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Controlling polymer properties through the shape of the molecular-weight distribution

Nature Reviews Materials volume 4, pages 761–774 (2019)Cite this article

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Abstract

The manipulation of a polymer’s properties without altering its chemical composition is a major challenge in polymer chemistry, materials science and engineering. Although variables such as chemical structure, branching, molecular weight and dispersity are routinely used to control the architecture and physical properties of polymers, little attention is given to the often profound effect of the breadth and shape of the molecular-weight distribution (MWD) on the properties of polymers. Synthetic strategies now make it possible to explore the importance of parameters such as skew and the higher moments of the MWD function beyond the average and standard deviation. In this Review, we describe early accounts of the effect of MWD shape on polymer properties; discuss synthetic strategies for controlling MWD shape; describe current endeavours to understand the influence of MWD shape on rheological and mechanical properties and phase behaviour; and provide insight into the future of using MWDs in the design of polymeric materials.

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Fig. 1: Reagent and polymer feed strategies for temporal control of polymer MWD shape.
Fig. 2: Alternative methods for control of polymer MWD shape with photochemical or centrifugal stimuli.
Fig. 3: Early work demonstrating the influence of MWD shape on the phase behaviour of block copolymers.
Fig. 4: Studies demonstrating the influence of MWD shape on the phase behaviour of block copolymers.
Fig. 5: Early theoretical and experimental work showing the influence of Ð and MWD shape on the rheological properties of polymers.
Fig. 6: Recent work showing the influence of MWD shape on the mechanical and rheological properties of homopolymers and block copolymers.

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References

  1. Bates, F. S. et al. Multiblock polymers: panacea or Pandora’s box? Science 336, 434–440 (2012).

    Article  CAS  Google Scholar 

  2. Bates, F. S. et al. Block copolymer thermodynamics: theory and experiment. Annu. Rev. Phys. Chem. 41, 525–557 (1990).

    Article  CAS  Google Scholar 

  3. Nichetti, D. et al. Influence of molecular parameters on material processability in extrusion processes. Polym. Eng. Sci. 39, 887–895 (1999).

    Article  CAS  Google Scholar 

  4. Collis, N. W. et al. The melt processing of monodisperse and polydisperse polystyrene melts within a slit entry and exit flow. J. Non-Newtonian Fluid Mech. 128, 29–41 (2005).

    Article  CAS  Google Scholar 

  5. Lynd, N. A. et al. Polydispersity and block copolymer self-assembly. Prog. Polym. Sci. 33, 875–893 (2008).

    Article  CAS  Google Scholar 

  6. Sides, S. W. et al. Continuous polydispersity in a self-consistent field theory for diblock copolymers. J. Chem. Phys. 121, 4974–4986 (2004).

    Article  CAS  Google Scholar 

  7. Lynd, N. A. et al. The role of polydispersity in the lamellar mesophase of model diblock copolymers. J. Polym. Sci. B Polym. Phys. 45, 3386–3393 (2007).

    Article  CAS  Google Scholar 

  8. Burger, C. et al. Polydispersity effects on the microphase-separation transition in block copolymers. Macromolecules 23, 3339–3346 (1990).

    Article  CAS  Google Scholar 

  9. Burger, C. et al. Polydispersity effects on the microphase-separation transition in block copolymers [Erratum to document cited in CA113(2):7140f]. Macromolecules 24, 816 (1991).

    Article  CAS  Google Scholar 

  10. Wolff, T. et al. Synchrotron SAXS study of the microphase separation transition in diblock copolymers. Macromolecules 26, 1707–1711 (1993).

    Article  CAS  Google Scholar 

  11. Widin, J. M. et al. Bulk and thin film morphological behavior of broad dispersity poly(styrene-b-methyl methacrylate) diblock copolymers. Macromolecules 46, 4472–4480 (2013).

    Article  CAS  Google Scholar 

  12. Nguyen, D. et al. Effect of ionic chain polydispersity on the size of spherical ionic microdomains in diblock ionomers. Macromolecules 27, 5173–5181 (1994).

