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Journal of Non-Crystalline Solids 353 (2007) 2521–2527

Percolation transition of siloxane domain in partiallyphenylated organic/inorganic hybrid glass

Yoshihiro Kamimura *, Ken-ichi Kurumada

Department of Environment and Information Science, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku,

Yokohama, Kanagawa-ken 240-8501, Japan

Received 23 October 2006; received in revised form 20 April 2007Available online 5 June 2007

Abstract

Organic–inorganic hybrid glass undergoes a percolation transition of the organic or inorganic moiety at a certain volume fraction ofeither phase. At the percolation threshold, various properties of the hybrid glass exhibit an abrupt change. We attempted to evaluate thethreshold volume fraction of the percolation transition in partially phenylated glass from the measurable or observable behavior at thepercolation transition. The volume fraction of the phenyl moiety in the hybrid glass was varied by variation of the mixed fraction of twostarting silicon alkoxides, TEOS (tetraethylorthosilicate) and PTES (phenyltriethoxysilane). The threshold volume fraction was esti-mated as the point at which the dye-colored state with hydrophilic/hydrophobic dye, the Vickers hardness and siloxane bonding lengthexhibited a significant change. The percolation threshold of the phenyl moiety was estimated to be approximately 50 vol.%. At thisthreshold, the Vickers hardness showed a abrupt and almost discrete decrease and noticeable elasticity appeared. At the same time,the siloxane bondings were stretched by approximately 20% on the percolation of the phenyl part. In partially phenylated glass preparedfrom mixture of TEOS and PTES, the siloxane bondings seem to have a strong tendency to form a percolated siloxane network, and as aresult of that, only the percolation of the phenyl moiety could be captured from the experimentally measurable quantities.� 2007 Elsevier B.V. All rights reserved.

PACS: 61.10.Nz; 61.43.Er; 61.43.Fs

Keywords: X-ray diffraction; Glass formation; Glasses; Percolation; Silica; Organic–inorganic hybrids

1. Introduction

Recently, partially modified glass by organic functionalgroups has been an attractive research subject because ofits potential usefulness as an engineering material [1–10].Among the variations of hybrid glass, a phenyl-modifiedcomposition is quite promising due to its commercial avail-ability. The authors have focused on the incorporation oforganic or hydrophobic functions in glass to address thetechnical problem of obtaining a stable colored state inglass with organic dyes [11–14]. For example, to stabilizeorganic dyes in a matrix of siloxane bonds, the incorpora-

0022-3093/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2007.04.023

* Corresponding author. Tel./fax: +81 453394307.E-mail addresses: d06tb001@ynu.ac.jp (Y. Kamimura), kurumada@

ynu.ac.jp (K.-i. Kurumada).

tion of an organic moiety in the glass is found to beeffective.

In that sense, the dye coloration of glass with encapsu-lated organic solvent species as submicron droplets is avery effective method. However, from a practical view-points, a matrix of siloxane bond equipped with the func-tionality of stable organic dye species in is more desirablefor its simplicity in processing. When we consider suchfunctions of hybrid glass, a phenyl-modified one is a prom-ising candidate. Here, the fraction (volume fraction) of thephenyl moiety in the hybrid glass will be a crucial parame-ter in determining the properties of hybrid glass. Particu-larly, the percolation of the phenylated parts in thehybrid glass will greatly influence the macroscopically mea-surable and observable properties of the hybrid glass.Simultaneously, we can assume that the percolation of

Table 1Molar fractions of TEOS and PTES for the preparation of 15 samples forthe dye diffusion experiment

Sample TEOS (%) TEOS (g) PTES (%) PTES (g)

