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Enhanced Heating of Salty Ice and Water
Under Microwaves: Molecular Dynamics
Study
Motohiko Tanaka* and Motoyasu Sato
Coordination Research Center, National Institute for Fusion Science
Oroshi-cho, Toki 509-5292, Japan
Phone: +81-572-58-2258
*
[email protected]
Through the use of molecular dynamics simulations, we have studied the enhanced heating of
salty ice and water by the electric field of applied microwaves at 2.5 GHz, and in the range of 2.5-10
GHz for the frequency dependence. We show that water molecules in salty ice are allowed to rotate
in response to the microwave electric field to the extent comparable to those in pure water because
the molecules in salty ice are loosely tied by hydrogen bonds with adjacent molecules unlike rigidly
bonded pure ice. The weakening of hydrogen-bonded network of molecules in salty ice is mainly due
to the electrostatic effect of salt ions rather than the short-range geometrical (size) effect of salt since
the presence of salt ions with small radii causes similar enhanced heating.
INTRODUCTION
Microwaves are frequently utilized as a highly
efficient and less carbon-oxide releasing energy
source for cooking or drying food, sintering
metals and ceramics. It is known that dielectric
materials including pure and salty water are
heated efficiently by absorbing the electric
field energy of microwaves [von Hippel, 1954;
Hobbs et al., 1966; Hasted, 1972; Buchner,
1999; Meissner and Wentz, 2004; Takei,
2007]. It is also known that metallic powders
and magnetic materials such as magnetite and
titanium oxides with oxygen defects TiO2-x(x>0)
are heated by the magnetic field of microwaves
[Roy et al., 1999; Peelamedu
��������� et al., 2002; Sato
Keywords: Microwave heating, salty water and ice,
electrostatic effects, molecular dynamics
42-4-62
Submission Date: 24 September 2007
Acceptance Date: 18 April 2008
Publication Date: 7 November 2008
et al., 2006; Suzuki et al,. 2008; Tanaka et al.,
2008].
In order to examine the mechanism of
microwave heating of water and ice at the
molecularlevel,weperformedmoleculardynamics
simulations [Tanaka and Sato, 2007]. Through
the simulations we showed mechanistically that
(i) rotational excitation of electric dipoles of water
coupled with irreversible energy relaxation to
the translational energy was responsible for the
microwave heating of water, (ii) pure ice was
not heated by microwaves because of strong
hydrogen bonds between water molecules��
�����������,
and (iii) the experimentally known enhanced
heating of salt water by microwaves was due
to acceleration of salt ions by the microwave
electric field, which is usually termed as Joule
heating. We numerically evaluated the time
Journal of Microwave Power & Electromagnetic Energy ONLINE
Vol. 42, No. 4, 2008
., 2008].
order
to examine the mechanism of microwave heating of water and ice at the
earheating
of water
and molecular
ice at the dynamics simulations [Tanaka and Sato, 2007].
level, we
performed
mulations
and Sato,that
2007].
we showed[Tanaka
mechanistically
(i) rotational excitation of electric dipoles of water
itation
of electricenergy
dipolesrelaxation
of waterto the translational energy was responsible for the
with irreversible
ional
energy
was
responsible
forice
thewas not heated
ave heating of water, (ii) pure
by microwaves
because
of strong
We
Westated
statedabove
abovethat
thatpure
pureice
iceisisnot
notheated
heatedby
bymicrowaves.
microwaves.However,
However,we
weh
d by
microwaves
because
of
strong
en
bonds
between
water
molecules,
(iii)
the
experimentally
known
enhanced
heating
integrated Joule heating termexperience
of salt ions,
ofofprocessing
in microwave
experience
processing(melting)
(melting)frozen
frozenfood
food
microwaveovens.
ovens. Our
Ourmotiv
moti
-2qinice
rimentally
known
enhanced
heating
water
by microwaves
wasthedue
to acceleration
of salt
ions by
the
microwave
electric
E•J,
and
work
associated present
with
rotation
of
work
is
to
examine
the
heating
of
salty
as
well
as
salty
water
present work is to examine the heating of salty ice as well as salty waterby
b
salt ions
byWe
thestated
microwave
electric
hich
is usually
termed
asdipoles,
Joule
Weissumming
numerically
evaluated
the
time
integrated
electric
E•dP,
by
above
thatheating.
pure ice
not
heatedup
bythe
microwaves.
However,
we
have
athe
daily
dynamic
simulation.
In
this
paper
we
use
with
GHz,
We
stated
that
pure
icemicrowaves
is not heated
by2.5
microwav
dynamic
simulation.
In
this
paperabove
wemainly
mainly
use
the
microwaves
with
2.5
GHz,e
rically term
evaluated
the
eating
of salt
ions
E<integrated
J and
associated
with
rotation
of examining
electricof+q
dipoles
contribution
of the
all work
atoms
or
molecules,
experience
oftime
processing
(melting)
frozen
food
in microwave
Our
motivation
of
the frozen of
10
microwaves
for
the
frequency
dependence
heating.
experience
processing
(melting)
food
microwave
10GHz
GHz
microwaves
forovens.
examining
the
frequency
dependence
ofthe
thein
heating.
rotation
of
electric
dipoles
E
dtted
bywith
summing
up
the
contribution
of
all
atoms
or
molecules,
where
is
the
electric
E to
is the
electric
of microwaves,
present where
work is
examine
thefield
heating
of salty ice aspresent
well aswork
salty iswater
by molecular
+q
to
examine
the
heating
of
salty
ice as wel
We
stated
above
that
pure
ice
is not
heated
by microwaves. How
++ and Cl
−− ions,
E
molecules,
where
is
the
electric
2.
Simulation
Procedures
microwaves,
J J=
=simulation.
q
v
is
the
current
carried
by
Na
and
P
=
d
is
is
the
current
carried
by
Na
and
Cl
dynamic
In
this
paper
we
mainly
use
the
microwaves
with
2.5
GHz,
except
for
5¦i i i
¦ s s(melting)
dynamic simulation.
