attachment and fragmentation cross-sections of water clusters
TRANSCRIPT
Att
ach
ment and fra
gm
enta
tion
cross
-sect
ions
of
wate
r cl
ust
ers
Sébast
ien Z
am
ithP
ierr
e L
abast
ie,
Pie
rre F
eid
en
Jean-M
arc
L’H
erm
ite
Labora
toire C
olli
sions
Agré
gats
Réact
ivité
CN
RS
/ U
niv
ers
ité d
e T
oulo
use
üA
ttach
ment
(Ecm
= 0
.1-1
eV
)
üF
ragm
enta
tion (
Ecm
= 1
-300 e
V)
(H2O
) n+
1H
+(H
2O
) nH
+H
2O
+
(H2O
) n-1
H+ +
Wate
r clu
ste
r-w
ate
r m
ole
cu
le c
oll
isio
n
üA
ttach
ment
(Ecm
= 0
.1-1
eV
) à
vibra
tional d
ynam
ics
üF
ragm
enta
tion (
Ecm
= 1
-300 e
V)
(H2O
) n+
1H
+(H
2O
) nH
+H
2O
+
(H2O
) n-1
H+ +
Wate
r clu
ste
r-w
ate
r m
ole
cu
le c
oll
isio
n
üA
ttach
ment
(Ecm
= 0
.1-1
eV
) à
vibra
tional d
ynam
ics
üF
ragm
enta
tion (
Ecm
= 1
-300 e
V) à
transp
are
ncy
(H2O
) n+
1H
+(H
2O
) nH
+H
2O
+
(H2O
) n-1
H+ +
Wate
r clu
ste
r-w
ate
r m
ole
cu
le c
oll
isio
n
Ou
tlin
e
•E
xperim
enta
l setu
p
•A
ttach
ment
cross
-sect
ions
(H2O
) nH
+
•F
ragm
enta
tion c
ross
-sect
ions
•C
oncl
usi
ons
and p
ers
pect
ives
Ou
tlin
e
•E
xperim
enta
l setu
p
•A
ttach
ment
cross
-sect
ions
(H2O
) nH
+
•F
ragm
enta
tion c
ross
-sect
ions
•C
oncl
usi
ons
and p
ers
pect
ives
•A
ttach
ment
cross
-sect
ions
(H2O
) nH
+
•F
ragm
enta
tion c
ross
-sect
ions
•C
oncl
usi
ons
and p
ers
pect
ives
Exp
eri
men
tal setu
p
Ec
m, T
(H2O
) n+
1H
+(H
2O
) nH
+H
2O
+
(H2O
) nH
+
1 <
n <
200
Pro
du
cti
on
an
d i
on
isati
on
:G
as a
gg
reg
ati
on
so
urc
e
Exp
eri
men
tal setu
p
Th
erm
ali
sati
on
:C
oll
isio
ns w
ith
th
e
carr
ier
gas (
Heli
um
)
(H2O
) nH
+
1 <
n <
20
0
T f
ixed
25 <
T <
350
K
Exp
eri
men
tal setu
p
Mass s
ele
cti
on
En
erg
y f
ocali
sati
on
Slo
win
g d
ow
n
(H2O
) nH
+
n f
ixed
T f
ixed
Ela
bfi
xed
Exp
eri
men
tal setu
p
Co
llis
ion
(s)
+
Ela
b, T
Exp
eri
men
tal setu
p
(H2O
) n+
1H
+(H
2O
) nH
+H
2O
Mass a
naly
sis
88
90
92
94
96
0,0
0,2
0,4
0,6
0,8
1,0
signal (arb.)n
Exp
eri
men
tal setu
p
ØS
low
ing d
ow
n to
Ela
b=
5 e
V(E
cm=
90
meV
for
n=
10
0)
Øgood
tra
nsm
issi
on: >
50
%
Øsm
all
energ
y dis
pers
ion: 2
eV
(45
meV
fo
r n
=10
0)
Øth
erm
alis
atio
n
25
< T
< 3
50
K
ØC
lust
ers
(H
2O
) nH
+1
< n
< 2
00
Cf.
Ch
iro
t et
co
ll.
Rev
. S
ci.
