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Characterization of Poly( silylenemethylene)s by Positron Annihilation Lifetime Spectroscopy. I. TAKUYA OGAWA, 1 TAKENORI SUZUKI, 2 MASASHI MURAKAMI 1 1 Research Center, Dow Corning Asia Ltd., Kishi, Yamakita, Kanagawa 258-01, Japan 2 High Energy Accelerator Research Organization ( KEK ) , Tsukuba, Ibaraki 305, Japan Received 13 February 1997; revised 22 July 1997; accepted 1 October 1997 ABSTRACT: Amorphous and crystalline poly ( silylenemethylene ) s with the repeating PhRSiCH 2 (R : Me or Ph) units were characterized by positron annihilation lifetime spectroscopy ( PALS ) to gain insights into the molecular motions of these polymers. The temperature dependence of the ortho-positronium lifetime ( t 3 ) and intensity ( I 3 ) was examined from 50 to 470 K for each sample. The glass transition temperature of each polymer was easily distinguished by a change in the slope of t 3 spectrum. Both polymers exhibited a steep drop of I 3 at 130–140 K being probably assignable to the transition arising from the motions of phenyl groups, which was almost undetectable by means of differential scanning calorimetry or dynamic mechanical analysis. Several other transitions of these polymers detected by PALS are also discussed. q 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 755–761, 1998 Keywords: positron annihilation lifetime spectroscopy; free volume; transition temper- atures; poly ( silylenemethylene ) s; dynamic mechanical analysis INTRODUCTION tion about free volume of polymeric materials. 2 This analytical tool is of great advantage in some cases due to its high sensitivity toward a smaller There are several analytical methods to provide change in polymer microstructures compared information about the transition behavior arising with the traditional analytical techniques men- from the molecular motions of polymers. Differen- tioned above. The mechanism of positron annihi- tial scanning calorimetry ( DSC ) and dynamic me- lation has already been well explained in that a chanical analysis (DMA) are examples of such positron picks up an electron to form a positro- methods that are used to understand the macro- scopic mechanical properties of polymers. The free nium (Ps) and is annihilated by being trapped in volume theory has been proposed in early fifties large cavities of a disordered area or in large free to explain the molecular motion and physical be- volumes in polymers. The lifetime ( t 3 ) and inten- havior of glassy and liquid states, 1 and quantify- sity ( I 3 ) of ortho-positronium ( o-Ps ) have been be- ing the relationship between the molecular mo- lieved to be related to the size and the number of tions and free-volume properties is one of the the free volumes, respectively. 3 It was reported focused issues in polymer research. Positron anni- that the temperature dependence of t 3 apprecia- hilation lifetime spectroscopy ( PALS ) in polymers bly altered at the glass transition temperature has recently been gathering much interest be- ( T g ) in most polymeric systems. 2 Behavior of I 3 , cause it has been established to provide informa- however, can sometimes not be explained by a change in the number of free volumes. In addition, the transition behavior at temperatures lower Correspondence to: T. Ogawa than the T g has not been fully investigated, while Journal of Polymer Science: Part B: Polymer Physics, Vol. 36, 755–761 (1998) q 1998 John Wiley & Sons, Inc. CCC 0887-6266/98 / 050755-07 few reports have been published dealing with the 755 9702007 / 8Q4F$$2007 01-23-98 15:56:37 polpa W: Poly Physics

Characterization of poly(silylenemethylene)s by positron annihilation lifetime spectroscopy. I

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Page 1: Characterization of poly(silylenemethylene)s by positron annihilation lifetime spectroscopy. I

Characterization of Poly(silylenemethylene)s by PositronAnnihilation Lifetime Spectroscopy. I.

