Model-based research toward design of innovative materials: Molecular weight prediction of bridged polysilsesquioxanes

Article abstract of DOI:10.1039/d0ra02909b

Toward the design and manipulation of innovative materials, we propose a new concept called "model-based research (MBR)". In MBR, measurable physical and chemical properties of materials are mathematically modelled by explanatory parameters obtained by computer simulation from an atomistic point of view. To demonstrate the potential of MBR, we modelled the molecular weights of a series of polysilsesquioxanes with respect to the H2O/silane molar ratio employed for the polymerization of monomers bis(triethoxysilyl)methane, ethane, ethylene, and acetylene (BTES-M, -E1, -E2, and -E3), as an example. The equation y = axn well reproduced the behaviour of the molecular weights of the BTES series, in which a and n were obtained using the calculated molecular parameters for monomers as the explanatory parameters. Detailed understanding and discussion were theoretically possible on the basis of the mathematical model. We predicted the molecular weights of polymers that would be obtained from monomers BTES-P and BTES-Ph with C3H6 and C6H4 as the spacer, respectively, using the mathematical model. Experimental validation of these polymers clearly showed the possibility of qualitative categorization. Our proposed concept, MBR, is a powerful tool to analyse materials science toward innovative materials design.

Full text of DOI:10.1039/d0ra02909b

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Model-based research toward design of innovative
materials: molecular weight prediction of bridged
polysilsesquioxanes†
Cite this: RSC Adv., 2020, 10, 28595
ab
*
Takayoshi Ishimoto,
Satoru Tsukada,a Shin Wakitani,c Kenji Sato,a Daiki Saito,d
Yuki Nakanishi,d Sakino Takase,d Takashi Hamada,ad Joji Ohshita
ade
*
a
*
and Hiroyuki Kai
Toward the design and manipulation of innovative materials, we propose a new concept called “model-
based research (MBR)”. In MBR, measurable physical and chemical properties of materials are
mathematically modelled by explanatory parameters obtained by computer simulation from an atomistic
point of view. To demonstrate the potential of MBR, we modelled the molecular weights of a series of
polysilsesquioxanes with respect to the H2O/silane molar ratio employed for the polymerization of
monomers bis(triethoxysilyl)methane, ethane, ethylene, and acetylene (BTES-M, -E1, -E2, and -E3), as an
example. The equation y ¼ axn well reproduced the behaviour of the molecular weights of the BTES
series, in which a and n were obtained using the calculated molecular parameters for monomers as the
explanatory parameters. Detailed understanding and discussion were theoretically possible on the basis
of the mathematical model. We predicted the molecular weights of polymers that would be obtained
from monomers BTES-P and BTES-Ph with C3H6 and C6H4 as the spacer, respectively, using the
mathematical model. Experimental validation of these polymers clearly showed the possibility of
qualitative categorization. Our proposed concept, MBR, is a powerful tool to analyse materials science
toward innovative materials design.
Received 31st March 2020
Accepted 10th July 2020
DOI: 10.1039/d0ra02909b
rsc.li/rsc-advances
intermolecular interaction, molecular alignment, and interfa-
cial structure, which are difficult to predict or oen unpredict-
Introduction
able yet exert
a signicant inuence on the material
Materials development based on simple molecular design is
generally difficult as the atomic-level molecular properties do
not always relate directly to the functionalities of materials that
are composed of a huge number of molecules in the condensed
states. Even though the molecular properties can be predicted
with high reliability by molecular simulation at a high level of
theory,1–5 many other large-scale factors exist, including
functionalities. This also applies to the monomer–polymer
relationship as the properties and functionalities of polymers
do not always directly reect those of monomers. For example,
network or highly branched polymers have molecular weights
that are difficult to control, in marked contrast to that linear
polymers have molecular weights that well depend on monomer
reactivity and can be much more easily controlled by, for
example, the loading ratio of the monomer and the terminating
and/or initiating reagent.6–8
Polysilsesquioxanes (PSQs) have received much attention as
typical organic–inorganic hybrid materials.9–13 They can be
prepared by the hydrolysis/condensation polymerization of tri-
functionalized silanes and consist of a three-dimensional
siloxane network that gives rise to thermal and mechanical
stability of the resulting PSQ materials. For the preparation of
PSQ lms, liquid PSQs prepared by controlled polymerization
are coated on a substrate and then calcined at a high temper-
