2 Carbon combustion and formation of CO

2.1 Oxidation of carbon grains

The oxidation of carbon particles is a process which has extensively been studied in the laboratory. In Duschl et al. (1996) and Finocchi et al. (1997a) the results for the basic oxidation mechanism of solid carbon obtained in the chemistry of flames are applied to the problem of destruction of carbon dust grains in protoplanetary accretion discs. Under conditions encountered in the early Solar Nebula the basic reaction scheme for oxidation of solid carbon into CO starts with the reaction

$$% latex2html id marker 231 \includegraphics[width=5cm,clip]{equation1.ps}$$ (1)

where a OH radical attacks a six-ring at the periphery of a large PAH and cracks carbon-carbon bonds. The rate for this starter reaction is

$$% R_{\rm car}=A_{\rm car}~n_{\rm OH}~v_{\rm th,OH}~\alpha_{\rm car}.$$ (2)

$A_{\rm car}$ is the total area of all carbon grains per unit volume (as defined in Paper I), $n_{\rm OH}$ the particle density of OH radicals, $v_{\rm th,OH}$their rms thermal velocity

$$% v_{\rm th,OH}=\sqrt{kT\over2\pi m_{\rm OH}}\cdot$$ (3)

$\alpha_{\rm car}$ is the efficiency for the reaction of OH with solid carbon, which is known from laboratory measurements on carbon combustion.

The details of the calculation of the rate $R_{\rm car}$ for an ensemble of carbon grains with different radii are described in Paper I.

2.2 The pathway to CO

The next step in the reaction sequence is (El-Gamal 1995)

$$% {\rm HCCO\ +\ H}\ {\buildrel k_0 \over \longrightarrow} \ {\rm CO\ +\ CH_2}~.$$ (4)

This reaction generates the first CO molecule in the gas phase following the chemi-sputtering reaction (1). The backwards reaction would be strongly endothermic and is forbidden. The HCCO also is formed from C₂H₂by the reaction

$$% \rm C_2H_2\ +\ O\ {\buildrel k_1 \over \longrightarrow}\ HCCO\ +\ H$$ (5)

where C₂H₂ is a follow up product from the CH₂ formed by reaction (4). The rate equation for the formation and destruction of HCCO is

$$% {{\rm d}~n_{\rm HCCO}\over{\rm d}~t}=R_{\rm car}-R_{01}+R_{30}$$ (6)

with

 

$$k_0n_{\rm H}n_{\rm HCCO}$$            R₀₁ = (7)

$$k_1n_{\rm C_2H_2}n_{\rm O}\cdot$$ R₃₀ = (8)

The CH₂ radical formed by reaction (4) then equilibrates with other hydrocarbons of the sequence CH_n ($n=0\dots4$) by means of the rapid exchange reactions

$${\rm C\ +\ H_2}\ {{k_{2}\atop{\displaystyle \longrightarrow}}\atop{{\displaystyle \longleftarrow}\atop k_{-2}}} \ {\rm CH\ +\ H}$$ (9)

$${\rm CH\ +\ H_2}\ {{k_{3}\atop{\displaystyle \longrightarrow}}\atop{{\displaystyle \longleftarrow} \atop k_{-3}}} \ {\rm CH_2\ +\ H}$$ (10)

$${\rm CH_2\ +\ H_2}\ {{k_{4}\atop{\displaystyle \longrightarrow}}\atop{{\displaystyle \longleftarrow}\atop k_{-4}}} \ {\rm CH_3\ +\ H}$$ (11)

$${\rm CH_3\ +\ H_2}\ {{k_{5}\atop{\displaystyle \longrightarrow}}\atop{{\displaystyle \longleftarrow}\atop k_{-5}}} \ {\rm CH_4\ +\ H}.$$ (12)

In the temperature region where carbon oxidation occurs these reactions are fast and in a quasi-equilibrium state. The corresponding set of rate equations is

