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Terminal relaxation behavior of entangled linear polymers blended with ring and dumbbell-shaped polymers in melts

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Abstract

We investigated the terminal relaxation behavior of entangled linear polystyrene L430 (with the entanglement number Z = M/Me ≃ 24, where M is the molecular weight and Me is the entanglement molecular weight) blended with ring R30 (MR ≃ 1.8 Me) and dumbbell-shaped D308030 (MR ≃ 1.8 Me and ML ≃ 4.7 Me) polymers. The L430/R30 blend exhibits a one-step relaxation unlike binary linear polymer blends with different molecular weights. The zero-shear viscosity η0 of the L430/R30 blend is slightly lower than that of the neat L430. These results suggest that spontaneous penetration of the linear chains into the rings occurs, but the rings do not act as entanglement cross-linkers. The L430/D308030 blend also exhibits a one-step relaxation, but its terminal relaxation is slower and broader than that for L430. This result is probably because two ring sections in D308030 are penetrated by the linear chains, and hence D308030 acts as a pseudo-entanglement point with longer characteristic time.

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References

  • Borger A, Wang W, O’Connor TC, Ge T, Grest GS, Jensen GV, Ahn J, Chang T, Hassager O, Mortensen K, Vlassopoulos D, Huang Q (2020) Threading-unthreading transition of linear-ring polymer blends in extensional flow. ACS Macro Lett 9:1452–1457

    Article  CAS  Google Scholar 

  • Doi Y, Matsubara K, Ohta Y, Nakano T, Kawaguchi D, Takahashi Y, Takano A, Matsushita Y (2015) Melt rheology of ring polystyrenes with ultrahigh purity. Macromolecules 48:3140–3147

    Article  CAS  Google Scholar 

  • Doi Y, Takano A, Takahashi Y, Matsushita Y (2015) Melt rheology of tadpole-shaped polystyrenes. Macromolecules 48:8667–8674

    Article  CAS  Google Scholar 

  • Doi Y, Takano A, Matsushita Y (2016) Synthesis and characterization of dumbbell-shaped polystyrene. Polymer 106:8–13

    Article  CAS  Google Scholar 

  • Doi Y, Matsumoto A, Inoue T, Iwamoto T, Takano A, Matsushita Y, Takahashi Y, Watanabe H (2017) Re-examination of terminal relaxation behavior of high-molecular-weight ring polystyrene melts. Rheol Acta 56:567–581

    Article  CAS  Google Scholar 

  • Doi Y, Takano A, Takahashi Y, Matsushita Y (2020) Melt rheology of tadpole-shaped polystyrene with different ring sizes. Soft Matter 16:8720–8724

    Article  CAS  Google Scholar 

  • Doi Y, Takano A, Takahashi Y, Matsushita Y (2021) Viscoelastic properties of dumbbell-shaped polystyrenes in bulk and solution. Macromolecules 54:1366–1374

    Article  CAS  Google Scholar 

  • Doi Y (2022) Rheological properties of ring polymers and their derivatives. Nihon Reoroji Gakk (J Soc Rheol Jpn) 50:7–62

  • Ferry JD (1980) Viscoelastic properties of polymers. John Wiley and Sons, New York

    Google Scholar 

  • Ge T, Panyukov S, Rubinstein M (2016) Self-similar conformations and dynamics in entangled melts and solutions of nonconcatenated ring polymers. Macromolecules 49:708–722

    Article  CAS  Google Scholar 

  • Goossen S, Kruteva M, Sharp M, Feoktystov A, Allgaier J, Pyckhout-Hintzen W, Wischnewski A, Richter D (2015) Sensing polymer chain dynamics through ring topology: a neutron spin echo study. Phys Rev Lett 115:148302

    Article  CAS  Google Scholar 

  • Hagita K, Murashima T (2021) Molecular dynamics simulations of ring shapes on a ring fraction in ring-linear polymer blends. Macromolecules 54:8043–8051

    Article  CAS  Google Scholar 

  • Halverson JD, Lee WB, Grest GS, Grosberg AY, Kremer K (2011) Molecular dynamics simulation study of nonconcatenated ring polymers. I Statics J Chem Phys 134:204904

    Article  Google Scholar 

  • Halverson JD, Grest GS, Grosberg AY, Kremer K (2012) Rheology of ring polymer melts: from linear contaminants to ring-linear blends. Phys Rev Lett 108:038301

    Article  CAS  Google Scholar 

  • Houli S, Iatrou H, Hadjichristidis N, Vlassopoulos D (2002) Synthesis and viscoelastic properties of model dumbbell copolymers consisting of a polystyrene connector and two 32-arm star polybutadiene. Macromolecules 35:6592–6597

