Kinetics of Dynamic Polymer Brush Formation - Macromolecules (ACS

Jul 11, 2017 - The kinetics of dynamic polymer brush formation, which is driven by interfacial segregation of amphiphilic block copolymers, was invest...
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Kinetics of Dynamic Polymer Brush Formation Hirokazu Tanoue,† Manabu Inutsuka,† Norifumi L. Yamada,‡ Kohzo Ito,† and Hideaki Yokoyama*,† †

Graduate School of Frontier Sciences, The University of Tokyo, Chiba 277-8561, Japan High Energy Accelerator Research Organization, Tsukuba, Ibaraki 319-1108, Japan

‡

S Supporting Information *

ABSTRACT: The kinetics of dynamic polymer brush formation, which is driven by interfacial segregation of amphiphilic block copolymers, was investigated by quartz crystal microbalance (QCM) and neutron reflectivity (NR). High speed formation kinetics in the early stage was probed by QCM, and the later stage, where the formation kinetics became relatively slow, was investigated by NR. QCM detected fairly the fast brush formation kinetics on the order of tens of seconds for the copolymers in use. The dynamic polymer brush rapidly grows initially and hence repairs itself when the surface is damaged and the brush is partly lost. This fast dynamic polymer brush formation is driven by relatively slow diffusion of block copolymers in the matrix. The slow diffusion suggests that the diffusion mechanism is not controlled by simple Rouse or reputational diffusion but by the activation hopping mechanism of selfassembled diblock copolymers.

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INTRODUCTION End-grafted polymer chains are called polymer brushes.1 Polymer brushes have been paid attention as tools for surface modification since they provide unique properties such as preventing adhesion onto solid surfaces,2−5 enhancing dispersion of particles,6−8 and lubrication.9−11 Polymer brushes have been fabricated mainly by two methods. One is the “grafting-to” method,12−14 in which end-functionalized polymers are grafted onto solid surfaces by physical or chemical adsorption. Another is the “grafting-from” method,15−17 in which surface anchored initiators polymerize the fed monomers to form brushes on solid surfaces. A new method for fabricating polymer brushes have been developed by Inutsuka et al.,18 where polymer brushes are fabricated by spontaneous segregation of amphiphilic block copolymers to water interface in a mixture with low-Tg elastomer. Surprisingly, this method leads to polymer brushes with high grafting density and high extension ratio as experimentally revealed. This extremely high grafting density using segregation of block copolymers is driven by the large hydration energy of poly(ethylene glycol) (PEG) integrated over the whole block which overcomes the elastic energy of extended block copolymer chains. To gain the maximum hydration energy by exposing the PEG blocks to water, the block copolymer squeeze themselves at the interface and increases the brush density. Because the copolymers are not solidly fixed at the surface of the elastomer, they can dynamically respond to environmental changes. Therefore, polymer brushes fabricated by this method can be named as “dynamic polymer brush”. Here we clarify the difference between the dynamic polymer brush and conventional graftingto brush systems: (a) The grafting-to brush is formed by © XXXX American Chemical Society

segregation of functional or block copolymers to the surface of solid from solution side. The dynamic polymer brush in this work is formed by segregation of block copolymers to the surface of elastomer from elastomer side. The grafting-to brush can only form in polymer solution, but the dynamic polymer brush can form in pure water. (b) The driving force for grafting-to is the interaction between the polymer and the solid surface. The driving force for the dynamic polymer brush is the interaction between the polymer and water, i.e., hydration energy of PEG. The integrated hydration energy (volume interaction) of a whole block is in general much larger than the interaction energy with solid surface (areal interaction) in grafting-to brushes. Such a large driving force for brush formation of dynamic polymer brush can make the brush density higher than typical grafting-to brushes.18 The unique property of dynamic polymer brush is the potential self-repairing function. Even if the copolymer chains at the brush layer are lost due to physical damage, the copolymer chains remaining in the matrix spontaneously segregate to and repair the damaged area. For practical applications of the dynamic polymer brush, it is important to investigate the time scale of the repair. However, it is experimentally difficult to measure the recovery time of the damaged area because one must do everything in liquid. In contrast, it is technically feasible to measure the initial formation kinetics of the dynamic polymer brush from fresh surface, and it is reasonable to assume that the formation kinetics and repairing kinetics are equivalent. Therefore, by Received: March 27, 2017 Revised: July 3, 2017

