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Jun 30, 2017 - Chemistry, University of Florida, Gainesville, Florida 32611, United States. •S Supporting Information. ABSTRACT: Silica nanoparticle...
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Chain Dispersity Effects on Brush Properties of Surface-Grafted Polycaprolactone-Modified Silica Nanoparticles: Unique Scaling Behavior in the Concentrated Polymer Brush Regime Kyle C. Bentz and Daniel A. Savin* George & Josephine Butler Polymer Research Laboratory, Center for Macromolecular Science & Engineering, Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States S Supporting Information *

ABSTRACT: Silica nanoparticles (Rh = 70 nm) were functionalized with high dispersity (Đ > 2.3) polycaprolactone at various grafting densities, and the brush properties were investigated using dynamic light scattering. Owing to recent advances in controlled polymerization techniques, low dispersity brushes are easily grafted from nanoparticle surfaces, and these systems have been well studied. However, the effect of high dispersity brushes on nanoparticle surfaces is largely unexplored. Here we discuss the brush properties of high dispersity polycaprolactone-grafted silica nanoparticles. Because of the polymerization conditions used, transesterification events are induced during the polymerization to give brushes with increasing dispersity both as brush length increases and as grafting density is increased (e.g., Đ from 1.32 to 2.39 for σ from 0.21 to 0.61 chains/nm2). All grafting densities showed extended chains in the concentrated polymer brush regime, with brush length, lb, scaling with degree of polymerization, lb ∼ Na, where a = 1.39, 1.47, and 1.84 for the high, mid, and low grafting density sets. This study provides the first experimental insight into the effects of increasing chain dispersity on brush properties of nanoparticle systems. Furthermore, this system offers a facile method to tune dispersity of grafted brushes concurrent with the grafting polymerization. We expect this work to be of significant interest to the ongoing study of fundamental properties of polymer brushes as well as these materials finding use in polymer composite applications and provide enhanced mechanical properties compared to their monodisperse analogues.

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INTRODUCTION Polymer-grafted nanoparticles are of considerable interest from both fundamental and practical viewpoints. It is crucial that efficient and well-understood methods are developed for the grafting of polymer chains onto nanoparticle surfaces. Both grafting-to1−5 and grafting-from6−19 are well established methods to covalently attach polymers to nanoparticle surfaces, with each technique possessing unique advantages and disadvantages.20 In the grafting-to process, preformed and end-functionalized polymer is tethered to the nanoparticle surface via reaction with orthogonal surface chemistry to the polymer end-group, such as ethoxysilanes,2 azide−alkyne,3 and thiol−ene chemistries.21 The grafting-to method has the advantage that the polymer is able to be fully characterized prior to its attachment to the nanoparticle surface but typically suffers from inability to achieve high grafting densities. In contrast, as the grafting-from method polymerizes monomer directly from initiator-functionalized surfaces, the formed polymer brush is unable to be characterized directly, although this method does easily allow for high grafting densities to be achieved. There is particular interest in understanding how grafting density can be controlled as well as the ramifications this has on © XXXX American Chemical Society

the resulting polymer brushes. Depending on the grafting density, polymer brushes exist in one of three regimes, characterized by the scaling behavior of the brush length, lb, as a function of degree of polymerization, N.22 At very low grafting densities, such that each chain occupies a surface area greater than or equal to twice the radius of gyration squared, 2Rg2, then lb ∼ N3/5, known as the “mushroom regime”. When grafting density is increased to a point at which intermolecular interactions occur, the chains must extend outward from the surface. In this regime, the semidilute polymer brush regime, pairwise interactions dominate, excluded volume effects become present, and lb ∼ N4/5. Finally, at very high grafting densities, the concentrated polymer brush regime is reached. Here, higher-order interactions dominate, and chain dimensions are non-Gaussian as chains are highly extended, such that l b ∼ N1 . Polymer-grafted nanoparticles in the concentrated brush regime regime are of considerable interest from both a practical and fundamental standpoint. Because of the unique chain Received: March 26, 2017 Revised: June 21, 2017

