Conformational properties of polymer brushes with aggrecan-like macromolecules under strong stretching conditions on a cubic lattice

Lukiev I.V., Mikhailov I.V., Borisov O.V. Conformational properties of polymer brushes with aggrecan-like macromolecules under strong stretching conditions on a cubic lattice. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2025, vol. 25, no. 3, pp. 396–405 (in Russian). doi: 10.17586/2226-1494-2025-25-3-396-405

The comb-like polymers are used to modify various surfaces due to their branched structure and a number of unique physical and chemical properties. With a sufficiently dense grafting, the macromolecules form a homogeneous polymer brush that completely covers the surface to be modified. Comb-like polymer brushes find applications as biomedical coatings, lubricants, sensors, targeted drug delivery systems, and many others. Given the wide demand for comb- like polymer coatings, it is of practical importance to predict their conformational properties as a function of the architecture of the grafted polymers. Сomb-like polymer brushes have been reasonably well studied both theoretically and experimentally at low grafting densities. However, there are no analytical models that quantitatively describe the properties of these brushes under conditions of high grafting densities and near-limit stretching of the macromolecular backbones. To study the conformational properties of planar polymer brushes made of comb-like polymers, two complementary approaches have been applied: analytical and numerical methods of the self-consistent field. The former was used for analytical description of the volume fraction profile of monomeric units of grafted macromolecules under their stretching on a body-centered cubic lattice, and the latter was used for validation of the proposed analytical model by comparing its results with the numerical calculation data on a simple cubic lattice. A universal analytical formula has been obtained that describes the profile of the volume fraction of monomeric units of grafted comb-like macromolecules in a wide range of grafting density values under conditions of athermal low-molecular-weight solvent. The study proceeded with the quantitative estimation of the average thickness of polymer brushes and the average density of monomeric units at different effective grafting densities of comb-like polymers. This was achieved by determining the ratio of the actual grafting density to the maximum possible grafting density of macromolecules with a given architecture as well as at different branching of these macromolecules. It has been demonstrated that, under conditions of athermal solvent, there is an increase in the average thickness of the polymer brush and a decrease in the average density of monomer units, as the branching degree of grafted macromolecules increases at a fixed grafting density and contour length of the main chain of macromolecules. Furthermore, at elevated levels of branching in grafted chains, the observed dependence of the average density on the effective grafting density approaches a linear relationship. The proposed analytical stretching model on a body-centered cubic lattice showed high agreement with the data obtained by numerical simulation on a simple cubic lattice. The findings of this study provide a foundation for predicting the conformational properties of polymer brushes under conditions of high grafting density and the degree of branching of grafted comb-like macromolecules.

1. Alexander S. Adsorption of chain molecules with a polar head a scaling description. Journal de Physique, 1977, vol. 38, no. 8, pp. 983–987. https://doi.org/10.1051/jphys:01977003808098300
2. de Gennes P.G. Conformations of polymers attached to an interface. Macromolecules, 1980, vol. 13, no. 5, pp. 1069–1075. https://doi.org/10.1021/ma60077a009
3. Schüwer N., Klok H.A. A potassium‐selective quartz crystal microbalance sensor based on crown‐ether functionalized polymer brushes. Advanced Materials, 2010, vol. 22, no. 30, pp. 3251–3255. https://doi.org/10.1002/adma.201000377
