CHINESE JOURNAL OF CHEMICAL PHYSICS
VOLUME 25, NUMBER 2
APRIL 27, 2012
ARTICLE
Molecular Dynamics Simulation on Scale Inhibition Mechanism of
Polyepoxysuccinic Acid to Calcium Sulphate
Jian-ping Zenga,b , Feng-he Wangc , Chen Zhoud , Xue-dong Gonga ∗
a. Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, China
b. School of Chemical and Biological Engineering, Yancheng Institute of Technology, Yancheng 224003,
China
c. Department of Environmental Science and Engineering, Nanjing Normal University, Nanjing 210042,
China
d. Zhejiang Electric Power Test and Research Institute, Hangzhou 310014, China
(Dated: Received on November 8, 2011; Accepted on January 5, 2012)
Molecular dynamics simulation has been performed to simulate the interaction between
PESA and the (001) face of anhydrite crystal CaSO4 at different temperatures with the
presence of various number of H2 O molecules. The results show that PESA can effectively
prevent the growth of CaSO4 scale at 323−343 K. At the same temperature, the binding
energy between PESA and the (001) face of CaSO4 for systems with various number of H2 O
has the order of Ebind (0H2 O)>Ebind (200−400H2 O)>Ebind (100H2 O). For the same system
at different temperatures the binding energies are close and are mainly contributed from
the Coulomb interaction, including ionic bonds. The bonds are formed between the calcium
atoms of anhydrite scale crystal and the oxygen atoms of the carboxyl group of PESA.
Hydrogen bonds are formed between the O atoms of the carboxyl group of PESA and the H
atoms of H2 O. van der Waals interaction is conducive to the stability of the system of PESA,
H2 O, and CaSO4 . The radial distribution functions of O(carbonyl of PESA)−H(H2 O),
O(CaSO4 )−H(H2 O), and O(CaSO4 )−H(PESA) imply that solvents have effects on the antiscale performance of PESA to CaSO4 .
Key words: Polyepoxysuccinic acid, Calcium sulphate, Molecular dynamics, Binding energy, Radial distribution function
growth, and coordination etc. [13−17]. Compared with
plentiful experimental researches, theoretical researches
at molecular level are limited. With the development
of computer technology, more and more people are able
to use molecular dynamics simulation [18−22] to study
the essence of the interaction between scale inhibitors
and inorganic scales [16, 23−30]. However, the effect
of solvents on scale inhibition performance and mechanism has not been considered. Since scale inhibitors
are generally used in solution, the influences of solvents
cannot be neglected; otherwise the obtained results will
disagree with the actual results [31].
In this work, under different temperature, molecular
dynamics (MD) simulations of the interaction between
the different configurations of PESA and CaSO4 crystal
were performed to interpret the scale inhibition mechanism of PESA using the COMPASS force field and
Discover module in Materials Studio 4.4 program [32].
In order to study the solvent effect, a different number
of water molecules were involved in the model.
I. INTRODUCTION
In the industrial cooling water process, adding scale
inhibitors is a convenient, economic and effective
method to prevent scale production. Polyepoxysuccinic acid (PESA) is a kind of nonnitrogenous, nonphosphorus and biodegradable organic compounds used
as inhibitors [1−5]. As an environmentally friendly water treatment agent, it has the merits of high efficiency
and good inhibition effects for the circulating cooling
water systems with high basicity and high-solid contents which has become a hot problem.
At present, experimental studies mainly focus on
the scale inhibition performance of PESA and its mixtures to the scales such as calcium carbonate, calcium phosphate, and calcium sulfate [6−12], further researches on the interaction mechanisms between scale
inhibitors and inorganic scales are required because the
interaction is a complicated physical and chemical process involving diffusion, adsorption, desorption, crystal
∗ Author
to whom correspondence should be addressed. E-mail:
[email protected]
DOI:10.1088/1674-0068/25/02/219-225
219
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Jian-ping Zeng et al.
FIG. 2 Total energy in the interaction process of PESA with
anyhdrite (001) face (343 K).
FIG. 1 Layer model of PESA-200H2 O-anhydrite. Line
structures: H2 O, chain and ball-stick structure: PESA, ballstick structures: anhydrite.