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DOI: 10.1021/acs.macromol.7b00636 Macromolecules XXXX, XXX, XXX−XXX

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Film Preparation. PEG-b-PDMS, H-PDMS, and PVDMS were dissolved in a mixed solvent of tetrahydrofuran (THF, Wako Pure Chemical Industries, Ltd.) and toluene (Wako Pure Chemical Industries, Ltd.), where the ratio of THF and toluene was 4 to 1 in volume. H-PDMS to PVDMS ratio was set to 9 to 1 in weight. We mixed 10 wt % of PEG-b-PDMS in (HPDMS + PVDMS) in the mixed solvent with the total polymer concentration of 3 wt %. Karstedt’s catalyst was added (0.05 wt %) to the solution, and 30 min later the solution was spin-casted at 2000 rpm for 60 s onto quartz substrates covered with gold electrode for NR and quartz sensors for QCM. Prepared solutions were filtrated (pore size of 0.2 μM), before spincasted onto substrates. After spin-casting films onto substrates, the films were annealed at 70 °C in vacuo for 12 h to complete crosslinking reaction. Neutron Reflectivity (NR). We conducted the NR measurement using Soft Interface Analyzer (SOFIA)27,28 at Beamline 16 of J-PARC MLF. For the NR experiment, D2O (99.9% deuterated, Aldrich, Inc.) was used to enhance the contrast at the polymer/water interfaces. We conducted time-resolved measurement for 7200 s after the 250 nM PEG-SH solution in D2O was introduced into a cell using a liquid injection system,29 in which wavelength of neutrons, λ, from 0.2 to 1.78 nm was used with the incident angle, θ, of 1.10° to observe the reflectivity depending on the absolute value of the neutron momentum transfer, q = 4π sin θ/λ, from 0.14 to 1.2 nm−1. After 7200 s, the absolute reflectivity with the total reflection was measured at an incident angle of 0.60°, and the time-resolved relative reflectivity at 1.10° was converted to absolute reflectivity by multiplying a factor to be overlapped with that at 0.60°. Finally, 24 h after the injection of D2O, we measured the reflectivity spectrum using the wavelength band from 0.2 to 0.88 nm with the incident angle of 0.30°, 0.75°, and 1.80° to cover the q-range from 0.075 to 2 nm−1. The scattering length density (SLD) profile normal to the quartz surface was computed by fitting the reflectivity spectra using MOTOFIT program30 in order to determine the polymer brush structure. We fitted the reflectivity spectra with a multilayer model consisting of quartz, PDMS matrix, PEG brush, and D2O. The SLD values of quartz, PDMS, PEG, and D2O were 4.18, 0.06, 0.64, and 6.36 × 10−6 Å2,31 respectively. We used one box model with roughness described by error function for the brush layer. We first fitted the spectrum measured 24 h after the injection of D2O and determined the structure of brush, thickness, and surface roughness of the PDMS matrix. When fitting spectra measured in time-resolved measurement, thickness and surface roughness of the PDMS matrix were fixed. It is reasonable to assume that thickness and surface roughness of the matrix are not affected by polymer brush formation. Quartz Crystal Microbalance (QCM). QCM experiments were conducted using a N2PK Vector Network Analyzer,32 and the data were obtained by software QTZ.33,34 We used AT-cut quartz crystals (Inficon, a diameter of 25.4 mm) with a gold electrode, which have the fundamental frequency of 5 MHz. Temperature of water was preset to 30.0 ± 0.1 °C, since the resonance frequency of quartz is extremely sensitive to temperature. The quartz substrates coated with elastomer films were also temperature controlled at 30.0 ± 0.1 °C in air until the complex frequency became stable and then were immersed into water. We observed negligible heat shock by immersing the quartz into the water. The resonance frequency shift Δf and dissipation rate shift ΔΓ were determined and recorded by fitting the spectrum only at the third overtone. In QCM measurements with network analyzer, several overtones were often measured sequentially in one measurement, but we restricted to only one overtone to enhance the time resolution. The third overtones were chosen because the higher overtones dissipated heavily in water, and the peak fitting became difficult. The measurement of fundamental (5 MHz) was omitted since the fundamental is known to be affected by various noise.35