(a) 100 4.20 0.00 0.00(b) 90.0 3.78 10.0 0.48(c) 80.0 3.36 20.0 0.96(d) 75.0 3.15 25.0 1.20(e) 70.0 2.94 30.0 1.44(f) 69.0 2.90 31.0 1.49(g) 68.0 2.85 32.0 1.53(h) 67.0 2.81 33.0 1.58(i) 66.0 2.77 34.0 1.63(j) 65.0 2.73 35.0 1.68(k) 60.0 2.52 40.0 1.92(l) 55.0 2.31 45.0 2.16(m) 50.0 2.10 50.0 2.40(n) 25.0 1.05 75.0 3.60(o) 0.00 0.00 100 4.80

2522 Y. Kamimura, K.-i. Kurumada / Journal of Non-Crystalline Solids 353 (2007) 2521–2527

the parts comprised of the siloxane bondings will be signif-icantly influential on these properties. Therefore, from theviewpoint of the materials design, the occurrence of perco-lation of the phenyl/siloxane parts will be useful. Neverthe-less, methods for monitoring the percolation transition inhybrid glass have not been established [15–18].

In this study, the authors prepared sol–gel derivedhybrid glass from mixtures of tetraethylorthosilicate(TEOS) and phenyltriethoxysilane (PTES) at varied molarfractions of these two alkoxides. PTES has a phenyl groupwhich is directly covalently bonded to the silicon atom atthe center. Actually, the presence of the phenyl functionsgreatly affects various bulk properties of the hybrid glass.In our previous work, the phenyl group was revealed to sig-nificantly decrease the softening temperature [19]. Use ofPTES-derived hybrid glass as an alternative to addingheavy metallic species like Pb is expected to contribute tothe reduction in the environmental burden. Since TEOSand PTES are mutually miscible in liquid state, we can pre-pare hybrid glasses at arbitrary molar ratios of PTES toTEOS. As the molar fraction of PTES is increased, the per-colation transition of the phenyl group will be induced. Wecan expect that the microstructural alteration will accom-pany abrupt changes of various measurable properties.Consequently, the experimental determination of the prep-aration condition of the hybrid glass at which the percola-tion transition occurs will be possible. At the same time,clarifying how the macroscopic properties of the hybridglass alter at the percolation point of the organic/siloxaneparts is an intriguing subject of the study itself.

In order to evaluate the abrupt changes in the propertiesof the hybrid glass at the percolation transition, the authorsattended to some typical properties in which the percolationcan induce prominent symptoms. Although there have beenmany previous works related to the percolation transition,the attempt to estimate the percolation threshold from themeasurable evidences will be useful. This is because mostearlier works are highly conceptual [15–18]. Thus, weattempt to propose experimental methods for estimatingor finding the percolation transition in the present work.

Based on the backgrounds as above, the authorsattempted to capture the percolation transition caused inhybrid glass comprised of phenylated and siloxane partsfrom some typical measurable symptoms in their macro-scopic properties. In addition to that, the microstructuralaspect in the structural alteration at the percolation transi-tion will be also discussed based on the results of X-rayscattering.

2. Experimental section

2.1. Materials

Tetraethylorthosilicate (TEOS), phenyltriethoxysilane(PTES), methyl orange and hexane were provided fromShinetsu Chemical, Japan, and used as provided. Hydro-chloric acid (1 M), ethanol, dimethylformamide (DMF),

and quinizarin green SS were purchased from Wako PureChemical, Japan, and used as provided. Water purifiedby ion exchange followed by distillation was used for sam-ple preparation.

2.2. Determination of percolation threshold by dye leakage

2.2.1. Specimen preparation

In the present work, hybrid glass samples were preparedby the conventional sol–gel method. As shown in Table 1,tetraethylorthosilicate (TEOS) and phenyltriethoxysilane(PTES) were mixed at various compositions with the totalmole number fixed at 2 · 10�2. The above mixtures werehydrolyzed with water, ethanol and hydrochloric acid atmolar ratios 4, 1 and 1 · 10�2, respectively. As the indica-tor, 1 · 10�3 g of quinizarin green SS or methyl orange wasadded. The hydrolysis was completed in 1 h with vigorousstirring. Subsequently, the above sols of the hybrid glasswere air-dried at room temperature on a dish. After 24 h,solid dyed hybrid glass samples were obtained.