II. MODEL CONSTRUCTION AND SIMULATION
METHOD
Anhydrite is the most popular structure of calcium
sulphate crystals. It belongs to the AMMA space group
[16], the lattice parameters are a=6.991 Å, b=6.996 Å,
c=6.238 Å, α=β=γ=90 Å. Each primary crystal cell
contains six molecules. According to the preceding work
[33], the surface cell was created from the main growth
face of anhydrite crystal, namely (001) face. The interactions between PESA and the (001) face of anhydrite
crystal were investigated using the layered mode under different temperatures. The simulated supercell of
anhydrite crystal was 27.964 Å×27.984 Å×9.1699 Å in
size, and the total number of atoms are 576 (O=384,
S=96, Ca=96).
The 3-dimension model of PESA molecule with a formula of C80 H82 O100 was built and optimized to most
stable configurations using molecular mechanics (MM)
method and COMPASS force field [34−36].
In order to investigate the effect of water on the
interactions between PESA and anhydrite crystal, the
amorphous cells composed of the optimized PESA
and various number of H2 O molecules (0, 100, 200,
300, and 400) were placed on the anhydrite (001) face
to construct the layer models. Taking the PESA200H2 O-anhydrite system as an example, the layer
model was shown in Fig.1. To eliminate the effect of
periodic boundary condition on the system, the vacuum
thickness was set to 50 Å. Then, the MM method was
used to optimize the system to produce the initial
configuration of MD simulation and the MD simulation
was carried out with the discover module. Because the
crystal grows along with rigid sequence and orientation,
in this study, the atoms in the (001) face of anhydrite
crystal were freezed during simulations as what was
done before, while all molecules were unconstrained.
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Considering the practical operation conditions of
circulating cooling water, the temperature range of
323−343 K was selected and MD simulation was carried out in the NVT ensemble [37−39]. The coupling
to the heating bath to control temperature was carried
out using the Berendsen method with a relaxation time
of 0.1 ps [40]. Simulation was started by taking initial velocities from a Maxwell distribution. Solution of
Newton’s laws of Motion was based on the assumptions
of periodic boundary condition and time average equal
to the ensemble average. Integral summation was performed with the Verlet velocity integrator. Non-bond
(van der Waals (vdW) and electrostatic) interactions for
each system were computed with the atom-based summation method, with a cutoff radius of 0.95 nm. The
time step was 1 fs, MD simulation ran for 3 ns. The
trajectory was recorded every 1 ps.
III. RESULTS AND DISCUSSION
A. Equilibrium criteria
Whether the model system has reached equilibrium
or not was ascertained by the equilibrium critera of
temperature and energy simultaneously [31, 40], i.e.,
the fluctuations of temperature and energy should be
confined to 5%−10%. Taking PESA-200H2 O-anhydrite
(343 K) as an example, according to the temperature
and energy curves from MD simulations (Fig.2), the
temperature fluctuates in the range of 343±20 K and
the fluctuation of energy is less than 0.5%, indicating
that the system has reached an equilibrium.
B. Binding energy
The anhydrite-inhibitor interaction energy (∆E) is
computed using the following equation [41−43]:
∆E = Ecomplex − (ESI + Esurface )
(1)
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Mechanism of Polyepoxysuccinic Acid to Calcium Sulphate
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TABLE I Binding energies between PESA and the (001) face of anhydrite with the presence of 200H2 O. All energies in
kJ/mol.
T /K
323
333
343
Ecomplex
2089702.33
2088546.81
2090306.68
ESI
408.51
Esurface
2148878.69
FIG. 3 Interaction configuration of PESA and 200H2 O with
the (001) face of anhydrite crystal from MD simulations at
343 K. Line structures: H2 O, chain and ball-stick structure:
PESA, ball-stick structures: anhydrite.
where Ecomplex is the total energy of the binded
anhydrite-inhibitor system from MD simulations, ESI
and Esurface are the single point energies of the free scale
inhibitor and the anhydrite surface, respectively. Obviously, a smaller ∆E indicates a stronger interaction
between the surface and the scale inhibitor. Binding energy was defined as Ebind =−∆E. A larger Ebind implies
the scale inhibitor combines with the anhydrite surface
more easily and tightly, as a result, the scale inhibition
performance is higher.
