Viscoelastic and Structural Properties of a Phenyl-Modified

Götze, W.; Sjögren, L. Relaxation progress in supercooled liquids. ...... Zhang , Gabriela Rodriguez , Quentin Picard , Mario Aparicio , Jadra Mosa ...
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J. Phys. Chem. B 2006, 110, 7321-7327

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Viscoelastic and Structural Properties of a Phenyl-Modified Polysiloxane System with a Three-Dimensional Structure Hiroshi Kakiuchida,*,‡ Masahide Takahashi,‡,§,† Yomei Tokuda,‡ Hirokazu Masai,‡ Minoru Kuniyoshi,‡,⊥ and Toshinobu Yoko‡ Institute for Chemical Research, Kyoto UniVersity, Uji, Kyoto-fu 611-0011, Japan, PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 322-0012, Japan, and Central Glass Co., Ltd., 3-7-1 Kandanishiki-cho, Chiyoda-ku, Tokyo-to 101-0054, Japan ReceiVed: December 16, 2005; In Final Form: February 14, 2006

The relationships between the viscoelastic and structural properties of glass-forming materials with polysiloxane bonds, which serve as network formers, and phenyl groups, which act as network terminators, are examined based on shear viscoelasticity, 29Si MAS NMR, and GPC measurements during the early stages of the networkforming process. The viscosities of the present samples do not depend on the frequency at temperatures up to 200 °C, suggesting that the origin of the viscous flow does not include intermolecular entanglement. According to the results of the strain dependence of the elastic modulus, the bridging-oxygen number, and molecular weight, the present polysiloxane system has a complex structure, or distribution of various-sized molecules composed of a polysiloxane network with various dimensionalities, and furthermore an elementary process of the viscosity is simple flow of these molecules. The structural factors that determine the viscosity and its temperature dependence are categorized into the molecular size and the intramolecular structure by using a theory based on the free-volume model. The relationship between the viscosity and the structure around the glass transition temperature is quantitatively examined and it is concluded that introducing larger numbers of Ph groups makes the viscosity less sensitive to structural factors.

1. Introduction When glass-forming liquid is cooled, the viscosity gradually increases and subsequently the liquid freezes into a glass state. This frozen-in process is called the glass transition and although it is not thoroughly understood, numerous researchers have comprehensively investigated this phenomenon.1-3 Furthermore, in recent years, the dominant factors of the frozen-in process have been examined by precisely controlling the microscopic structure.4 It has been documented that the frozen-in process is determined by cooling rate and that the viscosity is temperature dependent.5 The latter is an intrinsic property of materials, while the former is not. The temperature dependence of the viscosity for various kinds of glass-forming liquids has been examined. For example, a physical quantity, called the fragility, characterizes this dependence.6 Accordingly, the more fragile the glass, the greater the slope of the Arrhenius plot of viscosity scaled by the glass-transition temperature, Tg, as the temperature decreases toward the Tg region. Many organic materials have a large degree of fragility, while network-forming systems such as silica glass tend to behave as a strong glass. The relationship between the viscoelastic and structural properties has been investigated in many types of glass-forming materials. For example, the viscosity and elastic modulus of * Address correspondence to this author. Present address: Materials Research Institute for Sustainable Development, National Institute of Advanced Industrial Science and Technology (AIST), 2266-98 Anagahora, Shimoshidami, Moriyama, Nagoya, 463-8560 Japan. Phone: +81-52-7367528. Fax: +81-52-736-7282. E-mail: [email protected]. ‡ Kyoto University. § PRESTO, Japan Science and Technology Agency. ⊥ Central Glass Co., Ltd. † Phone: +81-774-38-3131. Fax: +81-774-33-5212. E-mail: [email protected].

