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.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Bates, F. S. et al. Multiblock polymers: panacea or Pandora’s box? Science 336, 434–440 (2012).
Bates, F. S. et al. Block copolymer thermodynamics: theory and experiment. Annu. Rev. Phys. Chem. 41, 525–557 (1990).
Nichetti, D. et al. Influence of molecular parameters on material processability in extrusion processes. Polym. Eng. Sci. 39, 887–895 (1999).
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).
Lynd, N. A. et al. Polydispersity and block copolymer self-assembly. Prog. Polym. Sci. 33, 875–893 (2008).
Sides, S. W. et al. Continuous polydispersity in a self-consistent field theory for diblock copolymers. J. Chem. Phys. 121, 4974–4986 (2004).
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).
Burger, C. et al. Polydispersity effects on the microphase-separation transition in block copolymers. Macromolecules 23, 3339–3346 (1990).
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).
Wolff, T. et al. Synchrotron SAXS study of the microphase separation transition in diblock copolymers. Macromolecules 26, 1707–1711 (1993).
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).
Nguyen, D. et al. Effect of ionic chain polydispersity on the size of spherical ionic microdomains in diblock ionomers. Macromolecules 27, 5173–5181 (1994).
Rane, S. S. et al. Polydispersity index: how accurately does it measure the breath of the molecular weight distribution? Chem. Mater. 17, 926 (2005).
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).
Gilbert, R. G. et al. Dispersity in polymer science. Pure Appl. Chem. 81, 351–353 (2009).
Carothers, W. H. Polymerization. Chem. Rev. 8, 353–426 (1931).
Svedberg, T. Sedimentation of molecules in centrifugal fields. Chem. Rev. 14, 1–15 (1934).
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).
Schulz, G. V. About the kinetics of chain polymerization. Z. Physik. Chem. B43, 25–46 (1939).
Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 13, 1602–1617 (1980).
Noro, A. et al. Effect of composition distribution on microphase-separated structure from BAB triblock copolymers. Macromolecules 37, 3804–3808 (2004).
Matsushita, Y. et al. Molecular weight dependence of lamellar domain spacing of diblock copolymers in bulk. Macromolecules 23, 4313–4316 (1990).
Matsushita, Y. et al. Effect of composition distribution on microphase-separated structure from diblock copolymers. Macromolecules 36, 8074–8077 (2003).
Noro, A. et al. Effect of molecular weight distribution on microphase-separated structures from block copolymers. Macromolecules 38, 4371–4376 (2005).
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).
Hadziioannou, G. et al. Structural study of mixtures of styrene isoprene two- and three-block copolymers. Macromolecules 15, 267–271 (1982).
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).
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).
Hustad, P. D. et al. Photonic polyethylene from self-assembled mesophases of polydisperse olefin block copolymers. Macromolecules 42, 3788–3794 (2009).
Lynd, N. A. et al. Influence of polydispersity on the self-assembly of diblock copolymers. Macromolecules 38, 8803–8810 (2005).
Lynd, N. A. et al. Effects of polydispersity on the order–disorder transition in block copolymer melts. Macromolecules 40, 8050–8055 (2007).
Plichta, A. et al. Tuning dispersity in diblock copolymers using ARGET ATRP. Macromol. Chem. Phys. 213, 2659–2668 (2012).
Listak, J. et al. Effect of symmetry of molecular weight distribution in block copolymers on formation of “metastable” morphologies. Macromolecules 41, 5919–5927 (2008).
Sarbu, T. et al. Polystyrene with designed molecular weight distribution by atom transfer radical coupling. Macromolecules 37, 3120–3127 (2004).
Weiss, E. D. et al. Atom transfer versus catalyst transfer: Deviations from ideal Poisson behavior in controlled polymerizations. Polymer 72, 226–237 (2015).
Liu, X. et al. Polymer dispersity control by organocatalyzed living radical polymerization. Angew. Chem. Int. Ed. 131, 5654–5659 (2019).
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).
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).
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).
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).
Farkas, E. et al. Molecular weight distribution design with living polymerization reactions. Ind. Eng. Chem. Res. 43, 7356–7360 (2004).
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).
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).
Litt, M. The effects of inadequate mixing in anionic polymerization: Laminar mixing hypothesis. J. Polym. Sci. 58, 429–454 (1962).
Gentekos, D. T. et al. Beyond dispersity: deterministic control of polymer molecular weight distribution. J. Am. Chem. Soc. 138, 1848–1851 (2016).
Hawker, C. J. et al. New polymer synthesis by nitroxide mediated living radical polymerizations. E. Chem. Rev. 101, 3661–3688 (2001).
Hadjichristidis, N. et al. Polymers with complex architecture by living anionic polymerization. Chem. Rev. 101, 3747–3792 (2001).
Kottisch, V. et al. “Shaping” the future of molecular weight distributions in anionic polymerization. ACS Macro Lett. 5, 796–800 (2016).
Corrigan, N. et al. Controlling molecular weight distributions through photoinduced flow polymerization. Macromolecules 50, 8438–8448 (2017).
