Abstract: Atomistic simulation methods for the quantification of free energies are in wide use. These methods operate by sampling the probability density of a system along a small set of suitable collective variables (CVs), which is, in turn, expressed in the form of a free energy surface (FES). This definition of the FES can capture the relative stability of metastable states but not that of the transition state because the barrier height is not invariant to the choice of CVs. Free energy barriers therefore cannot be consistently computed from the FES. Here, we present a simple approach to calculate the gauge correction necessary to eliminate this inconsistency. Using our procedure, the standard FES as well as its gauge-corrected counterpart can be obtained by reweighing the same simulated trajectory at little additional cost. We apply the method to a number of systems—a particle solvated in a Lennard-Jones fluid, a Diels–Alder reaction, and crystallization of liquid sodium—to demonstrate its ability to produce consistent free energy barriers that correctly capture the kinetics of chemical or physical transformations, and discuss the additional demands it puts on the chosen CVs. Because the FES can be converged at relatively short (sub-ns) time scales, a free energy-based description of reaction kinetics is a particularly attractive option to study chemical processes at more expensive quantum mechanical levels of theory.

Abstract: We discuss the synthesis of carbon nanotubes (CNTs) and graphene by catalytic chemical vapour deposition (CCVD) and plasma-enhanced CVD (PECVD), summarising the state-of-the-art understanding of mechanisms controlling their growth rate, chiral angle, number of layers (walls), diameter, length and quality (defects), before presenting a new model for 2D nucleation of a graphene sheet from amorphous carbon on a nickel surface. Although many groups have modelled this process using a variety of techniques, we ask whether there are any complementary ideas emerging from the different proposed growth mechanisms, and whether different modelling techniques can give the same answers for a given mechanism. Subsequently, by comparing the results of tight-binding, semi-empirical molecular orbital theory and reactive bond order force field calculations, we demonstrate that graphene on crystalline Ni(111) is thermodynamically stable with respect to the corresponding amorphous metal and carbon structures. Finally, we show in principle how a complementary heterogeneous nucleation step may play a key role in the transformation from amorphous carbon to graphene on the metal surface. We conclude that achieving the conditions under which this complementary crystallisation process can occur may be a promising method to gain better control over the growth processes of both graphene from flat metal surfaces and CNTs from catalyst nanoparticles.

Abstract: Understanding the fundamental dynamics in carbon nanotube (CNT) catalysts is of primary importance to understand CNT nucleation. This Letter reports on calculated bond switching (BS) rates in pure and carbon containing nickel nanoclusters. The rates are analyzed in terms of their temperature dependent spatial distribution and the mobility of the cluster atoms. The BS mechanism is found to change from vibrational to diffusional at around 900 K, with a corresponding strong increase in activation energy. Furthermore, the BS activation energy is observed to decrease as the carbon content in the cluster increases, resulting in an effective liquification of the cluster.