TAKUYA OGAWA,1 TAKENORI SUZUKI,2 MASASHI MURAKAMI1

1 Research Center, Dow Corning Asia Ltd., Kishi, Yamakita, Kanagawa 258-01, Japan

2 High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

Received 13 February 1997; revised 22 July 1997; accepted 1 October 1997

ABSTRACT: Amorphous and crystalline poly(silylenemethylene)s with the repeatingPhRSiCH2 (R : Me or Ph) units were characterized by positron annihilation lifetimespectroscopy (PALS) to gain insights into the molecular motions of these polymers.The temperature dependence of the ortho-positronium lifetime (t3) and intensity (I3)was examined from 50 to 470 K for each sample. The glass transition temperature ofeach polymer was easily distinguished by a change in the slope of t3 spectrum. Bothpolymers exhibited a steep drop of I3 at 130–140 K being probably assignable to thetransition arising from the motions of phenyl groups, which was almost undetectableby means of differential scanning calorimetry or dynamic mechanical analysis. Severalother transitions of these polymers detected by PALS are also discussed. q 1998 JohnWiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 755–761, 1998Keywords: positron annihilation lifetime spectroscopy; free volume; transition temper-atures; poly(silylenemethylene)s; dynamic mechanical analysis

INTRODUCTION tion about free volume of polymeric materials.2

This analytical tool is of great advantage in somecases due to its high sensitivity toward a smallerThere are several analytical methods to providechange in polymer microstructures comparedinformation about the transition behavior arisingwith the traditional analytical techniques men-from the molecular motions of polymers. Differen-tioned above. The mechanism of positron annihi-tial scanning calorimetry (DSC) and dynamic me-lation has already been well explained in that achanical analysis (DMA) are examples of suchpositron picks up an electron to form a positro-methods that are used to understand the macro-

scopic mechanical properties of polymers. The free nium (Ps) and is annihilated by being trapped involume theory has been proposed in early fifties large cavities of a disordered area or in large freeto explain the molecular motion and physical be- volumes in polymers. The lifetime (t3) and inten-havior of glassy and liquid states,1 and quantify- sity (I3) of ortho-positronium (o-Ps) have been be-ing the relationship between the molecular mo- lieved to be related to the size and the number oftions and free-volume properties is one of the the free volumes, respectively.3 It was reportedfocused issues in polymer research. Positron anni- that the temperature dependence of t3 apprecia-hilation lifetime spectroscopy (PALS) in polymers bly altered at the glass transition temperaturehas recently been gathering much interest be- (Tg ) in most polymeric systems.2 Behavior of I3 ,cause it has been established to provide informa- however, can sometimes not be explained by a

change in the number of free volumes. In addition,the transition behavior at temperatures lower

Correspondence to: T. Ogawathan the Tg has not been fully investigated, while

Journal of Polymer Science: Part B: Polymer Physics, Vol. 36, 755–761 (1998)q 1998 John Wiley & Sons, Inc. CCC 0887-6266/98/050755-07 few reports have been published dealing with the

755

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756 OGAWA, SUZUKI, AND MURAKAMI

temperature dependence of t3 and I3 for polyethyl-ene,4–6 long-chain paraffines,7 and polystyrene.8

We have been studying the synthesis and prop-erties of poly(silylenemethylene)s with the re-peating Si{C backbone units as a new class ofthermally stable silicon-based polymers. Poly(di-phenylsilylenemethylene) ([Ph2SiCH2]n; PDPSM)was found to be a thermally stable crystallinepolymer with the Tg and the melting temperature(Tm) at 140 and 3507C,9 respectively,10 whereaspoly(methylphenylsilylenemethylene) ([MePhSi-CH2]n ; PMPSM) is an amorphous polymer withthe Tg of around 257C.11 We have also reported thesynthesis and the preliminary characterization ofthe poly(silylenemethylene)-based polymer blends Figure 1. Dynamic moduli of two poly(silylenemeth-prepared by in situ polymerization.12 DMA indi- ylene)s as a function of temperature obtained by heat-

ing at a rate of 107C/min at a constant frequency of 1cated that PMPSM may exhibit a transition atHz and a constant strain of 0.05%. Square and circlearound 01207C, probably due to the motions ofdata points: PMPSM; cross in square and cross in circle:phenyl groups, but the assignment of this weakPDPSM. Melt processing in the presence (for PDPSM)transition was ambiguous.11 In addition, althoughor absence (for PMPSM) of two antioxidants at 3557CDMA of PDPSM depicted a weak transition at(for PDPSM) or at 1207C (for PMPSM) was applied toaround 60–707C, the cause of the transition hasprepare specimens with the following size: 10 (width)

not been fully understood.131 35 (length) 1 1 (thickness) mm3.

