The energy stored oln a capacitor of a given capacity is E=1/2 * C * V^2. Therefore when you double the voltage Vm the energy E becomes 4 times a high. This may be the rason for your observed 'more like logarithmic' characteristic (which isn't logarithimic at all, but square).

Assuming your original circuit of N capacitors with capacity C in parallel such that N equals the number of TECs (this is not necessary but simplifies the following consideration) and a max. voltage of the TECs of V0 (again the exact values are unimportant for the following consideration), the energy of the system at full charge state is

E0 = 1/2 * N * C * V0^2

Now connect all N TECs in series and use only a single capacitor (N=1), then the energy becomes E1 = 1/2 * C * (N*V0)^2 = 1/2 * N * C * V0^2

__* N__
The energy is now N times as high as in the parallel connection although you used less capacitors (1/N) and the same number of TECs.

Another experimental observation shows that by connecting TECs in series does increase voltage but decrease time of reaching 0.1 volts level in a ratio .

Small wonder:

When charging a capacitor wit a current I, the voltage increases as V(C)= C*integral(I) dt. Assuming (for simplicity) each TEC gives off a small fixed constant current I0, then this equation becomes V(C) = C* I0 * t.

Therefore for a single TEC (or stack of TECs) time to reach 0.1 V is t0 = 0.1V/(C * I0).

When you connect the TECs in parallel, the currents add up.

Therefore for a parallel connection of N TECs (or stack of TECs) time to reach 0.1 V is t(N) = 0.1V/(C * N * I0) = 1/N * t0.