Changes in the Viscoelastic Mechanisms of Polyisobutylene by

Sep 19, 2012 - tangent (tan δ), have found an additional shoulder. Following the interpretation of previous works, the shoulder is attributed to the ...
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Changes in the Viscoelastic Mechanisms of Polyisobutylene by Plasticization Jinrong Wu,† Guangsu Huang,†,* Xiaoan Wang,† Xiaojun He,† and Ben Xu‡ †

College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering, Sichuan University, Chengdu 610065, China ‡ Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409-3121, United States S Supporting Information *

ABSTRACT: Our dynamic mechanical measurements in the glass−rubber transition zone of polyisobutylene (PIB), expressed in terms of the relaxation spectrum H(τ) and loss tangent (tan δ), have found an additional shoulder. Following the interpretation of previous works, the shoulder is attributed to the sub-Rouse modes, which account for motions intermediate in length scale to the Rouse and local segmental modes. The fact that the sub-Rouse modes are well resolved in PIB and not in other amorphous polymers was traced to its weak intermolecular coupling, which ultimately originates from the compact and symmetrical structure of its repeat unit. We test this interpretation further by studying the change on adding liquid paraffin (LP) to PIB, which should disrupt the effective chain packing of undiluted PIB. We found on adding LP to PIB that the softening dispersion becomes narrower, and eventually the disappearance of the shoulder. The effect is due to the mobility of entropic Rouse modes enhanced significantly more than that of the sub-Rouse modes and the enthalpic local segmental motion on increasing the weight fraction of LP. Thus, the Rouse modes get closer to the sub-Rouse modes and local segmental motion. Incorporation of LP does not reduce much the intermolecular coupling, as evidenced by the small change of glass transition temperature. On the other hand, the disruption of the effective chain packing of PIB by adding LP endows higher mobility to the Rouse modes with longer motional units, while it has little effect on the local segmental relaxation and the subRouse modes. Consequently, there is the narrowing of the softening dispersion and eventually the disappearance of the shoulder in H(τ) and tan δ. The result supports the compact and symmetric chemical structure of the repeat unit of PIB, and the efficient chain packing is the root cause that engenders the broad softening dispersion, and the observation of the sub-Rouse modes in H(τ) and tan δ. Positron annihilation lifetime spectra are presented to show the average size and concentration of the freevolume holes increase with incorporation of LP and the disruption of the effective chain packing of PIB. of repeat units in each chain,30 are entropic in nature. Previous studies have shown that the local segmental motion and the Rouse modes together contribute only partially to the total compliance of the softening dispersion. The compliance originating from the local segmental motion of polystyrene is less than 5 × 10−9 Pa−1,5,31 and that from the Rouse modes is higher than about 10−6 Pa−1.32 Thus, some additional molecular mechanism must exist to fill the gap between 5 × 10−9 and 10−6 Pa−1. The additional molecular dynamics are attributed to subRouse modes by Plazek, Ngai, Roland and co-workers.5−12 The sub-Rouse modes are intermediate in time and length scale between the local segmental motion and the Rouse modes. Hence their motional units are larger than the local segments, but smaller than the Gaussian submolecules.5−12 The molecular origin of the local segmental motion can be gleaned from molecular dynamics simulations in some model polymers.

I. INTRODUCTION Glass transition is currently an active research field in many different classes of materials, but there is still no consensus on its fundamental understanding of the molecular dynamics leading to glass formation.1,2 More complicated are the glassforming polymers. Because of chain connectivity, amorphous polymers show richer and more complex molecular dynamics extending over a broad range of time and length scales. Naturally, the complexity makes comprehension more difficult despite the continued research efforts in glass transition and viscoelasticity of polymers.3,4 Recently, experimental evidence have accumulated showing that the softening dispersion from the glassy state to the rubbery state involves at least three different modes of molecular motion, namely the local segmental motions (LSM), sub-Rouse modes, and Rouse modes.5−29 Local segmental motion (also called the structural α-relaxation), a cooperative motion of neighboring chains each involve several repeat units, is enthalpic and determines the glass transition temperature (Tg). Rouse modes, based on the motions of Gaussian submolecules formed by sufficient number © 2012 American Chemical Society

