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. 2023 Feb 6;3(2):333–343. doi: 10.1021/jacsau.2c00638

Shaping the Structure and Response of Surface-Grafted Polymer Brushes via the Molecular Weight Distribution

Jacinta C Conrad 1,*, Megan L Robertson 1,*
PMCID: PMC9975839  PMID: 36873679

Abstract

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Breadth in the molecular weight distribution is an inherent feature of synthetic polymer systems. While in the past this was typically considered as an unavoidable consequence of polymer synthesis, multiple recent studies have shown that tailoring the molecular weight distribution can alter the properties of polymer brushes grafted to surfaces. In this Perspective, we describe recent advances in synthetic methods to control the molecular weight distribution of surface-grafted polymers and highlight studies that reveal how shaping this distribution can generate novel or enhanced functionality in these materials.

Keywords: surface-grafted polymer, dispersity, molecular weight distribution, polymer-grafted nanoparticle, polymer conformation, stimulus response

Introduction

Polymer brushes are an increasingly used route to generate soft, functional surfaces for applications in sustainable energy conversion and storage,1 sensing,2 and separations.3 In a polymer brush, one end of the polymer is tethered to a substrate via a covalent bond. Even a short brush, of thickness no more than a few nanometers, can dramatically modify the surface properties. For example, attaching a polymer brush to a surface can alter the surface wettability,4−6 tethering a zwitterionic polymer bearing both positive and negative charges can render a surface very low-fouling to proteins,7 and grafting a polymer that undergoes a stimulus-dependent conformational change (in response to, for example, light, solution pH, or salt concentration and valency) can render a surface “smart”8 (i.e., stimulus responsive) and even replicate functions of biological systems.9

Because the tether restricts the states available to the polymer, the conformations of polymers in brushes can markedly differ from those in solution. On a planar substrate, solvated brushes adopt “mushroom” conformations that are close to those in solution when the areal grafting density σ is low (Figure 1(a)), and the average brush height h scales with the number of monomers N as h ∼ N3/5. When the grafting density becomes comparable to the radius of gyration Rg of the polymer in solution, however, solvated chains experience (pairwise) excluded volume interactions with neighboring monomers. Competition between these excluded volume interactions and the polymer elasticity drives chains to become stretched orthogonally to the surface, leading to a “semidilute” brush whose height scales10,11 with both N and σ as h ∼ N1σ1/3 (Figure 1(b)). Further increasing the grafting density leads to a “concentrated” brush whose height scales10,11 as h ∼ N1σ1/2 (Figure 1(c)). Here, the σ1/2 scaling reflects higher-order interactions among the monomers.

Figure 1.

Figure 1

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Schematic illustration of the conformation of (a–c) planar and (d–f) spherical polymer brushes with increasing grafting density σ. The polymer radius of gyration Rg, brush height h, and (for spherical brushes) critical radius rc are shown. The dispersity Đ is the ratio of the weight-average and number-average molecular weights. Panels d–f are adapted with permission from ref (12). Copyright 2010 American Chemical Society.

Brushes grafted to the curved surface of a spherical nanoparticle also undergo a transition from mushroom to semidilute to concentrated as the grafting density at the particle surface is increased (Figure 1(d–f). Unlike planar brushes, however, the crowding from the polymers decreases away from the particle surface due to the curvature. Thus, spherical polymer brushes exhibit scaling behaviors distinct from those of planar brushes. In the semidilute regime, h ∼ (N1σ1/3)3/5 (refs (13, 14)). Brushes at high grafting densities transition from concentrated (near the brush surface) to semidilute (at the periphery) if they are sufficiently long (at distances greater than a critical radius rc (ref (15))), and h ∼ (N1σ1/2)x with 3/5 ≤ x ≤ 1 by analogy to flat brushes (refs (10, 11)).

These scaling relationships, however, are for the average brush height and do not account for an inherent feature of synthetic polymer systems: their molecular weight distribution. The number-average molecular weight Mn = ∑i = 1∞xiMi and weight-average molecular weight Mw = ∑i = 1wiMi, where xi and wi are, respectively, the number fraction and weight fraction of polymers with molecular weight Mi, do not typically coincide in synthetic polymers. Thus, for most synthetic polymers with a unimodal distribution, the dispersity Đ = Mw/Mn ≥ 1; moreover, surface-grown polymer brushes are more disperse than polymers synthesized concurrently in solution.16 For polymers with a unimodal molecular weight distribution, Đ (previously reported as PDI) is also directly related to the breadth of the molecular weight distribution, as Đ = (s/Mn)2 + 1, where s is the standard deviation. (For bimodal or multimodal molecular weight distributions, the dispersity is not related to the breadth.) Whereas the effects of dispersity on the properties of polymers in the melt or solution phase have been long investigated,17−21 recent studies have demonstrated new ways to control brush dispersity and thereby to explore its effects on functional properties.

In this Perspective, we highlight novel functionality in polymer-brush-grafted surfaces imparted through control over the molecular weight distribution. First, we describe recent advances in synthetic methods to control the dispersity of surface-grafted polymers (as opposed to polymers in solution). Then we summarize selected studies that reveal how modulating the molecular weight distribution can generate or enhance function in these soft interfaces, largely but not exclusively focusing on homopolymer systems. This focus is complementary to that of detailed reviews and perspectives on bidisperse mixed brush systems.22,23 Finally, we highlight avenues to develop the fundamental understanding required to generate novel surface function by shaping the molecular weight distribution of surface-grafted polymers.

Synthetic Methods To Control Brush Dispersity

There has been significant interest in developing synthetic methods to alter not only the breadth but also the shape of polymer molecular weight distributions.24−32 These methods offer exquisite control over the molecular weight distribution. Many of these methods, however, are not applicable to surface-tethered polymer chains, due to use of techniques such as metered addition of initiator24,25 and flow reactors in which narrowly dispersed samples accumulate in the vessel to build a targeted molecular weight distribution29 or the mixing of polymers of narrow size range.33 Furthermore, quantification of the molecular weight distribution of surface-grafted chains offers additional challenges34 due to insufficient mass of polymer present on the surface (such as on planar surfaces), preventing use of standard techniques such as gel permeation chromatography; instead, polymers must be chemically cleaved from the surface prior to characterization. Nonetheless, prior studies have carefully compared the molecular weight distribution of surface-grafted chains and those polymerized in solution, noting important differences: even in the case of targeting the synthesis of low dispersity polymers, the surface-tethered chains exhibited a bimodal distribution and were of higher dispersity than those in solution.16

Recent articles have reviewed the state-of-the-art in synthesis methods for tailoring the molecular weight distribution of polymer brushes.27,35,36 Techniques for synthesizing polymer brushes generally fall within two categories: grafting-to and grafting-from reactions, which each have their own advantages and drawbacks.37,38 In grafting-to reactions, preformed polymers are grafted to the functionalized surface. In this approach, a variety of methods could in theory be employed to vary the breadth and shape of the molecular weight distribution24,26−29 if the chain ends retain the required functionality for grafting to the surface; the grafting density obtained via this method, though, is typically low. By contrast, higher grafting densities are obtained through grafting-from techniques, in which the initiator is first attached to the surface, followed by polymerization from the surface-tethered initiator. As noted above, however, methods of varying the breadth and shape of the molecular weight distribution are limited.

Reversible deactivation radical polymerizations (RDRP, i.e. “controlled” or “living” radical polymerizations) are often employed in surface-initiated polymerizations, due to the diversity of monomer types that can be synthesized via these techniques, convenience of surface attachment of the required initiators, mild reaction conditions, and ease of obtaining relatively low dispersity (Đ ∼ 1.1–1.2) polymers. More recently, methods to tune dispersity in these polymerizations have been explored. In surface-initiated atom-transfer radical polymerization (ATRP), reduction of catalyst concentration,39 reduction of surface initiator concentration,40 addition of a reducing agent,40 and addition of a terminating agent41 have increased the dispersity. A bimodal distribution could also be obtained through methods such as partial deactivation of chain ends.42 In surface-initiated reversible addition–fragmentation chain-transfer (RAFT) polymerization, bidisperse/bimodal brushes have been produced by43 (i) attaching a RAFT initiator, (ii) synthesizing a surface-grafted polymer, (iii) cleaving the RAFT agent from the chain ends, (iv) attaching a second RAFT agent, and (v) synthesizing a second polymer brush of differing molecular weight from the first. Additionally, brushes with side-chain dispersity (as opposed to the traditional main-chain dispersity) have been synthesized through RAFT techniques.44 Organocatalyzed living radical polymerizations have also been used to synthesize brushes of varying dispersity, through temperature-selective radical generation45 and also through exploitation of simultaneous polymerization and chain-end substitution in the presence of sodium azide.46 Few existing studies report surface-initiated polymerizations of tunable dispersity that go beyond the use of RDRP; one notable example is the application of ring-opening polymerization in the presence of transesterification.47 Though much progress has been made in synthetic techniques to produce surface-grafted polymers of varying breadth in the molecular weight distribution , additional effort is required to apply recent advances in control over shape of the molecular weight distribution to surface-grafted chains.