ature to further facilitate the condensation, as shown in
Fig. 1.14,15
aAdvanced Materials Laboratory, Advanced Automotive Research Collaborative
Laboratory, Graduate School of Engineering, Hiroshima University, 1-4-1
Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan. E-mail: jo@
hiroshima-u.ac.jp; kaihi@hiroshima-u.ac.jp; tishimo@yokohama-cu.ac.jp
bGraduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-
ku, Yokohama 236-0027, Japan
cFundamentals of Model-Based Development, Graduate School of Advanced Science
and Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima,
Hiroshima 739-8527, Japan
dDepartment of Applied Chemistry, Graduate School of Advanced Science and
Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima,
Hiroshima 739-8527, Japan
eDivision of Materials Model-Based Research, Digital Monozukuri (Manufacturing)
Education and Research Center, Hiroshima University, Higashi-Hiroshima 739-
0046, Japan
In this process, the control of the molecular weights of the
liquid PSQs is of utmost importance. To avoid signicant
shrinking of the lm due to condensation, which may produce
† Electronic supplementary information (ESI) available. See DOI:
10.1039/d0ra02909b
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the atomic level is not precisely explained, they should have
a strong correlation that may be linked by an equation. This
concept is expected to provide a new strategy for the design of
materials at the atomic level.
MBR is based on the efficient automobile engine
manufacturing process called “model-based development
(MBD)”.21 The basic idea of MBD is to divide a complex whole-
engine system into simple parts that can be simulated by
a computer. In fact, MBD achieved a new high-performance
automobile engine by the so-called “V-type development
process”. Although MBD is very useful for efficient automobile
engine manufacture as it reduces both cost and time, the direct
application of MBD to materials development is difficult
because material properties are based on a high complexity of
multi-scale and multi-physics phenomena. To overcome such
difficulties in materials development, we proposed the new
concept, MBR, for efficient research in materials science, as
mentioned above.
We believe that acquiring a fundamental understanding at
the atomic level is one of the key factors for modelling material
properties. To construct a model for material properties, the
machine learning technique is a very powerful tool. The
collaboration of three techniques, i.e., measurement and anal-
ysis by experimental techniques, obtaining geometry and elec-
tronic structure by computer simulation, and modelling by
machine learning, are necessary in MBR. Based on a funda-
mental understanding of physical and chemical properties and
models, it will be possible to design and develop innovative
materials. Furthermore, the constructed models may be used
for the design of related materials. Here, we modelled the
measured molecular weights of the bridged PSQs by using
explanatory parameters based on geometry and electronic
structure obtained by computer simulation as an example of
MBR.
Fig. 1 Preparation of polysilsesquioxane by hydrolysis/condensation
of triethoxysilane, including controlled polymerization by partial
hydrolysis/condensation of EtO–Si bonds (a) and calcination in air to
further enhance network formation (b).
cracks and/or pinholes on the lm, the liquid PSQs should have
as high a polymerization degree, i.e., molecular weight, as
possible. However, an exceedingly high polymerization degree
should be avoided as it would result in the formation of non-
processible solid PSQs. We were able to prepare three types of
bridged PSQs from the corresponding monomers, as shown in
Fig. 2.14,15 However, to our surprise, their polymerization
behaviours were markedly different in spite of the fact that the
monomer structures were nearly the same except for the bond
orders of the bridging C2 units. Based on both experimental
and theoretical considerations, we concluded that the different
polymerization behaviours arise from the different rigidities of
the C2 bridges. However, the molecular weights of such network
polymers as PSQs are still difficult to predict precisely.
To approach this challenging problem, the key feature of our
work is the application of machine learning16,17 to understand
the driving force for the formation of macroscopic properties
from an atomistic point of view and to predict and design new
materials. The use of machine learning techniques in materials
science is still in its infancy and the applications are limited to
simple surface adsorption, stability of homogeneous materials,
derivatives of molecules, and so on.18–20 To apply machine
learning for macroscopic properties, such as thermal conduc-
tivity, hardness, density, and so on in complex systems, it is
necessary to propose a new strategy beyond the present
machine learning approaches.
