FMOSimulation Method Based on FMO Calculations



6 2 FMO
3
FMO-DPD
4 FMO
5

Nafion

DPD
X (SAXS)

MD
DPD

χ

SP Hildebrand16 17,18bicerano19
SP 20
χFan



Sepehr 2015
DFT Nafion
DPD 22Nafion MM



23 FMO

(PIE)FMOFMO

(Hexane-NitrobenzenePolyisobutylene-Diisobutyl KetonePolystyrene-Polyisoprene)


Fan
Fan 1
(i) 2

(ii)
(ii-1) Cartesian

ii-2
(ii-4) Metropolis MC
25 u′′
u′

(iii) Flory-Huggins (2)

Flory-Huggins
2
1 2
Metropolis MC


SCC
SCC ESP
HF
(5)
23
CT +mix ESEX CT +mix HF
DIMP2 PIEDAMM


6
=

S
SS
100 S Scaling factor

FMO
2,000
Metropolis 10,000
MC
1-2 2-1 2-2

2 29
χ
(10)
i j Scaling factor
1221
11

Tc

(i) Hexane-Nitrobenzene-
GAUSSIAN 09
Table 2
J-OCTA35
(Polyisobutylene, Polyisoprene, Polystyrene) 2 1
2
3 4 2

i j

Tc
general
Hexane-Nitrobenzene
PIEDA27,28
(ii) Polyisobuthylene-Diisobuthyl Ketone - (iii) Polyisoprene-
Polystyrene-
o Oxygen with one atom CH3CHO
on Oxygen of the nitro group CH3NO2
14
c3


Metropolis
3 Scaling factor
n-Scaling
factor 0.88

χc 2.0
Table 3 293K30 286K
10
(C) PIEDA

3
FMO DREIDING
”Present” MO

0
0.2
0.4
0.6
0.8
1
R D
Table 3. Hexane (label 1)-Nitrobenzene (label 2) 300K
(), scale factor(), ()
Tc (K)
S FMO FMOGAFF
Table 3
FMO = −. + . × / Fitting
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
χ
Temperature(T)
CIFIE FF
18
Table 4. Hexane (label 1)-Nitrobenzene(label 2) PIEDAESEXCT +
mix DI kcal / mol qMulliken charge transfer e
DREIDING AB C Figure 8

1-1
1-2
2-2
19
5 300K 3
Scaling factor Nitrobenzene

Table 6 292,
χ 10
Table 5. Polyisobuthylene (label 1) - Diisobuthyl Ketonelabel 2 300K
(), scale factor(), ()
1-1 -0.95 0.92 7.6
Mw Tc (K)
S FMO FMOGAFF
3 Table 6
FMO = −. + . × / Fitting

300K 3
Scaling factor Table 7 Polyisoprene
Polystyrene Ph
4
,
χ
Temperature(T)
(), scale factor(), ()
1-1 -1.16 0.84 8.0
pip-ps Mw 2000-2700, 2700-2100 0.15
FMO Tc)

22
S FMO FMOGAFF
3 Table 8
FMO = . × − + . × /Fitting


MODPD
(FCEWS) (http://www.cenav.org/fcews_ver1_rev2/)
ABINIT-MP
χ
Temperature(T)
Linux Windows
PBS, Torque, LSF, Lava
FOCUS
24
FMO-DPD

3.3-3.5
Hoogerbrugge Koelman 4,5Groot
7,8,15 DPD


1
2
7
/||



= {

thermal noise()
0 ≥
2

43
Groot Verlet λ = 0.65

FMO Poisson-Boltzmann (PB)
MO-PB 45

Figure 11
(iv)
ESP Okiyama 46,47
RichardsTannor 45 Szafran51

2 [|′| + ′′] (27)


A


Nafion®PFSA Nafion

X 53–57 58–60
TEM61AFM62IR63
Nafion

68–70
Nafion
Nafion 71–
77–79Kawakami Shigemoto
MD 80
81Nafion / Pt Nafion 82
Nafion Nafion

--SPEEK

PEM
LAMMPS92PEM MD
Okazaki 93Voth94Komarov95

DPD 7–9,15

100,101 DPD PEM Morohoshi
PEM DPD
MC 102 Neimark
.103–105 DPD 64,65,66
2 DPD


DPD 22
MO
DPD FMO


Simulation details
C: -CF2-CF2-SO3H)
A, C FB CF3Figure
13 PEEKNafionA, B, C
CH3(W)


5 Figure 14
Nafion, PEEK χ
B97D33/6-31G(d’,p’) Gaussian0932
J-OCTA35 2000
2 FMO2-MP2/6-
31G(d’) ABINIT-MP36
χ
Figure 14. H2O (a) Tetramer (b) Linear dimer
(c) Bifurcated dimer (d) Cyclic dimer (e) Monomer

DPD
Δt = 0.05 30 ρ = 3
81000 DPD 4
0.71nm 21.3nm
Figure 15 Nafion(a)-(c)
Equivalent Weight (EW)(b)
4 10000 500 DPD- time unit
(t) 10-30 2
100 step (5 DPD-time unit)
J-OCTA COGNAC
0.71nm Figure 12, Figure 13
AB C b Nafion 117EW = 1100
ac EW EW



Cs

(A-A, A-B, B-B) -1 kcal/mol
(C-C, C-W, W-W) -10 kcal/mol
0.9
0.5
W C,W χ
FMO χ A-B:-0.17C-
W:-4.1 A-W,B-W 20
11
χ

Table 10. Nafion 350K(kcal/mol) S Z
Segment 1
A B C W

S eg
. 2
A -0.76 0.89 7.2 -0.87 0.91 8.0 -0.82 0.83 8.1 -1.32 0.84 8.1
B -0.87 0.90 7.0 -0.95 0.89 8.0 -0.91 0.84 8.2 -1.38 0.83 7.3
C -0.82 0.92 7.6 -0.91 0.90 8.7 -4.26 0.46 8.6 -15.58 0.30 7.4
W -1.32 0.83 13.7 -1.38 0.83 12.3 -15.58 0.20 14.2 -9.87 0.51 10.6
Tetramer Dimer
12 (C-W) 0.24 0.23 0.25 0.20 0.20
21 (W-C) 0.45 0.27 0.44 0.30 0.52
35
This work Previous work11
Cs SPEEK 350K
Table 13 Nafion
1.5 PEEK π
C

(A-B, A-C, B-C) χ-0.75, 4.94, 3.53
A-W χ -3.78 SPEEK

(kcal/mol)
12 (C-W) 0.37 0.17 0.37 0.37 0.46
21 (W-C) 0.76 0.44 0.63 0.5 0.56
36
Segment 1
A B C W

S eg
. 2
A -1.27 0.82 8.2 -1.27 0.89 11.0 -2.38 0.76 9.6 -0.98 0.88 9.2
B -1.27 0.85 7.1 -1.28 0.89 9.2 -2.28 0.85 7.9 -1.25 0.87 8.3
C -2.38 0.77 7.5 -2.28 0.78 11.0 -6.38 0.55 8.3 -8.13 0.76 8.2
W -0.98 0.84 17.6 -1.25 0.88 24.5 -8.13 0.37 18.1 -9.89 0.50 10.6
Table 14. SPEEK χ(350K)
Figure 15 4 (b)
20 vol%