Enhancing Properties by Increasing Dispersity

Planar Brushes

Polymer Conformation

Theoretical studies using self-consistent field theory (SCFT) have revealed that the conformation of polymers grafted to flat surfaces is greatly altered by dispersity. Increasing the polymer dispersity increased the brush thickness and changed the shape of the density profile from convex to concave.48 Theory and Monte Carlo simulations confirmed this shape change and moreover showed that even small dispersity could suppress chain-end fluctuations and that the hydrodynamic penetration length generally increased with dispersity.49 For the case of bimodal brushes in which the length difference was varied, increasing the length difference at fixed total grafting density led to extended density profiles with two parts; the structure of the inner part (containing the ends of the short chains) did not depend on the length or fraction (at constant grafting density) of the long chains.50 The long brushes in a bimodal molecular weight distribution were stretched near the grafted surface, such that the longer chain ends were localized near the brush periphery.51 Densely grafted disperse chains adopted a “crown and stem” conformation, in which the polymers closest to the substrate (at higher grafting density) were stretched by interactions with neighboring chains; chains at the brush periphery, by contrast, were less extended and collapsed.52 These results were supported by Monte Carlo simulations, which confirmed that the short and long chains in a bimodal brush were vertically segregated due to chain stretching.53,54

Early experimental studies to probe dispersity effects employed bidisperse brushes (containing two different size polymers). Neutron reflectivity experiments on highly asymmetric poly(dimethylsiloxane)-polystyrene (PDMS–PS) diblock copolymers, for which the PDMS blocks were grafted to the surface and the PS blocks dangled into a good solvent, showed that the larger PS blocks were stretched by the presence of shorter PS blocks.55 The conformation of these brushes was well predicted by lattice-based self-consistent mean field theory.56 Likewise, neutron reflectivity experiments on bidisperse polystyrene brushes in a good solvent, toluene, found that longer chains were vertically stratified near the brush periphery (Figure 2(a,b)),57 as predicted by SCFT. In the melt limit (for which solvent did not penetrate the brush), bidisperse polyisoprene brushes in chloroform–ethanol mixtures also exhibited a stratified structure.58 Although the density profile measured with neutron reflectivity was not well described by the SCFT model of ref (48), a modified lattice-based self-consistent mean field theory approach provided closer agreement.59

Figure 2.

Figure 2

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Bidisperse brushes exhibit distinct conformation and functional properties. (a, b) Volume fraction of (a) short and (b) long PS chains as a function of the distance from the substrate in a polystyrene brush anchored by P2VP (short chain: deuterated 0.52 × 105 Da; long chains: 1.03 × 105 Da) in toluene, a good solvent. Adapted with permission from ref (57). Copyright 1998 American Chemical Society. (c, d) Long chains suppress autophobic dewetting in polymer films. (c) Optical micrograph of two typical cylindrical holes (indicated by the arrows) in a 900 Å thick polystyrene film on a 66 Å thick polystyrene brush after 8 min of annealing at 175 °C. Reproduced with permission from ref (60). Copyright 1996 American Chemical Society. (d) Schematic illustration of a moving rim of a thin film on a polymer brush, in which the capillary forces driving the motion compete against the force required to pull out the long polymer chains. Adapted with permission from ref (61). Copyright 1996 EDP Sciences.

SCFT has also been used to explore the structure of mixed binary brushes in which the solvent selectivity differed for two chemically distinct polymers. When the molecular weights of the two brush polymers were equal, the polymers phase separated such that the outer layer preferred the solvent.62,63 For bimodal brushes of long and short chains, however, two layered structures could form: one in which the outer layer was in its good solvent, and one in which the long chains (in their poor solvent) covered a layer of the short chains. When the fraction of short chains was low, these chains underwent a transition from a “coil” state (buried deep inside the brush) to a “flower” state (stretched at the periphery).55 Thus, the bimodal size distribution offers opportunities for generating switchable surfaces with a discontinuous phase transition.

Wetting and Miscibility

Thin polymer layers or films on surfaces are often unstable. Grafting a polymer brush to the surface can reduce the unfavorable enthalpic interactions that promote dewetting of the polymer film (Figure 2(c)); nevertheless, entropic interactions may still drive dewetting. Experiments showed that adding long brush molecules to a polystyrene brush could suppress this autophobic dewetting (depicted schematically in Figure 2(d)). SCFT calculations also confirmed that bidisperse brushes could eliminate dewetting,64 with fewer long brushes needed to suppress the dewetting as the bidispersity was increased. These SCFT calculations also indicated that the long chains reduced the entropic interfacial tension between the brush and free polymer interface.

Segregation

The phase behavior of binary disperse brushes grafted to a planar substrate depends on many parameters, including the grafting density σ, the grafting ratio (the ratio of the numbers of grafted chains of each species), and the asymmetry in the chain length; the latter two parameters are related to the bidispersity. When the polymers are immiscible, polymers constrained by surface tethers can phase separate laterally and/or vertically, leading to a variety of morphologies. These included a “layered” structure (in which one component vertically segregated to the substrate), a “rippled” state (in which the components laterally segregated), and “dimpled” or “micelle” states (in which lateral and vertical segregation both occurred).65,66 Mean field simulations revealed that the morphology of a given system depended on the grafting ratio67 and hence on the bidispersity.

Much experimental work exploring the effects of molecular weight distributions has focused on characterizing the conformation of binary bidisperse brushes with distinct solvent affinities. As one example, the morphology of binary mixed brushes of PS and poly(2-vinylpyridine) (P2VP) exposed to selective solvents depended on the asymmetry of the molecular weights (or chain lengths). When the chain length asymmetry was small, the brushes segregated both laterally and perpendicularly; increasing the asymmetry in chain length drove a transition from laterally segregated domains to a layered structure, tunable through the solvent selectivity.68 Similarly, both the surface structure of mixed brushes of poly(N-isopropylacrylamide) (PNIPAM) and PS in toluene (selective for PS) and its reorganization upon exposure to water–methanol (selective for PNIPAM) depended on the chain asymmetry.69 A more recent example used PMMA and PS brushes grafted at equal (high) densities to show that the transition from disorder to ripple to cylinder followed the phase behavior predicted from Monte Carlo simulations.70

Stimulus Response

Many studies have explored the responsive properties of bidisperse mixed polymer brushes.23 Such brushes, composed of two distinct polymers with different properties (such as solvent selectivity or temperature or pH response), can exhibit tunable responses. For example, the thickness, refractive index, and contact angle of mixed PAA/P2VP brushes varied with pH71 due to the formation of layers. At extreme pH values, the charged polymer (P2VP at low pH and PAA at high pH) stretched away from the substrate due to electrostatic repulsions, whereas the other polymer was collapsed and located near the substrate. As a second example, the ability of mixed PAA/poly(ethylene oxide) (PEO) brushes72 to adsorb and, when rinsed with salt solutions, desorb three proteins (human serum albumin, lysozyme, and fibrinogen) depended on the brush composition: PAA was required to adsorb lysozyme and fibrinogen, whereas a minimum PEO density was needed to release the proteins.73 The responsive properties of these and similar systems, however, arise from the use of two (or more polymers).

By contrast, the effects of dispersity on the response of homopolymer brushes is less studied. Our groups posited that changes in the homopolymer polymer conformation with dispersity would alter their functional properties. First, we examined the pH-dependent response of PAA brushes of various molecular weights at constant grafting density.74 Brushes exhibited a hysteric memory in the water contact angle around a decreasing-then-increasing pH cycle, with the contact angle upon pH decrease less than that upon pH increase. The extent of hysteresis, quantified as the difference in the pKa values extracted from the contact angle measurements upon decreasing and increasing pH (ΔpKa), increased as a function of brush length and dispersity (Figure 3(a)). In our original ATRP synthesis, however, brush dispersity increased concomitant with polymer molecular weight, hindering understanding of the driving physics. Other groups have reported hysteresis in stimulus-dependent conformation and/or response in surface-grafted weak polyelectrolytes on planar (PAA, poly(2-(diethylamino)ethyl methacrylate) (PDEA))75 and curved (PAA)76 surfaces. This hysteresis has been attributed to the difference in ionization of charged groups near the brush periphery and near the substrate77 and to formation of transient, metastable hydrogen-bonded networks.76 To decouple the effects of increasing length and dispersity, we developed a synthetic method to increase brush dispersity in ATRP through addition of a chain terminating agent, phenyl hydrazine.41 This approach allowed us to produce a series of brushes of near-constant length (and molecular weight) but varying dispersity. We found that ΔpKa increased with Đ when brush length was held constant, confirming that the hysteretic response was controlled in part by the dispersity (Figure 3(b)).

Figure 3.

Figure 3

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(a) Static contact angle as a function of pH upon decreasing (solid symbols) and increasing (open symbols) pH for PAA brushes of various lengths and dispersities. (b) Difference in the pKa for increasing and decreasing pH (ΔpKa) as a function of brush dispersity Đ. The solid symbols indicate a series of brushes for which the length was fixed; the open symbols indicate a series of brushes for which both length and dispersity were varied. Reproduced from ref (74). Copyright 2016 Royal Society of Chemistry.

