Molecule motion at polymer brush interfaces from single-molecule experimental perspectives

Authors


ABSTRACT

Polymer brushes have been widely used as functional surface coatings for broad applications including antifouling, energy storage, and lubrications. Understanding the molecule dynamics at polymer brush interfaces is important in unraveling the structure–property relationships in these materials and establishing a new materials design paradigm of novel functional polymer thin films with efficient interfacial transport. By applying modern fluorescence-based single-molecule spectroscopic and microscopic techniques, molecule dynamics at varied polymer brush interfaces have been experimentally investigated in recent years. New insights are given to the understandings of some unique and unusual materials properties of polymer brush thin films. This review summarizes some recent studies of molecular diffusion at polymer brush interfaces, highlights some new understandings of the interfacial properties of polymer brushes, and discusses future research opportunities in this field. © 2013 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2014, 52, 85–103

INTRODUCTION

A polymer brush is a brush-like, thin layer of polymer chains with one end attached to a solid surface and the other end extended away from the surface to the medium.[1-6] The densely packed, surface-tethered polymer chains in close proximity to each other result in a stretched, brush-like conformation that minimizes segment–segment interactions. This equilibrium situation, in which polymer chains are stretched along the direction normal to the grafting surface, is quite different from the typical conformational structures of polymer chains in solutions or melts where chains adopt a coil conformation. Because of such specific configuration, polymer brushes have exhibited many novel properties and have been used for wide applications from biology to tribology.[3-5, 7-12]

Polymer brush films have been developed as coatings and adhesive layers with desired antifouling features.[7, 13-18] Coating materials with antibiofouling surface properties, which can resist the nonspecific adsorption of proteins, cells, and other biological species, are important in a wide range of fields including biochips, medical implants, and marine applications.[9, 19-21] Because proteins generally possess both charged and hydrophobic patches, they can readily adsorb on a large variety of surfaces by electrostatic, hydrophobic, or other intermolecular attractions. In recent years, hydrophilic polymer brushes, such as poly(ethylene glycol) methacrylate (PEGMA), poly (2-hydroxyl ethyl methacrylate) (PHEMA), poly (N-isopropyl acrylamide) (PNIPAM), and zwitterionic polybetaines, have been demonstrated to serve as very effective antibiofouling coatings.[4] The mechanism is generally associated with enthalpic and/or entropic barriers for the adsorption of proteins on polymer brushes.[15, 22, 23] If proteins adsorb on a hydrophilic polymer brush surface, the water molecules intimately bound with polymer segments are disrupted from their hydration cage, and the chains are consequently compressed accordingly. Thus, the increase in enthalpy due to chain dehydration and the decrease in entropy due to the chain compression, combined together, can make the adsorption of proteins on a hydrophilic polymer brush unfavorable.

Polymer brushes have also been applied for producing low friction and lubricious surfaces. Experimental results have revealed that, in good solvents, a polymer brush can act as a lubricious layer to largely reduce the friction force between two sliding surfaces.[24, 25] Recently, hydrophilic polymer brushes have been examined as a simple model system to elucidate the biolubrication mechanism in complex biological environments such as medical implant systems, including artificial hip/knee joints or contact lenses.[26] The superlubricity of hydrophilic brushes has been reported, as they display an extremely low-friction coefficient in aqueous media.[27, 28] Further investigation has shown that the brush-like thin layers of charged polymers, including zwitterionic polyelectrolytes, tethered at substrate surfaces in aqueous media can provide lubrication superior to those surfaces coated with surfactants or neutral polymers.[29, 30] The measured friction coefficient was comparable to the one between articular cartilage surfaces in human synovial joints, which are considered as the most long-lasting superlubrication system in nature.

Among many polymer brush systems, charged polymer brushes in particular have been explored for energy storage applications. One of the best-known charged polymer films is Nafion (Dupont), which is composed of sulfonated polytetrafluoroethylene and used as a proton exchange membrane (PEM) for fuel cells. Despite the high charge mobility and resistance to the degradation of Nafion film, its high material cost and undesired environmental impact has limited its applications.[31] Polyelectrolyte films, particularly polyelectrolyte brushes, have been suggested as alternatives to Nafion for PEMs.[32-36] Although extensive research has been conducted to develop synthetic strategies for producing polyelectrolyte films with well-controlled structures and specific chemistry to facilitate proton transport,[10] the understanding of molecule and ion dynamics in highly conductive and crowded polymeric environments is inadequate. Despite recent advances in both experimental[37, 38] and theoretical modeling[39-41] studies of ion–polymer brush interactions, the mechanistic details about the interplay of local solvation dynamics, and characteristic lengths of polyelectrolyte brush chains are not explicitly revealed.

All the exceptional properties of polymer brush surfaces, as described with their major application areas above, are attributed to both the equilibrium structure and dynamic characteristics. Confining polymer chains at the surface can modify not only their conformational structures, but also their chain relaxation and interfacial dynamics. Although extensive studies have been performed on the structural properties of polymer brushes in equilibrium states, the dynamics of polymer brushes remains inadequately investigated or understood, partially due to the paucity of suitable sensitive techniques. Recently, single-molecule imaging and spectroscopic techniques have been used to investigate molecule diffusion and transport in polymer brushes, yielding important pictures of interfacial dynamics of polymer brush thin films.[42-44] In comparison to the extensive studies of fluid dynamics in bulk systems, molecular motion in solid–liquid interfaces and confined fluids remains a challenging problem, because the particular nature of surface chemistry and interfacial interactions can vastly complicate the matter.[45-47] Additionally, with the emerging interest in microfluidics, the surface effects—which strongly depend on the surface coating chemistry and structure—could become greatly pronounced due to a high surface-to-volume ratio and a varied boundary effect from no-slip to slip boundary conditions.[37, 38] Hence, a fundamental understanding of how surface properties affect the diffusive dynamics of molecules at polymer-coated surfaces or interfaces is critically important to the design and performance of advanced micro/nano-fluidic devices. An understanding of the molecular motion on polymer brush surfaces is also highly relevant to biotransport problems in nature such as protein transport across cell membranes and superlubricity of human joints.[48-50]

This review focuses on the molecular motion at polymer brush interfaces. It begins with a brief discussion of the structural properties of polymer brushes, which could critically govern the molecular dynamics processes at polymer brush interfaces. Some recent advances in the experimental study of dynamic behaviors of molecules at polymer brush surfaces are highlighted, which is intimately related to the broad scientific question of molecular dynamics in confined domains. The second section introduces modern fluorescence-based single-molecule techniques, which enable the study of the diffusion of single molecules at solid–liquid interfaces with high spatial and temporal resolutions. Next, recent experimental investigations of molecule diffusions at polymer brush interfaces are presented. Results obtained from three different yet typical cases are presented: small molecule diffusion atop polymer brushes, macromolecule diffusion atop polymer brushes, and small molecule diffusion inside polymer brushes. Finally, a brief perspective on the dynamic characteristics of polymer brush films is discussed.

FUNDAMENTALS OF POLYMER BRUSHES

Some unique properties of polymer brushes are determined by the specific structure of surface tethered polymer chains as often described by the grafting density, σ (unit: chain per area), or spacing between two neighboring chains, s (unit: length per neighboring chain pair). As the size of polymer chains approaches the spacing between two neighboring grafting points, the chains start to overlap and interact with their neighbors. This critical spacing is responsible for the conformational transition from a regime of isolated polymer chains like a “mushroom” or “pancake”, depending on the polymer–surface interaction, to a brush-like regime. A commonly used parameter to quantitatively determine the transition is the reduced tethered density,

display math(1)

where Rg is the radius of gyration of the polymer chain.[51] σ is theoretically derived as

display math(2)

where h is the polymer film thickness, ρ is the bulk density of the polymer, NA is Avogadro's constant and Mn is the molecular weight of the polymer. The physical interpretation of Σ is the number of chains occupying an area that a free nonoverlapping chain would closely fill under the same conditions.[51] Therefore, Σ from its definition stands for a reliable parameter to judge the brush-like character of a grafted polymer film. It is generally recognized that three regimes appear in the surface tethered polymer chains: (1) the mushroom or pancake regime (Σ < 1), (2) the crossover regime (Σ = 1), and (3) the brush-like regime (Σ > 1). However, in real situations, because of the statistical characteristics of grafting density and polydispersity in the molecular weight of polymer chains, the transition from the mushroom regime to the brush one is generally not sharp.[51, 52] In fact, the “true brush” formation is typically characterized by Σ > 5 in the literature, where the tethered polymer molecules can be described as highly stretched chains. The actual Σ value for the conformational transition is strongly affected by the excluded volume of polymers and thereby varies largely from system to system.[53-55]