Inst
rum
. 7
7, 6
31
08
(2
00
6)
Perf
orm
an
ce
s
Exp
eri
men
tal setu
p
•E
xperim
enta
l setu
p
•A
ttach
ment
cross
-sect
ions
(H2O
) nH
+
•F
ragm
enta
tion c
ross
-sect
ions
•C
oncl
usi
ons
and p
ers
pect
ives
Ou
tlin
e
•E
xperim
enta
l setu
p
•F
ragm
enta
tion c
ross
-sect
ions
•C
oncl
usi
ons
and p
ers
pect
ives
Att
ach
men
t cro
ss
-secti
on
sC
oll
isio
ns
(H2O
) n+
1H
+(H
2O
) nH
+H
2O
+
n
E
n
nT
knE
Ela
bB
lab
cm»
++
+=
123
1
1
0
++
+=
ncm
clu
ster
clu
ster
DE
EE
0 clu
ster
E
Att
ach
ment
cross
-section a
s a
function o
f siz
e,
colli
sio
n e
nerg
y, t
em
pera
ture
, …
with
out
eva
pora
tion!
No e
vapora
tion if
Ecl
ust
ersm
all
enough
1
0)
(21
)(
)/
ln(
--
÷÷ øöçç èæ
++
-=
a
ea
erf
aa
erf
l
II
a pr
s
Tn
kEa
Blab
=
99
100
101
102
103
104
Taille
n
I 0
I
-A
bso
lute
cro
ss-s
ect
ions
-Lin
ear
evo
lutio
n w
ith t
he c
olli
sion c
ell
pre
ssure
Meth
od
P =
8. 1
0-6 m
ba
r
P =
4.3
10
-5 m
ba
r
P =
1. 1
0-4 m
ba
r
148
150
152
154
156
P =
1.8
10
-4 m
ba
r
Tim
e o
f fl
igh
t (µ
s)
Att
ach
men
t cro
ss
-secti
on
s
Resu
lts f
or
po
sit
ively
ch
arg
ed
clu
ste
rs
(H2O
) nH
+ +
H2O
à(H
2O
) n+
1H
+
n=
40, E
cm=
0.6
eV
n=
200, E
cm=
0.1
5 e
V123
1+
++
=n
nT
knE
EB
lab
cmEla
b=
22 e
V
Att
ach
men
t cro
ss
-secti
on
s
20
30
40
50
60
70
80
901
00
200
300
100
1000
Attachment cross-section (Å2)
Siz
e
-Co
nve
rge a
t la
rge s
izes
-N
o s
tru
ctu
re-
Incre
ase w
ith
siz
e-
Decre
ase w
ith
co
llis
ion
en
erg
y
123
1+
++
=n
nT
knE
EB
labo
cm
(H2O
) nH
+ +
H2O
à(H
2O
) n+
1H
+
Att
ach
men
t cro
ss
-secti
on
s
20
30
40
50
60
70
80
901
00
200
300
100
1000
Ela
b =
6 e
V 1
0 e
V 1
8 e
V 2
2 e
V 3
3 e
V
Attachment cross-section (Å2)
Siz
e
Resu
lts f
or
po
sit
ively
ch
arg
ed
clu
ste
rs
20
30
40
50
60
70
80
901
00
200
300
100
1000
Ela
b =
6 e
V 1
0 e
V 1
8 e
V 2
2 e
V 3
3 e
V s
geo
Attachment cross-section (Å2)
Siz
e
Co
mp
ari
so
n w
ith
th
e g
eo
me
tric
cro
ss
-sec
tio
n
2 )(
rR
geo
+=
ps
2R
2
r
rn
R3/
1=
The m
easu
red a
ttach
ment
cross
-sect
ion is
sm
alle
r th
an t
he g
eom
etr
ic c
ross
-sect
ion!!