Antifouling

The effect of brush dispersity on the ability to repel particles was investigated using SCFT. For a single particle, the particle size determined the effect of brush dispersity on repellency. Small particles (e.g., proteins, whose radius R ∼ 1/√2) readily penetrated disperse brushes, so that uniform brushes best repelled these particles. By contrast, large particles such as a bacterium or colloid (for which the radius R → ∞) were less able to compress brushes of high than low dispersity; thus, disperse brushes were better able to prevent adsorption of large particles.78 To control adsorption of biological particles,79 both unimodal80 and bimodal81 mixed brushes have been designed.

In a contrasting approach, we showed that stimulus-induced changes in the conformation of disperse surface-grafted brushes could be used to tune the antifouling properties.82 We monitored the attachment (at low pH) and detachment (at high pH, after triggering the swelling of brushes) of Staphylococcus epidermidis bacteria on PAA-grafted substrates. The average length of the polymer brushes controlled bacterial attachment, which was not affected by brush dispersity (Figure 4(a,b)). A minimum in surface coverage at an intermediate brush thickness arose from the competition between steric repulsions (strong for short polymer chains) and hydrophobic attractions (strong for long chains). Triggering the brush response by increasing the pH led to detachment of some bacteria. In striking contrast to attachment, which was controlled only by brush length, increasing either the brush length or dispersity enhanced detachment (Figure 4(c,d)). Thus, tailoring the molecular weight distribution of the brushes offers the possibility of orthogonally controlling attachment and detachment of adherent particles.

Figure 4.

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(a, b) Attachment of Staphyloccocus epidermidis bacteria on PAA brushes (at pH = 4, quantified as the percentage of the surface covered by bacteria) as a function of (a) dry brush thickness and (b) brush dispersity. (c, d) Detachment, quantified as the difference in the percentage of surface coverage at pH 5 and pH 9, as a function of (c) dry brush thickness and (d) brush dispersity. Adapted with permission from ref (82). Copyright 2017 American Chemical Society.

Spherical Brushes

Polymer Conformation

Monte Carlo simulations coupled with Polymer Reference Interaction Site Model (PRISM) calculations applied to bimodal homopolymer brushes revealed differences in polymer conformation as compared to uniformly disperse brushes. When the number of grafted short and long polymers were equal, at low to medium grafting density the radius of gyration Rg of the short polymers was lower than that in a monodisperse brush, allowing the long brushes to maximize configurational entropy. The Rg of long polymers, however, was unaltered at low grafting densities but lower (i.e., less stretched) at intermediate grafting densities.83 Similar computational methods applied to disperse homopolymer brushes revealed that, for brushes of high dispersity, chains shorter than the number-average chain length Nn were more compressed but those longer than Nn stretched less than in a spherical brush with uniform dispersity.84 Overall, the changes in polymer conformation in a disperse brush caused the thickness of the grafted layer to increase with dispersity (Figure 5(a,b)).

Figure 5.

Figure 5

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Brush length depends on dispersity. (a, b) Representative conformations from molecular dynamics simulations of brushes with Đ of (a) 1.0 (uniform) and (b) 2.0. Panel a is reproduced with permission from ref (84). Copyright 2012 John Wiley and Sons. (c) Brush length lb as a function of the degree of polymerization N for PCL brushes with various grafting densities (high σ: 0.61 chains nm–2; mid σ: 0.43 chains nm–2; low σ: 0.21 chains nm–2). The upper and lower dashed lines indicate the contour length L and radius of gyration Rg, respectively. Panel c is reproduced with permission from ref (47). Copyright 2017 American Chemical Society. (d) Brush length lb as a function of the weight-average degree of polymerization Nw for PtBA brushes of various Đ, as indicated by the color bar. The dash-dot line indicates the full length of a linear PtBA chain Lc,w; the dotted line indicates the length of the all-trans configuration of a PtBA chain Lf,w; the dashed line indicates Rg. The arrow indicates the boundary between the semidilute and concentrated brush regimes calculated from theory. Panel d is reproduced with permission from ref (85). Copyright 2021 American Chemical Society.

Experimentally, the length of high-dispersity (Đ > 2.3) poly(caprolactone) (PCL) brushes with a continuous molecular weight distribution grafted to silica nanoparticles depended strongly on Đ.47 The length of three series of brushes at three grafting densities (0.21 to 0.61 chains nm–2), synthesized via a ring-opening polymerization and measured through dynamic light scattering (DLS), scaled differently with the brush molecular weight (Figure 5(c)): the scaling exponent (i.e., lb ∼ Nν) increased concomitant with grafting density. Moreover, ν > 1, counter to expectations for brushes in the concentrated regime. The differences in chain extension as lb increased and/or σ decreased were attributed to increased hydrodynamic friction, as the brushes transitioned from nondraining to freely draining.

Inspired by these results, we set out to understand the effects of dispersity on brush conformation. We synthesized poly(tert-butyl acrylate) (PtBA) brushes via ATRP and added phenyl hydrazine to tune the dispersity between 1.03 and 1.98.85 The brush length lb, measured through DLS, exhibited distinct dependencies on Đ in different ranges of Nw: at high Nw, lb was independent of Đ, whereas at low Nw, lb fell onto a bifurcated curve with separate branches for brushes of low and high Đ. The brush length at the onset of the bifurcation coincided with rc, the critical length at which the brush conformation transitions from semidilute to concentrated (Figure 5(d)).

Upon separating the brushes into semidilute and concentrated regimes, we found that the length of semidilute PtBA brushes of varying dispersity collapsed onto a master curve as a function of the predicted scaling parameter Nwσ1/3 along with semidilute brushes of PS12 and poly(ethylene oxide-block-propylene oxide-block-ethylene oxide) triblock copolymer (PEO-b-PPO-b-PEO)86 (Figure 6(a)). The length of concentrated brushes as a function of Nwσ1/2, however, followed a bifurcated curve for our PtBA brushes as well as those of PMMA,15 PS,12 and PCL47 (Figure 6(b)). The dispersity demarcating the low- and high-regimes was not constant across the polymers and depended on the monomer size and grafting density. Intriguingly, the boundary between the low- and high-dispersity regime was consistent with results from molecular dynamics simulations84 indicating that dispersity effects on brush conformation were negligible above a critical grafting density or degree of polymerization.

Figure 6.

Figure 6

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Brush length lb as a function of (a) the scaled weight-average molecular weight Nwσ1/3 in the semidilute polymer brush regime and (b) Nwσ1/2 in the concentrated polymer brush regime, in which the color shading indicates Đ. Colors indicate series of data on various spherical brushes taken from different sources: blue: PtBA-grafted silica nanoparticles (Đ = 1.03–1.98, σ = 0.5 ± 0.2 chains nm–2, ref (85)); green: PS-grafted silica nanoparticles (Đ = 1.05–1.13, σ = 0.05–0.55 chains nm–2, ref (12)); yellow: PMMA (Đ = 1.19–1.28, σ = 0.59–0.73 chains nm–2, ref (15)); purple: PEO-b-PPO-b-PEO adsorbed silica nanoparticles (Đ = 1.10–1.20, brush adsorbed amount Σ = 0.11–0.30 chains nm–2, ref (86)); orange: PCL-grafted silica nanoparticles (Đ = 1.42–2.39, σ = 0.21–0.61 chains nm–2, ref (47)). Reproduced with permission from ref (85). Copyright 2021 American Chemical Society.

Miscibility

The ability to tune dispersity has potential applications in nanocomposite materials for control over particle dispersion, as for planar surfaces. At high grafting densities, autophobic dewetting can drive polymer-grafted nanoparticles to phase separate from a polymer matrix: for sufficiently long chains, the entropic penalty from the stretching of free and grafting chains dominates over the entropy of mixing.87 Simulations and theory revealed, however, that highly disperse brushes could stabilize polymer-grafted nanoparticles in polymer melts.88 When the ratio of the molecular weight of free and grafted polymers Nw,f/Nw,g is large, high dispersity enhanced steric repulsion (due to interactions between long chains) and, importantly, allowed the matrix chains to penetrate the brush (Figure 7(a,b)). This enhanced wetting eliminated the attractive well that drives grafted nanoparticles to aggregate in melts and solutions. Experiments and self-consistent field theory confirmed that high brush dispersity reduced the attractive interaction (Figure 7(c)) and thereby mitigated the autophobic dewetting for small- to intermediate values of Nw,f/Nw,g.89 Interestingly, both Nw,f/Nw,g and Đ appeared to affect the dispersion of PMMA-grafted gold nanoparticles in PMMA matrixes: nanoparticles grafted with polymers of higher Đ remained well dispersed even at relatively high Nw,f/Nw,g (which favors phase separation of the grafted particles from the matrix) (Figure 7(d,e)).

Figure 7.