The grafting density σ is a critical structural parameter for polymer brushes. However, the measurement of σ is not straightforward because many experimental techniques used in the characterization of polymers are suitable for bulk polymer solutions or melts, but not for solid–liquid interfaces. The most commonly used method to measure σ is based on eq (2), with known brush thickness and molecular weight. The brush thickness can be generally measured by ellipsometry or atomic force microscope (AFM), whereas the molecular weight can be obtained by gel permeation chromatography (GPC) analysis after the cleavage of the polymer brush layer from a substrate.[2, 5] In practice, this method requires a large surface area, which can provide sufficient material for GPC analysis, and also special linkers, which can facilitate the brush cleavage from a substrate. Alternatively, the grafting density can be indirectly obtained by using the Alexander-de Gennes model.[56, 57] In this model, the minimization of the total free energy of the chains, which comprises the Gaussian elastic free energy and the repulsive excluded volume interaction energy between the chains, leads to a scaling behavior of polymer brush thickness as

display math(3)

where N is the polymerization degree, a is the monomer size, and v is the positive second viral coefficient between monomers. As the dry polymer brush thickness is linearly dependent on σ, the grafting density can be estimated by comparing the thicknesses in the dry and wet states.[58, 59] Recently, AFM has been utilized to measure the grafting density of polymer brushes. By compressing the film using an AFM tip and fitting the measured compression profiles with the Alexander-de Gennes model, the grafting density of polymer brushes can be indirectly obtained.[60-63]

EXPERIMENTAL METHODS TO STUDY DIFFUSIONS AT SOLID–LIQUID INTERFACES

The surface diffusion of atoms or molecules is critical to crystal and thin-film growth, surface chemical reactions and catalysis, and other surface and interfacial sciences.[64-66] For atomic or molecular dynamics at solid–solid or solid–gas interfaces, scanning tunneling microscopy and other high-vacuum surface characterization techniques have been sufficiently powerful and sensitive.[67] For systems where a solid–liquid or liquid–gas interface is involved, fluorescence-based techniques, including fluorescence correlation spectroscopy (FCS), fluorescence recovery after photobleaching (FRAP), and single-molecule tracking (SMT), have recently emerged as powerful experimental tools to study the structural or diffusive dynamics of molecules at liquid interfaces. Although the fluorescence-based techniques were initially developed and focused in the fields of molecular and cell biology, such methods have evolved as powerful tools in other scientific areas, including polymer systems, and colloid and interface sciences.

FCS was first introduced in the early 1970s,[68-71] yet the technique was not widely adopted in biophysics or materials research until the early 1990s, when FCS was combined with confocal microscopic illumination to reach the single-molecule detection sensitivity.[72] In the past two decades, FCS has been extensively exploited in biological studies, as detailed in excellent reviews on this topic.[73-75] Figure 1 shows a typical setup for FCS, which closely resembles that of a classical confocal microscope setup. A high numerical aperture water- or oil-immersed objective lens is used to focus a laser beam to a diffraction-limited spot into the sample. The fluorescence emission from the sample after laser excitation, before being collected by the same objective lens, passes through a dichroic mirror and an emission filter and then is imaged onto a confocal pinhole, which blocks the emitted light out of the focal plane. Thus, the detection volume is confined to typically less than 1 femtoliter. The detection of a fluorescence emission is conducted by sensitive photon detectors, typically either a single-photon counting avalanche photo diode or a photomultiplier tube. The temporal fluctuation in fluorescence intensity, math formula, caused by fluorescent species transporting in and out of the focal volume, is recorded and analyzed to produce an autocorrelation function as a function of lag time, τ, where

display math(4)
Figure 1.

(a) A schematic representation of a FCS setup. A laser beam passes through a beam expander and is focused by the objective lens to a diffraction-limited volume in the sample after being reflected by the dichroic mirror. The fluorescence emission is collected by the objective lens and recorded by a sensitive detector. The usage of the confocal pinhole ensures that only light coming from the focused spot effectively reaches the detector. (b) By calculating the autocorrelation function from the recorded fluorescence fluctuations, the dynamic characteristics on the fluorescence species can be obtained using suitable mathematical models.

The dynamic characteristics of fluorescence species can be obtained by fitting the obtained math formulawith a known physical model featuring the system. FCS has been widely used to determine the Brownian diffusive dynamic processes of molecules in different environments, in which local diffusion coefficients and mean residence time of a fluorescent species in the focal volume can be obtained with the known dimensions of the focal volume. For instance, for the Brownian diffusion of fluorescence molecules in a three-dimensional (3D) space, the decay of autocorrelation function can be fitted with the equation

display math(5)

where N is the average number of fluorescence species in the focal volume, τD is the mean residence time, ω0 of typically 300–500 nm, and z0 of typically 2–4 μm are the lateral and vertical dimensions of the focal volume, respectively. By fitting the obtained math formulawith eq (5) and known ω0 and z0, N and τD can be determined. Thus, the diffusion coefficient can be obtained from τD according to

display math(6)

For the diffusion of molecules at interface interested in this review article, the math formula obtained from two-dimensional (2D) diffusion of fluorescence probes can be fitted with the equation

display math(7)

Thus, the 2D diffusion coefficient at the interface can be determined using eq (6).

Another fluorescence technique using perturbative probes capable of measuring the diffusion of molecules is FRAP. Its principle is schematically illustrated in Figure 2. As its name implies, FRAP monitors the dynamics of fluorescence restoration after photobleaching, due to the diffusion influx from neighboring areas to the bleached area.[76, 77] An intense laser is briefly used to flash a region of the sample containing fluorescence-labeled probe molecules. After bleaching, a low-intensity laser is used to measure the recovery of fluorescence in the bleached region caused by concurrent fluxes of the inward diffusion of neighboring unbleached molecules into the bleached region, and the outward diffusion of bleached molecules. The analysis of the resulting fluorescence recovery in terms of the measured time-dependent fluorescence intensity, It, yields the characteristic time that is used to obtain the diffusion coefficient of molecules in different environments. For a single Brownian diffusion process, a fluorescence recovery curve obeys the equation

display math(8)

where I0 corresponds to the final recovered intensity plateau, and A is a fitting constant indicating the extent of photobleaching in the bleached spot. The diffusion coefficient D can be determined by using math formula, where a is the diameter of the bleached spot.

Figure 2.

A schematic representation of a typical FRAP experiment. With an intense laser beam, the fluorescent molecules are quickly photobleached inside a particular area. After photobleaching, the exchange of the bleached molecules in the bleached area with unbleached molecules in the neighboring areas occurs due to the molecular diffusion, resulting in a gradual recovery of the fluorescence inside the photobleached area. With a suitable mathematical model, the diffusion coefficient of fluorescence-labeled molecules can be extracted.