4. Sato T., Ruch R. Stabilization of Colloidal Dispersions by Polymer Adsorption. Marcel Dekker Inc., 1980, 176 p.
5. Klein J., Perahia D., Warburg S. Forces between polymer-bearing surfaces undergoing shear. Nature, 1991, vol. 352, no. 6331, pp. 143–145. https://doi.org/10.1038/352143a0
6. Kreer T. Polymer-brush lubrication: a review of recent theoretical advances. Soft Matter, 2016, vol. 12, no. 15, pp. 3479–3501. https://doi.org/10.1039/C5SM02919H
7. Ohm C., Welch M.E., Ober C.K. Materials for biosurfaces. Journal of Materials Chemistry, 2012, vol. 22, no. 37, pp. 19343–19347. https://doi.org/10.1039/C2JM90126A
8. Synytska A., Svetushkina E., Martina D., Bellmann C., Simon F., Ionov L., Stamm M., Creton C. Intelligent materials with adaptive adhesion properties based on comb-like polymer brushes. Langmuir, 2012, vol. 28, no. 47, pp. 16444–16454. https://doi.org/10.1021/la303773b
9. Zhai G., Cao Y., Gao J. Covalently tethered comb‐like polymer brushes on hydrogen‐terminated Si (100) surface via consecutive aqueous atom transfer radical polymerization of methacrylates. Journal of Applied Polymer Science, 2006, vol. 102, no. 3, pp. 2590–2599. https://doi.org/10.1002/app.24698
10. Naso M.F., Zimmermann D.R., Iozzo R.V. Characterization of the complete genomic structure of the human versican gene and functional analysis of its promoter. Journal of Biological Chemistry, 1994, vol. 269, no. 52, pp. 32999–33008. https://doi.org/10.1016/S0021-9258(20)30090-9
11. Wu Y.J., La Pierre D.P., Wu J., Yee A.J., Yang B.B.The interaction of versican with its binding partners. Cell Research, 2005, vol. 15, no. 7, pp. 483–494. https://doi.org/10.1038/sj.cr.7290318
12. Klein J. Molecular mechanisms of synovial joint lubrication. Proc. of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2006, vol. 220, no. 8, pp. 691–710. https://doi.org/10.1243/13506501JET143
13. Chen M., Briscoe W.H., Armes S.P., Klein J. Lubrication at physiological pressures by polyzwitterionic brushes. Science, 2009, vol. 323, no. 5922, pp. 1698–1701. https://doi.org/10.1126/science.1169399
14. Seror J., Merkher Y., Kampf N., Collinson L., Day A.J., Maroudas A., Klein J. Articular cartilage proteoglycans as boundary lubricants: structure and frictional interaction of surface-attached hyaluronan and hyaluronan–aggrecan complexes. Biomacromolecules, 2011. vol. 12, no. 10, pp. 3432–3443. https://doi.org/10.1021/bm2004912
15. Birshtein T.M., Karaev A.K Сonformation of macromolecules in interacting plane layers of grafted chains. Vysokomolekulyarnye Soedineniya. Seriya A, 1987, vol. 29, no. 9, pp. 1882–1887. (in Russian)
16. Cosgrove T., Heath T., Vanlent B., Leermakers F., Scheutjens J. Configuration of terminally attached chains at the solid/solvent interface: self-consistent field theory and a Monte Carlo model. Macromolecules, 1987, vol. 20, no. 7, pp. 1692–1696. https://doi.org/10.1021/ma00173a041
17. Skvortcov A.M., Pavlushkov I.V., Gorbunov A.A. On the structure of a monolayer of grafted polymer chains. Vysokomolekulyarnye Soedineniya. Seriya A, 1988, vol. 30, no. 3,pp. 503–508.(in Russian)
18. Skvortcov A.M., Pavlushkov I.V., Gorbunov A.A., Zhulina E.B., Borisov O.V., Priamitcyn V.A. Structure of dense-grafted polymer monolayers. Vysokomolekulyarnye Soedineniya. Seriya A, 1988,vol. 30,no. 8,pp. 1615–1622. (in Russian)
19. Zhulina E.B., Pryamitsyn V.A., Borisov O.V. Structure and conformational transitions in grafted polymer chains layers: new theory. Vysokomolekulyarnye Soedineniya. Seriya A, 1989,vol. 31,no. 1,pp. 185–194. (in Russian)
20. Milner S.T., Witten T.A., Cates M.E. A parabolic density profile for grafted polymers. Europhysics Letters, 1988, vol. 5, no. 5, pp. 413–418. https://doi.org/10.1209/0295-5075/5/5/006