20
Figure 15(b) 10 vol%, 20 vol%. 30vol%
1020
37
Figure 19 Figure 20 Nafion
SPEEK
Nafion
t = 100 t = 500
Figure 16. Figure 15 Nafion (b) 20 vol


38
Figure 18. Nafion 20 vol EW (a), (b),
(c) Figure 15

t = 100 t = 500
Figure 17. Figure 15 Nafion (b) 20 vol
40
Figure 19. Figure 15 Nafionbt =
50010, 20 30 vol

Figure 20. Figure 15 SPEEKt = 50010,
20 30 vol
40

b(Nafion 117) 10, 20 30 vol 3
RDF (t = 500)RDFFigure 22


6
2 1
Nafion
Figure 23
10-30 vol 3.3-5.3nm
4.4-6.3nm
4nm 5nm 53,67
EW
Morohoshi 102
10,20 30 vol
Figure 22. Nafiont = 500 RDF
10,20 30

0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
P ai
r d
is tr
In te
n si
Figure 15abc

(Mean Square Displacement; MSD)
() ( − 1) ±δ

30
τ = /(30)

Nafion
PEEK
Nafion
Nafion 117 10, 20 30 vol
λ 2.5, 6 10
Zawodzinski 108 0.8 × 10−6-
4.5 × 10−6 cm2/s 0.6 × 10−6- 3.2 × 10−6
cm2/s
Figure 24. Nafion, SPEEK
Figure 15 Nafion abc
SPEEK
D if
fu si
R(i, j) i j (34)
i j
M
= ∑ ()
=1
(35)
10-30% 2%
Δt = 0.05 10000 stept = 300-500 100
step Figure 25
Nafion(a), (b) 20 vol%(c)
30 vol% 1
SPEEK 30 vol Wu 109DPD

Figure 26Nafion 10% 109
EW Fontanella
110PEEK Nafion
PEEKPEEK
90%Nafion 100%
Nafion PEEK
Figure 15 Nafion
abc SPEEK
Figure 26. Nafion SPEEK100step
Figure 15 Nafion
abc SPEEK
0.0
0.2
0.4
0.6
0.8
1.0
W at
er c
W at
er c
73,85,94,97,111,112
(Cm)
Eigen-model (Wp)
FCEWS35 2000
FMO2-MP2/6-31G† ABINIT-



DPD
10000 (500 DPD- time unit (t))
DPD Figure 28 A,
B, C, Cm 0, 20, 40, 60, 80
10-30 2
Cm Wp
100 step(5 DPD-time unit)J-OCTA
COGNAC
aij = 0
DPD Figure 29



(Wp) Eigen-model
Figure 28. Nafion DPD
A, B, C, Cm
48
Table 15. Nafion A, B, C Figure 12
Cm, Wp Figure 27
Pair Χ aij
A-B -0.80 47.39
A-C 1.26 54.11
B-C 0.83 52.71
A-W 6.53 71.29
B-W 7.71 75.13
C-W -5.22 32.98
(Wp)
49
(W)
Figure 31. Nafion
× 0, 20, 40, 40, 80, 100%

0.0
0.5
1.0
1.5
2.0
neutral
20%
40%
60%
80%
100%
50

89 113
Amadeu2007

MD

117



Simulation details
7


51

FMO2-MP2/6-31G†
(36)
Δt = 0.05 30 ρ = 3
81000 DPD 4
0.71nm 21.3nm
Figure 347
POPC 100000
J-OCTA COGNAC 118
Figure 32. POPC




(A.B,C)-1kcal/mol
(E,W)-2.6kcal/mol
1PB
0.6

A B C
D E F
53
χ Table 18 χ 0
χ -6.64
A,B,C χ 10

t = 3000
= 500
t = 5000

17.7%
62-68Å2
Figure 38 ZZ
0.5
Table 16. (E)(F)(300K, kcal/mol)S
Tetramer C2V C2h Cs monomer
E
F
S12(C-W) - 0.90 0.92 - 0.91
S21(W-C) - 0.47 0.75 - 0.55
Segment 1
S eg
m en
t 2
B
C
S 0.89 0.90 0.88 0.87 0.62 - 0.91
Z 7.0 8.1 7.3 7.5 8.7 8.0 9.3
D
E
F
S 0.92 0.91 - 0.42 0.49 - 0.55
Z 5.7 6.5 6.2 6.5 7.0 6.6 7.7
W
55
Figure 35. DPD (POPC 13%)
(A, B, C, D)(E, F)

A -0.18 -0.23 1.39 4.75 4.76 12.08
B -0.61 0.71 5.46 5.81 12.66
C 1.18 4.81 5.74 10.56
D 1.99 -4.00 9.73
t = 5000 t = 3000
(POPC 13%) (A, B, C, D)
(E, F)
22.95
22.97
22.99
23.01
23.03
23.05
23.07

t = 5000 t = 3000
(A-C), (D), (F), (E), (W)


DPPD
DOTAP:DPPC = 0:1, 1:3, 1:1, 3:1, 1:0
Figure 40
Figure 33 A-F OH-(Wm)

25
(F) Wm 0
FMO-DPD
0.00
0.20
0.40
0.60
0.80
1.00
1.20

Z (nm)




A 24.1 28.1 45.2 28.5 25.3 79.8 117.6
B 30.4 39.1 33.3 31.5 83.7 131.0
C 49.9 34.8 27.8 75.6 126.5
D 31.7 2.3 76.6 112.4
E 0.0 49.4
F 65.6 0.0
124–128DPDFMO


CognacGAFF
C=160, =0.6 Harmonic
1 1-3 C=80, =1.2
Harmonic
FMODPD, MD COGNAC FMO ABINIT-MP
FMO2-MP2/6-31G(d’)
()


441000 DPD11000IFIE
Figure 45 Figure 45 (e2) IFIE

20kcal/mol Figure 46, Figure 47
5000 DPD 60000
6000 FMO Figure 47 (e2)


Figure 45. Nafion FMO Figure 44
(d) ( 11000 (e1)
(e2) IFIE

Figure 47. POPC FMO Figure 46
(d) ( 6000

(e2)
MP2 ()

2018/7/4
67

2000 1500 500
(MP2 kcal/mol)

