Effect of Substrate on the Mechanical Response and Adhesion of

Nov 27, 2012 - ... Mathematical Sciences, Murdoch University, Murdoch, WA 6150, Australia ... Kamron Ley , Andrew Christofferson , Matthew Penna , Dav...
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Effect of Substrate on the Mechanical Response and Adhesion of PEGylated Surfaces: Insights from All-Atom Simulations George Yiapanis,† David J. Henry,‡ Shane Maclaughlin,§ Evan Evans,§ and Irene Yarovsky*,† †

School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, GPO Box 2476, Victoria 3001, Australia School of Chemical and Mathematical Sciences, Murdoch University, Murdoch, WA 6150, Australia § BlueScope Steel Research, Port Kembla, Australia ‡

S Supporting Information *

ABSTRACT: Responsive surfaces show potential for many applications; however, the molecular mechanisms of their responsive behavior are often dependent on the nature and properties of the substrate and this dependence is not fully understood. We present a molecular dynamics study on the mechanical response of poly(ethylene glycol) (PEG) grafted on substrates of varying flexibility in “dry” conditions. Our in silico surface loading tests show that when PEG is grafted onto a hard substrate (silica), there is a significant reduction in adhesion to a solid surface, owing to augmented steric repulsions at the interface. However, when the same chains are tethered onto a soft substrate (polyester), interfacial adhesion is strengthened. We find that the deformable substrate allows significant rearrangement of the subsurface and grafted segments during loading. Asperities along the rough soft surface also provide free volume for the tethered chains to occupy, enabling them to carpet the surface and increasing the density at the interface. Our results explain the molecular basis of the mechanical response of PEG when grafted onto hard and soft substrates and provide a rationale for surface protection using PEG.

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INTRODUCTION

required that will impart contamination resistance in both a wet and a dry environment. One of the most successful approaches in protecting solid surfaces from contamination in aqueous environments is through poly(ethylene glycol) (PEG) grafting.7 PEG functionalization also has a number of advantages for application in environments of varying degrees of hydration including dry,8 due to its ability to satisfy processability requirements, which often include ease in surface modification or coupling, low cost, very little effect on bulk materials, and compatibility with the intended environment. Functionalization with PEG can also render a surface environmentally responsive,9 as it displays a unique ability to change conformation in response to various triggers which may be tailored to eject contaminants. It is believed that the protein-rejecting property of PEG in wet environments is associated with two main mechanisms:10 steric repulsions and hydration via formation of a structured water layer. Furthermore, it has been demonstrated that the ability of PEG to protect a solid surface is dependent on its chain length, grafting density,11 and the nature of the adhering contaminant.12 However, the chemistry, morphology, and mobility of the underlying substrate collectively define the extent to which a surface can resist adhesion.13 Protein

The ability to modify surface properties of solid materials through surface functionalization is critical in many practical applications. In biomedicine, surfaces are often functionalized by grafting with oligomers to achieve biocompatibility, often under permanently hydrated conditions.1 On the other hand, industrial coatings functionalized to improve durability and/or contamination resistance generally need to be designed to perform in a constantly changing hydration environment ranging from fully immersed through to totally dry.2 For example, carbon-based particulate such as soot can cause discoloration and degradation of industrial coatings. These small hydrophobic particles have a strong affinity for hydrophobic polyester coatings. It has been shown that functionalization of these coatings with polar groups (e.g., OH, CO2H, F) improves the contamination resistance both in a dry and in a fully hydrated environment.3 However, this improvement is short-lived, with subsequent aging of these functionalized surfaces in a dry environment resulting in migration of the polar groups into the coating (hydrophobic recovery) and loss of contamination resistance.4 In addition, our previous studies5 have shown that when contaminant particles come in contact with polyester surfaces under dry conditions, they access small cavities on the coating surface and become deeply embedded. Subsequent hydration is then ineffective at removing these particles.6 Therefore, a more robust form of functionalization is © 2012 American Chemical Society

Received: June 8, 2012 Revised: November 18, 2012 Published: November 27, 2012 17263

