I'm applying for a physics PhD programme in the UK which requires a personal statement to be submitted. Since I have done several research internships in the field, I would like to mention the supervisors I worked with in my personal statement. Is it a good idea to do so?
Personal statements are usually about your motivation to work in this area or department or with this supervisor. Your previous internships could definitely be a part of this, such as e.g. "Internship 1 involved lots of analysis and data testing, which I enjoyed tremendously, especially..." or "Internship 2 with Prof. Kumar was great: her enthusiasm for ABC was infectious and I would like to learn more about...", but I think your personal statement should focus primarily on why you want to work in this area.
I don't think just mentioning your supervisors is going to help with your application without more information how your experience with you shaped your experience. However, you should definitely mention your internship experience in your CV and ask your internship supervisors for letters of recommendation!