Seen from Fig.3, PESA has clung to the (001) face
of anhydrite and the O atoms of PESA and 200H2 O
molecules are downward. Meanwhile, some water
molecules have escaped from the simulation box, indicating there exist stronger attraction interactions between the inhibitors and the (001) face of anhydrite
crystal. The interaction energies of all PESA-anhydrite
systems at different temperature are shown in Table I
and Fig.4.
All binding energies in Table I and Fig.4 are positive and ∆E are negative, showing that the combination processes of PESA scale inhibitors with anhydrite
crystal are largely exothermic. This is mainly because
of huge Esurface resulting from the interaction between
all the atoms of the (001) face of anhydrite, and the
many strong π-π interactions between the π34 delocalized bonds of −COOH groups in PESA and the π46 delocalized bonds in the surface of anhydrite crystal [28, 44].
Comparing the Ebind of systems with different number
of H2 O molecules at the same temperature, we find that
DOI:10.1088/1674-0068/25/02/219-225
ESI +Esurface
2149287.20
∆E
−59584.88
−60740.40
−58980.53
Ebind
59584.88
60740.40
58980.53
FIG. 4 Binding energies between PESA and the (001) face
of anhydrite with different number of H2 O.
the Ebind of the system without H2 O are significantly
larger than those of the others. This indicates that
water molecules make the combination of PESA and
anhydrite more difficult because the existence of the
water molecules makes the contact probability of scale
inhibitor and anhydrite smaller.
At each temperature, Ebind (0H2 O)>Ebind (300H2 O)
≈Ebind (200H2 O)≈Ebind (400H2 O)>Ebind (100H2 O) (see
Fig.4). Ebind maintains a relatively stable value when
the number of H2 O is 200−400, but when that of
H2 O is 500, the Ebind decreases to approximately 0,
i.e., a threshold phenomenon of the scale inhibition
performance of PESA to calcium sulfate can be observed with the decreasing concentration of PESA.
The relatively higher Ebind in solution appears when
the number of H2 O is between 200 and 400. This is
because a higher Ca2+ concentration (i.e., the greater
solubility of CaSO4 ) in such solution may be observed
due to the formation of soluble chelate compounds
between PESA and Ca2+ . This is in accordance with
the reported results in Refs.[10, 45, 47]. Also seen
from Fig.4, all Ebind s are very close at 323−343 K
except for the systems with 100H2 O. This indicates
the inhibition perfermance of the scale inhibitors is not
greatly affected by temperature.
C. Deformation of PESA
The deformation degree of the PESA scale inhibitor is
a quantity reflecting the strength of interaction between
PESA and scale and can be evaluated by deformation
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TABLE II Non-bond interaction and deformation energies between PESA and (001) face of anhydritea . All energies in
kJ/mol.
nb
0
T /K
323
333
343
323
333
343
323
333
343
323
333
343
323
333
343
∆ECoulomb ∆Edisper-vdw ∆Erepul-vdw
∆Evdw
∆Enon-bond ∆Einhibitor Einhibitor-bind ∆Edeform
1465814.60
−5710.30
6531.63
821.33
5364608.79
14660.65
15509.61
848.96
1465976.45
−5752.18
6534.68
782.50
5113359.08
14660.65
15818.42
1157.78
1466068.45
−5990.90
6953.26
962.36
6691551.72
14660.65
15859.06
1198.41
100
1346448.85
−10256.80
15753.50
5496.70
1351945.551
−19.71
13772.92
13792.62
−164458.59
−5724.93
7905.59
2180.66 −162277.925
−19.71
1822.32
1842.00
−168100.12
−5986.35
8270.46
2284.12 −165816.002
−19.71
829.82
845.32
200
1514603.60
−12977.86
21953.32
8975.46
1523579.03
408.51
12034.36
11625.79
1514902.52
−13107.44
22414.12
9306.69
1524209.20
408.51
12047.56
11639.00
1515646.97
−13353.93
22523.72
9169.79
1524816.77
408.51
11860.43
11230.45
300
1514603.60
−12977.86
21953.32
8975.46
1523579.03
−356.93
10680.50
11037.42
1493499.29
−17601.81
30821.86 13220.04
1506719.33
−356.93
10416.81
10773.74
1494934.99
−17741.68
30904.83 13163.15
1508098.15
−356.93
10311.12
10668.03
400
1275858.93
−24936.38
44293.20 19356.83
1295215.76
−414.61
9134.94
9549.54
1276269.20
−25972.81
45880.47 19907.67
1296176.83
−414.61
10955.49
11370.10
1275453.31
−25679.75
45179.86 19500.12
1294953.42
−414.61
11189.54
11604.14
a
∆ECoulomb ∆Edisper-vdw , and ∆Erepul-vdw represent the difference between the Coulomb interaction energy, dispersive
van der Waals energy, and repulsive van der Waals energy, respectively, ∆Evdw is the sum of ∆Edisper-vdw and ∆Erepul-vdw ;
∆Enon-bond is the sum of ∆ECoulomb and ∆Evdw , Einhibitor-bind is the single point energy of the adsorbed inhibitor,
∆Edeform is the deformation energy of the inhibitor.