Figure 7

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Brush dispersity promotes wetting in homopolymer solutions of polymers. (a, b) Penetration depth λ (in units of the monomer diameter d) of matrix chains into the grafted layer (average degree of polymerization Ng,ave = 20) on nanoparticles as a function of Đ for grafting density of 0.10 chains d–2 (solid lines) or 0.25 chains d–2 (dashed lines) and matrix molecular weights Nmatrix of (a) 10 and (b) 40. In panels a and b the nanoparticle diameter is D = 5d. Panels a and b are reproduced with permission from ref (88). Copyright 2013 American Physical Society. (c) Depth of the potential well Umin/kBT as a function of Đ at various values of the ratio of molecular weight of free and grafted polymers Nw,f/Nw,g from SCFT; the particle radius is R = 2aN1/2 and the brush thickness is H = 2aN1/2, where a is the statistical segment length. (d, e) Cross-sectional TEM micrographs of PMMA-functionalized gold nanoparticles in PMMA matrixes; the caption indicates Nw,f/Nw,g and Đ for the grafted polymer. (d) Grafted molecular weight Mn = 5.3 kDaA, matrix molecular weight Mn = 24 kDa; (e) grafted molecular weight Mn = 11 kDa, matrix molecular weight Mn = 60 kDa. Panels (c) - (e) are reproduced with permission from ref (89). Copyright 2018 Royal Society of Chemistry.

The molecular weight distribution can also be tuned to control dispersion of polymer-grafted nanoparticles in polymer matrixes when the grafting density is lower. In this limit (allophobic dewetting), the grafted chains do not fully wet the nanoparticle surface and provide incomplete stabilization, leading to nanoparticle aggregation. Using RAFT polymerization in a stepwise fashion enabled separate control over the composition, molecular weight, and grafting density of two different polymers grafted to nanoparticles.43 These bimodal surface-grafted brushes can be used to greatly improve dispersion of grafted nanoparticles in polymer matrixes: the short chains provided steric stabilization, whereas the long chains entangled with the matrix polymers.90 Later synthetic studies advanced the control over the molecular weight of each species and confirmed that the entanglements from even a small fraction of long chains enhanced the toughness of grafted-nanoparticle films.42

Self-Assembly

The molecular weight distribution also affects how grafted nanoparticles assemble in polymeric matrixes. Isotropic nanoparticles bearing loosely grafted brushes (such that the cores were able to come into contact) assembled into anisotropic strings.91 This assembly was determined by a balance between the attractions between the core particles and the elasticity of the grafted polymers. Similarly, nanoparticles bearing loosely grafted disperse PMMA brushes could also self-assemble into string morphologies, driven by the attraction between bare surfaces on the particles.39 In addition to improving miscibility, bimodal brushes on nanoparticles can also generate a variety of particle assemblies. Nanoparticles bearing long PS polymers and short P2VP polymers self-assembled into vesicle-like structures when the grafting density of PS was low; in this system the short P2VP polymers were thought to reduce the core (particle–particle) attractions and thereby avoid a kinetically trapped nonequilibrium state.92 Vesicle-like morphologies were also observed for zirconium oxide nanoparticles functionalized with PS and PEO polymers.93 Thus, dispersity provides an additional parameter by which to modulate the interactions between grafted nanoparticles that drive assembly further or closer to equilibrium.

Stimulus Response

Binary mixed spherical polymer brushes are widely studied as responsive materials, as reviewed in ref (22). Differences in the stimulus response of the two polymers can drive nanoscale segregation of the polymers on the particle surface, leading to changes in wettability or interfacial affinity. In addition to the phase behavior observed for planar surfaces, the ratio of the particle radius of curvature to the polymer radius of gyration can affect the brush morphology under selective solvents. When this ratio is large, the surface appears effectively planar and surface-grafted brushes (e.g., PS–PMMA) could reorganize under selective solvents94 following theoretical predictions for planar substrates.95 In PtBA-PS mixed brushes, the polymers again exhibited microphase separation in response to selective solvents and the grafting density strongly affected the feature size.96 When the particle radius of curvature was comparable to the polymer Rg, the density of grafted chains substantially decreased, moving away from the particle surface. Indirect measurements of solvent response (for example, partitioning of PS–PVP cografted gold nanoparticles at the interface of PS and PVP blocks in a copolymer) also suggested that the surface polymers were able to rearrange in response to the solvent conditions.97

The effects of continuous dispersity distributions on responsive behavior have been less examined. Homopolymer brushes of stimulus-responsive polymers may show significant differences in their responsive properties depending on the conformation, which in turn should depend on dispersity as well as the molecular weight Mw and grafting density σ. Intriguingly, studies on different polymer brushes produce contrasting results. The normalized length of poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) brushes collapsed onto a master curve as a function of pH.98 By contrast, the pH-dependent length of PAA brushes depended on both brush molecular weight and grafting density.99 Thus, there remains incomplete understanding of how spherical brush parameters affect the stimulus response.

To address this question, we synthesized annealed brushes of a model weak polyelectrolyte, PAA, and compared the conformation and response of pairs of brushes of near-constant molecular weight but different dispersity.100 High-dispersity brushes of a relatively low degree of polymerization (Nw ≈ 45) were longer than low-dispersity brushes; at a higher degree of polymerization (Nw ≈ 813), however, the length did not substantially change with Đ. To understand how the changes in brush conformation were linked to brush charge, we also measured the degree of dissociation α via titration and the zeta potential for each brush pair. Brushes with higher dispersity (compared at constant Nw) or lower molecular weight (compared at constant Đ) had higher pKa values. The zeta potential was more negative (greater magnitude) for higher-Đ brushes (compared at constant Nw) or higher molecular weight brushes (compared at constant Đ).

To systematically compare results across brush lengths and charge states, we examined the normalized brush length lb/lb,max as a function of the degree of dissociation α (Figure 8(a)).100 For low-Nw brushes (Nw ≈ 45), the dispersity did not affect the scaling of lb/lb,max with α (scaling exponent of 0.04), but brushes with lower Đ were more extended at a given α. The very small scaling exponent indicated that the brush length was insensitive to changes in the degree of dissociation and that brushes were in the quasi-neutral-brush regime, where short-range excluded volume interactions dominate over long-range electrostatic interactions (Figure 8(b)). Indeed, lb/lb,max of the low-Đ brush was nearly 1, indicating that the excluded volume interactions caused the brush to stretch independent of α. The pH-independent length of the low-Nw, low-Đ PAA brushes was similar to that observed for the Nw = 153 PAA brushes of ref (99) (Figure 8(c)), suggesting that the conformation of these systems was dominated by the excluded volume interactions. For brushes with a high degree of polymerization (Nw ≈ 813), however, lb/lb,max for the two brushes fell onto a single curve as a function of α with scaling exponent of 0.23, consistent with a transition in brush conformation from collapsed to stretched as α was increased. Further, the normalized lengths of the PDMAEMA brushes from ref (98) collapsed onto a master curve with those of the high-Nw PAA as a function of pH. Thus, these comparisons suggest that the extent of stimulus response can be tuned through the molecular weight (and length) distribution of the grafted polymers.

Figure 8.

Figure 8

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Responsive conformation depends on the molecular weight and dispersity. (a) Normalized brush length lb/lb,max as a function of degree of dissociation α of the low-Nw PAA brush pair with Nw = 45, Đ = 1.09 (light blue open triangles) and Nw = 45, Đ = 1.69 (dark blue open squares) and the high-Nw PAA brush pair with Nw = 782, Đ = 1.23 (light blue closed triangles) and Nw = 837, Đ = 1.76 (dark blue closed squares). Solid lines indicate power-law fits for low-Nw brushes, and the dashed line indicates the fit for the high-Nw brushes, which collapsed onto a single curve and were fit together. (b) Schematic illustration of the variation in conformation with Đ and α for the low-Nw brush pair. (c) lb/lb,max as a function of pH for the low-Nw PAA brush pair compared to a Nw = 153 PAA from ref (99). Reproduced with permission from ref (100). Copyright 2021 Royal Society of Chemistry.

Conclusions and Outlook

The studies discussed here suggest that tailoring brush dispersity offers a unique route to control the conformation and responsive properties of surface-grafted polymers as summarized in Table 1. To realize the promise of imparting novel functionality to surfaces by controlling the molecular weight distribution of grafted polymers, we suggest several avenues for further investigations:

Table 1. Molecular Weight Distribution Used To Tailor Material Properties.

context planar brushes (refs) spherical brushes (refs)
polymer conformation (48,50−59,62,63) (47,83−85)
wetting and miscibility (64) (43,88−90)
segregation (65−70) –
stimulus response (71−74) (94,96,99,100)
antifouling (78,81,82) –
self-assembly – (39,92,93)
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• Most current surface-initiated methods to control dispersity are RDRP (such as ATRP or RAFT). Several recently developed methods for tailoring dispersity in solution polymerizations, e.g., using switchable RAFT agents31,32 or mixing RAFT agents,30 can likely be adapted to surface-initiated polymerizations but have not yet been demonstrated in this context. Further, little has been explored beyond RDRP methods; ref (47) is a notable exception using ring-opening polymerization to produce surface-grafted polymers of varying dispersity. More synthetic techniques to control the breadth and shape of the distribution applied to surface-initiated polymerizations are needed to open up new properties to be explored.

