Application of response surface method using rapid screening, support vector machine, and multiple regression on the acidity and activity of Si-Al-Zr ternary oxide

Article abstract of DOI:10.1021/cc900188g

To study the synergistic effect on the acidity and activity of Si-Al-Zr ternary oxide system, the mixture design of experiments was applied to prepare the ternary oxides by a sol-gel method, and rapid screening on dehydration of isopropanol and Friedel-Crafts reaction was conducted to determine the activities. These activities, amount of acid site determined by pyridine pulse, and specific surface area, were correlated with the oxide composition by means of support vector machine. Clear synergy among the Si-Al-Zr was observed on the acidic character and the surface area, whereas no synergy between Al-Zr was observed on the catalytic activities. Multiple regression was then conducted to find a relationship between the activities and the characters. The term of Si molar fraction in the oxide was essential for good regression, and acid strength determined by peak temperature of NH₃ desorption was related to the Si fraction. Thus, simple and rapid technique for activity test and characterization can be integrated by means of support vector machine and multiple regression, and some insights of the active site were obtained.

Full text of DOI:10.1021/cc900188g

J. Comb. Chem. 2010, 12, 435–444
435
Application of Response Surface Method using Rapid Screening,
Support Vector Machine, and Multiple Regression on the Acidity and
Activity of Si-Al-Zr Ternary Oxide
Kohji Omata,*,† Yuichiro Yamazaki,† Yasukazu Kobayashi,† and Muneyoshi Yamada‡
Department of Applied Chemistry, Graduate School of Engineering, Tohoku UniVersity, Aoba 6-6-07,
Aramaki, Aoba-ku, Sendai 980-8579, Japan, and Akita National College of Technology, Bunkyo-cho 1-1,
Iijima, Akita 011-8511, Japan
ReceiVed December 16, 2009
To study the synergistic effect on the acidity and activity of Si-Al-Zr ternary oxide system, the mixture
design of experiments was applied to prepare the ternary oxides by a sol-gel method, and rapid screening
on dehydration of isopropanol and Friedel-Crafts reaction was conducted to determine the activities. These
activities, amount of acid site determined by pyridine pulse, and specific surface area, were correlated with
the oxide composition by means of support vector machine. Clear synergy among the Si-Al-Zr was observed
on the acidic character and the surface area, whereas no synergy between Al-Zr was observed on the
catalytic activities. Multiple regression was then conducted to find a relationship between the activities and
the characters. The term of Si molar fraction in the oxide was essential for good regression, and acid strength
determined by peak temperature of NH3 desorption was related to the Si fraction. Thus, simple and rapid
technique for activity test and characterization can be integrated by means of support vector machine and
multiple regression, and some insights of the active site were obtained.
especially a radial basis function network,13,14 was success-
fully applied for the regression of catalytic phenomena
instead of the conventional polynomial equation. Such
methodology is effective for integrating the observation15
and the characterization.16-20
Recently, support vector machines (SVMs) attract much
attention because of their high generalization capability. SVM
was first reported in the field of solid catalysis as a
classifier.21,22 It can be used also for regression, and by SVM
the inputs are mapped into a high-dimensional space in
nonlinear manner and then the modified inputs are correlated
linearly with the output.23,24 These reported results show
clearly the superior generalization capability of a SVM and
better availability through open source program makes SVM
more applicable than an artificial neural network. In the
present study, SVM was used for the regression using libsVm
library24 through sVm function in package e1071 of statistic
language R.25
Considering the demands for rapid screening, a simplified
procedure of an activity test will be developed in the present
study. The catalytic activity test was conducted in test tubes
in parallel. The first test reaction was dehydration in a pulse
mode operated at 145 °C. Isopropanol dehydration on acid
cite was reported in a literature.26 The series of alumina
oxides decomposed isopropanol to mainly propylene and
small amount of di-isopropyl ether was observed. The activity
to propylene was dependent on the amount of the acid site.
The second test reaction is Friedel-Crafts reaction in batch
mode at 150 °C. Benzylation of anisole was reported to
proceed on Brønsted acid, whereas dibenzyl ether was
formed on Lewis acid site.27
Introduction
Solid acids are required to play a significant role in the
green chemistry of fine and specialty chemicals manufactur-
ing process.1 A variety of industrial processes using solid
acids, such as alkylation, isomerization, cracking, and
etherification, have been established, and catalysts, such as
zeolites, oxides, mixed oxides, phosphates, ion-exchange
resins, and clays, are industrialized.2 Among them, mixed
metal oxides provide much functionality. Whereas the acidity
of binary metal oxide can be predicted by Tanabe theory,3
prediction of those of ternary or more complex mixed oxides
is not established because of their combinatorial explosion.