2.2.2. Observation of dye leakage

Subsequently, the dyed hybrid glass samples wereimmersed in solvent which readily dissolves the dye. Thesamples dyed with hydrophobic quinizarin green SS orwith hydrophilic methyl orange were immersed in 5 g ofn-hexane and ethanol, respectively. They were kept at restfor 168 h at room temperature. The point of observationis whether the dye leaks out of the hybrid glass into theimmersing solvent or not. As discussed later, the percola-tion threshold of the siloxane/phenyl domain could bedetermined by the retention or leakage of the dye.

2.3. Determination of percolation threshold from the Vickers

hardness

2.3.1. Specimen preparation

For correct measurements of the Vickers hardness, weneed to obtain sample pieces with suitable thickness and

Table 2Molar fractions of TEOS and PTES for the preparation of 16 samples forthe measurement of the Vickers hardness

Sample TEOS (%) TEOS (g) PTES (%) PTES (g)

(a) 100 4.20 0.00 0.00(b) 98.0 4.11 2.00 0.10(c) 95.0 3.99 5.00 0.24(d) 92.0 3.86 8.00 0.38(e) 90.0 3.78 10.0 0.48(f) 80.0 3.36 20.0 0.96(g) 75.0 3.15 25.0 1.20(h) 70.0 2.94 30.0 1.44(i) 65.0 2.73 35.0 1.68(j) 60.0 2.52 40.0 1.92(k) 50.0 2.10 50.0 2.40(l) 40.0 1.68 60.0 2.88(m) 30.0 1.26 70.0 3.36(n) 20.0 0.84 80.0 3.84(o) 10.0 0.42 90.0 4.32(p) 0.00 0.00 100 4.80

Table 3Molar fractions of TEOS and PTES for the preparation of 11 samples forthe measurement of the X-ray scattering

Sample TEOS (%) TEOS (g) PTES (%) PTES (g)

(a) 100 4.20 0.00 0.00(b) 90.0 3.78 10.0 0.48(c) 80.0 3.36 20.0 0.96(d) 70.0 2.94 30.0 1.44(e) 60.0 2.52 40.0 1.92(f) 50.0 2.10 50.0 2.40(g) 40.0 1.68 60.0 2.88(h) 30.0 1.26 70.0 3.36(i) 20.0 0.84 80.0 3.84(j) 10.0 0.42 90.0 4.32(k) 0.00 0.00 100 4.80

Y. Kamimura, K.-i. Kurumada / Journal of Non-Crystalline Solids 353 (2007) 2521–2527 2523

flatness. For this purpose, the hybrid glass samples for themeasurements of the Vickers hardness were prepared withdimethylformamide (DMF) added to retard the drying.The mixed fractions of TEOS and PTES are shown inTable 2 with the total mole number fixed at 2 · 10�2.Water, ethanol and hydrochloric acid were added at themolar ratio 4, 1 and 1 · 10�2, respectively, as in the caseof the dye leakage experiments. The only difference is thatDMF was added at the molar ratio shown in Table 2. Thehydrolysis was carried out with vigorous stirring of theabove mixtures for 1 h at room temperature. Subsequently,the hydrolyzed sol for the hybrid glass samples with DMFwas aged for 48 h at 80 �C with a seal to prevent the vapor-ization during the aging. After that, the aged samples wereair-dried at 80 �C for 48 h being open to the air. Finally,crack-free bulk hybrid glass samples with sufficient thick-ness and flatness could be obtained.

2.3.2. Measurement of the Vickers hardness

The Vickers hardness was measured using a Vickershardness-testing instrument (Akashi AVK-C1). Each sam-ple was indented using diamond indentor with 0.5 kgf ofloading for 15 s. Indentation was made 15 times for a singlemeasurement. The average of the above 15 measurementswas taken as the experimental result. The way of determin-ing the percolation threshold of the siloxane domain is tobe discussed later.