21. Milner S.T., Witten T.A., Cates M.E. Theory of the grafted polymer brush. Macromolecules, 1988, vol. 21, no. 8, pp. 2610–2619. https://doi.org/10.1021/ma00186a051
22. Pickett G.T. Classical path analysis of end-grafted dendrimers: dendrimer forest. Macromolecules, 2001, vol. 34, no. 25, pp. 8784–8791. https://doi.org/10.1021/ma010917y
23. Zhulina E.B., Mikhailov I.V., Borisov O.V. Theory of mesophases of triblock comb-shaped copolymers: effects of dead zones and bridging. Macromolecules, 2022, vol. 55, no. 14, pp. 6040–6055 https://doi.org/10.1021/acs.macromol.2c00418
24. Polotsky A.A., Leermakers F.A.M.,Zhulina E.B.,Birshtein T.M.On the two-population structure of brushes made of arm-grafted polymer stars. Macromolecules, 2012, vol. 45, no. 17, pp. 7260–7273. https://doi.org/10.1021/ma300691b
25. Zhulina E.B., Leermakers F.A.M., Borisov O.V. Theory of Brushes Formed by Ψ-Shaped Macromolecules at Solid–Liquid Interfaces. Langmuir, 2015, vol. 31, no. 23, pp. 6514–6522. https://doi.org/10.1021/acs.langmuir.5b00947
26. Zhulina E.B., Leermakers F.A.M., Borisov O.V. Ideal mixing in multicomponent brushes of branched polymers. Macromolecules, 2015, vol. 48, no. 21, pp. 8025–8035. https://doi.org/10.1021/acs.macromol.5b01722
27. Shim D.F.K., Cates M.E. Finite extensibility and density saturation effects in the polymer brush. Journal de Physique, 1989, vol. 50, no. 24, pp. 3535–3551. https://doi.org/10.1051/jphys:0198900500240353500
28. Amoskov V.M., Pryamitsyn V.A. Theory of monolayers of non-Gaussian polymer chains grafted onto a surface. Part 1. — General theory. Journal of the Chemical Society, Faraday Transactions, 1994, vol. 90, no. 6, pp. 889–893. https://doi.org/10.1039/FT9949000889
29. Amoskov V.M., Priamitcyn V.A. Theory of grafted polymer monolayers. Chains models with finite extensibility. Vysokomolekulyarnye Soedineniya. Seriya A,1995, vol. 37, no. 7,pp. 1198–1205. (in Russian)
30. Scheutjens J., Fleer G.J. Statistical theory of the adsorption of interacting chain molecules. 1. Partition function, segment density distribution, and adsorption isotherms. Journal of Physical Chemistry, 1979, vol. 83, no. 12, pp. 1619–1635. https://doi.org/10.1021/j100475a012
31. Scheutjens J., Fleer G.J. Statistical theory of the adsorption of interacting chain molecules. 2. Train, loop, and tail size distribution. The Journal of Physical Chemistry, 1980, vol. 84, no. 2, pp. 178–190. https://doi.org/10.1021/j100439a011
32. Semenov A.N. Contribution to the theory of microphase layering in block-copolymer melts. JETP, 1985, vol. 61, no. 4, pp. 733–742.
33. Leuty G.M., Tsige M.,Grest G.S., Rubinstein M. Tension amplification in tethered layers of bottle-brush polymers. Macromolecules, 2016, vol. 49, no. 5, pp. 1950–1960. https://doi.org/10.1021/acs.macromol.5b02305
34. Viktorovich I. Theory of bending stiffness of polymer brushes from graft dendrons. Dissertation for the degree of candidate of physical and mathematical sciences. 2018. Available at: https://macro.ru/OLD_DOC/council/dis/MihailovIV/MihailovIV_dis.pdf (accessed: 10.01.2025). (in Russian)
35. Lukiev I.V., Mikhailov I.V., Borisov O.V. Impact of solvent quality on tribological properties of polymer brushes. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2024, vol. 24, no. 5, pp. 751–757. (in Russian). https://doi.org/10.17586/2226-1494-2024-24-5-751-757
36. Fleer G.J., Cohen Stuart M.A., Scheutjens J.M.H.M., Cosgrove T., Vincent B. Polymers at Interfaces. Springer Science & Business Media, 1993, 496 p.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License