Received: January 17, 2012 Revised: September 3, 2012 Published: September 19, 2012 8051

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Examples are the work by Takeuchi and Roe,33 and by Bennemann et al.34 For the sub-Rouse modes, although shown to exist by experiments, the molecular motion of the modes has not been determined by anyone either theoretically or by simulations. Williams32 had suggested 5 monomer units in the case of polystyrene. However this is purely his hypothesis based on the assumption that the minimum number of monomers required to have a Gaussian submolecule for the Rouse modes. Currently, there is a lack of knowledge of exact number of monomer units involved in the sub-Rouse modes. Although the different modes of molecular motion mentioned in the above are present in the softening dispersion region of all amorphous polymers, not all of them are necessarily observed together in an experiment using one technique. For example, nuclear magnetic resonance, differential scanning calorimetry and quasi-elastic neutron scattering usually probe primarily the local segmental motion.9 Although dynamic mechanical spectroscopy is sensitive to all modes of molecular motion, it is difficult to resolve the contribution of each mode from one another due to overlap. Only in the ideal case of polyisobutylene (PIB), which has a very broad softening dispersion, has the sub-Rouse modes been resolved from the Rouse modes. Recently, Wu et al25−28 separated the sub-Rouse modes and Rouse modes from the local segmental motion in several polymers and polymer blends using a modified lowfrequency inverted torsion pendulum. Paluch et al.29 made a pioneering work by using dielectric spectroscopy to resolve the sub-Rouse modes. More recently, we were able to discern all the three modes of molecular motion simultaneously by using dielectric probes and two-dimensional correlation analysis.22−24 Although all amorphous polymers are expected to have all modes of molecular motion, only in polyisobutylene (PIB) they were well-resolved. The dynamic mechanical loss tangent (tan δ) reveals an asymmetrical double-peak structure with a maximum on the low-frequency (or high-temperature) side and a shoulder on the other side, the latter is attributed to the sub-Rouse modes.6,13,14 The reason why the softening dispersion of PIB is so broad, and favorable for resolving the sub-Rouse modes has been rationalized by its molecular structure and molecular packing.5−9 The smooth, symmetric and flexible molecular structure of PIB leads to the weak intermolecular coupling of segmental relaxation according to the coupling model. This attribute of the structure engenders fast local segmental motion and alleviates the encroachment of the local segmental motion toward the Rouse modes, resulting in PIB slightly deviating from thermorheological simplicity compared with other amorphous polymers such as polystyrene (PS).5−12 For this reason, the overlap of different modes of molecular motion of PIB is weak, allowing us to resolve these modes experimentally. In addition to the molecular structure, the aggregation structure may be another important factor to account for the well-resolved different modes of molecular motion. Previous results of positron annihilation lifetime spectroscopy show that the free volume holes of PIB are relatively small compared with other amorphous polymers and expand slowly with temperature above Tg until 290 K (corresponding to the well-known low gas permeability), which indicates the effective chain packing of PIB.17,18,35,36 Intuitively, the motion of longer chain segments requires larger volume, while the effective chain packing and slow expansion process of free-volume holes do not afford such a condition, which inevitably retards the Rouse modes. By contrast, the local segmental motion is little affected due to the small size. As a

