Especially vs Particularly

(Grammar Questions I Couldn't Answer)

I was helping one of my students proofread her cover-letter for an internship application.
She had written:
"I'm a really passionate person and love studying the law.  Especially, I love studying domestic law."

Based on my native speaker intuition alone, I said, " 'Particularly' would be better here."

The student was a bit surprised.  I think she had been taught that "especially" and "particularly" were the same.

I struggled to explain the difference, but failed. 

Actually, although this is the first time I've blogged about it, I feel like this question has come up a lot over my years of teaching. 

(Further thought....Upon re-reading that sentence, the "especially" would work if I just changed the word order.  "I especially love studying domestic law."  Maybe it's a syntax thing instead of a meaning thing.)