    Article  CAS  Google Scholar 

  13. Rane, S. S. et al. Polydispersity index: how accurately does it measure the breath of the molecular weight distribution? Chem. Mater. 17, 926 (2005).

    Article  CAS  Google Scholar 

  14. Harrisson, S. The downside of dispersity: why the standard deviation is a better measure of dispersion in precision polymerization. Polym. Chem. 9, 1366–1370 (2018).

    Article  CAS  Google Scholar 

  15. Gilbert, R. G. et al. Dispersity in polymer science. Pure Appl. Chem. 81, 351–353 (2009).

    Article  CAS  Google Scholar 

  16. Carothers, W. H. Polymerization. Chem. Rev. 8, 353–426 (1931).

    Article  CAS  Google Scholar 

  17. Svedberg, T. Sedimentation of molecules in centrifugal fields. Chem. Rev. 14, 1–15 (1934).

    Article  Google Scholar 

  18. Zimm, B. H. Apparatus and methods for measurement and interpretation of the angular variation of light scattering; preliminary results on polystyrene solutions. J. Chem. Phys. 16, 1099–1116 (1948).

    Article  CAS  Google Scholar 

  19. Schulz, G. V. About the kinetics of chain polymerization. Z. Physik. Chem. B43, 25–46 (1939).

    CAS  Google Scholar 

  20. Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 13, 1602–1617 (1980).

    Article  CAS  Google Scholar 

  21. Noro, A. et al. Effect of composition distribution on microphase-separated structure from BAB triblock copolymers. Macromolecules 37, 3804–3808 (2004).

    Article  CAS  Google Scholar 

  22. Matsushita, Y. et al. Molecular weight dependence of lamellar domain spacing of diblock copolymers in bulk. Macromolecules 23, 4313–4316 (1990).

    Article  CAS  Google Scholar 

  23. Matsushita, Y. et al. Effect of composition distribution on microphase-separated structure from diblock copolymers. Macromolecules 36, 8074–8077 (2003).

    Article  CAS  Google Scholar 

  24. Noro, A. et al. Effect of molecular weight distribution on microphase-separated structures from block copolymers. Macromolecules 38, 4371–4376 (2005).

    Article  CAS  Google Scholar 

  25. Noro, A. et al. Chain localization and interfacial thickness in microphase-separated structures of block copolymers with variable composition distributions. Macromolecules 39, 7654–7661 (2006).

    Article  CAS  Google Scholar 

  26. Hadziioannou, G. et al. Structural study of mixtures of styrene isoprene two- and three-block copolymers. Macromolecules 15, 267–271 (1982).

    Article  CAS  Google Scholar 

  27. Widin, J. M. et al. Unexpected consequences of block polydispersity on the self-assembly of ABA triblock copolymers. J. Am. Chem. Soc. 134, 3834–3844 (2012).

    Article  CAS  Google Scholar 

  28. Bendejacq, D. et al. Well-ordered microdomain structures in polydisperse poly(styrene)-poly(acrylic acid) diblock copolymers from controlled radical polymerization. Macromolecules 35, 6645–6649 (2002).

    Article  CAS  Google Scholar 

  29. Hustad, P. D. et al. Photonic polyethylene from self-assembled mesophases of polydisperse olefin block copolymers. Macromolecules 42, 3788–3794 (2009).

    Article  CAS  Google Scholar 

  30. Lynd, N. A. et al. Influence of polydispersity on the self-assembly of diblock copolymers. Macromolecules 38, 8803–8810 (2005).

    Article  CAS  Google Scholar 

  31. Lynd, N. A. et al. Effects of polydispersity on the order–disorder transition in block copolymer melts. Macromolecules 40, 8050–8055 (2007).

    Article  CAS  Google Scholar 

  32. Plichta, A. et al. Tuning dispersity in diblock copolymers using ARGET ATRP. Macromol. Chem. Phys. 213, 2659–2668 (2012).

    Article  CAS  Google Scholar 

  33. Listak, J. et al. Effect of symmetry of molecular weight distribution in block copolymers on formation of “metastable” morphologies. Macromolecules 41, 5919–5927 (2008).