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DOI: 10.1021/acs.macromol.7b00608 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules conformations only accessible in the concentrated brush regime, a variety of properties are significantly enhanced in these materials over their counterparts with polymers grafted at low densities, such as encapsulation and loading capabilities,23 thermally induced demixing,24 cell interactions,25 and many significant mechanical properties in composites, such as increased glass transition temperature,26 fracture strain, elastic modulus,27 and improved electrical strength.28 The effect of molecular weight of the polymer brush on the matrix compatibility is well studied.29 It has been shown experimentally30−32 and computationally33,34 that in high grafting density particles the brush molecular weight must be higher than the matrix (identical polymer as brush) polymer molecular weight. Far less studied, however, are the effects of chain molecular weight dispersity in these systems.35 Polydisperse brushes (Đ > 1) on planar surfaces have been studied and found to affect the brush properties significantly versus monodisperse brushes (Đ = 1).36−39 Simulations have shown that in polydisperse grafted systems the average stretching of chains is reduced due to the ability for chains to more easily adopt more entropically favorable conformations. However, in spite of this, there is an overall increase in the grafted layer thickness. In simulations40 and experiments41,42 of bidisperse systems, it has been shown that short chains are compressed in an inner layer, forcing the longer chains to be more stretched than in the monodisperse case. Theoretical work by de Vos and Leermakers showed that when dispersity is increased, the density distribution of chain ends shifts its maximum to lower values.37 Importantly, however, the overall density distribution function levels off at greater distances from the surface as dispersity is increased. In addition to unique chain conformations, studies have also shown that polydisperse brushes increase the compatibility in homopolymer/nanoparticle mixtures. In attractive or athermal mixtures, as dispersity is increased from 1.0 to 3.0 enhanced mixing is observed.38 Studies of disperse brushes on nonplanar, spherical surfaces are even more limited. Dodd and Jayaraman have shown through simulations that chain conformations on nanoparticles grafted with disperse brushes deviates significantly from the monodisperse brush.43 When degree of polymerization was held constant, as dispersity was increased brush height was increased. Quantitatively, the increase in brush height with increasing dispersity was quite dramatic even with modest increases in dispersity. For the three grafting densities studied increasing dispersity from 1.5 to 2.5 resulted in ∼20% increase in brush height. To the best of our knowledge, our study is the first to verify these findings experimentally. Recent simulation work in the Jayaraman group has shown that the attractive well observed at intermediate particle distances in monodisperse grafted nanoparticles is eliminated in nanoparticles grafted with equal numbers of short and long chains.34 The effect of polydisperse brushes has also been studied, showing that a critical Đ is required in order to eliminate the intermediate distance attractive well, and this was found to occur at Đ = 1.40 in their particular system.44 A very limited number of experimental studies have explicitly examined the effect of brush dispersity on solution properties or composite materials. Recently, the Benicewicz group has studied silica nanoparticles grafted with bimodal brushes and found these particles to be more compatible with the monodisperse matrix polymer than particles with monodisperse brushes of the same length as the long brush in the bimodal grafted particles.45−47

Clearly, there is a need for additional studies to be conducted on disperse brush nanoparticle systems. Polycaprolactone (PCL)-grafted nanoparticles are a particularly interesting system to study due to the complex nature of the polymerization. While the ring-opening polymerization of ε-caprolactone is generally a controlled polymerization technique, characterized by predictable molecular weights governed by the ratio of [monomer] to [initiator], and narrow dispersities,48 when polymerizing chains in close proximity, as in our system, there are additional effects that occur during the polymerization. Because of the extremely close proximity of growing chain ends to brush backbones, liberated water from the silica surface,49 and polymerization temperatures of 130 °C, chain scission and transesterification events readily occur. These effects allow the unique opportunity to directly alter the brush dispersity and study the resulting brush properties. While PCLgrafted nanoparticles have been synthesized and studied prior to this,12,50−52 no effort has been made to directly study effects of dispersity on brush structure. Here we show that brush dispersity in PCL-grafted silica nanoparticles leads to previously unobserved solution brush properties, such as scaling effects whereby lb ∼ N>1. By functionalization of the silica nanoparticle surface with various ratios of initiator functional (diol) glycidoxypropyl)dimethylethoxysilane (GPDMES) and the inert spacer molecule trimethylethoxysilane (TMES), we were able to study grafting densities of 0.61, 0.43, and 0.21 nm−2. Brush length was found to scale with degree of polymerization as N>1 due to swelling effects in polydisperse brushes. Because dispersity increased with increasing degree of polymerization, nonlinear scaling behavior in brush length was observed. Grafting density is shown to have a direct correlation with brush dispersity, where both the absolute dispersity and rate of change of dispersity are higher as grafting density, σ, is increased.

