Astrochemistry Lecture 2 Basic Processes (cont d)

Astrochemistry Lecture 2 Basic Processes (cont d) Ewine F. van Dishoeck Leiden Observatory Spring 2008

Types of chemical reactions Formation of bonds Radiative association: X + + Y XY + + hν Associative detachment X - + Y Æ XY + e Grain surface: X + Y:g XY + g Destruction of bonds Photo-dissociation: XY + hν X + Y Dissociative recombination: XY + + e X + Y Collisional dissociation: XY + M X + Y + M Rearrangement of bonds Ion-molecule reactions: X + + YZ XY + + Z Charge-transfer reactions: X + + YZ X + YZ + Neutral-neutral reactions: X + YZ XY + Z

2.1 Ion-molecule reactions Ion induces dipole moment in molecule when it approaches it => long-range attraction which goes as μ1/r 4 Reaction is rapid even at low T if the reaction is exothermic; rate can be readily computed by classical capture theory developed by Langevin 1905 Energy X + + YZ XY + + Z XYZ + Reaction path

Classical capture theory X + b c YZ - Reaction only occurs if impact parameter b small enough that X + is captured, i.e., spends enough time near YZ for reaction to take place

Langevin rate Langevin rate Interaction potential (induced dipole + centrifugal barrier): V ( e b eff R )= 2 2 2 α μ v + 4 2 V eff has maximum value: Critical impact parameter: 1 2 2R 2R 2 2 2 2 ( μb v ) /(8 αe ) F 2 14 2 2 2 2 2 > v = H G I / ( b ) /(8 e ) b 2 K J crit μv μ α Centrifugal barrier 4αe μv Rate coefficient is independent of T: α=polarizability b=impact parameter v=velocity k e = σ πb = π α 2 9 v = critv 2 10 cm s μ 2 3 1

Ion-molecule processes X + + YZ Æ XY + + Z exchange Æ X + YZ + charge transfer Many experiments performed at room T, some at low T. Most reactions (>90%) indeed proceed at Langevin rate, but some exceptions known NH 3+ + H 2 Æ NH 4+ + H

Experiments M. Smith 1993 -Rate coefficients for ion-polar reactions may be factors of 10-100 larger than Langevin values at low T, because V(R)μR -2 Example: C + + OH Æ CO + + H

Unusual case: N + + H 2 -Potentially initiates much of nitrogen chemistry -Rate decreases rapidly at low T, however, because reaction slightly endothermic at T<100 K

2.2 Neutral-neutral reactions Long-range attraction weak: van der Waals interaction μ 1/R 6 Potential barriers may occur in entrance and exit channels => reactions thought to be slow at low T Experiments: reactions can be fast at low T! Energy X + YZ XY + Z entrance XYZ exit Reaction path

CN + C 2 H 6 : or why extrapolation is unreliable k / 10-11 cm 3 molec -1 sec -1 T/K 1000 7 500 300 6 5 4 3 1.0 2.0 3.3 4.0 10 3 /(T/K) I. Sims et al. Rennes/Birmingham

CN + C 2 H 6 : or why extrapolation is unreliable T/K k / cm 3 molec -1 sec -1 1000 10-9 100 50 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 1.0 10.0 20.0 T/K k / cm 3 molec -1 sec -1 1000 300 200 10-10 10-11 10-12 20 1.0 50.0 3.3 5.0 T/K 10 3 / (T/K) k / 10-11 cm 3 molec -1 sec -1 1000 7 500 300 6 5 100 4 3 1.0 2.0 3.3 10 3 /(T/K) 10.0 4.0 10 3 / (T/K)

CN + C 2 H 6 : or why extrapolation is unreliable T/K k / cm 3 molec -1 sec -1 1000 10-9 100 50 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 1.0 10.0 20.0 T/K k / cm 3 molec -1 sec -1 1000 300 200 10-10 10-11 10-12 20 1.0 50.0 3.3 5.0 T/K 10 3 / (T/K) k / 10-11 cm 3 molec -1 sec -1 1000 7 500 300 6 5 100 4 3 1.0 2.0 3.3 10 3 /(T/K) 10.0 4.0 10 3 / (T/K)

CN + C 2 H 6 : reaction stays rapid at low T! k / cm 3 molec -1 sec -1 1000 100 50 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 1.0 10.0 20.0 T/K I. R. Sims, J. L. Queffelec, D. Travers, B. R. Rowe, L. B. Herbert, J. Karthäuser, and I. W. M. Smith, Chem. Phys. Lett. 211 (4-5), 461 (1993). 10 3 / (T/K) 20 50.0

Isentropic expansion CRESU technique and 50-100 slm carrier gas (He, Ar or N 2 ) + precursor + reagent uniform supersonic flow axisymmetric Laval nozzle boundary layer sets scale of apparatus nozzle throat diameter 3 mm 5 cm uniform supersonic flow T = 7 220 K ρ = 10 16 10 18 cm 3 Laval nozzle and isentropic flow chamber pressure 0.1 0.25 mbar pumping speed 30000 m 3 hr -1

