Vegetation: Transport Processes Inside and Outside of Plants - Transport in the Atmosphere-Vegetation-Soil Continuum - page 225

where q ci and q ce are the speciic CO 2 concentrations 1 inside the substomatal cavity
and just above the stomate, respectively, and r s,c is the stomatal resistance for CO 2
transport. Note that we take A n positive when the assimilation is positive. In that case
the CO 2 lux F c is negative as it is directed towards the leaf. 2
Despite the similarity in pathways, the resistances for CO 2 transport differ from
those for water vapour transport. The transport at this scale is due to molecular diffu-
sion and the respective diffusion coeficients D v and D c are contained in the resistances:
r s = l / D v (where l is the diffusion path length). According to Graham's law, the molec-
ular diffusion coeficient is inversely proportional to the molecular mass of the gas
under consideration (Willmer and Fricker, 1996 ). Thus DMMD

1
16

= / ≈ D

c v c v v

.

and the relationship between the stomatal resistances for CO 2 and water vapour
becomes r =1. r . Consequently, Eq. ( 6.23 ) can be written as 3 :

s,c s

qq
r
qq
r

−

A = ρ

ce ci

n

s,c

(6.24)

− g

− ( ) = ρ

ce ci

=

s

ρ qq

ce ci

16 . 16 .

s

For a steady-state situation, the net CO 2 lux entering the leaf is equal to that entering
the mesophyll cells. This means that, referring to Figure 6.12 , the lux can also be
written as:

qq −

A = ρ

ci cc

(6.25)

n

r

m

With the use of this expression we can look at the difference between C 3 and C 4
plants. Because C 4 plants use a more eficient enzyme in the irst ixation step they
can have a lower intracell CO 2 concentration q cc than C 3 plants: 4·10 -6 kg kg -1 rather
than 70·10 -6 kg kg -1 . At the same time the mesophyll resistance r m is also lower in C 4
plants than in C 3 plants: 60 s m -1 rather than 140 s m -1 (Ronda et al., 2001 ). Thus for
a given net uptake of CO 2 , C 4 plants can maintain a lower internal CO 2 concentration

A

because q =

n

rq + . A lower q ci in turn means that for a given net CO 2 uptake

ci mcc

ρ

1 Note that in literature CO 2 concentrations are often given as densities ( ρρ
c

= q ) or as volume fractions

c

M
M

( f

= q

, where M CO2 is the molar mass of CO 2 ). Volume fractions are usually given in parts per million by

c c

CO

2

volume (ppmv). See also Appendix B .
2 This sign convention is consistent with the notion that transport occurs generally down the gradient, in this case
of CO 2 .
3 Here we ignore the fact that the diffusion of water vapour and CO 2 will interact, leading to a modiication of
the relationship between net assimilation and CO 2 concentration difference (see Von Caemmerer and Farquhar,
1981 ).