In this paper we mainly use the microwav
2. Simulation Procedures
−
experience
ofare
processing
frozen food in microwave
ovens.
and
liquid
water
characterized
and
Na
and10ClGHz
ions,
and
P P=
=water
isthe sumthe
of +electric
dipoles
of
all
molecules,
with
q
and
v
the
charge
and
velocity
of
ions,
and
ofIce
electric
dipoles
microwaves
frequency
dependence
of
the
heating.
¦fors dexamining
s is
i
Ice i and liquid
water
aremicrowaves
characterized
by a a completely
completely
and dependence
10 GHz
forby
examining
the frequency
present
work
is obtained
to ofexamine
the
heating of salty ice as well as salt
partially
ordered
network
molecules,
2O
qm,
v i the charge
velocity
respectively,
d
electricofdipole
molecule.
We
the
ofand
all and
water
withmoment
qi and
viof
thes-th
charge
partially
ordered
network
of HH
respectively,
i and
s the molecules,
Figure
1. Three-atom
rigid-bodyrespectively,
model
for a
2O molecules,
dynamic
simulation.
In
this
paper
we
mainly
use
the
microwaves with
mediated
by
hydrogen
bonds
connecting
adjacent
two
molecules
Procedures
t |of
obtained
the
E<s-th
J | ≈2.molecule.
2Simulation
E<dand
P / dtWe
for
dilute
saline
solution
of
1
mol%
salinity
and
10
GHz
velocity of
i-th atom,mediated
respectively,
by hydrogen
bonds
connecting
2.water
Simulation
Procedures
molecule
(SPC/Eadjacent
model)two
withmolecules
partial
[Matsumoto
et
2002].
this
reason,
we
adopt
GHz
microwaves
for
examining
thecharacterized
frequency
dependence
of the he
Ice and
liquid
are dipole
characterized
by
a 10completely
andFor
of [Tanaka
1 mol%
salinity
10 GHz
ave
and
Sato,
2007].
[Matsumoto
etal.,
al.,
2002].
For
this
reason,
we
adoptananexplicit
explicit
and
ds and
thewater
electric
moment
of the
s-th
Ice
and
liquid
water
are
by a completely
charges
on atom
sites.
water
model
with
three
point
charges
the
SPC/E
water
model
partiallymolecule.
ordered We
network
O water
molecules,
respectively,
model 2with
three point
chargesnetwork
- the SPC/E
model
partially
ordered
of Hwater
respectiv
obtainedoftheH2relation
⎜E•J⎜≈
2O molecules,
[Toukan
and
Rahman,
1985;
Berendsen
etbonds
al.,
1987].
AAtypical
2.
Simulation
Procedures
mediated
by
hydrogen
bonds
connecting
adjacent
two
molecules
[Toukan
and
Rahman,
1985;
Berendsen
et
al.,
1987].
typical
mediated
by
hydrogen
connecting
adjacent
two
molec
⎜E•dP/dt⎜ for dilute saline solution of 1 mol%
simulation
run
requires
the
computation
time
of
a
few
days
for
times.
Ice
and
liquid
water
are
characterized
by
a
completely
and
[Matsumoto
et
al.,
2002].
For
this
reason,
we
adopt
an
explicit
run requires
the computation
timeFor
of this
a few
days we
for adopt an exp
[Matsumoto
et al., 2002].
reason,
salinity and 10 GHz microwavesimulation
[Tanaka
and
Fig.1
Three-a
3000
water
molecules
on
our
Opteron-based
cluster
We
follow
the
same
procedures
asSPC/E
partially
ordered
network
ofnumerical
H−2O charges
molecules,
respectively,
water model with three point chargesroughly
- the SPC/E
water
model
Fig.1
Threeroughly
3000
water
molecules
on
our
Opteron-based
cluster
water
model
with
three
point
the
water
m
Sato, 2007].
model
for
a awa
machine
(usually
four
processors
per
job).
Although
the
model
those
used
previously
[Tanaka
and
Sato
2007].
mediated
by
hydrogen
bonds
connecting
adjacent
two
molecules
model
for
w
[Toukan and Rahman, 1985; Berendsen
et
al.,
1987].
A
typical
machine
(usually
four processors
per job).
Although
the model
[Toukan
and Rahman,
1985;
Berendsen
et al., 1987].
A
typ
(SPC/E
model
We stated previously thathas
pure
ice is
not electrostatic
(SPC/E
mod
reasonable
properties,
for
more
accurate
We
start
all
the
simulations
with
the
crystal
ice
[Matsumoto
et
al.,
2002].
For
this
reason,
we
adopt
an
explicit
simulation run requires the computation
of a few simulation
days
for runproperties,
hastime
reasonable
electrostatic
more accurate
requires theforcomputation
time ofcharges
acharges
few ondays
onato
at
microwaves.
we
have
a model
of
the
energy
absorption,
the
use
of
TIP4P-FQ
model
and
relax
it
to
the
desired
temperature
before
water
with
three
point
charges
the
SPC/E
water
model
Fig.1
Three-atom
rigid-body
roughlyheated
3000 by
water
moleculesHowever,
on calculation
our
Opteron-based
cluster
calculation of the roughly
energy absorption,
the molecules
use of TIP4P-FQ
3000 water
on ourmodel
Opteron-based clu
experience
of processing
frozen
model
for MacElroy,
aMacElroy,
water
molecule
with
effect
[English
and
microwaves
are1985;
applied.
This
is2003;
done
��������
because�
[Toukan
and
Rahman,
Berendsen
et
al.,English,
1987].Although
A typical
machinedaily
(usually
four processors
per(melting)
job).polarization
Although
the
model
with
polarization
effect
[English
and
2003;
English,
machine
(usually
four
processors
per
job).
the m
(SPC/E
model)
with
partial
food
in
microwave
ovens.
Our
motivation
for
2006]
may
be
preferred
but
with
small
number
of
water
molecules
simulation
run
requires
the
computation
time
of
a
few
days
for
molecules
of
initially
random
orientations
take
has reasonable electrostatic properties,
for
more
accurate
2006] may be preferred
but with
small
of water
molecules
has reasonable
electrostatic
properties,
for more accu
charges
onnumber
atom sites.
