CNT assumes that a single energy barrier separates the parent liquid from a bulk crystal in equilibrium with a solution. It also assumes that the surface tension and the shape factor equating 𝜎 ′ are unchanging as a function of 𝑛. This is the so-called capillary approximation which likely fails for the smallest crystals whose shape and faceting are expected to deviate from that of the bulk crystal. Extensions of the theory can be made to account for varying surface tension. The crystal embryo growth is assumed to occur by the transfer of monomers from the solution to the crystal. This is justified by considering the probability of finding clusters of size 𝑛: 𝑝(𝑛) ∝ exp (-Δ𝐹 (𝑛)∕𝑘 B 𝑇 ), where 𝑘 B is Boltzmann's constant and 𝑇 is temperature. If Δ𝐹 (𝑛 * ) ≫ 𝑘 B 𝑇 and 𝑛 * is relatively small; it is reasonable to expect the transfer of growth units from the solution to the crystal to be dominated by solute monomers. The rate, 𝐽 , of formation of clusters of size 𝑛 per unit volume of the solution and per unit time takes an Arrhenius-type form: ]