Bimetallic Nanoparticles - Nanotechnologies for Water Environment Applications - page 174

where w n is the weight fraction of hydrocarbon containing n carbon atoms and α is the
chain-growth probability factor defined as:

r
+

p

α = (Eq. 7.11)

r r p t

where r p and r t are the rates of propagation and termination (1/h), respectively. Flory
noted that the two equations (Eq. 7.9 and 7.10) are equivalent when α > 0.5. A larger
value of α
than 4. Eq. 7.11 can be expressed in a logarithmic form:

indicates a better chance to develop hydrocarbons with carbon number greater

2

w n ( − α )

log ( ) = n log ( α ) + log ( ) (Eq. 7.12)

n α

If the possibility of chain growth and chain termination is independent of chain length,
then a plot of log ( w n /n) versus n should be a straight line. In other words, should be a

constant. Eq. 7.12 can also be used to determine whether the products of reactions have
an ASF distribution or not. A linear plot of log ( w n /n) versus n and the approximately
equal value of α as determined from the slope and the intercept with the y-axis indicate
the ASF product distribution.

α

Production of hydrocarbons through the dechlorination of carbon tetrachloride by
bimetallic Pd/Fe nanoparticles is shown in Figure 7.9. Experiments were conducted
using 0.25g bimetallic Pd/Fe nanoparticles in a 50 mL aqueous solution with 150 mg/L
carbon tetrachloride. The use of high concentrations of carbon tetrachloride is because
the quantification of hydrocarbons under low concentrations is difficult. The rate of
hydrocarbon production decreases significantly as the chain length grows. Hydrocarbons
including methane, ethylene, ethane, propane, propylene, propyne, and n-butane were
detected after 100 hours (Table 7.4). Methane was the major product, accounting for
approximately 50% of the initial molar concentration of carbon tetrachloride whereas
concentrations of C 2 and C 3 compounds were much lower.

Using the data listed in Table 7.4, a plot of log ( w n /n) versus n was generated
with linear regression using Eq. 7.12 (Figure 7.10). The values of were calculated to be

0.66 and 0.64 from the slope and y-axis intercept, respectively. The α values determined
were approximately equal and reasonably close to the Hardy and Gillham's results
showing an average α value of 0.54 (Hardy and Gillham, 1996). This suggests an ASF
distribution appeared in the transformation of carbon tetrachloride by bimetallic Pd/Fe
nanoparticles. It should be pointed out that the linear regression as shown in Figure 7.10
did not incorporate methane because of the very high concentration of methane. A high

α