Although both FCS and FRAP can be used to measure lateral diffusion, there are two advantages in using FCS. First, the concentration of fluorescent probes for FCS can be extremely low, typically less than one probe per fL. The high sensitivity of FCS allows a much smaller quantity of fluorophores per field of view to be used than that of FRAP, causing little disruption of the system.[78] Second, FCS offers a higher spatial resolution than FRAP, which is very important in the study of heterogeneous systems such as porous networks, hydrogel films, phase separated polymer blends, and solid–liquid or liquid–liquid interfaces.[79, 80] Yet FRAP has its own advantage in the measurement of slow dynamics. Because of the potential photobleaching during the transport of fluorescence molecules in the focal volume, FCS is limited to measuring moderately fast molecular diffusion with a residence time of usually less than 1 s, corresponding to a diffusion coefficient larger than ∼0.02 μm2/s. Additionally, the laser intensity used for FRAP could be much lower than FCS, allowing FRAP to detect molecular diffusion at much slower rates.[81]

In addition to single-molecule fluorescence spectroscopy, SMT or single-particle tracking (SPT) has become a popular and powerful tool that allows direct microscopic observation of dynamic processes at a molecular level. For FCS and FRAP, while fluorescence fluctuation is the result of single molecules, the mathematical analysis is performed over a certain time period comprising many fluctuations so that the results resemble the ensemble average of many molecules. Distinctly, SMT is a fluorescence microscopy technique capable of visualizing the motion of individual molecules directly. In the past two decades, SMT has become a viable research tool, thanks to technological advancements in the detection device efficiency and in the sensitivity of the measured fluorophore quantum yield and lifetime.[82, 83] Although the sizes of molecules are typically below the diffraction limit, that is, ∼100–200 nm of the fluorescence microscope, molecules can be treated as dots of light with a Gaussian-like intensity distribution. By fitting the intensity distribution, the position of the molecules can be calculated with a sub-100-nm resolution.[84, 85] Although the fluorescence emitted by one molecule is generally dim in comparison to the background, the total internal reflection fluorescence (TIRF) microscope minimizes the background noise to obtain images with a sufficient signal-to-noise (S/N) ratio for SMT. A schematic illustration of the objective-based TIRF microscope is shown in Figure 3(a). The incident light is totally and internally reflected at the glass–water interface to generate an evanescent electromagnetic field, which decays exponentially from the interface, and thus penetrate to ∼100 nm in sample depth.[86] The fluorescence background is strongly suppressed to improve the S/N ratio of rendered images. Subsequently, the trajectories derived from time-dependent images can be analyzed to determine the modes of motion and the associated dynamic characteristic parameters. SMT has already been applied to study various complex material systems such as membrane-incorporated molecule diffusion in cells, molecular transport in sol-gel films, and intracellular delivery of nanomedicines.[87-89] The example in Figure 3(b) exhibits the trajectories of individual fluorescence probes inside a polymer brush layer obtained by combining SMT with TIRF.[90]

Figure 3.

(a) A schematic representation of an objective lense-based TIRF microscope setup. The incident light is totally internally reflected at the glass–water interface to generate an evanescent electromagnetic field, which decays exponentially from the interface and penetrates into the sample of ∼100 nm in depth. (b) Single-molecule trajectories of Rhodamine 6G (R6G) in PNIPAM brushes grafted on a glass coverslip surface at T = 23 °C; (inset) a blow-out view over a 20 × 20 µm2 expanded area. Different colors represent different trajectories, which may appear to overlap but actually occur at different times. (Reproduced from Ref. 90, with permission from the American Chemical Society.)

The application of advanced fluorescence-based experimental tools such as FCS, FRAP, and SMT has extended from the initial scientific areas in molecular and cell biology to soft matters. This review summarizes recent advances in the study of molecule diffusion at polymer brush interfaces.

DIFFUSION OF SMALL MOLECULES AND MACROMOLECULES ATOP POLYMER BRUSHES

Using the SPT method, Tu et al. investigated the diffusion of silica nanoparticles on thermo-responsive polymer brushes.[91] PNIPAM used in this study is a well-studied thermo-responsive polymer that had a lower critical solution temperature (LCST) around 32 °C.[92, 93] When the solution temperature was raised across its LCST, the PNIPAM brush chain underwent a transition from a stretched conformation to a collapsed one, leading to a change in surface wettability from a hydrophilic surface to a hydrophobic one. In their experiment, PNIPAM brushes on a quartz coverslip were prepared by surface-initiated atom transfer radical polymerization (ATRP), and an inverted phase contrast microscopy was used to observe the near-surface diffusion of surface-functionalized silica particles in solutions atop the coverslip. They reported that the diffusion coefficient of silica particles coated with PNIPAM brushes on a flat PNIPAM brush surface increased abruptly with increasing temperature, as Dsurface/Dbulk ≈ 0.6 at T < 32 °C was raised to ≈0.8–0.9 at T > 32 °C. At first glance this result seemed counter-intuitive because it is well-understood that the hydrophobic attraction between a PNIPAM brush-coated particles and a PNIPAM brush surface increases as the temperature increases. Tu et al. suggested two possible pictures for their surprising observation. First, the reduction in the particle mobility at the surface was partially attributed to the hydrodynamic coupling between the particle and the polymer surface. Yet the hydrodynamic coupling was weakened at higher temperatures due to the collapse of PNIPAM chains on the surface. However, the suggested weakened hydrodynamic coupling was not sufficient to explain the nearly 50% increase of the measured diffusion coefficient at T > LCST. Hence, Tu et al. suggested a second and main reason for the residual negative charges of silica particles and substrate. With the collapse of the PNIPAM brush chain at increased temperature across LCST, the local dielectric permittivity was found to decrease from ∼48 at T = 25 °C to ∼12 at T = 36 °C, leading to an enhanced electrostatic repulsion. Although the hydrophobic attraction term increased with temperature, the net attractive interaction conversely decreased with enhanced electrostatic repulsion. As a result, a rapid increase in the surface diffusion coefficient of a PNIPMA-coated particle on a PNIPAM surface became plausible. This work pointed out that various environmental parameters could affect the diffusive dynamics of molecules or particles on stimuli-responsive polymer brush surfaces.

Surface roughness plays an important role in the study of the surface diffusion of a molecule or particle. To exclude the effect of surface defects, such as charge residues and topographical roughness, on the diffusion of molecules on polymer brushes, Wang and Zhu developed a method by introducing an extremely homogeneous and smooth initiator monolayer to graft polymer brushes with high smoothness and homogeneity from a solid surface.[59] Using FCS, Wang and Zhu studied the diffusion of two small fluorescence molecules, Rhodamine 6G (R6G) and Rhodamine 123 (R123), on homogenous PNIPAM brushes.[42] The stimuli-responsive characteristics of the PNIPAM brush surface made it an excellent model surface to systematically study molecular diffusion on polymer brush–liquid interfaces with varied conformational and dynamical properties. The sample cell for FCS experiments was built with a quartz coverslip grafted with PNIPAM brushes as the top substrate, and a thin microscope coverslip as the bottom substrate, bonded together by a thin spacer with a thickness of ∼50 μm. Two tiny openings were previously drilled on quartz coverslips for the introduction and drainage of solutions. The sample cell was first filled with a very dilute solution (∼10−9 M) of fluorescent probes, and sufficient incubation time was allowed for the thorough adsorption of the fluorescent probes. Afterward, a copious amount of deionized water was rinsed through the sample cell to remove any residual unadsorbed fluorescent probes in the solution. This sample preparation protocol is commonly adopted in molecular diffusion studies at liquid–solid interface by FCS or SMT. Figure 4(a) presents the picture of molecule diffusion on PNIPAM brushes immersed in aqueous solution by FCS. The possible effect of residue charges on PNIPAM brushes to the molecular surface diffusion was excluded based on control experimental results of the adsorptions of probe molecules on smooth PNIPAM brushes and initiator monolayers.[42] Wang et al. concluded that the hydrophobic interaction between PNIPAM segments and the small molecule was the dominant attraction responsible for the molecule adsorption, while the electrostatic interaction contribution could be neglected. As shown in Figure 4(b), the surface diffusion coefficient of probe molecules continuously decreased when the temperature was increased across LCST, which was contrary to the results observed with PNIPAM-coated silica particles where the surface defects could conversely dominate the interfacial interaction.[91] On swelled PNIPAM brushes at T < LCST, the diffusion of R6G or R110 showed a strong dependence on the brush thickness and grafting density dependent. As shown in Figure 4(c), a nonmonotonic dependence of the diffusion coefficient on PNIPAM brush thickness was observed: the diffusion coefficient of R6G first increased as the PNIPAM brush thickness increased to reach a plateau, and was then followed by a decrease in the diffusion coefficient when the brush thickness was further increased to exceed a critical value.

Figure 4.

(a) A schematic illustration of the FCS study of the diffusion of a small molecular probe, R6G on a PNIPAM brush interface. (b) Measured D of R6G on PNIPAM surface of grafting density, σ = 0.62 chain/nm2 but varied dry thickness, h = 2.5 nm (▪) and 10.8 nm (•) versus solution temperature, T. (c) Measured D of R6G on PNIPAM surfaces of constant σ = 0.62 chain/nm2 versus h at T = 25 °C. Dashed lines are used to indicate three distinct regions in observed surface dynamical behaviors. Insert: Growth of PNIPAM brush thickness versus ATRP time. (Reproduced from Ref. 42, with permission from the Royal Chemical Society.)

