Context: Studies based on high-precision abundance determinations revealed that chemical patterns of solar twins are characterised by the correlation between the differential abundances relative to the Sun and the condensation temperatures (Tc) of the elements. It has been suggested that the origin of this relation is related to the chemical evolution of the Galactic disk, but other processes, associated with the presence of planets around stars, might also be involved. Aims: We analyse HIRES spectra of 14 solar twins and the Sun to provide new insights on the mechanisms that can determine the relation between [X/H] and Tc. Methods: Our spectroscopic analysis produced stellar parameters (Teff, log g, [Fe/H], and $\xi$), ages, masses, and abundances of 22 elements (C, O, Na, Mg, Al, Si, S, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Y, and Ba). We used these determinations to place new constraints on the chemical evolution of the Galactic disk and to verify whether this process alone can explain the different [X/H]-Tc slopes observed so far. Results: We confirm that the [X/Fe] ratios of all the species correlate with age. The slopes of these relations allow us to describe the effect that the chemical evolution of the Galactic disk has on the chemical patterns of the solar twins. After subtracting the chemical evolution effect, we find that the unevolved [X/H]-Tc slope values do not depend on the stellar ages anymore. However, the wide diversity among these [X/H]-Tc slopes, covering a range of $\pm$4~10$^{-5}$ dex K$^{-1}$, indicates that processes in addition to the chemical evolution may affect the [X/H]-Tc slopes. Conclusions: The wide range of unevolved [X/H]-Tc slope values spanned at all ages by our sample could reflect the wide diversity among exo-planetary systems observed so far and the variety of fates that the matter in circumstellar disks can experience.