    

$${{\rm d}~n_{\rm C}\over{\rm d}~t}=-k_2n_{\rm H_2}n_{\rm C}+k_{-2}n_{\rm H}n_{\rm CH}$$ (13)

$${{\rm d}~n_{\rm CH}\over{\rm d}~t}=+k_2n_{\rm H_2}n_{\rm C}-k_{-2}n_{\rm H}n_{\rm CH}$$

$$\qquad\;\;\; -k_3n_{\rm H_2}n_{\rm CH}+k_{-3}n_{\rm H}n_{\rm CH_2}$$ (14)

$${{\rm d}~n_{\rm CH_2}\over{\rm d}~t}=+k_3n_{\rm H_2}n_{\rm CH}-k_{-3}n_{\rm H}n_{\rm CH_2}$$

$$\qquad\quad -k_4n_{\rm H_2}n_{\rm CH_2}+k_{-4}n_{\rm H}n_{\rm CH_3}$$

$$\qquad\quad +R_{01}+R_{34}$$ (15)

$${{\rm d}~n_{\rm CH_3}\over{\rm d}~t}=+k_4n_{\rm H_2}n_{\rm CH_2}-k_{-4}n_{\rm H}n_{\rm CH_3}$$

$$\qquad\quad -k_5n_{\rm H_2}n_{\rm CH_3}+k_{-5}n_{\rm H}n_{\rm CH_4}-R_{12}$$ (16)

$${{\rm d}~n_{\rm CH_4}\over{\rm d}~t}=+k_5n_{\rm H_2}n_{\rm CH_3}-k_{-5}n_{\rm H}n_{\rm CH_4}~.$$ (17)

In Eq. (15) the rate term R₀₁ describes the gain of CH₂by reaction (4). The rate terms R₃₄ and R₁₂ will be explained soon.

The carbon dust oxidation reaction (1) leads to production of CO molecules in the reaction step (4) and to the buildup of a population of hydrocarbon molecules CH_n ($n=1\dots4$), most of which are in the form of CH₄. The main loss process for this group of molecules is the reaction between two CH₃ molecules

$$% {\rm CH_3\ +\ CH_3}\ {\buildrel k_6 \over \longrightarrow} \ {\rm C_2H_4\ +\ H_2},$$ (18)

which forms a C = C bond. The rate for this process is

$$% R_{12}=k_6n_{\rm CH_3}^2.$$ (19)

This rate occurs as loss term in (16). The reverse reaction is endothermic and can be neglected.

Reactions between two CH₃ molecules also result in the formation of C₂H₅ and C₂H₆, but this is followed by reactions finally leading back to CH₃. This side-chain of reactions is considered separately.

The ethylene formed by reaction (18) is in equilibrium with C₂H₃ by means of the fast exchange reaction

$$% {\rm C_2H_3\ +\ H_2}\ {{k_{7}\atop{\displaystyle \longrigh... ...laystyle \longleftarrow} \atop k_{-7}}} \ {\rm C_2H_4\ +\ H}.$$ (20)

The C₂H₃ is destroyed by the reaction

$$% {\rm C_2H_3\ +\ H}\ {{k_{8}\atop{\displaystyle \longrighta... ...aystyle \longleftarrow} \atop k_{-8}}} \ {\rm C_2H_2\ +\ H_2}.$$ (21)

The backwards reaction is endothermic, but not to such an extent that it can be neglected. The rate term for C₂H₃ destruction is

$$% R_{23}=k_8n_{\rm H}n_{\rm C_2H_3}$$ (22)

and that for re-formation

$$% R_{32}=k_{-8}n_{\rm H_2}n_{\rm C_2H_2}.$$ (23)