tracing the formation kinetics of dynamic polymer brush, the time scale of self-repairing can be estimated. Structure analysis of embedded interfaces in a nanometer scale remains a difficult problem. Even the growth of polymer brush from fresh surface cannot be probed easily. Neutron reflectivity (NR) has been widely used to measure equilibrium polymer brush structures.19−21 In contrast, NR has not been used for kinetics measurement due to its poor time resolution. In the previous study,18 the formation kinetics of the dynamic polymer brush was attempted to be followed by NR, but the brush formation was too fast to be observed successfully even with shortest available exposure time, a few minutes, of NR, indicating that the dynamic polymer brush forms in less than a few minutes. Ellipsometry has also been used to measure polymer brush structures in situ;22,23 however, the optical analytical methods such as ellispsometry lack in accuracy for very thin film such as 10 nm thick films. Measuring timedependent water contact angles to understand the formation kinetics was carried out,24 but the dependence of contact angles on the brush density was far complicated due to inhomogeneous segregation around the water droplet, and the kinetics cannot be directly discussed. Therefore, another effective method with high sensitivity and high time resolution is desired. In order to measure high speed brush formation kinetics, we used quartz crystal microbalance (QCM). QCM has a time resolution of second order and sensitive to structural changes at the surface and interfaces; therefore, QCM has a potential to measure the high speed brush formation kinetics. The drawback of QCM, however, is the complexity of the response to brush formation because QCM is sensitive not only to the mass change but also to viscous and elastic response of an interfacial layer. We recently developed the effective way of using QCM to detect the change of viscoelastic properties of a brush layer on solid surface.38 QCM can reveal the crossover from viscous to elastic brush layers as the brush density increases with time. The crossover time, at which the brush density reaches the characteristic brush density and crossovers from viscous to elastic, is determined using QCM. In particular with PEG of 2000 in molecular weight, the crossover brush density was revealed to be 0.17 chains/nm2. The crossover time can be used as the time that the brush reaches the characteristic brush density. In addition to the QCM measurement, we conducted time-resolved NR measurement for the late stage of the dynamic polymer brush formation. NR has been suffered from poor time resolution, but in recent years, time solution of NR significantly improved. Therefore, still the early stage brush formation is out of reach for NR, but the late stage brush formation kinetics can be traced by the NR using the new generation of neutron source at J-PARC.

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EXPERIMENTAL SECTION

Materials. We used poly(ethylene glycol)-b-poly(dimethylsiloxane) (PEG-b-PDMS) (Polymer Source, Inc.) as an amphiphilic block copolymer. Molecular weights of PEG and PDMS blocks are 2100 and 5000 g/mol, respectively. The elastomer matrix was fabricated by cross-linking silane-terminated PDMS with molecular weight of ∼62 700 (H-PDMS, Gelest, Inc.) and poly(vinylmethylsiloxane-r-dimethylsiloxane) with molecular weight of ∼30 000 (4−5% of vinylmethylsiloxane, PVDMS, Gelest, Inc.) via hydrosilylation.25,26 The platinum−1,3-divinyl-1,1,3,3-tetramethyldisiloxane complex (Karstedt’s catalyst) in xylene (∼2% platinum, Aldrich, Inc.) was used as a catalyst for hydrosilylation.