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study6a simulating oxidation via a UV/ozone process.18 The resultant polyester substrate has 5.4 OH groups/nm2 which is close to that of fully hydroxylated silica. The hydroxyl modified polyester which is denoted Poly-OH, was subsequently tethered with poly(ethylene glycol) (PEG) molecules. To model the inorganic substrate, a vitreous silica surface based on the work of Garofalini and co-workers19 was selected. The silica substrate has terminating hydroxyl (OH) groups with a density of 5.4 OH groups/nm2 which represents a fully hydrated silica film.20 Prior to PEGylation, the silica substrate was relaxed by undertaking NPT dynamics. The density of the resulting substrate is 3 g/cm3, the average film thickness is 14 Å, and the surface area is 743 Å2 with equilateral dimensions of 27.3 Å in the x and y directions, to which PBC were applied during MD simulations. We explored poly(ethylene glycol) grafting of both polyester and silica substrates, on the latter via two PEG derivatives: poly(ethylene glycol) and poly(ethylene glycol) silane (2-[methoxy(polyethyleneoxy)propyl]trimethoxysilane). The reason we considered an additional PEG derivative is that the silyl ester group (Si−O−C) associated with direct grafting is considered hydrolytically unstable.21 All schemes considered involve a condensation reaction between hydroxyl groups (OH) at the substrate’s surface and terminal OH groups of the PEG derivative, in line with experiment.1b,22,23 The condensation reaction was modeled by fusing the oxygen of randomly identified alcohol groups along the substrate surface, with the terminal oxygen of the PEG molecule. The resultant PEGylated surfaces were then energy minimized, relieving any strain due to the formation of new bonds and re-equilibrated using molecular dynamics in the constant volume and temperature ensemble (4 ns). The PEGylated polyester and silica substrates are denoted Poly-ρPEGn and SilicaρPEGn, respectively, while Silica-ρPEGn-Silane denotes the PEG-silane functionalized silica. The parameter ρ, represents the grafting density of PEG chains in units of PEG molecules per unit area, and n represents the degree of oligomerization. We examined varying grafting densities, by tethering PEG pentamers at a surface density of 0.3 and 0.6 PEG/nm2. Additionally, to examine the effect of chain length, PEG octamers were also considered, tethered at a surface density of 0.3 PEG/nm2 (Poly-0.3PEG8). In a nonaqueous environment, the free pentamer and octamer chains in question display a radius of gyration of 3.1 ± 0.3 and 4.3 ± 0.7 Å, respectively. The summary of all substrates examined is presented in Table 1. We note the low molecular weight PEG oligomers considered here enable high grafting densities to be achieved which are of particular interest for self-cleaning surface design. In Silico Loading of Substrates with Graphite. Having grafted the polymer substrate with PEG or PEG-silanes, we then employed a procedure that emulates a surface loading experiment, typical of atomic force microscopy (AFM) measurements, to evaluate the

adsorption trends have been shown to be influenced by interactions between substrate and grafted PEG chains with these interactions playing an important role in the conformation and stability of the grafted layer.14 These studies represent only a sample of the extensive investigations of PEGylated surfaces in aqueous environments. Similarly, the majority of molecular dynamics studies have so far concentrated on the conformation, chain dimension and overall behavior of PEG chains in solution.15 However, in order to assess the value of PEG for use as a surface protector in industrial applications, it is necessary to study adhesion to PEG surfaces in dry conditions and investigate the robustness of these modified films as a function of substrate properties in particular, hardness. Moreover, according to the Young−Dupré equation,16 “dry adhesion” is the first of the three major components defining adhesion in a three-phase environment (surface, contaminant, and liquid medium): Wslc = Wsc − γl(cos θ ls + cos θ lc)

(1)

where Wslc is the energy required to separate the contaminant from the solid surface in a liquid medium, Wsc is the energy change in separating the contaminant from the solid surface in vacuum (dry adhesion), γl is the surface free energy of the liquid, and cos θls and cos θlc are the contact angles formed by the liquid droplet on the solid and contaminant surfaces, respectively. To the best of our knowledge, there has been no fully atomistic molecular dynamics study investigating the dynamic response of grafted PEG chains to another approaching surface under dry conditions and on substrates of varying flexibility. In this study, we use force-field molecular dynamics and in silico loading simulations, to explore the mechanical response and adhesion energetics of various PEGylated substrates in contact with a flat hydrophobic surface (graphite) under dry conditions. Substrates include rigid inorganic and flexible organic films with various PEG grafting densities and chain lengths examined. These interfaces are prominent in industrial coatings, and understanding of the behavior and interactions in these systems at the nanoscale will facilitate design of contamination resistant surfaces for architectural and engineering applications which may also have the potential to be environmentally responsive and self-cleaning.

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MODELS AND METHODS

Models of the PEG Grafted Organic and Inorganic Substrates. The polyester substrate used in this work represents a typical industrial paint coating and is composed of polyester chains that contain on average 15 units of 2-butyl-2-ethyl-1,3-propanediol, 2 units of trimethylolpropane, and 16 units of isophthalic acid. These chains have been packed in a three-dimensional cell and cross-linked with tributoxymethyl-melamine, resulting in cross-linked polyester substrate. A detailed description of the procedure used to construct the model is presented in the theoretical study by Yarovsky and Evans.17 Prior to the surface PEGylation, molecular dynamics was undertaken for 3 ns at 298 K and 1 atm in the NPT (constant pressure and temperature) ensemble so that the system’s density reached an equilibrium value. The resulting substrate, termed ungrafted polyester, displays a density of 1.3 g/cm3, which is comparable to experiment, an average film thickness of 15 Å, and a surface area of 1399 Å2 with equilateral dimensions of 37.4 Å in the x and y directions. This constitutes a basic unit cell that was periodically replicated in three dimensions when periodic boundary conditions (PBC) were applied. For modeling of PEGylated polyester substrates, a “pretreatment” step was initially required. Specifically, the organic substrate was first functionalized with hydroxyl (OH) groups, as described in a previous

Table 1. Summary of Examined Polymer Substrates

substrate polyester Poly-OH Poly0.3PEG5 Poly0.3PEG8 Poly0.6PEG5 silica Silica0.3PEG5 Silica0.3PEG5Silane 17264

description ungrafted polyester hydroxylated polyester PEGylated polyester PEGylated polyester PEGylated polyester ungrafted silica PEGylated silica silane-PEG grafted silica

PEG grafting density (PEG/nm2)