In this article, we describe the characterizationof poly(silylenemethylene)s with the repeatingPhRSiCH2 (R : Me or Ph) units by PALS. The weights (Mws) and the polydispersities (PDs) of

PMPSM calculated using polystyrene standardspurpose of the present study is to probe the transi-tions in these polymers that could not be suffi- were 5.5 1 105 and 2.7, respectively. Differential

scanning calorimetry (DSC) was carried out un-ciently identified by DSC and DMA. Some differ-ences between these silicon-based polymers and der a nitrogen atmosphere using a Perkin–Elmer

DSC 7/1022 system. The melting temperaturetraditional carbon-based polymers may be clari-fied by this analytical method. The transition be- (Tm ) of PDPSM was obtained in the second heat-

ing scan at a heating rate of 107C/min. The glasshavior is informative and leads to effective under-standing of polymer–polymer interactions in the transition temperatures (Tgs) of the samples pre-

pared by quenching a molten polymers were ob-polymer blends.tained from the second heating scan at a heatingrate of 207C/min. Dynamic mechanical propertiesof these samples were examined with a Rheome-EXPERIMENTALtrics RDA II dynamic analyzer in a torsion modeusing melt-processed specimens. The temper-Materials and Characterization Methodsature dependence of the dynamic moduli of twopoly(silylenemethylene)s is displayed in Fig-Two antioxidants (IRGANOX 1010 and phthalo-

cyanine) were purchased from Ciba–Geigy Japan ure 1.Ltd. and Wako Pure Chemical Ind. Ltd., respec-tively. PMPSM and PDPSM were synthesized by

PALS of Poly(silylenemethylene)sring-opening polymerization of 1,3-dimethyl-1,3-diphenyl-1,3-disilacyclobutane (DDDC) and 1,1,- PALS experiments were conducted with a conven-

tional fast-fast coincidence system having a life-3,3-tetraphenyl-1,3-disilacyclobutane (TPDC) ,respectively without a catalyst.10,11 Gel perme- time resolution of 270 ps full width at the half

maximum. The details are described elsewhere.14ation chromatography (GPC) was performed us-ing chloroform as an eluent with a Tosoh HLC- A 22Na positron source was sandwiched by two

poly(silylenemethylene) sample in a size 10 1 108020 gel permeation chromatograph equippedwith two TSK gel GMHHR-H columns and a mm with 1 mm thickness for each PALS experi-

ment.refractometer. The weight-average molecular

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CHARACTERIZATION OF POLY(SILYLENEMETHYLENE)S BY PALS 757

A cryogenic system, IWATANI S030-CW303,was employed for a low temperature experimentbetween 50 and 300 K. The experimental proce-dure for the temperature profile of each samplewas as follows: a sample was kept at room temper-ature for ca. 1 h to collect several data points andthen cooled down to 50 K for approximately 40min. This temperature was kept for about 200 h,during which PALS data were collected everyhour. The sample was then heated with a 5 K stepbefore holding for 10 min to collect data, and thisprocess was repeated to 300 K.

Each sample placed in a heat cell was heatedfrom 300 to 470 K, then cooled down to 300 Kat a rate of 5 K/h under flowing nitrogen. Three Figure 2. The time dependence of t3 and I3 forlifetime components were resolved from the PALS PMPSM and PDPSM. The sample was kept at 300 Kdata by using ‘‘POSITRONFIT EXTENDED.’’ 15

for the first hour, then cooled to 50 K for the subsequent130 h in the case of PMPSM (square and circle) andfor the subsequent 220 h in the case of PDPSM (crossin square and cross in circle) .RESULTS AND DISCUSSION

Transition Behavior of Poly(silylenemethylene)smovements accompanied by the change in the sizeby DMA and DSCof free volumes did not take place while this was