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RESULTS AND DISCUSSION Neutron Reflectivity. The spectra of the films with and without block copolymers in contact with D2O for 24 h are shown in Figure 1a. In the spectrum of the film with block B

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Figure 1. (a) NR spectra of the films without (green circles) and with block copolymers (purple circles) in contact with D2O with fitting curves (black lines). (b) SLD depth profiles of films without (green line) and with block copolymers (purple line). 0 nm corresponds to the surface of PDMS elastomer.

Figure 3. (a) Neutron reflectivity spectra measured at 250 s (red circles), 850 s (yellow circles), 950 s (green circles), 1550 s (sky blue circles), 2450 s (blue circles), 4700 s (pink circles), 7100 s (orange circles), 24 h (purple circles), and fitting curves (black lines). For the time slices up to 2450 s, the intensity was integrated within ±50 s. For the time slices 4700 s and beyond, the intensity was integrated within ±100 s. (b) SLD depth profiles at 250 s (red line), 850 s (yellow line), 950 s (green line), 1550 s (sky blue line), 2450 s (blue line), 4700 s (pink line), 7100 s (orange line), and 24 h (purple line).

copolymers, only the narrow fringes in the low q range, which correspond to the total thickness of PDMS elastomer, are observed. In contrast, in the spectrum of the film with block copolymers, the additional wider fringes with a minimum at 1 nm−1 are found, which indicates the presence of a thin brush layer. We confirmed from the SLD profile (Figure 1b) that the brush layer formed on the PDMS elastomer. The graft density and thickness of the film are 1.1 chains/nm2 and 3.6 nm, respectively, which confirm the dense PEG brush formed in 24 h after the injection of D2O. We defined the thickness of the brush as the length from the surface of PDMS to the inflection point of the error function (Figure 1b). Figure 2 is the time-resolved NR spectra of the PEG brushes in the first 7200 s from the injection of D2O. Within 2000 s, the

Figure 4. Graft density (red circles) and brush thickness (blue circles) plotted against time.

overlap at the graft density of 0.08 chains/nm2 or above. Thus, the brush structures detected using NR are all in brush regime. The structure even detected at 250 s, the shortest accessible time by NR, is brush; therefore, NR does not have an access to the graft density range of the mushroom regime, where segregated PEG chains are not overlapping. We employed QCM in order to measure the earlier stage of brush formation kinetics within 250 s. Quartz Crystal Microbalance (QCM). The time evolution of complex frequency shifts of the films with and without copolymers after the films were immersed into water are shown in Figure 5a. The film without block copolymers shows the complex frequency shifting significantly, and instantaneously at time zero, the moment film was immersed into water. The complex frequency shifts are solely from the effect of the water viscosity. In contrast, after the film with block copolymers were immersed into water, the complex frequency immediately shifted and further drifted for more than 1000 s. The absolute values of the complex frequency shifts were much larger than those for the film without block copolymers. In air, the block copolymer chains are embedded in the PDMS elastomer as explained in the Supporting Information. Therefore, the brush formation occurred in this time range. The unique complex frequency shift was observed in the first 100 s; −Δf and ΔΓ increased rapidly and presented the peaks at around 10 and 20 s, respectively, and then decreased as shown in Figure 5b. At first glance, it might appear that the brush immediately formed

Figure 2. Time-resolved NR spectra of PEG brushes in the first 7200 s after the injection of D2O.

NR spectra change drastically; however, after 2000 s, no remarkable change is found. In order to discuss the structure of the brush as a function of time in detail, we extracted and fit the reflectivity curves at 250, 850, 950, 1550, 2450, 4700, and 7100 s. The spectra and fitting curves and the SLD depth profiles computed from fitting are show in Figures 3a and 3b, respectively. The graft density and brush thickness were calculated from the SLD profiles in Figure 3 and plotted as a function of time in Figure 4. At the shortest accessible time of 250 s, the graft density is already 0.29 chains/ nm2; the graft density initially increases significantly and then saturates to approximately 0.9 chains/nm2. Segregation slows down after 2000 s probably because segregation of additional chains is hindered by the already segregated brush chains at the later stage. Using the molecular characteristics of the PEG block,36 the overlap density of EG chains is approximately calculated to be 0.08 chains/nm2, and therefore the PEG chains C