Fi
due
toto
large
computation
times.
roughly
water
Opteron-based
cluster m
the present
work isabsorption,
to examine
the
heating
of calculation
a3000
very
long
time
to energy
arrive
aton
theour
equilibrium
withof TIP4P-FQ
calculation
of the energy
the
use
of
TIP4P-FQ
model
due
large
computation
times.
of molecules
the
absorption,
the use
m
We
follow
the
same
numerical
procedures
as
those
used
previously
[Tanak
machine
(usually
four processors
per as
job).
Although
the model
properly
ordered
hydrogen-bonded
network.
salty ice aseffect
well [English
as salty water
byWe
molecular
with polarization
and MacElroy,
2003;
English,
follow
thewith
samepolarization
numerical
procedures
those
used A
previously
effect
[English
and
MacElroy,
2003; [Tana
Eng
(S
2007].
start
all
the
with
crystal
ice
relax
toaccurate
the
has
properties,
for
more1ititof
water
molecule
ofwith
thethe
SPC/E
model
in
Figure
dynamic
simulation.
In this
paper
weWe
mainly
2006] may
be preferred
but with
small
number
of
water
molecules
2007].
We
startreasonable
all
thesimulations
simulations
the
crystal
iceand
and
relax
towater
thedesired
desired
2006]
mayelectrostatic
be preferred
but
with
small
number
molec
ch
are
applied.
This
isatoms
molecules
ofofinitially
random
calculation
ofto
the
energy
absorption,
the
of triangle
TIP4P-FQ
model
illustrates
that
three
form
ause
rigid
due to large
computationwith
times.
use microwaves
2.5 GHz,before
except
for
5-10 due
beforemicrowaves
microwaves
are
applied.
This
isbecause
because
molecules
initially
random
large
computation
times.
take
time
totopreviously
arrive
at
the
equilibrium
with
properly
with
polarization
effect
[English
and
2003;
English,
H-O-H
with
partial
charges
(=0.424e)
and ordered
We GHz
follow
the same for
numerical
procedures
aslong
those
used
[Tanaka
andqMacElroy,
Sato
take
avery
very
long
time
arrive
atthe
the
equilibrium
with
properly
ordered
hydr
microwaves
examining
theafrequency
We
follow
same
numerical
procedures
as
thosehydro
used
network.
A
water
molecule
of
the
SPC/E
model
in
Fig.1
illustrates
that
three
ata
2006]
may
be
preferred
but
with
small
number
of
water
molecules
−2��
q
residing
���������
at
���
the
����
hydrogen
���������
and
����
oxygen
�������
2007]. We
start
all
the
simulations
with
the
crystal
ice
and
relax
it
to
the
desired
temperature
network. A water 2007].
molecule
theall
SPC/E
model in Fig.1
illustrates
threerel
dependence of the heating.
Weofstart
the simulations
with the
crystal that
ice and
triangle
H-O-H
with
partial
(=0.424e)
and
residing
atatthe
due
to
large
computation
times.
sites,
The
electrostatic
forces
are
before microwaves are applied. This rigid
isrigid
because
molecules
of respectively.
initially
random
triangle
H-O-H
with
partialcharges
charges
qapplied.
(=0.424e)
and
−2q
residing
thehy
before
microwaves
areqorientations
This
is−2q
because
molecules
oh
oxygen
sites,
respectively.
The
electrostatic
forces
are
calculated
for
pairs
of
We
follow
the
same
numerical
procedures
as
those
used
previou
calculated
for
pairs
of
these
atoms
while
the
take a very
long
time
to
arrive
at
the
equilibrium
with
properly
ordered
hydrogen-bonded
oxygen sites, respectively.
Thelong
electrostatic
forcesatare
forwith
pairsprop
of
take a very
time to arrive
the calculated
equilibrium
SIMULATION PROCEDURES
while
the
Lennard-Jones
forces
are
calculated
only
for
the
pairs
of
oxygen
We
start all
simulations
the
ice
and in
relax
it to
Lennard-Jones
forces
are with
calculated
only
for
network. A water molecule of the SPC/E
model
in
Fig.1
illustrates
that
three
atoms
form
acrystal
while
the2007].
Lennard-Jones
forces
are
calculated
only
for
the
pairs
ofFig.1
oxygen
network.
Athe
water
molecule
of
the
SPC/E
model
illuth
equations
of
are
before
microwaves
applied.
This
is and
because
molecules
of and
initiall
the
ofareoxygen
The
equations
of
rigid triangle
H-O-H
partial
q (=0.424e)
−2q
residing
at the atoms.
hydrogen
equations
ofmotion
motion
arepairs
rigid
triangle
H-O-H
with
partial
charges
q (=0.424e)
−2
Ice and
liquidwith
water
are charges
characterized
by
a and
take
a
very
long
time
to
arrive
at
the
equilibrium
with
properly
orde
motion
are:
oxygen completely
sites, respectively.
The electrostatic
forces are calculated
for respectively.
pairs of theseThe
atoms
oxygen sites,
electrostatic
forces
are
calcu
and partially
ordered network
12
6
ªofª oxygen
12
­§­σThe
½6 º illustrates th
network.
Adthe
water
molecule
of the
SPC/E
in
·model
§calculated
·Fig.1
while the
forces
are calculated
only forwhile
pairs
atoms.
q
q
σ
v
°
the
Lennard-Jones
forces
are
for the
of Lennard-Jones
H2O molecules,
respectively,
mediated
i
j
ij
ij
§
·
§
·°½°» º+ only
q
q
σ
σ
i
d
v
«
°
i
j
ij
ij
i
=
−∇
+
−
m
ε
48
,,
EEmwresidin
¨¨ ¨ ¸¸ ¸¾and
« ¦ partial
» +q−2q
H-O-H
charges
q¸¸ ¸(=0.424e)
¦
i
ij ®¨
iq
= −∇
+
−
m
ε
48
equations
motion are
¨
¨
®
¾
i dt
ij
i
mw
equations
of«with
motion
are
byofhydrogen
bonds connecting adjacentrigid
twotriangle
»
r
r
r
¨
¸
¨
¸
j
ij
ij
ij
°¯©°© rij¹ ¹ forces
°¿°¼ »calculated for
dt
© © rij¹ ¹are
electrostatic
ij
¬ «¬ j rThe
¯
¿¼
molecules [Matsumoto et al., 2002]. Foroxygen
this12 sites, respectively.