To explain their observations, Wang and Zhu proposed a model in which the molecule diffusion on polymer brushes was a coupling process between thermally activated Brownian motion and the dynamics of underlying polymer brush chains.[42] Considering that the strength of interactions between probe molecules and underlying PNIPAM chains was nearly the same, Wang et al. contended that molecule diffusion on a polymer surface of slower chain dynamics (or relaxation) could be further retarded due to the coupling effect. As PNIPAM brush film thickness grew, PNIPAM chains were repelled from each other and further stretched to form uniform extended brushes, resulting in an increase in the surface diffusion coefficient due to the increased surface homogeneity. When the brush thickness was further increased, the PNIPAM chain length became more polydispersed, and the segment density at the brush-water interface decreased. The resultant reduction in the surface dynamics of polymer end segments at polymer–water interfaces led to a decrease in the surface diffusion coefficient of probe molecules absorbed on the end-segments of PNIPAM brushes.

By investigating the effects of different chemical structures of fluorescence probe molecules and polymer brush grafting density on the surface diffusion coefficient of probe molecules, the generality of the coupling effect of molecule surface diffusion and polymer interfacial dynamics was confirmed. The authors established a naïve scaling dependence of the molecule diffusion coefficient on polymer brush grafting density, σ, as math formula, which was significantly stronger than the theoretically predicted math formula. Wang et al. speculated that the deviation was due to the difference in the diffusion modes at varied grafting densities: molecules on the brush with low grafting density could actually penetrate into the brush layer, resulting in surface diffusion in a mixed 2D and 3D manner. It thus suggested that the diffusion of molecules at the polymer brush-liquid interface was distinct from that inside a polymer brush layer. This study provided insights on polymer brush dynamics and its impact on local friction and lubrication.

In a subsequent study, Wang et al. extended the coupling diffusion model to describe molecular surface diffusion on other solid and soft surfaces, including biomembranes, with different interfacial dynamic characteristics.[94] In this general model, the coupling of molecule diffusion with underlying surface dynamics can be described by

display math(9)

where τ is the characteristic time of molecule diffusion at the surface, τm is the characteristic time of thermally activated Brownian dynamics of absorbed molecules, τs is the characteristic time of the dynamics of the underling surface, and math formula corresponds to the coupling degree between τs and τm. To qualitatively verify this model, the authors intentionally prepared hard, soft, and fluid surfaces and selected same molecule probes to ensure that the interactions between the probe molecule and three distinct surfaces were of the same origin. Table 1 summarizes the results. Despite the strongest attraction between the probe molecule and the self-assembled monolayer of octadecyltrioethylsilane (OTE) on a solid substrate, the probe diffusion on the OTE hard surface was not the slowest. It was surprising to observe that the surface diffusion of probe molecules on soft PNIPAM brushes or a fluid α-PC lipid bilayer appeared slower than on the hard OTE surface. Such an observation can be explained by the coupling diffusion model. The interfacial interaction for probe molecules on fluid lipid bilayer surfaces derived from the experimental results using eq (9) agreed well with the reported theoretical value, further supporting the generality of this coupling model.

Table 1. Static Water Contact Angles and Surface Diffusion Coefficients of R6G and R123 on Quartz Coverslips Coated with OTE Monolayer, α-PC Lipid Bilayer at 25 °C, and PNIPAM Brush Layer at 25 and 45 °C
  PNIPAM Brush (h = 2.5 nm, σ = 0.62 chains/nm2) 
 OTE SAM (T = 25 °C)(T = 25 ° C)(T = 45 ° C)α-PC Lipid Bilayer (T = 25 °C)
  1. Reproduced from Ref. 94, with permission from the Royal Chemical Society.

Static water contact angle (°)110 ± 155 ± 272 ± 2∼2–5
D of R6G (µm2/s)10.9 ± 2.27.2 ± 1.11.8 ± 0.56.3 ± 0.7
D of R123 (µm2/s)21.9 ± 2.7(No adsorption)13.6 ± 1.933.9 ± 2.4

Compared with silica particles or small molecules, macromolecules (polymers) diffuse on polymer brush surfaces in a much more complicated manner. Unlike some nanocolloidal particles or molecules whose structure is isotropic and static, polymer chains at the interface adopt either a pancake-like or loop-train-tail conformation.[95, 96] The adsorption of polymers at the interface often involves multiple contacting sites along a polymer chain, and the polymer surface diffusion is a result of the cooperative motion of such adjacent sites. Because the conformation of a polymer chain is not fixed but fluctuates, the coupling between the thermal activation and the dynamics of underlying polymer brush chains would be also affected by the dynamics of absorbed polymers themselves. A complicated scenario is visualized for the diffusion of adsorbed polymers on polymer brush surfaces at a single-molecule level.[44] Wang et al. used FCS to study the diffusion of a single polyelectrolyte chain, poly(2-vinyl pyridine) (P2VP), on thermo-responsive PNIPAM brushes.[44] As shown in Figure 5, the most striking finding was that the diffusion coefficient, D, of P2VP exhibited a nonmonotonic dependence on the temperature: D increased from ∼2 μm2/s at T = 15 °C to ∼ 6 μm2/s at 30 °C, at both of which the PNIPAM surface was hydrophilic, and then continuously decreased to ∼4.5 μm2/s at 40 °C, at which the PNIPAM surface was hydrophobic. This result may be partially attributed to the decrease of water viscosity at T < 32 °C and the hardening of PNIPAM brush surface at T > 32 °C. However, the two-fold increase in D could not be fully explained by the effect of water viscosity (η), as η only decreases about 30% from T = 15 to 30 °C.[97] The significant increase of D was not observed in other simple systems such as the diffusion of silica particles or small molecules on PNIPAM brushes.[42, 91] It was speculated that the reason for this may be the high flexibility of absorbed P2VP chains. Because hydrodynamic coupling greatly contributed to the interaction between P2VP and the PNIPAM brush,[98, 99] the weakened hydrodynamic coupling due to the increased T could result in a decrease in the interaction between P2VP and the PNIPAM brush. D inversely depended on brush thickness, which was similar to the diffusion of small molecules on PNIPAM brushes.[44] The mechanism clearly pointed to the retarded dynamics of the PNIPAM brush surface with the increased thickness and resulting polydispersity in segment density.

Figure 5.

(a) A schematic illustration of the study of the diffusion for a polymer, P2VP (Mn = 109,800 gmol−1), on a PNIPAM brush interface. (b) The measured surface diffusion coefficient, D of P2VP as a function of T on PNIPAM brushes of three different thicknesses: 16.0 nm (O), 49 nm (Δ), and 90.0 nm (□). (Reproduced from Rref. 44, with permission from the American Chemical Society.)

In addition to thermo-responsive polymers such as PNIPAM, another type of “smart” polymer is the polyelectrolyte, which is pH- or ionic strength- or both-responsive. The polyelectrolyte brush surface generally exhibits a high osmotic pressure, which endows some unique and unusual features.[10, 100] Using FCS, Zhang et al. studied the diffusion of small ionic fluorescence probe molecules on polyelectrolyte brushes with opposite charges.[101] For both of the two systems examined in their work—a negatively charged sulforhodamine B probe on a positively charged poly([2-(methylacryloyloxyl)ethyl] trimethylammonium chloride) (PMETAC) brush surface, and a positively charged R6G probe on a negatively charged poly(sodium polystyrene sulfonate) (PSSNa) brush—strong photobleaching was observed even at the minimal low laser intensity of 0.15 × 108 W/m2 before reaching a steady fluorescence intensity.

This suggested that, due to a strong electrostatic attraction, a large number of ionic probes absorbed onto the surface-tethered polyelectrolyte brush chains, resulting in a nearly zero or very low mobility of D < 0.01 μm2/s. This observation was distinct from the case of molecular diffusion on neutral PNIPAM brushes, in which no photobleaching was measured.[42, 44] This indicated that photobleaching resulted from the trapping of molecules in the polyelectrolyte brush layer, while molecules at the top of the brush layer contributed residual fluorescence intensity. Zhang et al. concluded that the FCS-measured diffusion coefficient was associated with those ionic probes atop the polyelectrolyte brush.