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EXPERIMENTAL SECTION

Chemicals and Reagents. (3-Glycidoxypropyl)dimethylethoxysilane (GPDMES) and trimethylethoxysilane (TMES) were purchased from Gelest, Inc., and used as received. Calcium hydride, tetrahydrofuran, sodium hydroxide, dicholoromethane, Aliquat 336, and hydrofluoric acid (48 wt % in water) were purchased from SigmaAldrich and used as received. ε-Caprolactone was purchased from AlfaAesar, dried overnight over calcium hydride, and distilled under reduced pressure immediately before use. Silica nanoparticles (IPAST-ZL), 30 wt % in isopropyl alcohol (Rh = 70 nm, RTEM = 56 nm), were kindly donated by Nissan Chemical Co. Synthesis of Variable Initiator Functional SiNPs. Silica nanoparticles (SiNPs) (10 mL, 30 wt % in isopropyl alcohol) were centrifuged and redispersed in deionized water three times, with the final solution concentration as 3 g of SNPs in 200 mL of deionized water. The solution pH was adjusted to 11 using 0.1 M sodium hydroxide solution. In an example synthesis of high graft density initiator-functional particles, (3-glycidoxypropyl)dimethylethoxysilane (GPDMES) (1.89 g, 8.64 mmol) and trimethylethoxysilane (TMES) (0.256 g, 2.16 mmol) were added simultaneously and dropwise to a rapidly stirring solution of SiNPs. For the mid and low grafting density particles 4.32 and 2.16 mmol of GPDMES and 6.48 and 8.64 mmol of TMES were used, respectively. The reaction mixture was held at reflux for 24 h, centrifuged and redispersed in deionized water three times, and dried in vacuo at 50 °C for 24 h. Synthesis of Variable Brush Length PCL Functional SiNPs. Initiator-functionalized silica nanoparticles (1.80 g) were added to a 100 mL Schlenk flask, and vacuum was applied while stirring for 3 h to remove moisture from the reaction flask, periodically backfilling with dry argon. Freshly distilled ε-caprolactone (54 mL) was added via syringe. The flask was placed into a bath sonicator for 1 h to yield a B

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Figure 1. Schematic of variable surface density initiator-functional SiNPs. clear, colorless dispersion. A solution of stannous octoate (180 mg in 1.00 mL of o-xylene) was added via syringe. This solution was transferred in equal volumes via cannula to dry, argon-purged 25 mL round-bottom flasks equipped with magnetic stir bars. The roundbottom flasks were heated to 130 °C for variable amounts of time (e.g., 40, 80, 120, 160, 200, and 240 min). To terminate the polymerizations, 10 mL of THF was rapidly added. The polycaprolactone-functionalized SiNPs were purified by repeated centrifugation and redispersal in THF. Cleavage of PCL Brushes Using Hydrofluoric Acid. In order to determine the chain properties of the grafted PCL, functionalized nanoparticles (300 mg) were dispersed in dichloromethane (5 mL). Phase transfer catalyst (Aliquat 336, 100 mg) was added, followed by hydrofluoric acid (5 mL, 48 wt % in water). The reaction was allowed to proceed for 16 h with stirring at room temperature. After reaction, the solution was poured into a large excess of 1 M sodium bicarbonate and stirred until bubbling ceased, about 30 min. The dichloromethane layer was collected and evaporated using rotary evaporation to yield an off-white solid. Dynamic Light Scattering Measurements. Dynamic light scattering (DLS) analysis was performed on an ALV/CGS-3 fourangle, compact goniometer system (Langen, Germany), which consisted of a 22 mW HeNe linear polarized laser operating at a wavelength of λ = 632.8 nm and scattering angles from θ = 42°−150°. Fluctuations in the scattering intensity were measured via a ALV/LSE5004 multiple tau digital correlator and analyzed via the intensity autocorrelation function (g(2)(τ)). Decay rates, Γ, were obtained from single-exponential fits using a second-order cumulant analysis, and the mutual diffusion coefficient, Dm, was calculated through the relation

Γ = q2Dm

sample was deposited on a platinum pan and heated under 10 mL/min nitrogen flow at a rate of 20 °C/min, held at isotherm at 100 °C for 10 min, and then heated to 600 °C at a rate of 20 °C/min.