• Theory and simulation studies are needed to understand how the molecular weight distribution alters polymer conformation, particularly for charged polymers and for spherical brushes (here, building on refs (83, 84, 88)). For example, studies of bimodal brushes in which each polymer’s molecular weight distribution is narrow (which cannot be experimentally synthesized) or broad (to connect to experiments) are likely to generate clear understanding of the effects of dispersity on brush conformation and (for weak polyelectrolytes) stimulus response, which remains largely unexplored.

• Likewise, detailed experimental studies of the effects of molecular weight distributions on brush conformation are still needed. Atomic force microscopy is widely employed for planar brushes but may not be sufficiently sensitive to capture structural differences arising from tailored dispersity. Neutron scattering methods, including neutron reflectivity for planar brushes101,102 and small-angle neutron scattering for spherical brushes,103 offer opportunities to characterize the structure of brushes as a function of the distance from the substrate. Further, the structure of individual components can be isolated through contrast-matching, providing a powerful tool by which to link, e.g., the conformation of a polymer brush to its dispersion in homopolymer matrixes (as one example). Application of these methods to characterize the effects of dispersity on the brush structure is essential for linking the brush structure to the functional properties.

• To date, most work has focused on the effects of dispersity in linear grafted homopolymers. Polymer chemists, however, can create many other polymer architectures. A recent study, for example, showed that increasing the dispersity of the oligomeric side chains in poly(methacrylate)-based comb polymers generated brushes that were more hydrated and less adhesive than those with a more uniform structure.44 Whether dispersity may affect the properties of other architectures, including bottlebrushes,104 to our knowledge has not been systematically studied on surfaces, although theorists have begun to develop phase diagrams for bulk melt systems.105 We anticipate that synthetic methods to controllably generate and characterize brushes of complex architectures will lead to unanticipated responsive properties.

• While our studies described here have provided some insight into the effects of dispersity on pH-response, there are a variety of stimuli that are applied to polymers, including solvent conditions, temperature, and salt concentration and valency (recently characterized for bidisperse polyelectrolyte brushes106,107). Additional studies are needed to understand how the molecular weight distribution affects the polymer response to these different stimuli across a range of polymer chemistries.

• Finally, there remains a gap between the many advanced techniques for synthesizing brushes with controlled molecular weight distribution and their use in applications. For example, we anticipate that disperse brushes may exhibit, e.g., unusual mechanical or adhesive properties (the latter suggested by refs (61) and (44)) that are distinct from those of uniform brushes, opening new opportunities for applications in sensing, self-assembly, catalysis, nanocomposite processing, and antifouling.

Acknowledgments

J.C.C. thanks the National Science Foundation (CBET-2113769) and the Welch Foundation (E-1869) for support. M.L.R. thanks the National Science Foundation (DMR-1906009) for support.

Author Contributions

CRediT: Jacinta C. Conrad conceptualization, writing-original draft, writing-review & editing; Megan L. Robertson conceptualization, writing-original draft, writing-review & editing.

The authors declare no competing financial interest.

