Quantifying entropic barriers in single-molecule surface diffusion

Abstract

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 kBT/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.

Highly sensitive work function type room temperature gas sensor based on Ti doped hBN monolayer for sensing CO2, CO, H2S, HF and NO. A DFT study

“…y o indicates the attempt frequency, which is 10 12 Hz at room temperature. 53 The values of recovery time at room temperature with visible light exposure (10 12 Hz attempt frequency) are 4.82 × 10 −10 , 3.361 × 10 −9 , 5.088 × 10 −7 , 3.420 × 10 −8 and 1.551 × 10 −9 seconds for CO 2 , CO, H 2 S, HF and NO gas molecules respectively. Such microsecond recovery time is too small (instantaneous desorption) to make electronic properties of hBN monolayer alter.…”

Electrostatic Reaction Inhibition in Nanoparticle Catalysis

“…This valency dependence of the prefactor in Kramers' theory is not so easy to interpret and could be due to valency effects on the mobility/noise or entropic effects. 63 Interesting is also the observation that the escape (or activation) energy is significantly smaller than ε s by a scaling factor b ≃ 0.45 for both valencies. We suspect that the reason is electrostatic cooperativity between the products for larger adsorptions: a product particle feels the repulsion from other adsorbed products on the curved spherical particle that decreases the activation energy for escape (the curvature leads to a net force radially out from the sphere).…”

“…However, we find that, irrespectively of the interaction energy, the desorption rate k off for reactant/product valency Z = 2 is 2 times larger than for Z = 1. This valency dependence of the prefactor in Kramers’ theory is not so easy to interpret and could be due to valency effects on the mobility/noise or entropic effects . Interesting is also the observation that the escape (or activation) energy is significantly smaller than ε s by a scaling factor b ≃ 0.45 for both valencies.…”

Electrostatic reaction inhibition in nanoparticle catalysis

“…This valency dependence of the prefactor in Kramers' theory is not so easy to interpret and could be due to changes in mobility/noise or entropic effects. 63 Interesting is also the observation that the escape (or activation) energy is significantly smaller than εs by a scaling factor b 0.45 for both valencies. We suspect that the reason is electrostatic cooperativity between the products for larger adsorptions: a product particle feels the repulsion from other adsorbed products on the curved spherical particle which decreases the activation energy for escape.…”