The rate equations for the formation and destruction of C₂H₄ and C₂H₃ thus are

  

$${{\rm d}~n_{\rm C_2H_4}\over{\rm d}~t} R_{12}-k_{-7}n_{\rm H}n_{\rm C_2H_4}+k_7n_{\rm H_2} n_{\rm C_2H_3}$$ = (24)

$${{\rm d}~n_{\rm C_2H_3}\over{\rm d}~t} k_{-7}n_{\rm H}n_{\rm C_2H_4}-k_7n_{\rm H_2} n_{\rm C_2H_3}-R_{23}+R_{32}.$$ = (25)

The acetylene formed in reaction (21) is in equilibrium with C₂H by means of the fast exchange reaction

$$% {\rm C_2H_2\ +\ H}\ {{k_{9}\atop{\displaystyle \longrighta... ...laystyle \longleftarrow} \atop k_{-9}}} \ {\rm C_2H\ +\ H_2}.$$ (26)

Thus, following reaction (18) a population of C₂H_n ( $n=1\dots4$) molecules is build up.

The main loss process for this group of hydrocarbons are the oxidation reactions

  

$${\rm C_2H_2\ +\ O~} {\buildrel k_1 \over \longrightarrow} {~\rm HCCO\ +\ H}$$ (27)

$${\rm C_2H_2\ +\ O~} {\buildrel k_{10} \over \longrightarrow} {~\rm CH_2\ +\ CO}$$ (28)

$${\rm C_2H\ +\ O~} {\buildrel k_{11} \over \longrightarrow} {~\rm CH\ +\ CO}.$$ (29)

In all three reactions a CO molecule is formed, either directly or in a second step (reaction 4) following reaction (27). Because all three reactions have nearly equal rate coefficients, the first two reactions are more efficient in forming CO than the third one because of a much higher C₂H₂ abundance. These two reactions form the second CO molecule from the two C atoms injected into the gas phase as HCCO by reaction (1). The rate of CO formation by reaction (28) is

$$% R_{34}=k_{10}n_{\rm O}n_{\rm C_2H_2}.$$ (30)

At the same time one of the two CH₃ molecules consumed in reaction (18) is recycled as CH₂ molecule which is introduced back into the chain of reactions (13), ... (17). This occurs in Eq. (15) as the source term R₃₄. The rate of looping back to HCCO by reaction (27) is R₃₀ defined by (8). The rate equations for the formation and destruction of C₂H₂ and C₂H now are

  

$${{\rm d}~n_{\rm C_2H_2}\over{\rm d}~t}=R_{23}-R_{32}-R_{34}-R_{30} -k_{-9}n_{\rm H}n_{\rm C_2H_2}+k_9n_{\rm H_2} n_{\rm C_2H}$$ (31)

$${{\rm d}~n_{\rm C_2H}\over{\rm d}~t}=k_{-9}n_{\rm H}n_{\rm C_2H_2}-k_9n_{\rm H_2} n_{\rm C_2H}.$$ (32)

Figure 1: Reaction cycle for the conversion of the second carbon atom into CO.

The conversion of the two carbon atoms liberated by the starter reaction (1) into CO occurs in two steps. The first CO molecule is formed at once by reaction (4), the rate term R₀₁ in (33) corresponds to this process, while the second CO molecule is formed by the sequence of reactions just described, the rate term R₃₄ in (33) corresponds to this second process. The formation of the second CO molecule occurs via a cyclic process, by which one CH₃ molecule acts as a catalyst which undergoes a sequence of reactions, starting by reacting with a second CH₃ molecule, until finally one CH₃ molecule is converted into CO while the other CH₃ molecule is recovered. Figure 1 schematically shows this reaction cycle.

Besides these reactions, a number of less efficient side-reactions of the reaction chain leading to CO and other hydrocarbons are active. Some of them are discussed in Finocchi et al. (1997a). These reaction path's are not included in the present model calculation. We consider only the main route to CO which accounts for the dominating part of the CO formation rate. More detailed calculations based on a big reaction network are given in Finocchi & Gail (1997b), but the results for CO production based on the extended reaction network are not significantly different from what one obtains from the present reduced set of reaction equations.