Thus, rapid technology is potentially required to predict the
synergistic effect.
To avoid the combinatorial explosion of the oxide
composition, the design of experiments (DOE) has been
effectively utilized. Multiple regression using polynomial
equation is applied to draw response surface from the
experimental results as so-called response surface method
(RSM). In the field of catalyst research, however, application
of the RSM was limited probably because of the complexity
and nonlinearity of the catalytic phenomena.
As reviewed in the introduction of ref 4, modeling
methodologies were suggested in the research field of
catalysis to overcome the complexity and nonlinearity.5-12
It was also reported that an artificial neural network,
* To whom correspondence should be addressed. E-mail: omata@
erec.che.tohoku.ac.jp.
† Tohoku University.
‡ Akita National College of Technology.
10.1021/cc900188g  2010 American Chemical Society
Published on Web 05/20/2010

436 Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4
Omata et al.
Various indicator and techniques for solid surface acid-base
characterization have been proposed, such as isoelectric point
by electrokinetic titration, H0,max by indicator dye adsorption,
chemical shift by XPS, and the heat of adsorption of probe
gases by calorimetry or inverse gas chromatography.28 In
addition to the gas adsorption, model reactions can be used
to characterize the acidity if all the properties of the active
sites is known.29 For example, as reported recently,30 model
reaction was successfully applied as a probe of the acidity
of supported catalyst. In such cases other catalyst factors
such as surface area, pore structures, location of active sites
and so on, are similar each other, and thus the relation
between the activity and acidity is simple. So we think not
only the activity and acidity but also other factors should be
included in order to find the nonlinear relationship using new
method such as support vector machine. From the view
points of simplicity and quantitative analysis, pulse adsorp-
tion of pyridine was applied in the present study.
too many because it takes a few weeks using the conventional
one-by-one method. So, a new rapid screening method is
required. According to the terms of combinatorial chemistry
rapid library synthesis are highly recommended in such a
situation. Affinity of liquid procedure, such as a sol-gel
method, is high for automated procedure of rapid library
synthesis and thus the ternary Si-Al-Zr mixed oxides
were prepared by a sol-gel method. Aluminum nitrate
(Al(NO3)39H2O), zirconyl nitrate (Zr(NO3)2O 2H2O), and
ethyl orthosilicate (Si(CH3CH2O)4) for 100 mg oxide were
solved in 2 mL of mixed solvent (ethanol/water ) 1:1) in a
test tube (φ15 mm, 150 mm). Ammonia water (28%, 1 mL)
was then added for the gelation. After removal of the solvent
at 80-110 °C, the dry gel was calcined at 550 °C for 6 h in
air. The preparation of 15 kinds of oxide was conducted in
parallel.
Activity Test of Isopropanol Dehydration. Mixed oxide
(40 mg) was sampled in a test tube (φ15 mm, 150 mm) and
sealed by doubled-cap made of silicone. One hundred twenty
seconds after isopropanol (4 µL) was dropped in the test
tube at 145 °C, the test tube was cooled in water at room
temperature. After it was punctured by a injection needle,
the test tube was connected to a gas detector tube (Gastec,
No.172 for ethylene) through another injection needle and
then the gas (50 mL) was sampled. The gas detector showed
high sensitivity also for detection of propylene. The 15
samples were tested in parallel intended for rapid screening.
Actually, activity of 15 kinds of oxide was determined in
few hours.
The integration of the simple and rapid techniques for
activity test and characterization was conducted by means
of SVM and multiple regression to find rapidly the synergistic
effect among the ternary oxide system.
Experimental Section
Preparation of Ternary Oxides. The notation of mixed
oxide is like Si25Al50Zr25 when Si/Al/Zr ) 25:50:25 mol %.