    Article  CAS  Google Scholar 

  34. Sarbu, T. et al. Polystyrene with designed molecular weight distribution by atom transfer radical coupling. Macromolecules 37, 3120–3127 (2004).

    Article  CAS  Google Scholar 

  35. Weiss, E. D. et al. Atom transfer versus catalyst transfer: Deviations from ideal Poisson behavior in controlled polymerizations. Polymer 72, 226–237 (2015).

    Article  CAS  Google Scholar 

  36. Liu, X. et al. Polymer dispersity control by organocatalyzed living radical polymerization. Angew. Chem. Int. Ed. 131, 5654–5659 (2019).

    Article  Google Scholar 

  37. Li, H. et al. Tuning the molecular weight distribution atom transfer radical polymerization using deep reinforcement learning. Mol. Syst. Des. Eng. 3, 496–508 (2018).

    Article  CAS  Google Scholar 

  38. Meira, G. R. et al. Molecular weight distribution control in continuous “living” polymerizations through periodic operation of the monomer feed. Polym. Eng. Sci. 21, 415–423 (1981).

    Article  CAS  Google Scholar 

  39. Alassia, L. M. et al. Molecular weight distribution control in a semibatch living-anionic polymerization. II. Experimental study. J. Appl. Polym. Sci. 36, 481–494 (1988).

    Article  CAS  Google Scholar 

  40. Couso, D. A. et al. Molecular weight distribution control in a semibatch living-anionic polymerization. I. Theoretical study. J. Appl. Polym. Sci. 30, 3249–3265 (1985).

    Article  CAS  Google Scholar 

  41. Farkas, E. et al. Molecular weight distribution design with living polymerization reactions. Ind. Eng. Chem. Res. 43, 7356–7360 (2004).

    Article  CAS  Google Scholar 

  42. Meszena, Z. G. et al. Towards tailored molecular weight distributions through controlled living polymerisation reactors: a simple predictive algorithm. Polym. React. Eng. 71, 71–95 (1999).

    Article  Google Scholar 

  43. Seno, K. I. et al. Thermosensitive diblock copolymers with designed molecular weight distribution: Synthesis by continuous living cationic polymerization and micellization behavior. J. Polym. Sci. A Polym. Chem. 46, 2212–2221 (2008).

    Article  CAS  Google Scholar 

  44. Litt, M. The effects of inadequate mixing in anionic polymerization: Laminar mixing hypothesis. J. Polym. Sci. 58, 429–454 (1962).

    Article  CAS  Google Scholar 

  45. Gentekos, D. T. et al. Beyond dispersity: deterministic control of polymer molecular weight distribution. J. Am. Chem. Soc. 138, 1848–1851 (2016).

    Article  CAS  Google Scholar 

  46. Hawker, C. J. et al. New polymer synthesis by nitroxide mediated living radical polymerizations. E. Chem. Rev. 101, 3661–3688 (2001).

    Article  CAS  Google Scholar 

  47. Hadjichristidis, N. et al. Polymers with complex architecture by living anionic polymerization. Chem. Rev. 101, 3747–3792 (2001).

    Article  CAS  Google Scholar 

  48. Kottisch, V. et al. “Shaping” the future of molecular weight distributions in anionic polymerization. ACS Macro Lett. 5, 796–800 (2016).

    Article  CAS  Google Scholar 

  49. Corrigan, N. et al. Controlling molecular weight distributions through photoinduced flow polymerization. Macromolecules 50, 8438–8448 (2017).

    Article  CAS  Google Scholar 

  50. Corrigan, N. et al. Copolymers with controlled molecular weight distributions and compositional gradients through flow polymerization. Macromolecules 51, 4553–4563 (2018).

    Article  CAS  Google Scholar 

  51. Spinnrock, A. et al. Control of molar mass distribution by polymerization in the analytical ultracentrifuge. Angew. Chem. Int. Ed. 57, 8284–8287 (2018).

    Article  CAS  Google Scholar 

  52. Fredrickson, G. H. et al. Fluctuation effects in the theory of microphase separation in block copolymers. J. Chem. Phys. 87, 697–705 (1987).