The equation for CO formation by carbon combustion is

$$% {{\rm d}~n_{\rm CO}\over{\rm d}~t}=R_{01}+R_{34}.$$ (33)

   
2.3 Grouping of equations

For computational purposes we found it to be advantageous to combine the set of equations into a few groups. We define

$$n_{\rm HCCO}$$                            n₀ = (34)

$$n_{\rm C}+n_{\rm CH}+n_{\rm CH_2}+n_{\rm CH_3}+n_{\rm CH_4}$$ n₁ = (35)

$$n_{\rm C_2H_4}+n_{\rm C_2H_3}$$ n₂ = (36)

$$n_{\rm C_2H_2}+n_{\rm C_2H}.$$ n₃ = (37)

For n₀ we have the equation

$$% {{\rm d}~n_0\over{\rm d}~t}=R_{\rm car}+R_{30}-R_{01}.$$ (38)

Adding Eqs. (13)...(17) yields the equation

$$% {{\rm d}~n_1\over{\rm d}~t}=R_{01}+R_{34}-R_{12}.$$ (39)

Similar, adding Eqs. (24) and (25) yields

$$% {{\rm d}~n_2\over{\rm d}~t}=R_{12}-R_{23}$$ (40)

and finally adding Eqs. (31) and (32) yields

$$% {{\rm d}~n_3\over{\rm d}~t}=R_{23}-R_{34}-R_{30}.$$ (41)

This set of equations is a closed system for calculating n₀, n₁, n₂, and n₃. The rate of creation of any molecule of the groups described by n₀, n₁, n₂, and n₃ is $R_{\rm car}$ while the loss rate for all groups together is R₀₁+R₃₄.

Within each of the groups 1, 2, and 3 the relative abundance of the group members is determined by the fast exchange reactions with H and H₂. The reactions for transition from one group to the next are much slower (cf. Fig. 3 or Tables 3 and 4 in Finocchi et al. 1997a). For determining the relative abundances within the groups we may use the stationary equations with the intergroup transition terms neglected and solve for the individual particle densities in terms of the group densities. We obtain

$$% n_{\rm CH_4}={n_1\over{\cal N}_1}$$ (42)

with

$$% {\cal N}_1= \left[ 1+{k_{-5}n_{\rm H}\over k_5n_{\rm H_2}} \lef... ...t( 1+{k_{-2}n_{\rm H}\over k_2n_{\rm H_2}} \right) \right) \right) \right]\cdot$$ (43)

The particle densities of the other members of this group follow from

$$% n_{{\rm CH}_{m-1}}={k_{-m}n_{\rm H}\over k_mn_{\rm H_2}}~n_{{\rm CH}_m}.$$ (44)

For the rate R₁₂ one then obtains

$$% R_{12}=k_6\left({k_{-5}n_{\rm H}\over k_5n_{\rm H_2}}\right)^2{n_1^2\over{\cal N}_1^2}\cdot$$ (45)

For the second group we obtain

$$% n_{\rm C_2H_4} {n_2 k_7n_{\rm H_2}\over k_7n_{\rm H_2}+k_{-7}n_{\rm H}}$$ = (46)

$$n_{\rm C_2H_3} {n_2 k_{-7}n_{\rm H}\over k_7n_{\rm H_2}+k_{-7}n_{\rm H}}\cdot$$ = (47)

For the rate R₂₃ we obtain

$$% R_{23}=k_8{k_{-7}n_{\rm H}\over k_{-7}n_{\rm H}+k_7n_{\rm H_2}}~n_{\rm H}~n_2.$$ (48)