    Article  CAS  Google Scholar 

  • Iwamoto T, Doi Y, Kinoshita K, Ohta Y, Takano A, Takahashi Y, Nagao M, Matsushita Y (2018) Conformation of ring polystyrenes in bulk studied by SANS. Macromolecules 51:1539–1548

    Article  CAS  Google Scholar 

  • Iwamoto T, Doi Y, Kinoshita K, Takano A, Takahashi Y, Kim E, Kim TH, Takata S, Nagao M, Matsushita Y (2018) Conformation of ring polystyrenes in semidilute solutions and in linear polymer matrices studied by SANS. Macromolecules 51:6836–6847

    Article  CAS  Google Scholar 

  • Iyer BVS, Lele AK, Shanbhag S (2007) What is the size of ring polymer in a ring-linear blend? Macromolecules 40:5995–6000

    Article  CAS  Google Scholar 

  • Kapnistos M, Lang M, Vlassopoulos D, Pyckhout-Hintzen W, Richter D, Cho D, Chang T, Rubinstein M (2008) Unexpected power-law stress relaxation of entangled ring polymers. Nat Mater 7:997–1002

    Article  CAS  Google Scholar 

  • Kong D, Banik S, San Francisco BM, Lee M, Robertson-Anderson RM, Schroeder CM, McKenna GB (2022) Rheology of entangled solutions of ring-linear DNA blends. Macromolecules 55:1205–1217

    Article  CAS  Google Scholar 

  • Kruteva M, Allgaier J, Richter D (2017) Direct observation of two distinct diffusive modes for polymer rings in linear polymer matrices by pulsed field gradient (PFG) NMR. Macromolecules 50:9482–9493

    Article  CAS  Google Scholar 

  • Kruteva M, Monkenbusch M, Allgaier J, Holderer O, Pasini S, Hoffmann I, Richter D (2020) Self-similar dynamics of large rings: a neutron spin echo study. Phys Rev Lett 125:238004

    Article  CAS  Google Scholar 

  • Kruteva M, Allgaier J, Monkenbusch M, Porcar L, Richter D (2020) Self-similar polymer ring conformations based on elementary loop: a direct observation by SANS. ACS Macro Lett 9:507–511

    Article  CAS  Google Scholar 

  • Lee HC, Lee H, Lee W, Chang T, Roovers J (2000) Fractionation of cyclic polystyrene from linear precursor by HPLC at the chromatographic critical condition. Macromolecules 33:8119–8121

    Article  CAS  Google Scholar 

  • Mayumi K, Ito K (2010) Structure and dynamics of polyrotaxane and slide-ring materials. Polymer 51:959–967

    Article  CAS  Google Scholar 

  • McKenna GB, Hostetter BJ, Hadjichristidis N, Fetters LJ, Plazek DJ (1989) A study of the linear viscoelastic properties of cyclic polystyrenes using creep and recovery measurements. Macromolecules 22:1834–1852

    Article  CAS  Google Scholar 

  • Montfort JP, Marin G, Monge P (1984) Effects of constraint release on the dynamics of entangled linear polymer melts. Macromolecules 17:1551–1560

    Article  CAS  Google Scholar 

  • Nam S, Leisen J, Breedveld V, Beckham HW (2009) Melt dynamics of blended poly(oxyethylene) chains and rings. Macromolecules 42:3121–3128

    Article  CAS  Google Scholar 

  • Obukhov SP, Rubinstein M, Duke T (1994) Dynamics of a ring polymer in a gel. Phys Rev Lett 73:1263–1266

    Article  CAS  Google Scholar 

  • Okumura Y, Ito K (2001) The polyrotaxane gels: a topological gel by figure-of-eight cross-links. Adv Mater 13:485–487

    Article  CAS  Google Scholar 

  • Parisi D, Ahn J, Chang T, Vlassopoulos D, Rubinstein M (2020) Stress relaxation in symmetric ring-linear polymer blends at low ring fractions. Macromolecules 53:1685–1693

    Article  CAS  Google Scholar 

  • Plazek DJ, O’Rourke VM (1971) Viscoelastic behavior of low molecular weight polystyrene. J Polym Sci Part A-2: Polym Phys 9:209–243

    Article  CAS  Google Scholar 

  • Qian Z, McKenna GB (2018) Expanding the application of the van Gurp-Palmen plot: new insights into polymer melt rheology. Polymer 155:208–217

    Article  CAS  Google Scholar 

  • Read DJ, Jagannathan K, Sukmaran SK, Auhl D (2012) A full-chain constitutive model for bidisperse blends of linear polymers. J Rheol 56:823–873

