Universal properties of branched copolymers in dilute solutions

K. Haydukivska; V. Blavatska

doi:10.5488/cmp.27.13301

Authors

K. Haydukivska Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine; Institute of Physics, University of Silesia, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland https://orcid.org/0000-0002-3118-7010
V. Blavatska Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine; Dioscuri Centre for Physics and Chemistry of Bacteria, Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland https://orcid.org/0000-0001-6158-1636

DOI:

https://doi.org/10.5488/cmp.27.13301

Keywords:

polymers, scaling, universal properties, renormalization group, numerical simulations

Abstract

We analyze the universal conformational properties of complex copolymer macromolecules, based on two topologies: the rosette structure containing f_c linear branches and f_r closed loops grafted to the central core, and the symmetric pom-pom structure, consisting of a backbone linear chain terminated by two branching points with functionalities f. We assume that the constituent strands (branches) of these structures can be of two different chemical species a and b. Depending on the solvent conditions, the inter- or intrachain interactions of some links may vanish, which corresponds to Θ-state of the corresponding polymer species. Applying both the analytical approach within the frames of direct polymer renormalization and numerical simulations based on the lattice model of polymer, we evaluated the set of parameters characterizing the size properties of constituent parts of two complex topologies and estimated quantitatively the impact of interactions between constituent parts on these size characteristics.

References

Gao C., Yan D., Prog. Polym. Sci., 2004, 29, 183–275, https://doi.org/10.1016/j.progpolymsci.2003.12.002. DOI: https://doi.org/10.1016/j.progpolymsci.2003.12.002

Yates C. R., Hayes W., Eur. Polym. J., 2004, 40, 1257–1281, https://doi.org/10.1016/j.eurpolymj.2004.02.007. DOI: https://doi.org/10.1016/j.eurpolymj.2004.02.007

Voit B. I., Lederer A., Chem. Rev., 2009, 109, 5924–5973, https://doi.org/10.1021/cr900068q. DOI: https://doi.org/10.1021/cr900068q

Wang D., Zhao T., Zhu X., Yan D.,WangW., Chem. Soc. Rev., 2015, 44, 4023–4071, https://doi.org/10.1039/C4CS00229F. DOI: https://doi.org/10.1039/C4CS00229F

Cook A. B., Perrier S., Adv. Funct. Mater., 2020, 30, 1901001, https://doi.org/10.1002/adfm.201901001. DOI: https://doi.org/10.1002/adfm.201901001

Schubert C., Osterwinter C., Tonhauser C., Schömer M., Wilms D., Frey H., Friedrich C., Macromolecules, 2016, 49, 8722–8737, https://doi.org/10.1021/acs.macromol.6b00674. DOI: https://doi.org/10.1021/acs.macromol.6b00674

Khabaz F., Khare R., J. Chem. Phys., 2014, 141, 214904, https://doi.org/10.1063/1.4902052. DOI: https://doi.org/10.1063/1.4902052

Knauss D. M., Huang T., Macromolecules, 2002, 35, 2055–2062, https://doi.org/10.1021/ma010949l. DOI: https://doi.org/10.1021/ma010949l

Warner J. J., Wang P., Mellor W. M., Hwang H. H., Park J. H., Pyo S. H., Chen S., Polym. Chem., 2019, 10, 4665–4674, https://doi.org/10.1039/C9PY00999J. DOI: https://doi.org/10.1039/C9PY00999J

Zimm B. H., Stockmayer W. H., J. Chem. Phys., 1949, 17, 1301–1314, https://doi.org/10.1063/1.1747157. DOI: https://doi.org/10.1063/1.1747157

Kalyuzhnyi O., Haidukivska K., Blavatska V., Ilnytskyi J., Macromol. Theory Simul., 2019, 28, 1900012, https://doi.org/10.1002/mats.201900012. DOI: https://doi.org/10.1002/mats.201900012

Ilnytskyi J., Patsahan T., Holovko M., Krouskop P. E., Makowski M. P., Macromolecules, 2008, 41, 9904–9913, https://doi.org/10.1021/ma801045z. DOI: https://doi.org/10.1021/ma801045z

Kalyuzhnyi O., Ilnytskyi J., Holovatch Yu., von Ferber C., J. Phys.: Condens. Matter, 2018, 30, 215101, https://doi.org/10.1088/1361-648X/aabc16. DOI: https://doi.org/10.1088/1361-648X/aabc16

Blavatska V., Metzler R., J. Phys. A: Math. Theor., 2015, 48, 135001, https://doi.org/10.1088/1751-8113/48/13/135001. DOI: https://doi.org/10.1088/1751-8113/48/13/135001