For the effective regression of oxide composition, composi-
tion of the mixed oxide was determined by mixture design
using gen.mixture function in AlgDesign package as
Activity Test of Benzylation of Anisole. The 15 kinds
of mixed oxides (40 mg) were sampled in test tubes (φ15
mm, 150 mm) in parallel. Benzyl alcohol (0.2 g) and anisole
(2.0 g) were mixed in the each tube. After 2 h reaction at
150 °C in open air, the product was analyzed by gas
chromatograph (Shimadzu GC-8A, Ar carrier, Dexil 300 GC
packed column at 120-190 °C) equipped with flame-
ionization-detector. The main product was benzyl anisole and
a small amount of dibenzyl ether was formed. Because GC
analysis was time-consuming, the 15 activity tests were
conducted in 2 days since the oxide preparation.
library(AlgDesign)
datϽϪgen.mixture(5,c(ꢀꢀSiꢀꢀ,ꢀꢀAlꢀꢀ,Zrꢀꢀ))*100
library(vcd)
ternaryplot(dat,scaleϭ100,mainϭ==)
where total 15 experiments were designed. The designed
composition is illustrated in Figure 1 as a ternary plot. Red
circles in the figure show the composition of the designed
oxides.
Using DOE, the number of experiments can be drastically
reduced. However, the 15 experiments in this case is still
Characterization of Oxides. X-ray diffraction (Rigaku,
Miniflex) was used to identify the oxide phase. The Cu KR
radiation was used as an X-ray source. The X-ray tube was
operated at 30 kV and 15 mA. Diffraction intensities were
recorded at 2θ from 10 to 90° at the rate of 1°/min. The
observed diffraction patterns were identified by the Joint
Committee on the Powder Diffraction Standards (JCPDS)
card.
Specific surface area was measured by a BET method at
-196 °C (Monosorb MS-19, Quantachrome) using N2 30%/
He 70 gas. The amount of acid site was determined by
pyridine pulse adsorption. The mixed oxide (20 mg) was
charged in flow type cell connected in the GC carrier line
(GC-8A, thermal conductivity detector, He carrier, Shi-
madzu). After calcination for 20 min at 300 °C, 5 pyridine
pulses (size ) 0.5 µL) was introduced at 270 °C. After the
first or second pulse, the peak area reached to steady state.
The adsorbed pyridine amount was estimated from the
differences. It is certain from the TPD profile of NH3 that
Figure 1. Ternary plot of mixture design of Si-Al-Zr ternary
oxide.

Application of Response Surface Method
Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4 437
Figure 2. Curve fitting of TPD profile.
acid cites have a variety of strength. In our experiments,
therefore, only strong acid site was detected by pyridine
adsorption by conducting the pulse reaction at this temper-
ature. The amount of acid sites determined by this pyridine
pulse and that of strong site by NH3-TPD was identical.
While the method is no longer rapid, a part of the mixed
oxides was characterized by NH3-TPD. The sample was
pretreated in Ar flow from room temperature to 500 °C (10
K/min), held at 500 °C for 60 min. After cooling-down, NH3
was adsorbed at room temperature for 30 min in NH3/He
(10% NH3) flow. After removal of the vapor phase NH3 at
room temperature for 60 min in Ar flow, desorbed NH3
profile was observed at room temperature to 700 °C (10
K/min) in Ar flow. The TPD profile was fitted to 2 peaks
using an extreme function as shown in Figure 2 for
chemisorbed NH3 on weak acid site and on strong acid site,
respectively. The strength of the strong acid site was
determined as the highest peak temperature of the TPD
profile.
Figure 3. X-ray diffraction patterns of the designed oxides.
Prior to the analysis, libraries and experimental result were
loaded.
library(AlgDesign)
library(e1071)
datϽϪgen.mixture(5,c(ꢀꢀSiꢀꢀ,ꢀꢀAlꢀꢀ,ꢀꢀZrꢀꢀ))*100
dat$activityϽϪc(0,450,310,60,0,650,240,20,5,190,
5,0,10,0,0)
Regression was conducted by polynomial equation in model 1.
Coefficient ꢀ in eq 1 was optimized by least-squares method as
follows:
Informatics. Statistic programing language R25 was used
for informatics procedure. AlgDesign package31 was used
for a design of mixture experiments with assistance of vcd
package32 for ternary plot. sVm function in e1071 package33
was used for the regression by support vector machine
(SVM).