Methods
General procedure for synthesis
In this study, we propose a new concept on the basis of
machine learning toward materials design, using the control of
the molecular weights of the bridged PSQs as an example. We
call this “model-based research (MBR)”, which is clearly
different from the conventional machine learning approach. In
MBR, material properties that are usually difficult to predict are
analysed by using a uniform mathematical model equation with
rather accurate parameters that are readily obtained by theo-
retical simulation at the atomic level. Even though the rela-
tionship between the material properties and the parameters at
Bis(triethoxysilyl)methane (BTES-M) was purchased from Gel-
est, Inc. 1,4-Bis(triethoxysilyl)benzene (BTES-Ph) and chlor-
oplatinic acid hexahydrate were purchased from Sigma-Aldrich
Co. LLC. Ethanol (super dehydrated (99.5)) and 6 mol Lꢀ1
hydrochloric acid used as the reaction solvent and catalyst,
respectively, were purchased from Wako Pure Chemical
Industries. These reagents were used as received without puri-
cation. Allyltriethoxysilane and triethoxysilane were purchased
from Tokyo Chemical Industry Co., Ltd. Toluene was purchased
from Nacalai Tesque, Inc., distilled from calcium hydride, and
ꢀ
dried over 4 A molecular sieves. The structures are shown in
Fig. 4. Gel permeation chromatography (GPC) was performed
with a high-performance liquid chromatograph (Shimadzu)
using three directly connected TSKgel G6000H columns (LC-
20AD pump, CTO-20A, and an RID-10A detector (Shimadzu))
with THF as the eluent at the ow rate of 1.0 mL minꢀ1. A 5–
10 wt% solution of sample was introduced aer ltration
through a 0.20 mm diameter membrane lter (DISMIC-13JP,
ADVANTEC). Polystyrene samples were used as standards.
Fig. 2 Monomers of bridged PSQs.
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NMR spectra were measured on
spectrometer.
a Varian System500
Machine learning
The least absolute shrinkage and selection operator (LASSO)26
method was used for logistic regression analysis because this
method provides a prediction model even when the number of
data is smaller than that of parameters. This method can
perform both variable selection and regularization to optimize
the regression model while avoiding overtting. The LASSO has
been extensively used for material science elds.27–32 The big
data analysis is generally popular approach for materials
science.27,31 However, it is sometimes difficult to prepare many
experimental or calculation data directly. Recently, the LASSO
was applied to small datasets for materials science.28 The
preparation of enough datasets for molecular weight of our
target polymer is also quite difficult due to the difficulty of
experiments and need long time for experimental cost. It is
necessary to analyse molecular weight trend from small data-
sets. Therefore, the LASSO method was adopted to optimize the
prediction model tting of the experimental values with the
molecular parameters. We rst determined the tting parame-
ters of experimental results (molecular weight). The tting
parameters and calculated values from electronic structure
calculations were prepared as objective and explanatory vari-
ables, respectively. By using LASSO analysis, we obtained the
explanatory parameters based on electronic structure calcula-
tion for tting parameters of experimental data of molecular
weight. Detailed procedure of model equation construction in
this study was shown in ESI.†
Synthesis of 1,4-bis(triethoxysilyl)propane (BTES-P)
BTES-P was synthesized with a slight modication of a previ-
ously reported method.22 The reaction was carried out under dry
air. A toluene solution (50 mL) of 3-(triethoxysilyl)propene (22.6
mL, 0.100 mol), triethoxysilane (22.5 mL, 0.120 mol), and
chloroplatinic acid hexahydrate (62.1 mg, 0.120 mmol) was
stirred for 22 hours at room temperature. Chloroplatinic acid
hexahydrate (51.8 mg, 0.100 mmol) was added and the reaction
mixture was stirred for another 16 hours. The reaction mixture
was evaporated and distilled under reduced pressure to yield
BTES-P as a clear colorless liquid (29.2 g, 79%). Bp 101–103 ꢁC
1
3
(0.21 torr). H NMR (500 MHz, CDCl3) d 0.73 (t, JHH ¼ 10 Hz,
4H), 1.22 (t, 3JHH ¼ 5 Hz, 18H), 1.54–1.58 (m, 2H), 3.81 (q, 3JHH
¼
5 Hz, 12H). 13C{1H} NMR (126 MHz, CDCl3) d 14.46, 16.63,
18.45, 58.42. 29Si{1H} NMR (99 MHz, CDCl3) d ꢀ45.3.