PEG chain length (no. of monomer units)

n/a

n/a

n/a

n/a

0.3

5

0.3

8

0.6

5

n/a 0.3

n/a 5

0.3

5

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parameters were obtained:25 the equilibrium separation of the substrate/graphite interface (d0), the adhesive force defined as the maximum attractive force per unit of area (Fadh), and the work of adhesion (Wadh), which is the free energy required to separate the interface into two isolated phases.16 In the context of this study, these three interaction parameters provide a quantitative measure of the contaminant-rejecting properties of the grafted substrates. We sampled the conformations of the tethered PEG chains during loading, by monitoring their radius of gyration in directions parallel and perpendicular to the surface plane. We also calculated the mean squared displacement (MSD) of the chains at each interfacial separation. To monitor the response of the entire polymer substrate to the approaching graphite surface, we generated three-dimensional topographic images of the substrate’s surfaces at each loading step. Each image spans the entire xy surface plane of the substrate, and was generated by subdividing the plane into n square grids with 3 Å side lengths. Within each grid interval, the topmost position of the substrate’s surface atoms (zi) was detected, thus forming a timeaveraged three-dimensional topographic surface profile. These topography maps were then used both as a visualization tool and to determine the surface boundary, surface roughness, and density of the substrates during loading. The surface boundary was obtained by averaging the topmost positions across all grids of the topography map (z). ̅ The root-mean-squared surface roughness Rrms of each substrate was subsequently determined, according to the following equation:

adhesion attributes and dynamic response of each substrate, to interactions with a hard hydrophobic surface represented by a model comprising six ideally flat graphitic (001) layers.24 The constituent atoms of graphite are sp2 hybridized carbon atoms and do not carry any partial atomic charge to maintain overall neutrality of the graphite structure. Since electrostatic interactions between graphite and opposing polymer substrates are absent, all measured interaction energies are a result of van der Waals (vdW) forces. The in silico loading procedure involved first forming an interface between the substrate and graphite in a unit cell. The boundary of the substrate was identified by generating three-dimensional topography maps of the substrate’s surface. The details of this procedure will be explained below. Subsequently, the separation between the substrate and loading material was obtained as the distance between the boundaries of the substrate and graphite surface. The graphite layer was initially placed at a vertical distance of at least 26 Å from the substrate’s surface boundary, where its interaction with the substrate is negligible. A schematic diagram of a typical substrate/graphite interface is shown in Figure 1. The cell is extended in the direction

n

R rms = [∑ (zi − z ̅ )2 /n]1/2 i=1

(2)

where zi is the topmost position of surface atoms within the ith grid, z̅ is the surface boundary, and n is the number of grids. Lastly, the atomic density of each substrate was defined as the number of atoms per unit volume where the volume of each substrate is calculated as the surface area of the film multiplied by its average thickness. The thickness was obtained by calculating the upper and lower boundaries of the substrate from topography maps of the top and bottom surface planes, respectively. Computational Details. All simulations were carried out using DISCOVER MD code from Materials Studio Inc. Intermolecular interactions were evaluated using the COMPASS forcefield.26 Optimized for the simulation of condensed phase polymers and organic/inorganic interfaces, the COMPASS forcefield has been demonstrated to predict cohesive properties of an extensive number of polymers including poly(ethylene glycol) oligomers27 as well as silica−organic interface properties.28 For energy minimization, the nonbonded interactions, including the Coulomb term for electrostatics and 6−9 Lennard−Jones potential for vdW, were calculated using the Ewald procedure with an accuracy of 0.01 kcal/mol and an update width of 1.0 Å. The conjugate gradient algorithm was used for energy minimization, with an energy convergence criterion of 0.01 kcal/mol/ Å. To retain computational tractability during MD, nonbonded interactions were calculated using the atom-based summation method, with a cutoff radius of 15.5 Å, a spline width of 5 Å, and a buffer width of 2 Å. A long-range vdW tail correction was applied for nonbonded interactions larger than the cutoff radius. A 1.0 fs time step was used for MD with the Andersen thermostat29 employed to control the temperature at 298 K with a collision ratio of 1.0. Prior to the surface modifications, the NPT (constant pressure and temperature) ensemble with the Berendsen barostat was used to control the pressure (1 atm) and equilibrate the densities of the substrates. During this stage, simulations were run for at least 3 ns. During loading, the NVT (constant volume and temperature) ensemble was selected with molecular dynamics undertaken for 1 ns following each displacement of the graphite surface. Trajectories were generated by saving the system’s coordinates in 10 ps time intervals. Prior to the force calculations, all systems were equilibrated by ensuring that no energy drifts occur during the data collection stage of MD, and the radius of gyration of the tethered chains attained a steady value. All systems reached equilibrium within the first 500 ps. The force Fz, together with the radius of gyration and MSD of the chains, was averaged over the