polystyrene, a typical organic polymer, monotonically increase as the molecular weight increases and above a certain value the frequency dependence of the modulus becomes weak and a rubbery state appears, which is due to strong intermolecular entanglement.7 The elementary process of the viscous flow in this organic polymer is regarded as a forced translation of molecules that interact. The larger the molecular weight, the lower the molecular mobility, in other words, the larger the viscosity. Moreover, the rubbery state appears when the intermolecular interaction is enhanced or entangled between such large molecular chains. Another example is the poly(dimethylsiloxane) system, which is end-linked with tetrasilane crosslinkers. This rheological property changes from a viscous liquid toward a viscoelastic solid as the reaction progresses.8 This change results from the increased number of cross-linkages at the terminal groups and consequent intermolecular entanglement. On the other hand, silica glass, which is composed of an ideal siloxane network, has a viscosity that obeys the Arrhenius equation.9 The origin of this viscous flow is due to rearrangements in the SiO4-tetrahedral units, which form a threedimensional siloxane network,10 and the viscosity decreases as the number of network terminators such as alkali metals, halogen elements, etc. increases.11,12 As aforementioned, the structural factors that dominate the viscoelastic properties are different for materials formed by organic linear polymers and those formed by three-dimensional siloxane networks. The present samples, which consist of a siloxane network and organic functional groups, Ph4-mSi[O-]m/2 units, may possess ideal structures for determining the primal factors that govern the viscosity of a complex structure formed by molecules composed of a three-dimensional siloxane network. m in Ph4-mSi[O-]m/2 is the number of bridging

10.1021/jp0573543 CCC: $33.50 © 2006 American Chemical Society Published on Web 03/17/2006

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Figure 1. Sample preparation procedure.

oxygens per silicon and Ph is the phenyl group. The formation of the polysiloxane-network structure progresses with dehydration and polycondensation in a sol-gel reaction. The structure strongly depends on the composition of the starting materials and the heat-treatment conditions. The complex structure should form in the early stages of the polycondensation reaction. On the other hand, the Ph group is a convenient network terminator for examining the influence of the organic functional group on the viscoelastic property since the Ph group has a large occupation volume compared to that of the siloxane-unit volume. The Ph group is also important for controlling the softening behavior after a long heat-treatment time. It has been reported that introducing the Ph group into the present siloxane system prevents the viscosity from increasing during an extended heat treatment,13 although the origin of the Ph group’s effect has yet to be explained. Most of the major structure is believed to form early in the heat treatment. Therefore, studying the influence of the Ph group on the structural and viscoelastic properties during the early stage is significant to determine why the siloxane system with a larger number of Ph groups has a softening behavior that is more stable against long heat-treatment times. The viscoelastic and structural properties of the present systems, which have different starting compositions and heattreatment durations, were quantitatively investigated with use of a rheometer, 29Si MAS NMR, and Gel Permeation Chromatography (GPC) apparatuses. The relationship between the viscoelastic and structural properties is discussed by using a theory based on the free-volume model. 2. Experimental Section Two starting materials, monophenyltriethoxysilane (PhSi(OEt)3) and diphenyldiethoxysilane (Ph2Si(OEt)2), were used to prepare the samples by the sol-gel method shown in Figure 1. A mixture of ethanol, water, and hydrochloric acid was added, dropwise, to a mixture of PhSi(OEt)3 and ethanol. The resultant solution was stirred for 3 h at room temperature in air and then a mixture of Ph2Si(OEt)2 and ethanol was added, dropwise. Afterward, ammonia was introduced and the solution was stirred for an additional 3 h. Stirring for a few days at room temperature caused the solution to gel. The gel became glassy by heating for 1 day at 110 °C in air. To remove the NH4Cl microcrystals, which may have formed in the samples, the bulk gels were crushed into powders and rinsed with water. The resultant powders were dried for 1 h at 110 °C in a decompression