ٙ
regϽϪlm(activity˜. 2,dat)
summary(reg)
reg1ϽϪstep(reg)
summary(reg1)
activity ) ꢀ0 + ꢀ1Si + ꢀ2Al + ꢀ3Zr + ꢀ12Si ×
Al + ꢀ13Si × Zr + ꢀ23Al × Zr (1)
Result and Discussion
Phase of Mixed Oxide. X-ray diffraction patterns of the
prepared oxides are illustrated in Figure 3. The numbers are
same as those in Table 1. Profiles of nos. 1-4 were corrected
by the profile of blank where peaks of the sample plate
(aluminum metal) were recorded. Broad peaks suggest that
crystalline size is small and almost part of the oxides are
amorphous. Single oxide was silica (no. 1), γ-alumina (no.
5), and orthorhombic zirconia (no. 15). Peaks in no. 9 were
assigned to Alx Zr1-xOy mixed oxide. Main peak of SiO2 on
No.1 gradually shifts to higher angle in Si-Al binary
mixtures (nos. 1, 2, 3, and 4), and it suggests that silica and
alumina were mixed in atomic scale. The similar mixtures
were observed in Si-Zr binary system (nos. 1, 6, 10, and
13), whereas no clear trend was observed in Al-Zr binary
system (nos. 5, 9, 12, 14, and 15).
Table 1. Mixture Design of Ternary Oxide and the Activity for
Isopropanol Dehydration
oxide (mol-%)
no.
Si
Al
Zr
propylene (ppm)
1
2
3
4
5
6
7
8
100
75
50
25
0
75
50
25
0
50
25
0
25
0
0
0
0
0
0
0
25
25
25
25
50
50
50
75
75
100
0
450
310
60
25
50
75
100
0
25
50
75
0
25
50
0
25
0
0
650
240
20
∼5
190
∼5
0
10
0
0
9
10
11
12
13
14
15
Activity for Isopropanol Dehydration. Composition of
the ternary oxides and the activity for isopropanol
dehydration are summarized in Table 1. The relationship
between the composition and the activity was analyzed
by conventional multiple regression and SVM.
0

438 Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4
Omata et al.
Figure 4. Change of the fitted activity in model 2: (a) cost ) 1, (b) cost ) 10, (c) cost ) 15, and (d) cost ) 20.
The result of analysis was summarized as follows:
basis function (RBF) was used as the kernel function. In
model 2, a parameter of SVM was optimized as follows:
estimate
-59.3571
3.1179
0.3357
0.0579
0.0639
-0.0040
std error
157.0029
2.1566
2.1566
0.0668
0.0668
0.0668
t value
-0.38
1.45
0.16
0.87
0.96
-0.06
Pr(>|t|)
0.7141
0.1822
0.8797
0.4091
0.3642
0.9536
intercept
Si
Al
Si/Al
Si/Zr
AL/Zr
reg2ϽϪsvm(activityϳ.,dat, kernelϭꢀꢀradialꢀꢀ,costϭ15)
Whereas parameter “gamma” was used as default () 1/(data
dimension)), the “cost” parameter (the penalty parameter of
the error term) was increased from the default value 1 with
checking the plot as shown in Figure 4. When no change
was observed, the least value () 15) was used for the
regression. The final parameters were as follows: cost )
15, gamma ) 1/3, number of support vectors ) 12. They
were input to reg2 variable for the prediction of activity
in the following step.
On the basis of the t-value, the statistical significance of Si, the
interaction of Si × Al, and the interaction of Si × Zr are more
remarkable than others. To find the influential factors, variables
were selected by step function using AIC as an index. After
trial-error steps by the function, the regression equation was
simplified as expressed in eq 2. AIC of the model was
improved from 160.2 to 154.59. In the final model, only Si
was included in spite of the high t-value of Si × Al and Si
× Zr terms in the initial model.
In model 3, another gamma parameter (the kernel param-
eter of the RBFs) of SVM was also optimized simultaneously
using a grid search24 to decrease the sum of squared error
between the experimental and the predicted acidity by
tune.sVm function as follows:
activity ) -1.4286 + 3.9229 × Si
(2)
ٙ
costϽϪ2 c(seq(Ϫ2,10,0.25))
estimate
-1.4286
3.9229
std error
61.4498
1.3463
t value
-0.02
2.91
Pr(>|t|)
0.9818
0.0121
ٙ
gammaϽϪ2 c(seq(Ϫ8,0,0.25))
intercept
Si
modelϽϪtune.svm(activityϳ., dataϭdat,
gammaϭgamma, costϭcost, scaleϭF,
tunecontrolϭtune.control(samplingϭꢀꢀfixꢀꢀ),
validation.xϭdat[,-ncol(dat)],validation.