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RESULTS AND DISCUSSION Variable Surface Density Initiator Immobilization. In order to initiate polymerization of ε-caprolactone, hydroxyl functionality was required on the nanoparticle surface. To impart hydroxyl functionality on the SiNP surface, GPDMES was used; as during surface immobilization conditions, the epoxide ring is opened to give a diol. Additionally, TMES, which bears functionality inert to the polymerization conditions, i.e., methyl groups, was used as a way to control initiator density. By varying the molar ratios of GPDMES and TMES, different surface densities of initiating species were achieved, as illustrated schematically in Figure 1. Specifically, molar ratios of GPDMES:TMES of 80:20 (high σ), 40:60 (mid σ), and 20:80 (low σ) were used. Constant total moles of silane were used during surface immobilization reactions, such that molsilane,total = molsilane,initiator + molsilane,inert was equal for all three grafting density particles. Because each silane contains only one surface reactive site, the total moles of silane far exceeded the silanol content of the nanoparticles, ensuring full surface coverage, as excess silane is easily removed from the supernatant after centrifugation. Thermogravimetric analysis was used to quantify the density of initiating sites of the surface, as shown in Figure 2 (details of the calculations can be found in the Supporting Information). For the high σ, mid σ, and low σ the surface density of initiating sites was found to be 1.55, 0.58, and 0.14 initiators/nm2, respectively. These values are in agreement with previous

(1)

2

where q is the scalar magnitude of the scattering vector. The hydrodynamic radius (Rh) was calculated through the Stokes−Einstein equation Dm ≈ D0 =

kBT 6πηsR h

(2)

where Dm is approximately equal to the tracer diffusion coefficient, D0, kB is the Boltzmann constant, T is the absolute temperature, and ηs is the solvent viscosity. Light scattering measurements were performed at 25 °C. Samples were diluted to 0.1 mg/mL solutions in THF, passed through a 0.45 μm poly(vinylidene fluoride) syringe filter into a borosilicate, precleaned cuvette for analysis. Plots of decay rate, Γ from cumulant analysis, as a function of squared scattering angle vector, q2, for all particles analyzed in this study can be found in the Supporting Information, Figures S1−S17. Gel Permeation Chromatography. Gel permeation chromatography (GPC) was performed at 40 °C using an Agilent Technologies 1260 Infinity Series liquid chromatography system with an internal differential refractive index detector and two Waters Styragel HR-5E columns (7.8 mm i.d., 300 mm length, guard column 7.8 mm i.d., 25 mm length) at a flow rate of 1.0 mL/min, using narrow molecular weight polystyrene standards. Thermogravimetric Analysis. Thermogravimetric analysis (TGA) was performed on a TA Instruments Q5000. About 5 mg of

Figure 2. TGA mass loss profiles for high (red), mid (blue), and low (black) density initiator functional particles, calculated to be 1.55, 0.58, and 0.14 nm−2, respectively. C

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Macromolecules studies using similar silanes to immobilize initiators on SiNP surfaces.53 Grafting-From Polymerization of ε-Caprolactone on Variable Initiator Density SiNPs. The synthesis of PCLgrafted SiNPs was carried out under bulk polymerization conditions, and reaction time was varied in order to achieve brushes of different lengths (Scheme 1). Small amounts of oScheme 1. Synthesis of Polymer-Grafted Silica Nanoparticles

Figure 3. Brush grafting density as a function of initiator grafting density. The line is added as a guide for the eye.