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Figure 5. (a) Complex frequency shift as a function of time after films containing (red lines) and not containing (blue lines) block copolymers were immersed into water. Solid lines denote −Δf, and dashed lines denote ΔΓ. (b) Complex frequency shift in the first 100 s after the film containing block copolymers was immersed into water. Solid line denotes −Δf, and dashed line denotes ΔΓ. The data can be divided into three time domains. Time domain I: 0−10 s where both −Δf and ΔΓ are both increasing. Time domain II: 10−20 s where ΔΓ is increasing while −Δf is decreasing. Time domain III: 20 s where both −Δf and ΔΓ are both decreasing.

rigid spheres oscillating in water, the viscous friction would be generated as if spherical objects are dragged in viscous fluid with the Stoke’s law37 as shown in Figure 6. This friction dissipates the energy of oscillation, which leads to the increase of the dissipation rate ΔΓ. Consequently, in the time domain I, the segregated PEG chains are in the mushroom regime. In the time domain II, 10−20 s, −Δf presents a peak at around 10 s and then decreases, while ΔΓ is still monotonically increasing. With the increasing graft density, the PEG mushrooms eventually overlap and crossover to the brush regime. The hydrodynamic mass increases up to the maximum value when the mushrooms are closely packed on the surface and then begins to decreases after brush chains begin to overlap. The water in the brush layer is excluded by segregated PEG chains, and the mass of water dragged by brush chains decreases. Therefore, hydrodynamic mass or −Δf shows a peak at certain brush density. We recall that PEG chains are already included in the film; therefore, segregated PEG chains will not contribute to the mass change of the film. It should be noted that such a peak of −Δf does not appear in the case of simple “grafting-to” brushes where the mass of grafting chains is additional.38 Consequently, the peak of −Δf represents the crossover from mushroom to brush regime. From the molecular characteristics of PEG, the estimated overlap density is ∼0.08 chains/nm2.36 Therefore, at 10 s it is reasonable to consider that the graft density reaches 0.08 chains/nm2. In the time domain III, 20 s, ΔΓ presents a peak at 20 s and begins to decrease. In the previous study38 it was found that the peak of ΔΓ corresponds to the crossover time from viscous to elastic brushes. With the increasing brush density, the volume fraction of PEG in the brush layer and hence the viscosity of brush layer increase. At some point, the brush reaches the characteristic brush density, where brush chains cannot fully relax in the frequency of the QCM measurement, and begins to behave as an elastic layer such as hydrogels at 20 s. In addition, for PEG with Mw = 2000, the crossover from viscous to elastic brush occurs at the graft density of ≈0.17 chains/nm2,38 and therefore it is reasonable to consider that the graft density of the dynamic polymer brush reaches 0.17 chains/nm2 and began to behave as an elastic layer in 20 s. The peaks in −Δf and ΔΓ may also be originated from film resonance in which the acoustic waves in the elastomer film constructively interfere. However, the dynamic brush layer appeared is only 5 nm thick on the 200 nm PDMS layer. The

and then disappeared, but such a scenario must be denied because the NR experiment shows the graft density increasing monotonically as a function of time, and the values of complex frequency shifts of QCM are much larger than the film without block copolymers in any time zone. We also found no evidence of brush chains leaving the interface from the stable film thickness observed by NR. Those unique frequency shifts of QCM cannot be explained simply by the mass or viscosity but are rather related to the hydrodynamic interactions of PEG chains and water. We will divide the measured complex frequency shift into three time domains, 0−10 s, 10−20 s, and 20 s in Figure 5b, and discuss the frequency shift in each domain with the brush structures. In the time domain I, 0−10 s, both −Δf and ΔΓ are increasing monotonically. In this early stage of brush formation, the brush is sparse or even in the mushroom regime where the polymer chains are isolated and random coil. Isolated polymer chains in a dilute polymer solution diffuse by dragging the solvent within the coils by hydrodynamic interaction and behave like rigid spheres with an average hydrodynamic radius RH.37 Therefore, isolated chains on the elastomer surface, mushrooms, also drag the solvent inside of the mushrooms and oscillate with the quartz oscillator. With the increasing number of mushrooms, the effective mass of the water included within mushrooms increases as schematically drawn in Figure 6. We