6
ª qwater
º
while
the
Lennard-Jones
forces are calculated
only for
o
­
½
ª
r
d
­§ σthe·12pairs
§
·
§
·
q
σ
σ
reason, we adopt
an
explicit
model
with
dv i
ir ij
° ij
°. »
§ σ ij
qi q j
i j
d
d
v
°
ij
i
=
v
ࠉࠉࠉ
«
i
equations
of
motion
are
= −∇
48ε ij ®model
¨¨ ¸¸ −dt¨¨ =¸¸vi ¾i . + qi Emw , mi
¦ r +water
=(1)−∇ « ¦
+ 48(1)
−¨
ε ij ®¨ ¸ ࠉࠉࠉ
i
three pointmcharges
– the
« jSPC/E
¨r ¸
¨
dt
rij ¹
dtrij ¹ °»
«
dt
r
ij
°
©
©
j
ij
ij
°© ¹ 6 © rij
¿¼
¬
[Toukan and Rahman, 1985;
Berendsen¯et al.,
¬
12 ¯
ª ofqi-th
º qi
­respectively,
½and
rirand
vvi are
the position and
atom,
Here,
§ σm
i· and
velocity
ofi qi-th
atom,respectively,
q
Here,
v i velocity
°§ σ ij ·
1987]. A typical
simulation run
requires
j
ij m
dri
i andthe
i are the positiondand
i °
«
» j-th
r
d
m
=
−∇
+
ε
−
+
q
48
i | ¦
¨
¸
¨
¸
and
charge,
respectively,
and
r
=
|
r
−
r
is
the
distance
between
i-th
and
®
¾
=
.
(2)
v
ࠉࠉࠉࠉ
(2)
i
ij
i
j = v . the distance¨ between
andfor
charge,
respectively, and ijrdt
¸
¨ i-th
¸ and
computationdt timei of a few days
roughly
i
» j-th
ij = | ri − r j« | jis
rij
°¯© rij ¹serves
© rijfor¹ °¿two
dt ¬
second
term
in
the
bracket
on
the
right-hand
side
of
Eq.(2)
¼twoa
second
term
in
the
bracket
on
the
right-hand
side
of
Eq.(2)
serves
for
3000 water molecules on our Opteron-based
overlap
other,
where
the
sum
ofof
radii
ofoftwo
Le
Here,
vand
areqthe
position
and
velocity
Here, ricluster
and v i are
the position
and velocity
ofeach
i-th
atom,
respectively,
are
its mass
overlap
each
other,Here,
where
σijdrijriisi and
isvm
the
radii
twoatoms
atomsand
andε εij ijisisthe
the
L
i sum
riσand
resp
machine.
Although
the
model
has
i iare the i position and velocity of i-th atom,
=
.
v
energy.
For
water,
0.65kJ
/
mol
ε
=
and
σ
=
0.317nm
.
Salt
ions
are
put
r
of
the
i-th
atom,
m
and
q
are
its
i respectively,
and charge,
respectively,
and
r
=
|
r
−
r
|
is
the
distance
between
i-th
and
j-th
atoms.
The
ww
ww
energy.
For
water,
0.65kJ
/
mol
ε
=
and
σ
=
0.317nm
.
Salt
ions
are
put
andwwcharge,
i
j for a more
reasonable electrostatic ijproperties,
ww rij i = | ri − ir j | is the distance bet
dt respectively, and
space
avoiding
water
molecules
and
are
treated
asas
isolated
with
cha
mass
and
charge,
respectively,
and
=⎜rispecies
-rspecies
⎜ is side
second accurate
term in the
bracket of
onthe
theenergy
right-hand
side of
Eq.(2)
serves
for
two
atoms
not
torijright-hand
space
avoiding
water
molecules
and
are
treatedon
isolated
with
the
ch
j
second
term
in
the
bracket
the
ofthe
Eq.(2
calculation
absorption,
the
diameter
2
σ
=
0.26nm
and
the
Lennard-Jones
energy
ε
=
0.062
kJ/mol
f
r
and
v
are
the
position
and
velocity
of
i-th
atom,
respectively,
Here,
the
distance
between
i-th
and
j-th
atoms.
The
overlap the�����������������
each
other,
where
σ
is
the
sum
of
radii
of
two
atoms
and
ε
is
the
Lennard-Jones
Na
Na
i
i
the
diameter
2
σ
=
0.26nm
and
the
Lennard-Jones
energy
ε
=
0.062
kJ/mol
use of TIP4P-FQij model
������������������������
with polarization Naoverlap eachij other, where σ ij is the- sum ofNaradii of two atom
-the
σ
==0.44nm
and
ε εClwater,
=are
0.446
Cl
AMBER
, ,2008];
the
and
and
rkJ/mol
= | ri on
−for
rfor
| in
is [right-hand
distance
between
i-t
second
term
in
the
energy. effect
For water,
/ mol q2003;
ε wwand
= 0.65kJ
and
. respectively,
Salt
ions
put
Cl
ijrandomly
j the
qCl==−σ−eww
e, ,2=
20.317nm
σClClcharge,
0.44nm
and
kJ/mol
Cl
[AMBER
2008];
thehybri
hyb
energy.
For
εbracket
[English
MacElroy,
English,
Cl = 0.446
ww = 0.65kJ / mol and σ ww = 0.317nm .