Corrigan, N. et al. Copolymers with controlled molecular weight distributions and compositional gradients through flow polymerization. Macromolecules 51, 4553–4563 (2018).
Spinnrock, A. et al. Control of molar mass distribution by polymerization in the analytical ultracentrifuge. Angew. Chem. Int. Ed. 57, 8284–8287 (2018).
Fredrickson, G. H. et al. Fluctuation effects in the theory of microphase separation in block copolymers. J. Chem. Phys. 87, 697–705 (1987).
Erukhimovich, I. et al. A statistical theory of polydisperse block copolymer systems under weak supercrystallization. Macromol. Symp. 81, 253–315 (1994).
Semenov, A. N. Contribution to the theory of microphase layering in block-copolymer melts. Sov. Phys. JETP 61, 733–742 (1985).
Milner, S. T. et al. Effects of polydispersity in the end-grafted polymer brush. Macromolecules 22, 853–861 (1989).
Dobrynin, A. et al. Theory of polydisperse multiblock copolymers. Macromolecules 30, 4756–4765 (1997).
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).
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).
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).
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).
Wolff, T. et al. Synchrotron SAXS study of the microphase separation transition in diblock copolymers. Macromolecules 26, 1707–1711 (1993).
Cooke, D. M. et al. Effects of polydispersity on phase behavior of diblock copolymers. Macromolecules 39, 6661–6671 (2006).
Lynd, N. A. et al. Theory of polydisperse block copolymer melts: beyond the Schulz–Zimm distribution. Macromolecules 41, 4531–4533 (2008).
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).
Woo, S. et al. Domain swelling in ARB-type triblock copolymers via self-adjusting effective dispersity. Soft Matter 13, 5527–5534 (2017).
Broseta, D. et al. Molecular weight and polydispersity effects at polymer-polymer interfaces. Macromolecules 23, 132–139 (1990).
Fredrickson, G. H. et al. Theory of polydisperse inhomogeneous polymers. Macromolecules 36, 5415–5423 (2003).
Matsen, M. W. Phase behavior of block copolymer/homopolymer blends. Macromolecules 28, 5765–5773 (1995).
Loo, Y.-L. A highly regular hexagonally perforated lamellar structure in a quiescent diblock copolymer. Macromolecules 38, 4947–4949 (2005).
Hashimoto, T. et al. Observation of “mesh” and “strut” structures in block copolymer/homopolymer mixtures. Macromolecules 25, 1433–1439 (1992).
Hajduk, D. A. et al. Stability of the perforated layer (PL) phase in diblock copolymer melts. Macromolecules 30, 3788–3795 (1997).
Matsen, M. W. Polydispersity-induced macrophase separation in diblock copolymer melts. Phys. Rev. Lett. 99, 148304 (2007).
Matsen, M. W. et al. Unifying weak- and strong-segregation block copolymer theories. Macromolecules 29, 1091–1098 (1996).
Matsen, M. W. et al. Origins of complex self-assembly in block copolymers. Macromolecules 29, 7641–7644 (1996).
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).
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).
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).
Pao, Y. H. Dependence of intrinsic viscosity of dilute solutions of macromolecules on velocity gradient. J. Chem. Phys. 25, 1294–1295 (1956).
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).
Rouse, P. E. A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21, 1272–1280 (1953).
Pao, Y. H. Hydrodynamic theory for the flow of a viscoelastic fluid. J. Appl. Phys. 28, 591–598 (1957).
Graessley, W. W. Molecular entanglement theory of flow behavior in amorphous polymers. J. Chem. Phys. 43, 2696–2703 (1965).
Dunleavy, J. E. et al. Correlation of shear behavior of solutions of polyisobutylene. Trans. Soc. Rheol. 10, 157–168 (1966).
Bremner, T. et al. Melt flow index values and molecular weight distributions of commercial thermoplastics. J. Appl. Poly. Sci. 41, 1617–1627 (1990).
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).
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).
Aho, J. et al. Rheology as a tool for evaluation of melt processability of innovative dosage forms. Int. J. Pharm. 494, 623–642 (2015).
Ansari, M. et al. Rheology of Ziegler–Natta and metallocene high-density polyethylenes: broad molecular weight distribution effects. Rheol. Acta 50, 17–27 (2011).
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).
Middleman, S. Effect of molecular weight distribution on viscosity of polymeric fluids. J. Appl. Poly. Sci. 11, 417–424 (1967).
Colby, R. H. et al. The melt viscosity-molecular weight relationship for linear polymers. Macromol. 20, 2226–2237 (1987).
Cross, M. M. Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems. J. Colloid. Sci. 20, 417–437 (1965).
Des Cloiseaux, J. Double reptation vs. simple reptation in polymer melts. Europhys. Lett. 5, 437–442 (1988).
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).
Nichetti, D. et al. Viscosity model for polydisperse polymer melts. J. Rheol. 42, 951–969 (1998).