result, the local segmental motion and the Rouse modes separate from each other further in time or temperature scale, which allows the resolution of sub-Rouse modes. In order confirm generality of the coexistent of different modes of molecular motion in the softening dispersion by mechanical spectroscopy, it is necessary to confirm the findings in other amorphous polymers other than PIB. However, it is hard to find some other amorphous polymers that have similar viscoelastic properties with PIB, because the majority of amorphous polymers have stronger intermolecular coupling. For example, PS has strong intermolecular coupling because of the bulky phenyl side group in its repeat unit. To get out of this quandary, Ngai and Plazek11 added a diluent, m-tricresyl phosphate (TCP), to PS to weaken the intermolecular coupling. Increase in the separation between the repeating units leads to lower intermolecular coupling, less encroachment of the local segmental motion toward the Rouse modes, and the desired broad softening dispersion. Consequently, the viscoelastic properties of the diluted PS at the softening dispersion region are nearly identical to that of PIB, and its tan δ also shows an asymmetrical double-peak structure indicating the presence of the sub-Rouse mode well resolved from the Rouse modes.11 The work of Ngai and Plazek11 inspires us to study PIB diluted by a plasticizer, which reduces the intermolecular coupling but the effective chain packing is disrupted. As given in detail in the next sections, the addition of the plasticizer in PIB leads to narrower softening dispersion on the dynamic mechanical spectrum and finally the disappearance of the double-peak structure of tan δ.

II. EXPERIMENTAL SECTION Polyisobutylene (PIB, from BASF Company) with a number-average molecular weight of 1.032 × 105 g/mol and a polydispersity of 2.7 was fractionated with hexane and acetone at a concentration of 1 wt %. Liquid paraffin (LP) used as the plasticizer of PIB is purchased from Changzheng Chemicals Co. Ltd., Chengdu. The number-average molecular weight of LP is 352 with a polydispersity of 1.2, as determined by gel permeation chromatography (HLC-8320GPC, TOSOH) in tetrahydrofuran at 40 °C using polystyrene samples as the elution standard. PIB and LP were both dissolved in cyclohexane to obtain a homogeneous solution under stirring, and then the solvent was evaporated at 60 °C while kept stirring. Subsequently, the mixture was put in a vacuum oven at 60 °C for 72 h to remove any residual solvent, and marked as PIB-nLP, where the number n indicated the weight fraction of LP in the mixture. The samples used for dynamic mechanical analysis were compression molded at 100 °C for 5 min to form sheets with dimensions of 30 × 12 × 3 mm. The dynamic mechanical spectra of PIB and PIB-nLP were tested by dynamic mechanical analysis (DMA Q800, TA Instruments) using a dual cantilever clamp and a testing method of temperature stepfrequency sweep with each temperature step of 2−5 °C. The oscillation strain amplitude was set at 25 μm with a frequency range between 0.1 Hz to 60 Hz. Temperature modulated differential scanning calorimetry (TMDSC) was performed using Q200 (TA Instruments). The mass of the sample was about 6−8 mg. The samples were first cooled from room temperature to −90 °C at a cooling rate of 10 °C/min and then stabilized for 5 min. Afterward the heat capacity data of the samples were recorded at a heating rate of 1 °C/min with a superimposed temperature modulation of ±1.00 °C every 60 s. For the measurement of positron annihilation lifetime spectra, a 30 μCi 22Na positron source sealed between two sheets of nickel foil (1 mg/cm2) was sandwiched between two pieces of the samples and mounted to a cooling head of liquid-nitrogen cryostat with 8052

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Table 1. Values of Tg and Fwhm Determined by MDSC for PIB with Different LP Weight Fraction

temperature stability better than 0.5 K. Positron lifetime spectra were measured using a conventional fast−fast coincidence spectrometer. Each spectrum contained approximately 106 counts for PATFIT, by which all of the measured positron lifetime spectra were resolved into three components after the background and positron source correction was subtracted. The shortest lifetime (τ1 ≈ 0.12 ns) is the lifetime of singlet-positronium (p-Ps) and the intermediate lifetime (τ2 ≈ 0.40 ns) is the lifetime of the positron. The longest lifetime (τ3≈1−3 ns) is due to the orthopositronium (o-Ps) pick-off annihilation in the freevolume holes in amorphous phase. Because only the o-Ps component is sensitive to the change in the microstructure of the amorphous region, in the present study, we employ the results of o-Ps lifetime to obtain the mean free-volume parameters.

samples

MDSC Tg (°C)

fwhm (°C)