1/
2
second
term
in
the
bracket
on
the
right-hand
side
of
Eq.(2)
serves
sidespecies
ofavoiding
formolecules
space avoiding
water
molecules
treated
as isolated
with
qNa
=σand
enot
, to
1/,2 charge
εEq.(2)
ε(εiεserves
)the
σtwo
==atoms
σ
space
areoverlap
treated as isolated(3)
sp
2006] may
be preferred
butand
withare
a small
number
j water
εij ij==(where
σijthe
σi++i +of
σj radii
i ε j ) σ ,isisthe
ij sum
j radiiof
overlap
each
other,
sum
of
oftwo
two atoms
and ε(3
each
other,
where
the diameter
2
σ
=
0.26nm
and
the
Lennard-Jones
energy
ε
=
0.062
kJ/mol
for
Na
,
and
2σ Na =ij 0.26nm and the Lennard-Jones
energy
εi
Na
of water Na
molecules due to large computation - the diameter
isisused
when
i
and
j
are
encountering.
The
diameter
of
Cl
ion
is
- comp
energy.
For
water,
0.65kJ
/
mol
ε
=
and
σ
=
0.317nm
.
Salt
ions
qCl = −e , 2σ Cl = 0.44nm and ε Cl = 0.446
kJ/mol
fortwo
Cl
AMBER
,
2008];
the
hybrid
rule
ww
ww
used
when
two[species
species
i
and
j
are
encountering.
The
diameter
of
Cl
ion
is
com
qCl = −e , 2σ Cl = 0.44nm and ε Cl = 0.446 kJ/mol for Cl [AMBE
size
ofofspace
the
network
cell
whose
building
blocks
six-membered
rings.
avoiding
water
molecules
and areare
treated
as isolatedwater
species
wi
1/ 2the
the
size
the
network
cell
whose
building
are
six-membered
water
rings
ε ij = (εInstitute
, σ ij = σ i + σ j
(3) blocks
ε ij Lennard-Jones
= (ε iε j )1/ 2 , 42-4-63
σ ijenergy
= σ i + σε j = 0.06
iε j )
International Microwave Power
the diameter 2σ Na = 0.26nm and the
Na
= −diameter
e ,is2used
σ Cl =of
0.44nm
and
ε
=
0.446
kJ/mol
for
Cl
[
AMBER
, 2008
is used when two species i and j are encountering.qClThe
Cl
ion
is
comparable
with
Cl i and j are encountering. The diamet
when two species
1/
2
the size of the network cell whose building blocks are six-membered
water
The
SHAKE
the size of the
network
εrings.
= (εcell
ε ) whose
, σbuilding
= σ + σblocks are six-mem
while the Lennard-Jones forces
¬ are calculated only for the pairs
¼ of oxygen atoms. The
12
6
ª
­
equations of motion
are
§ σ ij ·
§ σ ij · ½°º
12 qi q j
6
d
v
°
ª drqi q= m
º
i
­
½
«
v ii . =°§−∇
qi Emw , (2) (1)
σ ij ·¦ § σ ij +· 48
dv
° ε ij ®¨ ¸ − ¨ ¸¸ ¾» +ࠉࠉࠉࠉ
»
mi i = −∇ « ¦dt i j + 48
dtε ij ®ª¨ «¸ j − ¨rij ¸ ­¾» +°q¨©i12Erijmw¸¹, ¨©6 ½rijº(1)
°
¹
¨ r q¬¸q ¨ r ¸ °§»σ ¯·
§ σ ij · ° ¿¼
« j rijdv i
dt
ij
°¯and
°¿¼ atom,
© ijvelocity
¹i j +©48ijof
¹i-th
«
=
−∇
ε
−
, qi are(1)its mass
Ei mwand
the
position
respectively,
Here, ri and v i ¬are m
¨
¸
¨¨ ¸¸ ¾» + qim
®
¦j r
i
ij ¨
¸
dri
«
»
dt
r
r
ij
ij
ij
°
°
©
¹
©
¹
=
ࠉࠉࠉࠉ
anddrcharge,
respectively, andv irij.¬ = | ri − r j | is the¯ distance between
atoms. (2)
The
¿¼ i-th and j-th
i
-30
= term
(2) for
v i .ε isinthe
ࠉࠉࠉࠉ
dt on the
atom
s and
Lennard-Jones
energy.
For
our
simulations,
where
d≈7.8x10
is
the
dipole
second
the
bracket
right-hand
side
of
Eq.(2)
serves
two
atoms
not
to
ij
dt
dri
moment
of
the
model
water
molecule.
=
.
(2)
v
ࠉࠉࠉࠉ
overlap
is the sum
of radii of
of i-th
twoatom,
atomsrespectively,
and ε ij is themiLennard-Jones
water,
εwweach
= 0.65kJ/mol
and i σposition
Salt
ri other,
and vwhere
and velocity
and qi are its mass
Here,
ij =0.317nm.
ww
i are the
dt
are
the
position
and
velocity
of
i-th
atom,
respectively,
m
and
q
are
its
mass
Here, ri and v iions
energy.
For
water,
0.65kJ
/
mol
ε
=
and
σ
=
0.317nm
.
Salt
ions
are
put
randomly in
i
i
and
respectively,
and rij =water
| ri − rww
are
putcharge,
randomly
in
ww space avoiding
j | is the distance between i-th and j-th atoms. The
and charge, respectively,
and
r
=
|
r
−
r
|
is
the
distance
between
i-th
and
j-th
atoms.
The
RESULTS
AND
DISCUSSION
space
avoiding
molecules
and
are
treated
as atom,
isolated
charge
= e not
, to
i the
j isolated
ri and are
v iijwater
are
position
and
of i-th
mithe
and
qitwo
are qatoms
its
Here,second
term
inthe
bracket
onvelocity
thewith
right-hand
side respectively,
ofspecies
Eq.(2) with
serves
for
molecules
treated
as
species
Na mass
+
second term inthe
thecharge
bracket
on
the
right-hand
side
of
Eq.(2)
serves
for
two
atoms
not
to
the
diameter
2
σ
=
0.26nm
and
the
Lennard-Jones
energy
ε
=
0.062
kJ/mol
for
Na
,
and
and
charge,
respectively,
and
r
=
|
r
−
r
|
is
the
distance
between
i-th
and
j-th
atoms.