Haydukivska K., Blavatska V., Phys. Rev. E, 2018, 97, 032502, https://doi.org/10.1103/PhysRevE.97.032502. DOI: https://doi.org/10.1103/PhysRevE.97.032502

Haydukivska K., Blavatska V., Paturej J., Sci. Rep., 2020, 10, 14127, https://doi.org/10.1038/s41598-020-70649-z. DOI: https://doi.org/10.1038/s41598-020-70649-z

Bishko G., McLeish T. C. B., Harlen O. G., Larson R. G., Phys. Rev. Lett., 1997, 79, 2352–2355, https://doi.org/10.1103/PhysRevLett.79.2352. DOI: https://doi.org/10.1103/PhysRevLett.79.2352

McLeish T. C. B., Larson R. G., J. Rheol., 1998, 42, 81–110, https://doi.org/10.1122/1.550933. DOI: https://doi.org/10.1122/1.550933

Haydukivska K., Kalyuzhnyi O., Blavatska V., Ilnytskyi J., J. Mol. Liq., 2021, 328, 115456, https://doi.org/10.1016/j.molliq.2021.115456. DOI: https://doi.org/10.1016/j.molliq.2021.115456

Haydukivska K., Kalyuzhnyi O., Blavatska V., Ilnytskyi J., Condens. Matter Phys., 2022, 25, 23302, https://doi.org/10.5488/CMP.25.23302. DOI: https://doi.org/10.5488/CMP.25.23302

Haydukivska K., Blavatska V., Condens. Matter Phys., 2023, 26, 23301, https://doi.org/10.5488/CMP.26.23301. DOI: https://doi.org/10.5488/CMP.26.23301

Mathur V., Satrawala Y., Rajput M. S., Inventi Impact: NDDS, 2010, 1, 1–4. DOI: https://doi.org/10.4103/0973-8398.72115

Ilnytskyi J., Lintuvuori J. S.,Wilson M. R., Condens. Matter Phys., 2010, 13, 33001, https://doi.org/10.5488/CMP.13.33001. DOI: https://doi.org/10.5488/CMP.13.33001

Singh A. N., Thakre R. D., More J. C., Sharma P. K., Agrawal Y. K., Polym.-Plast. Technol. Eng., 2015, 54, 1077–1095, https://doi.org/10.1080/03602559.2014.986811. DOI: https://doi.org/10.1080/03602559.2014.986811

Brendel J. C., Schacher F. H., Chem. – Asian J., 2018, 13, 230–239, https://doi.org/10.1002/asia.201701542. DOI: https://doi.org/10.1002/asia.201701542

Oss-Ronen L., Schmidt J.,AbetzV., Radulescu A., CohenY., TalmonY., Macromolecules, 2012, 45, 9631–9642, https://doi.org/10.1021/ma301611c. DOI: https://doi.org/10.1021/ma301611c

Meng F., Zhong Z., Feĳen J., Biomacromolecules, 2009, 10, 197–209, https://doi.org/10.1021/bm801127d. DOI: https://doi.org/10.1021/bm801127d

Mann J. L., Grosskopf A. K., Smith A. A. A., Appel E. A., Biomacromolecules, 2021, 22, 86–94, https://doi.org/10.1021/acs.biomac.0c00539. DOI: https://doi.org/10.1021/acs.biomac.0c00539

Lin Q., Ow V., Boo Y. J., Teo V. T. A., Wong J. H. M., Tan R. P. T., Xue K., Lim J. Y. C., Loh X. J., Front. Bioeng. Biotechnol., 2022, 10, 864372, https://doi.org//10.3389/fbioe.2022.864372. DOI: https://doi.org/10.3389/fbioe.2022.864372

Hadjichristidis N., Pispas S., Floudas G., Block Copolymers: Synthetic Strategies, Physical Properties, and Applications, John Wiley & Sons, Inc., New Jersey, 2003. DOI: https://doi.org/10.1002/0471269808

Matsen M. W., Bates F. S., Macromolecules, 1996, 29, 7641– 7644, https://doi.org/10.1021/ma960744q. DOI: https://doi.org/10.1021/ma960744q

Mai Y., Eisenberg A., Chem. Soc. Rev., 2012, 41, 5969–5985, https://doi.org/10.1039/C2CS35115C. DOI: https://doi.org/10.1039/c2cs35115c

Jackson E. A., Hillmyer M. A., ACS Nano, 2010, 4, 3548–3553, https://doi.org/10.1021/nn1014006. DOI: https://doi.org/10.1021/nn1014006