yϭdat[,ncol(dat)])
Ternary plot of activity by model 1 is illustrated in Figure 5 as
a function of oxide composition. No synergy between Si-Al
nor Si-Zr was observed in the figure, and as shown in eq 2,
this regression failed to predict the drastic decline of the
activity at high Si content resulting in the low activity of
pure silica.
reg3ϽϪmodel$best.model
The final parameters were as follows: cost ) 29.25, gamma )
2-7.75, number of support vector ) 15. The parameters of the
best model after the grid search were input to reg3 variable for
the prediction of activity in the following step.
Other regression was conducted using SVM in models
2-4. sVm function in e1071 package was used, and a radial

Application of Response Surface Method
Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4 439
In model 4, leave-one-out method (in this case, 15-fold
cross validation) were used in the grid search to prevent the
overfitting problem as follows:
of overfitting. The maximum activity of the binary Si-Al
or Si-Zr is too low in model 4 and in model 5. As a
result, the fitting by model 2 was the best among the svm
models 2-5. While no significant synergy between Al and
Zr was observed in this model, synergy between Si-Zr
or Si-Al was clearly expressed by the regression.
Regression by SVM was suggested as the best meth-
odology for the response surface. Regression by model 2
was used hereafter for the activity for Friedel-Crafts
reaction and characterization of the oxides.
ٙ
costϽϪ2 c(seq(7,11,0.25))
ٙ
gammaϽϪ2 c(seq(Ϫ14,Ϫ9,0.25))
modelϽϪtune.svm(activityϳ., dataϭdat,
gammaϭgamma, costϭcost, scaleϭF,
tunecontrolϭtune.control(samplingϭꢀꢀcrossꢀꢀ,
crossϭ15))
reg4ϽϪmodel$best.model
The final parameters were as follows: cost ) 27.25, gamma )
2-11.00, number of support vector ) 15.
In model 5, another kind of kernel (polynomial kernel)
Activity for Benzylation of Anisole. The composition of
mixed oxides and the activity for Friedel-Crafts reaction
are summarized in Table 2. The relationship between the
composition and the activity was analyzed by SVM.
was employed as follows:
reg5ϽϪsvm(activityϳ., dat, kernelϭꢀꢀpolynomialꢀꢀ,
degreeϭ3)
The relationship between the oxide composition and the
activity was correlated by SVM (model 2) as follows:
The default degree of the polynomial is 3.
Ternary plots of specific activity by these SVMs are also
illustrated in Figure 5.
In addition to Figure 5, regression results by models
1-5 are compared for binary Si-Al oxide or Si-Zr oxide
in Figure 6. Model 1 suffers from the nonlinearity of the
response of activity, and model 3 clearly shows features
library(AlgDesign)
library(e1071)
datϽϪgen.mixture(5,c(ꢀꢀSiꢀꢀ,ꢀꢀAlꢀꢀ,ꢀꢀZrꢀꢀ))*100
dat$activityϽϪc(4.5, 91.7, 67.1, 37.3, 0, 71.7,
52.1, 22.1, 1.0, 60.1, 10.9, 0, 8.1, 0, 0)
reg_FCϽϪsvm(activityϳ.,dat, kernelϭꢀꢀradialꢀꢀ,costϭ9)
Figure 5. Response surface of activity for isopropanol dehydration by model 1-5 from upper left to down right.

440 Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4
Omata et al.
Table 3. Mixture Design of Ternary Oxide and the Oxide
Character
oxide (mol %)
surface area acid amount acid density
no.
Si
Al
Zr
(m2 /g)
(µmol/g)
(µmol/m2)
1
2
3
4
5
6
7
8
100
75
50
25
0
75
50
25
0
50
25
0
25
0
0
0
0
0
0
0
25
25
25
25
50
50
50
75
75
100
6
176
237
338
250
334
369
341
197
294
328
222
247
169
47
0
51
89
89
33
106
173
137
32
129
147
58
123
50
19
0.00
0.29
0.38
0.26
0.13
0.32
0.47
0.40
0.16
0.44
0.45
0.26
0.50
0.29
0.41
25
50
75
100
0
25
50
75
0
25
50
0
25
0
9
10
11
12
13
14
15
0
dehydration, suggesting that the both reaction proceed on
the same active site.