Laval nozzles on rockets

Types of neutral-neutral reactions E A /k V(R) Molecule-molecule >10 4 K E.g., H 2 +D 2 Æ 2HD Radical-saturated mol ~2000 E.g., OH + H 2 Æ H 2 O + H Radical-unsaturated mol ~0 E.g., OH + CO Æ CO 2 + H Radical-radical -100 E.g., O + OH Æ O 2 + H

Rate coefficient V Blow-up entrance channel J>0 J=0 V = V ( R) + J / 2μR eff A 2 2 R c R - Determined by shape entrance potential - Low energy collisions: R c large

Adiabatic capture approximation If collision energy < V eff (R c ): reaction probability=0 If collision energy > V eff (R c ): reaction probability=1 This implies that one needs to know the potential surface in the entrance channel very well! Advantages Analytical formulae for rate constants for easy use in chemical networks Disadvantages Ignores angular dependence potential Ignores short range forces Ignores quantum effects (e.g., tunneling) Assumes no activation energy D. Clary 1993

Adiabatic capture theory 2 1 + Rate coefficient kt T n 2 ( ) as T Æ 0 for potentials of the form R -n Interaction Potential Low T dep. Charge-induced dipole R -4 T 0 Charge-dipole R -2 T -1/2 Charge-quadrupole R -3 T -1/6 Dipole-dipole R -3 T -1/6 Dipole-quadrupole R -4 T 0 Dispersion R -6 T 1/6

Experiments: examples -Some reactions are faster at low T than at high T - These neutral-neutral reactions are typically only a factor of 5 slower than ion-molecule reactions at low T => cannot be neglected in networks!

-Reactions with O( 3 P 2 ), S( 3 P 2 ), (non-zero J lowest fine-structure level) are fast, but with C( 3 P 0 ), Si( 3 P 0 ),. (J=0 lowest fine-structure level) are slow? Radical-atom reactions Importance of fine-structure excitation N + OH ÆNO + H O(J=2) O + OH ÆO 2 + H Exp Rate at low T controversial!

2.3 Gas-grain chemistry: H 2 Evidence for gas-grain chemistry H 2 in interstellar clouds NH in diffuse clouds Abundances H 2 O, CO 2, CH 3 OH, in ices higher than expected from freeze-out of gas phase

Formation mechanisms Diffusive mechanism (Langmuir-Hinshelwood) X + g:y Æ X:g:Y Æ X-Y:g Æ XY + g sticking diffusion + desorption molecule formation Direct mechanism (Eley-Rideal) X + Y:g Æ X-Y:g ÆXY + g direct reaction desorption Surface can be silicates, carbonaceous, ice,

Grain surface processes diffusive vs. direct

Diffusive mechanism X + g: Y X: g: Y X Y: g XY + g sticking diffusion+ desorption mol.form Process proceeds in several steps: 1. H atom must collide with grain: H + g 2. Colliding atom must stick to surface: H + g H : g 3. H atom must be retained until another atom gets absorbed: H : g H : g : H 4. H atoms must be mobile to find each other and form bond: H : g : H H H : g 5. H 2 must be ejected from surface: H H : g H 2 + g Probabilities of 2, 3+4 and 5 are η S, η r, η d

H 2 formation on grains 3+4 5.

1. Collision rate with grain Collision rate: rc = πa 2 vh ngn( H) where πa 2 =geometrical cross section v H =10 4 T 1/2 cm s -1 ~10 5 at 100 K n g =number density of grains Observations of extinction: πa n 3 10 rc 3 10 17 nhn( H) 2 22 g Compare with required H 2 formation rate (from obs) R = 3 10 17 nhn( H)η η η f S r d => all probabilities must be nearly unity n H

2. Adsorption time Classical expression: t = 1 E kt ν exp( / ) a d With E d =binding energy; ν=e d /k~10 12 s -1 Physical adsorption: E d ~400 K => t a =3x10 5 s at T=10 K t a =2x10-8 s at T=40 K Chemisorption: E d ~20000 K => t a = at 100 K => H atoms will evaporate above 40 K before forming H 2, unless the grain has strong binding sites

3. Arrival of second H atom Consider t a of first H atom with time for collision of second H atom with grain t C 1 = = 3 10 4 s for n(h) = 1 rn( H) C = 3 10 s for n(h) = 100 cm 2 3 t C <t a if T<15 K for physical absorption At higher temperatures, need chemisorption to retain first H

4. Surface hopping In diffuse clouds: T>15 K, T d >15 K => need chemisorption to retain H Assume second H atom is physically adsorbed Hopping time second H atom: t h ~10-9 s For random 2D walk: where r=distance between sites ~1.5 Å 2 => t M <t a for T<20 K with Second H atom can find first H atom before evaporation t M π( a / 2) = th 10 2 r 3 s

5. Ejection Since there are no strong H 2 -grain bonds, H 2 is now physically adsorbed and will be rapidly ejected From 1-5 it is plausible that η S η r η d ª1, provided the dust temperature is not too high

