Rotational relaxation - Revision history

129.69.120.36 at 06:23, 21 October 2016

2016-10-21T06:23:52Z

← Older revision		Revision as of 08:23, 21 October 2016
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	According to simple [[rotational diffusion]] theory, the relaxation time		According to simple [[rotational diffusion]] theory, the relaxation time
	for <math>c_1(t)</math> would be given by		for <math>c_1(t)</math> would be given by
	<math>\tau_1 = 1/2D_\mathrm{rot}</math>, and the relaxation time for		<math>\tau_1 = \frac{1}{2D_\mathrm{rot}}</math>, and the relaxation time for
	<math>c_2(t)</math> would be <math>\tau_2 = 1/6D_\mathrm{rot}</math>.		<math>c_2(t)</math> would be <math>\tau_2 = \frac{1}{6D_\mathrm{rot}}</math>.
	Therefore, <math>\tau_1= 3 \tau_2</math>. This ratio is actually lower in simulations,		Therefore, <math>\tau_1= 3 \tau_2</math>. This ratio is actually lower in simulations,
	and closer to <math>2</math>; the departure from a value of 3 signals rotation		and closer to <math>2</math>; the departure from a value of 3 signals rotation
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	\| HH \|\| H-H axis \|\| <math>\tau_2=2.0</math>ps (H-H dipolar relaxation NMR)		\| HH \|\| H-H axis \|\| <math>\tau_2=2.0</math>ps (H-H dipolar relaxation NMR)
	\|-		\|-
	\| OH \|\| O-H axis \|\| <math>\tau_2=1.95</math>ps (<~~math~~>^{17}</~~math~~>O-H dipolar relaxation NMR)		\| OH \|\| O-H axis \|\| <math>\tau_2=1.95</math>ps (<sup>17</sup>O-H dipolar relaxation NMR)
	\|-		\|-
	\| <math>\mu</math> \|\| dipolar axis \|\| not measurable, but related to bulk dielectric relaxation		\| <math>\mu</math> \|\| dipolar axis \|\| not measurable, but related to bulk dielectric relaxation

Carl McBride: Changed subscript from 1 to 2

2015-02-23T09:58:38Z

Changed subscript from 1 to 2

← Older revision		Revision as of 11:58, 23 February 2015
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	however. Rather, relaxation times of the second		however. Rather, relaxation times of the second
	[[spherical harmonics\|spherical harmonic]] are obtained:		[[spherical harmonics\|spherical harmonic]] are obtained:
	:<math>~~c_1~~(t)=\langle P_2( \mathbf{n}(0)\cdot\mathbf{n}(t) ) \rangle,</math>		:<math>c_2(t)=\langle P_2( \mathbf{n}(0)\cdot\mathbf{n}(t) ) \rangle,</math>
	where <math>P_2(x)</math> is the second [[Legendre polynomials\|Legendre polynomial]].		where <math>P_2(x)</math> is the second [[Legendre polynomials\|Legendre polynomial]].

Carl McBride: Added an internal link.

2008-06-27T12:57:17Z

Added an internal link.

← Older revision		Revision as of 14:57, 27 June 2008
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	processes "rougher" than what is assumed in simple [[rotational diffusion]] (Ref 1).		processes "rougher" than what is assumed in simple [[rotational diffusion]] (Ref 1).
	==Water==		==Water==
			:''Main article [[Rotational relaxation of water]]
	Often, molecules are more complex geometrically and can not be described by a single		Often, molecules are more complex geometrically and can not be described by a single
	orientation. In this case, several vectors should be considered, each with its own		orientation. In this case, several vectors should be considered, each with its own
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	\|}		\|}
	==See also==		==See also==

	*[[Rotational diffusion]]		*[[Rotational diffusion]]
	*[[Diffusion]]		*[[Diffusion]]
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	==References==		==References==
	#[http://dx.doi.org/10.1063/1.476482 David van der Spoel, Paul J. van Maaren, and Herman J. C. Berendsen "A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field", J. Chem. Phys. '''108''' 10220 (1998)]		#[http://dx.doi.org/10.1063/1.476482 David van der Spoel, Paul J. van Maaren, and Herman J. C. Berendsen "A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field", J. Chem. Phys. '''108''' 10220 (1998)]



	[[Category: Non-equilibrium thermodynamics]]		[[Category: Non-equilibrium thermodynamics]]

Carl McBride: Trivial tidy up.

2008-06-27T12:52:43Z

Trivial tidy up.