For the dynamics of ionic probe molecules atop the oppositely charged polyelectrolyte brush surface, Figure 6 shows that D decreased as the NaCl concentration increased. More intriguingly, in comparison to the critical NaCl concentration for the onset of the decrease in the polyelectrolyte brush thickness, the critical salt concentration for the onset of decreasing D was three orders of magnitude lower. The decrease of D with the increasing salt concentration was contrary to the anticipation that the electrostatic attraction between the ionic probe and the polyelectrolyte brush would be weakened due to the screening effect. Zhang et al. argued that the decrease of D was possibly due to the penetration of ionic probe molecules from the brush aqueous interface to the inner part of the polyelectrolyte brush layer. The increase of added salt concentration actually led to a higher osmotic pressure inside the brush layer so that the oppositely charged probe molecules, which could act as the counterions to polyelectrolytes, were driven to the brushes, resulting in the retardation of their diffusive dynamics.

Figure 6.

(a) A schematic illustration of the study of the diffusion of an ionic molecular probe on an oppositely charged polyelectrolyte brush interface. (b) Measured D (left y-coordinate axis) of R6G on PMETAC brushes and measured brush thickness, d (right y-coordinate axis) of a solution-immersed PMETAC layer as a function of NaCl concentration. (c) Measured D (left y-coordinate axis) of sulforhodamine B on poly(styrene sulfonate sodium) (PSSNa) brushes and measured brush thickness, d (right y-coordinate axis) of solution-immersed PSSNa layer as a function of NaCl concentration. (Reproduced from Ref. 101, with permission from the American Chemical Society.)

However, this scenario should be taken cautiously by considering how the counterions were distributed near polyelectrolyte chains. Because the size of ionic probes was larger than other simple counterions present in the system, such as Na+ or Cl, it could also be anticipated that the addition of salt could lead to the release of some ionic probes due to counterion exchange. As previously mentioned, a large number of ionic probes could adhere to oppositely charged polyelectrolyte brush chains, so a spatial distribution of ionic probes could be expected, which could be at least qualitatively evaluated by measuring the fluorescence intensity inside the polyelectrolyte brush layer at varied salt concentrations, probably via the TIRF approach.

Regarding the critical salt concentration for the slowing-down of the probe surface diffusion, which was observed as lower than that for the decrease of polyelectrolyte brush thickness, the authors attributed it to the nonuniform collapse of the polyelectrolyte brush chain: the outer portion of the brush collapsed at a lower salt concentration than the inner portion. However, questions remain about some perplexing observations of ionic molecular diffusion on oppositely charged polyelectrolyte brush surfaces. For instance, the measured D of sulforhodamine B on the PMETAC brush is ∼22 μm2/s, which was in sharp contrast to D ∼0.55 μm2/s for R6G on the PSSNa brush. What was the origin for such a striking difference in measured diffusion coefficients between two highly similar systems?

Yanagishima et al. studied the diffusion of poly(ethylene glycol) (PEG)-coated colloidal particles on λ-DNA brushes.[102] Using SPT, they found that the D of silica particles of diameter d = 1.16 μm and coated with a ∼2 nm thick PEG layer on a λ-DNA brush varies largely from 0 to 0.25 μm2/s. The modification of the colloid surface was completed by treating the glass particles in the aqueous solutions of poly-L-lysine-PEG at varied pH values. Because the charge density of the bare silica surface was tunable by pH, the surface coverage of the PEG coating layer and the PEG chain conformation was dependent on the pH of the incubating solution. The authors found that the PEG-coated silica particles prepared at different pH values showed varied affinities to the DNA surface, even though the electrostatic environment of the λ-DNA brush surface was kept the same. In the pH range from 7.0 to 9.0, when the incubation pH was higher, the diffusivity of colloid increased and fewer PEG-coated particles were stuck to the surface. It was confirmed that at a higher incubation pH, the zeta potential of the silica particle surface was higher, leading to a denser PEG coating layer. Because the particle affinity resulted from the hydrophobic interaction between unpaired end segments of λ-DNA and hydrophobic patches on the particle surface that are not covered by PEG chains, a denser PEG layer would conversely reduce the attraction due to the enhanced steric effect. When the incubation pH was 9.0, the observed D = 0.25 μm2/s at the DNA surface was the same as that of a silica particle in a bulk solution, exhibiting a “nonfouling” effect on the PEG-coated silica particle surface. In contrast, when the incubation pH was decreased to 7.0, most particles adhered on the surface. This work has important implications for the choice of protocols for the surface modification of colloidal particles using polymers. It also sets a good example of using the diffusivity measurement to study intermolecular interactions in complex polymer and colloidal interfaces.[103]

ADSORPTION OF MOLECULES ON THE POLYMER BRUSH SURFACE: ATOP OR INSIDE THE BRUSH LAYER?

So far, this review has considered work on the diffusion of molecules or colloids at the polymer brush-liquid interface, mainly atop the brush layer. However, an intimately related question needs to be answered: do the adsorbed molecules or colloids stay atop the polymer brush layer or inside it? For colloids or macromolecules, the answer is quite obvious considering that their size is typically larger than the spacing between two neighboring polymer brush chains. However, for small molecules that are comparable in size to, or smaller than, the spacing between two neighboring polymer brush chains, the answer is not so straightforward. The penetration of molecules into a polymer brush surface layer is dictated by the total free energy change in the system including three major contributions:

display math(10)

where math formula is the enthalpic contribution, math formula is the mixing entropic contribution, and math formulais the confinement energy of polymer brush chains that result from the trapping of adsorbed molecules. For embedding a molecule to a polymer brush layer, math formula could be negative or positive, relying on the relative strength of molecule–polymer interaction versus molecule–solvent interaction. math formula is always negative and favors molecule–polymer mixing, and consequently molecular trapping. math formulais always positive but highly depends on the grafting density of polymer brushes. If the size of cavities inside the polymer brush layer is lower than the molecular size, the adsorption of molecules inside the polymer brush layer can cause a local bending of the surrounding polymer brush chain, resulting in a significant increase in the total free energy. Because the volume of the polymer brush layer is usually much smaller than that of the bulk solution, the mixing entropy contribution to the total free energy change is generally negligible. The occurrence of adsorbed molecules inside a polymer brush layer is thus dictated by the competition between the math formula and the math formula. Different systems could be classified into three distinct categories:

  1. When the grafting density of the polymer brush is sufficiently high and the molecule–polymer attraction is weak, the math formula term dominates the total free energy so that the embedding of molecules inside a polymer brush layer is energetically unfavorable. One example is that the adsorption of R6G or R123 mainly occurs atop, not inside, a PNIPAM brush surface of a high grafting density greater than 0.33 chains/nm2, equivalent to a spacing of smaller than 1.74 nm between two adjacent brush chains. The adsorption of R6G or R123 on a PNIPAM surface is driven by the weak hydrophobic attraction of approximately 1–2 kT.[42]
  2. Conversely, when the molecule–polymer attraction is strong and the grafting density is low, the math formula term dominates the total free energy so that adsorbed molecules inside a polymer brush layer are energetically favored. This is the common case for the adsorption of ionic molecules on oppositely charged polyelectrolyte brushes. For instance, it was reported that sulforhodamine B were embedded in PMETAC brush thin films of a low grafting density at 0.1 chains/nm2.101
  3. The situation becomes complicated between categories 1 and 2 if (a) the molecule–polymer attraction is strong and the grafting density of polymer brushes is high, or (b) the attraction is weak and the grafting density is low. For both cases (a) and (b), whether adsorbed molecules are embedded inside a brush layer is determined by the relative strength of the intermolecular interaction and the math formula. Because the math formulastrongly depends on the grafting density, it is relatively weak when the spacing between two neighboring brush chains is larger than the molecular size. Yet, it increases exponentially with the increasing grafting density when the brush spacing becomes smaller than the molecular size. This is the exact reason why a R6G of ∼1.0 nm in diameter was found to be embedded into a PNIPAM brush layer of grafting spacing ∼3.1 nm between two neighboring brushes, but adsorbed atop denser PNIPAM brushes.[42] For polyelectrolyte brushes, the grafting density is usually lower than that of neutral polymer brushes.[101] Therefore, because of the strong electrostatic attraction and the low grafting density of polyelectrolyte brushes, small ionic molecules tend to penetrate into oppositely charged polyelectrolyte brush layers.

