Role of Epitaxy in Heterogeneous Nucleation

1 Theory For simplicity, we assume that at most one nucleus can nucleate on one NA, that Cna is dilute enough, and that all NA crystals are active. If epitaxy controls the nucleation rate, the prefactor of I 

When we assume that all NAs have similar shapes, A is given by A oc The proportionality coefficient will change according to the shape of NA. v a is defined by the ratio of the total weight of NA per unit volume (Mna) and the weight of one NA (mNA), that is, 

From Equation (4.53), Equation (4.54), and Equation (4.55), we have the formula. 

In this condition, one crystal with size aobs forms on one NA crystal. Since it includes only one NA crystal, the other NA crystals can work as fresh 

which we call active NA crystals. Therefore, we expect a straight line of I(a a ). 

---

Recall that in Section 4.6.3 we predicted theoretically that /oc Cna na" (Eq. 4.56).The purpose of Section 4.6.4 is to confirm this relationship by controlling a A from the order of nm to pm, which clarifies the important role of epitaxy in heterogeneous nucleation. 

Section 4.6 described the essential role of epitaxy in heterogeneous nucleation by formulating and confirming a relationship, / /q oe Cna/ na, where I is the nucleation rate of polymer crystals, lo is a prefactor of I, Cna is the concentration of NA in the mixture of NA and... 

---