(MSE)
Br Bromobenzene
MO

130
131

) A B 2
AB 2
A B 4 MD
69
(v) FMO: MDFMO

i IFIEn
(,

FMO ABINIT-MP MD COGNAC118

xyz
FMO Figure 50 (a)-(d)
5.2.14MD(a)
)(c)MD(d)
3DPD
Figure 51 10000 10000

Figure 50. MD (a)
(b) 3 MD
1(c)
1
- 15- 5
σ 5
OH/π
Exptl.131
32.25
47.65


7
Table 21, Figure 52



2
Figure 54
1-2(bond), 1-

MorseDPD = 0.0051000
Chignolin
, NC
Figure 54. Chignolin
0Gly N
170 Asp Glu

(b)(c)
Gly Gly(N) Gly(C) Tyr Asp Pro Glu Thr Trp Wat
Gly 110.6 111.4 141.0 152.0 116.8 105.2 125.6 113.2 150.0 170.8
Gly(N) 170.4 0.0 169.3 0.0 126.6 59.3 130.5 154.5 80.2
Gly(C) 145.2 114.3 139.5 103.4 152.0 70.0 98.7 70.2
Tyr 138.1 81.0 131.2 160.3 132.8 170.8 235.5
Asp 130.2 95.8 129.1 95.2 78.5 39.2
Pro 66.2 103.6 82.0 111.5 132.8
Glu 140.2 107.7 156.4 36.1
Thr 58.6 122.0 117.0
(b)(c) DPD

(c)
Ketone-PolyisobutylenePolystyrene-Polyisoprene)
χ
Nafion
119–123DDS


JSOL
J-OCTADPD

79

1. : K. Okuwaki, Y. Mochizuki, H. Doi and T. Ozawa
: Fragment Molecular Orbital Based Parametrization Procedure for Mesoscopic
Structure Prediction of Polymeric Materials
: J. Phys. Chem. B, 2018, 122, 338–347
2. : K. Okuwaki, Y. Mochizuki, H. Doi, S. Kawada, T. Ozawa and K. Yasuoka
: Theoretical Analyses on Water Cluster Structures in Polymer Electrolyte
Membrane by Using Dissipative Particle Dynamics Simulations with Fragment
Molecular Orbital Based Effective Parameters
: RSC Adv., 2018, 8, 34582–34595.
3. : K. Okuwaki, H. Doi and Y. Mochizuki
:An Automated Framework to Evaluate Effective Interaction parameters for
Dissipative Particle Dynamics Simulations Based on the Fragment Molecular Orbital
(FMO) Method
: J. Comput. Chem. Japan, 2018, 17, 102–109.
4. : K. Okuwaki, H. Doi, Y. Mochizuki, T. Ozawa, K. Yasuoka and K. Fukuzawa
: Development and Application of FMO Calculation − DPD Simulation
Conbination Scheme
: J. Comput. Chem. Japan, 2018, 17, 144–146.
5. : H. Doi, K. Okuwaki, Y. Mochizuki, T. Ozawa and K. Yasuoka
: Dissipative Particle Dynamics (DPD) Simulations with Fragment Molecular
Orbital (FMO) Based Effective Parameters for 1-Palmitoyl-2-Oleoyl Phosphatidyl
Choline (POPC) Membrane
: Chem. Phys. Lett., 2017, 684, 427–432.
6. : H. Doi, K. Okuwaki, T. Naito, S. Saitou and Y. Mochizuki
: A Portable Code for Dissipative Particle Dynamics (DPD) Simulations with
Additional Specific Interactions.
: Chem-Bio Informatics J., 2018, 18, 70–85.
7. : E. Shinsho, K. Okuwaki, H. Doi, Y. Mochizuki, T. Furuishi, K. Fukuzawa and
E. Yonemochi
: Formation Mechanism of Lipid Membrane and Vesicle Using Small Angle X-
ray Scattering and Dissipative Particle Dynamics (DPD) Method
: J. Comput. Chem. Japan, 2018, 17, 172-179.
80
8. : S. Saitou, J. Iijima, M. Fujimoto, Y. Mochizuki, K. Okuwaki, H. Doi and Y.
Komeiji
: Application of TensorFlow to Recognition of Visualized Results of Fragment
Molecular Orbital (FMO) Calculations
: Chem-Bio Informatics J., 2018, 18, 58–69.
9. : H. Doi, K. Okuwaki, Y. Mochizuki and T. Ozawa
: A New Treatment for Water near the Interface between Lipid Membrane and
Silica in Dissipative Particle Dynamics Simulation
: J. Comput. Chem. Japan, 2017, 16, 28–31.
10. : H. Doi, S. Saitou, K. Okuwaki, T. Naito and Y. Mochizuki
:Development and Performance Evaluation of a Simulation Code for
Dissipative Particle Dynamics (DPD) CAMUS
: J. Comput. Chem. Japan, 2018, 16, 126–128.
11. : A. Rossberg, T. Abe, K. Okuwaki, A. Barkleit, K. Fukuzawa, T. Nakano, Y.
Mochizuki, and S. Tsushima
: Destabilization of DNA through Interstrand Crosslinking by UO2 2+
: Chem. Commun. 2019, doi:10.1039/C8CC09329F.
81