The
overlap
each
other,
where2ijσNaij =0.267nm
isi thej sum of radii of twoNaatoms and ε ij is the Lennard-Jones
qNa=e,
the
diameter
Na
- is the condition
overlap each other,
where
is= the
the
sum
two
atoms
εof
The
of two
the
simulation
qsecond
−eLennard-Jones
, 2σσijClFor
0.44nm
and
=of=0.062kJ/
0.446
kJ/mol
for
[0.317nm
AMBER
,serves
the
hybrid
rulerandomly
term
in
bracket
on
right-hand
side
Eq.(2)Lennard-Jones
not to is in
energy.
water,
/ mol
εofwwradii
=ε Cl0.65kJ
andand
σ wwCl
=ijinitial
.2008];
Salt for
ions
areatoms
put
and
the
energy
εthe
Cl =
Na
energy. For water,
0.65kJ
/
mol
ε
=
and
σ
=
0.317nm
.
Salt
ions
are
put
randomly
in
prepared
by generating
crystal
of the
+
ww Na
wwis the1/ 2nm
overlap
each
other,
sum
two
atoms
and
ε ij iswith
the (3)
Lennard-Jones
space
avoiding
waterε2σ
molecules
are=radii
treated
as isolated
species
the ice
charge
qNa I=c e ,
mol
for
, and
qCIwhere
=-e,
ij =0.44
(ε ias
ε j )isolated
,andand
σof
σ i +of
σwith
CI
ij =
ijspecies
j
space avoidingεwater
molecules
and
are
treated
the
charge
q
=
e
,
structure,
and
adding
Na
and
Cl
ions
of
1
mol%
Na are put
energy.
water,
0.65kJ /and
mol
andthe
σ ww = 0.317nmenergy
. Salt εions
randomly
the For
diameter
==0.26nm
the
Lennard-Jones
kJ/mol
for Nain+, and
=0.446
kJ/mol
for2σεClww
2008];
Na [AMBER,
Na =+ 0.062
CI
the diameter 2σ
=
0.26nm
and
the
Lennard-Jones
energy
ε
=
0.062
kJ/mol
for
Na
,
and
concentration
(roughly
3is
wt%)
when
salty
isspace
when twoσspecies
i and and
j are
diameter
of Clwith
comparable
with
Naused
NakJ/mol
avoiding
molecules
and
treated
asThe
isolated
the
charge
qNa
= e ice
,
qrule
εencountering.
for
Cl species
[AMBER
,ion
2008];
the
hybrid
rule
hybrid
Cl = −e , 2water
Cl = 0.44nm
Clare
-= 0.446
+
qCl = −e , 2σ Cl =the
0.44nm
and
ε
=
0.446
kJ/mol
for
Cl
[
AMBER
,
2008];
the
hybrid
rule
or
water
is
prepared.
The
I
ice
is
isotropic
of the 2network
cell whose
building1/ 2blocks are energy
six-membered
water
rings.
TheNa
SHAKE
Cl
thesize
diameter
σ Na = 0.26nm
and
ε Na = 0.062
kJ/mol
for
, andin
c
ε ij the
= (εLennard-Jones
, σ ijthree
= σ i directions
(3)
iε j )
-+ σ j
1/ 2
properties
are
qCl = −e ,ε2ijσ=Cl(ε=iε0.44nm
ε = 0.446 kJ/mol
for Cl [AMBER
2008]; physical
the hybrid
rule
(3)
, σand
(3), whose
j)
ij = σCli + σ j
quite
similar
to
those
of
the
ordinary
ice
of
the
1/
is used when two species
j 2are
encountering.
The diameter of Cl ion (3)
is comparable with
ε ij = i(εand
,diameter
σ ij = σof
σ jion
i εThe
j)
i +Cl
is used when two species
i
and
j
are
encountering.
is
comparable
with
I
structure
[Eisenberg
and
Kauzman,
the
size
of
the
network
cell
whose
building
blocks
are
six-membered
water
rings. The1969;
SHAKE
h
is used when two species ������������
i and j are
the size of the network
cell
whose
building
blocks
are
six-membered
water
rings.
The
SHAKE
Matsumoto
et
al.,
2002];
we
swap
the
O-H
is used when two
species
i andofj are
The diameter of Cl ion is comparable with
encountering.
The
��������������������������
diameter
Clencountering.
ion is
bonds
of water molecules
until an
the
size
of
the
network
cell
whose
building
blocks
are
six-membered
water successively
rings. The SHAKE
comparable with the size of the network cell
isotropic
state
has
been
reached.
The
initial
whose building blocks are six-membered water
structure is equilibrated for 100 ps at a given
rings. The SHAKE and RATTLE algorithm
[Andersen, 1983] is adopted in time integration temperature, and then the microwave electric
of Eq.(1) and (2) to keep the rigid triangular�
����������� field of 2.5 GHz frequency is applied.
Figure 2 shows the time history of (a) the
shape of the molecule. The time step for
temperature (starting at 230 K) of the salty ice
integration is 1fs.
Our simulation system consists of a cubic system, (b) time integrated value of the Joule
box of each side 4.2nm that contains (14)3 water heating and dipole heating terms, (c) the average
velocity of Na+ along the x direction, and (d)
molecules when salt is not added. The periodic
that of Cl−. It is noted that the temperature
boundary condition is imposed under the
of salty ice increases monotonically after the
constant system volume. Thus, the Ewald sum
microwave is turned on. The velocities of salt
for infinite number of periodic image charges
panels (c) and
(d) remain
is takenalgorithm
to correctly
account 1983]
for theis electric
and RATTLE
[Andersen,
adopted in ions
timeinintegration
of Eq.(1)
andsmall
(2) tocompared
those
salty water
fieldrigid
in triangular
which theshape
particle-particle
particlekeep the
of the molecule.
The timetostep
forinintegration
is in
1fs.Figure 3 until the ice
approaches
the
melting
temperature.