PIB PIB-5LP PIB-10LP PIB-20LP

−65.88 −67.04 −67.73 −69.30

5.85 5.92 6.02 6.14

Here ω refers to the weight fraction, and K is a constant. Subscripts 1 and 2 correspond to the two components, designated here as LP and PIB, respectively. Equation 1 can be used to well fit the experimental data and gives a Tg1 value of −80.3 °C for LP. By analyzing the lower inset of Figure 1, it is also convenient to determine the full width at half-maximum (fwhm) of the dH(Rev)/dT peak that can be used to represent the width of glass transition region. The result in Table 1 suggests that fwhm shows a small increase with incorporation of LP, thus spatial heterogeneity caused by concentration fluctuations is unimportant. The reason for this is likely due to the good miscibility between LP and PIB. The isochronal tan δ spectra of neat PIB and plasticized PIB with different LP weight fraction are presented in Figure 2.

III. RESULTS LP used in the present work is composed of alkanes with different chain lengths. The average number of repeating units is around 25. It is liquid-like at room temperature, but DSC measurement indicates that it crystallizes around −35 °C if it is subjected to cooling. During subsequent heating, the crystals exhibit a melting peak around −26 °C. However, the crystallization and melting are absent in the PIB/LP blends, even when the LP weight fraction is increased up to 20%. Such behavior can be understood by the fact that solvation takes place between the LP molecules and the polymer chains. The noncrystallizable LP molecules certainly have higher mobility than the PIB chains due to their low molecular weight, thus playing the role of plasticizer in the blends. In order to evaluate the influence of LP on the molecular dynamics of PIB, TMDSC measurement was performed. The resulting reversing heat flow, H(Rev), and the derivatives of reversing heat flow, dH(Rev)/dT, are shown in Figure 1. It is clear that the curves

Figure 2. Isochronal tan δ spectra of PIB with different LP weight fraction at 1 Hz.

Incorporating LP into PIB gradually shifts the tan δ curves toward lower temperature. At the same time, the shape of the tan δ peak is significantly altered. The tan δ peak of neat PIB is quite broad, covering a temperature range from −70 to 20 °C, and it displays an asymmetrical double-peak structure with a maximum on the high temperature side and a shoulder on the low temperature side. However, on increasing LP weight fraction, the tan δ peak becomes narrower and narrower, indicating that its fwhm becomes smaller. On closer examination, we find that the maximum shifts toward lower temperature faster than the shoulder, eclipsing the shoulder and making the tan δ peak narrower. When the LP weight fraction is up to 20%, the shoulder is totally submerged and not discernible. Using the time−temperature superposition (TTS) principle, frequency dependent viscoelastic data at various temperatures are shifted along the frequency axis to a reference temperature to construct a master curve. In the present work, −65 °C is designated as the reference temperature, and the resulting master curves of tan δ are shown in Figure 3a. In the isothermal presentation, the tan δ peak is shifted toward higher frequency with the gradual disappearance of the shoulder with increasing

Figure 1. Temperature dependence of reversible heat flow of PIB with different LP weight fraction. The derivatives of reversible heat flow are shown in the inset. Key: (1) PIB; (2) PIB-5LP; (3) PIB-10LP; (4) PIB-20LP.

are systematically shifted toward lower temperature with increasing LP weight fraction. From the plot of dH(Rev)/dT against T, the glass transition temperature, Tg, is determined by the peak temperature. As illustrated in Table 1, Tg of PIB decreases monotonically with LP weight fraction, suggesting that LP enhances the molecular mobility of PIB. For miscible blends with relatively weak specific interactions between the two components, Tg can be described by the Gordon−Taylor equation:37 Tg = (ω1Tg1 + Kω2Tg 2)/(ω1 + Kω2)

(1) 8053

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shift toward the left. On the contrary, the right side of the softening dispersion region where H(τ) has a slope of −1/2 evidently shifts toward the short-time side. Thus, the width of the softening dispersion region is reduced with incorporation of LP, as shown in the lower inset of Figure 4. On the other hand, H(τ) of PIB also shows an evident shoulder on the right side of the peak, nevertheless the shoulder gradually disappears with increasing LP weight fraction, similar to what happens to the shoulder of tan δ peak in Figure 3.