General procedure for preparation of poly(BTES-M),
poly(BTES-P), and poly(BTES-Ph)
The reactions were carried out in a fashion similar to that for
the polymerization of BTES-E1, -E2, and -E3.14,15 Into a four-
necked ask equipped with nitrogen inlet and outlet tubes
and a mechanical stirrer, BTES-R (5.00 mmol) and EtOH (50.00
mmol) were charged and the reaction mixture was cooled on an
ice bath for 10 minutes with stirring at 150 rpm under nitrogen
ow (360 mL minꢀ1). 6 mol Lꢀ1 Hydrochloric acid (0.525 mmol)
and distilled water were added in molar ratios of 0.9–3.2 for
H2O/BTES-monomer. The reaction mixture was stirred for an
additional 10 minutes at 0 ꢁC and then warmed to room
temperature and further stirred for 10 minutes. The reaction
mixture was stirred for 3 hours at 80 ꢁC to generate the polymer
as a viscous liquid. Molecular weights were determined by GPC
analysis.
Results and discussion
Polymer molecular weights
Fig. 3 shows the plots of molecular weight versus amount of
water for the polymerization of BTES-E1, -E2, and -E3, as re-
ported previously,16 together with those for BTES-M obtained in
the present study (Fig. 4).
The behaviour of the molecular weight changes of BTES-M is
similar to that of BTES-E1. To check the detailed structure of
BTES-M, we analysed the gel permeation chromatography (GPC)
and 29Si nuclear magnetic resonance (NMR) for BTES-M as
shown in Fig. 5.
Computational details
To obtain the explanatory parameters for the molecular weights
of the four types of alkoxysilanes, geometry optimization
calculations for the monomers were done by using B3LYP/6-
31G(d) level of theory. Solvent effects from ethanol were
considered by the polarized continuum model (PCM).23 All
ethoxy groups in the monomers were substituted by hydroxyl
groups in this study. As an explanatory variable for reactivity,
the dimerization energy of two monomers was calculated. The
proton association energy to a hydroxyl group, which is one of
the most important reaction steps for dimerization, was also
calculated. The exibilities between Si and Si stretching and Si–
X–Si (X ¼ C2H4, C2H2, C2, CH2, C3H6, and C6H4) bending in the
monomer structure were considered by ab initio molecular
dynamics (MD) calculation under B3LYP/6-31G(d). The time
step of 1.0 fs was used in the Verlet method.24 Iterative calcu-
lations were done until 10 000 steps. All electronic structure
calculations were performed by using the general atomic and
molecular electronic structure system (GAMESS).25 We also
modied GAMESS program for ab initio MD calculations.
The broad multiple peaks in Fig. 5(a) indicated the growth of
the polymer chain of BTES-M. A single sharp peak in the low
Fig. 3 Regression curves for BTES-M, -E1, -E2, and -E3 obtained by
LASSO method. Experimental results of molecular weight are also
plotted.
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Table 1 Optimized parameters a and n in y ¼ axn and coefficients of
determination of BTES-M, -E1, -E2, and -E3
R2
Fig. 4 Monomer structure of BTES-M.
a
n
BTES-M
BTES-E1
BTES-E2
BTES-E3
0.204
0.616
2.951
6.326
3.409
2.676
3.421
3.920
0.8142
0.8606
0.9263
0.8537
only two parameters, this equation well reproduced the exper-
imental molecular weights for all the BTES series, i.e., the R2
values were higher than 0.8, as shown in Table 1. Parameter
a was the smallest for BTES-M. For the C2-linked BTES
compounds, parameter a increased with increasing bond order
of the bridges. On the other hand, parameter n was the smallest
for BTES-E1.
Fig. 5 (a) GPC chart and (b) 29Si NMR spectrum of BTES-M. Sample
was synthesized under the H2O/silane molar ratio ¼ 2.6.
molecular weight region means the cyclic dimer formation. In
the NMR spectra shown in Fig. 5(b), the T2 and T3 mean two and
three dimensional bridged structures, respectively. The T2 and
T3 structures are mixed in BTES-M. The GPC chart and NMR
spectrum of BTES-M were also similar to the BTES-E1.7 This
behaviour markedly differed from our previous consideration
that higher molecular weights would be obtained as molecular
rigidity was enhanced. We had assumed that more exible
monomers should provide cyclic oligomers more easily, thereby
suppressing the molecular weight increase (Fig. 6).
