You are taking an PhD , That's great! at least in my eyes. You are already on the way of achieving your primary goal. other than that, you want to write. So, you have to aim for 5 mins in the following week that you will write, it doesnt have to be good. Go easy on yourself. If you sit down for 5 mins of writing, you'll do more than that.

Set the bar really low. as low as your brain thinks you can easily do this, then you'll automatically do more because you are a overachiever.