1 For interpretation of color in Fig. 1, the reader is referred to the webversion of this article.

2.4. Determination of percolation threshold from X-ray

scattering

X-ray scattering measurements were carried out for thesamples listed in Table 3. The sample preparation proce-dure was the same as that in Section 2.2.1 except that nodye was used for the samples for the X-ray scattering.The scattered profile was taken in the range of the scatter-ing angle 2h of 5–80� using CuKa (k = 1.548A, 50 kV,

200 mA, Rigaku RINT 2000). The data were taken at thescanning step angle 0.010� with the scanning speed 4�/min. The scattered wave number k is given as follows:

k ¼ 4p sin h=k; ð1Þwhere k (A�1), h (rad) and k (A) are the scattered wavenumber, scattering angle and incident wavelength,respectively.

The details of the way of determining the percolationthreshold from the scattered profiles measured at variousmixed fractions of TEOS and PTES are discussed later.

3. Results

3.1. Determination of percolation threshold from dye leakage

Fig. 1 presents six magnified images of the dyed hybridglass samples. The symbol each image corresponds to thosein Table 1. The state of the dye leakage into the solvent wasobserved by optical microscopy (OLYMPUS SZ61). Thesephotographs were taken from an upward position from aglass tube filled with the solvent in which the dyed glasswas immersed in. As seen in Fig. 1,1 the diffusion of thedye was visibly seen by the colored state of the glass-immersing solvents (n-hexane (blue) or ethanol (yellow)).In the hybrid glass samples dyed with methyl orange(hydrophilic dye), the dye is stabilized in the domains com-prised of siloxane bondings. The dye leakage to ethanolwas seen when the molar fraction of TEOS was below69% (see Fig. 1(a)). In case where the samples were dyedwith quinizarin green SS (hydrophobic dye), the dye leak-age to n-hexane, on the contrary, occurs when the molarfraction of TEOS was above 69% (see Fig. 1(b)). The aboveresults show that the bulk property of the hybrid glassexhibits an abrupt change between 68% and 69% of themolar fraction of TEOS. It should be noted that the extentof the dye leakage to the solvent decreased as the fractionof the respective dye-immobilizing part was increased.

Dyed with quinizarin green SS.

(1) TEOS 68% (2) TEOS 69% (3) TEOS 100% (Sample (g)) (Sample (f)) (Sample (a))

1cm

1cm

Dyed with methyl orange.

(1) TEOS 69% (2)TEOS 68% (3) PTES 100% (Sample (f)) (Sample (g)) (Sample (o))

a

b

Fig. 1. Magnified view of dye diffusion of the dyed hybrid glass at themolar fraction of TEOS 100%, TEOS 69%, TEOS 68% and PTES 100%.These photographs present the transparent appearance of the immersingsolvent of the sample. (a) Dyed glass with hydrophilic methyl orangeimmersed in the ethanol. (b) Dyed glass with hydrophobic quinizaringreen SS immersed in the n-hexane.

Molar Fraction of PTES (%)

0

10

20

30

40

50

(a)

PTE

S0

%

(b)

PTE

S2

%

(c)

PTE

S5 %

(d)

PTE

S8

%

(e)

PTE

S10

%(f

) PT

ES

20 %

(g)

PTE

S25

%(h

) PT

ES

30 %

(i)

PTE

S35

%(j

) PT

ES4

0 %

(k)

PTE

S50

%(l

) P

TE

S60

%(m

)PT

ES7

0 %

(n)

PTE

S80

%(o

) PT

ES

90 %

(p)

PT

ES1

00 %

Vic

kers

Har

dnes

s (k

gf/m

m2)

Fig. 2. Dependence of the Vickers hardness on the molar fraction ofPTES. The left and right end of the abscissa correspond to 100% of TEOSand PTES, respectively. The standard deviation of the measured data isindicated on the top of the bar for each sample.