    Article  CAS  Google Scholar 

  • Read DJ, Shivokhin ME, Likhtman AE (2018) Contour length fluctuations and constraint release in entangled polymers: slop-spring simulations and their implications for binary blend rheology. J Rheol 62:1017–1036

    Article  CAS  Google Scholar 

  • Richter D, Goossen S, Wischnewski A (2015) Celebrating Soft Matter’s 10th anniversary: topology matters: structure and dynamics of ring polymers. Soft Matter 11:8535–8549

    Article  CAS  Google Scholar 

  • Robertson RM, Smith DE (2007) Self-diffusion of entangled linear and circular DNA molecules: dependence on length and concentration. Macromolecules 40:3373–3377

    Article  CAS  Google Scholar 

  • Roovers J (1985) Viscoelastic properties of ring polystyrenes. Macromolecules 18:1359–1361

    Article  CAS  Google Scholar 

  • Stadler FJ, Rajan M, Agarwal US, Liu CY, George KE, Lemstra PJ, Bailly C (2011) Rheological characterization in shear of a model dumbbell polymer concentrated solution. Rheol Acta 50:491–501

    Article  CAS  Google Scholar 

  • Subramanian G, Shanbhag S (2008) Conformational properties of blends of cyclic and linear polymer melts. Phys Rev E 77:011801

    Article  CAS  Google Scholar 

  • Suzuki J, Takano A, Deguchi T, Matsushita Y (2009) Dimension of ring polymers in bulk studied by Monte-Carlo simulation and self-consistent theory. J Chem Phys 131:144902

    Article  CAS  Google Scholar 

  • Trinkle S, Friedrich C (2001) Van Gurp-Palmen-plot: a way to characterize polydispersity of linear polymers. Rheol Acta 40:322–328

    Article  CAS  Google Scholar 

  • Trinkle S, Walter P, Friedrich C (2002) Van Gurp-Palmen plot II – classification of long chain branched polymers by their topology. Rheol Acta 41:103–113

    Article  CAS  Google Scholar 

  • Tsalikis DG, Mavrantzas VG (2014) Threading of ring poly(ethylene oxide) molecules by linear chains in the melt. ACS Macro Lett 3:763–766

    Article  CAS  Google Scholar 

  • Tsalikis DG, Mavrantzas VG (2020) Size and diffusivity of polymer rings in linear polymer matrices: the key role of threading events. Macromolecules 53:803–820

    Article  CAS  Google Scholar 

  • Van Gurp M, Palmen J (1998) Time temperature superposition for polymeric blends. Rheol Bull 67:5–8

    Google Scholar 

  • Vlassopoulos D (2016) Molecular topology and rheology: beyond the tube model. Rheol Acta 55:613–632

    Article  CAS  Google Scholar 

  • Watanabe H (1999) Viscoelasticity and dynamics of entangled polymers. Prog Polym Sci 24:1253–1403

    Article  CAS  Google Scholar 

  • Young CD, Zhou Y, Schroeder CM, Sing CE (2021) Dynamics and rheology of ring-linear blend semidilute solutions in extensional flow. Part I: modeling and molecular simulations. J Rheol 65:757–777

    Article  CAS  Google Scholar 

  • Zhou Y, Hsiao KW, Regan KE, Kong D, McKenna GB, Robertson-Anderson RM, Schroeder CM (2019) Effect of molecular architecture on ring polymer dynamics in semidilute linear polymer solutions. Nat Commun 10:1753

    Article  CAS  Google Scholar 

  • Zhou Y, Young CD, Lee M, Banik S, Kong D, McKenna GB, Robertson-Anderson RM, Sing CE, Schroeder CM (2021) Dynamics and rheology of ring-linear blend semidilute solutions in extensional flow: Single molecule experiments. J Rheol 65:729–744

    Article  CAS  Google Scholar 

  • Zoller P, Walsh D (1995) Standard pressure-volume-temperature data for polymers. Technomic Pub, Lancaster

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Acknowledgements

The authors acknowledge Prof. Hiroshi Watanabe at Kyoto University and Prof. Yuichi Masubuchi at Nagoya University for their helpful discussion. The authors acknowledge Prof. Tadashi Inoue at Nagoya University for providing us with the 4 mm diameter parallel plate geometry for rheological measurements.

Funding

This work was partly supported by JSPS KAKENHI Grant Numbers 21K14682 for Y.D., 24350056 for A.T., and 25248048 for Y.M.

