What does “use social media to the chagrin of their administrators” mean?

Question

I learned the sentence in bold from the transcript of a podcast in 60-Second Science:

Eysenbach tracked more than 4200 tweets that cited 286 articles in his own journal. Three quarters of articles that got tweeted a lot (or, to use the study’s nomenclature, had a lot of tweetations) turned out to get a lot of citations. Only 7 percent of poorly tweeted pieces wound up highly cited. As the article notes: "Social media activity either increases citations or reflects the underlying qualities of the article that also predict citations." But I predict that young researchers who use social media to the chagrin of their administrators will cite this journal article. Or tweet about it.

I don't understand what is the meaning of "use social media to the chagrin of their administrators". Is there a phrase of the pattern "use something to something"?

Answer 1

We use:

to the + emotion + of + somebody

or

to + possessive determiner + emotion

to show somebody's emotional response to the sentence. E.g.

To the delight of the spectators, he went on to score another goal.

Our neighbour is learning to play the drums, much to our annoyance.

So, in your example sentence, administrators feel chagrin that young people use social media. It is these young people who will cite the journal article.

Answer 2

cha·grin (sh-grn)
A keen feeling of mental unease, as of annoyance or embarrassment

"to the chagrin of" means to cause annoyance or embarassment to

Answer 3

... young researchers who use social media, to the chagrin of their administrators will cite this journal article.
... young researchers who use social media to the chagrin of their administrators, will cite this journal article.

Above, I added commas to part of the quote in two different ways. The two forms may be recast somewhat as follows:

... young researchers who use social media will cite this journal article to the chagrin of their administrators.
... young researchers who will cite this journal article use social media to the chagrin of their administrators.

Unfortunately the original quote does not have commas in it. The writer could have intended either meaning; it supports both equally well (or equally badly, for that matter). Absent a comma, syntactic patterns don't reveal which meaning was intended.