Kakiuchida et al. chamber. The samples were further heat treated at 200 °C in air for the prescribed durations and then subjected to several measurements to examine their viscoelastic and structural properties. The dynamic shear modulus was measured with a rheometer (UBM Co., Ltd., Model G-2000). Dynamic torsion was applied to a sample sandwiched between two parallel plates, which had a 20 mm diameter with a 1 mm gap, and respondent stress was detected. The accuracy of the system was examined with use of silicone oil, which is a common standard with a known viscosity (Nippon Grease Co., Ltd., JS160000). The measured value agreed with the standard within a deviation of (10%. The frequency dependence of the elastic modulus in the range of 10-3 to 10 Hz was examined at temperatures between room temperature and 200 °C. The time required for this measurement was as short as possible to avoid undesirable structural changes. Furthermore, after each sample was measured at the maximum temperature and cooled, it was remeasured at low temperature to confirm that undesirable changes in the viscosity were within 5%. The viscoelastic behavior as a function of frequency was assumed to be equivalent to that as a function of temperature,14 which has been documented for many glass-forming materials.15-17 Thus, the elastic-modulus spectra obtained at various temperatures were superposed by shifting the spectra along the frequency axis. On the other hand, to obtain the structural information, which is connected to the elementary process of viscous flow, the strain dependence of the elastic modulus was examined. The present system contained a three-dimensional network, Ph4-mSi[O-]m/2, which is composed of PhSi[O-]3 (T-) units and Ph2Si[O-]2 (D-) units. The number of bridging oxygens per silicon, m, can be controlled by varying the ratio of T- to D-units. The spatially averaged number of bridging oxygens, 〈m〉, was estimated from the ratio of the deconvoluted-peak areas in the spectrum obtained by a 29Si MAS NMR (Chemagnetics, Model CMX-400). All the measurements were conducted at a spin rate of 3 kHz and a pulse delay of 240 s at room temperature. The internal standard was polydimethylsilane. The molecular-volume distribution was measured by Gel Permeation Chromatography (GPC, Tosoh Co., Ltd., Model RI8000). The samples were dissolved in tetrahydrofuran (THF) and eluted at a flow rate of 1 mL/min in the GPC column at 40 °C. Before each measurement the GPC apparatus was calibrated by using three poly(dimethylsiloxane)s (PDMS) with different molecular weights (Aldrich Chemical Co., Inc.). Since the value obtained by GPC is, in principle, related to the hydrodynamic volume of the molecules, the molecular weight of the PDMS standard with the same elution time as the present sample is regarded as an indicator of the molecular volume in the present samples. 3. Results The viscoelastic properties of samples with different compositions of (1 - x)PhSi(OEt)3:xPh2Si(OEt)2 were examined as a function of heat-treatment time. The frequency dependences of the elastic moduli in samples with x ) 0, 0.1, 0.2, and 0.3 were measured. The viscosity, η, was estimated from the imaginary part of the elastic modulus, G′′, and the angular frequency, ω, that is, η ) G′′/ω. Parts a and b of Figure 2 plot the logarithms of η for samples with x ) 0.1 and 0.3 against the reciprocal of temperature, respectively. The insets show the relationships between G′′ and ω at 100 °C, which were obtained by shifting along the ω-axis to superimpose the respective spectra. All the G′′ spectra were approximated by a line with a

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Figure 3. Real part of elastic moduli of samples with different x as a function of strain. The elastic moduli are measured at temperatures where the real part is larger than the imaginary one. The temperatures for the respective samples are shown in parentheses. The results are obtained after a 4-h heat treatment at 200 °C.

Figure 2. Temperature dependence of the viscosity for samples prepared from different starting material compositions, (1 - x)PhSi(OEt)3:xPh2Si(OEt)2. Solid curves are fitted with eq 2 as expressed in the Discussion section. Insets show the relationship between the imaginary part of elastic modulus, G′′, and the angular frequency, ω. For comparison, the solid lines with a slope of unity are shown.

slope of unity, which indicated that the viscosities of the present samples are independent of ω, or are Newtonian. The solid curves in the figures were fitted by using eq 2 as discussed in the next section. As the duration of the heat treatment increased, η increased, while the viscosity remained a Newtonian flow. In a viscous fluid, G′′ is generally larger than the real part of the elastic modulus, G′. However, as the temperature decreases, G′ increases faster than G′′ and the value of G′ exceeds G′′ at a certain temperature where the material behaves like an elastic body rather than a viscous fluid. The strain dependence of the elastic modulus in this state helps to obtain a microscopic view of the viscoelastic mechanism. Figure 3 shows G′ for samples with varying x values as a function of strain at a temperature where G′ is larger than G′′. Numerous condensed polymers have G′ independent of strain up to about 100%.18,19 On the other hand, G′ for suspension systems tends to decrease as the strain increases above a few percent.20,21 The present G′ decreased at a strain above 3%, which is similar to suspension systems. This similarity led to the conjecture that the present system contains various-sized molecules and the molecules with smaller volumes may assist those with larger volumes to smoothly and flexibly move. More detailed structural information was obtained by using the NMR and GPC measurements. The number of bridging oxygens per silicon, m, as a function of x and heat-treatment time was examined by 29Si MAS NMR. Parts a and b of Figure 4 show the NMR spectra of samples with x ) 0.1 and 0.3, respectively. The line profiles located near chemical shifts of

Figure 4. 29Si MAS NMR spectra of samples prepared from different starting material compositions, x, by a heat treatment with various durations. The broken curves are deconvoluted peaks. Insets show the average number of bridging oxygens, 〈m〉, which are estimated from the ratio of the deconvoluted-peak areas as a function of heat-treatment time.