Characterization of the Ternary Oxides. The composi-
tion of mixed oxides and the result of oxide characterization
are summarized in Table 3. The relationship between the
oxide composition and the characters were correlated by
SVM (model 2) using the optimized cost parameters as
follows:
library(AlgDesign)
library(e1071)
datϽϪgen.mixture(5,c(ꢀꢀSiꢀꢀ,ꢀꢀAlꢀꢀ,ꢀꢀZrꢀꢀ))*100
dat$BETϽϪc(6, 176, 237, 338, 250, 334, 369, 341,
197, 294, 328, 222, 247, 169, 47)
dat$acidϽϪc(0, 51, 89, 89, 33, 106, 173, 137, 32,
129, 147, 58, 123, 50, 19)
dat$densityϽϪc(0.00, 0.29, 0.38, 0.26, 0.13,
0.32, 0.47, 0.40, 0.16, 0.44, 0.45, 0.26, 0.50,
0.29, 0.41)
Figure 6. Comparison of regression to Si-Al or Si-Zr composi-
reg_BETϽϪsvm(BETϳSiϩAlϩZr, dat,
kernelϭꢀꢀradialꢀꢀ, costϭ10)
tion. Solid line: By multiple regression. Broken line: By SVM.
reg_acidϽϪsvm(acidϳSiϩAlϩZr, dat,
kernelϭꢀꢀradialꢀꢀ, costϭ7)
reg_densityϽϪsvm(densityϳSiϩAlϩZr, dat,
kernelϭꢀꢀradialꢀꢀ, costϭ5)
Table 2. Mixture Design of Ternary Oxide and the Activity for
Benzylation of Anisole
oxide (mol %)
Al
benzyl anisole
yield (%)
To discuss the precision of prediction by the developing
model, more new test data sets should be added. One of the
no.
Si
Zr
1
2
3
4
5
6
7
8
100
75
50
25
0
75
50
25
0
50
25
0
25
0
0
25
50
75
100
0
25
50
75
0
25
50
0
25
0
0
0
0
0
0
25
25
25
25
50
50
50
75
75
100
4.5
91.7
67.1
37.3
0
71.7
52.1
22.1
1.0
60.1
10.9
0
9
10
11
12
13
14
15
8.1
0
0
0
The parameter cost was optimized using the same method as
shown in Figure 4.
The response surface of the activity is illustrated in Figure
8. Similar result was obtained with those for isopropanol
Figure 7. Verification of the prediction of Friedel-Crafts activity,
specific surface area, acid amount, and acid density of Si41Al25Zr34.

Application of Response Surface Method
Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4 441
Figure 8. Response surface of activity and characters of the ternay oxides: (a) Activity for Friedel-Crafts reaction, (b) surface area, (c)
amount of acid site, and (d) density of acid site from upper left to down right.
amount and the catalytic activity was not observed,
main problem of catalyst development is, however, that the
multiple regression using second-order polynomial equa-
tion was conducted to find correlation between them as
follows:
preparation and activity test are time-consuming and labori-
ous. Therefore a rapid methodology with which catalytic
activity can be predicted from few experimental results are
required and addition of extra test data sets is not favored
ٙ
regϽϪlm(activityϳ(acidityϩBETϩdensity) 2ϩ
ٙ
ٙ
ٙ
I(acidity 2) ϩ I(BET 2)ϩI(density 2),exp)
tuned ϽϪ step(reg)
for the catalyst research. Among the regression by model
1-5, it was clearly shown that SVM with RBF kernel with
adequate parameters is superior for the regression of the
catalysis. Thus only one extra oxide was prepared for the
activity test and the characterization. From the response
surface it is predicted that the maximum amount of acid site
is 177 µmol/g of Si41Al25Zr34. In Figure 7, the predicted
characters and activity of Si41Al25Zr34 were compared with
those of experimentally determined. The similarity shows
the predictions are precise and the regression models are
valid.
summary(tuned)
where experimental result was included in the data frame
exp. As a result of variables selection by step function,
the regression equation was
activity ϳ acidity ϩ BET ϩ density ϩ
ٙ
I(density 2) ϩ BET:density
and the adjusted R-squared was as low as 0.2942. The term
means the following equation where coefficient γ was optimized
by step function.