1 C. F. Fan, B. D. Olafson, M. Blanco and S. L. Hsu, Application of Molecular
Simulation to Derive Phase Diagrams of Binary Mixtures, Macromolecules,
1992, 25, 3667–3676.
2 J. G. E. M. Fraaije, B. A. C. van Vlimmeren, N. M. Maurits, M. Postma, O. A.
Evers, C. Hoffmann, P. Altevogt and G. Goldbeck-Wood, The Dynamic Mean-
Field Density Functional Method and Its Application to The Mesoscopic
Dynamics of Quenched Block Copolymer Melts, J. Chem. Phys., 1997, 106,
4260–4269.
3 R. Hasegawa and M. Doi, Dynamical Mean Field Calculation of Grafting
Reaction of End-Functionalized Polymer, Macromolecules, 1997, 30, 5490–
5493.
4 P. J. Hoogerbrugge and J. M. V. A. Koelman, Simulating Microscopic
Hydrodynamic Phenomena with Dissipative Particle Dynamics, Europhys. Lett.,
1992, 19, 155–160.
5 J. M. V. A. Koelman and P. J. Hoogerbrugge, Dynamic Simulations of Hard-
Sphere Suspensions Under Steady Shear, EPL (Europhysics Lett., 1993, 21, 363.
6 A. D. Mackie, J. B. Avalos and V. Navas, Dissipative Particle Dynamics with
Energy Conservation: Modelling of Heat Flow, Phys. Chem. Chem. Phys., 1999,
1, 2039–2049.
7 R. D. Groot and P. B. Warren, Dissipative Particle Dynamics: Bridging The Gap
Between Atomistic And Mesoscopic Simulation, J. Chem. Phys., 1997, 107,
4423–4435.
8 R. D. Groot and T. J. Madden, Dynamic Simulation of Diblock Copolymer
Microphase Separation, J. Chem. Phys., 1998, 108, 8713–8724.
9 C. M. Wijmans, B. Smit and R. D. Groot, Phase Behavior Of Monomeric
Mixtures and Polymer Solutions with Soft Interaction Potentials, J. Chem. Phys.,
2001, 114, 7644–7654.
10 N. Yamamoto, S. Fujishita and T. Tominaga, Structural Analysis of Hydrocarbon
Proton Conductive Membranes for Fuel Cell, 2014, 22–25.
11 S. Yamamoto, S. Hyodo and K. E. Y. Words, A Computer Simulation Study of
the Mesoscopic Structure of the Polyelectrolyte Membrane Nafion, Polym. J.,
2003, 35, 519–527.
82
12 N. Arai, Structural Analysis of Telechelic Polymer Solution using Dissipative
Particle Dynamics Simulations, Mol. Simul., 2015, 41, 996–1001.
13 J. C. Shillcock and R. Lipowsky, Equilibrium Structure and Lateral Stress
Distribution of Amphiphilic Bilayers from Dissipative Particle Dynamics
Simulations, J. Chem. Phys., 2002, 117, 5048–5061.
14 P. J. Flory and W. R. Krigbaum, Thermodynamics of High Polymer Solutions,
Annu. Rev. Phys. Chem., 1951, 2, 383–402.
15 R. D. D. Groot and K. L. L. Rabone, Mesoscopic Simulation of Cell Membrane
Damage, Morphology Change and Rupture by Nonionic Surfactants., Biophys. J.,
2001, 81, 725–736.
16 H. A. Benesi and J. H. Hildebrand, A Spectrophotometric Investigation of The
Interaction of Iodine with Aromatic Hydrocarbons, J. Am. Chem. Soc., 1949, 71,
2703–2707.
17 K. Van and D. W. In, Properties of Polymers: Their Estimation and Correlation
with Chemical Structure, Amsterdam, Elsevier, 1976.
18 M. M. Coleman, C. J. Serman, D. E. Bhagwagar and P. C. Painter, A Practical
Guide to Polymer Miscibility, Polymer (Guildf)., 1990, 31, 1187–1203.
19 J. Bicerano, Prediction Of Polymer Properties, CRC Press, 2002.
20 B. Prathab, V. Subramanian and T. M. Aminabhavi, Molecular Dynamics
Simulations to Investigate Polymer–Polymer and Polymer–Metal Oxide
Interactions, Polymer (Guildf)., 2007, 48, 409–416.
21 S. S. Jawalkar, S. G. Adoor, M. Sairam, M. N. Nadagouda and T. M.
Aminabhavi, Molecular Modeling on the Binary Blend Compatibility of
Poly(vinyl alcohol) and Poly(methyl methacrylate): An Atomistic Simulation and
Thermodynamic Approach, J. Phys. Chem. B, 2005, 109, 15611–15620.
22 F. Sepehr and S. J. Paddison, Dissipative Particle Dynamics Interaction
Parameters from Ab Initio Calculations, Chem. Phys. Lett., 2016, 645, 20–26.
23 D. G. Fedorov and K. Kitaura, The FRAGMENT MOLECULAR ORBIAL
METHOD: Practical Applications to Large Molecular Systems, CRC Press, Boca
Raton, 2009.
24 Paul, D. R., Polymer Blends, Academic Press:, New York, 1978.
25 N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller,
Equation of State Calculations by Fast Computing Machines, J. Chem. Phys.,
1953, 21, 1087–1092.
83
26 K. Kitaura, E. Ikeo, T. Asada, T. Nakano and M. Uebayasi, Fragment Molecular
Orbital Method: An Approximate Computational Method for Large Molecules,
Chem. Phys. Lett., 1999, 313, 701–706.
27 D. G. Fedorov and K. Kitaura, Pair Interaction Energy Decomposition Analysis,
J. Comput. Chem., 2007, 28, 222–237.
28 T. Tsukamoto, K. Kato, A. Kato, T. Nakano, Y. Mochizuki and K. Fukuzawa,
Implementation of Pair Interaction Energy DecompositionAnalysis and Its
Applications to Protein-Ligand Systems, J. Comput. Chem. Japan, 2015, 14, 1–9.
29 P. J. Flory, Principles of Polymer Chemistry, Comell University Press, NY, 1953.
30 P. Atkins and J. de Paula, Atkins’ Physical Chemistry, Oxford, 2nd edn., 1982.
31 W. J. Moore, Physical Chemistry, Prentice-Hall, 5th edn., 1999.
32 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R.
Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H.
Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G.
Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J.
Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.
A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E.
Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K.
Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N.
Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J.
Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C.
Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A.
Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B.
Foresman, J. V Ortiz, J. Cioslowski and D. J. Fox, .
33 S. Grimme, Semiempirical GGA-Type Density Functional Constructed with A
Long-Range Dispersion Correction., J. Comput. Chem., 2006, 27, 1787–1799.
34 C. Lee, W. Yang and R. G. Parr, Development of the Colle-Salvetti Correlation-
Energy Formula into A Functional of The Electron Density., Phys. Rev. B
Condens. Matter Mater. Phys., 1988, 37, 785–789.
35 https://www.j-octa.com/.
36 S. Tanaka, Y. Mochizuki, Y. Komeiji, Y. Okiyama and K. Fukuzawa, Electron-
Correlated Fragment-Molecular-Orbital Calculations for Biomolecular and Nano
Systems, Phys. Chem. Chem. Phys., 2014, 16, 10310–10344.
84
37 S. L. Mayo, B. D. Olafson, W. a G. Iii, E. Eb and E. a E. T. El, DREIDING: A
Generic Force Field for Molecular Simulations, J. Phys. Chem., 1990, 101,
8897–8909.
38 D. McIntyre, N. Rounds and E. Campos-Lopez, Thermodynamic and Structural
Parameters in Tri-Block Polymers., Polym. Prepr. (American Chem. Soc. Div.
Polym. Chem., 1969, 10, 531–537.
39 R. Koningsveld and L. A. Kleintjens, Thermodynamics of Multicomponent
Polymer Systems, Macromolecular Chemistry−8, 1973, 8, 197–230.
40 R. Koningsveld, L. A. Kleintjens and H. M. Schoffeleers, Thermodynamic
Aspects of Polymer Compatibility, Pure Appl. Chem., 1974, 39, 1–32.
41 A. Bondi, van der Waals Volumes and Radii, J. Phys. Chem., 1964, 68, 441–451.
42 A. K. Rappé, C. J. Casewit, K. S. Colwell, W. A. Goddard and W. M. Skiff, UFF,
a Full Periodic Table Force Field for Molecular Mechanics and Molecular
Dynamics Simulations, J. Am. Chem. Soc., 1992, 114, 10024–10035.
43 A. G. Schlijper, P. J. Hoogerbrugge and C. W. Manke, Computer Simulation of
Dilute Polymer Solutions with The Dissipative Particle Dynamics Method, J.
Rheol. (N. Y. N. Y)., 1995, 39, 567–579.
44 H. Watanabe, Y. Okiyama, T. Nakano and S. Tanaka, Incorporation of Solvation
Effects into The Fragment Molecular Orbital Calculations with The Poisson-
Boltzmann Equation, Chem. Phys. Lett., 2010, 500, 116–119.
45 D. J. Tannor, B. Marten, R. Murphy, R. A. Friesner, D. Sitkoff, A. Nicholls, M.
Ringnalda, W. A. Goddard and B. Honig, Accurate First Principles Calculation
of Molecular Charge Distributions and Solvation Energies from Ab Initio
Quantum Mechanics and Continuum Dielectric Theory, J. Am. Chem. SOC,
1994, 116, 11875–11882.
46 Y. Okiyama, H. Watanabe, K. Fukuzawa, T. Nakano, Y. Mochizuki, T. Ishikawa,
S. Tanaka and K. Ebina, Application of The Fragment Molecular Orbital Method
for Determination of Atomic Charges on Polypeptides, Chem. Phys. Lett., 2007,
449, 329–335.
47 Y. Okiyama, H. Watanabe, K. Fukuzawa, T. Nakano, Y. Mochizuki, T. Ishikawa,
K. Ebina and S. Tanaka, Application of The Fragment Molecular Orbital Method
for Determination of Atomic Charges on Polypeptides. II. Towards an
Improvement of Force Fields Used for Classical Molecular Dynamics
Simulations, Chem. Phys. Lett., 2009, 467, 417–423.
85
48 U. C. Singh and P. A. Kollman, An Approach to Computing Electrostatic
Charges for Molecules, J. Comput. Chem., 1984, 5, 129–145.
49 Y. Okiyama, T. Nakano, C. Watanabe, K. Fukuzawa, Y. Mochizuki and S.
Tanaka, Fragment Molecular Orbital Calculations with Implicit Solvent Based on