As depicted in Figure 1, PMPSM showed a very in the relaxation process, as shown by the I3 pro-steep drop of G * accompanied by a sharp peak of files. On the other hand, a gradual increase of t3G 9, both of which are typical properties of amor- was observed for PDPSM, indicating that the freephous polymers. On the other hand, the G * of volumes of this polymer increase even at low tem-PDPSM remained at values higher than 109 dyne/ peratures. The frozen structures of the amor-cm2 at temperatures above its Tg (ca. 413 K) be- phous parts of this polymer, which might be af-cause of the relatively high crystallinity of this fected by the crystalline parts, may not be thematerial. In addition, this polymer evidently ex- most thermodynamically stable, and thereforehibited a transition at around 483 K, which is were transformed to the more stable structures bybelieved to reflect a crystalline–crystalline transi- extending its free volumes during this relaxationtion.13 Both of these polymers also seem to possess period. One can also find that PDPSM exhibitsa transition in a temperature between 155 and larger t3 than PMPSM. This evidently indicates185 K, but are ambiguous due to the scatter in that the former has the larger intermoleculardata caused by an insufficient grip of the mechani- spaces or larger free volumes than the latter duecal analyzer at such low temperatures. An analy- to the larger number of bulky phenyl groups. Itsis using DSC yielded information about the Tgs, has been reported that the values of t3 of polysty-but no other transition was detected for both poly- rene at temperatures lower than 280 K was largermers. than those of polypropylene.16

Each sample displayed a monotonous increaseof I3 , indicating that the local motions of the mo-The Lifetime and Intensity oflecular chains were getting frozen during this pe-Poly(silylenemethylene)s at 50 Kriod. The probability that o-Ps is trapped in freevolumes is presented in terms of I3 , and decreasesThe lifetime (t3) and intensity (I3) of PMPSM and

PDPSM at a constant temperature of 50 K are by the local motions of molecules. Hence, suppres-sion or freezing of the molecular motions leadsdepicted in Figure 2. Both polymers showed a

rapid decrease of t3 and I3 when cooled to 50 K to an increase of the probability and, therefore,increases the values of I3 .4,6,17 It also should bedue to a thermal shrinkage of the intermolecular

space holes in which Ps can be trapped. While noted that a longer time was required for PDPSMto reach an almost constant values of I3 . Thisbeing maintained at 50 K, PMPSM showed almost

constant values of t3 , suggesting that molecular must be related to the gradually increased t3 de-

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758 OGAWA, SUZUKI, AND MURAKAMI

using Figure 4, in which PALS data at highertemperatures are presented.

The I3 profile is very informative in under-standing the molecular motions of this polymer.Figure 3 displays minimum I3 at ca. 270 K andincreased with increasing temperature above thattemperature. The increase in I3 seems to relate tothe increased slope of t3 and can be assigned tothe micro-Brownian motions of molecules. Abovethis temperature, a relatively long segment ofpolymer main chains starts moving to lead theglass transition. Polystyrene has been reported toexhibit the minimum in I3 at around 250–260 K,while the Tg of this polymer is not in the tempera-Figure 3. The temperature dependence of t3 and I3ture range.8 The difference between PMPSM andfor PMPSM obtained by heating at a rate of 5 K/h.polystyrene would be caused by the intermolecu-lar interaction. The interaction via phenyl groupsin PMPSM may be smaller than that in polysty-

scribed above, and seems ascribed to the slower rene due to the presence of methyl groups. Thererelaxation process than that of PMPSM. There are several nonlinear regions below 270 K, al-is a notable difference in the I3 values, which is though a complete linearity of t3 was observeddefinitely attributed to the degree of crystallinity below 284 K. A steep increase in decreasing tem-of the samples because a Ps is formed and annihi- perature at ca. 230–270 K and a plateau regionlated only in free volumes in amorphous materi- at ca. 140–230 K followed by a small but a definiteals.2c PMPSM is an amorphous polymer, while discontinuity at around 140 K were recorded. Be-PDPSM shows its relatively high degree of crys- cause it is unreasonable that the number or con-tallinity of about 50%.13

centration of free volumes increase with decreas-ing temperature, the I3 increase does not neces-sarily indicate an increase of free-volumeconcentration. The increase thus observed wouldTemperature Dependence of t3 and I3 for PMPSMbe explained by the freezing of the local molecularmotions as described in the previous section. AtThe temperature dependence of t3 and I3 between