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Authors and Affiliations

  1. Department of Molecular and Macromolecular Chemistry, Nagoya University, Nagoya, 4648603, Japan

    Yuya Doi, Atsushi Takano & Yushu Matsushita

  2. Department of Materials Physics, Nagoya University, Nagoya, 4648603, Japan

    Yuya Doi

  3. Institute of Materials Chemistry and Engineering, Kyushu University, Kasuga, Fukuoka, 8168580, Japan

    Yoshiaki Takahashi

  4. Toyota Physical and Chemical Research Institute, Nagakute, Aichi, 4801192, Japan

    Yushu Matsushita

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  1. Yuya Doi
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Appendix

Appendix

Figure 5 shows the van Gurp-Palmen (vGP) plot (i.e., the absolute value of the complex modulus |G*|= {(G′)2 + (G″)2}1/2 vs phase angle δ; van Gurp and Palmen 1998) for L430/D30/80/30 compared with those for L430, L430/L80, and L430/R30 at Tr = 160 °C. The vGP-plot is known to be sensitive to the differences in molecular architecture and molecular weight distribution of the samples (Trinkle and Friedrich 2001; Trinkle et al. 2002; Qian and McKenna 2018). We can see from Fig. 5 that time–temperature superposition (TTS) is hold for all the samples examined in this study, as confirmed in Figs. 1 and 2 in the main text. Compared to L430, L430/L80 clearly shows a different vGP plot shape, which is due to the fact that L430 and L80 relax separately on different time scales, as confirmed in Fig. 1 in the main text. In contrast, L430/R30 and L430/D308030 exhibit vGP plot apparently similar to those of L430. A more careful look at Fig. 5 reveals that the L430/D308030 blend shows a more gradual increase in δ with respect to the decrease in |G*|. This result corresponds to the fact that L430/D308030 exhibits a broader terminal relaxation than L430.

Fig. 5
figure 5

van-Gurp-Palmen plot of L430, L430/L80, L430/R30, and L430/D308030 reduced at Tr = 160 °C.

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Figure 6 shows the molecular weight dependence of η0 for linear PS samples reported by various researchers (Doi et al. 2015a; Roovers 1985; McKenna et al. 1989; Plazek and O'Rourke 1971; Montfort et al. 1984). As is well known, η0 increases in proportion to Mw in the Mw range below the critical molecular weight Mc ≃ 2Me = 36.0 kg/mol, while η0 shows a dependence on Mw3.4 at Mw above Mc (Ferry 1980). We also plotted η0 for the series of blend samples examined in this study at Mw = 427 kg/mol. Although there is some variation in the reported η0 values of linear PSs, the η0 of L430/D308030 in this study is considerably higher than that of L430 in Fig. 6.

Fig. 6
figure 6

Molecular weight dependence of η0 for linear PS samples (Doi et al. 2015a; Roovers 1985; McKenna et al. 1989; Plazek and O'Rourke 1971; Montfort et al. 1984) compared with that for L430/L80, L430/R30, and L430/D308030 at Tr = 160 °C

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Figure 7 shows G′, G″ and tan δ for L430/S3080 compared with those for L430, L430/L80 and L430/R30 at Tr = 160 °C. Note that S3080 indicates the single-tail tadpole-shaped PS, which was obtained in the synthesis process of D308030 as reported previously (Doi et al. 2016). The temperature dependence of aT of L430/S3080 is exactly the same with that of other blends as well as L430. Figure 7 shows that G*(ω) in the high ω limit (i.e., ωaT = 102 s−1) agrees well with that of L430 and other blends. The terminal relaxation behavior of L430/S3080 at ωaT ≤ 10−1 s−1 is also in good agreement with that of L430/R30. On the other hand, there is a difference between L430/S3080 and the other blends in the middle ω region of 10−1 ≤ ωaT /s−1 ≤ 101. That is, in this ω range, there is no difference in G′ between the samples, while G″ of L430/S3080 is higher than that of L430 and L430/R30, but lower than that of L430/L80. Based on the results in the main text, it is expected that the ring part in S3080 is also penetrated by L430. Therefore, in the middle ω range, the linear tail part of S3080 can be relaxed, but the whole S3080 molecule cannot be relaxed due to the ring part bounded by the penetration.

Fig. 7
figure 7

Master curves of a G′, G″ and b tan δ for L430, L430/L80, and L430/R30 and L430/S3080, reduced at Tr = 160 °C

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Doi, Y., Takano, A., Takahashi, Y. et al. Terminal relaxation behavior of entangled linear polymers blended with ring and dumbbell-shaped polymers in melts. Rheol Acta 61, 681–688 (2022). https://doi.org/10.1007/s00397-022-01355-y

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