How to split a dataframe according to a column with duplicated rows

Question

I have the following dataframe:

data.frame(type = c("cell", "cell", "protein", "protein"), value = c(1,5,3,8))

I would like to split this dataframe into 2 different dataframes so as to have in each a unique value for the type column, like the following example:

type      value
cell       1
protein    3





  type      value
    cell       5
    protein    8

How can I do this in R? Thank you!