    Article  CAS  Google Scholar 

  53. Erukhimovich, I. et al. A statistical theory of polydisperse block copolymer systems under weak supercrystallization. Macromol. Symp. 81, 253–315 (1994).

    Article  CAS  Google Scholar 

  54. Semenov, A. N. Contribution to the theory of microphase layering in block-copolymer melts. Sov. Phys. JETP 61, 733–742 (1985).

    Google Scholar 

  55. Milner, S. T. et al. Effects of polydispersity in the end-grafted polymer brush. Macromolecules 22, 853–861 (1989).

    Article  CAS  Google Scholar 

  56. Dobrynin, A. et al. Theory of polydisperse multiblock copolymers. Macromolecules 30, 4756–4765 (1997).

    Article  CAS  Google Scholar 

  57. Spontak, R. J. et al. Prediction of microstructures for polydisperse block copolymers, using continuous thermodynamics. J. Polym. Sci. B Polym. Phys. 28, 1379–1407 (1990).

    Article  CAS  Google Scholar 

  58. Bates, F. S. et al. Block copolymers near the microphase separation transition. 3. Small-angle neutron scattering study of the homogeneous melt state. Macromolecules 18, 2478–2486 (1985).

    Article  CAS  Google Scholar 

  59. Mori, K. et al. Small-angle X-ray scattering from block copolymers in disordered state: 2. Effect of molecular weight distribution. Polymer 30, 1389–1398 (1989).

    Article  CAS  Google Scholar 

  60. Sakurai, S. et al. Evaluation of segmental interaction by small-angle X-ray scattering based on the random-phase approximation for asymmetric, polydisperse triblock copolymers. Macromolecules 25, 2679–2691 (1992).

    Article  CAS  Google Scholar 

  61. Wolff, T. et al. Synchrotron SAXS study of the microphase separation transition in diblock copolymers. Macromolecules 26, 1707–1711 (1993).

    Article  CAS  Google Scholar 

  62. Cooke, D. M. et al. Effects of polydispersity on phase behavior of diblock copolymers. Macromolecules 39, 6661–6671 (2006).

    Article  CAS  Google Scholar 

  63. Lynd, N. A. et al. Theory of polydisperse block copolymer melts: beyond the Schulz–Zimm distribution. Macromolecules 41, 4531–4533 (2008).

    Article  CAS  Google Scholar 

  64. Matsen, M. W. Effect of large degrees of polydispersity on strongly segregated block copolymers. Eur. Phys. J. E Soft Matter Biol. Phys. 21, 199–207 (2006).

    Article  CAS  Google Scholar 

  65. Woo, S. et al. Domain swelling in ARB-type triblock copolymers via self-adjusting effective dispersity. Soft Matter 13, 5527–5534 (2017).

    Article  CAS  Google Scholar 

  66. Broseta, D. et al. Molecular weight and polydispersity effects at polymer-polymer interfaces. Macromolecules 23, 132–139 (1990).

    Article  CAS  Google Scholar 

  67. Fredrickson, G. H. et al. Theory of polydisperse inhomogeneous polymers. Macromolecules 36, 5415–5423 (2003).

    Article  CAS  Google Scholar 

  68. Matsen, M. W. Phase behavior of block copolymer/homopolymer blends. Macromolecules 28, 5765–5773 (1995).

    Article  CAS  Google Scholar 

  69. Loo, Y.-L. A highly regular hexagonally perforated lamellar structure in a quiescent diblock copolymer. Macromolecules 38, 4947–4949 (2005).

    Article  CAS  Google Scholar 

  70. Hashimoto, T. et al. Observation of “mesh” and “strut” structures in block copolymer/homopolymer mixtures. Macromolecules 25, 1433–1439 (1992).

    Article  CAS  Google Scholar 

  71. Hajduk, D. A. et al. Stability of the perforated layer (PL) phase in diblock copolymer melts. Macromolecules 30, 3788–3795 (1997).

    Article  CAS  Google Scholar 

  72. Matsen, M. W. Polydispersity-induced macrophase separation in diblock copolymer melts. Phys. Rev. Lett. 99, 148304 (2007).