Bates F. S., Fredrickson G. H., Hucul D., Hahn S. F., AIChE J., 2001, 47, 762–765, https://doi.org/10.1002/aic.690470402. DOI: https://doi.org/10.1002/aic.690470402

Burchard W., In: Branched Polymers II, Advances in Polymer Science, Vol. 143, Roovers J. (Ed.), Springer, Berlin, Heidelberg, 1999, 113–194, https://doi.org/10.1007/3-540-49780-3_3. DOI: https://doi.org/10.1007/3-540-49780-3_3

de Gennes P. G., Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, 1979.

des Cloizeaux J., Jannink G., Polymers in Solutions: Their Modelling and Structure, Clarendon Press, Oxford, 1990. DOI: https://doi.org/10.1093/oso/9780198520368.001.0001

Clisby N., Dünweg B., Phys. Rev. E, 2016, 94, 052102, https://doi.org/10.1103/PhysRevE.94.052102. DOI: https://doi.org/10.1103/PhysRevE.94.052102

Duplantier B., J. Chem. Phys., 1987, 86, 4233–4244, https://doi.org/10.1063/1.451884. DOI: https://doi.org/10.1063/1.451884

Joanny J. F., Leibler L., Ball R., J. Chem. Phys., 1984, 81, 4640–4655, https://doi.org/10.1063/1.447399. DOI: https://doi.org/10.1063/1.447399

Douglas J. F., Fried K. F., J. Chem. Phys., 1987, 86, 4280–4293, https://doi.org/10.1063/1.451888. DOI: https://doi.org/10.1063/1.451888

Vlahos C. H., Horta A., Molina L. A., Freire J. J., Macromolecules, 1994, 27, 2726–2731, https://doi.org/10.1021/ma00088a012. DOI: https://doi.org/10.1021/ma00088a012

Olaj O. F., Neubauer B., Ziferer G., Macromol. Theory Simul., 1998, 7, 181–188, https://doi.org/10.1002/(SICI)1521-3919(19980101)7:1<181::AID-MATS181>3.0.CO;2-Q. DOI: https://doi.org/10.1002/(SICI)1521-3919(19980101)7:1<181::AID-MATS181>3.0.CO;2-Q

Molina L. A., Rodriguez A. L., Freire J. J., Macromolecules, 1994, 27, 1160–1165, https://doi.org/10.1021/ma00083a013. DOI: https://doi.org/10.1021/ma00083a013

McMullenW. E., Freed K. F., Cherayil B. J., Macromolecules, 1989, 22, 1853–1862, https://doi.org/10.1021/ma00194a057. DOI: https://doi.org/10.1021/ma00194a057

Binder K., Müller M., Curr. Opin. Colloid Interface Sci., 2000, 5, 314–322, https://doi.org/10.1016/S1359-0294(00)00074-1. DOI: https://doi.org/10.1016/S1359-0294(00)00074-1

Vlahos C., Hadjichristidis N., Kosmas M. K., Rubio A. M., Freire J. J., Macromolecules, 1995, 28, 6854–6859, https://doi.org/10.1021/ma00124a021. DOI: https://doi.org/10.1021/ma00124a021

Rubio A. M., Brea P., Freire J. J., Vlahos C., Macromolecules, 2000, 33, 207–216, https://doi.org/10.1021/ma9913156. DOI: https://doi.org/10.1021/ma9913156

Zifferer G., Eggerstorfer D., Macromol. Theory Simul., 2010, 19, 458–482, https://doi.org/10.1002/mats.201000027. DOI: https://doi.org/10.1002/mats.201000027

Edwards S. F., Proc. Phys. Soc., London, 1965, 85, 613–624, https://doi.org/10.1088/0370-1328/85/4/301. DOI: https://doi.org/10.1088/0370-1328/85/4/301

Haydukivska K., Blavatska V., J. Phys. A: Math. Theor., 2019, 52, 505004, https://doi.org/10.1088/1751-8121/ab2660. DOI: https://doi.org/10.1088/1751-8121/ab2660

Vlahos C. H., Horta A., Freire J. J., Macromolecules, 1992, 25, 5974–5980, https://doi.org/10.1021/ma00048a018. DOI: https://doi.org/10.1021/ma00048a018

Clisby N., Phys. Rev. Lett., 2010, 104, 055702, https://doi.org/10.1103/PhysRevLett.104.055702. DOI: https://doi.org/10.1103/PhysRevLett.104.055702

Madras N., Sokal A. D., J. Stat. Phys., 1988, 50, 109–186, https://doi.org/10.1007/BF01022990. DOI: https://doi.org/10.1007/BF01022990