  We propose a simple scaling theory describing the variation of the mean first
passage time (MFPT) $\tau(N,M)$ of a regular block copolymer of chain length
$N$ and block size $M$ which is dragged through a selective liquid-liquid
interface by an external field $B$. The theory predicts a non-Arrhenian $\tau$
vs. $B$ relationship which depends strongly on the size of the blocks, $M$, and
rather weakly on the total polymer length, $N$. The overall behavior is
strongly influenced by the degree of selectivity between the two solvents
$\chi$.
  The variation of $\tau(N,M)$ with $N$ and $M$ in the regimes of weak and
strong selectivity of the interface is also studied by means of computer
simulations using a dynamic Monte Carlo coarse-grained model. Good qualitative
agreement with theoretical predictions is found. The MFPT distribution is found
to be well described by a $\Gamma$ - distribution. Transition dynamics of ring-
and telechelic polymers is also examined and compared to that of the linear
chains.
  The strong sensitivity of the ``capture'' time $\tau(N,M)$ with respect to
block length $M$ suggests a possible application as a new type of
chromatography designed to separate and purify complex mixtures with different
block sizes of the individual macromolecules.