b
The number of H2 O molecule.
energy (∆Edeform ) [16, 26, 27]:
∆Edeform = EPESA-bind − EPESA
(2)
where EPESA-bind and EPESA are single point energies of PESA in adsorbed and free states, respectively. Taking PESA-200H2 O-anhydrite at 343 K
(Fig.3) as an example, the obtained ∆Edeform of PESA
is 11230.45 kJ/mol, indicating that PESA has deformed
obviously. The deformation of PESA on the (001) face
of anhydrite crystal under other temperatures with various number of water molecule is similar, and the results
are listed in Table II. From Table II, at the same temperature, the ∆Edeform of PESA in the system without
water is obviously less than those of the systems with
200−400 H2 O molecules, which does not agree with the
change of Ebind from Table I. But for the systems with
a various number of water molecules, the changes of
∆Edeform and Ebind are largely accordant. This indicates it is necessary to involve H2 O molecules into the
simulation models.
The distortion of anhydrite crystal occurs when it
adsorbs PESA. This will lead to the fracture of anhydrite crystal surfaces and hinder the growth of anhydrite
crystal, as observed in experiments [29, 47]. We can
also see from Tables I and II, the defomation energies
are much smaller than the non-bond energies and the
binding energies in magnitudes. That is why PESA can
overcome the intense deformation and closely combine
with the surface of anhydrite crystal.
From Table II, it can also be seen that ∆ECoulomb of
DOI:10.1088/1674-0068/25/02/219-225
TABLE III Natural bond orbital charges (in e) of PESA
monomer.
Atom
Charge
Atom
Charge
C1
0.840
O6
−0.219
C2
−0.029
O7
−0.583
C3
0.280
O8
−0.226
O9
−0.253
C4
0.815
O5
−0.590
FIG. 5 PESA monomer.
the interaction systems are positive except for 100H2 O,
and ∆Edisper-vdw are negative. This indicates the
Coulomb and dispersive vdW interactions are helpful
for the combination of scale inhibitors with anhydrite
crystal. On the other hand, the total vdW interactions
are positive due to ∆Erepul-vdw being larger than the
absolute value of ∆Edisper-vdw . ∆ECoulomb is significantly greater than ∆Evdw , which means the contribution from Coulomb interaction is significantly greater
than that from vdW interaction. Natural bond orbital
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Mechanism of Polyepoxysuccinic Acid to Calcium Sulphate
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(2)
(4)
(1)
(3)
FIG. 7 Chemical bonds and hydrogen bonds formed in the
system of PESA and anhydrite (001) face in water at 343 K.
The distance of (1) Ca(CaSO4 )−O(carbonyl of PESA)
2.354 Å, (2) O(carbonyl of PESA)−H(H2 O) 2.340 Å, (3)
O(CaSO4 )−H(H2 O) 3.442 Å, and (4) O(CaSO4 )−H(PESA)
2.901 Å. Line structures: H2 O, chain and ball-stick structure: PESA, ball-stick structures: anhydrite.
FIG. 6 Pair correlation functions g(r)Ca−O (a) and g(r)O−H
(b) of PESA with the (001) face of anhydrite crystal in water
solution at 343 K.
charges (Table III) of PESA monomer (Fig.5) calculated by B3LYP/6-31G∗ method using Gaussian 03 program [48] show that negative charges on the O5 and O6
atoms of the carboxyl groups are much more than that
on other positions. Therefore, strong adsorption can be
raised by the Coulomb interaction between the negatively charged groups of the scale inhibitor PESA and
the positively charged calcium ion of anhydrite crystal
[26, 27, 29, 47]. Thereby, PESA can occupy the growing point of anhydrite crystal and hinder the further
sediment of the scale ions.