(H2O
) nH
+ +
H2O
à(H
2O
) n+
1H
+
Att
ach
men
t cro
ss
-secti
on
s
Hyp
oth
ese
s
üE
vapora
tion
(H2O
) n-1
D2O
H+
+
(H2O
) nH
++
D2O
+
H2O
2n
12
üE
xchange r
eact
ion
OH
HO
HH
OH
OH
HO
Hn
nn
22
*
12
22
)(
))
(()
(+
®®
++
++
+
++
+®
+O
HO
HO
HH
OH
nn
32
22
)(
)(
üC
harg
e e
xchange
+
Att
ach
men
t cro
ss
-secti
on
s
Hyp
oth
esis
üE
vapora
tion
(H2O
) nH
+ +
(H2O
) nH
++
H2O
H2O
üE
xchange r
eact
ion
OH
HO
HH
OH
OH
HO
Hn
nn
22
*
12
22
)(
))
(()
(+
®®
++
++
+
++
+®
+O
HO
HO
HH
OH
nn
32
22
)(
)(
üC
harg
e e
xchange
Att
ach
men
t cro
ss
-secti
on
s
üE
vapora
tion
OH
HO
HH
OH
OH
HO
Hn
nn
2HH
2HH
*
12
HH2
HH2
HH)
()
)((
)(
+®
®+
++
++
+
2n
+
Hyp
oth
esis
üE
vapora
tion
(H2O
) nH
+ +
(H2O
) nH
++
H2O
H2O
üE
xchange r
eact
ion
OH
HO
HH
OH
OH
HO
Hn
nn
22
*
12
22
)(
))
(()
(+
®®
++
++
+
++
+®
+O
HO
HO
HH
OH
nn
32
22
)(
)(
üC
harg
e e
xchange
Att
ach
men
t cro
ss
-secti
on
s
üE
vapora
tion
OH
HO
HH
OH
OH
HO
Hn
nn
2HH
2HH
*
12
HH2
HH2
HH)
()
)((
)(
+®
®+
++
++
++
+®
+O
HO
HO
HH
OH
nn
3HH
2HH
2HH
2HH
)(
)(
üC
harg
e e
xchange
+
2n
+
Hyp
oth
esis
üE
vapora
tion
(H2O
) nH
+ +
(H2O
) nH
++
H2O
+
H2O
üE
xchange r
eact
ion
OH
HO
HH
OH
OH
HO
Hn
nn
22
*
12
22
)(
))
(()
(+
®®
++
++
+
++
+®
+O
HO
HO
HH
OH
nn
32
22
)(
)(
üC
harg
e e
xchange
+
Att
ach
men
t cro
ss
-secti
on
s
üE
vapora
tion
(H2
(H(HO
) nH
nn+
HH+
(H2
(H(HO
) nH
nn+
HH+
H2
HHO
+
2H
2HH
Oü
Exc
hange r
eact
ion
OH
HO
HH
OH
OH
HO
Hn
nn
2HH
2HH
*
12
HH2
HH2
HH)
()
)((
)(
+®
®+
++
++
++
+®
+O
HO
HO
HH
OH
nn
3HH
2HH
2HH
2HH
)(
)(
üC
harg
e e
xchange
+
Hyp
oth
esis
üE
vapora
tion
(H2O
) nH
+ +
(H2O
) nH
++
H2O
+
H2O
üE
xchange r
eact
ion
OH
HO
HH
OH
OH
HO
Hn
nn
22
*
12
22
)(
))
(()
(+
®®
++
++
+
++
+®
+O
HO
HO
HH
OH
nn
32
22
)(
)(
üC
harg
e e
xchange
+
Att
ach
men
t cro
ss
-secti
on
s
üE
vapora
tion
(H2
(H(HO
) nH
nn+
HH+
(H2
(H(HO
) nH
nn+
HH+
H2
HHO
+
2H
2HH
Oü
Exc
hange r
eact
ion
OH
HO
HH
OH
OH
HO
Hn
nn
2HH
2HH
*
12
HH2
HH2
HH)
()
)((
)(
+®
®+
++
++
++
+®
+O
HO
HO
HH
OH
nn
3HH
2HH
2HH
2HH
)(
)(
üC
harg
e e
xchange
+
Co
llis
ion
du
rati
on
2n
1/3
rm
Tk
nm
E
rn
Bla
bo
c3
2
23/
1
+
=t
For
exa
mple
, n=
70,
Ela
b=
22 e
VÞ
t c=
1 p
s
üIf
the c
olli
sion d
ura
tion is
short
er
than t
he c
hara
cterist
ic t
ime t
vfo
r in
tern
al e
nerg
y re
dis
trib
utio
n (
IVR
) à
No a
ttach
ment
Adia
batic
itypara
mete
r:
vc ttx
=
üR
ate
of
«non s
ticki
ng
» c
olli
sions:
geo
geo s
ss
exp
-
20
30
40
50
60
70
80
901
00
200
300
100
500
1000
Section efficace (Å2)
Ta
ille
Att
ach
men
t cro
ss
-secti
on
s
-All
the d
ata
fall
on t
he
sam
e c
urv
e
-E
xponentia
l fit:
v
c
et
tt
0-
-
ps
v7.
0=
tÛ
~ 6
meV
Vib
ratio
nnals
urf
ace
mode (
O•
•O•
•O)
measure
d in c
luste
rs a
t 5.1
meV
J. B
rud
erm
an
n, P
. L
oh
bra
ndt,
U.