xylene were used to facilitate accurate transfer of stannous octoate catalyst. The resulting nanoparticles were analyzed using thermogravimetric analysis, dynamic light scattering, and GPC of free polymer and polymer brushes after cleavage upon core digestion with hydrofluoric acid. TGA revealed brush grafting densities of 0.61, 0.43, and 0.21 chains/nm2 termed herein as high, mid, and low σ, respectively (details of these calculations can be found in the Supporting Information). Polymer-grafted nanoparticle properties are shown in Table 1. It has been shown that as surface bound initiator density increases, so too does polymer graft density, but that eventually this reaches a plateau of ∼0.7 chains/nm2.53 Similar behavior was observed in this study, shown in Figure 3, as our high σ nanoparticles contained 1.55 initiators/nm2, but the resulting polymer brush was grafted at a density of 0.61 nm−2. The mid σ system showed a reduction in surface density of initiators at 0.58 nm−2 to chains grafted at 0.43 nm−2. Finally, the low σ system contained initiators at 0.14 nm−2 and chains at 0.21 nm−2. This apparent increase in surface density may be due to the slight ability of the secondary alcohol from GPDMES to initiate polymerization. Brush Thickness for Polydisperse Grafts. Figure 4 shows brush length as a function of brush molecular weight, for high, mid, and low σ PCL-functional SiNPs. Brush length was determined as lb = R h,PCL − SiNP − R h,SiNP

Figure 4. Brush length as a function of brush number-average degree of polymerization for three different grafting densities, high (black circles, σ = 0.61 nm−2), mid (blue squares, σ = 0.43 nm−2), and low (red triangles, σ = 0.21 nm−2). Dashed lines represent extreme limits of brush dimensions. Upper limit represents the contour length, L; lower limit represents radius of gyration, Rg. Solid lines are fits to the equation lb = b + cNa, where a = 1.39 (R2 = 0.99), 1.47 (R2 = 0.99), and 1.84 (R2 = 0.99) for high, mid, and low σ, respectively. Typical error in the data points is ±2 nm.

the bare particle. For all three grafting densities, the brush thickness lb scales as Na where the scaling exponent a = 1.39, 1.47, and 1.84 for the high, mid, and low σ sets, respectively. This manifests as an upward curvature in Figure 4 for all grafting densities. These results further indicate that all three sets of brushes are in the concentrated polymer brush regime (vide inf ra). In the concentrated brush regime, due to excluded

(3)

where Rh,PCL−SiNP is the hydrodynamic radius of the polymer grafted nanoparticle and Rh,SiNP is the hydrodynamic radius of Table 1. Polycaprolactone-Grafted Nanoparticle Properties high grafting density

mid grafting density

low grafting density

brush length (nm)

Mn brush (g/mol)

Đ brush

brush length (nm)

Mn brush (g/mol)

Đ brush

brush length (nm)

Mn brush (g/mol)

Đ brush

26 31 43 60 65 84

3700 6000 8900 13000 14300 18300

1.69 1.88 2.02 2.39 2.35 2.39

8 15 28 44 53 73

4600 7900 11900 17300 19700 24300

1.56 1.68 1.86 2.06 1.98 2.06

1 7 14 27 36

3300 7800 11600 16800 19200

1.32 1.42 1.43 1.55 1.64

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Figure 5. Gel permeation chromatograms for cleaved (left) and free (right) polymer for high grafting density system as a function of polymerization time.

Rg of a grafted polymer chain is lower than half the square root

volume effects and non-Gaussian chain dimensions, lb scales as Na where a = 1 when dispersity is held constant.22,54−56 Brush length increases with increasing dispersity at constant degree of polymerization. In this system, because dispersity increases as a function of degree of polymerization (see Figure 6), the brush length scales with degree of polymerization in a nonlinear fashion. This study demonstrates the first experimental evidence of this behavior that had only previously been shown in simulation and theory. Surface curvature plays an important role in the behavior of polymer brushes. On planar surfaces, the available volume for chains to occupy does not change as a function of distance from the surface (assuming monodisperse brushes). However, when brushes are grafted on spherical surfaces, the available volume for a chain to occupy increases with increased distance from the surface, leading to crossover in chain dimensions with increasing radial distance. For example, it has been shown by Ohno et al.54 and Dukes et al.22 that there exists a critical radius, rc, where a transition from concentrated brush regime to semidilute brush regime occurs rc = rcoreσ *1/2ν* − 1