Figure 1. Typical model setup for in silico loading experiments, showing a PEGylated substrate loaded with graphite. perpendicular to the interface, so that when periodic boundary conditions are applied, a two-dimensional interface is emulated. Following the interface construction, the graphite layer was displaced by an initial step size of 3 Å in the vertical direction, toward the substrate as indicated in Figure 1. After each displacement, molecular dynamics was undertaken for 1 ns, during which the PEG chains and the underlying polymer were equilibrated. The details of the equilibration are described in the next section. During molecular dynamics, the force and distance between graphite and substrate were measured, in the direction perpendicular to the interface while the graphite model was kept in a fixed geometry maintaining graphite’s structural integrity through the entire loading procedure. The lowermost portion of the polymer substrate (3 atom %) was also constrained, providing a rigid support during loading. Hence, 97 atom % of the polymer substrate was free to move during molecular dynamics. When a graphite−substrate separation of at least 12 Å was attained, the step size was reduced to 0.25 Å, and the loading procedure continued. Loading was terminated when the graphite surface advanced well past the point of interfacial equilibrium, defined as the position where the net force between graphite and substrate surface is zero. This loading procedure was used to generate a force versus separation curve. A more detailed description of the entire loading process has been presented elsewhere.6a Free energy plots were obtained by integrating the force with respect to the distance. From the resultant force and energy curves, the following interaction 17265

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final 500 ps of dynamics, while the topographic images were averaged over the final 50 ps of dynamics.

monotonic rise in the force. When the net force reaches zero, the point of interfacial equilibrium is attained. The inflection or force basin was determined by applying an exponential fit similar to the universal binding-energy relation (a modified Rydberg function)32 to the data near the force well. To investigate the dynamic evolution of the atomistic structure of the ungrafted polyester during loading, we monitored its density and RMS surface roughness (Figure 3).

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RESULTS AND DISCUSSION In this section, the simulation results are presented and where possible are compared with experimental data. Response to Loading of Grafted and Ungrafted Soft Organic Substrates. During the loading of the surfaces with the contaminant, the structure and properties of the surfaces undergo a number of significant changes. These changes are driven by the intermolecular interactions between the substrate, the load, and any functionalization, if present, and determine the shape of the force plot. Figure 2 presents the force plot

Figure 3. Plot showing induced changes in density and roughness of ungrafted polyester during loading with graphite.

Clearly, both the density and roughness of the polyester vary in accordance with fluctuations in force. In the noncontacting regime (region I), a decrease in separation leads to a reduction in density and an increase in roughness. Thus, long-range attractive forces between graphite and polyester induce swelling of the polymer layer and roughening of its surface. Once direct contact has been made (region II), further decreases in separation lead to an increase in density and a reduction in roughness; that is, short-range repulsive forces induce compression of the substrate and flattening of its surface. The deformation of the ungrafted polymer substrate is visually demonstrated by three-dimensional topographic images of the polyester during loading (Figure 4). The unperturbed

Figure 2. Force plot obtained during simulated loading of ungrafted polyester with graphite. The force curve shows an attractive (negative) force component and repulsive (positive) force component. Red solid line represents an exponential function fitted to the data near the bottom of the force well.

obtained from in silico loading experiments of ungrafted polyester and is representative of loading curves for systems with flexible substrates. Negative force values indicate a net attraction between graphite and the polyester substrate, while positive force values indicate a net repulsion. The shape of the curve resembles that of a “standard” intermolecular force plot obtained from typical AFM experiments.30 From this plot, we identified three major regions to illustrate where the loading material (graphite) and polymer substrate are separated but interacting through long-range dispersive forces (I), where they are in direct contact, adhering to one another and interacting through a combination of dispersive and repulsive forces (II), and where they are repelling each other through a dominating short-range repulsive force (III). The “point of contact” marks the boundary between regions I and II and also characterizes the onset of repulsive forces. It is often identified by a change in the curvature of the force curve, and for two nondeformable interacting surfaces, usually occurs near the position of the force basin.30 In our case, due to the flexible nature of the polyester substrate, nonmonotonic variations in the force curve are observed,31 making the exact contact point difficult to determine. We identify contact, at the position just prior to where a rise in the force curve is first noted, from the right of the axis. At distances less than the “contact” value, both attractive and repulsive components increase, at a rate that is dependent on the deformability of the substrate (region II).30 Eventually, at the “inflection point”, the repulsive component begins to dominate, and further advancement of the indenter past the inflection leads to a largely

Figure 4. Surface profiles of ungrafted polyester during loading with a graphite surface at (a) 12.56 Å, (b) 7.71 Å, and (c) 4.83 Å. Colors indicate the degree of extension of the substrate surface in the z direction.

surface (Figure 4a) exhibits a gently undulating profile with a low level of roughness. In comparison, at the point of contact (Figure 4b), the substrate fragments are seen to “jump up” to meet the approaching surface with the fragments protruding into the interface region. This leads to an increase in roughness and reduction in the density of the polymer (Figure 3). This jump to contact is caused by the long-range vdW attraction between the two components of the interface (polymer− graphite). We note that electrostatic interactions are not playing a role in this phenomenon due to the lack of charges on the graphite surface. As the loading material is further advanced toward the polyester (Figure 4c) additional substrate moieties 17266