IV. DISCUSSION Although dynamic mechanical analysis is sensitive to all modes of molecular motion, it is difficult to separate independently the contribution of each mode from one another. However, there is an exception. Thanks to the weak intermolecular coupling and high packing efficiency of PIB, the local segmental motion and sub-Rouse modes have less encroachment toward the Rouse modes than in other amorphous polymers. Therefore, in the dynamical mechanical spectrum of PIB different modes of molecular motion are separated in either the temperature or time scale, which makes it possible to resolve the Rouse, the sub-Rouse and the local segmental modes. As shown in Figure 4, the peak on the short-time side of H(τ) of PIB is attributed to the local segmental motion, while the long-time side of H(τ) which has a slope of −1/2 corresponds to the Rouse modes.30 The shoulder in the between, having a time scale between the local segmental motion and the Rouse modes, can be attributed to the sub-Rouse modes. By adding LP, the peak on the shorttime side slightly moves toward the left, which indicates that the presence of LP molecules slightly improves the molecular mobility of the local segments of PIB. Meanwhile, the long-time side of H(τ) with a slope of −1/2 remarkably shifts toward short-time side, suggesting that the molecular mobility of the Rouse modes of PIB is greatly enhanced. Thus, with the increase of LP weight fraction, the Rouse modes gradually encroach the local segmental motion, which results in narrower softening dispersion region and the disappearance of the shoulder of H(τ). Consequently, the sub-Rouse modes are merged when the LP weight fraction is 20%. In order to study the molecular mechanism of the shoulder of the tan δ peak, we first take curve IV in Figure 3-3 of Ferry’s book by Enaguge Digitizer (V4.1, Mark Mitchell) as the standard H(τ), which involves segmental and Rouse modes but with no detectable sub-Rouse modes.30 Then, a “small” and a “big” protuberance corresponding to the sub-Rouse modes are added to the standard H(τ) to construct H(τ)s and H(τ)b, respectively, which thus look like H(τ) of PIB as shown in Figure 4. The standard H(τ), and the constructed H(τ)s and H(τ)b are presented in Figure 5. Thereafter, G′(ω) and G″(ω) are calculated by TA orchestrator from H(τ) to obtain tan δ data, as shown in Figure 6. It is clear that the tan δ peak calculated from the standard H(τ) with no detectable subRouse modes shows no shoulder. However, by adding the protuberance, an evident shoulder on the high-frequency side of the tan δ peak is present and observed, and “bigger” protuberance leads to more prominent shoulder. Thus, the shoulder of the tan δ peak should be attributed to the subRouse modes. According to the above analysis, the tan δ peak of PIB also suggests the existence of different modes of molecular motion. But we should bear in mind that it is not accurate to use tan δ peak to split different modes of molecular motion, because the tan δ peak around the softening dispersion region is a complex

Figure 3. Master curves of tan δ at the reference temperature of −65 °C (a), and the normalized representation of tan δ spectra (b) of PIB with different LP weight fraction. In the normalized representation, each curve is normalized by the corresponding maximum tan δ value, tan δmax, and the resulting curves are shifted horizontally along the frequency axis so that the maximum of each curve appears at the same position.