← Older revision		Revision as of 14:52, 27 June 2008
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	'''Rotational relaxation''' refers to the decay of certain [[autocorrelation]]		'''Rotational relaxation''' refers to the decay of certain [[autocorrelation]]
	magnitudes related to the orientation of molecules.		magnitudes related to the orientation of molecules.
			If a molecule has an orientation along a unit vector <math>{\mathbf n}</math>, its autocorrelation
	If a molecule has an orientation along a unit vector ~~'''~~n~~'''~~, its autocorrelation
	will be given by		will be given by
	:<math>c_1(t)=\langle \mathbf{n}(0)\cdot\mathbf{n}(t) \rangle.</math>		:<math>c_1(t)=\langle \mathbf{n}(0)\cdot\mathbf{n}(t) \rangle.</math>
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	a characteristic relaxation time (either from the long-time exponential decay, or		a characteristic relaxation time (either from the long-time exponential decay, or
	from its total integral, see [[autocorrelation]]). This magnitude, which		from its total integral, see [[autocorrelation]]). This magnitude, which
	is readily computed in a [[simulation]] is not directly accessible experimentally,		is readily computed in a [[Computer simulation techniques \|simulation]] is not directly accessible experimentally,
	however. Rather, relaxation times of the second		however. Rather, relaxation times of the second
	[[spherical harmonics\|spherical harmonic]] are obtained:		[[spherical harmonics\|spherical harmonic]] are obtained:
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	and closer to <math>2</math>; the departure from a value of 3 signals rotation		and closer to <math>2</math>; the departure from a value of 3 signals rotation
	processes "rougher" than what is assumed in simple [[rotational diffusion]] (Ref 1).		processes "rougher" than what is assumed in simple [[rotational diffusion]] (Ref 1).


	==Water==		==Water==

	Often, molecules are more complex geometrically and can not be described by a single		Often, molecules are more complex geometrically and can not be described by a single
	orientation. In this case, several vectors should be considered, each with its own		orientation. In this case, several vectors should be considered, each with its own
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	\|-		\|-
	\|}		\|}



	==See also==		==See also==

Carl McBride: Style: interchanged 'see also' and 'references' sections.

2008-06-20T12:26:30Z

Style: interchanged 'see also' and 'references' sections.

← Older revision		Revision as of 14:26, 20 June 2008
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	~~==References==~~

	*[http://dx.doi.org/10.1063/1.476482 David van der Spoel, Paul J. van Maaren, and Herman J. C. Berendsen "A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field", J. Chem. Phys. '''108''' 10220 (1998)]		==See also==

	==~~See also~~==		*[[Rotational diffusion]]
			*[[Diffusion]]
			*[[Autocorrelation]]
			==References==
			#[http://dx.doi.org/10.1063/1.476482 David van der Spoel, Paul J. van Maaren, and Herman J. C. Berendsen "A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field", J. Chem. Phys. '''108''' 10220 (1998)]

	*[[rotational diffusion]]
	*[[diffusion]]
	*[[autocorrelation]]


	[[Category: Non-equilibrium thermodynamics]]		[[Category: Non-equilibrium thermodynamics]]

Dduque: New page: '''Rotational relaxation''' refers to the decay of certain autocorrelation magnitudes related to the orientation of molecules. If a molecule has an orientation along a unit vector '''...

2008-06-20T10:46:29Z

New page: '''Rotational relaxation''' refers to the decay of certain autocorrelation magnitudes related to the orientation of molecules. If a molecule has an orientation along a unit vector '''...

New page

'''Rotational relaxation''' refers to the decay of certain [[autocorrelation]]
magnitudes related to the orientation of molecules.

If a molecule has an orientation along a unit vector '''n''', its autocorrelation
will be given by
:<math>c_1(t)=\langle \mathbf{n}(0)\cdot\mathbf{n}(t) \rangle.</math>
From the time decay, or relaxation, of this function, one may extract
a characteristic relaxation time (either from the long-time exponential decay, or
from its total integral, see [[autocorrelation]]). This magnitude, which
is readily computed in a [[simulation]] is not directly accessible experimentally,
however. Rather, relaxation times of the second
[[spherical harmonics|spherical harmonic]] are obtained:
:<math>c_1(t)=\langle P_2( \mathbf{n}(0)\cdot\mathbf{n}(t) ) \rangle,</math>
where <math>P_2(x)</math> is the second [[Legendre polynomials|Legendre polynomial]].

According to simple [[rotational diffusion]] theory, the relaxation time
for <math>c_1(t)</math> would be given by
<math>\tau_1 = 1/2D_\mathrm{rot}</math>, and the relaxation time for
<math>c_2(t)</math> would be <math>\tau_2 = 1/6D_\mathrm{rot}</math>.
Therefore, <math>\tau_1= 3 \tau_2</math>. This ratio is actually lower in simulations,
and closer to <math>2</math>; the departure from a value of 3 signals rotation
processes "rougher" than what is assumed in simple [[rotational diffusion]] (Ref 1).

==Water==

Often, molecules are more complex geometrically and can not be described by a single
orientation. In this case, several vectors should be considered, each with its own
autocorrelation. E.g., typical choices for [[water]] molecules would be:

{| border="1"
|-
| symbol || explanation || experimental value, and method
|-
| HH || H-H axis || <math>\tau_2=2.0</math>ps (H-H dipolar relaxation NMR)
|-
| OH || O-H axis || <math>\tau_2=1.95</math>ps (<math>^{17}</math>O-H dipolar relaxation NMR)
|-
| <math>\mu</math> || dipolar axis || not measurable, but related to bulk dielectric relaxation
|-
| <math>\perp</math> || normal to the molecule plane|| not measurable
|-
|}

==References==

*[http://dx.doi.org/10.1063/1.476482 David van der Spoel, Paul J. van Maaren, and Herman J. C. Berendsen "A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field", J. Chem. Phys. '''108''' 10220 (1998)]

==See also==

*[[rotational diffusion]]
*[[diffusion]]
*[[autocorrelation]]

[[Category: Non-equilibrium thermodynamics]]