How to motivate young team members when they are working for no monetary benefit?

You said "sophomores who constantly need to be reminded of deadlines, performing duties" gives me a narrow view of your situation and to give you a spot on "course of action", more background is needed.

I am against unpaid internship. Paid or not, what are your rules of engagement. Has anyone deliberately missed a deadline, with younger workers, you have to understand they are used to schedules, task lists, activities and try to make it similar to what they know and are used to.

We have had younger workers who appear to be slacking off on the job because they are surfing the internet, shopping online or playing games on the computers but in actuality get work done faster than some older employees.

As planner, do an experiment and see how they respond. Assign tasks with deadlines that you have added some slack to without telling them. Don't remind them of deadlines and see how they do. If they miss the deadline, it would be a great teaching moment. This should give you a clearer view of how they are really doing. Reminding them on performing tasks is literarily akin to what they hear from their parents. So unless you are in the business of parenting, you should give them as much of what to expect in the workplace. No micro-managing or reminders.

If they miss a deadline, remind them of what it means. 3 strikes and you are out or whatever your organization deems is the right course of action. There are many sophomores who will like an internship of sorts, if there are no consequences, most people don't really learn. I hope my experiment works out for you. Let us know how everything goes.