Exact String Compare in R?

Dear R users:
Here's a barebones example of what I can't make work. 
As you can see, regexpr() does not perform an exact string match, which only
occurs in row 1 of these data frames. Instead, as it's supposed to do, it
finds "b" in "bb" and "c" in "cc". Does anybody know what function I can use
such that only the first rows would be matched (ie, exact string match?)
I've also tried simply using the == operator, in which case i get the
error:"level sets of factors are different"

Thank you in advance, 
B

## two toy data frames, containing character arrays
D1=as.data.frame(c("a","b","c"))
D2=as.data.frame(c("a","bb","cc"))

## loop through each comparing the strings in each row
i=1 #counter
while (regexpr(D1[i,1], D2[i,1]) == TRUE) {

+        cat("identical match on row #", i, "\n")
+        i=i+1 
+         if (i>3) break 
+ }
identical match on row # 1 
identical match on row # 2 
identical match on row # 3

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