50 and 370 K for PMPSM is illustrated in Figure the plateau region, almost no change in I3 wasobserved, probably because polymers are in static3. The t3 values increased with increasing tem-

perature as expected for a thermal expansion ofthe free volumes, and an easily distinguishablebreaking point where the slope of increasechanges was observed at around 284 K. This tem-perature can be assigned to the Tg of this polymer,which is appreciably lower than that (294 K) de-termined by DSC. Tgs of amorphous polymers de-termined by PALS are consistently lower thanthose measured by DSC because of the followingtwo reasons.2a,18 (1) Only a local heating of theholes by o-Ps was required in a PALS measure-ment. (2) A remarkably slow scanning rate of ca. 5K/h was employed for PALS, whereas the heatingrate of 207C/min was used for DSC. The observedincrease in slope at temperatures higher than itsTg can be interpreted by an increased size of free Figure 4. The temperature dependence of t3 and I3volumes caused by the activated micro-Brownian at temperatures higher than 300 K for PMPSM ob-motions of molecules. One may find another data tained at a rate of 5 K/h by heating (square and circle)point at around 350 K, at which the slope alters and subsequent cooling after 3 h holding at 470 K (cross

in square and cross in circle) .in the t3 spectrum. This will be explained below

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CHARACTERIZATION OF POLY(SILYLENEMETHYLENE)S BY PALS 759

state. The definite discontinuity at around 140 Kwill be attributed to a transition by the motionssuch as vibrational motions of phenyl groups onthe polymer backbone. An increase in I3 with adecreasing temperature was also found at ca.100–130 K for polystyrene and was interpretedas local motions of phenyl groups,8 but the I3 in-crease in that report was not dramatic. Takingthe sterical bulkiness of PMPSM imposed by anadditional methyl group into account, the flexibil-ity of the main chain of PMPSM would be respon-sible for the steepness of the I3 change observed.One can find an additional nonlinear point ataround 100 K above and below which the values Figure 5. The temperature dependence of t3 and I3of I3 increase with decreasing temperature. The for PDPSM obtained by heating at a rate of 5 K/h.cause of nonlinearity has not been identified, butthe behavior at 100–140 K could be ascribed tothe other motions of phenyl groups, and one possi- DSC analysis. Crystalline polypropylene showed

a change in slope of t3 at around 390 K, whereble explanation for the behavior below 100 K ismotions by methyl groups. Because no change in crystallization takes place.16 Linear and branched

polyethylenes also exhibited a breaking point ofthe slope of t3 was observed as mentioned before,it is evident that these transitions occur without t4 , the longest lived component, at 313 K, above

which the molecular motions in the crystallinealtering the size of free volumes. DMA indicatesthat PMPSM seemed to exhibit a weak transition region are suggested to occur.4 Differences be-

tween heating and cooling spectra were not ob-at the temperature between 155 and 185 K, whichcan probably be assigned to the motions of phenyl served, suggesting that an effect of thermal his-

tory on I3 can be ignored for this polymer.groups.11 The present PALS method was demon-strated to be effective to probe minor transitionsthat sometimes cannot be detected by DMA

Temperature Dependence of t3 and I3 for PDPSMand DSC.The temperature dependence of t3 and I3 in therange between 50 to 370 K for PDPSM are shown

Temperature Dependence of t3 and I3 in Figure 5. The t3 profile seems to be dividedabove 300 K for PMPSM into several linear lines. First, the temperature

coefficient of t3 at 165–295 K is calculated to beThe temperature dependence of t3 and I3 was alsostudied at temperatures higher than 300 K in a 1.5 1 1003 K01 ,19 being very close to that for

PMPSM below 284 K. Hence, the t3 increase ob-nitrogen atmosphere, and the results are plottedin Figure 4. A cooling spectrum as well as a heat- served at this temperature range can be ascribed

to the thermal expansion of the free volumes. Aing spectrum was recorded to see an effect of ther-mal history on the data of PALS. t3 increased with gradual decrease of I3 in this region presents a

striking contrast to the temperature profile ofincreasing temperature, but its slope decreasedabove ca. 350 K. In contrast to a distinct breaking PMPSM. This may be explained by slight motions

of the polymer backbones of PDPSM, whilepoint observed at 284 K in Figure 3, the changein the slope of t3 at 350 K was ambiguous. Al- PMPSM exhibited a plateau and a steep decrease

in increasing temperature probably due to thethough this transition was not detected by DSC orDMA, and therefore, has not been fully identified, more flexible main chains than the PDPSM. It

should be noted that the temperature coefficientssome degree of rearrangement of polymer chainsmight be a possible reason of this phenomenon. In of both t3 and I3 change at around 295 K where

the slope of t3 increases and the I3 values start toother word, the activation of the micro-Brownianmotions of molecules by heating was suppressed increase. This temperature profiles of t3 and I3 at

around 295 K are very similar to those of PMPSMabove 350 K, probably due to the slightly regu-lated polymer structures. A very small content of at around 280 K, but they are not caused by the