References

  1. Giussi J. M.; Cortez M. L.; Marmisollé W. A.; Azzaroni O. Practical use of polymer brushes in sustainable energy applications: interfacial nanoarchitectonics for high-efficiency devices. Chem. Soc. Rev. 2019, 48, 814–849. 10.1039/C8CS00705E. [DOI] [PubMed] [Google Scholar]
  2. Li D.; Xu L.; Wang J.; Gautrot J. E. Responsive Polymer Brush Design and Emerging Applications for Nanotheranostics. Adv. Healthcare Mater. 2021, 10, 2000953. 10.1002/adhm.202000953. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Keating J. J.; Imbrogno J.; Belfort G. Polymer Brushes for Membrane Separations: A Review. ACS Appl. Mater. Interfaces 2016, 8, 28383–28399. 10.1021/acsami.6b09068. [DOI] [PubMed] [Google Scholar]
  4. Zhou F.; Huck W. T. S. Three-stage switching of surface wetting using phosphate-bearing polymer brushes. Chem. Commun. 2005, 5999–6001. 10.1039/b512106j. [DOI] [PubMed] [Google Scholar]
  5. Kobayashi M.; Terayama Y.; Yamaguchi H.; Terada M.; Murakami D.; Ishihara K.; Takahara A. Wettability and Antifouling Behavior on the Surfaces of Superhydrophilic Polymer Brushes. Langmuir 2012, 28, 7212–7222. 10.1021/la301033h. [DOI] [PubMed] [Google Scholar]
  6. Dunderdale G. J.; England M. W.; Urata C.; Hozumi A. Polymer Brush Surfaces Showing Superhydrophobicity and Air-Bubble Repellency in a Variety of Organic Liquids. ACS Appl. Mater. Interfaces 2015, 7, 12220–12229. 10.1021/acsami.5b02634. [DOI] [PubMed] [Google Scholar]
  7. Ladd J.; Zhang Z.; Chen S.; Hower J. C.; Jiang S. Zwitterionic Polymers Exhibiting High Resistance to Nonspecific Protein Adsorption from Human Serum and Plasma. Biomacromolecules 2008, 9, 1357–1361. 10.1021/bm701301s. [DOI] [PubMed] [Google Scholar]
  8. Zhou F.; Huck W. T. S. Surface grafted polymer brushes as ideal building blocks for “smart” surfaces. Phys. Chem. Chem. Phys. 2006, 8, 3815–3823. 10.1039/B606415A. [DOI] [PubMed] [Google Scholar]
  9. Conrad J. C.; Robertson M. L. Towards mimicking biological function with responsive surface-grafted polymer brushes. Curr. Opin. Solid State Mater. Sci. 2019, 23, 1–12. 10.1016/j.cossms.2018.09.004. [DOI] [Google Scholar]
  10. Alexander S. Adsorption of chain molecules with a polar head a scaling description. J. Phys. (Paris) 1977, 38, 983–987. 10.1051/jphys:01977003808098300. [DOI] [Google Scholar]
  11. de Gennes P. G. Conformations of Polymers Attached to an Interface. Macromolecules 1980, 13, 1069–1075. 10.1021/ma60077a009. [DOI] [Google Scholar]
  12. Dukes D.; Li Y.; Lewis S.; Benicewicz B.; Schadler L.; Kumar S. K. Conformational Transitions of Spherical Polymer Brushes: Synthesis, Characterization, and Theory. Macromolecules 2010, 43, 1564–1570. 10.1021/ma901228t. [DOI] [Google Scholar]
  13. Daoud M.; Cotton J. P. Star shaped polymers: a model for the conformation and its concentration dependence. J. Phys. (Paris) 1982, 43, 531–538. 10.1051/jphys:01982004303053100. [DOI] [Google Scholar]
  14. Birshtein T. M.; Borisov O. V.; Zhulina Y. B.; Khokhlov A. R.; Yurasova T. A. Conformations of comb-like macromolecules. Polymer Science U.S.S.R. 1987, 29, 1293–1300. 10.1016/0032-3950(87)90374-1. [DOI] [Google Scholar]
  15. Ohno K.; Morinaga T.; Takeno S.; Tsujii Y.; Fukuda T. Suspensions of Silica Particles Grafted with Concentrated Polymer Brush: Effects of Graft Chain Length on Brush Layer Thickness and Colloidal Crystallization. Macromolecules 2007, 40, 9143–9150. 10.1021/ma071770z. [DOI] [Google Scholar]
  16. Martinez A. P.; Carrillo J.-M. Y.; Dobrynin A. V.; Adamson D. H. Distribution of Chains in Polymer Brushes Produced by a “Grafting From” Mechanism. Macromolecules 2016, 49, 547–553. 10.1021/acs.macromol.5b02261. [DOI] [Google Scholar]
  17. Di Landro L.; Levi M.; Nichetti D.; Consolo A. Experimental determination of rheological properties of polydimethylsiloxane. Eur. Polym. J. 2003, 39, 1831–1838. 10.1016/S0014-3057(03)00104-6. [DOI] [Google Scholar]
  18. Ye X.; Sridhar T. Effects of the Polydispersity on Rheological Properties of Entangled Polystyrene Solutions. Macromolecules 2005, 38, 3442–3449. 10.1021/ma049642n. [DOI] [Google Scholar]
  19. Nielsen J. K.; Rasmussen H. K.; Hassager O.; McKinley G. H. Elongational viscosity of monodisperse and bidisperse polystyrene melts. J. Rheol. 2006, 50, 453–476. 10.1122/1.2206711. [DOI] [Google Scholar]
  20. Roy D.; Giller C. B.; Hogan T. E.; Roland C. M. The rheology and gelation of bidisperse 1,4-polybutadiene. Polymer 2015, 81, 111–118. 10.1016/j.polymer.2015.11.004. [DOI] [Google Scholar]
  21. Nadgorny M.; Gentekos D. T.; Xiao Z.; Singleton S. P.; Fors B. P.; Connal L. A. Manipulation of Molecular Weight Distribution Shape as a New Strategy to Control Processing Parameters. Macromol. Rapid Commun. 2017, 38, 1700352. 10.1002/marc.201700352. [DOI] [PubMed] [Google Scholar]
  22. Zhao B.; Zhu L. Mixed Polymer Brush-Grafted Particles: A New Class of Environmentally Responsive Nanostructured Materials. Macromolecules 2009, 42, 9369–9383. 10.1021/ma902042x. [DOI] [Google Scholar]
  23. Li M.; Pester C. W. Mixed Polymer Brushes for “Smart” Surfaces. Polymers 2020, 12, 1553. 10.3390/polym12071553. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Gentekos D. T.; Dupuis L. N.; Fors B. P. Beyond Dispersity: Deterministic Control of Polymer Molecular Weight Distribution. J. Am. Chem. Soc. 2016, 138, 1848–1851. 10.1021/jacs.5b13565. [DOI] [PubMed] [Google Scholar]
  25. Li H.; Collins C. R.; Ribelli T. G.; Matyjaszewski K.; Gordon G. J.; Kowalewski T.; Yaron D. J. Tuning the molecular weight distribution from atom transfer radical polymerization using deep reinforcement learning. Molecular Systems Design & Engineering 2018, 3, 496–508. 10.1039/C7ME00131B. [DOI] [Google Scholar]
  26. Gentekos D. T.; Sifri R. J.; Fors B. P. Controlling polymer properties through the shape of the molecular-weight distribution. Nature Review Materials 2019, 4, 761–774. 10.1038/s41578-019-0138-8. [DOI] [Google Scholar]
  27. Whitfield R.; Truong N. P.; Messmer D.; Parkatzidis K.; Rolland M.; Anastasaki A. Tailoring polymer dispersity and shape of molecular weight distributions: methods and applications. Chemical Science 2019, 10, 8724–8734. 10.1039/C9SC03546J. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Junkers T. Polymers in the Blender. Macromol. Chem. Phys. 2020, 221, 2000234. 10.1002/macp.202000234. [DOI] [Google Scholar]
  29. Walsh D. J.; Schinski D. A.; Schneider R. A.; Guironnet D. General route to design polymer molecular weight distributions through flow chemistry. Nat. Commun. 2020, 11, 3094. 10.1038/s41467-020-16874-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Whitfield R.; Parkatzidis K.; Truong N. P.; Junkers T.; Anastasaki A. Tailoring Polymer Dispersity by RAFT Polymerization: A Versatile Approach. Chem. 2020, 6, 1340–1352. 10.1016/j.chempr.2020.04.020. [DOI] [Google Scholar]
  31. Antonopoulou M.-H.; Whitfield R.; Truong N. P.; Wyers D.; Harrisson S.; Junkers T.; Anastasaki A. Concurrent control over sequence and dispersity in multiblock copolymers. Nat. Chem. 2022, 14, 304–312. 10.1038/s41557-021-00818-8. [DOI] [PubMed] [Google Scholar]
  32. Antonopoulou M.-N.; Whitfield R.; Truong N. P.; Anastasaki A. Controlling polymer dispersity using switchable RAFT agents: Unravelling the effect of the organic content and degree of polymerization. Eur. Polym. J. 2022, 174, 111326. 10.1016/j.eurpolymj.2022.111326. [DOI] [Google Scholar]
  33. Whitfield R.; Truong N. P.; Anastasaki A. Precise Control of Both Dispersity and Molecular Weight Distribution Shape by Polymer Blending. Angew. Chem., Int. Ed. 2021, 60, 19383–19388. 10.1002/anie.202106729. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Zoppe J. O.; Ataman N. C.; Mocny P.; Wang J.; Moraes J.; Klok H.-A. Surface-Initiated Controlled Radical Polymerization: State-of-the-Art, Opportunities, and Challenges in Surface and Interface Engineering with Polymer Brushes. Chem. Rev. 2017, 117, 1105–1318. 10.1021/acs.chemrev.6b00314. [DOI] [PubMed] [Google Scholar]
  35. Yin R.; Wang Z.; Bockstaller M. R.; Matyjaszewski K. Tuning dispersity of linear polymers and polymeric brushes grown from nanoparticles by atom transfer radical polymerization. Polym. Chem. 2021, 12, 6071–6082. 10.1039/D1PY01178B. [DOI] [Google Scholar]
  36. Pester C. W.; Benetti E. M. Modulation of Polymer Brush Properties by Tuning Dispersity. Advanced Materials Interfaces 2022, 9, 2201439. 10.1002/admi.202201439. [DOI] [Google Scholar]
  37. Chen W.-L.; Cordero R.; Tran H.; Ober C. K. 50th Anniversary Perspective: Polymer Brushes: Novel Surfaces for Future Materials. Macromolecules 2017, 50, 4089–4113. 10.1021/acs.macromol.7b00450. [DOI] [Google Scholar]
