Paste a string of variable names into function in R

I've got two strings of variable names that looks like this

> names_a = paste(paste0('a', seq(0,6,1)), collapse = ", ")
> names_a
[1] "a0, a1, a2, a3, a4, a5, a6"> names_b = paste(paste0('b', seq(0,6,1)), collapse = ", ")
> names_b
[1] "b0, b1, b2, b3, b4, b5, b6"

Eacha and b variable contains a vector of ids, for example:

> head(a3)
[1] "1234""56567""457659"...

I aim to get all possible pairs of a and b ids. For this purpose I try to paste variables' names rigth into function rbind and then to expand.grid

pairs = expand.grid(rbind(parse(text = names_a), rbind(parse(text = names_b))

I mean I try to collapse all a0 to a6 vectors into a single vector using rbind, let it be named a, the same for all b's vectors and then find all pairs of values in a and b

surprisingly nothing works. Can it be fixed?