�����������
o clarify
mesh
algorithmsystem
is adopted
[Deserno
Holm,
Our
simulation
consists
of a and
cubic
box of each side 4.2nm that contains
(14)3T����������
the heatingcondition
mechanism,
the Joule
heating term
The when
real space
distance
forperiodic
both boundary
water1998].
molecules
salt iscutoff
not added.
The
is imposed
under
E•J
(dotted
and
dashed
lines
for
the
the electrostatic
and Lennard-Jones
forcessum
is for infinite number of periodic image total salt
the constant
system volume.
Thus, the Ewald
+
and
Nain
, respectively)
and the dipole heating
1.0 isnm,
and to
32correctly
spatial grids
are used
for electric
the
charges
taken
account
for the
field
which the particle-particle
E•dP/dt
(solid
line)
are plotted
Fourier-space
calculation
the nonlocal
particle-mesh
algorithm
is adoptedof[Deserno
and Holm, term
1998].
The real
space
cutoff
distanceseparately
in
(b).
Evidently,
the
excitation
electrostatic
forces.and Lennard-Jones forces is 1.0 nm, and 32 spatial grids are used forof dipole
for both
the electrostatic
After ancalculation
equilibration
phase
of 100electrostatic
ps, a rotation
the Fourier-space
of the
nonlocal
forces.is the principal heating mechanism of
salty
ice.
spatially
homogeneous
microwave
electric
field homogeneous
After
an equilibration
phase
of 100 ps,
a spatially
microwave electric field
The heating
is unless
compared with
the form
of theofform
Emw (tE) mw
= (t)=E
E0 sin0 ωt xˆ isis applied.
applied.The
Thewave
wave frequency
f = ω / 2of
π salty
is 2.5ice
GHz
that
of
salty
water
in
Figure
3.
Salty
water with
frequency
f= ω/2π
2.5 GHz unless
otherwisenoises in the simulation, the used wave
otherwise
specified.
To isovercome
the numerical
6
mol% salinity
is prepared
the same way
specified.
overcome
the which
numerical
noises
amplitude
is E0To
= 2.3
×10 V/cm
is large
but its1 associated
energy
with the in
electric
as
for
salty
ice,
and
is
melted
and
equilibrated
thea simulation,
the used
amplitude
dipolein of
water molecule
is wave
less than
the thermal energy at room temperature
6
for use
100 of
ps this
at 300
K. Forfield
the salty
V/cmcondition
which isassures
large but
its safe
E0 d / is
k BTE3000=2.3x10
us the
electric
in ourwater, the
K ≈ 0.4 . This
−30
heating
rate
increases
with
a
temperature
above
associated
energy
with
the electric
dipole
of amoment of the model water molecule.
simulations,
where
d ≈ 7.8
× 10
Cm is the
dipole
water molecule is less than the thermal energy at 350 K, as seen in Figure 3(a) at which the slope
room and
temperature
E0d/kBT300K≈0.4. This condition of the curve becomes steeper. The velocity
3. Results
Discussion
oscillations
of Na
in (c) and (d) also
assures
us the safe
usesimulation
of this electric
field in
The initial
condition
of the
is prepared
by generating
crystal
iceand
of Cl
theions
Ic structure,
and putting Na and Cl ions of 1 mol% concentration (roughly 3 wt%) when salty ice or water
is prepared. The Ic ice is isotropic in three directions whose physical properties are quite
Journalice
of Microwave
& Electromagnetic
Energyand
ONLINE
42, No. 4, 2008
similar42-4-64
to those of the ordinary
of the IPower
[Eisenberg
Kauzman, Vol.
1969;
h structure
Matsumoto et al., 2002]; we swap the O-H bonds of water molecules successively until an
200
1.0
(b)
0.0
3.0
(c)
0.0
−3.0
3.0
(d)
0.0
−3.0
0
2
4
6
8
10
12 14
time (×102 ps)
T (K)
Q/Q0
300
Vx(+) /v0
(a)
Vx(−) /v0
T (K)
Q/Q0
Vx(+) /v0
Vx(−) /v0
400
400
(a)
300
200
1.0
(b)
0.0
3.0
(c)
0.0
−3.0
3.0
(d)
0.0
−3.0
0
2
4
6
8
10
12 14
time (×10 ps)
2
Figure 2. The time history of the heating of
salty ice, (a) temperature of the whole system in
Kelvin, (b) the dipole heating term (solid line),
the Joule heating term of all salt (dotted) and that
of Na ion (dashed), (c) the x-component velocity
of Na ions, and (d) that of Cl ions with v0=10m/s,
Q0= 10-9 J/s. The amplitude of the microwave
electric field is shown by dotted lines in (c )
and (d), where the electric field of 2.5 GHz is
turned on just after the equilibration phase at
time 0 of the figure.
Figure 3. The time history of the heating
of salty water, (a) temperature of the whole
system in Kelvin, (b) the dipole heating term
(solid line), the Joule heating term of all salt
(dotted) and that of Na ion (dashed), (c) the
x-component velocity of Na ions, and (d) that
of Cl ions with v0=10m/s and Q0= 10-9 J/s.
The amplitude of the microwave electric
field is shown by dotted lines in (c ) and (d),
where the electric field is turned on just after
the equilibration phase at time 0 of the figure.
increase in time and are much larger than those
for salty ice. The large oscillations at later times
reveal de-trapping of salt ions from the cell of
the water network, which accelerates the heating
due to large oscillations. A striking difference is
found in the heating terms in panel (b): the Joule
heating term much exceeds the dipole heating
term, where the former is twice as big as the latter
as shown previously [Tanaka and Sato, 2007].
It is interesting����������������������������������
���������������������������������������������
that Cl ions with a heavier mass
and a larger radius respond more than Na ions to
the microwave electric field. This implies that Cl
ions are not stably contained in the cells of the
hydrogen-bonded network of water molecules,
which makes them more easily to be de-trapped
and move through the network.
As for reference, the heating of pure
water against 2.5 GHz microwave is shown
in Figure 4. In this case, the excitation of
dipole rotation is the only mechanism of
energy absorption from the microwave.
