Magnetic field dependence of chemical reactions

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
  

H
2

n

 n

 n kT

s
s
H


may be
big

mean field equation for the particle concentration d n dt n
0

I
 
0 n
2  n


 s n




I

0


1 / 2 in a stationary
, case n

 n

 n
 
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 of amplitude particles of created fluctuatio in a ns volume of the difference of the
L d during the time t number is
 
1 / 2 d
The diffusion is time on
  n
A the
 n
B
L
2
 length

L is

IL 2
 d D

1
1

/
D
2 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 n
 d
 n


I
 dt
  r
 t
 

0 n
 n

  
0
 n

 n
 n


 
0
, n

 
 n

 n

I

0
 r n
 t n




I n


 s
 
I , n

D
  n


I

, n
 n


 n


 n


 s
 n

0
 
I

 

, and

 r are random Langevin sources

I

 

I

 

I
  r
 r '
  t
 t '

;

I

 

I

 

I K
 r
 r '
  




K

0
  n
2   r
 r '
  t
 t ' ,
 



 
0 n
2   r
 r '
  t
 t '

K

I means
δ
 r r '
 that particles means
 s that
 
 are created particles
 s
 are at

H
 s uncorrelat created

2
 at ed the locations same points

 
I n
2
 
0
  
0
2
 d Q
D Q
2
1

1




1

K

0 n
2


, L



D


1

/ 2
,
1

 d


1 s

1

1
 rec
;
L x
 rec is the recombinat ion time
 L z
, L y
; the role of dimensionality of space
L x
 L

; d

2 L x
, L y
 L z
; d

3 L x
, L y
, L z
 L


D


L x
, L y
 L



0



0


Dl
0
Dl
,


0
Dl l
L z ln
L

, l lL

L z
L y
,
D

3
D

2
D

1
K

0 l is the mean free path

in 3d case the magnetic field dependence of the rate requires a special analysis

 
 
   

0
Dl
 l
0

L

L

( H )


( 0 ) L

 
(
L

2
0






( 0 )
 d Q
;
H )
D Q
2
1



1
 
  d Q
1
D Q
2 


1
 
L


D


( 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
 rec

 g
A
 g
B
 
H

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
?
S z
=
1 0 1
In the absence of spin relaxation and magnetic field spins are aligned (S z
=0), and there is no light absorption. In a stationary situation the excited level is populated only because of mixing of S z
=0 level with S z
=1,-1 levels. Only the component of the magnetic field, H mixing. z parallel to the beam contributes to the

Non-stationary case. Zeldovich approach
In the mean field approximation there is no H-dependence of the particle concentration d n
  dt
  
0 n
 
2
, n
A
 
 n
B
 
 n
 

1
 
0
1 n
  t
The role of fluctuations: t=L 2 /D
  
n

L
 
 n

 

1 t d / 4

 s d / 4 t
, t
  s
( Zeldovich 1977 ) t
  s

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 ?