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substrate. The point of contact is seen to differ significantly, depending on the composition of the substrate’s surface. For PEG-grafted substrates, the point of contact occurs at a greater distance from graphite compared to ungrafted or hydroxyl modified substrates. The flexible PEG segments are more easily drawn toward the load at larger separations, permitting the formation of a partially collapsed bridge connecting the substrate and graphite (Figure 5b). Braithwaite et al.33 have witnessed similar behavior when investigating the interaction of poly(ethylene glycol) with glass using modified AFM. In particular, they observed that when the surfaces approached one another, there was a bridging effect where the “dangling” segments of the polymers on one surface attained contact and partially adsorbed onto the other surface. The second significant difference arising from functionalization is associated with the inflection point, which marks the position where the repulsive interactions begin to dominate. It can be seen from Figure 6 that, for PEG functionalized surfaces, the inflection point occurs at a distance that is approximately equal to or less than that displayed by the ungrafted polyester. Initially, this may appear to be counterintuitive, since a surface functionalized with PEG residues that attains contact with the hydrophobe at a longer distance and begins to repel it at a greater separation (see point of contact, Figure 6) should be expected to display an inflection point at a greater interfacial distance. However, this behavior reflects the fact that the flexible PEG chains on the polyester substrate can alter conformation upon contact and minimize their steric repulsion with the opposing adherent. In turn, the attractive interaction continues to rise with decreasing interfacial separation, despite the tethered chains maintaining contact with the load. This can lead to a large variation between the contacting and inflection positions of these interfaces, particularly for films with a low grafting density (Poly-0.3PEGn). In contrast, for ungrafted and hydroxyl modified substrates, the inflection positions are more closely aligned with the contact points, due to the much more limited surface flexibility. According to the radius of gyration monitored during loading (Supporting Information Table S1), the tethered chains initially display a preferential parallel orientation with respect to the surface. However, upon contact, they display a transition to a mushroom-like state. Upon further approach of the hydrophobic surface, the PEG chains again become stretched parallel to the surface and contracted perpendicular to the surface. This behavior showed no significant dependence on the chain length or grafting density for the systems examined. The force constant obtained from the slope of the force− distance curve in region III can be related to Young’s modulus and the ability of the surface to withstand compression by the loading material.34 We obtain force constants of 265 and 284 N/m for ungrafted and hydroxyl modified polyesters, respectively (Figure 6). The force constant of the densely PEGylated polyester (Poly-0.6PEG5) is also in this range (264 N/m). However, PEGylated surfaces of low grafting density (Poly-0.3PEG5 and Poly-0.3PEG8) demonstrate an increase in surface rigidity of up to 30% (345 and 332 N/m, respectively). The higher force-constant values are a consequence of a dense surface layer formed by significant compression and confinement of the sparsely tethered chains during contact with the graphite layer. The free energy change ΔW, between graphite and each polyester substrate was determined by numerical integration of the force curves (Figure 7). The work of adhesion (Wadh)

are displaced toward graphite while the protruding ones are compressed, resulting in an overall flattening of the polymer surface. Loading of polyesters functionalized with hydroxyl groups or with PEG exhibit a similar response to that displayed by the unfunctionalized coating (e.g., Figure 5a). In all cases, long-

Figure 5. (a) Typical force and density plots obtained during loading of a PEGylated polyester surface, Polyester0.3PEG5. (b) Snapshot of the PEGylated layer in contact with graphite. At the point of contact, the tethered PEG chains form a partially collapsed bridge connecting the substrate with the graphite surface.

range attractive forces between graphite and substrate initially induce swelling, while short-range repulsive forces ultimately lead to substrate compression. All polyester-based surfaces were seen to expand by up to 7−12% of their intrinsic density value, which highlights their significant flexibility. Despite this similar response, a number of differences between the original and functionalized surfaces were identified, illustrated by the contacting and inflection positions of the interface (Figure 6). The point of contact represents the position where repulsive interactions begin to contribute to the net force. It is marked by the onset of instabilities along the force curve as the graphite is advanced toward the polymer

Figure 6. Bar chart representation of the deformation parameters of polyester substrates, obtained during loading with a graphite surface. The parameters include the contact point, where repulsive forces at the interface are first detected, the inflection point, where repulsive forces become dominant, and the force constant, which describes the stiffness of the substrate during compression. All error bars with the exception of the force constant represent deviations in the mean value within a confidence interval of 95%. The force constant error bars represent the standard error of the mean value obtained using t-statistic of a linear regression. 17267

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The mobility of the surface chains during contact also makes a contribution to the interaction with the adherent. It has been well documented that steric repulsion is one of the key mechanisms of contamination-resistant properties of PEGylated surfaces.1b,10,12 When a contaminant gets close to a PEG-covered surface, the available volume for each chain segment is reduced, and consequently a steric repulsive force is developed owing to loss of conformational freedom.1b However, we have found that, for functionalized polyesters, steric repulsions between the grafted compounds and graphite are diminished. The natural flexibility of the polyester substrate allows significant movement of the surface chains during loading, while asperities along the surface of the polyester provide ample volume for the tethered chains and functional groups to occupy. Both of these factors diminish the entropic penalty associated with reduced mobility of the grafted compounds, diminishing steric repulsions during contact, leading to increased adhesion. To illustrate these effects, Figure 8 shows atomic concentration gradients for each polyester substrate examined,

Figure 7. Change in free energy (ΔW) between graphite and polyester substrates as a function of polymer−graphite separation. The depth of each potential well is associated with the work of adhesion. This is the energy required to separate an interface into two isolated surfaces. Plots show that functionalization of polyester with OH or PEG groups signficantly increases adhesion between polyester and graphite.

values are presented in Table 2, together with other interaction parameters obtained from simulations. The errors displayed Table 2. Adhesion Properties of Polyester Substrates Interacting with a Graphite Surface substrate polyester Poly-OH Poly0.3PEG5 Poly0.3PEG8 Poly0.6PEG5

work of adhesion, Wadh (mJ m−2)

adhesive force, Fadh (N mm−2)

equilibrium separation, d0 (Å)