0.08mm0.08mm0.08mm

(1) TEOS 100% (Sample (a))

0.08mm0.08mm0.08mm

(2) TEOS 65% (Sample (i))

0.08mm0.08mm0.08mm

(3) PTES 100% (Sample (p))

a

b c

Fig. 3. Indentation pattern obtained at molar fractions (a) TEOS 100%(Sample (a)), (b) TEOS 65% (Sample (i)) and (c) PTES 100% (Sample (p)).

2524 Y. Kamimura, K.-i. Kurumada / Journal of Non-Crystalline Solids 353 (2007) 2521–2527

3.2. Determination of percolation threshold from the Vickers

hardness

Fig. 2 presents the dependence of the Vickers hardnessof hybrid glass prepared at various molar fractions shownin Table 2. Fig. 3 shows three typical indentation patternsobtained in the three different regions as explained below.The Vickers hardness was obtained as approximately40 kgf/mm2 at the molar fraction of TEOS 100% and stee-ply decreased to approximately 20 kgf/mm2 when PTESwas added at 2% in the molar fraction. Interestingly, theVickers hardness was almost irrespective of the molar frac-tion of TEOS between 98% and 70%. When the molar frac-tion of TEOS was decreased below 70%, the hybrid glassvirtually lost the Vickers hardness. Fig. 3 shows the magni-fied indentation patterns in the above three regions. Whenthe glass sample was prepared at TEOS 100%, the indenta-tion pattern had a clear diamond shape as shown inFig. 3(a). The Vickers hardness was evaluated from thedimension of this diamond shape. Fig. 3(b) shows an exam-ple obtained between TEOS 98% and 70%. The indentationpattern in this region was obviously more obscure than thatobtained at TEOS 100%. From TEOS 98% to 70%, thoseindentation patterns were quite similar to each other result-ing in the almost constant value of the Vickers hardnessapproximately at 20 kgf/mm2. When the molar fractionof TEOS was below 70%, the hybrid glass exhibited notice-

able elasticity, and as a result of that, a clear indentationpattern was not obtained after taking the indentor off thesample surface. Therefore, almost no indentation patterncould be seen as shown in Fig. 3(c) in this region of themolar fraction. This abrupt elimination of the Vickershardness caused at the molar fraction of TEOS between70% and 65% is quite indicative of some major microstruc-tural change in the hybrid glass.

3.3. Determination of percolation threshold from wide-angle

X-ray scattered profiles

Fig. 4 presents the wide-angle X-ray scattered profilesobtained at various molar fractions of PTES and TEOS

0

Inte

nsity

PTES 100%

PTES 20%

PTES 30%

PTES 40%

PTES 50%

PTES 60%

PTES 70%

PTES 80%

PTES 90%

Scattered Wave Number k (Å-1)

PTES 10%

PTES 0%

0.5 1 1.5 2 2.5

Fig. 4. Wide-angle X-ray scattered profiles at various molar fractions ofTEOS and PTES. The exact peak positions are shown by arrows.

Y. Kamimura, K.-i. Kurumada / Journal of Non-Crystalline Solids 353 (2007) 2521–2527 2525

listed in Table 3. The scattered intensity was plotted againstthe scattered wave number k corresponding to the range ofthe scattering angle 5–40�. Since no sharp peak character-istic of diffraction from a crystalline lattice was seen inFig. 4, all the samples prepared for the present work wereamorphous. Although the scattered profiles have no peaksto be attributed to crystalline structure, each peak in Fig. 4has a broad peak at k = 1.3–1.7 nm�1. These peaks areattributed to the average distance of adjoining Si atoms.Therefore, the k-values at these peaks are considered tocorrespond to the siloxane bonding length. Fig. 5 showsthe dependence of 2p/k at the above peaks on the molar

10 20 30 40 50 60 70 80 9003.5

4

4.5

5

Silo

xane

Bon

ding

Len

gth

2/k

(Å

)

10 20 30 40 50 60 70 80 900 100

Silo

xane

Bon

ding

Len

gth

2/k

(Å

)