the Poisson-Boltzmann Equation: Implementation and DNA Study, J. Phys.
Chem. B, 2018, 122, 4457–4471.
50 W. Rocchia, S. Sridharan, A. Nicholls, E. Alexov, A. Chiabrera and B. Honig,
Rapid Grid-Based Construction of The Molecular Surface and The Use of
Induced Surface Charge to Calculate Reaction Field Energies: Applications to
The Molecular Systems and Geometric Objects, J. Comput. Chem., 2002, 23,
128–137.
51 M. Szafran, M. M. Karelson, A. R. Katritzky, J. Koput and M. C. Zerner,
Reconsideration of Solvent Effects Calculated by Semiempirical Quantum
Chemical Methods, J. Comput. Chem., 1993, 14, 371–377.
52 K. A. Mauritz and R. B. Moore, State of Understanding of Nafion, Chem. Rev.,
2004, 104, 4535–4585.
53 T. D. Gierke, G. E. Munn and F. C. Wilson, The Morphology in Nafion
Perfluorinated Membrane Products, as Determined by Wide- and Small-Angle X-
Ray Studies, J. Polym. Sci. Polym. Phys. Ed., 1981, 19, 1687–1704.
54 H.-G. Haubold, T. Vad, H. Jungbluth and P. Hiller, Nano Structure of Nafion: a
SAXS study, Electrochim. Acta, 2001, 46, 1559–1563.
55 A. Saccà, A. Carbone, R. Pedicini, G. Portale, L. D’Ilario, A. Longo, A.
Martorana and E. Passalacqua, Structural and Electrochemical Investigation on
Re-Cast Nafion Membranes for Polymer Electrolyte Fuel Cells (PEFCS)
Application, J. Memb. Sci., 2006, 278, 105–113.
56 V. Barbi, S. S. Funari, R. Gehrke, N. Scharnagl and N. Stribeck, Nanostructure of
Nafion Membrane Material as A Function of Mechanical Load Studied by
SAXS, Polymer (Guildf)., 2003, 44, 4853–4861.
57 M. Fujimura, T. Hashimoto and H. Kawai, Small-Angle X-Ray Scattering Study
of Perfluorinated Ionomer Membranes. 2. Models for Ionic Scattering Maximum,
Macromolecules, 1982, 15, 136–144.
58 J. A. Dura, V. S. Murthi, M. Hartman, S. K. Satija and C. F. Majkrzak,
Multilamellar Interface Structures in Nafion, Macromolecules, 2009, 42, 4769–
4774.
86
59 F. Xu, O. Diat, G. Gebel and A. Morin, Determination of Transverse Water
Concentration Profile Through MEA in a Fuel Cell Using Neutron Scattering, J.
Electrochem. Soc., 2007, 154, B1389.
60 G. Gebel, Structural Evolution of Water Swollen Perfluorosulfonated Ionomers
from Dry Membrane to Solution, Polymer (Guildf)., 2000, 41, 5829–5838.
61 Z. Porat, J. R. Fryer, M. Huxham and I. Rubinstein, Electron Microscopy
Investigation of the Microstructure of Nafion Films, J. Phys. Chem., 1995, 99,
4667–4671.
62 P. J. James, J. A. Elliott, T. J. McMaster, J. M. Newton, A. M. S. Elliott, S.
Hanna and M. J. Miles, Hydration of Nafion studied by AFM and X-ray
scattering, J. Mater. Sci., 2000, 35, 5111–5119.
63 R. Buzzoni, S. Bordiga, G. Ricchiardi, G. Spoto and A. Zecchina, Interaction of
H2O, CH3OH, (CH3)2O, CH3CN, and Pyridine with the Superacid
Perfluorosulfonic Membrane Nafion: An IR and Raman Study, J. Phys. Chem.,
1995, 99, 11937–11951.
64 K. a. Mauritz and C. E. Rogers, A Water Sorption Isotherm Model for Ionomer
Membranes with Cluster Morphologies, Macromolecules, 1985, 18, 483–491.
65 M. Eikerling, A. A. Kornyshev and U. Stimming, Electrophysical Properties of
Polymer Electrolyte Membranes: A Random Network Model, J. Phys. Chem. B,
1997, 101, 10807–10820.
66 P. A. Cirkel and T. Okada, A Comparison of Mechanical and Electrical
Percolation during the Gelling of Nafion Solutions, Macromolecules, 2000, 33,
4921–4925.
67 W. Y. Hsu and T. D. Gierke, Ion Transport and Clustering in Nafion
Perfluorinated Membranes, J. Memb. Sci., 1983, 13, 307–326.
68 R. Uegaki, Y. Akiyama, S. Tojo, Y. Honda and S. Nishijima, Radical-Induced
Degradation Mechanism of Perfluorinated Polymer Electrolyte Membrane, J.
Power Sources, 2011, 196, 9856–9861.
69 M. K. Kadirov, A. Bosnjakovic and S. Schlick, Membrane-Derived Fluorinated
Radicals Detected by Electron Spin Resonance in UV-Irradiated Nafion and Dow
Ionomers: Effect of Counterions and H 2 O 2, J. Phys. Chem. B, 2005, 109,
7664–7670.
87
70 A. Panchenko, H. Dilger, E. Möller, T. Sixt and E. Roduner, In Situ EPR
Investigation of Polymer Electrolyte Membrane Degradation in Fuel Cell
Applications, J. Power Sources, 2004, 127, 325–330.
71 M. K. Petersen and G. A. Voth, Characterization of the Solvation and Transport
of the Hydrated Proton in the Perfluorosulfonic Acid Membrane Nafion, J. Phys.
Chem. B, 2006, 110, 18594–18600.
72 M. K. Petersen, F. Wang, N. P. Blake, H. Metiu and G. A. Voth, Excess Proton
Solvation and Delocalization in a Hydrophilic Pocket of the Proton Conducting
Polymer Membrane Nafion, J. Phys. Chem. B, 2005, 109, 3727–3730.
73 S. Feng and G. A. Voth, Proton Solvation and Transport in Hydrated Nafion, J.
Phys. Chem. B, 2011, 115, 5903–5912.
74 Y.-K. Choe, E. Tsuchida and T. Ikeshoji, First-principles Molecular Dynamics
Study on Aqueous Sulfuric Acid Solutions, J. Chem. Phys., 2007, 126, 154510.
75 Y.-K. Choe, E. Tsuchida, T. Ikeshoji, S. Yamakawa and S. Hyodo, Nature of
Water Transport and Electro-Osmosis in Nafion: Insights from First-Principles
Molecular Dynamics Simulations under an Electric Field, J. Phys. Chem. B,
2008, 112, 11586–11594.
76 Y.-K. Choe, E. Tsuchida, T. Ikeshoji, S. Yamakawa and S.-A. Hyodo, Nature of
Proton Dynamics in a Polymer Electrolyte Membrane, Nafion: A First-Principles
Molecular Dynamics Study, Phys. Chem. Chem. Phys., 2009, 11, 3892.
77 R. Devanathan, A. Venkatnathan, R. Rousseau, M. Dupuis, T. Frigato, W. Gu
and V. Helms, Atomistic Simulation of Water Percolation and Proton Hopping in
Nafion Fuel Cell Membrane, J. Phys. Chem. B, 2010, 114, 13681–13690.
78 R. Devanathan, A. Venkatnathan and M. Dupuis, Atomistic Simulation of Nafion
Membrane: I. Effect of Hydration on Membrane Nanostructure, J. Phys. Chem.
B, 2007, 111, 8069–8079.
79 A. Venkatnathan, R. Devanathan and M. Dupuis, Atomistic Simulations of
Hydrated Nafion and Temperature Effects on Hydronium Ion Mobility, J. Phys.
Chem. B, 2007, 111, 7234–7244.
80 T. Kawakami and I. Shigemoto, Molecular Dynamics Studies on The Structures
of Polymer Electrolyte Membranes and Diffusion Mechanism of Protons and
Small Molecules, Polymer (Guildf)., 2014, 55, 6309–6319.
88
81 J. Kabrane and A. J. a Aquino, Electronic Structure and Vibrational Mode Study
of Nafion Membrane Interfacial Water Interactions, J. Phys. Chem. A, 2015, 119,
1754–1764.
82 T. H. Yu, Y. Sha, W.-G. Liu, B. V Merinov, P. Shirvanian and W. A. Goddard,
Mechanism for Degradation of Nafion in PEM Fuel Cells from Quantum
Mechanics Calculations, J. Am. Chem. Soc., 2011, 133, 19857–19863.
83 K. D. Kreuer, M. Schuster, B. Obliers, O. Diat, U. Traub, A. Fuchs, U. Klock, S.
J. Paddison and J. Maier, Short-Side-Chain Proton Conducting Perfluorosulfonic
Acid Ionomers: Why They Perform Better in PEM Fuel Cells, J. Power Sources,
2008, 178, 499–509.
84 D. Brandell, J. Karo, A. Liivat and J. O. Thomas, Molecular Dynamics Studies of
the Nafion®, Dow® and Aciplex® Fuel-Cell Polymer Membrane Systems, J.
Mol. Model., 2007, 13, 1039–1046.
85 R. Devanathan and M. Dupuis, Insight From Molecular Modelling: Does The
Polymer Side Chain Length Matter For Transport Properties of Perfluorosulfonic
Acid Membranes, Phys. Chem. Chem. Phys., 2012, 14, 11281.
86 J. Pozuelo, E. Riande, E. Saiz and V. Compañ, Molecular Dynamics Simulations
of Proton Conduction in Sulfonated Poly(phenyl sulfone)s, Macromolecules,
2006, 39, 8862–8866.
87 S. Roy, D. Markova, A. Kumar, M. Klapper and F. Muller-Plathe, Morphology
of Phosphonic Acid-Functionalized Block Copolymers Studied by Dissipative
Particle Dynamics, Macromolecules, 2009, 42, 841–848.
88 J. Miyake, R. Taki, T. Mochizuki, R. Shimizu, R. Akiyama, M. Uchida and K.
Miyatake, Design of Flexible Polyphenylene Proton-Conducting Membrane for
Next-Generation Fuel Cells, Sci. Adv., 2017, 3, eaao0476.
89 Y. Andoh, S. Okazaki and R. Ueoka, Molecular Dynamics Study of Lipid
Bilayers Modeling the Plasma Membranes of Normal Murine Thymocytes and
Leukemic GRSL Cells, Biochim. Biophys. Acta - Biomembr., 2013, 1828, 1259–
1270.
90 M. J. Abraham, T. Murtola, R. Schulz, S. Páll, J. C. Smith, B. Hess and E.
Lindah, Gromacs: High Performance Molecular Simulations Through Multi-
Level Parallelism from Laptops to Supercomputers, SoftwareX, 2015, 1–2, 19–
25.
89
91 J. C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C.
Chipot, R. D. Skeel, L. Kalé and K. Schulten, Scalable Molecular Dynamics with
NAMD, J. Comput. Chem., 2005, 26, 1781–1802.
92 S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J.
Comput. Phys., 1995, 117, 1–19.
93 A.-T. Kuo, W. Shinoda and S. Okazaki, Molecular Dynamics Study of the
Morphology of Hydrated Perfluorosulfonic Acid Polymer Membranes, J. Phys.
Chem. C, 2016, 120, 25832–25842.
94 C. K. Knox and G. A. Voth, Probing Selected Morphological Models of
Hydrated Nafion Using Large-Scale Molecular Dynamics Simulations, J. Phys.