Using a theoretical approach, the adsorption of molecules on the polymer brush surface mainly focused on large entities including proteins and nanoparticles. Self-consistent field (SCF) theory and scaling arguments were developed to understand the adsorption mechanism of proteins on polymer brush surfaces.[104, 105] Increasing grafting density and the degree of polymerization can lead to the decreased amount of adsorbed protein, and hydrophilic polymers can prevent adsorption much better than hydrophobic polymers. It was also found that upon weak inclusion, the free energy scales had the particle size, d as math formula (d is the particle size), whereas for strong inclusion, the scaling became math formula.[106] In a recent Monte Carlo computer simulation study, it was suggested that the surface also contributes to the inclusion free energy and becomes increasingly important at low grafting densities.[107] Recent molecular dynamics simulations on the inclusion free energy of nanoparticles in polymer brushes reported that a universal scaling regime was restricted to very low grafting densities, and the scaling factor of free energy on particle size varied between 2 and 3 for varied grafting densities.[108]

The total adsorption energy of molecules on polymer brushes is the sum of polymer–molecule interaction and the energy penalty due to the polymer chain confinement. The measurement of the adsorption energy of molecules on a polymer surface from solution is challenging due to the paucity of experimental techniques. Force-based techniques, including surface forces apparatus (SFA) and AFM, are among the few techniques capable of measuring molecule–surface interactions.[109-114] For polymer brushes, previous experimental results have discovered the weak attractive interaction and low adsorption energy for molecules at the polymer brush interface, suggesting good antifouling properties of polymer brushes. The molecule–polymer brush interaction also shows strong dependence on the structure of polymer brush chains, which can be controlled by grafting density, thickness, and solvent quality.

Regarding the distribution of adsorbed molecules on polymer brush chains, the density of segments in the polymer brush along the direction normal to the substrate is not uniformly distributed. The segment density math formula is the highest in the region adjacent to the substrate and decreases with the distance away from the substrate by following a theoretical prediction,

display math(11)

where math formula is the segment density immediately adjacent to the substrate, z is the vertical distance away from the substrate, and h is the swollen brush thickness in a liquid medium.[115-118] An intermediate dense polymer layer may exist between the bulk solution and the densest brush region near the substrate, indicating an interfacial layer with a finite thickness favoring molecular adsorption. Thus, molecules could stay in the interfacial layer, not necessarily trapped deep inside the brush layer.

Experimentally determining the location and distribution of absorbed molecules on polymer brushes is particularly challenging, considering that the associated length scales are largely beyond the resolution of traditional optical measurements. Neutron reflectometry (NR) and X-ray reflectometry (XR) are among the few techniques with an Å-level resolution suitable for such experimental investigations,[119, 120] and they have been used to study the density profile of polymer brushes at varied solvent conditions and monitor the LCST behavior of hydrated PNIPAM brushes.[121, 122] Recently, Elliott et al. utilized NR to study the adsorption and distribution of a small drug molecule, isoniazid, onto PNIPAM brushes at varied temperatures.[123] They found that the concentration of isoniazid in a fully swollen PNIPAM brush was ∼14% larger than that in the bulk solution, whereas the concentration in the collapsed brush was doubled compared to the bulk, even though water was expelled. They also pictured the density profile of the PNIPAM brush layer with or without the loading of isoniazid from their NR results. Figure 7 illustrates their main discoveries, which demonstrated that the segment density of the PNIPAM brush near the substrate was higher than that near the brush-water interface. Isoniazid was found to penetrate into the PNIPAM brush layer, but it was not partitioned into the well-defined layers of high segment density adjacent to the substrate. The observation of embedded isoniazid molecules in PNIPAM brushes was consistent with the finding of R6G penetration into PNIPAM brushes of low grafting density about 0.13 chains/nm2.42 It was clearly demonstrated that NR or XR can provide detailed structural information on the location and distribution of molecules absorbed on polymer brushes.

Figure 7.

A schematic depiction of the configurations of PNIPAM brush and the distribution of one drug molecule, isoniazid inside the polymer brush derived from NR measurements. The polymer brush thickness and root-mean-square roughness from NR are reported on the left and right corners of each sample schematic. Isoniazid molecules are depicted by red circles, and the volume percent of isoniazid inside the brush is provided at each temperature. (Reproduced from Ref. 123, with permission from the American Chemical Society.)

DIFFUSION OF MOLECULES INSIDE POLYMER BRUSHES

As previously mentioned, when the attraction between a molecule and polymer segments is strong and the grafting density is low, the embedding of molecules into polymer brushes is energetically favored. This is the common scenario for the adsorption of charged molecules onto oppositely charged polyelectrolyte brushes. For years, polyelectrolyte brush thin films have attracted interest due to their potential energy storage application, and it is fundamentally important to understand the transport behavior of charged molecules or ions in polyelectrolyte brush networks.[32-36] Using FCS, Reznik et al. studied the diffusion of R6G inside PSSNa brushes of ∼50 nm thick in the dry state without a known grafting density.[124] They measured the D of R6G in PSSNa brushes at about 0.05–0.09 μm2/s, much lower than that in the bulk or in neutral polymer brushes such as PNIPAM brushes.[42] A fast decay that typically corresponds to the Brownian diffusion of R6G in solution was not observed in their FCS autocorrelation curves, indicating that most R6G molecules stay inside the PSSNa brush layer. Compared to the reported D of 6–10 and 0.5 μm2/s for R6G atop PNIPAM[42] and PSSNa[101] brushes, respectively, the much lower D measured in this study[124] was attributed to the slow motion of R6G inside the PSSNa brush layer. D increased from 0.065 to 0.34 μm2/s when the pH was decreased from 7.0 to 3.5. Decreasing pH, or increasing ionic strength, imposed two effects on the PSSNa brush layer: (1) The viscosity inside polymer brush increased due to the increase of brush density with weakened electrostatic repulsion between PSSNa chains, and (2) The electrostatic attraction weakened between the R6G and PSSNa brush chain. Reznik et al. argued that pH-responsive diffusion characteristics were dominated by the change in the R6G-PSSNa electrostatic interaction, yet the effect from the variance in brush density was negligible.

Reznik et al. recently combined single-molecule polarization with FCS to study the transport mechanisms of molecular ions within polyelectrolyte brushes.[125] They used circularly polarized excitation light to determine the time-dependent change in the orientation of R6G in PSSNa brushes by using a reduced linear dichroism. This tool has been previously used to evaluate the rotational dynamics of molecules embedded in glassy materials where rotational diffusion time scale was on the order of hundreds of milliseconds to tens of seconds.[126, 127] Because the temporal resolution of this technique is about 1 ms, only the slow rotational dynamics of probe molecules could be recorded. The most interesting result they reported is the heterogeneous transport of molecular ions in polyelectrolyte brush systems. Three distinct modes of molecule diffusive motion existed in the R6G-PSSNa brush system: (1) restricted, that is, slow or stationary, rotational diffusion with or without translational diffusion; (2) translational diffusion with fast rotation (faster than the 1 ms time scale); and (3) full adsorption, in which neither translation nor rotation was observed within the time window comparable to the instrument temporal resolution. Among the three dynamic modes, the restricted orientation combined with the occurrence of quick switching between different polarization states suggested the existence of local minimum binding energy between R6G and PSSNa brushes, albeit the exact mechanism remains unclear. We instead speculate that the defects possibly present in PSSNa brushes could have been responsible for their observation. Interestingly, a significant increase of the R6G transport rate in PSSNa brushes was observed when the pH was lowered from 7.0 to 3.5, yet little interpretation was provided. We instead speculate that the increase of R6G diffusion as pH < 3.5 could have been the result of the change in the electrostatic potential of PSSNa brush chains. Because the concentration of local protons in the vicinity of a polyelectrolyte chain was always different from that in the bulk solution due to the distinct electrostatic environment near a polyelectrolyte chain, the ionization constant, pKa or pKb, of respective polyacid or polybase chains is usually higher than that of their corresponding monomers and strongly depends on the polyelectrolyte materials and solution parameters, such as polyelectrolyte molecular weight, solution pH, and ionic strength, which all affected the counterion condensation of polyelectrolytes.[128-132] Furthermore, it was observed that poly(acrylic acid) brushes had an even higher pKa than that of the polymer in the bulk,[133] due to the high osmotic pressure causing a strong condensation of counterions on polyelectrolyte chains. In a similar manner, the pKa of PSSNa brushes could be much higher than that of its sulfonic acid monomer (pKa = 1).[134] When the pH was below 3.5, PSSNa brushes became less ionized, which can promote the diffusion of R6G molecules inside less charged PSSNa brush layers.