-70 and -40 ppm were due to the T- and D-units, respectively.22 These spectra were deconvoluted into Gaussian peaks as shown by the broken curves. The T 3 peak resulted from silicon, which had three bridging oxygens, that is, PhSi[O-]3. The T 2OEt and T 2OH peaks originated from PhSi[O-]2OEt and PhSi[O-]2OH, respectively, where Et is the ethoxyl group. The T 1 peak was ascribed to silicon with one bridging and two nonbridging oxygens. On the other hand, the D2 peak was due to Ph2Si[O-]2, while the D1 peak was due to silicon with one bridging and one nonbridging oxygens. The Dcycl peak was from

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Kakiuchida et al. Changing the compositions of the starting materials or the heat-treatment time extends the distribution of the molecular volume from 3 000 to 200 000 in terms of PDMS’s molecular weight. These experimental results imply that the flow of these widely distributed molecules directly influences the viscosity. Two structural parameters, the average number of bridging oxygens, 〈m〉, and the average molecular weight, 〈M〉, characterize the molecular structure in the present materials. Hence, the structure influences the molecular flow and consequently the viscosity. The influence of these structural parameters on the viscosity is discussed by using a theory based on the free-volume model. The temperature dependence of viscosity during glass formation is often interpreted by using a free-volume model and a thermally activated process.24-26 This interpretation has been reliably employed for analyzing the frozen-in process for a plethora of materials.27,28 Free volume is an excess space for rearranging the molecular configurations and the rearrangement corresponds to the elementary process of viscous flow. In this model, the viscosity, η, as a function of temperature, T, is expressed by

η ) η0 exp

Figure 5. GPC profiles of the samples prepared from different starting material compositions, x, by heat treating for various durations. M is an indicator of the molecular volume of the measured samples. Insets show the weight-average molecular weight, 〈M〉, which is estimated from the profiles as a function of heat-treatment time.

hexaphenylcyclosiloxane.23 The presence of a T 2, T 1, or D1 peak indicated that the reaction was not complete after the sample was prepared as shown in Figure 1 and the areas of the T 2, T 1, and D1 peaks decreased upon further heat treatment, while the areas of the T 3 and D2 peaks increased. Since the peak area was proportional to the number of silicons, the average number of bridging oxygens, 〈m〉, was estimated from these deconvoluted-peak areas. The insets plot the estimated values of 〈m〉 against heat-treatment time. As the duration of the heat treatment increased, 〈m〉 obviously increased. Variations in the molecular volume with heat-treatment time were examined with use of the GPC apparatus. Parts a and b of Figure 5 show the molecular weight distributions, M, for samples with x ) 0.1 and 0.3, respectively. The distribution widened toward large values as the heat-treatment time increased. The weight-average molecular weight, 〈M〉, was estimated from the distribution, which is equivalent to the average molecular volume of the present system. As shown in the insets, the values exponentially increased as the heat-treatment time increased. 4. Discussion The viscoelastic properties in the early stages of polycondensation were examined. The elastic modulus remains constant for small strain and the modulus decreases as the strain increases above 3%. The present NMR and GPC results provide structural information, that is, the present system possesses molecules with widely distributed molecular weights and the molecules consist of a three-dimensional polysiloxane network.

( ) (

Ea γ exp kBT Rf(T - T0)

)

(1)

where kB is the Boltzmann constant and η0 is the preexponential factor. The first exponential term on the right-hand side indicates the attempt frequency of the molecular jump toward selfdiffusion, which obeys a thermally activated process with activation energy of Ea. The last exponential term corresponds to the probability that a free volume exists. In other words, the excess space is sufficient for the jumped molecules to move into it. T0 is the temperature where the free volume disappears, while Rf is the thermal expansion coefficient of the free volume and γ is a constant that relates to the overlap of free spaces. When T is much higher than T0, the last exponential term is nearly constant and eq 1 obeys the Arrhenius equation. When T is slightly larger than T0, the first exponential term in eq 1 is regarded as constant compared with the change in the second term and then eq 1 is replaced by the VTF formula,29-31

η ) η0′ exp

(

γ Rf(T - T0)

)