For the third group we obtain

$$n_{\rm C_2H_2}={n_3 k_9n_{\rm H_2}\over\displaystyle k_9n_{\rm H_2}+ k_{-9}n_{\rm H}}$$ (49)

$$n_{\rm C_2H}={n_3 k_{-9}n_{\rm H}\over k_9n_{\rm H_2}+k_{-9}n_{\rm H}}$$ (50)

and the rate R₃₄ follows as

$$% R_{34}=k_{10}{k_{-9}n_{\rm H}\over k_{-9}n_{\rm H}+k_9n_{\rm H_2}}~n_{\rm O}~n_3.$$ (51)

These equations define the set of rate equations which we solve in order to determine the abundance of the combustion products of carbon grains in the protostellar accretion disc. The production rate of CO is given by (33).

2.4 Formation of CO₂

CO is the dominating carbon-oxygen compound at high temperatures in the inner disc regions. Also at very low temperatures the carbon not bound in carbon grains is mainly bound in CO, other carbon bearing species having only very low abundances in the outer part of the protoplanetary disc, provided the composition in that region equals that of the parent molecular cloud. At medium temperatures, however, if it is assumed that conversion to CH₄ is kinetically forbidden (e.g. Fegley & Prinn 1989), most of the CO will be converted into CO₂. The most efficient reaction for the interconversion of CO and CO₂ is

$$% {\rm CO\ +\ H_2O}\ {{k_{12}\atop{\displaystyle \longrighta... ...splaystyle \longleftarrow} \atop k_{-12}}} {\rm CO_2\ +\ H_2}.$$ (52)

At high temperatures also

$$% {\rm CO\ +\ OH}\ {{k_{13}\atop{\displaystyle \longrightarr... ...displaystyle \longleftarrow} \atop k_{-13}}} {\rm CO_2\ +\ H}$$ (53)

becomes important. These reactions are responsible first for the formation of CO₂ from CO as the disc material slowly spirals inwards into regions of increasingly higher temperature and reaction (52) proceeds from the left to right. Later, by continued inwards migration of the disc material, temperatures become unfavourably high for the existence of CO₂ and reactions (52) and (53) then proceeds from the right to the left and in this way are responsible for the re-formation of CO from CO₂. Thus, Eq. (33) has to be changed into

 

$$% {{\rm d}~n_{\rm CO}\over{\rm d}~t}=R_{01}+R_{34}-k_{12}n_{\rm C... ...{\rm CO_2}n_{\rm H_2} -k_{13}n_{\rm CO}n_{\rm OH} +k_{-13}n_{\rm CO_2}n_{\rm H}$$ (54)

to account for the reactions (52) and (53) and we have to add to our system the equation for CO₂

 

$$% {{\rm d}~n_{\rm CO_2}\over{\rm d}~t}=+k_{12}n_{\rm CO}n_{\rm H_... ...\rm CO_2}n_{\rm H_2} +k_{13}n_{\rm CO}n_{\rm OH} -k_{-13}n_{\rm CO_2}n_{\rm H}.$$ (55)

2.5 Formation of C₂H₅ and C₂H₆

The formation of C₂H₅ and of ethane is possible by a side chain of the main reaction route from carbon dust to CO and CO₂ considered up to now. These molecules may be formed by the following reactions

$$% {\rm CH_3\ +\ CH_3}\ {{k_{14}\atop{\displaystyle \longrigh... ...isplaystyle \longleftarrow} \atop k_{-14}}} {\rm C_2H_5\ +\ H}$$ (56)

and

$$% {\rm C_2H_5\ +\ H_2}\ {{k_{15}\atop{\displaystyle \longrig... ...splaystyle \longleftarrow} \atop k_{-15}}} {\rm C_2H_6\ +\ H}.$$ (57)

This fast exchange reaction establishes an equilibrium between C₂H₅ and C₂H₆. A second route to ethane formation is the three-particle reaction

$$% {\rm CH_3\ +\ CH_3\ +\ M}\ {\buildrel k_{16}\over\longrightarrow}\ {\rm C_2H_6\ +\ M}$$ (58)

which occurs at a small but non-negligible rate since pressures in the inner region of the accretion disc are not as low as they usually use to be in astrophysical problems. A third route to ethane is

$$% {\rm CH_4\ +\ CH_4}\ {\buildrel k_{17}\over\longrightarrow}\ {\rm C_2H_6\ +\ H_2}~.$$ (59)

 

 

Table 1: Rate coefficients for the chemical reactions used in the model calculation.