of the inverse grafting density, σ −1 /2 , there should be no neighboring chain interactions. The low σ set begins with brush lengths near the radius of gyration (lower dashed boundary in Figure 4). As the brush molecular weight increases to a critical mass such that the Rg exceeds the maximum non-neighboring interaction area, the brush length rapidly increases and, as in the case of the mid σ particles, exhibits a scaling factor a > 1. While all three grafting density sets show that lb scales with N nonlinearly, the scaling exponent increases with decreasing grafting density. The cause of this, we hypothesize, is due to the additional conformational freedom afforded by lower grafting density. Increasing brush dispersity results in a net increase in system entropy.36,57 Short chains will tend to form a coil near the surface, resulting in extension of long chains near the surface when surrounded by neighboring chains. The surface proximate extension of long chains is an entropically unfavorable process but is balanced by the additional entropic freedom gained by long chains near the end of the brush layer when neighboring interactions are reduced. The net result is an increase in brush length over the monodisperse analogue. As grafting density is reduced, the ability for short chains to coil near the surface is enhanced and the effect of dispersity on brush length is magnified, leading to the trend of scaling exponents increasing with decreasing grafting density. Evolution of Molecular Weight Distribution and Dispersity during Polymerization. The ring-opening polymerization of ε-caprolactone carried out with stannous octoate catalyst is generally a controlled polymerization, characterized by low dispersities and molecular weights given by the ratio [M]/[I], where [M] and [I] are the concentration of monomer and initiator, respectively.48,58 However, more complicated behavior was observed in the system explored in this study. Figure 5 shows GPC chromatograms for the cleaved polymer (left) and free polymer (right) (cleaved polymer and free polymer chromatograms directly overlaid can be seen in Figures S18−S34). As the polymerization begins, propagation events predominately occur from the surface of the SiNP. However, at the polymerization temperature of 130 °C surreptitious water can be liberated from the SiNP surface.49 As water is liberated from the nanoparticle surface, chain scission events begin to occur which leads to both a broadening in the molecular weight distribution of surface grafted chains and liberation of a free polymer into solution that continues to propagate. This process continues, along with continued

(4)

where rcore is the radius of the silica nanoparticle, σ* is the reduced grafting density, given by σ* = b2σ, and ν* = ν/(4π)1/2, where ν is the excluded volume parameter, and b is the statistical segment length. As surface curvature (held constant in this study) increases or graft density decreases, the critical radius decreases. Because the value rc includes the core radius, the critical brush length, lb,c, for the concentrated brush regime to semidilute brush regime transition is easily calculated from the difference in rc and the core radius. We calculate the lb,c in our high, mid, and low σ particles to be 228, 181, and 105 nm, respectively, much higher than the brush thicknesses observed here. As such, based on the molecular weight of polymer formed on our SiNPs and the brush lengths measured, this system does not crossover into the semidilute brush regime. Additionally, the high σ set shows brush lengths at low molecular weights as nearly fully extended to the contour length, L, represented as the dashed upper boundary in Figure 4. Because the brushes are grafted to a spherical substrate, even though no crossover to the semidilute brush regime is calculated to occur, the available volume each chain can occupy continually increases with increasing distance from the surface. As such, the available volume as a function of brush length is proportionally smallest close to the surface. Conversely, if the E

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Macromolecules propagation and molecular weight growth of both surface grafted chains and free polymer, until all monomer is consumed. Free polymer molecular weight distributions remain much narrower than the corresponding surface bound polymer due to effective local concentration of chain ends being much lower. Lastly, a high molecular weight shoulder was observed at high polymerization times for the free polymer. We attributed this to chain−chain coupling events near the end of the polymerization when the ratio of [chains ends]/[monomer] is high, as stannous octoate catalyst can act as an esterification catalyst.59 The effect of chain end proximity to neighboring chains on dispersity can be inferred from Figure 6, which presents

Figure 7. Ratio of number-average molecular weight for free polymer chains to number-average molecular weight for surface bound chains as a function of grafting density. Inset: free chain dispersity as a function of grafting density.

