Download Magnetic-field dependence of chemical reactions

Magnetic field dependence of chemical
reactions
B.Spivak
University of Washington
Magnetic field dependence of chemical reactions at room
temperature
Turro N.1983
Salikhov K, Molin Yu, Sagdeev R. , Buchachenko S. 1984
Steiner U., Ulrich T. 1989
B. Spivak, Fei Zhou 1994
Hypothetic magnetic sense of animals. See for reviews
Able 1984, Wiltchenko 2005, Johnsen 2005
Orientation of migratory birds is light dependent
W. Witchenko 1981
Resonance effects (EPR) in avian navigation
T. Ritz at all 2004
Critic: K.V. Kavokin, Bioelectromagnetics 30, 402, 2009
Magnetic field dependence of luminescence in light
emitting organic diodes
can chemical reaction rates depend on
magnetic field at room temperature ?
A model: particles with spin ½ are created randomly in
space and time with an average intensity <I>. They
diffuse, and recombine into a singlet state
   singlet
 H 
n  n  n

  0!
 kT 
spin relaxation time τ s ( H ) may strongly depend
2
on magnetic filed :
τs  μH  may
be big !
mean field equation for the particle
concentration
0
d n
dt
 I 0 n 
2
n  n
s
,
n  n  nt 
1/ 2
 I 
nt    
0 
in a stationary case
In this approximation there is no magnetic field
dependence of n(t)! If the particles are created
uniformly in space, there is also no dependence of on
the diffusion coefficient D.
Fluctuation “corrections” to the mean field
results
Qualitative picture, stationary case, and 1/s=0
ABC
The amplitude of fluctuatio ns of the difference of the number
 
of particles created in a volume Ld during the time t is ItLd
The diffusion time on the length L is
 n A  nB   IL2 d D 1 
1/ 2
L2
D
1/ 2
d is the dimensiona lity of space, D is the diffusion coefficien t
a. the fluctuation corrections are determined by
particle diffusion.
b. in d=2 (marginal case) there is no stationary
solution, and the concentration diverges
logarithmically as a function of time.
Fluctuational correction to the recombination rate.
Langevin approach.
d n
dt
  0 n n   0 nn 
n r, t   n  n ,
n  n
s
I  r, t   I  I ,
 I ,
n n
n  0
dn r, t 
n  n
  0 n n   0n n  Dn  
 I     ,
dt
s
I  r, t  and   r, t  are random Langevin sources
I  I    I  r  r ' t  t ';
     n  r  r ' t  t ',
2
I  I    I K r  r ' t  t 
     0 n  r  r ' t  t '
2
K  0 means that particles are created at uncorrelat ed locations
K  I δr - r ' means that particles are created at the same points

 s H    s 0 1  H s 2

 
I
n
1


1
s
2
  0   02  dQ
 K Q  
1 
,
2 
1 

n
2
0

DQ 
1
L H   D  H  ,
1/ 2


1
 rec
;
 rec is the recombinat ion time
the role of dimensionality of space
d  1 Lx  Lz , Ly ;
d  2 Lx , Ly  Lz ;
Lx  L ;
Lx , Ly  L
d  3 Lx , Ly , Lz  L  D 



0
0
Dl
D3
,
0
L
l

ln
, D2
Dl Lz
l

0
lL
Dl Lz Ly
,
D 1
l is the mean free path
K 0
in 3d case the magnetic field dependence of the rate requires a
special analysis




 H    0
1
1

  02   dQ
  dQ
1
1 
0

DQ 2 
DQ 2 

  H 
  0 

 0 l L ( H )  L (0) 

;
L  D  ( H )
Dl L (0) L ( H )
a) the recombination rate is strongly H-dependent
b) the expression for the correction to the recombination
rate is similar to the weak localization correction to
conductivity
Do an entanglement between spins and spin coherence play any
role?
At room temperatures the diffusion is classical and incoherent.
However, spins are quantum on the time scale smaller than the
spin relaxation time s
A     B     Csinglet 
1
1
1


  g A  g B H
  H    H   rec
Is it possible that n(t,H) depends on the
direction of the magnetic field at high temperature?
An example: a particle has spin 1 in the ground state and spin zero
in an exited state. There is an unplolarized light beam in z-direction
0
Sz =
1
0
?
1
In the absence of spin relaxation and magnetic field spins are
aligned (Sz =0), and there is no light absorption. In a stationary
situation the excited level is populated only because
of mixing of Sz =0 level with Sz =1,-1 levels. Only the component
of the magnetic field, Hz parallel to the beam contributes to the
mixing.
Non-stationary case. Zeldovich approach
In the mean field approximation there is no H-dependence
of the particle concentration
d nt 
1
2
  0 nt  ,
n A t   nB t   nt  
dt
1   0 n0 t
The role of fluctuations: t=L2 /D
   singlet
L
n t   n t  

1
t
d /4
,
 sd / 4 H 
t
t s
t s
( Zeldovich 1977)
Conclusion:
chemical reaction rates can depend on the magnitude of
the magnetic field at room temperature
in the presence of unpolarized light it is relatively easy to
construct a model where the rate depends on the direction
of the magnetic field as (sin q)2 , where q is the angle between
the magnetic field and the light beam direction
to get this dependence proportional to (sin q
(avian navigation) one has to have circularly polarized light
is it possible that the avian navigation involves nuclear spin
polarization ?