45.97 ± 21.14 83.21 ± 21.18 86.18 ± 30.99

119.19 ± 20.08 176.28 ± 16.90 176.63 ± 26.80

4.83 ± 0.23 4.23 ± 0.21 3.67 ± 0.22

91.56 ± 31.94

190.88 ± 20.05

3.62 ± 0.21

79.85 ± 30.02

178.77 ± 18.16

4.27 ± 0.23

Figure 8. Atomic concentration profiles of polyester films along the direction perpendicular to the surface plane. The profiles were generated with the polyester/graphite interfaces at equilibrium.

represent the deviation in the mean measurement, with a confidence level of 95%. It can be seen from the table and figure that the presence of surface functional groups (OH and PEG groups) affects the adhesion properties of the interface, with all functionalized polyesters displaying a significantly higher work of adhesion with graphite (74−99%) than the unfunctionalized polymer. The grafted substrates also exhibit a larger adhesive force (46−59%) than the bare polyester surface, and a shorter equilibrium separation (Δd0 ∼ 0.6 −1.2 Å). These results suggest that, at these grafting densities, it is unlikely that PEG or hydroxyl modifications will improve the ability of polyester to resist adhesion to carbonaceous materials such as graphite, in a solvent-free environment. Under dry conditions and in the absence of electrostatic forces, the interaction energies are dominated by vdW forces which in turn are strongly influenced by the chemical composition of the extruding surface residues. Functionalized layers generally display a stronger long-range vdW attraction with graphite compared to ungrafted polyester, because of the increased number of heavy atoms in the surface layer. For example, at an interfacial separation of 9 Å (Figure 7), where the dispersive interactions are dominant, the hydroxyl modified polyester already exhibits a significantly stronger interaction (43%) with graphite compared to ungrafted polyester. Therefore, the fact that functionalized polyesters such as Poly-OH display a stronger adhesion with graphite compared to ungrafted polyester may be attributed at least in part to augmentation of dispersive interactions at the interface.

depicting the atomic number density of the polymer as a function of distance from the graphite surface. The concentration is measured along the z direction, that is, perpendicular to the plane of the substrates, and each concentration gradient is generated when the polymer/graphite interfaces are at equilibrium. All polyesters display an increase in concentration close to the interface, as a result of film compression during loading. However, it can be seen that the concentration of atoms at the interface increases significantly with the addition of poly(ethylene glycol) (PEG) and hydroxyl (OH) residues, indicating that PEG and OH groups are more compacted by the interaction with graphite. In addition, the grafted substrates are seen to display smoother surface profiles with reduced RMS roughness values (1.12−1.81 Å) compared to ungrafted polyester (2.63 Å). Israelachvili and co-workers1b showed that PEG molecules grafted onto an irregular substrate can carpet its surface by filling cavities and reducing asperities, which corresponds with the behavior in our simulations. Surface smoothing combined with increased concentration of atoms at the interface assist in augmenting the interfacial contact and adhesion between polymer and graphite. These effects highlight the ability of the tethered chains and surface hydroxyl groups to respond to the adhesive force with minimal steric penalty. In a recent study,35 an innovative method known as the “blister test”, was used to investigate the adhesion 17268

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strength of graphite and graphene with various substrates. It was found that the adhesion strength between the two interacting surfaces is strongly dependent on their deformability. When at least one interacting surface is flexible, the interfacial contact is maximized, making their interfacial interactions more liquidlike than solidlike. Our simulation results suggest that such behavior may be affected by the density of the anchored chains. In particular, a high PEG grafting density leads to crowding of the chains and reduced chain mobility during adhesion. This explains our observation that, among all PEGylated substrates examined, the densely PEGylated polyester Poly-0.6PEG5 displays the largest equilibrium separation (d0 ∼4.3 Å) and the lowest interfacial adhesion (Wadh ∼ 79.9 mJ m−2) with graphite. Finally, the difference in force constants observed for the various polyester based substrates is related to molecular confinement and extent of surface carpeting. PEGylated surfaces of relatively low grafting density (Poly-0.3PEG5 and Poly-0.3PEG8) display the most compressed and densely packed structures, and also exhibit the largest force constants during compression by the graphite layer. Response to Loading of Ungrafted and Grafted Hard Inorganic Substrates. Figure 9 presents the force plot

Figure 10. Change in free energy ΔW, during loading of silica based substrates with graphite. Also included for comparison is the energy plot of the polyester/graphite interface. Plots show that PEG grafted silicas adhere weakly to graphite compared to bare silica.

chemical nature of the two substrates. The vdW potential between graphite and silica is larger than polyester because siloxane (O−Si−OH) terminal groups along the surface of silica, provide greater dispersive interaction than the methyl CH3, and methylene CH2 groups that terminate the polyester surface. In particular, the silicon−carbon pair associated with siloxane/graphite composites display a dispersive coefficient that is 2.4 times larger than that displayed by the carbon− carbon pair associated with the polyester/graphite interfaces. Consequently silica displays a stronger interfacial adhesion with graphite in a solvent-free environment. In comparison PEG-grafted silicas show notable signs of deformation and mechanical response, when interacting with graphite. First, the PEG chains swell slightly (2 - 3%) and contact with graphite is observed at a larger interfacial separation, compared to that of ungrafted silica (Figure 11).