Rudd, J. The effect of molecular weight distribution on the rheological properties of polystyrene. J. Polym. Sci. A Polym. Chem. 44, 459–474 (1960).
González-González, V. A. et al. Polypropylene chain scissions and molecular weight changes in multiple extrusion. Polym. Degrad. Stab. 60, 33–42 (1998).
Wasserman, S. H. et al. Effects of polydispersity on linear viscoelasticity in entangled polymer melts. J. Rheol. 36, 543–572 (1992).
Stürzel, M. et al. From multisite polymerization catalysis to sustainable materials and all-polyolefin composites. Chem. Rev. 116, 1398–1433 (2016).
Nadgorny, M. et al. Manipulation of molecular weight distribution shape as a new strategy to control processing parameters. Macromol. Rapid. Commun. 38, 1700352 (2017).
Rubber industry sees value in MWD. Chem. Eng. News Archive 43, 40–41 (1965).
Fink, Y. et al. Block copolymers as photonic bandgap materials. J. Lightwave Technol. 17, 1963–1969 (1999).
Stefik, M. et al. Block copolymer self-assembly for nanophotonics. Chem. Soc. Rev. 44, 5076–5091 (2015).
Kang, Y. et al. Broad-wavelength-range chemically tunable block-copolymer photonic gels. Nat. Mater. 6, 957–960 (2007).
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).
Urbas, A. M. et al. Bicontinuous cubic block copolymer photonic crystals. Adv. Mater. 14, 1850–1853 (2002).
Park, M. et al. Block copolymer lithography: periodic arrays of ~1011 holes in 1 square centimeter. Science 276, 1401–1404 (1997).
Honeker, C. C. et al. Impact of morphological orientation in determining mechanical properties in triblock copolymer systems. Chem. Mater. 8, 1702–1714 (1996).
Bang, J. et al. Block copolymer nanolithography: translation of molecular level control to nanoscale patterns. Adv. Mater. 21, 4769–4792 (2009).
Ruiz, R. et al. Density multiplication and improved lithography by directed block copolymer assembly. Science 321, 936–939 (2008).
Kim, S. O. et al. Epitaxial self-assembly of block copolymers on lithographically defined nanopatterned substrates. Nature 424, 411–414 (2003).
Chen, L. et al. Robust nanoporous membranes templated by a doubly reactive block copolymer. J. Am. Chem. Soc. 129, 13786–13787 (2007).
Quirk, R. et al. in Thermoplastic Elastomers 2nd edn (eds Holden, G. et al.) 72–100 (Hanser Publishers, 1996).
Jackson, E. A. et al. Nanoporous membranes derived from block copolymers; from drug delivery to water filtration. ACS Nano 4, 3548–3553 (2010).
Ahn, H. et al. Nanoporous block copolymer membranes for ultrafiltration: a simple approach to size tunability. ACS Nano 8, 11745–11752 (2014).
Zhao, D. et al. Triblock copolymer syntheses of mesoporous silica with periodic 50 to 300 angstrom pores. Science 279, 548–552 (1998).
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).
Jeong, B. et al. Biodegradable block copolymers as injectable drug-delivery systems. Nature 388, 860–862 (1997).
Kataoka, K. et al. Block copolymer micelles for drug delivery: design, characterization and biological significance. Adv. Drug Deliv. Rev. 64, 37–48 (2012).
Fischer, W. et al. Anionic polymerization process. US6444762 B1 (1997).
Wyatt, P. J. Light scattering and the absolute characterization of macromolecules. Anal. Chim. Acta. 272, 1–40 (1993).
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).
Determann, H. in Gel Chromatography · Gel Filtration · Gel Permeation. · Molecular Sieves, A Laboratory Handbook 2nd edn (Springer, 1969).
Matyjaszewski, K. et al. Atom transfer radical polymerization. Chem. Rev. 101, 2921–2990 (2001).
Flory, P. J. Molecular size distribution in linear condensation polymers. J. Am. Chem. Soc. 58, 1877–1885 (1936).
Ryu, J. et al. Molecular weight distribution of branched polystyrene: Propagation of Poisson distribution. Macromolecules 37, 8805–8807 (2004).
Peebles, L. H., Jr. in Molecular Weight Distributions in Polymers (Interscience, 1971).
Rudin, A. Molecular weight distributions of polymers. J. Chem. Educ. 46, 595 (1969).
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).
Chem, S.-A. et al. The skewness of polymer molecular weight distributions. J. Polym. Sci. Polym. Chem. Ed. 21, 3373–3380 (1983).
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).
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.
The authors declare no competing interests.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
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
ACS Macro Letters (2020)
Polymer Chemistry (2020)
Tailor-made thermoplastic elastomers: customisable materials via modulation of molecular weight distributions
Chemical Science (2020)
A method for determining the uniquely high molecular weight of chitin extracted from raw shrimp shells using ionic iquids
Green Chemistry (2020)
Designing molecular weight distributions of arbitrary shape with selectable average molecular weight and dispersity
European Polymer Journal (2020)