There are different theories of graphene growth by chemical vapour deposition (CVD) techniques (e.g., microwave-CVD, plasma-CVD, thermal-CVD etc.) on a catalytic transition-metal substrate (commonly copper/nickel) is proposed by researchers.
Kindly put your expert insight whether there are any particular established mathematical relations/equations that follows carbon atoms diffusion in catalytic substrate or nucleation in surface to predict mono-layer/few-layers of graphene synthesis (considering the catalytic substrate is devoid of possible microstructural defects).