  38. Hansson S.; Trouillet V.; Tischer T.; Goldmann A. S.; Carlmark A.; Barner-Kowollik C.; Malmström E. Grafting Efficiency of Synthetic Polymers onto Biomaterials: A Comparative Study of Grafting-from versus Grafting-to. Biomacromolecules 2013, 14, 64–74. 10.1021/bm3013132. [DOI] [PubMed] [Google Scholar]
  39. Wang Z.; Yan J.; Liu T.; Wei Q.; Li S.; Olszewski M.; Wu J.; Sobieski J.; Fantin M.; Bockstaller M. R.; Matyjaszewski K. Control of Dispersity and Grafting Density of Particle Brushes by Variation of ATRP Catalyst Concentration. ACS Macro Lett. 2019, 8, 859–864. 10.1021/acsmacrolett.9b00405. [DOI] [PubMed] [Google Scholar]
  40. Wang Z.; Fantin M.; Sobieski J.; Wang Z.; Yan J.; Lee J.; Liu T.; Li S.; Olszewski M.; Bockstaller M. R.; Matyjaszewski K. Pushing the Limit: Synthesis of SiO2-g-PMMA/PS Particle Brushes via ATRP with Very Low Concentration of Functionalized SiO2–Br Nanoparticles. Macromolecules 2019, 52, 8713–8723. 10.1021/acs.macromol.9b01973. [DOI] [Google Scholar]
  41. Yadav V.; Hashmi N.; Ding W.; Li T.-H.; Mahanthappa M. K.; Conrad J. C.; Robertson M. L. Dispersity control in atom transfer radical polymerizations through addition of phenylhydrazine. Polym. Chem. 2018, 9, 4332–4342. 10.1039/C8PY00033F. [DOI] [Google Scholar]
  42. Yan J.; Kristufek T.; Schmitt M.; Wang Z.; Xie G.; Dang A.; Hui C. M.; Pietrasik J.; Bockstaller M. R.; Matyjaszewski K. Matrix-free Particle Brush System with Bimodal Molecular Weight Distribution Prepared by SI-ATRP. Macromolecules 2015, 48, 8208–8218. 10.1021/acs.macromol.5b01905. [DOI] [Google Scholar]
  43. Rungta A.; Natarajan B.; Neely T.; Dukes D.; Schadler L. S.; Benicewicz B. C. Grafting Bimodal Polymer Brushes on Nanoparticles Using Controlled Radical Polymerization. Macromolecules 2012, 45, 9303–9311. 10.1021/ma3018876. [DOI] [Google Scholar]
  44. Romio M.; Grob B.; Trachsel L.; Mattarei A.; Morgese G.; Ramakrishna S. N.; Niccolai F.; Guazzelli E.; Paradisi C.; Martinelli E.; Spencer N. D.; Benetti E. M. Dispersity within Brushes Plays a Major Role in Determining Their Interfacial Properties: The Case of Oligoxazoline-Based Graft Polymers. J. Am. Chem. Soc. 2021, 143, 19067–19077. 10.1021/jacs.1c08383. [DOI] [PMC free article] [PubMed] [Google Scholar]
  45. Liu X.; Wang C.; Goto A. Polymer Dispersity Control by Organocatalyzed Living Radical Polymerization. Angew. Chem., Int. Ed. 2019, 58, 5598–5603. 10.1002/anie.201814573. [DOI] [PubMed] [Google Scholar]
  46. Wang C.-G.; Chong A. M. L.; Goto A. One Reagent with Two Functions: Simultaneous Living Radical Polymerization and Chain-End Substitution for Tailoring Polymer Dispersity. ACS Macro Lett. 2021, 10, 584–590. 10.1021/acsmacrolett.1c00179. [DOI] [PubMed] [Google Scholar]
  47. Bentz K. C.; Savin D. A. Chain Dispersity Effects on Brush Properties of Surface-Grafted Polycaprolactone-Modified Silica Nanoparticles: Unique Scaling Behavior in the Concentrated Polymer Brush Regime. Macromolecules 2017, 50, 5565–5573. 10.1021/acs.macromol.7b00608. [DOI] [Google Scholar]
  48. Milner S. T.; Witten T. A.; Cates M. E. Effects of polydispersity in the end-grafted polymer brush. Macromolecules 1989, 22, 853–861. 10.1021/ma00192a057. [DOI] [Google Scholar]
  49. Qi S.; Klushin L. I.; Skvortsov A. M.; Schmid F. Polydisperse Polymer Brushes: Internal Structure, Critical Behavior, and Interaction with Flow. Macromolecules 2016, 49, 9665–9683. 10.1021/acs.macromol.6b02026. [DOI] [Google Scholar]
  50. Birshtein T.; Liatskaya Y.; Zhulina E. Theory of supermolecular structures of polydisperse block copolymers: 1. Planar layers of grafted chains. Polymer 1990, 31, 2185–2196. 10.1016/0032-3861(90)90094-F. [DOI] [Google Scholar]
  51. Dan N.; Tirrell M. Effect of bimodal molecular weight distribution on the polymer brush. Macromolecules 1993, 26, 6467–6473. 10.1021/ma00076a024. [DOI] [Google Scholar]
  52. de Vos W. M.; Leermakers F. A. M. Modeling the structure of a polydisperse polymer brush. Polymer 2009, 50, 305–316. 10.1016/j.polymer.2008.10.025. [DOI] [Google Scholar]
  53. Chakrabarti A.; Toral R. Density profile of terminally anchored polymer chains: a Monte Carlo study. Macromolecules 1990, 23, 2016–2021. 10.1021/ma00209a023. [DOI] [Google Scholar]
  54. Lai P. Y.; Zhulina E. B. Structure of a bidisperse polymer brush: Monte Carlo simulation and self-consistent field results. Macromolecules 1992, 25, 5201–5207. 10.1021/ma00046a014. [DOI] [Google Scholar]
  55. Kent M. S.; Factor B. J.; Satija S.; Gallagher P.; Smith G. S. Structure of Bimodal Polymer Brushes in a Good Solvent by Neutron Reflectivity. Macromolecules 1996, 29, 2843–2849. 10.1021/ma951497d. [DOI] [Google Scholar]
  56. Kritikos G.; Terzis A. F. Structure of bimodal and polydisperse polymer brushes in a good solvent studied by numerical mean field theory. Polymer 2005, 46, 8355–8365. 10.1016/j.polymer.2005.06.076. [DOI] [Google Scholar]
  57. Levicky R.; Koneripalli N.; Tirrell M.; Satija S. K. Stratification in Bidisperse Polymer Brushes from Neutron Reflectivity. Macromolecules 1998, 31, 2616–2621. 10.1021/ma971278n. [DOI] [PubMed] [Google Scholar]
  58. Goedel W. A.; Luap C.; Oeser R.; Lang P.; Braun C.; Steitz R. Stratification in Monolayers of a Bidisperse Melt Polymer Brush As Revealed by Neutron Reflectivity. Macromolecules 1999, 32, 7599–7609. 10.1021/ma981900r. [DOI] [Google Scholar]
  59. Terzis A. F. Bidisperse melt polymer brush studied by self-consistent field model. Polymer 2002, 43, 2435–2444. 10.1016/S0032-3861(01)00812-6. [DOI] [Google Scholar]
  60. Reiter G.; Auroy P.; Auvray L. Instabilities of Thin Polymer Films on Layers of Chemically Identical Grafted Molecules. Macromolecules 1996, 29, 2150–2157. 10.1021/ma950297z. [DOI] [Google Scholar]
  61. Reiter G.; Schultz J.; Auroy P.; Auvray L. Improving adhesion via connector polymers to stabilize non-wetting liquid films. Europhys. Lett. 1996, 33, 29–34. 10.1209/epl/i1996-00299-3. [DOI] [Google Scholar]
  62. Witten T. A.; Milner S. T. Two-Component Grafted Polymer Layers. MRS Online Proceedings Library 1989, 177, 37–45. 10.1557/PROC-177-37. [DOI] [Google Scholar]
  63. Lai P. Binary mixture of grafted polymer chains: A Monte Carlo simulation. J. Chem. Phys. 1994, 100, 3351–3357. 10.1063/1.466427. [DOI] [Google Scholar]
  64. Edgecombe S. R.; Gardiner J. M.; Matsen M. W. Suppressing Autophobic Dewetting by Using a Bimodal Brush. Macromolecules 2002, 35, 6475–6477. 10.1021/ma020476y. [DOI] [Google Scholar]
  65. Marko J. F.; Witten T. A. Phase separation in a grafted polymer layer. Phys. Rev. Lett. 1991, 66, 1541–1544. 10.1103/PhysRevLett.66.1541. [DOI] [PubMed] [Google Scholar]
  66. Müller M. Phase diagram of a mixed polymer brush. Phys. Rev. E 2002, 65, 030802. 10.1103/PhysRevE.65.030802. [DOI] [PubMed] [Google Scholar]
  67. Wang J.; Müller M. Microphase Separation of Mixed Polymer Brushes: Dependence of the Morphology on Grafting Density, Composition, Chain-Length Asymmetry, Solvent Quality, and Selectivity. J. Phys. Chem. B 2009, 113, 11384–11402. 10.1021/jp903161j. [DOI] [PubMed] [Google Scholar]
  68. Minko S.; Luzinov I.; Luchnikov V.; Müller M.; Patil S.; Stamm M. Bidisperse Mixed Brushes: Synthesis and Study of Segregation in Selective Solvent. Macromolecules 2003, 36, 7268–7279. 10.1021/ma034160h. [DOI] [Google Scholar]
  69. Estillore N. C.; Advincula R. C. Stimuli-Responsive Binary Mixed Polymer Brushes and Free-Standing Films by LbL-SIP. Langmuir 2011, 27, 5997–6008. 10.1021/la200089x. [DOI] [PubMed] [Google Scholar]
  70. Wei W.; Kim T.-Y.; Balamurugan A.; Sun J.; Chen R.; Ghosh A.; Rodolakis F.; McChesney J. L.; Lakkham A.; Evans P. G.; Hur S.-M.; Gopalan P. Phase Behavior of Mixed Polymer Brushes Grown from Ultrathin Coatings. ACS Macro Lett. 2019, 8, 1086–1090. 10.1021/acsmacrolett.9b00501. [DOI] [PubMed] [Google Scholar]
  71. Houbenov N.; Minko S.; Stamm M. Mixed Polyelectrolyte Brush from Oppositely Charged Polymers for Switching of Surface Charge and Composition in Aqueous Environment. Macromolecules 2003, 36, 5897–5901. 10.1021/ma0341869. [DOI] [Google Scholar]
  72. Delcroix M. F.; Huet G. L.; Conard T.; Demoustier-Champagne S.; Du Prez F. E.; Landoulsi J.; Dupont-Gillain C. C. Design of Mixed PEO/PAA Brushes with Switchable Properties Toward Protein Adsorption. Biomacromolecules 2013, 14, 215–225. 10.1021/bm301637h. [DOI] [PubMed] [Google Scholar]
  73. Bratek-Skicki A.; Eloy P.; Morga M.; Dupont-Gillain C. Reversible Protein Adsorption on Mixed PEO/PAA Polymer Brushes: Role of Ionic Strength and PEO Content. Langmuir 2018, 34, 3037–3048. 10.1021/acs.langmuir.7b04179. [DOI] [PubMed] [Google Scholar]