In a subsequent study, Reznik et al. used three-angle polarization-resolved fluorescence detection method to determine the orientation of R6G in PSSNa brushes,[135] as depicted in Figure 8(a). The fluorescence emission of R6G in PSSNa brushes was recorded by three detectors at right angles, and the molecular orientation was inferred from the relative ratios among the measured fluorescence intensities by each detector. Representative data for a single R6G diffusion event in the polymer brush are shown in Figure 8(b), where two types of molecular motions are classified. Fast rotational dynamics, evidenced by the equal signals detected by all three channels, is termed as “Type 1.” Restricted rotational motions, marked by the clear inequality detected among the three channels and over a long-standing time period, is designated as “Type 2.” They calculated the distributions of azimuthal and polarized angles for Type 1 and Type 2 by analyzing a 5-min long trajectory of R6G diffusion. Using R6G embedded in Poly(methyl methacrylate) (PMMA) film as the control experiment, the angle resolution limited by the experimental noise was estimated to be 5°. As shown in Figure 8(c), the azimuthal angle distribution for Type 1 was relatively smooth and peaked at ±45°. Along with the polar angle centered at 23°, the results clearly indicated that Type 1 corresponded to the diffusion with a free rotation. Conversely, the clustering of azimuthal angles for Type 2 suggested a strong preferential orientation for R6G molecules interacting with the PSSNa brush. In contrast, such preferential orientation was not observed for R6G imbedded in an isotropic PMMA polymer film. Thus, the observed orientational preference could be related to the orientational direction of surface-tethered PSSNa chains. This was first time that anisotropic diffusional and rotational dynamics of molecules in a polyelectrolyte brush layer were quantified experimentally. For broad applications, this three-angle polarization-resolved fluorescence method could have great potential for evaluating the diffusive dynamics and molecular transport in a variety of structurally ordered complex systems.

Figure 8.

(a) A scheme of the polarization-resolved fluorescence detection with its coordinate axes depicted with R6G and the emission dipole. The fluorescence emission of R6G was recorded by three detectors at X, Y, and Z directions, and the molecular orientation was inferred from the relative ratios among the measured fluorescence intensities. (b) A blow-out (bottom panel) of the measured time-dependent photon counts (top panel) for a single-molecule transport through the laser focal volume, showing the intensity traces acquired by three detectors. The region labeled as Type 1 indicates a nonoriented diffusion with rapid rotation, whereas the region labeled as Type 2 indicates an oriented diffusion with restricted rotation. (c) Probability distribution of R6G azimuthal angle, Θ (left panel) and polar angle, Φ (right panel), sampled in a polymer brush and measured over all diffusion events during a 5-min period. The two types of diffusion, the nonoriented mode as Type 1 and the oriented mode as Type 2, are shown in the separate blue and red histograms, respectively. The polar angle distributions can be well-fit by a Gaussian. The azimuthal angle distributions suggest the presence of a number of subpopulations and can be fit by up to four Gaussian curves without converge. (Reproduced from Ref. 135, with permission from the American Chemical Society.)

Although the combination of FCS and single-molecule polarization is useful in examining the diffusive and orientational dynamics of fluorescence probes in polymer brushes, it lacks spatial resolution and is incapable of detecting spatial heterogeneity in translational diffusions. Using SMT, Elliott et al. investigated the diffusion of small fluorescent probes inside PNIPAM brushes of an estimated grafting density of ∼0.1 chains/nm2 and a swollen brush thickness of 115 nm in deionized water, which is comparable to the excitation depth in a TIRF microscopic setup.[90, 136] Figure 9 shows representative results. The mean square displacement (MSD) of two probe molecules showed a nonlinear dependence on lag time, indicating a non-Brownian motion of probes in PNIPAM brushes. Moreover, the molecular motions could be decoupled into two distinct Brownian motions of fast and slow rates. For example, the trajectory of 1,1′-dioctadecyl-3,3,3′,3′-tetramethylindocarbocyanine (DiIC18) probe exhibited a long-time period in an “arrested” confinement state with a small diffusion coefficient of Dconf = 0.024 μm2/s and also short time periods in a highly mobile state with a fast diffusion coefficient of Dfree = 1.74 μm2/s. Consistent with the observation by Reznik et al., this result was possibly the result of the chemical or spatial heterogeneity in the polymer brush layer. The result also indicates that the ensemble-averaged D with either intermittent diffusions or multiple populations to derive a simple diffusive dynamic could neglect some true characteristics of molecular motions inside polymer brushes. However, because the analysis of MSD is highly model-dependent, that the selection of parameters for curve fitting is critical. To accurately differentiate between intermittent states of diffusion, Dfast should be at least 10 times larger than Dslow.[105] Curve-fitting using multiple components can usually lead to more accurate results, while two-component-fitting may not be ideal for the system despite its advantage over the one-component-fitting. Elliott et al. tracked the fluorescence probes in the collapsed PNIPAM brush layer at solution temperatures greater than its LCST.[137] Of particular interest, the probe motion in the collapsed PNIPAM brush layer appears to be arrested in localized confinement areas, showing a high fraction of confined segments and a greater propensity to undergo larger jumps between confined zones. This observation also implies an increase in structural heterogeneity of polymer brush film upon chain collapse.

Figure 9.

The ensemble-averaged diffusion coefficient for (a) “free” and (b) “confined” portions of a probe from the tracked trajectories analyzed based on MSD. The largely different scales plot in the y-coordinate axis between (a) and (b) are noteworthy. (c) Diffusion coefficients of fast and slow subpopulations in the lateral diffusion as determined through different confinement degree from (a) and (b). The percentage of measured steps in each category is labeled next to their corresponding columns with their ensemble-averaged diffusion coefficients. (Reproduced from Ref. 136, with permission from the Royal Chemical Society.)

Besides fluorescence-based experimental techniques, another method to measure the molecular diffusion in polymer brushes is electrochemical impedance spectroscopy introduced by Gervasi and coauthors.[138] In principle, the measured impedance of polymer brush-modified electrodes is correlated to the diffusion of redox probes. Gervasi et al. derived a model to correlate the measured impedance with the double-layer capacity, solution conductivity, and diffusion coefficient of redox probe. Using their method, Gervasi et al. investigated the diffusion of K3[Fe(CN)6]/K4[Fe(CN)6] redox probe in PMETAC and PNIPAM brushes. With PMETAC brushes, the D of oppositely charged redox probe was measured to be 4–8 × 10−6 μm2/s, which was about 8 orders lower than that in the bulk solution. This value was also much lower than the measured D, in the range of 0.065–0.34 μm2/s, of R6G in the PSSNa brush by FCS. A significant difference existed between the D of the redox probes measured in math formula and other electrolytes, including Cl and math formula, at the same ionic strengths. The unique effect of math formula could be attributed to the specific interaction between the quaternary ammonium group and math formula. Regarding the diffusion of the K3[Fe(CN)6]/K4[Fe(CN)6] probe in neutral PNIPAM brushes, Gervasi et al. observed a strong grafting density dependence: in the PNIPAM brushes of high grafting densities, the measured D of the redox probe was 7 orders of magnitude smaller than that in the bulk solution. Yet in the PNIPAM brushes of low grafting densities, the measured D was the same as that on the self-assembled monolayer of initiators before brush synthesis.[139] It seemed that the strong dependence of D on grafting density originated from the blocking effect of active sites on Au electrode surfaces for the impedance measurements. The pinholes or discontinuity in the thiol monolayer on Au surfaces could have served as short paths for the conduction of electrons, so the electric properties of subsequently grafted polymer brushes could have been exposed for the impedance detection only when such pinholes were blocked. Thus, the D reported in this work was indirectly measured via electrochemical impedance spectroscopy. Caution must be taken on the premises of the simplified physical model before retrieving the diffusion data. This method is limited to broad applications because of its restrictions on conductive substrates and redox probes.

IMPLICATIONS OF DYNAMIC CHARACTERISTICS AND APPLICATIONS OF POLYMER BRUSHES

The study of molecule diffusion atop or inside polymer brushes provides insight into some extraordinary material properties of polymer brushes, opening new avenues for some emerging environmental, energy, and biomedical applications.