D. Radial distribution functions of the interaction system
Radial distribution functions (RDFs) of the scale
inhibitor and anhydrite crystal supermolecular systems
in water solution, g(r), are obtained by analyzing the MD simulation trajectories.
The RDFs
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of Ca(CaSO4 )−O(carbonyl of PESA), O(carbonyl
of
PESA)−H(H2 O),
O(CaSO4 )−H(H2 O),
and
O(CaSO4 )−H(PESA) pairs at 343 K are shown
in Fig.6. Generally, the peak in the g(r)-r curve within
3.5 Å is caused by the hydrogen bonds and chemical
bonds, and that outside 3.5 Å is from the non-bond
(Coulomb and vdW) interactions [26, 27, 31].
It can be seen from Fig.6(a) that the peak of
g(r)Ca−O -r curve appears around 2.35 Å for the system without water, which is slightly shorter than the
bond length of Ca−O (2.39 Å), indicating the Ca−O
bonds formed between the calcium atoms of anhydrite
scale crystal and the oxygen atoms of carbonyls groups
of PESA (see Fig.7). In addition, there is also a second
weaker peak presented in the range of 5−6 Å, which
can be explained as the weak interactions from farther
departured O and Ca. From Fig.6(a), we can also find
that there are no significant strong peaks when various
number of water molecules are involved into the system,
and the peak of the system with 100H2 O is the lowest,
which means the binding energy between PESA and the
(001) face of anhydrite crystal of the system without water is the largest and that of the system with 100 water
molecules is the smallest as was seen in Fig.5. This indicates the existence of water weakens the interaction
between PESA and anhydrite crystal.
From Fig.6(b), one sees that the strong peak of
g(r)O−H -r of O(carbonyl of PESA)−H(H2 O) appears
around 2.3 Å, which is close to the length of hydrogen bonds [48, 49]. The high probability of O(carbonyl
of PESA)−H(H2 O) distance around 2.3 Å reflects the
formation of hydrogen bonds between the O atoms
of the carbonyl of PESA and the H atoms of H2 O.
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From Fig.6(b), we can also find that there are no
strong peaks on the g(r)O−H curves and g(r)O−H3 of
O(CaSO4 )−H(H2 O) and O(CaSO4 )−H(PESA) around
2.3 Å, which indicates the low probabilty of the
formation of hydrogen bonds between the O atoms
of CaSO4 and the H atoms of H2 O and PESA.
The stronger peaks of O(carbonyl of PESA)−H(H2 O),
O(CaSO4 )−H(H2 O), and O(CaSO4 )−H(PESA) pairs
outside 5.0 Å are raised by the non-bond interactions
from farther departured O and H atoms. This means
that in water solution, inhibitors do not interact directly
with anhydrite crystal, but indirectly through the chemical bonds, hydrogen bonds, and non-bond interactions
formed between PESA-H2 O-anhydrite. This result is
different from that in vacuum where H2 O is absent [16,
26, 27, 29].
IV. CONCLUSION
The interaction between polyepoxysuccinic acid
(PESA) and anhydrite crystal was simulated with
the molecular dynamics. At different temperature
in water solution, PESA can effectively prevent the
growth of CaSO4 scale. At all temperatures, the order of binding energy is Ebind (0H2 O)>Ebind (300H2 O)≈
Ebind (200H2 O)≈Ebind (400H2 O)>Ebind (100H2 O), and
the Ebind are very close for one system at different temperature except for 100H2 O. The molecular dynamics
results show that PESA deforms obviously when it combines with the anhydrite crystal, while the deformation
energies are much smaller than the non-bonding energies. The bonds can be formed between the calcium
atoms of the (001) face of anhydrite crystal and the
oxygen atoms of carbonyl group of PESA. Hydrogen
bonds are formed between the O atoms of the carbonyl
group of PESA and the H atoms of H2 O. The non-bond
interactions are conducive to the stability of the interaction system of PESA, H2 O, and CaSO4 crystal. The
existence of water molecules weakens the interaction between PESA and anhydrite crystal. The main contribution to the binding energies comes from the Coulomb
interaction.
V. ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (No.41101287) and the Priority Academic Program Development of Jiangsu Higher
Education Institutions.
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