The heating rate of salty ice with 1 mol%
salinity is comparable to that for pure water.
The velocity oscillations are shown for (c)
hydrogen atoms and (d) oxygen atoms, which
are small compared with those in Figure 3
and are out of phase with each other since
the center of the mass of water molecules is
fixed because of the charge neutrality.
As pure ice is not heated by microwaves
International Microwave Power Institute
42-4-65
T (K)
400
(a)
Vx(−) /v1
Vx(+) /v1
Q/Q0
300
200
1.0
(b)
0.0
1.0
(c)
0.0
−1.0
1.0
(d)
0.0
−1.0
0
2
4
6
8
10
12 14
time (×102 ps)
0.3
(a)
(c)
0.0
−0.3
−1.0
0.3
Vx(−) /v1
Px (eÅ)
0.0
1.0
0.0
Vx(+) /v1
Px (eÅ)
Q/Q0
T (K)
Figure 4. The time history of 400
the heating of pure water, (a) temperature(a)
in Kelvin, (b) the dipole
heating term, (c) the x-component velocity of hydrogen atoms, and (d) that of oxygen atoms with
v1=1m/s and Q0= 10-9 J/s. The300
amplitude of the microwave electric field is shown by dotted lines
in (c ) and (d), where the electric field of 2.5 GHz is turned on just after the equilibration phase
200
at time 0 of the figure.
1.0
(b)
1.0
(b)
(d)
0.0
0.0
−1.0
−0.3
0 0 2 2 4 4 6 88 1010 121214 14
22
time (×10
(×10ps)
ps)
time
Figure 5. Time history of the sum of all electric dipoles in the x direction for (a) pure water
(corresponding to Figure 4) and (b) salty ice (Figure 2). Solid lines show the value of electric
dipoles, and dashed lines show the amplitude of the electric field of microwaves.
42-4-66
Journal of Microwave Power & Electromagnetic Energy ONLINE
Vol. 42, No. 4, 2008
(a)
(b)
Figure 6. (color online) 3D view of water molecules and salt ions for salty ice (230 K) at (a)
the initial stage, and (b) after 100 ps without microwave application. Chained gray and white
spheres represent oxygen and hydrogen atoms, respectively. Na and Cl ions are shown by isolated small and large spheres, respectively.
of the GHz band, the presence of salt in ice
should play a decisive role in the heating
(melting) process in the microwave electric
field. We showed on the energy basis in Figure
2 that it was not the Joule heating, but the
excitation of dipole rotation that is responsible
for the heating. It follows that electric dipoles
of water molecules are allowed to rotate in
salty ice, which occurs ���������������������
because��������������
of the local
breaking of water network by salt ions. This is
well recognized in Figure 5 which shows the
time history of the sum of the electric dipoles
for (a) pure water and (b) salty ice. For pure
water, molecules begin rotational motions
immediately with ������������������������������
the���������������������������
microwave electric field.
In the early phase when microwaves are applied
to salty ice, the rotational motion of the dipoles
begins which is somewhat retarded and small
compared to the case of pure water. This is
completely��������������������������������������
different from the case of pure ice.
Figure 6 shows that the rigid network of
ice is distorted quickly in the presence of salt
ions even before microwave is applied, as
seen in (b). Experimentally, anomalously high
permittivity was reported for salty ice [Zhong
et al., 1988]. Here, it is confirmed by numerical
simulation at the molecular level that the high
response of salty ice to microwaves is caused
by the presence of salt ions in ice which weaken
International Microwave Power Institute
the hydrogen-bonded rigid network of water
molecules.
The weakening of the hydrogen-bonded
network of water molecules which occurs
in salty ice is also confirmed by specially
designed simulation: the diameter of charged
salt ions is ����������������������������������
artificially����������������������
reduced to 0.2 nm so
that they fit nicely in the cell of the network.
Even in such a condition, heating of salty ice
does occur, and the heating rate is almost three
quarters that of the normal case. This proves
that the weakening of the network in salty ice
is caused mainly by the electrostatic effect of
salt ions which is long-ranged, rather than the
short-range geometrical effect.
The dependence of the heating rate on the
microwave's frequency is examined for pure
and salty water and salty ice, as depicted in
Figure 7. Microwaves of three frequencies 2.5,
5 and 10 GHz are used, and the temperature
increase in the 1.4 ns interval is plotted for pure
water (filled circles), salty water (open circles��
���������)
and salty ice (triangles). The salinity of salty
ice and water is 1 mol%, and initial temperature
is 300 K for water and 230 K for ice. The line
fitting yields the frequency dependence of dT/
dt∝ω1.4 and ω1.2 for pure water and salty ice,
respectively. For salty water, we obtain dT/
dt∝ω0.7. The proximity of the scaling laws for
42-4-67
300
∆T (K)
200
100
30
20
10
1
2
3
4
5
10
20
f (GHz)
Figure 7. The dependence of heating rate on microwave frequency. Open circles and triangles
correspond to salty water and salty ice with 1 mol% salinity, respectively, and filled circles correspond to pure water at 300 K.
pure water and salty ice indicates that water
No.18070005 (FY2006-2010) from the Japan
molecules in salty ice under microwaves rotate
Ministry of Education, Science and Culture
Fig.5. Tanakafor
and
Sato Area Research Project “������������
as freely as those in pure water.
Prime
�������������
Science and
Technology of Microwave-Induced Thermally
SUMMARY
Non-Equilibrium Reaction Fields���
”��. ��������
Present
computation was performed using our cluster
Through molecular dynamics simulation, we
machine consisting of 64-cpu Opteron 254 (2.8
studied the heating process of salty ice, which GHz, single core) processors and high-speed
we encounter daily when we melt frozen food InfiniBand interconnect.
in a microwave oven. We confirmed that
the heating of salty ice is attributed to the REFERENCES
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ACKNOWLEDGMENTS
The authors thank Dr. M. Matsumoto for
fruitful discussions on the structure of ice.
This work was supported by the Grant-in-Aid
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