The C1 bridge of BTES-M is much less exible than the
ethylene C2 bridge of BTES-E1. However, BTES-M gave polymers
with lower molecular weights than BTES-E1, indicating that
there may be important factors affecting the molecular weights
other than bridge exibility.
Construction of equation
To nd the controlling factors for a and n, regression analysis
was carried out by using the least absolute shrinkage and
selection operator (LASSO) method. As the rst step, we selected
atomic-scale parameters that had been obtained by computer
simulation of the compounds in ethanol as the potential
controlling factors. Meso-scale information, such as the
branching degree of the polymer structures and the reactivity of
the polymers/oligomers, seems to be also important factors that
control the polymerization reactions. It is also likely that larger
scale information, including viscosity of the polymer solution
and polymer shape (linear, coil, rod-like, etc.), exerts an inu-
ence on GPC analysis, thereby also affecting the molecular
weights. However, these meso-scale information may be under
the control of monomer molecular factors directly or indirectly.
It should be worthwhile if we could nd some monomer-scale
parameters that strongly affect the meso-scale properties,
such as the molecular weights of the polymers in the present
work, as this would prove the possibility of materials design by
atomic-scale tuning of geometry and electronic structure. As the
explanatory parameters for objective variables a and n, geom-
etry, electronic structure, and exibility parameters of the
monomer structures of BTES-M, -E1, -E2, and -E3 were selected.
The potential explanatory parameters examined in this study
are listed in Table 2.
The numbers of carbon and hydrogen atoms in the spacers
and their ratio (H/C), the surface area, and the volume of
monomers are the geometry parameters of the monomers. The
energy levels of the highest-occupied molecular orbital (HOMO)
and the lowest-unoccupied molecular orbital (LUMO) and the
atomic charges of silicon and oxygen are the electronic structure
parameters. The solvation energy was also calculated and the
proton association energy (DEassociation) was calculated by the
following eqn (1), where X is the spacer in the unit structure
(CH2, C2H4, C2H2, and C2).
Fitting of molecular weight
To nd a mathematical t of the plots in Fig. 3, we assumed the
equation y ¼ axn. Although this equation is simple, it is suitable
to extract the fundamental and important factors because only
two parameters are included. Based on the least squares
method, the parameters in the equation, a and n, were opti-
mized, as listed in Table 1, together with the coefficient of
determination (R2). Generally, with increasing the number of
parameters, the R2 is improved. While the equation y ¼ axn has
Fig. 6 Molecular weight changes depending on the reaction modes.
With two water molecules, a linear reaction gives a trimer, whereas
cyclization allows only the dimer formation.
DEassociation ¼ E((OH)3Si–X–Si(OH)2(OH2)+) ꢀ [E((OH)3Si–X–
Si(OH)3) + E(H+)]
(1)
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Table
2 Explanatory parameters based on geometry, electronic
weight change of PSQs and to nd the key mechanisms to
control the molecular weights for new targets by using these
equations.
structure, reactivity, and dynamics of unit structures of BTES-M, -E1,
-E2, and -E3
In our previous work on the reaction mechanism in the
polymerization of BTES-E1, -E2, and -E3,16 we demonstrated
that all the water used in the reactions was consumed to convert
ethoxy groups into silanol or disiloxane bonds. We also found
that the formation of cyclic units was mainly responsible for
suppressing the molecular weight increase in BTES-E1. We,
therefore, consider that the reactivity of silanol towards
condensation to form disiloxane bonds and the reaction selec-
tivity, i.e., linear chain growth or cyclization, signicantly affect
the molecular weights of the polymers.