The response surface of these characters are illustrated in
Figure 8. Synergistic effect was clearly observed among the
ternary Si-Al-Zr system in contrast to that of catalytic
activity, where synergy of only Si-Al or Si-Zr was
observed. The synergy for acid site was not responsible for
the catalytic activity. In the each binary system, Si42Al58 or
Si44Zr56 showed the highest amount of acid site. The optimum
compositions are rather silica-lean from the Tanabe theory3
where the binary oxides Si60Al40 or Si65Zr35 would show the
maximum.
activity ) γ0 + γ1acidity + γ2BET + γ3density +
γ33density × density + γ23BET × density (3)
The response surface by this regression is illustrated in
Figure 9. The complexity and the low R2 suggest that the
regression using only the physical properties of oxide is
incomplete for good response.
Then regression using both the physical properties and
catalyst composition was conducted as follows:
Multiple Regression of Characters to the Catalytic
Activity. Because simple relationship between the acid

442 Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4
Omata et al.
Figure 9. Response surface for the activity by regression using
second-order polynomial equation of physical properties.
Figure 11. Relationship between the NH3-TPD reak temperature
and the density/Si term.
Si25Al75, Si75Zr25, and Si25Zr75, the intimate relationship
between the acid strength (i.e., peak temperature of TPD)
and the Si:density term was suggested as shown in Figure
11. Whereas it was reported that the total amount of
chemisorbed NH3 at 80 °C was proportional to the
formation rate of propylene from isopropanol dehydration
26
on SO42-/Al2O3 and that the amount of Brønsted acid
site was proportional to the benzyl anisole yield with
Nb2O5/Al2O3 catalyst,27 the detailed analysis in the present
study unveiled that the acid site strength can be also
Figure 10. Response surface for the activity by regression using
Si/density term.
regϽϪlm(activityϳ(acidityϩBETϩdensity)ϩ
(acidityϩBETϩdensity):(SiϩAlϩZr),exp)
tuned ϽϪ step(reg)
summary(tuned)
Then the best regression by which the adjusted R-squared is
0.9737 was obtained.
activity ϳ acidity ϩ BET ϩ density ϩ acidity:Al ϩ
BET:Si ϩ BET:Al ϩ density:Si ϩ density:Al
To simplify the equation, items with high t value were selected
and the final regression was conducted as
regϽϪlm(activity ϳ acidity ϩ BET ϩ
Si:density,exp)
tuned ϽϪ step(reg)
summary(tuned)
Regression with high adjusted R-squared of 0.9178 was obtained
as shown below.
Figure 12. Augmented simplex lattice design.
estimate
3.21426
-0.45665
0.09631
3.98888
std error
6.10980
0.10312
0.04392
0.34515
t value
0.526
-4.428
2.193
Pr(>|t|)
Table 4. Augmented Simplex Lattice Design of Ternary Oxide
and the Activity for Benzylation of Anisole
intercept
acidity
BET
0.60927
0.00101
0.05070
1.71×107
oxide (mol %)
Al
benzyl anisole
yield (%)
Si/density
11.557
no.
Si
Zr
0.0
0.0
100.0
0.0
50.0
50.0
16.7
16.7
66.7
33.3
The high t value suggests statistical significance of Si/density
term. The response surface by this regression is illustrated
in Figure 10. The similarity of the activity in Figure 8 with
that in Figure 10 confirms the validity of this regression
in accordance with the high adjusted R2. However, the
origin of the importance of the Si/density term was not
suggested from the experiments included in Tables 2 and
3. On the basis of the NH3-TPD of oxides Si75Al25,
1
2
3
4
5
6
7
8
9
10
100.0
0.0
0.0
50.0
0.0
50.0
66.7
16.7
16.7
33.3
0.0
100.0
0.0
50.0
50.0
0.0
16.7
66.7
16.7
33.3
4.5
0.0
0.0
67.1
0.0
60.1
83.3
13.7
2.2
19.8

Application of Response Surface Method
Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4 443
Figure 13. Comparison of experimental designs for response surface of the activity for benzylation of anisole using Si-Al-Zr oxides: (a)
from simplex lattice design, (b) from augmented simplex lattice design, and (c) from the combined expepriments.