Eley-Rideal mechanism X + Y: g X Y: g XY + g direct reaction desorption If there are enough chemisorption sites so that grain is saturated with H atoms, formation rate of H 2 is controlled by rate of arrival of H atoms at surface It is assumed that H 2 is formed at every encounter, and rapidly ejected back into gas phase This process is important especially at higher T

Simulations diffuse mechanism Takahashi et al. 1998

Simulation Eley-Rideal mechanism

H 2 formation Recent flurry of experiments and theory Experiments provide constraints on mobility of adsorbed H and on binding and diffusion energies on various materials: silicates, carbonaceous material (graphite), ices Modeling of experimental data somewhat controversial Roughness/irregularity of surface and temperature fluctuations play a role as well Pironello et al. 1997 Biham et al. 2001 Cazaux & Tielens 2004 Hornekaer et al. 2003 Vidali et al. 2007 Cuppen & Herbst 2007

2.4 Gas-grain chemistry: other species Only diffusive mechanisms considered Typical day in the life on the surface of a grain in a dense cloud A few molecules or atoms land on the icy surface All species except He stick with η S =1 If sufficiently light, the particle can migrate over the surface by tunneling or thermal hopping Migrating species: H, O, C, N Perhaps: CH, NH, OH, NH 2, CH 2, CH 3 Reactions may occur if activation barriers sufficiently low

Relevant time scales See Sect. 2.3 for formulae adsorption (=residence) and migration (=thermal hopping) times Tunneling only important for H, H 2 Limiting activation barriers of reactions at T d =10 K H 3500 K H 4500 K 2 O,C,N 450 K

Types of surface reactions 1. Atom-atom reactions, e.g., N + O Æ NO 2. Radical- atom reactions, e.g., H + NOÆ HNO 3. Radical-radical reactions, e.g., CH 3 + OH Æ CH 3 OH 4. Radical-H 2 reactions, e.g., OH + H 2 Æ H 2 O + H 5. Molecule atom reactions, e.g., CO + O Æ CO 2 6. Hydrogen abstraction reactions, e.g., H 2 CO + H Æ HCO + H 2 Type 1,2,3: No activation barrier (typically) Type 4,5,6: Activation barrier

Example: H 2 O formation Tielens & Hagen 1982

Example: CH 3 OH and HCOOH

Experimental simulation Condensation of ice (CO, O 2, N 2, ) in UHV chamber Bombardment by cooled atomic beam (H,O) produced in microwave or DC discharge Analysis of products by Reflection Absorption InfraRed Spectroscopy (RAIRS) and Mass Spectrometry Few groups around the world capable of these experiments, including Sackler laboratory in Leiden

Main QMS From FTIR Spectrometer To rotary stage Secondary QMS H 2 7:1 / 45:8 ellipsoidal mirror H 2 :18 off-axis parabolic mirror 100 K gas InSb / MCT l.n 2 cooled IR detector External link to FTIR Spectrometer Atomic Source To rotary stage Turbo Pump Turbo Pump To rotary stage

Some experimental results Hiraoka et al. 1994, 1995, 1998, 2002 H bombardment of activated N 2, CO, N 2 O ices (10-30 monolayers containing few % of N, C, O) 1% yield of NH 3, CH 4, H 2 O => Hydrogenation of N, C, O is efficient H can penetrate into apolar matrices H bombardment of CO ice ~0.01% yield of H 2 CO and CH 3 OH: low! Watanabe et al. 2002, 2003, 2005 H bombardment of CO-H2O and CO matrix ~10% yield of H2CO and CH3OH: high! Yield CH 3 OH is optimal at 15 K Fuchs et al. 2008 H bombardment of CO-H 2 O and CO matrix Results consistent with both groups, depending on H flux CH 3 OH can be formed at low T!

CH 3 OH experiment IR spectroscopy to monitor products Max. CH 3 OH yield at 15 K Higher T => less sticking of H Watanabe et al.2003

2.5 Photochemistry in ices Ices in dark clouds can be irradiated by UV due to Penetration interstellar radiation: up to A V =5 mag Cosmic ray photons Internal sources (young stellar objects) => ~10 UV photons per molecule in 10 5 yr Many experiments in laboratories on different ice mixtures => rapid formation of CO 2, H 2 CO, in H 2 O:CO irradiated ices Experiments with UV and high-energy particle bombardment => large data base Interstellar applications need to take competition with reactions with H into account No strong observational evidence yet for UV photolysis of ices

Types of reactions 1. Photodissociation, e.g., H2O + hn Æ OH + H 2. Molecule - radical reactions, e.g., CO + OH Æ COOH 3. Radical-radical reactions, e.g., COOH + H Æ HCOOH CONH 2 + NH 2 Æ HNCO + NH 3 4. Acid-base reactions, e.g., HCOOH + NH3 Æ HCOO- + NH4+ 5. Thermal reactions, e.g., CO + O Æ CO 2 6. Hydrogen abstraction reactions, e.g., H 2 CO + H Æ HCO + H 2 Type 1,2,3: No activation barrier Type 4,5,6: Activation barrier