Parameters
BTES-M BTES-E1 BTES-E2 BTES-E3
Number of carbons
Number of hydrogens
H/C
1
2
2
4
2
2
2
0
2
2
1
0
ꢀ2
Surface area (A )
162.6
133.4
195.2
152.3
188.0
146.9
181.2
141.4
ꢀ3
Volume (A )
HOMO (Ha)
LUMO (Ha)
ꢀ0.2903 ꢀ0.2780 ꢀ0.2813 ꢀ0.2881
0.0248
1.021
0.0375 ꢀ0.0336 ꢀ0.0189
0.973 0.950 0.852
Atomic charge of Si
Atomic charge of O
Solvation energy (kcal molꢀ1
ꢀ0.629 ꢀ0.625 ꢀ0.621 ꢀ0.602
)
ꢀ6.59 ꢀ12.29 ꢀ10.68 ꢀ12.70
DEassociation (kcal molꢀ1
)
5.73
ꢀ15.24
3.057
0.320
109.7
16.8
4.93
ꢀ5.91
4.535
0.279
148.0
15.8
3.96
ꢀ5.39
4.580
0.193
156.1
9.8
ꢀ0.68
ꢀ6.34
4.898
0.207
176.7
11.8
The atomic charges of oxygen and silicon and the H/C ratios
are involved in eqn (3) as the controlling factors of a. The atomic
charges of silicon are decreased in the order of BTES-M > BTES-
E1 > BTES-E2 > BTES-E3. Silicon is a p-acceptor as well as a s-
donor.34 As p-acceptors, the silicon atoms in BTES-E2 and BTES-
E3 accept a negative charge from ethylene and acetylene units.
In fact, the s*(Si)–p(C) interaction is clearly seen in the HOMO
of these molecules in addition to the n(O)–s*(Si) interaction
(Fig. 7). For BTES-M and BTES-E1 with a saturated carbon
spacer, however, the delocalization of s- and n-electrons is
observed to a smaller extent. In these molecules, the silicon
atoms seem to act as a s-donor. The smaller number of rela-
tively more electronegative carbons in BTES-M would lead to
a higher atomic charge of the silicon atoms than that in BTES-
E1. Usually, the higher atomic charge of silicon and the lower
atomic charge of oxygen would accelerate condensation reac-
tions that proceed via a substitution reaction of oxygen nucle-
ophile at the silicon centre. However, this contrasts with that
the higher atomic charge of silicon and the lower atomic charge
of oxygen decrease parameter a, suppressing the molecular
weight increase. Therefore, it is likely that parameter a is related
to the reaction selectivity. Entropically favoured linear chain
growth seems to be relatively enhanced under the milder situ-
ation with a lower atomic charge of silicon and a higher atomic
charge of oxygen, compared to cyclization. The H/C ratio reects
chain exibility: a higher ratio leads to lower chain-growth/
cyclization selectivity, thereby decreasing the molecular weight.
On the other hand, the LUMO energy level, the molecular
volume, and the number of hydrogen atoms on the spacer
contribute to parameter n. In general, the lower-lying LUMO
DEdimerization (kcal molꢀ1
)
ꢀ
R(Si/Si)Ave. (A)
a
ꢀ
DR(Si/Si) (A)
:(Si/C/Si)Ave. (ꢁ)
D:(Si/C/Si)a (ꢁ)
a
Difference of maximum and minimum values.
Proton association is considered an important step in acid-
catalyzed reactions. The dimerization energy of the unit struc-
ture (DEdimerization) was also calculated on the basis of the
following equation,
DEdimerization ¼ E((OH)3Si–X–Si(OH)2O(OH)2Si–X–Si(OH)3) +
E(H2O) ꢀ 2E((OH)3Si–X–Si(OH)3).
(2)
To take the structural exibility of the monomers into
account, ab initio molecular dynamics (MD) calculations were
performed for BTES-M, -E1, -E2, and -E3. We focused on the
averages of the Si/Si distance and the Si/C/Si angle during
the MD simulations. Differences between the maximum and the
minimum of those motions were also analysed.
To obtain the mathematical model equation for parameters
a and n, we analysed the relationship between these explanatory
parameters and the objective parameters. By applying the
LASSO method, which is one of the most common techniques
for machine learning, three explanatory parameters were found
as the important controlling factors for each of a and n in y ¼
axn. Based on these results, the model equations for a and n are
shown in eqn (3) and (4), respectively.
a ¼ 45.64 (atomic charge of O) ꢀ 4.04 (atomic charge of Si) ꢀ 2.00
(H/C) + 37.13
(3)
n ¼ ꢀ2.38 (LUMO) ꢀ 0.24 (number of hydrogen atoms) ꢀ 0.01
(volume) + 5.23 (4)
The atomic charges of oxygen and silicon strongly affect
parameter a. Parameter n includes a large contribution from the
LUMO of the unit structure. We clearly found different
controlling factors for parameters a and n. As shown in Fig. 3,
these equations were clearly reproduced the experimental
results. It is effective to understand the reason for the molecular
Fig.