Chem. B, 2010, 114, 3205–3218.
95 P. V. Komarov, P. G. Khalatur and A. R. Khokhlov, Large-Scale Atomistic and
Quantum-Mechanical Simulations of a Nafion Membrane: Morphology, Proton
Solvation and Charge Transport, Beilstein J. Nanotechnol., 2013, 4, 567–587.
96 S. Liu, J. Savage and G. A. Voth, Mesoscale Study of Proton Transport in Proton
Exchange Membranes: Role of Morphology, J. Phys. Chem. C, 2015, 119, 1753–
1762.
97 R. Jorn and G. A. Voth, Mesoscale Simulation of Proton Transport in Proton
Exchange Membranes, J. Phys. Chem. C, 2012, 116, 10476–10489.
98 J. T. Wescott, Y. Qi, L. Subramanian and T. Weston Capehart, Mesoscale
Simulation of Morphology in Hydrated Perfluorosulfonic Acid Membranes, J.
Chem. Phys., 2006, 124, 134702.
99 D. Y. Galperin and A. R. Khokhlov, Mesoscopic Morphology of Proton-
Conducting Polyelectrolyte Membranes of Nafion Type: A Self-Consistent Mean
Field Simulation, Macromol. Theory Simulations, 2006, 15, 137–146.
100 K. Malek, M. Eikerling, Q. Wang, Z. Liu, S. Otsuka, K. Akizuki and M. Abe,
Nanophase Segregation and Water Dynamics in Hydrated Nafion: Molecular
Modeling and Experimental Validation, J. Chem. Phys., 2008, 129, 204702.
101 M. Ghelichi, K. Malek and M. H. Eikerling, Ionomer Self-Assembly in Dilute
Solution Studied by Coarse-Grained Molecular Dynamics, Macromolecules,
2016, 49, 1479–1489.
102 G. Dorenbos and K. Morohoshi, Modeling Gas Permeation Through Membranes
by Kinetic Monte Carlo: Applications to H 2 , O 2 , and N 2 in Hydrated Nafion
®, J. Chem. Phys., 2011, 134, 044133.
90
103 M.-T. Lee, A. Vishnyakov and A. V. Neimark, Coarse-Grained Model of Water
Diffusion and Proton Conductivity in Hydrated Polyelectrolyte Membrane, J.
Chem. Phys., 2016, 144, 014902.
104 M.-T. Lee, A. Vishnyakov and A. V. Neimark, Modeling Proton Dissociation
and Transfer Using Dissipative Particle Dynamics Simulation, J. Chem. Theory
Comput., 2015, 11, 4395–4403.
105 A. Vishnyakov and A. V. Neimark, Self-Assembly in Nafion Membranes upon
Hydration: Water Mobility and Adsorption Isotherms, J. Phys. Chem. B, 2014,
118, 11353–11364.
106 P. V. Komarov, I. N. Veselov, P. P. Chu, P. G. Khalatur and A. R. Khokhlov,
Atomistic and Mesoscale Simulation of Polymer Electrolyte Membranes Based
on Sulfonated Poly(Ether Ether Ketone), Chem. Phys. Lett., 2010, 487, 291–296.
107 D. Wu, S. J. Paddison and J. A. Elliott, A Comparative Study of The Hydrated
Morphologies of Perfluorosulfonic Acid Fuel Cell Membranes with Mesoscopic
Simulations, Energy Environ. Sci., 2008, 1, 284.
108 T. A. Zawodzinski, M. Neeman, L. O. Sillerud and S. Gottesfeld, Determination
of Water Diffusion Coefficients in Perfluorosulfonate Ionomeric Membranes, J.
Phys. Chem., 1991, 95, 6040–6044.
109 X. Wu, X. Wang, G. He and J. Benziger, Differences in Water Sorption and
Proton Conductivity between Nafion and SPEEK, J. Polym. Sci. Part B Polym.
Phys., 2011, 49, 1437–1445.
110 J. J. Fontanella, C. A. Edmondson, M. C. Wintersgill, Y. Wu and S. G.
Greenbaum, High-Pressure Electrical Conductivity and NMR Studies in Variable
Equivalent Weight NAFION Membranes, Macromolecules, 1996, 29, 4944–
4951.
111 R. Devanathan, A. Venkatnathan, R. Rousseau, M. Dupuis, T. Frigato, W. Gu
and V. Helms, Atomistic Simulation of Water Percolation and Proton Hopping in
Nation Fuel Cell Membrane, J. Phys. Chem. B, 2010, 114, 13681–13690.
112 J. M. J. Swanson, C. M. Maupin, H. Chen, M. K. Petersen, J. Xu, Y. Wu and G.
A. Voth, Proton Solvation and Transport in Aqueous and Biomolecular Systems:
Insights from Computer Simulations, J. Phys. Chem. B, 2007, 111, 4300–4314.
113 S. Kawamoto, M. L. Klein and W. Shinoda, Coarse-grained Molecular Dynamics
Study of Membrane Fusion: Curvature Effects on Free Energy Barriers Along
The Stalk Mechanism, J. Chem. Phys., 2015, 143, 243112
91
114 S. Leekumjorn and A. K. Sum, Molecular Characterization of Gel and Liquid-
Crystalline Structures of Fully Hydrated POPC and POPE Bilayers, J. Phys.
Chem. B, 2007, 111, 6026–6033.
115 R. J. Muckom, F. Stanzione, R. D. Gandour and A. K. Sum, Dendritic
Amphiphiles Strongly Affect the Biophysical Properties of DPPC Bilayer
Membranes, J. Phys. Chem. B, 2013, 117, 1810–1818.
116 M. Hu, F. Stanzione, A. K. Sum, R. Faller and M. Deserno, Design Principles for
Nanoparticles Enveloped by A Polymer-Tethered Lipid Membrane, ACS Nano,
2015, 9, 9942–9954.
117 B. Peng, X.-Y. Ding, C. Sun, W. Liu, J. Z. H. Zhang and X. Zhao, The Effect of
POPC Acyl Chains Packing by Aromatic Amino Acid Methyl Esters Investigated
by ATR-FTIR Combined with QM Calculations., RSC Adv., 2016, 6, 45569–
45577.
118 T. Aoyagi, F. Sawa, T. Shoji, H. Fukunaga, J. Takimoto and M. Doi, A General-
Purpose Coarse-Grained Molecular Dynamics Program, Comput. Phys.
Commun., 2002, 145, 267–279.
119 N. Kuerka, S. Tristram-Nagle and J. F. Nagle, Structure of Fully Hydrated Fluid
Phase Lipid Bilayers with Monounsaturated Chains, J. Membr. Biol., 2006, 208,
193–202.
120 N. Kuerka, M. P. Nieh and J. Katsaras, Fluid Phase Lipid Areas And Bilayer
Thicknesses of Commonly Used Phosphatidylcholines as A Function of
Temperature, Biochim. Biophys. Acta - Biomembr., 2011, 1808, 2761–2771.
121 P. Jurkiewicz, L. Cwiklik, A. Vojtíšková, P. Jungwirth and M. Hof, Structure,
Dynamics, and Hydration of POPC/POPS Bilayers Suspended in NaCl, KCl, and
CsCl Solutions, Biochim. Biophys. Acta - Biomembr., 2012, 1818, 609–616.
122 A. A. Gurtovenko and I. Vattulainen, Effect of NaCl and KCl on
Phosphatidylcholine and Phosphatidylethanolamine Lipid Membranes: Insight
from Atomic-Scale Simulations for Understanding Salt-Induced Effects in The
Plasma Membrane, J. Phys. Chem. B, 2008, 112, 1953–1962.
123 F. a Nezil and M. Bloom, Combined Influence of Cholesterol and Synthetic
Amphiphillic Peptides Upon Bilayer Thickness in Model Membranes., Biophys.
J., 1992, 61, 1176–1183.
92
124 G. Kacar, C. Atilgan and A. S. Özen, Mapping and Reverse-Mapping of The
Morphologies for A Molecular Understanding of The Self-assembly of
Fluorinated Block Copolymers, J. Phys. Chem. C, 2010, 114, 370–382.
125 V. A. Harmandaris, N. P. Adhikari, N. F. A. Van Der Vegt and K. Kremer,
Hierarchical Modeling of Polystyrene: From Atomistic to Coarse-Grained
Simulations, Macromolecules, 2006, 39, 6708–6719.
126 P. Doruker and W. L. Mattice, A Second Generation of Mapping/Reverse
Mapping of Coarse-Grained and Fully Atomistic Models of Polymer Melts,
Macromol. Theory Simulations, 1999, 8, 463–478.
127 P. Doruker and W. L. Mattice, Reverse Mapping of Coarse-Grained Polyethylene
Chains from The Second Nearest Neighbor Diamond Lattice to An Atomistic
Model in Continuous Space, Macromolecules, 1997, 30, 5520–5526.
128 T. Spyriouni, C. Tzoumanekas, D. Theodorou, F. Müller-Plathe, G. Milano, F.
Mu, G. Milano, F. Müller-Plathe and G. Milano, Coarse-Grained And Reverse-
Mapped United-Atom Simulations of Long-Chain Atactic Polystyrene Melts:
Structure, Thermodynamic Properties, Chain Conformation, and Entanglements,
Macromolecules, 2007, 40, 3876–3885.
129 A. Maiti and S. McGrother, Bead–Bead Interaction Parameters in Dissipative
Particle Dynamics: Relation to Bead-Size, Solubility Parameter, and Surface
Tension, J. Chem. Phys., 2004, 120, 1594–1601.
130 H. Goel, P. R. Chandran, K. Mitra, S. Majumdar and P. Ray, Estimation of
Interfacial Tension for Immiscible and Partially Miscible Liquid Systems by
Dissipative Particle Dynamics, Chem. Phys. Lett., 2014, 600, 62–67.
131 E. Mayoral and a G. Goicochea, Modeling The Temperature Dependent
Interfacial Tension Between Organic Solvents and Water Using Dissipative
Particle Dynamics, J. Chem. Phys., 2013, 138, 094703.
132 N. M. O’Boyle, M. Banck, C. A. James, C. Morley, T. Vandermeersch and G. R.
Hutchison, Open Babel: An Open Chemical Toolbox, J. Cheminform., 2011, 3,
1–14.
133 K. Lindorff-Larsen, S. Piana, R. O. Dror and D. E. Shaw, How Fast-Folding
Proteins Fold., Science, 2011, 334, 517–20.
134 H. Doi, S. Saitou, K. Okuwaki, T. Naito and Y. Mochizuki, Development And
Performance Evaluation of a Simulation Code for Dissipative Particle Dynamics
(DPD) CAMUS, J. Comput. Chem. Japan, 2018, 16, 126–128.
93
135 H. Doi, K. Okuwaki, T. Naito, S. Saitou and Y. Mochizuki, A Portable Code for
Dissipative Particle Dynamics (DPD) Simulations with Additional Specific
Interactions, Chem-Bio Informatics J., 2018, 18, 70–85.
136 S. Honda, K. Yamasaki, Y. Sawada and H. Morii, 10 Residue Folded Peptide
Designed by Segment Statistics, Structure, 2004, 12, 1507–1518.
137 S. Honda, T. Akiba, Y. S. Kato, Y. Sawada, M. Sekijima, M. Ishimura, A.
Ooishi, H. Watanabe, T. Odahara and K. Harata, Crystal Structure of a Ten-
Amino Acid Protein Crystal Structure of a Ten-Amino Acid Protein, J. Am.
Chem. Soc., 2008, 130, 15327–15331.
94