Molar Fractionof PTES (%)

Silo

xane

Bon

ding

Len

gth

2π/k

(Å

)

Fig. 5. Dependence of 2p/k at the peak in the vicinity of 20� on the molarfraction of PTES.

fraction of PTES. The 2p/k-value monotonously increaseswith the molar fraction of PTES. It should be noted that2p/k shows a prominent increase between 30% and 40%of the molar fraction of PTES. Furthermore, anotherbroad peak was seen in the vicinity of the lower cutoff ofk, for example, in the case of PTES 100%. Since these peaksappear in a range of much smaller k-values than the aboveones, these peaks at the smaller k-values are considered asan indication of some domain-like structures in the hybridglass samples. The k-value at the peak increased with themolar fraction of PTES. On the contrary to the peak posi-tions in the larger k-region, these peaks in the smallerk-region increased with the molar fraction of PTES. There-fore, the peaks in the smaller k-region reflect some struc-ture which becomes smaller as the fraction of the phenylmoiety is increased.

4. Discussion

In this section, we will deduce the percolation thresholdfrom the experimental results. Intuitively, the percolationtransition is closely linked with the abrupt alteration inthe measured property. Here, we will discuss the percola-tion of the siloxane bonding network or phenyl functionslinked with the above mentioned abrupt alteration in themeasured properties. In case where those deduced percola-tion thresholds from different measured properties coincidewith each other, we can conclude that the percolationthreshold could be consistently evaluated from the obser-vable quantities. Of course, the percolation threshold needsto be deduced from the result in a physically understand-able manner.

The three kinds of experiments carried out in the presentwork all show that the property of the hybrid glassabruptly alters between 30% and 40% of the molar fractionof PTES. Here, we attempt to estimate the volume frac-tions of the siloxane bondings and phenyl functions atthe above boundary fraction. For this purpose, the bulkmass densities were given as 2.2 · 103 kg/m3 and8.4 · 102 kg/m3 for the siloxane bondings and phenyl func-tions, respectively. Here, these values were tentativelyderived from the bulk mass densities of silica glass and ben-zene, respectively. Using these values of the densities, thepercolation threshold of the siloxane bonding or phenylfunction was estimated to be approximately 50 vol.%. Thispercolation threshold looks considerably smaller than nor-mal values (60–70 vol.%), the reason for which will be dis-cussed later. Next, we discuss the features of thepercolation behavior of the present systems based on com-parison to other systems comprised of siloxane bondings.Earlier works reported that Zr-modified glass undergoestwo-step percolation at 30 vol.% and 70 vol.% of the silox-ane bondings [20–23]. On the other hand, apparently, ourpresent system seems to have only one percolation thresh-old approximately at 50 vol.%. These significant differencessuggest that our partially phenylated glass has distinctstructural features from those of the earlier reports

