For D ! F transition, although f produces Pin on
particles, f only leads to a negative effect on D ! F transition
when d is small since PF
inV F
m in Eq. (6) is proportional
to 1/d1/2 in terms of Eqs. (7) and (9) while
PD
inV D
m is proportional to 1/d, which is induced by gradually
decreased size of V F
m as d decreases. Thus, there
must be a size where DGD!F
e ¼ 0. As shown in Fig. 2,
this size is about 5 nm. Although the same case is present
in the calculation of DGD!F
s based on Eqs. (2) and
(3) due to the size dependence of AF
m induced by V F
m, this
effect on DGD!F
s is absent since cF 0 in terms of Eq. (5)
has been employed. As a result, DGD!F
s cDAD
m is always
negative, which is the same thing for D! O transition
as shown in Fig. 2.