Figure 5. ................................................................ 13
Figure 6. Nitrobenzene-NitrobenzeneMC
Figure 9. Polyisobuthylene- Diisobuthyl Ketone χ ...................... 20
Figure 10. Polyisoprene -Polystyrene χ ....................................... 22
Figure 11. FMO-PB ............................................................... 27
Figure 13. PEEK ............................................ 31
Figure 15. Nafion SPEEK DPD ...................................... 33
Figure 16. Figure 15 Nafion (b) 20 vol
................................................................................ 37
Figure 17. Figure 15 Nafion (b) 20 vol
........................................................................ 38
Figure 19. Figure 15 Nafionbt =
500 .............................................................................................................. 39
Figure 20. Figure 15 SPEEKt = 500 . 39
Figure 21. Nafion(t = 500) .................................................. 41
Figure 22. Nafiont = 500 RDF 41
Figure 23. Nafion (10,20,30 vol%)..... 42
Figure 24. Nafion, SPEEK ................ 43
Figure 25. Nafion SPEEK .................................... 45
Figure 26. Nafion SPEEK .................................... 45
Figure 27. Nafion .......................... 47
Figure 28. Nafion DPD .................................................... 47
Figure 29. Nafion DPD ............................................................... 48
Figure 31. Nafion ...... 49
Figure 32. POPC ........................................................ 51
Figure 33. POPC ............................ 52
Figure 34. POPC DPD .................................................................................. 52
Figure 35. DPD (POPC 13%) ............................ 55
Figure 36. DPD POPC 20% .......................... 56
Figure 37. POPC XYZ ..... 56
Figure 38. POPC ............................................ 57
Figure 39. DPPC, DOTAP ........................................... 58
Figure 40. OH-(Wm) ...................................... 58
.................................................................................................................... 59
............................................................................................ 63
Figure 45. Nafion FMO ........................................................ 64
Figure 46. POPC FMO ............................................. 65
Figure 47. POPC FMO ......................................... 65
Figure 48. Hexane-Hexane scikit-learn
............................................................................................................ 66
................................................................................................ 67
Figure 52. FMO
........................................................................................................ 73
Figure 54. Chignolin ......................... 74
Figure 55. Chignolin DPD .................................................................... 76
Figure 56. Super Chignolin DPD ......................................................... 76
96