(2)

where η0′ ≈ η0 exp(Ea/kBT) is the constant. In eq 2, the viscosity approaches infinity as T approaches T0 and this change is affected by Rf/γ. On the other hand, η0′ is determined by the thermally activated process of the molecular jump, which includes viscosity information at high temperature compared to T0. The viscosity parameters, T0, Rf/γ, and logη0′, are obtained by fitting eq 2 to the temperature dependence of the viscosity, which are shown by the solid curves in Figure 2. The viscosity and structural parameters are listed in Table 1. In parts a-c in Figure 6 the viscosity parameters are plotted against the structural parameters, 〈m〉, and log〈M〉, since the structural parameters are equivalent to the degrees of the network dimension and the volume of the molecules, respectively. The bird’s eye views show that the viscosity parameters systematically change with these structural parameters. The viscosity parameters of all the samples are fitted to planes, which are the simplest empirical function in three-dimensional plots,

T0, (Rf/γ), or (logη0′) ) a〈m〉 + b log〈M〉 + c ) PS + c (3)

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TABLE 1: Structural and Viscosity Parameters of the Present Samples 〈m〉

log〈M〉

T0

Rf/γ

logη0

0 0 0 0 0 0 0

2.44 2.46 2.48 2.50 2.52 2.56 2.61

3.83 3.84 3.88 3.96 3.99 4.09 4.18

14.12 11.53 13.79 15.29 25.79 33.60 40.71

3.48 3.51 3.49 3.47 3.35 3.26 3.19

-3.48 -3.30 -3.08 -3.95 -2.59 -2.38 -2.05

0.1 0.1 0.1 0.1

2.16 2.32 2.35 2.38

3.94 4.16 4.51 4.84

-7.18 7.62 33.22 50.76

3.76 3.56 3.27 3.09

-4.57 -2.42 -0.72 0.06

0.2 0.2 0.2 0.2

2.13 2.35 2.39 2.42

3.94 4.29 4.47 4.68

-7.14 11.29 19.93 24.87

3.76 3.52 3.41 3.36

-3.89 -2.50 -1.42 -1.40

0.3 0.3 0.3 0.3 0.3

2.03 2.27 2.27 2.30 2.32

3.80 3.88 3.94 4.00 4.07

-5.88 0.97 1.61 2.11 10.03

3.74 3.65 3.64 3.63 3.53

-3.37 -3.48 -2.69 -2.68 -1.97

x

as shown in Figure 6, parts a-c, where a, b, and c are the fitting parameters and the parameter PS, which is defined as (a〈m〉 + b log〈M〉). Parts a-c of Figure 7 are the plots viewed along the cross-lines of the fitted planes with the 〈m〉 - log〈M〉 plane in Figure 6, parts a-c, respectively, where the solid lines in Figure 7a-c are the cross-section profiles of the fitted planes. All the viscosity parameters are within a certain deviation of the solid lines. This result strongly suggests that two parameters, the number of bridging oxygens and the molecular volume, are the primary structural factors that determine the viscous behavior. The fittings shown in Figure 7 provide information on how strongly the structural parameters contribute to the viscosity parameters. The fraction of the contributions of 〈m〉 and log〈M〉 are regarded as the ratio of the coefficients in eq 3, a:b. The estimated ratios for T0, Rf/γ, and log η0′ are 0.69:0.31, -0.71:-0.29, and 0.23:0.77, respectively. The parameters T0 and Rf/γ characterize the free volume, while η0′ is related to the thermally activated process of the molecular jump as expressed in eq 2. According to these ratios, the contribution of the bridging-oxygen number to the free volume is relatively strong, but the molecular volume more strongly contributes to the thermally activated process. The present results are summarized as follows: 1. The samples likely possess a complex structure. The THF solvent unravels the molecules that are weakly bound to each other. Each molecular unit consists of three-dimensional siloxane bonds, which form the network, and Ph groups, which serve as network terminators. 2. The viscosity is independent of ω, which corresponds to Newtonian viscosity. 3. The elementary process of the viscous flow is similar to that of common suspension systems since the elastic modulus monotonically decreases as the strain increases beyond about 3%. 4. T0 should increase by 1 °C, when 〈m〉 or log〈M〉 increases by (1/67.8) or (1/30.4), respectively. On the other hand, reducing Rf/γ by 1 × 10-3 K-1 can be realized by increasing 〈m〉 or log〈M〉 by (1/0.843) or (1/0.348), respectively. 5. Increasing 〈m〉 or log 〈M〉 by (1/0.96) or (1/3.25), respectively, increases η0′ 10-fold. Summaries 1-3 suggest that the factor dominating the viscosity is the flow of molecules without strong interactions