Bu
ck a
nd
V.
Bu
ch, P
hys
. R
ev.
Le
tt. 8
0, 2
82
1 (
19
98
)
(6.2
meV
for
the b
ulk
)
Att
ach
men
t cro
ss
-secti
on
sC
oll
isio
n d
ura
tio
n
0.5
1.0
1.5
2.0
2.5
0.0
0.2
0.4
0.6
0.8
1.0
(sgeo-sexp)/sgeo
t c (p
s)
100
500
1000
30
02
00
10
09
08
07
06
05
04
03
02
0
Ela
b =
6 e
V 1
0 e
V 1
8 e
V 2
2 e
V 3
3 e
V
Attachement cross-section (Å
2)
Siz
e
)1(
/)(
0v
ce
geo
coll
age
tt
ts
s-
--
=
S. Z
am
ith e
t al,
Phys
. R
ev.
Lett
. 104, 1
03401 (
2010)
Att
ach
men
t cro
ss
-secti
on
sC
oll
isio
n d
ura
tio
n
•E
xperim
enta
l setu
p
•A
ttach
ment
cross
-sect
ions
(H2O
) nH
+
•F
ragm
enta
tion c
ross
-sect
ions
•C
oncl
usi
ons
and p
ers
pect
ives
Ou
tlin
e
•E
xperim
enta
l setu
p
•A
ttach
ment
cross
-sect
ions
(H2O
) nH
+
•C
oncl
usi
ons
and p
ers
pect
ives
05
10
15
20
25
30
35
Siz
e
Fra
gm
en
tati
on
cro
ss-s
ecti
on
s
(H2O
) n-1
H+
(H2O
) nH
+H
2O
+
(H2O
) n-x
H+
xH
2O
+
Direct
dis
soci
atio
n ~
ps
(im
puls
ive t
ransf
er)
Eva
pora
tion ~
µs-
s(t
herm
al e
mis
sion)
Co
llis
ion
s
(2
)
Ela
b=
70 e
VT
th=
25 K
(H2O
) 30H
+ c
lust
ers
Therm
alis
ed a
t 25K
Resu
lts
110
100
0
50
100
150
200
250
s (Å2)
Ecm (
eV
)
Fra
gm
en
tati
on
cro
ss-s
ecti
on
s
At lo
w c
olli
sion e
nerg
y,
tem
pera
ture
effe
ct:
Sta
tistic
al f
ragm
enta
tion
(eva
pora
tion)
Resu
lts
110
100
0
50
100
150
200
250
(H2O
) 30H
+
Tth
= 2
5 K
Tth
= 1
00 K
s (Å2)
Ecm (
eV
)
Fra
gm
en
tati
on
cro
ss-s
ecti
on
s
EED
nW
n
geo
73
3 0
1
)6
3(8
-
÷ øöç èæ
--
=s
mp
n
Mo
del b
n : C
lust
er
size
,n 0
:inte
r-m
ole
cula
r vi
bra
tion (
183 c
m-1
),m
: re
duce
d m
ass
,s
ge
o: geom
etr
ic c
ross
-sect
ion,
D : d
isso
ciatio
n e
nerg
ies,
E : C
lust
er
inte
rnal e
nerg
y.
K. H
an
sen
et a
l, J.
Che
m. P
hys
. 1
31
, 1
24
30
3 (
20
09
)
05
10
15
20
25
30
35
40
45
50
0.3
0.4
0.5
0.6
0.7
0.8
0.9
D (eV)
Ta
ille
üE
vapora
tion r
ate
:
üE
nerg
y tr
ansf
er
during c
olli
sion :
)1(
22
RbE
Ecm
T-
=
üM
onte
-Carlo s
imula
tion (
dis
trib
utio
n o
f in
tern
al e
nerg
y, c
olli
sion e
nerg
y, e
tc.)