Table 3. Hexane (label 1)-Nitrobenzene (label 2) 300K
(), scale factor(), () ................... 16
Table 4. Hexane (label 1)-Nitrobenzene(label 2) PIEDA ................... 18
Table 5. Polyisobuthylene (label 1) - Diisobuthyl Ketonelabel 2 300K
(), scale factor(), () ............................... 19
Table 6. Polyisobuthylene-Diisobuthyl Ketonedib ...................... 19
Table 7. Polyisoprene (label 1)-Polystyrene (label 2) 300K
(), scale factor(), () ....................................................... 21
Table 8. 300K Polyisoprene (pip)-Polystyrene (ps) ............ 21
Table 9. Nafion 350K C ......... 34
Table 10. Nafion 350K (kcal/mol) S Z . 34
Table 11. Nafion χ aij (350K) ............................................................. 35
Table 12. SPEEK 350K C ...... 35
Table 13. SPEEK 350K (kcal/mol) S Z 36
Table 14. SPEEK χ(350K) ................................................................ 36
Table 15. Nafion ............................. 48
Table 16. (E)(F)(300K, kcal/mol)S ............. 53
Table 17. POPC 300K (kcal/mol) S, Z ... 54
Table 18. POPC χ (300K) .................................................................... 55
Table 19. DPD .............................................. 59
Table 20. -- (dyn/cm, 300K) ........... 71
Table 21. (10-10Pa-1) ........ 72
....................................................................................................................... 75
2.5.