As long as there is a potential difference across R1, current will flow through it and into C2. This capacitor will eventually charge up to the point where no current can flow through R1, which implies that the voltage at both ends of the resistor is the same (V=R*I, if R!=0 and I=0 then V=0).
At this point, your capacitor C1 sees the voltage V1 at both terminals, i.e. the voltage across your C1 capacitor will be zero, hence it holds zero charge.
A easy way to visualize capacitors in DC circuits is to view them as open circuits as time tends towards infinity. Basically, if you remove C1 and C2 from your circuit, your R1 is left "dangling" in the air. If you now look at the terminals where C1 was, you have the terminal connected to V1, and another connected to your "dangling" resistor. Again, since no current flows through the resistor, the voltage in both terminals is V1 in reference to ground, hence no voltage across the resistor nor across the nodes from where you removed the capacitor.