densities for reasons due to chain conformations. As discussed above, in the case of high dispersity, shorter chains will coil toward to surface, the entropic penalty for which is balanced by the entropic gain of the longer chains having access to additional conformation states. When short chains bury themselves near the surface, they are unavailable for further polymerization and, thus, effectively terminated. This lowers the average molecular weight compared to the situation where all chains propagate, and the dispersity then increases as the longest chains become even longer. The second effect may be due to increased difficulty in monomer diffusion through the most densely grafted brushes, resulting in lower average brush molecular weights. Furthermore, it was found that free chain dispersity is independent of grafting density (see inset in Figure 7 and Figure S38), as expected for normal bulk polymerization of ε-caprolactone. Hydrodynamics of Disperse Brushes. One way to quantitatively express the degree to which a brush polymer is extended is by introducing a parameter we have defined as the extension ratio, ξ, given by the relationship

Figure 6. Brush dispersity as a function of brush molecular weight for three different grafting densities: high (black, σ = 0.61 nm−2), mid (blue, σ = 0.43 nm−2), low (red, σ = 0.21 nm−2).

dispersity as a function of surface bound polymer molecular weight for the three grafting densities probed in this study. Because of the ability of chains ends to cause transesterification, it was observed that higher grafting densities resulted in higher brush dispersity. In the low grafting density samples, the dispersity of chains for the first measured sample (corresponding to a molecular weight of 3300 g/mol) was 1.32. As the polymerization proceeded, a steady increase was observed, up to 1.64 for the final sample. As grafting density was increased, the dispersities of the lowest molecular weight grafting sample increased to 1.56 and 1.69, for the mid and high σ, respectively. Likewise, the final dispersities increased as σ increased, with values of 2.06 and 2.39 for the mid and high σ samples, respectively. Finally, the rate at which Đ increased as a function of molecular weight increased with grafting density. It is expected that the rate of change in Đ would increase with increasing grafting density, as increasing grafting density essentially increases the local concentration of both reactive chain ends and backbone ester linkages. These results provide direct evidence of the effects decreasing proximity of chain ends to neighboring chains as grafting density is increased. The effect of grafting density on molecular weight dispersity was also reflected in the ratio of the free chain molecular weight to surface tethered chain molecular weight. Figure 7 shows this ratio as a function of grafting density. A linear relationship of increasing disparity between free and brush chain molecular weight with grafting density was observed, consistent with what has been observed in other systems.60 This behavior has two likely sources. The first is that at higher grafting densities more chains are effectively “terminated” than at lower grafting

ξ=

lb L

(5)

where lb is the observed brush length and L is the contour length. This ratio approaches unity for chains that are fully extended. As chain length increases (i.e., increasing distance from the nanoparticle surface), this ratio should decrease, eventually reaching an asymptotic limit of zero. A decrease in grafting density will accelerate this effect. In the limit of infinite molecular weight, at any grafting density, on any spherical surface, the brush dimensions will approach that of a free chain in solution, governed by the relationship R g ∼ N3/5

(6)

while the contour length scales as

L ∼ N1

(7)

Therefore, in the limit of infinite molecular weight, because ξ scales with N−2/5, the ratio approaches zero. This does not take into account the crossover behavior from concentrated brush regime to semidilute brush regime to mushroom regimes, as the scaling of lb with N is reduced in these transitions. The ξ ratio, F

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able to more effectively penetrate the brush layer with increasing Đ and decreasing σ, then as the nanoparticle diffuses through solution, higher friction should be experienced by the particle. In other words, as σ decreases and/or brush length increases, a shift from highly nondraining to more free draining occurs, which leads to increased friction factor, f, experienced by each chain. An increase in f leads to a decrease in the diffusion coefficient, leading to higher hydrodynamic radii. While polymer chains in solution exhibit mostly nondraining behavior, the effect may be pronounced in a system such as ours where tens of thousands of chains are grafted to the particle surface. Ultimately, if solvent is able to more easily penetrate the brush layer, chain friction may contribute a significant portion to the hydrodynamics of the system, causing positive deviations from the ratio ξ, as seen in the mid and low σ cases in Figure 8.