Rate	A	$\alpha$	Ea/k	Source
	$\rm cm^3s^{-1}$		[K]
k0	$2.50\times10^{-10}$	0	16 100	1
k1	$3.60\times10^{-18}$	2.10	790	3
k2	$6.64\times10^{-10}$	0	11 700	2
k3	$2.40\times10^{-10}$	0	1760	3
k4	$1.20\times10^{-10}$	0	0	3
k5	$1.14\times10^{-20}$	2.74	4740	3
k6	$1.66\times10^{-8}$	0	16 500	2,1
k7	$2.00\times10^{-11}$	0	0	1
k8	$2.00\times10^{-11}$	0	0	3
k9	$1.00\times10^{-10}$	0	14 000	3
k10	$8.40\times10^{-18}$	2.10	790	3
k11	$1.70\times10^{-11}$	0	0	3
k-12	$2.94\times10^{-14}$	0.50	7550	2
k13	$1.05\times10^{-17}$	1.50	250	3
k14	$5.00\times10^{-11}$	0	6800	3
k-14	$6.00\times10^{-11}$	0	0	3
k15	$5.10\times10^{-24}$	3.60	4250	3
k-15	$2.15\times10^{-24}$	1.50	3370	3
k17	$1.70\times10^{-15}$	1.00	22 640	4
k18	$3.75\times10^{-10}$	0	7800	1

Sources:
(1): El-Gamal (1995), (2): UMIST data-file (Millar et al. 1997),
(3): Baulch et al. (1994), (4) NIST.

2.6 Formation of methanol CH₃OH

According to observations of cometary nuclei, methanol is a very abundant component in the ice mixture of comets. For this reason we include in our calculation of the chemistry as a test case the reactions for the formation of CH₃OH by

$$% {\rm CH_3\ +\ OH}\ {{k_{18}\atop{\displaystyle \longrighta... ...isplaystyle \longleftarrow} \atop k_{-18}}} {\rm CH_3O\ +\ H}.$$ (60)

The CH₃O is in equilibrium with CH₃OH by means of the rapid hydrogen addition/abstraction reaction

$$% {\rm CH_3O\ +\ H_2}\ {{k_{19}\atop{\displaystyle \longrigh... ...isplaystyle \longleftarrow} \atop k_{-19}}} {\rm CH_3OH\ +\ H}$$ (61)

CH₃O and CH₄OH are treated in the calculation as a single group as before.

2.7 Reaction rates and equilibrium constants

The rate coefficients are approximated in the standard Arrhenius form

$$% k=A~T^\alpha~{\rm e}^{-E_a/kT}.$$ (62)

The coefficients of this representation used in the model calculation are listed in Table 1 together with the sources, where the data have been taken from. The rate k₁₆ is taken from Baulch et al. (1994).

The rate coefficients for the reverse reactions are calculated by means of the principle of detailed balancing from rate coefficients of the forward reactions and the mass action constant for the reaction in chemical equilibrium. The mass action constants are calculated from thermodynamical data given in Barin (1995). The free enthalpy of formation of molecules from the free atoms is fitted by the following expression

$$% \Delta G={a\over T}+b+cT+dT^2+eT^3.$$ (63)

Results for the fit coefficients for the molecules used in the present calculation are given in Table 2. The accuracy of this analytical fit to the tabular values is generally better than 10^-3 in the temperature region 300 ... 2000 K.