Figure 9. Force and density plots obtained during loading of a “bare” silica surface.

obtained during loading of a silica surface with graphite. The force curve shows no discontinuities or jumps in striking contrast to the force fluctuations observed during loading of the polyester substrate (Figure 1). This can be explained by the high substrate stability due to the hard nature of silica surfaces. Moreover, silica attains contact with the graphite surface at a separation of 5.77 Å, which is significantly shorter than for bare polyester surface (7.71 Å), due to the lower roughness and deformability of silica. Furthermore, there is no initial expansion and the subsequent compression is negligible (1%), as shown by the density plot of Figure 9. At small separations, the rise in the force curve for silica is noticeably greater than for the soft polyester coating. In fact, the stiffness coefficient of silica is 25% higher than that of ungrafted polyester. Collectively, these observations suggest that silica is significantly more robust (rigid) than the organic polyester layer. Despite silica’s enhanced stability, our simulations show that it displays a significantly stronger adhesion with graphite in comparison to ungrafted polyester. This is reflected by an almost 2-fold increase in the work of adhesion (Wadh) (Figure 10). The reason for this may be found by considering the

Figure 11. Bar chart representation of the deformation parameters of silica substrates, obtained during loading with a graphite surface. All error bars with the exception of the force constant represent deviations in the mean value with a confidence level of 95%. The force constant error bars represent the standard error of the mean value obtained using t-statistic of a linear regression.

When the functionalized silica surfaces attain contact with graphite, PEG segments form a bridge connecting the underlying substrate with the loading material (Figure 12). Furthermore, the functionalized silica films display a larger deviation between their contact and inflection positions (Figure 11), highlighting the ability of the tethered PEG chains to alter conformation upon interfacial contact and maximize dispersive 17269

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to a slight increased interaction between the surfaces, possibly due to additional vdW interactions. We also note that upon approach of the graphite surface the PEG-silane segments adopt flatter conformations, with a more preferential parallel orientation with respect to the surface (see Figure 12c). Three-dimensional topographic images of the silica-based substrates are presented in Figure 13. The images have been

Figure 12. Snaphots of (a) ungrafted silica, (b) PEGylated silica, and (c) Silane-PEG grafted silica in contact with graphite. At the point of contact, the grafted chains form a connecting bridge between the substrate and graphite surface.

interactions at the interface. The above results signify an increased mechanical response for grafted silica surfaces as a result of tethering flexible PEG chains. According to the radius of gyration (Supporting Information Table S1), the tethered PEG segments transition from a pancake-like to a mushroomlike conformation upon contact and transition back to a pancake conformation upon further compression. No significant difference is observed as a result of the silane linker. Despite these clear signs of deformation, Figure 11 shows that when the silica substrate is grafted with PEG or PEG-silane oligomers, the inflection point occurs at a greater distance from the graphite surface, compared to the ungrafted silica. Since the inflection marks the distance where repulsive interactions between the substrate and the load become the dominant type, its observed shift signifies that, in the presence of the tethered segments, repulsive interactions between silica and graphite are enhanced by the PEG chains. This is in a striking contrast to the behavior observed for the polyester/graphite interface where steric repulsion between grafted PEG chains and graphite are significantly mitigated by the underlying substrate flexibility. Grafting the silica surface with PEG or PEG-silane also leads to a reduction of 20−27% in substrate stiffness compared to ungrafted silica (Figure 11). This is again in striking contrast to the behavior observed for polyester based substrates. The observed difference in the responsive behavior of the hard and soft surfaces can have a profound effect on the adhesion strength at the interface. The related interaction parameters and energy plots are displayed in Table 3 and

Figure 13. Three-dimensional topographic images of (a) bare silica, (b) Silica-0.3PEG5, and (c) Silica-0.3PEG5-Silane at equilibrium.

taken when the substrates are at their equilibrium position relative to the graphite surface. The silica substrate (Figure 13a) displays a relatively smooth surface profile with an RMS roughness of 1.8 Å. In comparison, the PEGylated silicas exhibit more irregular surface morphologies with a greater RMS roughness (2.3 Å), despite conformational deformation of the PEG chains during loading. This differs significantly from the “carpeting” behavior observed in the case of the PEGylated polyester. It also highlights the fact that when tethered onto silica substrate, the PEG segments display a reduced mobility compared to when they are grafted onto a flexible underlying substrate such as polyester. Therefore, with the inclusion of PEG or PEG-silane chains, steric repulsions at the silica/ graphite interface are augmented. The concentration of atoms for each silica-based substrate was examined along the direction perpendicular to the plane of the substrates. The resulting concentration profiles were generated with the silica/graphite interfaces at equilibrium and are presented in Figure 14. All

Table 3. Adhesion Properties of Silica Substrates Interacting with a Graphite Surface substrate silica Silica0.3PEG5 Silica0.3PEG5Silane

work of adhesion, Wadh (mJ m−2)

adhesive force, Fadh (N mm−2)

equilibrium separation, d0 (Å)