2526 Y. Kamimura, K.-i. Kurumada / Journal of Non-Crystalline Solids 353 (2007) 2521–2527

[20–23]. Even in the case where only PTES was used as thestarting alkoxide, a solid sample was obtained. This solid-ification indicates that the percolated siloxane bonding net-work is formed even when the volume fraction of thesiloxane bonding is only 20%. Therefore, the percolatednetwork of siloxane bonding exist at any mixed fractionof PTES/TEOS. As a result of that, only one percolationthreshold was captured when the mixed fraction of PTESwas varied in the all range from 0% to 100%. Thus, thethreshold at 50 vol.% corresponds to the percolation ofthe phenyl functions because the percolated network struc-ture of the siloxane bonding is present at any mixed molarfractions of PTES. For example, an abrupt loss in the Vick-ers hardness occurred between 30% and 40% of the molarfraction of PTES. Therefore, this abrupt loss in the Vickershardness is caused by the percolation of the phenyl func-tions. Above this molar fraction of PTES, the hybrid glasshas both the percolated siloxane bonding network and per-colated cluster of the phenyl functions. In this region, themechanical properties of the hybrid glass seem to be dom-inated by the percolated cluster of the phenyl functions. Onthe other hand, below this threshold fraction of PTES, themechanical properties do not depend on the molar frac-tions of PTES. Thus, the siloxane bondings dominantlywork to exhibit the Vickers hardness in this region wherethe percolated cluster of the phenyl function is not present(Fig. 2). However, the Vickers hardness exhibits an excep-tional decrease when only a slight amount of PTES wasadded to TEOS as shown at the left-hand end of Fig. 2.When the molar fraction of PTES is quite small, for exam-ple at 2%, the phenyl functions are dispersed in a matrix ofthe siloxane bondings. The phenyl functions embedded inthe siloxane bondings will give some deformability (free-dom of deformation) because they are not covalentlybonded to a silicon atom. Due to the A-scale void betweenthe phenyl function and the surrounding siloxane bon-dings, macroscopic strain will be absorbed. Therefore, thehybrid glass exhibits some macroscopic elasticity whichhardly appears in the case where the hybrid glass was pre-pared only from TEOS.

Finally, we discuss the relationship between the A-scalemicrostructure of the hybrid glass and the percolation tran-sition. The wide-angle X-ray scattering profiles show abroad peak approximately at 20� of the scattering anglewhich corresponds to the average siloxane bonding length(Fig. 5). Here, the average siloxane bonding length can beestimated as 2p/k at the peak where k denotes the scatteredwave number. As shown in Fig. 5, the average siloxanebonding length gradually increases with the molar fractionof PTES. The relatively abrupt increase in 2p/k between30% and 40% of the molar fraction of PTES is to be linkedwith the percolation of the phenyl functions. The overalltrend of the gradual increase with the fraction of the phenylfunctions is caused by the intercalation of the phenylgroups in the matrix of the siloxane bondings. However,it should be noted that the siloxane bonding length increaseonly by 20% in the whole range of the molar fractions of

PTES. This limited magnitude of the increase in the silox-ane bonding length suggests that the percolated network ofthe siloxane bondings is retained at any molar fraction ofPTES. Otherwise, the value of 2p/k would more steeplyincrease where Si atoms would have a dispersed structurein the matrix of the phenyl functions. Therefore, the phenylfunctions tend to be hindered from forming their clustersbecause each of them is topologically constrained by thedirect covalent bonding to a Si atom. As a result of that,the percolation of the phenyl functions requires approxi-mately 50 vol.%, which is 20 vol.% larger than the thresh-old found in the earlier works [20–23].

5. Conclusion

We presumed that the various properties of partiallyphenylated organic–inorganic hybrid glass significantlydepend on the percolation/non-percolation of the siloxanebondings and phenyl functions. Therefore, we attempted toevaluate the threshold volume fraction of the percolationtransition from various measurable or observable proper-ties of sol–gel derived hybrid glasses prepared from TEOS(tetraethylorthosilicate) and PTES (phenyltriethoxysilane).The percolation threshold was estimated from the relativelyabrupt alternation in the behavior of the dye-colored statewith hydrophilic/hydrophobic dye, the Vickers hardnessand siloxane bonding length. Each of the above experi-ments consistently resulted in an abrupt alteration in themeasured property between 30% and 40% of the molarfraction of PTES. This result shows that the percolationoccurs in the above range. The above threshold corre-sponds to approximately 50% of the volume fraction ofthe phenyl function. A Since percolated siloxane bondingnetwork is present at any mixed molar fraction of PTES,the partially phenylated glass prepared from TEOS andPTES undergoes only one percolation transition at50 vol.% of the phenyl functions.

Acknowledgements

The authors gratefully acknowledge Dr K. Susa, Mr H.Kambara, Mr H. Banno, Mr S. Takanezawa and Mr K.Morita for useful comments in many discussions. They alsogreatly thank Dr T. Wakihara for his thorough technicalsupport in our measurements of the Vickers hardness.

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