Fra
gm
en
tati
on
cro
ss-s
ecti
on
s
Mo
del:
co
mp
ari
so
n w
ith
fra
gm
en
tati
on
sp
ectr
a
05
10
15
20
25
30
05
10
15
20
25
30
35
Ecm =
2.3
eV
Ecm =
3.3
eV
Ecm =
6.5
eV
Ecm =
13 e
V
Siz
e
(H2O
) 30H
+ +
H2O
Fra
gm
en
tati
on
cro
ss-s
ecti
on
s
Mo
del:
co
mp
ari
so
n w
ith
exp
eri
men
tal
cro
ss
-sec
tio
ns
110
100
0
50
100
150
200
250
(H2O
) 30H
+
Tth
= 2
5 K
Tth
= 1
00 K
s (Å2)
Ecm (
eV
)
Model g
ives
the g
ood t
rends
for
the c
ross
-sect
ion a
s a
funct
ion o
f te
mpera
ture
and
colli
sion e
nerg
y
Fra
gm
en
tati
on
cro
ss-s
ecti
on
s
Sim
ple
model re
pro
duces q
ualit
atively
the b
ehavio
ur
at lo
w c
olli
sio
n e
nerg
ies,
but…
… o
nly
70%
of
the g
eom
etr
ic c
ross-s
ect
ion
r =
1.9
8 Å
, n=
30
sge
o=
210 Å
2
Co
mp
ari
so
n w
ith
th
e g
eo
me
tric
cro
ss
-sec
tio
n
110
100
0
50
100
150
200
250
(H2O
) 30H
+
Tth
= 2
5 K
Tth
= 1
00 K
s (Å2)
Ecm (
eV
)
In the s
imula
tions,
r =
0.8
2 x
1.9
8 ÅF
rag
men
tati
on
cro
ss-s
ecti
on
s
110
100
0.0
0.2
0.4
0.6
0.8
1.0
sfrag/sgeo
Ecm
(e
V)
(D2O
) nD
+, n
= 5
, 1
0
20
, 3
0,
45
-P
late
au b
etw
een 3
and 1
00 e
V-
Behavi
our
size
dependant
at lo
w c
olli
sion e
nerg
y
-s
= 6
0%
of
sgeo
-s
decr
ease
s fo
rE
cm>
100eV
«T
ran
sp
are
nc
y»
Fra
gm
en
tati
on
cro
ss-s
ecti
on
s
110
100
0.0
0.2
0.4
0.6
0.8
1.0
sfrag/sgeo
Ecm
(e
V)
(D2O
) nD
+, n
= 5
, 1
0
20
, 3
0,
45
-P
late
au b
etw
een 3
and 1
00 e
V-
Behavi
our
size
dependant
at lo
w c
olli
sion e
nerg
y
-s
= 6
0%
of
sgeo
-s
decr
ease
s fo
rE
cm>
100eV
Fra
gm
en
tati
on
cro
ss-s
ecti
on
sS
aa
lman
n e
t a
l, P
hys
. R
ev.
Le
tt.
80
, 3
21
3–
3216 (
19
98
)
sg
eo
«T
ran
sp
are
nc
y»
0.0
10.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(D2O
) nD
+, n
= 5
, 1
0
20
, 3
0,
45
sfrag/sgeo
t (
ps)
t vi
b
0.0
10.1
0.0
0.2
0.4
0.6
0.8
1.0
(H2O
) nH
+, n
=3
0,
50
s/sgeo
t c (p
s)
t vib
Inte
r-m
ole
cula
r vi
bra
tion:
183 c
m-1
Û180 f
s(1
90 f
sfo
r D
2O
)
Fra
gm
en
tati
on
cro
ss-s
ecti
on
s
•E
xperim
enta
l setu
p
•A
ttach
ment
cross
-sect
ions
(H2O
) nH
+
•F
ragm
enta
tion c
ross
-sect
ions
•C
oncl
usi
ons
and p
ers
pect
ives
Ou
tlin
e
•E
xperim
enta
l setu
p
•A
ttach
ment
cross
-sect
ions
(H2O
) nH
+
•F
ragm
enta
tion c
ross
-sect
ions
Co
nclu
sio
n &
pers
pecti
ve
s
Att
ach
men
t an
d f
rag
men
tati
on
cro
ss
-se
cti
on
s
üM
easu
rem
ent
of
abso
lute
cro
ss-s
ect
ions
(att
ach
ment
and f
ragm
enta
tion)
üIm
port
ance
of
vibra
tional d
ynam
ics:
-
Dyn
am
ical e
ffect
s lo
wer
the a
ttach
ment
cross
-sect
ion
-T
ransp
are
ncy
effe
ct f
or
fragm
enta
tion
üC
alc
ula
tions
in p
rogre
ss (
F. C
alv
o,
LA
SIM
, Ly
on)
üC
harg
e e
ffect
?
(H2O
) nO
H-vs
(H2O
) nH
+
üIn
fluence
of im
puritie
s?