Antibiofouling of Polymer Brushes

Polymer brushes have been increasingly used in microfluidic devices or lab-on-chips as antibiofouling coatings, where surface effects often play critical roles due to their high surface-to-volume ratio in such systems.[9, 140] Although most biomacromolecules are depleted from hydrophilic polymer brush layers, coexisting small molecules in biological solutions can interact with polymer brushes nontrivially. For example, in some biochips, drug molecules, which are anticipated to function cooperatively with biomacromolecules, can be attracted and embedded in the polymer brush layer.[123, 141, 142] The controlled adsorption and transport of small molecules on polymer brushes thus becomes increasingly important in the fabrication of microfluidic devices with the best antibiofouling performance. The adsorption of proteins or nanoparticles on polymer brushes is dependent on the grafting density and thickness of polymer brushes.[107, 143-145] Given that polymer brushes can be produced with a wide variety of chain chemistry and architectures, this approach of controlling the adsorption of single molecules by polymer brush nanostructures is appealing to those interested in fabricating biochips with minimal undesirable biofouling capability and maximal specific biorecognition functionality.

Polymer Brushes as Potential PEMs

Nafion, a commercial polyelectrolyte product of DuPont Company, and its related and modified polymer derivatives have been used as PEMs in fuel cells for sustainable energy resources for years.[146] The PEM currently used in fuel cells is a semipermeable membrane to conduct protons while being impermeable to gases such as oxygen or hydrogen.[147, 148] Desirable material properties for PEMs include high charge storage and mobility, low rates of degradation, and low cost. Nafion membranes exhibit a high charge mobility and a low tendency to degrade. However, as a derivative of perfluorinated polymer (Polytetrafluoroethylene, PTFE), Nafion has an expensive material cost and raises environmental concerns.[119] Polyelectrolyte brushes have long been considered as potential alternative materials for energy storage and conversion. Related to the currently targeted improvement in PEM design, polyelectrolyte brush films show great promise in that both polyelectrolyte nanostructures and local solvation dynamics can be tuned and optimized to facilitate ion transport.[149] Recent studies of ion transport in polyelectrolyte brush films shed light on the understanding of charge transport in confined polyelectrolyte systems. Although it is recognized that fluorescent probes are larger than protons shuttled in fuel cells, the study of intrabrush solvation of single-counterion probes provides a valuable approach to examine disparate hypotheses on how ions and charges are transported inside polyelectrolyte films. It was recently reported that both electrostatic interaction and the steric effect strongly influence the transport of counterion probes inside polyelectrolyte brushes.[43] The diffusion of probes can be described as a combination of “free” translational motion with unrestricted rotation and orientational hopping with restricted rotation. More importantly, the orientational dynamics of ion probes can exhibit a unique preference to the orientation of individual polyelectrolyte brush chains. Such results give insight into the design and synthesis of polyelectrolyte brushes as potential PEMs in fuel cells with improved charge transfer rates. To further benefit the design of polyelectrolyte brush films as PEMs, future studies should investigate the relative contribution of axial versus lateral transport as a function of brush grafting density, thickness, and hydration degree to optimize the charge storage and release properties.

Lubrication of Polymer Brushes

Some polymer brush surfaces, particularly polyelectrolyte ones in aqueous media, exhibit superlubricity, which contributes to the strong hydration of polymer brushes in good solvent conditions.[26] In aqueous systems, as water molecules associated with hydrophilic polymer chains can rapidly exchange with free water molecules in the bulk, the polymer brush layer is expected to be lubricious at shear rates lower than the water-exchange rate due to high osmotic repulsion between polymer brushes.[150] Most studies on the lubrication properties of polymer brushes were conducted by a force-based measurement such as SFA or AFM. However, ensemble-averaged friction measurements can mask unexpected and unusual dynamic events of molecules at polymer brush-liquid interfaces. For example, spatial and temporal-resolved FCS measurements with nonadsorbing fluorescent probes embedded in confined fluids between two solid surfaces have revealed significant dynamic heterogeneity in the confined fluid: the diffusion coefficient of probes near the center of fluid-lubricated surface contact is by orders of magnitude slower than that near the periphery.[151] It has been demonstrated that the dynamics of polymer brushes is coupled with the diffusion of molecular probes interacting with the brushes, and thus the faster dynamics of polymer brush chains can effectively promote the diffusion of probes.[42, 94] Conversely, the slow dynamics of polymer brush chains could retard the molecular surface diffusion and increase local friction coefficient, which may be correlated to the recent observation of the brush thickness dependent friction coefficient on the polymer brush surface.[42, 44, 152] Accordingly, the modulation of the water-exchange rate near polymer brushes for superlubricity could be sought by altering the dynamics of polymer brushes in a similar manner. Future single-molecule studies on polymer brushes in response to the hydrated water dynamics could lead to a deeper understanding of the mechanism of the superlubricity of polymer brush layers in liquid media.

CONCLUSIONS AND PERSPECTIVES

This review summarizes recent experimental investigations of molecular diffusion at polymer brush interfaces mainly by single-molecule spectroscopic and microscopic techniques and highlights some new understandings and future research opportunities. Single-molecule fluorescence-based techniques, such as FCS and SMT, have been demonstrated to be sensitive and powerful in examining molecule dynamics in various complex systems. In polymer brush systems, the diffusion of molecules is intrinsically coupled with the dynamics of the underlying polymer brush chain due to various intermolecular interactions, no matter whether the adsorbed molecules stay atop the brush-solvent interface or are embedded into the brush layer. For molecules embedded into the polymer brush layer, their dynamics is highly affected by the structural and dynamic heterogeneity of underlying polymer brushes and can be decoupled to “free” and “restricted” rotational motions in addition to retarded translational diffusion. The physical insights derived from single-molecule studies at polymer brush interfaces can further deepen the understanding of some unique and unusual material properties of polymer brushes as emerging functional materials for wide applications including antibiofouling coatings, energy storage membranes, and superlubrication.

The studies surveyed in this review mostly involve fluorescence-based techniques, in which the fluorescence probes are often bigger than solvent molecules and charges. Measurements of molecule diffusion inside polymer brushes have raised ancillary questions on how molecules are oriented and arranged with polymer brushes of varied nanostructures. Scattering techniques with high spatial resolution, such as X-ray or neutron diffraction and reflectivity methods, can address this puzzle.[153, 154] Another research opportunity is centered on the dynamics of water molecules or protons inside charged polymer brushes, because the exchange of water molecules with polymer chains is vital to the solvation and charge transport of polymer brushes in their applications. The pulsed-field gradient nuclear magnetic resonance (PFG-NMR) technique might be one of the few experimental tools capable of examining the dynamics of interfacial water near a polymer brush interface.[155, 156]

ACKNOWLEDGMENT

B. Jing and Y. Zhu acknowledge the financial support from the US Department of Energy, Office of Basic Sciences, Division of Materials Science and Engineering under grant No. DE-FG02-07ER46390.

Biographies

  • Image of creator

    Shengqin Wang received his B.S. in Chemistry from Wuhan University (2002) and Ph.D. in Polymer Physics and Chemistry from the Institute of Chemistry, Chinese Academy of Sciences (2007). He is currently a research scientist in the Institute of Materials Research and Engineering of Singapore. His research interest focuses on the polymer interface and functional coatings.

  • Image of creator

    Benxin Jing received his B.S in Polymer Science and Engineering from Zhengzhou University (2002), M.S in Materials Engineering from Beijing University of Chemical Technology (2005), and Ph.D. in Polymer Physics and Chemistry from Institute of Chemistry, Chinese Academy of Sciences (2009). Since 2009, he has worjed as a postdoctoral research associate in Prof. Zhu's group at the University of Notre Dame. His research interest focuses on lipid and polymer membranes and nanocolloid-lipid complexes.

  • Image of creator

    Yingxi Zhu received her B.S. in Chemical Engineering and Polymer Science from Tsinghua University in 1997 and a Ph.D. in Materials Science and Engineering from the University of Illinois at Urbana-Champaign in 2001. Currently she is an associated professor in the departments of Chemical and Biomolecular Engineering, and Chemistry and Biochemistry at the University of Notre Dame. Her research focuses on soft matters and interfacial science.