7
Visualization33 of the highest occupied molecular orbital
(HOMO) and the lowest unoccupied molecular orbital (LUMO) of
BTES-M, -E1, -E2, and -E3.
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Table 3 Explanatory parameters of unit structures of BTES-P and
BTES-Ph
and the higher-lying HOMO lead to higher reactivity. As can be
seen in Fig. 7, the LUMOs are rather delocalized over the
molecules with the contribution of silicon s* orbitals, whereas
the HOMOs are more localized mainly on the oxygen n-orbitals.
As a result, the HOMO energy levels are nearly the same
regardless of the monomer structure (ꢀ0.2903 eV to ꢀ0.2780
eV), whereas the LUMO energy levels widely range from
0.0375 eV to ꢀ0.0336 eV depending on the structure, thereby
largely affecting parameter n. The lower LUMO levels for
unsaturated BTES-E2 and -E3 than saturated BTES-M and -E1
are understood in terms of the s*(Si)–p*(C) interaction.
Molecular volume is related to molecular diffusion, and thus to
reactivity. Increasing the number of hydrogen atoms seems to
suppress reactivity due to steric hindrance of the spacer.
From the results described above, we can denitely conclude
that parameters a and n have different controlling factors.
Although it is not easy to explain why these explanatory
parameters are selected as the controlling factors for parame-
ters a and n, it is true that the molecular weights can be
reproduced on the basis of these molecular factors of the
monomers.
Parameters
BTES-P
6
BTES-Ph
4
Number of
hydrogens
H/C
2
0.667
190.6
ꢀ3
Volume (A )
169.3
0.0389
0.975
ꢀ0.622
0.791
2.042
LUMO (Ha)
Atomic charge of Si
Atomic charge of O
a
n
ꢀ0.0330
0.907
ꢀ0.617
3.965
2.498
Fig. 9 shows the selected plots of molecular weight changes for
BTES-Ph polymerization and the all the plots are given in
Fig. S2.† To compare predicted curve and experimental data of
BTES-P and -Ph, two category separation which comes from
difference of C–C and C]C/C^C bonds of monomers, was
succeeded. The gap between predicted curve and experimental
data is improved by adding other data, although the Fig. 9
shows qualitatively good t of the experimental plots by the
predicted curves.
Prediction of molecular weight from proposed equation
Compared to BTES-E1 and -M, BTES-P showed even lower
molecular weights in both prediction and experiments. BTES-P
is known to easily undergo intramolecular cyclization to form
stable six-membered cyclic disilsesquioxanes in acid-catalysed
hydrolytic polycondensation reactions.35,36 On the other hand,
the unsaturated phenylene bridge in BTES-Ph led to the
generation of high molecular weight polymers and gelation
even with low water content, similar to BTES-E3. The GPC charts
of BTES-P and -Ph synthesized under the H2O/silane ratio ¼ 3.0
and 1.0, respectively, are shown in Fig. 10.
As well as the BTES-E1 (and -M), a single sharp peak in the
low molecular weight region was observed in the case of BTES-P
including single C–C single bonds. Total shape of GPC chart for
BTES-Ph having linear main structure was similar to the BTES-
E3 (and also -E2), although some small peaks are observed in
the low molecular weight region. One of the reasons of shape
difference of GPC charts is that the cyclic compounds of BTES-
Based on the proposed equation of molecular weight, the pre-
dicted curves of molecular weights were analysed. We simulated
two monomers BTES-P and BTES-Ph with C3H6 and C6H4
spacers, respectively (Fig. 8).
The controlling factors for BTES-P and BTES-Ph obtained by
electronic structure calculation from GAMESS are listed in
Table 3.
Using those parameters, we predicted the curves of molec-
ular weights with respect to the H2O/silane molar ratio, as
shown in Fig. 9.
Reecting the similarity of parameter a, the curve for BTES-P
is close to those for BTES-M and BTES-E1, and the curve for
BTES-Ph is near those for BTES-E2 and -E3. To validate this
prediction, we synthesized polymers from BTES-P and BTES-Ph
(Table 4) and the molecular weight changes depending on the
amount of water are plotted in Fig. 9. When the ratio exceeded
1.0, gelation occurred to form insoluble polymeric materials.