LP weight fraction. For comparison, the tan δ master curves are shifted horizontally along the frequency axis so that the maxima of all appear at the same position. Also the peak heights are normalized by the maximum values, tan δmax. The results are shown in Figure 3b. It is evident from Figure 3b that adding LP gradually suppresses the shoulder, while the shape of the maximum remains unchanged. The relaxation spectra, H(τ), calculated by TA orchestrator (V7.2.0.4, TA Instruments) from the storage modulus of neat PIB and plasticized PIB with different LP weight fraction, are displayed in Figure 4 with a accuracy within ±30% (see the Supporting Information about the accuracy of H(τ)). It can be seen that although H(τ) decreases with increasing LP weight fraction, the peak on the short-time side only shows a small

Figure 4. Relaxation spectra, H(τ), calculated by TA orchestrator from the storage modulus of neat PIB and plasticized PIB with different LP weight fraction. The arrows between the two dashed lines indicate the width of softening dispersion of PIB. The influence of LP weight fraction on the width of softening dispersion is shown in the inset. 8054

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place. Adding LP with its Tg only about 10 deg lower than that for PIB does not change the intermolecular coupling much. However, the disruption of the effective chain packing of PIB by the presence of LP seems to play a dominant role here. To confirm this, positron annihilation lifetime spectra were measured for PIB and PIB with 20 wt % of LP. Figure 7

Figure 5. Standard H(τ) taken from curve IV in Figure 3-3 of Ferry’s book,30 and the simulated H(τ)s and H(τ)b with “small” and “big” subRouse modes.

Figure 7. Temperature dependence of o-Ps lifetime and intensity of PIB and PIB-20LP.

shows the o-Ps lifetime and intensity, which directly reflect the average size and concentration of the free-volume holes, respectively. It is found that both the average size and concentration of the free-volume holes increase with incorporation of LP, leading to the disruption of the effective chain packing of PIB. It endows larger motion units (Rouse modes) with higher mobility, while has little effect on the smaller ones (local segments and sub-Rouse modes). Thus, the Rouse modes show an evident shift toward the local segmental motion. As a result, the softening dispersion becomes narrower on the dynamic mechanical spectrum and the shoulder both in H(τ) and tan δ peak finally disappears, making the dynamic mechanical spectra of PIB to resemble those of most amorphous polymers that show narrow softening dispersion region and have no shoulder in H(τ) and tan δ peak. The result in turn suggests that the high molecular packing efficiency also contributes to the broad softening dispersion region and the well resolved sub-Rouse modes in H(τ) and tan δ peak of PIB. It is worthwhile to discuss further the contrast between our present findings in PIB diluted by LP and the work of Ngai and Plazek 11 by disolving PS into TCP to diminish the intermolecular coupling. The addition of TCP widens the width of the softening disperion of PS. When the TCP concentration is as high as 83%, the softening dispersion of the solution resembles the bulk PIB, and its tan δ has a double-peak structure showing the resolved sub-Rouse and Rouse modes. To understand the contrasting behavior, we have to distinguish the starting polymer PS from PIB. In the case of PS, the intermolecular cooperativity of the local segmental relaxation is high (corresponding to its larger coupling parameter, n = 0.63, compared with n = 0.45 of PIB).6,38 Its relaxation time, τLSM, as well as that of the sub-Rouse modes, τsR, have temperature dependence much stronger than that of the Rouse modes, τR, according to the coupling model. Consequently, the local segmental relaxation and the sub-Rouse modes of PS encroach the Rouse modes. This is why the softening dispersion of PS is very narrow compared with PIB, and the different modes of molecular motion cannot be resolved. Addition of the diluent TCP to PS reduces the intermolecular cooperativity of the local

Figure 6. Tan δ calculated from the standard H(τ), and the simulated H(τ)s and H(τ)b.

combination of the contributions from different modes, as indicated in the following equation: tan δ = {

∞ {Hsegmental(τ ) + Hsub ‐ Rouse(τ ) + HRouse(τ )} ∫ −∞

ωτ d[ln τ ]}/{Ge 1 + ω 2τ 2 ∞

+

∫−∞ {Hsegmental(τ) + Hsub‐Rouse(τ) + HRouse(τ)}

ω 2τ 2 d[ln τ ]} 1 + ω 2τ 2

(2)