    Article  CAS  Google Scholar 

  73. Matsen, M. W. et al. Unifying weak- and strong-segregation block copolymer theories. Macromolecules 29, 1091–1098 (1996).

    Article  CAS  Google Scholar 

  74. Matsen, M. W. et al. Origins of complex self-assembly in block copolymers. Macromolecules 29, 7641–7644 (1996).

    Article  CAS  Google Scholar 

  75. Gentekos, D. T. et al. Exploiting molecular weight distribution shape to tune domain spacing in block copolymer thin films. J. Am. Chem. Soc. 140, 4639–4648 (2018).

    Article  CAS  Google Scholar 

  76. Busch, P. et al. Lamellar diblock copolymer thin films investigated by tapping mode atomic force microscopy: Molar-mass dependence of surface ordering. Macromolecules 36, 8717–8727 (2003).

    Article  CAS  Google Scholar 

  77. Gentekos, D. T. et al. Molecular weight distribution shape as a versatile approach to tailoring block copolymer phase behavior. ACS Macro Lett. 7, 677–682 (2018).

    Article  CAS  Google Scholar 

  78. Pao, Y. H. Dependence of intrinsic viscosity of dilute solutions of macromolecules on velocity gradient. J. Chem. Phys. 25, 1294–1295 (1956).

    Article  CAS  Google Scholar 

  79. Bueche, F. Influence of rate of shear on the apparent viscosity of A—dilute polymer solutions, and B—bulk polymers. J. Chem. Phys. 22, 1570–1576 (1954).

    Article  CAS  Google Scholar 

  80. Rouse, P. E. A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21, 1272–1280 (1953).

    Article  CAS  Google Scholar 

  81. Pao, Y. H. Hydrodynamic theory for the flow of a viscoelastic fluid. J. Appl. Phys. 28, 591–598 (1957).

    Article  CAS  Google Scholar 

  82. Graessley, W. W. Molecular entanglement theory of flow behavior in amorphous polymers. J. Chem. Phys. 43, 2696–2703 (1965).

    Article  CAS  Google Scholar 

  83. Dunleavy, J. E. et al. Correlation of shear behavior of solutions of polyisobutylene. Trans. Soc. Rheol. 10, 157–168 (1966).

    Article  CAS  Google Scholar 

  84. Bremner, T. et al. Melt flow index values and molecular weight distributions of commercial thermoplastics. J. Appl. Poly. Sci. 41, 1617–1627 (1990).

    Article  CAS  Google Scholar 

  85. Rodríguez-Hernández, M. T. et al. Determination of the molecular characteristics of commercial polyethylenes with different architectures and the relation with the melt flow index. J. Appl. Poly. Sci. 104, 1572–1578 (2007).

    Article  CAS  Google Scholar 

  86. Utracki, L. A. et al. Linear low density polyethylenes and their blends: Part 2. Shear flow of LLDPE’s. Polym. Eng. Sci. 27, 367–379 (1987).

    Article  CAS  Google Scholar 

  87. Aho, J. et al. Rheology as a tool for evaluation of melt processability of innovative dosage forms. Int. J. Pharm. 494, 623–642 (2015).

    Article  CAS  Google Scholar 

  88. Ansari, M. et al. Rheology of Ziegler–Natta and metallocene high-density polyethylenes: broad molecular weight distribution effects. Rheol. Acta 50, 17–27 (2011).

    Article  CAS  Google Scholar 

  89. Ballman, R. L. et al. The influence of molecular weight distribution on some properties of polystyrene melt. J. Polym. Sci. A Gen. Papers 2, 3557–3575 (1964).

    Article  CAS  Google Scholar 

  90. Middleman, S. Effect of molecular weight distribution on viscosity of polymeric fluids. J. Appl. Poly. Sci. 11, 417–424 (1967).

    Article  CAS  Google Scholar 

  91. Colby, R. H. et al. The melt viscosity-molecular weight relationship for linear polymers. Macromol. 20, 2226–2237 (1987).