Tg , as will be discussed in the next section. Wea crystalline region might contribute this transi-tion, while no melting transition was found by a assigned this transition to the motions by short

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760 OGAWA, SUZUKI, AND MURAKAMI

that determined by DSC, as discussed above. Noother transitions were found from the t3 spec-trum. In both heating and cooling spectra of I3 ,an ambiguous breaking point was observed near400 K. The onset of molecular motions in the crys-talline region would contribute this transition. Asa matter of fact, it has been reported that polysty-rene did not exhibit a change in the slope of I3

near the Tg regardless of the molecular weightsof the samples.20 A slight difference was indicatedbetween the heating and cooling spectra. The I3

values of the cooling sample were slightly largerthan those of heating sample at temperatureslower than the Tg . This may be indicative of poly-Figure 6. The temperature dependence of t3 and I3mer chain rearrangements taking place such thatat temperatures higher than 300 K for PDPSM ob-the rearranged structures may not have recoveredtained at a rate of 5 K/h by heating (square and circle)before the cooling run was performed despite aand subsequent cooling after 3 h holding at 470 K (crosslong holding period of 3 h.in square and cross in circle) .

polymer segments because this is the closest tran- CONCLUSIONSsition below Tg in the I3 profile, although no dis-tinct transition could be found by DMA. Above The present study gave several pieces of informa-this temperature, the micro-Brownian motions of tion about the transition temperatures of twomolecules are activated. In addition, there ap- poly(silylenemethylene)s with the repeatingpears to be a discontinuity at around 340 K in the PhRSiCH2 (R : Me or Ph) units. Besides the glassI3 spectrum, whereas a change in the slope of t3 transition, several subtransitions, which couldis not very clear. We have reported an existence not be probed by DSC or DMA, were identified byof a very weak transition at 60–707C (333–343 the temperature dependence of t3 and I3 in PALSK) for this polymer in DMA spectrum,13 which measurements. The most evident subtransitionmay relate to the discontinuity observed by PALS. was observed by a steep drop of I3 at 130–140 K,

The t3 increased with an increasing tempera- probably due to the motions of phenyl groups inture until ca. 110 K and was almost constant at each polymer. Because t3 was constant in this110–165 K. Because the slope of increasing t3 temperature range, it is suggested that this sub-below 110 K is quite similar to that observed at transition takes place without changing the free165–295 K, the reason of this increase is assign- volumes of polymers. The temperature range of I3able to the thermal expansion of the free volumes. decrease reflecting this transition was larger forAn appreciable decrease of I3 was observed at PDPSM than that for PMPSM. This indicates that110–150 K, suggesting that the motions of phenyl PDPSM has stronger intermolecular interactiongroups on the polymer backbone take place, as via the larger numbers of phenyl groups thanwas detected for PMPSM. The temperature range PMPSM. PMPSM exhibited a transition at tem-in which the I3 decreased was larger than that peratures higher than the Tg , which may be basedobserved for PMPSM, probably due to the on the rearrangements of polymer chains. It hasstronger intermolecular interaction in PDPSM been demonstrated that the I3 profiles of polymersvia larger numbers of phenyl groups as well as its did not necessarily imply a change in the numberbetter structural symmetry. of free volumes, but reflected a relaxation process.

The authors appreciate the support of the New EnergyTemperature Dependence of t3 and I3 aboveand Industrial Technology Development Organization300 K for PDPSMand Japan High Polymer Center for this work, which

The data of PALS above 300 K measured in nitro- was carried out as an Industrial Science and Technol-gen are depicted in Figure 6. An evident breaking ogy Frontier Program. The authors are also grateful topoint at around 405 K in the t3 trace is assignable Drs. Brian M. Naasz and Binh T. Nguyen of Dow Corn-

ing Corp. for generous gifts of disilacyclobutanes.to the Tg of PDPSM, which is slightly lower than

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Kyoto, and T. Uozumi, J. Polym. Sci., Part B:REFERENCES AND NOTESPolym. Phys., 34, 2145 (1996).

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