentiality policy of the journal.
Additionally, you will not know the names of the reviewers to who are revieweing your manuscript. Even if a journal asks the authors to name a few preferred reviewers, it does not necessarily mean that the paper will be sent to the same reviewers. The selection of reviewers depends entirely on the editor. In fact, the paper might not have been sent to any of the reviewers whose name you have suggested. So there is no point in writing to the reviewers.
You should, in fact, keep sending emails to the journal every two to three weeks, asking about the status of the manuscript and requesting them to expedite the process.