However, for a rough discussion, we can still see from Figure 2 that with increasing LP weight fraction, the maximum of the tan δ peak corresponding to the Rouse modes shifts more toward the low-temperature side, as a result, the shoulder of the tan δ peak is gradually smeared, like what has been observed in the relaxation spectra. All the effects seen above on adding LP to PIB is opposite to those found on adding TCP to PS by Ngai and Plazek.11 There addition of TCP lowers the Tg of PS by a large amount, and widens the softening dispersion of PS considerably. It is true that adding LP to PIB still has the effect of reducing the intermolecular coupling, but the reduction is much smaller than in the case of adding TCP to PS. This is obvious from the fact that the decrease of Tg by adding 20% LP to PIB is merely a few degrees. Another contributor to the opposite behavior is the already weak intermolecular coupling of PIB, which allows the different modes of molecular motion to be resolved in the first 8055

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segmental relaxation and the sub-Rouse modes. At about 17% PS solution in TCP, the intermolecular coupling was so low that the segmental dynamics and width of softening dispersion of the solution become like PIB, and in particular the subRouse modes are resolved. Now let us consider what happen if we continue to add more TCP to PS past the previous work. As the solution becomes more dilute, the PS chains become more flexible and the Rouse modes of shorter wavelengths (and higher frequencies) not possible before, now become applicable. More of these Rouse modes at shorter wavelengths and higher frequencies become active on further increase of TCP to PS. These higher frequency Rouse modes are introduced into the viscoelastic spectrum in the domain of and at the expense of the sub-Rouse modes. The effect is the depletion of the sub-Rouse shoulder in the tan δ plot against frequency or temperature. In the extreme dilute polymer limit, the dynamics will become more like the modified Rouse model, i.e., the Zimm model, extended to diluted polymer predicts,30 which has no sub-Rouse modes to consider. This is confirmed by Plazek’s creep data of dilute solutions of PS. He found the Rouse spectrum but no subRouse modes.39 We can also go back to the more distant past literature on dilute solutions. There the Zimm model works and no more sub-Rouse modes can be found appearing at higher frequencies.30 Returning to PIB, since PIB has similar softening dispersion as 17% PS solution in TCP, we can consider them equivalent in dynamics. Thus, the effect of adding LP to PIB can be likened to further diluting the 17% PS solution in TCP. Borrowing the arguments given in the previous paragraph on dilute solution of PS (i.e., the introduction of Rouse modes of shorter wavelength and high mobility at the expense of depletion of the sub-Rouse modes, and the tendency in approaching the Zimm model prediction in dilute solutions), we can expect the gradual lack of distinction between the sub-Rouse and the Rouse modes of PIB with increasing LP weight fraction. This leads to the decrease of separation between them and suppression of the shoulder in H(τ) and tan δ peak at higher LP contents.

Article

ASSOCIATED CONTENT

S Supporting Information *

Analysis of the accuracy of the relaxation spectrum. This material is available free of charge via the Internet at http:// pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51203096 and 50873070), the Office of Naval Research under Project Number N00014-06-1-0922, and the John R. Bradford endowment at Texas Tech University. We also appreciate the helpful comments from the reviewers.

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V. CONCLUSIONS In the present study, by adding liquid paraffin to PIB, the effective chain packing of PIB is changed with support provided by positron annihilation lifetime measurements. The disruption of effective chain packing strongly enhances the mobility of the Rouse modes because of their entropic nature and the involvement of Gaussian submolecules of longer length scale in the global motion. On the other hand, the reduction in the intermolecular coupling on the mobility of the enthalpic local segmental relaxation and the sub-Rouse modes is minimal, because of the small change in glass transition temperature on adding LP. As a result, the Rouse modes come closer to the sub-Rouse modes and local segmental relaxation, resulting in narrower softening dispersion of the dynamic mechanical spectra, and eventually the disappearance of the shoulder of H(τ) and tan δ peak of PIB. Hence we confirm that the compact and symmetric molecular structure and its high molecular packing efficiency of PIB is the major factor that leads to the broad softening dispersion, and the resolution of the sub-Rouse modes in H(τ) and tan δ. 8056

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dx.doi.org/10.1021/ma3001274 | Macromolecules 2012, 45, 8051−8057