    Article  CAS  Google Scholar 

  92. Cross, M. M. Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems. J. Colloid. Sci. 20, 417–437 (1965).

    Article  CAS  Google Scholar 

  93. Des Cloiseaux, J. Double reptation vs. simple reptation in polymer melts. Europhys. Lett. 5, 437–442 (1988).

    Article  Google Scholar 

  94. Gloor, W. E. The numerical evaluation of parameters in distribution functions of polymers from their molecular weight distributions. J. Appl. Polym. Sci. 22, 1177–1182 (1978).

    Article  CAS  Google Scholar 

  95. Nichetti, D. et al. Viscosity model for polydisperse polymer melts. J. Rheol. 42, 951–969 (1998).

    Article  CAS  Google Scholar 

  96. Rudd, J. The effect of molecular weight distribution on the rheological properties of polystyrene. J. Polym. Sci. A Polym. Chem. 44, 459–474 (1960).

    CAS  Google Scholar 

  97. González-González, V. A. et al. Polypropylene chain scissions and molecular weight changes in multiple extrusion. Polym. Degrad. Stab. 60, 33–42 (1998).

    Article  Google Scholar 

  98. Wasserman, S. H. et al. Effects of polydispersity on linear viscoelasticity in entangled polymer melts. J. Rheol. 36, 543–572 (1992).

    Article  CAS  Google Scholar 

  99. Stürzel, M. et al. From multisite polymerization catalysis to sustainable materials and all-polyolefin composites. Chem. Rev. 116, 1398–1433 (2016).

    Article  CAS  Google Scholar 

  100. Nadgorny, M. et al. Manipulation of molecular weight distribution shape as a new strategy to control processing parameters. Macromol. Rapid. Commun. 38, 1700352 (2017).

    Article  CAS  Google Scholar 

  101. Rubber industry sees value in MWD. Chem. Eng. News Archive 43, 40–41 (1965).

  102. Fink, Y. et al. Block copolymers as photonic bandgap materials. J. Lightwave Technol. 17, 1963–1969 (1999).

    Article  CAS  Google Scholar 

  103. Stefik, M. et al. Block copolymer self-assembly for nanophotonics. Chem. Soc. Rev. 44, 5076–5091 (2015).

    Article  CAS  Google Scholar 

  104. Kang, Y. et al. Broad-wavelength-range chemically tunable block-copolymer photonic gels. Nat. Mater. 6, 957–960 (2007).

    Article  CAS  Google Scholar 

  105. Kang, C. et al. Full color stop bands in hybrid organic/inorganic block copolymer photonic gels by swelling-freezing. J. Am. Chem. Soc. 131, 7538–7539 (2009).

    Article  CAS  Google Scholar 

  106. Urbas, A. M. et al. Bicontinuous cubic block copolymer photonic crystals. Adv. Mater. 14, 1850–1853 (2002).

    Article  CAS  Google Scholar 

  107. Park, M. et al. Block copolymer lithography: periodic arrays of ~1011 holes in 1 square centimeter. Science 276, 1401–1404 (1997).

    Article  CAS  Google Scholar 

  108. Honeker, C. C. et al. Impact of morphological orientation in determining mechanical properties in triblock copolymer systems. Chem. Mater. 8, 1702–1714 (1996).

    Article  CAS  Google Scholar 

  109. Bang, J. et al. Block copolymer nanolithography: translation of molecular level control to nanoscale patterns. Adv. Mater. 21, 4769–4792 (2009).

    Article  CAS  Google Scholar 

  110. Ruiz, R. et al. Density multiplication and improved lithography by directed block copolymer assembly. Science 321, 936–939 (2008).

    Article  CAS  Google Scholar 

  111. Kim, S. O. et al. Epitaxial self-assembly of block copolymers on lithographically defined nanopatterned substrates. Nature 424, 411–414 (2003).

    Article  CAS  Google Scholar 

  112. Chen, L. et al. Robust nanoporous membranes templated by a doubly reactive block copolymer. J. Am. Chem. Soc. 129, 13786–13787 (2007).

    Article  CAS  Google Scholar 

  113. Quirk, R. et al. in Thermoplastic Elastomers 2nd edn (eds Holden, G. et al.) 72–100 (Hanser Publishers, 1996).

  114. Jackson, E. A. et al. Nanoporous membranes derived from block copolymers; from drug delivery to water filtration. ACS Nano 4, 3548–3553 (2010).