  74. Yadav V.; Harkin A. V.; Robertson M. L.; Conrad J. C. Hysteretic memory in pH-response of water contact angle on poly(acrylic acid) brushes. Soft Matter 2016, 12, 3589–3599. 10.1039/C5SM03134F. [DOI] [PubMed] [Google Scholar]
  75. Aulich D.; Hoy O.; Luzinov I.; Brücher M.; Hergenröder R.; Bittrich E.; Eichhorn K.-J.; Uhlmann P.; Stamm M.; Esser N.; Hinrichs K. In Situ Studies on the Switching Behavior of Ultrathin Poly(acrylic acid) Polyelectrolyte Brushes in Different Aqueous Environments. Langmuir 2010, 26, 12926–12932. 10.1021/la101762f. [DOI] [PubMed] [Google Scholar]
  76. Weidman J. L.; Mulvenna R. A.; Boudouris B. W.; Phillip W. A. Unusually Stable Hysteresis in the pH-Response of Poly(Acrylic Acid) Brushes Confined within Nanoporous Block Polymer Thin Films. J. Am. Chem. Soc. 2016, 138, 7030–7039. 10.1021/jacs.6b01618. [DOI] [PubMed] [Google Scholar]
  77. Dong R.; Lindau M.; Ober C. K. Dissociation Behavior of Weak Polyelectrolyte Brushes on a Planar Surface. Langmuir 2009, 25, 4774–4779. 10.1021/la8039384. [DOI] [PubMed] [Google Scholar]
  78. de Vos W. M.; Leermakers F. A. M.; de Keizer A.; Kleijn J. M.; Cohen Stuart M. A. Interaction of Particles with a Polydisperse Brush: A Self-Consistent-Field Analysis. Macromolecules 2009, 42, 5881–5891. 10.1021/ma900819b. [DOI] [Google Scholar]
  79. Badoux M.; Billing M.; Klok H.-A. Polymer brush interfaces for protein biosensing prepared by surface-initiated controlled radical polymerization. Polym. Chem. 2019, 10, 2925–2951. 10.1039/C9PY00163H. [DOI] [Google Scholar]
  80. Lau K. H. A.; Ren C.; Park S. H.; Szleifer I.; Messersmith P. B. An Experimental–Theoretical Analysis of Protein Adsorption on Peptidomimetic Polymer Brushes. Langmuir 2012, 28, 2288–2298. 10.1021/la203905g. [DOI] [PMC free article] [PubMed] [Google Scholar]
  81. Bosker W. T. E.; Iakovlev P. A.; Norde W.; Cohen Stuart M. A. BSA adsorption on bimodal PEO brushes. J. Colloid Interface Sci. 2005, 286, 496–503. 10.1016/j.jcis.2005.01.091. [DOI] [PubMed] [Google Scholar]
  82. Yadav V.; Jaimes-Lizcano Y. A.; Dewangan N. K.; Park N.; Li T.-H.; Robertson M. L.; Conrad J. C. Tuning Bacterial Attachment and Detachment via the Thickness and Dispersity of a pH-Responsive Polymer Brush. ACS Appl. Mater. Interfaces 2017, 9, 44900–44910. 10.1021/acsami.7b14416. [DOI] [PubMed] [Google Scholar]
  83. Nair N.; Wentzel N.; Jayaraman A. Effect of bidispersity in grafted chain length on grafted chain conformations and potential of mean force between polymer grafted nanoparticles in a homopolymer matrix. J. Chem. Phys. 2011, 134, 194906. 10.1063/1.3590275. [DOI] [PubMed] [Google Scholar]
  84. Dodd P. M.; Jayaraman A. Monte Carlo simulations of polydisperse polymers grafted on spherical surfaces. J. Polym. Sci., Part B: Polym. Phys. 2012, 50, 694–705. 10.1002/polb.23057. [DOI] [Google Scholar]
  85. Li T.-H.; Yadav V.; Conrad J. C.; Robertson M. L. Effect of Dispersity on the Conformation of Spherical Polymer Brushes. ACS Macro Lett. 2021, 10, 518–524. 10.1021/acsmacrolett.0c00898. [DOI] [PubMed] [Google Scholar]
  86. Petroff M. G.; Garcia E. A.; Dengler R. A.; Herrera-Alonso M.; Bevan M. A. kT-Scale Interactions and Stability of Colloids with Adsorbed Zwitterionic and Ethylene Oxide Copolymers. Macromolecules 2018, 51, 9156–9164. 10.1021/acs.macromol.8b01792. [DOI] [Google Scholar]
  87. Koh C.; Grest G. S.; Kumar S. K. Assembly of Polymer-Grafted Nanoparticles in Polymer Matrices. ACS Nano 2020, 14, 13491–13499. 10.1021/acsnano.0c05495. [DOI] [PubMed] [Google Scholar]
  88. Martin T. B.; Dodd P. M.; Jayaraman A. Polydispersity for Tuning the Potential of Mean Force between Polymer Grafted Nanoparticles in a Polymer Matrix. Phys. Rev. Lett. 2013, 110, 018301. 10.1103/PhysRevLett.110.018301. [DOI] [PubMed] [Google Scholar]
  89. Park S. J.; Kim S.; Yong D.; Choe Y.; Bang J.; Kim J. U. Interactions between brush-grafted nanoparticles within chemically identical homopolymers: the effect of brush polydispersity. Soft Matter 2018, 14, 1026–1042. 10.1039/C7SM02483E. [DOI] [PubMed] [Google Scholar]
  90. Li Y.; Tao P.; Viswanath A.; Benicewicz B. C.; Schadler L. S. Bimodal Surface Ligand Engineering: The Key to Tunable Nanocomposites. Langmuir 2013, 29, 1211–1220. 10.1021/la3036192. [DOI] [PubMed] [Google Scholar]
  91. Akcora P.; Liu H.; Kumar S. K.; Moll J.; Li Y.; Benicewicz B. C.; Schadler L. S.; Acehan D.; Panagiotopoulos A. Z.; Pryamitsyn V.; Ganesan V.; Ilavsky J.; Thiyagarajan P.; Colby R. H.; Douglas J. F. Anisotropic self-assembly of spherical polymer-grafted nanoparticles. Nat. Mater. 2009, 8, 354–359. 10.1038/nmat2404. [DOI] [PubMed] [Google Scholar]
  92. Zhao D.; Di Nicola M.; Khani M. M.; Jestin J.; Benicewicz B. C.; Kumar S. K. Self-Assembly of Monodisperse versus Bidisperse Polymer-Grafted Nanoparticles. ACS Macro Lett. 2016, 5, 790–795. 10.1021/acsmacrolett.6b00349. [DOI] [PubMed] [Google Scholar]
  93. Guzman-Juarez B.; Abdelaal A.; Kim K.; Toader V.; Reven L. Fabrication of Amphiphilic Nanoparticles via Mixed Homopolymer Brushes and NMR Characterization of Surface Phase Separation. Macromolecules 2018, 51, 9951–9960. 10.1021/acs.macromol.8b01959. [DOI] [Google Scholar]
  94. Li D.; Sheng X.; Zhao B. Environmentally Responsive “Hairy” Nanoparticles: Mixed Homopolymer Brushes on Silica Nanoparticles Synthesized by Living Radical Polymerization Techniques. J. Am. Chem. Soc. 2005, 127, 6248–6256. 10.1021/ja0422561. [DOI] [PubMed] [Google Scholar]
  95. Zhao B.; Zhu L. Nanoscale Phase Separation in Mixed Poly(tert-butyl acrylate)/Polystyrene Brushes on Silica Nanoparticles under Equilibrium Melt Conditions. J. Am. Chem. Soc. 2006, 128, 4574–4575. 10.1021/ja058560r. [DOI] [PubMed] [Google Scholar]
  96. Jiang X.; Zhao B.; Zhong G.; Jin N.; Horton J. M.; Zhu L.; Hafner R. S.; Lodge T. P. Microphase Separation of High Grafting Density Asymmetric Mixed Homopolymer Brushes on Silica Particles. Macromolecules 2010, 43, 8209–8217. 10.1021/ma101518a. [DOI] [Google Scholar]
  97. Chiu J. J.; Kim B. J.; Kramer E. J.; Pine D. J. Control of Nanoparticle Location in Block Copolymers. J. Am. Chem. Soc. 2005, 127, 5036–5037. 10.1021/ja050376i. [DOI] [PubMed] [Google Scholar]
  98. Iqbal D.; Yan J.; Matyjaszewski K.; Tilton R. D. Swelling of multi-responsive spherical polyelectrolyte brushes across a wide range of grafting densities. Colloid Polym. Sci. 2020, 298, 35–49. 10.1007/s00396-019-04585-4. [DOI] [Google Scholar]
  99. Zhang C.; Carlson T.; Yang S.; Akcora P. Ordering pH-Responsive Polyelectrolyte-Grafted Nanoparticles in a Flow Coating Process. Advanced Materials Interfaces 2018, 5, 1701318. 10.1002/admi.201701318. [DOI] [Google Scholar]
  100. Li T.-H.; Robertson M. L.; Conrad J. C. Molecular weight and dispersity affect chain conformation and pH-response in weak polyelectrolyte brushes. Polym. Chem. 2021, 12, 6737–6744. 10.1039/D1PY01056E. [DOI] [Google Scholar]
  101. Field J. B.; Toprakcioglu C.; Ball R. C.; Stanley H. B.; Dai L.; Barford W.; Penfold J.; Smith G.; Hamilton W. Determination of end-adsorbed polymer density profiles by neutron reflectometry. Macromolecules 1992, 25, 434–439. 10.1021/ma00027a067. [DOI] [Google Scholar]
  102. Kilbey S. M.; Ankner J. F. Neutron reflectivity as a tool to understand polyelectrolyte brushes. Curr. Opin. Colloid Interface Sci. 2012, 17, 83–89. 10.1016/j.cocis.2011.08.007. [DOI] [Google Scholar]
  103. Wei Y.; Hore M. J. A. Characterizing polymer structure with small-angle neutron scattering: A Tutorial. J. Appl. Phys. 2021, 129, 171101. 10.1063/5.0045841. [DOI] [Google Scholar]
  104. Verduzco R.; Li X.; Pesek S. L.; Stein G. E. Structure, function, self-assembly, and applications of bottlebrush copolymers. Chem. Soc. Rev. 2015, 44, 2405–2420. 10.1039/C4CS00329B. [DOI] [PubMed] [Google Scholar]
  105. Starvaggi H.; Tian Y.; Liang H.; Dobrynin A. V. Bottlebrushes and Combs with Bimodal Distribution of the Side Chains: Diagram of States and Scattering Function. Macromolecules 2021, 54, 1818–1828. 10.1021/acs.macromol.0c02610. [DOI] [Google Scholar]
  106. Li Y.; Hao Q.-H.; Xia S.-Y.; Yan D.-X.; Tan H.-G. Morphologies of spherical bidisperse polyelectrolyte brushes in the presence of trivalent counterions. Chem. Phys. 2020, 539, 110941. 10.1016/j.chemphys.2020.110941. [DOI] [Google Scholar]
  107. Hao Q.-H.; Cheng J. Morphologies of a spherical bimodal polyelectrolyte brush induced by polydispersity and solvent selectivity. Chinese Physics B 2021, 30, 068201. 10.1088/1674-1056/abd7d2. [DOI] [Google Scholar]

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