Figure 6. A bird’s eye view of the plots of the viscosity parameters, (a) T0, (b) Rf/γ, and (c) logη0′, as functions of the structural parameters, 〈m〉 and log〈M〉, for different values of x and heat-treatment times. Note that the planes are the fittings of all the measured results to eq 3.

such as intermolecular entanglements. The free volume in the present system is the excess space required for the flow of these molecules. This space decreases and the molecular mobility is depressed when T0 increases or (Rf/γ) decreases. According to eq 2, the free volume dominates the viscosity at temperatures near the glass transition, while the thermally activated process influences the viscosity at high temperatures. Summaries 4 and 5 suggest that changing the bridging-oxygen number and/or the molecular volume flexibly controls the fragility with regard to temperature dependence of viscosity. Furthermore, the organic functional group in the present system affects the viscoelastic property. The number of bridging oxygens and the molecular volume are significant factors that govern the viscoelastic behavior as shown by the thick solid lines in Figure 7a-c. In addition to these structural parameters, the sections irrelevant to siloxane-network formation, that is,

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Figure 8. PS dependences of the viscosity parameters, T0, Rf/γ, and logη0′, which correspond to the slopes of thin lines in Figure 7, as a function of the number of Ph groups. The broken curves for T0 and Rf/γ are to guide the eye.

and d(Rf/γ)/dPS, become weak as (1 + x) increases, while d(logη0′)/dPS is independent of (1 + x). These observations indicate that the Ph groups prevent variations in the free volume when either the number of bridging oxygens or the molecular volume changes. The present result indicates that the viscosity near the glass transition region for a polysiloxane system with a larger number of Ph groups is less sensitive to the changes in the network structure and molecular volume. 5. Conclusion

Figure 7. The viscosity parameters, (a) T0, (b) Rf/γ, and (c) logη0′, as a function of PS ) a〈m〉 + b log〈M〉 where a and b are the constants determined by the planar fittings expressed by eq 3 for the plots in Figure 6, parts a to c, respectively. For comparison, insets plot the viscosity parameters against 〈m〉 or log〈M〉. The four types of thin lines are linear fits of the results for the respective values of x.

the Ph groups in the present system, influence the relationship between the structural and viscoelastic parameters. The average number of Ph groups per silicon is estimated from the ratio of the starting materials as (1 + x), where x is defined in the Results section. If the existence of the Ph groups strongly affects the viscosity, the relationships between the viscosity parameters, T0, Rf/γ, and logη0′, and the structural parameter, PS, should depend on the Ph number. The four types of thin lines drawn in Figure 7 are linear fits of the results for the respective values of x. Figure 8 plots their slopes, dT0/dPS, d(Rf/γ)/dPS, and d(logη0′)/dPS, against (1 + x), so that the slopes correspond to the extent of the contributions of 〈m〉 and log〈M〉 to the viscosity. The PS dependences of the free-volume parameters, dT0/dPS

The viscoelastic and structural properties of glass-forming materials, which consist of a polysiloxane network and phenyl groups, Ph4-mSi[O-]m/2, were examined, where m is the number of bridging oxygens. The results of the elastic moduli as functions of the applied frequency and strain amplitude indicate that the present system does not contain strong interactions between the molecules in the early stage of network formation. The NMR and GPC measurements imply that the samples most likely possess complex structures. That is, the molecules consist of a three-dimensional siloxane network and Ph groups, and are distributed to maintain weak bonds with each other. The flow of the molecules is connected to the molecular volume and intramolecular structure by using a theory based on the freevolume model. The viscosity is dominated by both the number of bridging oxygens and the molecular volume. The manner of this influence is different for a free-volume process and a thermally activated process since the former is strongly influenced by the number of bridging oxygens, while the latter is strongly affected by the molecular volume. Furthermore, the Ph groups, which serve as organic network terminators, suppress the influences of the molecular structure on the viscoelastic property. Acknowledgment. The authors thank Professor H. Watanabe and his colleagues at the Institute for Chemical Research, Kyoto University, for GPC measurements and stimulating comments. References and Notes (1) Ja¨ckle, J. Theory of glass transitions new thoughts about old facts. Philos. Mag. B 1987, 56 (2), 113-127. (2) Sastry, S. The relationship between fragility, configurational entropy and the potential energy landscape of glass-forming liquids. Nature 2001, 409, 164-167. (3) Go¨tze, W.; Sjo¨gren, L. Relaxation progress in supercooled liquids. Rep. Prog. Phys. 1992 55 (3), 241-376.

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