Chromebooks have tiny amounts of local storage, the one I got my mom has 16 gigs. If these files need to be run you won't be able to do that either. It will view photos and play music/videos but that's about all you get if you're not connected to the Internet.
It'd help to know what you mean by 'research'. Are you going to need a lot of CPU power to run sims, or even CUDA? An i7 or something with an nvidia gpu would be what you wanted, respectively.
Are you going to be looking at massive high res photos? You'll want a lot of ram.
Do you just need to do everyday college-y stuff? An i5 or even i3 with 4-8 gigs of ram will be fine, and an SSD will make the system exceptionally smooth, though I doubt you'll find anything good with an SSD in your price range but you could always add it yourself.
Every time I try to go where I really wanna be it's already where I am, 'cuz I'm already there XBL, PSN, Steam, Origin, BSN, GFAQs, MC: PhilOnDez
If your research consists of consulting medical journals etc, yes, you can find a laptop for under $700 with a decent amount of storage. If you need to do 3D rendering/CPU intensive calculations etc, no, a $700 or under laptop is not going to be anywhere near powerful enough for those tasks - you're going to need to invest in a mobile workstation, and it's not going to be cheap ($2000+).
it's for my brother-in-law he is doing his fellowship right now, so he tends to use my laptop for multiple pdf files, youtube/news channels (live) and sometimes hi-res pictures. He is not using any 3D rendering applications.