Quantifying entropic barriers in single-molecule surface diffusion

The quantitative role of entropy in the surface diffusion of molecules with many degrees of freedom is still not well understood. Here, we quantify entropic diffusion barriers as well as attempt frequencies by performing a systematic decomposition of the Arrhenius equation for single oligophenyl molecules of various lengths (two to six phenyl rings and benzene as the reference) on an amorphous silica surface using extensive molecular dynamics simulations. Attempt frequencies evaluated from velocity auto-correlation functions are found close to k_BT/h, the frequency factor of transition state theory. Importantly, we find large positive entropy contributions to the free energy barrier of diffusion up to 55%, increasing with molecular length with 4.1 kJ/mol/phenyl ring. The entropic barrier is about 40%-60% of the entropy of the molecule surface adsorption free energy, revealing that at the transition states, the molecules can liberate a major part of their conformational states, increasing with length. The substantial role of the internal degrees of freedom for the diffusive dynamics is explicitly demonstrated by studying internally constrained, "rigid" version of the molecules. Finally, we discuss also rotational diffusion and the role of surface vibrations. Our results affirm that it is essential for quantitative studies and interpretation of surface diffusion of complex molecules to consider internal entropic effects.