    Article  CAS  Google Scholar 

  115. Ahn, H. et al. Nanoporous block copolymer membranes for ultrafiltration: a simple approach to size tunability. ACS Nano 8, 11745–11752 (2014).

    Article  CAS  Google Scholar 

  116. Zhao, D. et al. Triblock copolymer syntheses of mesoporous silica with periodic 50 to 300 angstrom pores. Science 279, 548–552 (1998).

    Article  CAS  Google Scholar 

  117. Liang, C. et al. Synthesis of a large-scale highly ordered porous carbon film by self-assembly of block copolymers. Angew. Chem. Int. Ed. 43, 5785–5789 (2004).

    Article  CAS  Google Scholar 

  118. Jeong, B. et al. Biodegradable block copolymers as injectable drug-delivery systems. Nature 388, 860–862 (1997).

    Article  CAS  Google Scholar 

  119. Kataoka, K. et al. Block copolymer micelles for drug delivery: design, characterization and biological significance. Adv. Drug Deliv. Rev. 64, 37–48 (2012).

    Article  Google Scholar 

  120. Fischer, W. et al. Anionic polymerization process. US6444762 B1 (1997).

  121. Wyatt, P. J. Light scattering and the absolute characterization of macromolecules. Anal. Chim. Acta. 272, 1–40 (1993).

    Article  CAS  Google Scholar 

  122. Lange, H. et al. Gel permeation chromatography in determining molecular weights of lignins: critical aspects revisited for improved utility in the development of novel materials. ACS Sustain. Chem. Eng. 4, 5167–5180 (2016).

    Article  CAS  Google Scholar 

  123. Determann, H. in Gel Chromatography · Gel Filtration · Gel Permeation. · Molecular Sieves, A Laboratory Handbook 2nd edn (Springer, 1969).

  124. Matyjaszewski, K. et al. Atom transfer radical polymerization. Chem. Rev. 101, 2921–2990 (2001).

    Article  CAS  Google Scholar 

  125. Flory, P. J. Molecular size distribution in linear condensation polymers. J. Am. Chem. Soc. 58, 1877–1885 (1936).

    Article  CAS  Google Scholar 

  126. Ryu, J. et al. Molecular weight distribution of branched polystyrene: Propagation of Poisson distribution. Macromolecules 37, 8805–8807 (2004).

    Article  CAS  Google Scholar 

  127. Peebles, L. H., Jr. in Molecular Weight Distributions in Polymers (Interscience, 1971).

  128. Rudin, A. Molecular weight distributions of polymers. J. Chem. Educ. 46, 595 (1969).

    Article  CAS  Google Scholar 

  129. Gong, X. et al. Molecular weight distribution characteristics (of a polymer) derived from a stretched-exponential PGSTE NMR response function—simulation. Macromol. Chem. Phys. 213, 278–284 (2012).

    Article  CAS  Google Scholar 

  130. Chem, S.-A. et al. The skewness of polymer molecular weight distributions. J. Polym. Sci. Polym. Chem. Ed. 21, 3373–3380 (1983).

    Article  Google Scholar 

  131. Kirkland, J. J. et al. Sampling and extra-column effects in high-performance liquid chromatography; influence of peak skew on plate count calculations. J. Chromatogr. Sci. 15, 303–316 (1977).

    Article  CAS  Google Scholar 

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Acknowledgements

The authors acknowledge the Cornell Center for Materials Research (CCMR) through the National Science Foundation (NSF) Materials Research Science and Engineering Centers (MRSEC) program (DMR-1719875). B.P.F. thanks 3M and the Sloan Foundation for partially supporting this work.

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  1. Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA

    Dillon T. Gentekos, Renee J. Sifri & Brett P. Fors

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Gentekos, D.T., Sifri, R.J. & Fors, B.P. Controlling polymer properties through the shape of the molecular-weight distribution. Nat Rev Mater 4, 761–774 (2019). https://doi.org/10.1038/s41578-019-0138-8

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