On the other hand, BTES-P showed no evident molecular weight
changes up to water/silane ratio of 2.3 and at the ratio of 3.2
gelation occurred. The gelation of BTES-Ph at rather low H2O/
silane ratio is likely due to the phenylene bridge that is rigid
and have high tendency to form p–p stacking. Reproducibility
of molecular weight determination by GPC is a little low for
BTES-Ph polymers, likely due to the formation of insoluble gel
to an extent, which was conrmed by Tyndall scattering of the
solutions even at H2O/silane ratios smaller than 1.0. However,
the quick molecular weight increase could be traced cleanly.
Fig. 9 Predicted curves of molecular weights for BTES-P and BTES-Ph
as shown by black and purple line, respectively. Open triangle and
open circle dots are molecular weights for BTES-P and BTES-Ph,
respectively, obtained by experiment. Red, blue, orange, and green
dashed lines are regression curves for BTES-M, -E1, -E2, and -E3 as
shown in Fig. 3.
Fig. 8 Monomer structure of BTES-P and -Mh.
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Table 4 Results of sol–gel reactionsa
Conclusions
Molecular weightb
We have proposed a new concept called “MBR”, which is based
on the machine learning technique, with an eye to enhancing
materials design. In MBR, macroscopic properties are mathe-
matically modelled by explanatory parameters obtained by
computer simulation from an atomistic point of view. As an
example, we modelled the molecular weights of bridged PSQs by
using MBR. The equation y ¼ axn well reproduced the behaviour
of the molecular weights of BTES-M, -E1, -E2, and -E3. Param-
eters a and n were modelled by using the explanatory parame-
ters of geometry, electronic structure, reactivity, and dynamics
of monomer structures. The explanatory parameters were
essential to understanding the controlling factors for the poly-
merization of PSQs. Based on the model for molecular weight,
we predicted the molecular weight theoretically. Our experi-
mental results for the two types of spacers (C3H6 and C6H4)
could be categorized on the basis of the predicted curves. This
indicates that the model developed in this study includes the
fundamental characteristics of molecular weight change with
respect to the H2O/silane molar ratio, although further
improvement of the model is necessary for accurate analysis.
We have clearly shown the usefulness of concept of MBR for
molecular weight prediction and nding of controlling factors.
The MBR approach is a powerful tool in materials science with
an eye to realizing innovative materials design.
H2O/silane
molar ratio
Silane
Entry
Mw/g molꢀ1
BTES-P
1
2
3
4
1
2
3
4
2.3
2.7
3.0
3.2
0.7
0.8
0.9
1.0
420
2600
8800
12 100
2600
5300
5800
12 800
BTES-Ph
a
Scale in operation: silane 5 mmol, molar ratios: EtOH/silane ¼ 50 mmol.
b
Determined by GPC relative to polystyrene standards.
Fig. 10 GPC charts (a) BTES-P and (b) BTES-Ph.
Ph was obtained due to the rigidity of main structure. However,
overall shape of GPC chart and molecular weight curve of BTES-
P and -Ph were similar to the BTES-E1, -M and BTES-E2, -E3,
respectively. In this sense, we clearly demonstrated the reliable
categorization of PSQ derivatives with respect to the molecular
weight based on the concept of MBR.
Conflicts of interest
The authors declare no competing interests.
Acknowledgements
The 29Si NMR spectra of BTES-P and -Ph are presented in
Fig. 11, together with signal assignments based on comparison
with the literature data.16,35,36 The spectrum of BTES-P reveals
sharp T1 and T2 signals ascribed to cyclic dimers and/or cyclic
units involved in the polymer structure. Relatively large and
broad signals likely due to the polymer T2 and T3 structures are
also seen in the spectrum, similarly to that of BTES-E1.16 In
contrast, the spectrum of BTES-Ph shows only tiny T3 signals,
suggesting that BTES-Ph should have more linear backbone
than BTES-P, like BTES-E2 and -E3.16 These agree well with the
categorization based on their GPC analysis mentioned above.
Research activities carried out in the Advanced Automotive
Research Collaborative Laboratory at Hiroshima University are
supported by Mazda Motor Corporation, Japan.
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