however, does capture the effects of additional volume for chains to occupy as they extend from a curved interface and therefore adopt more entropically favorable conformations. In practice, the molecular weights required to reach the asymptotic limit of this ratio are unrealistically large, so this behavior is not observed presently. However, in the low molecular weight limit, which is easily accessed, the behavior of ξ approaching unity and decreasing with N−2/5 is observed, as seen in Figure 8. Here, ξ is plotted as a function of molecular

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CONCLUSIONS In summary, we have shown that polycaprolactone-grafted silica nanoparticles are an ideal system to study the effects of surface bound chain molecular weight dispersity on brush properties. Brush length behavior in solution exceeds the typical scaling observed in concentrated brush regime systems, with brushes obtained in this study scaling with N>1, previously only observed in simulation and theory Furthermore, chain grafting density had a remarkable effect on grafted chain dispersity during the course of the polymerization. As grafting density increased, not only did dispersity increase, but the rate at which dispersity increased was enhanced as well. Because of the observed dispersity of the grafted polymer chains, unique brush behavior was observed, as quantified by the so-called “extension ratio”. Here, even at lower grafting densities, apparent increases in chain constraints were observed due to swelling effects and additional hydrodynamic interactions. The ability to tune dispersity simply by adjusting grafting density is expected to give exceptional control over nanoparticle dispersibility in composite materials.

Figure 8. Extension ratio as a function of brush molecular weight for three different grafting densities: high (black circles, σ = 0.61 nm−2), mid (blue squares, σ = 0.43 nm−2), low (red triangles, σ = 0.21 nm−2).

weight for the three grafting densities probed in this study. As expected, for the high σ case, as brush length increases, and therefore as distance from the surface increases, the chain is able to access higher volumes. This allows the chain to adopt a more entropically favorable conformation, leading to a reduction in ξ. Anomalously, however, the extension ratio for the mid and low σ samples does not obey the N−2/5 scaling behavior. We hypothesize that this behavior is due to differing contributions to hydrodynamic interactions. At very high grafting densities, solvent is unable to effectively penetrate the brush layer. Indeed, for monodisperse brushes on planar surfaces the solvent penetration length, lp, scales as σ−2/3.61 However, as dispersity is increased, lp scales much more weakly with grafting density, going as σ−1/6.62 At very high grafting densities, solvent penetration is greatly reduced and so too are hydrodynamic interactions leading to primarily nondraining behavior. Because of this, the brush scaling behaves as expected and ξ scales with N−2/5. However, in the mid and low σ cases, the grafting density is such that solvent is able to effectively penetrate the brush layer. Even using the scaling relationship lp ∼ σ−1/6, the solvent penetration length for the low graft density set is more than 20% greater than that of the high graft density set. As solvent penetrates and solvates the brushes, swelling is induced and hydrodynamic interactions are reduced, leading to brush lengths higher than expected. This leads to an apparent increase in ξ with increasing N. Furthermore, it has recently been shown by Qi and co-workers in simulation and theory that not only does lp depend on N but also a crossover in scaling occurs with increasing dispersity.62 In monodisperse and weakly polydisperse brushes, lp scales as N1/2, but in strongly polydisperse brushes (Đ = 2) lp scales as N2/3. If solvent is

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00608. Dynamic light scattering; decay rates (Γ) as a function of squared scattering angle vector (q2); thermogravimetric analysis; plots of weight percent as a function of temperature; gel permeation chromatography; refractive index as a function of retention time; calculations of grafting density for initiator and polymer functional particles (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]fl.edu; Tel 352-392-9150; Fax 352-3929741. ORCID

Daniel A. Savin: 0000-0002-9235-517X Notes

The authors declare no competing financial interest. G

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ACKNOWLEDGMENTS This research was made possible by a grant from The Gulf of Mexico Research Initiative under GoMRI-II-798. K.C.B. was also funded in part by a fellowship from the Eastman Chemical Company. Data are publicly available through the Gulf of Mexico Research Initiative Information & Data Cooperative (GRIIDC) at https://data.gulfresearchinitiative.org (UDI: R2.x227.000:0005). The authors thank Nissan Chemical Co. for the donation of silica nanoparticles as well as Prof. Arthi Jayaraman (UD), Prof. Scott Grayson (Tulane) and Dr. Michael Bell for useful discussions throughout the study.

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