 

 

Table 2: Fit coefficients for the approximation (63) for the free enthalpy of formation $\Delta G$ of a compound from the free atoms. Units are J/mole, pressures are in bar. Data from Barin (1995).

Molecule	a	b	c	d	e
H2	$1.06769\times10^6$	$-4.41615\times10^5$	$1.03979\times10^2$	$6.40612\times10^{-3}$	$-7.56253\times10^{-7}$
CH	$7.43838\times10^5$	$-3.44391\times10^5$	$9.20348\times10^1$	$8.53870\times10^{-3}$	$-1.55497\times10^{-6}$
CH2	$1.74071\times10^6$	$-7.75871\times10^5$	$2.02387\times10^2$	$1.41851\times10^{-2}$	$-2.42352\times10^{-6}$
CH3	$2.79512\times10^6$	$-1.24068\times10^6$	$3.23768\times10^2$	$2.03837\times10^{-2}$	$-3.57358\times10^{-6}$
CH4	$4.59997\times10^6$	$-1.68987\times10^6$	$4.60008\times10^2$	$2.72121\times10^{-2}$	$-5.02918\times10^{-6}$
C2	$-5.18061\times10^3$	$-5.94870\times10^5$	$1.12562\times10^2$	$5.90139\times10^{-3}$	$-9.83454\times10^{-7}$
C2H	$1.42354\times10^6$	$-1.09086\times10^6$	$2.29673\times10^2$	$9.62207\times10^{-3}$	$-2.02675\times10^{-6}$
C2H2	$2.35939\times10^6$	$-1.65637\times10^6$	$3.60940\times10^2$	$1.28570\times10^{-2}$	$-2.49538\times10^{-6}$
C2H3	$4.23944\times10^6$	$-1.85210\times10^6$	$4.57332\times10^2$	$2.09662\times10^{-2}$	$-3.89347\times10^{-6}$
C2H4	$5.36679\times10^6$	$-2.28443\times10^6$	$5.94532\times10^2$	$2.52283\times10^{-2}$	$-4.83266\times10^{-6}$
C2H5	$6.63096\times10^6$	$-2.45504\times10^6$	$6.85807\times10^2$	$3.26708\times10^{-2}$	$-6.19303\times10^{-6}$
C2H6	$3.97121\times10^6$	$-2.84507\times10^6$	$7.68025\times10^2$	$9.61891\times10^{-2}$	$-2.78540\times10^{-5}$
OH	$1.15321\times10^6$	$-4.34309\times10^5$	$9.81838\times10^1$	$5.95049\times10^{-3}$	$-6.97288\times10^{-7}$
H2O	$2.74226\times10^6$	$-9.42013\times10^5$	$2.18481\times10^2$	$1.08875\times10^{-2}$	$-1.34636\times10^{-6}$
CO	$1.26946\times10^6$	$-1.08346\times10^6$	$1.30093\times10^2$	$3.94470\times10^{-3}$	$-4.33689\times10^{-7}$
CO2	$2.22110\times10^6$	$-1.62175\times10^6$	$2.85410\times10^2$	$2.69311\times10^{-3}$	$-3.80432\times10^{-7}$
CH3O	$6.18606\times10^6$	$-1.64280\times10^6$	$4.79459\times10^2$	$1.06008\times10^{-2}$	$-1.52592\times10^{-6}$
CH3OH	$2.84997\times10^6$	$-2.05244\times10^6$	$5.31756\times10^2$	$7.14428\times10^{-2}$	$-2.01010\times10^{-5}$

Figure 2: Radial disc structure in models for a stationary accretion disc including radial mixing processes for the three different accretion rates indicated at the lines (in units $10^{-7}~M_\odot~\rm yr^{-1}$). Top left: temperature in the midplane. Top right: pressure in the midplane. Bottom left: degree of condensation of carbon in carbon grains. Bottom right: fraction of the oxygen not bound in solids and CO, which is condensed as water ice.