88.16 ± 11.75 38.83 ± 14.74

349.84 ± 5.89 155.21 ± 12.53

4.85 ± 0.10 6.30 ± 0.14

50.97 ± 18.10

170.78 ± 9.05

6.08 ± 0.19

Figure 14. Atomic concentration profiles of the silica-based substrates at interfacial equilibrium. Profiles are displayed as a function of position through the substrate in the direction normal to the interface.

plots display a similar atomic concentration at a distance greater than ∼10 Å, marking the onset of the bulk region of the substrates. As the graphite boundary is approached, all silica based substrates exhibit a reduction in their number density, marking the onset of the silica/graphite interface. The plots show that, for the ungrafted silica, the concentration of atoms decreases relatively abruptly through the interface region, highlighting a narrow interface with significant interfacial contact with the load (graphite). In comparison, for PEGylated

Figure 10. The errors displayed in Table 3 represent the deviation in the mean within a confidence interval of 95%. It can be seen that grafting of silica with PEG and PEG-silane segments affects the adhesion properties of the interface. In particular, all grafted silicas exhibit a significantly weaker adhesion (42 and 56%), a weaker adhesive force (51 and 56%), and a larger equilibrium separation (Δd0 ∼1.2 and 1.5 Å) with graphite. In the case of PEG-silane grafted silica, the linker leads 17270

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When PEG chains are grafted onto a hard surface such as silica their contamination-resistant properties are enhanced, while when tethered onto a highly flexible and irregular polymer substrate, these properties are significantly alleviated.

silicas, the edge of the concentration profile can be characterized by a more gradual reduction in the number density, with a distinct extrusion at a distance of ∼4 Å from the graphite surface associated with the protruding tethered PEG chains. For PEGylated silicas, the atomic density within the interface region is less compared to ungrafted silica. Hence, interfacial contact between PEGylated silica and graphite is lower, and thus, interfacial adhesion is significantly diminished. The reduction in chain density at the interface also correlates with the force constant variations observed in Figure 11. In particular, the low density surface layers that precede the PEGylated silica substrates present a far more compressible region than that presented by the bare silica substrate. To clarify our findings, we partitioned the free energy change ΔW, into contributions from the internal energy ΔU (the kinetic and potential energy) and entropy of the system ΔS,

ΔW = ΔU − T ΔS

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CONCLUSION In this molecular dynamics study, we investigated the adhesion attributes and mechanical response of poly(ethylene glycol) grafted substrates interacting with a hydrophobic, solid surface (graphite). The simulated substrates include a hard inorganic (silica) and soft organic (polyester) coating with or without poly(ethylene glycol) tethered chains. Our in silico loading tests show that when poly(ethylene glycol) chains are grafted onto a hard substrate, there is a significant reduction in adhesion to another hard surface due to augmented steric repulsions between PEG segments and the approaching surface. However, when the chains are tethered onto a soft, flexible substrate, the adhesion is enhanced due to significant rearrangement of the subsurface and grafted chains during loading. In addition, asperities along the surface of the soft substrate provide free volume for the tethered chains to occupy, enabling them to carpet the surface. These studies explain the molecular basis of PEG’s responsive behavior when grafted onto hard and soft substrates and enable us to numerically estimate the work of adhesion in a dry environment, one of the major components of adhesion in a three-phase system containing two solid components and a solvent.

(3)

The internal energy was calculated from the Hamiltonian at each separation value. Changes in entropy directly calculated from eq 3 for selected PEGylated surfaces are shown in Figure 15a and reveal a significant dependence of entropy loss on the

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ASSOCIATED CONTENT

S Supporting Information *

Radius of gyration of PEG chains calculated at various stages of loading. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 15. (a) Changes in entropy for selected PEGylated surfaces reveal a significant dependence of entropy loss on substrate composition. (b) Mean-squared displacement curves for tethered PEG chains showing a position and substrate dependency.

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AUTHOR INFORMATION

Corresponding Author

* To whom correspondence should be addressed. E-mail: [email protected].

chemistry of the substrate. In particular, PEGylated polyesters are seen to lose a greater amount of entropy than their silica counterparts, correlating well with the observed carpeting and compression of polyester. However, as our simulations of PEGylated polyesters have shown, unlike silica-based substrates, the former’s loss in entropy is not entirely manifested in the development of a steric repulsive force, due to the significant rearrangement of the polyester subsurface and grafted chains during loading. This can be observed from the inflection and contacting positions of the interface but is further confirmed from the difference in chain mobility, demonstrated from the position-dependent mean-squared-displacement (MSD) curves of the chains (Figure 15b). The MSD curves represent the spatial extent of random motion of the tethered chains, and their comparison with Figure 15a demonstrates a general correlation between the chain dynamics and entropy loss, particularly evident around 7−9 Å, following the bridging of the chains with the graphite surface manifested in increased chain mobility and a slight increase in entropy. Most importantly, the MSD curves show that the natural flexibility of the polyester substrate, allows significant movement of the surface chains despite compression, in contrast to silica-based substrates. In summary, our results indicate that the composition and structure of the underlying substrate that determine its hardness has a significant impact on the load/ contamination-resistant properties of the PEGylated surfaces.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the award of an Australian Research Council Linkage Grant in partnership with BlueScope Steel to carry out this work. We also gratefully acknowledge allocations of computing time from both the National Computing Facility (NCI), iVEC and from the Victorian Partnership for Advanced Computing (VPAC).

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