Table 5. Verification of the Predictions of the Activity for
Benzylation of Anisole
related to the catalytic activity of Si-Al-Zr ternary
system.
prediction by
Comparison of Experimental Design
simplex
item
compositiona
Zr34Al25 Si41
lattice
augmented experimental
The mixture design in Figure 1 is so-called “simplex lattice
design”.34 Among the 15 experiments, 3 are for single oxide,
9 are for binary oxides, and only 3 are for ternary oxides.
Because the binary oxides of Si-Al and Si-Zr are known
as strong solid acid and small amount of additve such as Al
or Zr to SiO2 gives the drastic increase in their acidity,3
assignment of many experiments to binary oxide were
accordingly favorable in this study and the predictions were
precise. Furthermore, attention should be paid to the per-
formance of SVM. It can trace the rapid change of the
response as shown in Figure 6 and showed better generaliza-
tion ability than the conventional multiple regression. As a
result, the combination of the simplex lattice design and SVM
showed good performance.
max acid site
max activity by Zr0Al31 Si69
simplex lattice
max activity by Zr13Al22 Si65
augmented
35.1
92.0
40.9
77.1
36.9
98.0
81.5
80.6
80.2
a Optimum composition for the highest activity (99.3% yield)
predicted by SVM based on the combined data: Zr0Al30 Si70.
was superior in every case. Of course it is not concluded that
simplex lattice design is always superior because the activity
of Si-Al binary oxide showed the highest activity by chance
and synergy among the ternary or more component system
usually shows better performance in many cases. A better
mixture design should be developed in future.
However, synergy among the ternary oxide should be
more included in the experimental design to find a new
acidic oxide and an augmented simplex lattice design34
(as shown in Figure 12) was compared with the simple
simplex lattice design. The experimental results are
summarized in Table 4.
These results were analyzed by SVM according to the
procedures below and the response surfaces are illustrated
in Figure 13. All the experimental results in Tables 2 and
4 were combined and used to illustrate the response
surface in the right-hand side in the figure.
Conclusion
The synergistic effect on the activity and acidity of
Si-Al-Zr ternary oxide system was investigated. Rapid
screening on dehydration of isopropanol and Friedel-Crafts
reaction was conducted to determine the catalytic activi-
ties. Mixture experimental design by simplex lattice
applied to the ternary mixed oxide was effective to reduce
the number of the experiments. The regression of experi-
mental results on 15 kinds of oxide were successfully
conducted by support vector machine (SVM) for nonlinear
response surface of the catalytic activity, specific surface
area, acid amount, and acid density. Synergy among the
Si-Al-Zr was observed on the acidic character and the
surface area whereas no synergy between Al-Zr was
observed on the catalytic activities. The discrepancy was
resolved by the multiple regression to find a relationship
between the activities and the characters: the term of Si
molar fraction in the oxide was essential. Acid strength
was suggested to be related to the importance of the Si
fraction. Thus, simple and rapid technique for activity test
and characterization can be integrated by means of support
vector machine and multiple regression, and some insights
of the active site were obtained. It is also probable that
this technique can be applied to increase the amount of
information in database as catalysts descriptors.35,36 In that
case, unknown interactions among the experimental results
can be unveiled. If so many factors are included in the
training data, the precision of the prediction of SVM
should be low. The quantitative prediction by SVM should
library(e1071)
SiϽϪc(1, 0, 0, 1/2, 0, 1/2, 2/3, 1/6, 1/6,
1/3)*100
AlϽϪc(0, 1, 0, 1/2, 1/2, 0, 1/6, 2/3, 1/6,
1/3)*100
ZrϽϪc(0, 0, 1, 0, 1/2, 1/2, 1/6, 1/6, 2/3,
1/3)*100
datϽϪdata.frame(SiASi,AlϭAl,ZrAZr)
activityϽϪc(4.5,0,0,67.1,0,60.1,83.3,
13.7,2.2,19.8)
datϽϪdata.frame(SiASi,AlϭAl,ZrAZr,
activityϭactivity)
reg_FC2ϽϪsvm(activityϳ.,dat,
kernelϭꢀꢀradialꢀꢀ,costϭ15)
Despite the decreased number of experiments, the aug-
mented simplex lattice design gave the response surface
similar to those by the all data. However, the predicted
activity is rather lower than those by simplex lattice design
with 15 experiments. The activity of oxide with the highest acid
site, and the highest activiy predicted by each design were
compared in Table 5. The prediction by simplex lattice design

444 Journal of Combinatorial Chemistry, 2010 Vol. 12, No. 4
Omata et al.
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