When is it appropriate for a PhD student to discuss personal problems affecting his productivity with his advisor?
As soon as possible. Problems are made to be transcended, not pushed over time. You already said your adviser is a cool guy, right? Go ahead and talk with him, say the truth.
It's a long said term, even cliche sometimes, but the first step to change is recognizing that you have a problem. You already recognized you have it, so now it's time to fix it. Don't be afraid of what he'll think about you, what really matters is that it's true. If he can't understand your situation, then he doesn't really know how to be a adviser.
Also, you're a student, you're there to learn. Better learn now where you can be mistaken with no serious consequences, then out there, where your problem can really damage you financially and/or much more emotionally, since people don't know how to handle with other people's problems, or know and just don't care.
Well look at it from the point of view of an academic, most of understand that students have problems in their lives outside the lab which can affect their performance in the lab.
The student has a choice.
- Fix their problem themselves, if they can do this then fine all is sorted.
- Seek help from someone / somewhere such as student health services and then fix their problem there nice and quick, maybe even their supervisor might not notice.
- Ask their supervisor for help (or tell them about the problem). Their supervisor may be able to help them, they might not be able to help directly but will point you in the right direction or they might be no help.
- Fail to fix problem and then your work will take a nose dive, you may appear to the supervisor as a lazy toad if you disappear from the workplace and do not tell them that you are ill or have a problem.
Now consider the following,
My student has not appeared in the department for two weeks, none of the rest of the group have any idea of where they are. What do I start thinking (hint "lazy toad").
Student has not appeared in the lab for three days, on day three I get a email explaining that they are very ill. They are laid up in hospital and will not be back for over a week. What do I start thinking (hint "Oh dear, my student is ill")
Student comes to me and tells me my child is sick or my dad has just died. Unless I am a totally evil toad, I will give the student some time off and try to help as much as I can.
My advice is to try to establish and maintain a honest and open relationship with your PhD supervisor. They are not the evil toad enemy ! There are somethings you might not feel happy talking about with your supervisor, somethings might not be suitable topics of discussion with your supervisor.
Rather than telling your supervisor that you have embrassing problems like relationship problems (like your partner has just run off with your best friend). You can tell them "I have a serious problem in my life, I will need two weeks to deal with it". While it is not going to be music to the supervisors ears it is better than just vanishing off the face of the earth for two weeks.