Figure 6. Schematic diagram of water flowing along the surface of a mushroom. The polymer drags the water inside its pervaded volume.

name this effective mass as “hydrodynamic mass”. The mass of PEG chains is already included even before appearing at the interface; thus, only the hydrodynamic mass of water within mushrooms contributes to the increments of mass and −Δf. However, such hydrodynamic mass does not contribute effectively to the change of ΔΓ. Increasing ΔΓ can be explained by the increasing viscous friction between the surface of mushroom and surrounding water. Since mushrooms behave as D

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Macromolecules difference in thickness is too small to make a film resonance peak. However, even for the films thinner than film resonant thickness, the Sauerbrey relation is not valid, and −Δf and ΔΓ increase tangentially with a load toward the film resonance. Therefore, the growth of brush causes enhanced response in −Δf and ΔΓ compared to the response of the brush directly grown on a QCM sensor. In the QCM measurement, the crossovers from mushroom to brush regime and from a viscous to an elastic layer were observed at 10 and 20 s with the graft density of 0.08 and 0.17 chains/nm2, respectively. We succeeded in tracing the formation kinetics in the early stage of dynamic polymer brush formation using QCM, which was too fast to be monitored by NR. Although quantitative measurement of the graft density at a given time by QCM has still not been achieved, we found two characteristic times and brush densities using complex frequency shift peaks of QCM. Diffusion-Controlled Dynamic Polymer Brush Formation. From the NR and QCM measurements, the graft density of the dynamic polymer brush was successfully monitored and are plotted against square root of time in Figure 7. The results

Figure 8. Schematic diagram the model for calculating the graft density as a function of time. Block copolymers diffuse through discrete layers.

distributed throughout the layers. We also assumed that the copolymer chains having arrived at the water/matrix interface, which is the top layer of 100 layers, instantly move to the polymer brush layer irreversibly, and the concentration of the top layer becomes zero. Thus, in this model the dynamic polymer brush formation is solely controlled by the diffusion of block copolymers to the top layer. The best fit of the simulation is shown with the red solid line in Figure 8 with the diffusion coefficient of D ≈ 2 × 10−18 m2/s. The simulation fits the data very well up to 2400 s and the graft density of 0.80 chains/nm2. This result suggests that until the graft density of 0.80 chains/ nm2, which is surprisingly high, the brush formation is dominated by the diffusion of block copolymers. We should pay attention to the value of diffusion coefficient, D ≈ 2 × 10−18 m2/s. The diffusion coefficient of homo-PDMS with molecular weight similar to the block copolymer used in the experiments in PDMS matrix is D ∼ 10−10 m2/s,39 so the diffusion coefficient of block copolymer is 10−8 times smaller than that of homo-PDMS. Therefore, compared with the homo-PDMS, the block copolymer is almost frozen. It should be noted that even with this extremely slow diffusion, the dynamic polymer brush formation occurred within a minute. This abnormally slow diffusion can be explained by “hopping diffusion”40−42 of block copolymer between micelles as schematically shown in Figure 9. The presence of block copolymer micelles in PDMS is confirmed as presented in the Supporting Information. When the block copolymer chains form micelles in the matrix, block copolymer chains are trapped in micelles; thus, the motion of polymer chains becomes abnormally slow. Another possible explanation could be the

Figure 7. Graft density plotted against square root of time. Red circles are data points from NR, and blue squares are data points from QCM. Red line is the fitting line from model calculation.

from QCM in the earlier stage agrees well with the trend in later stage revealed by NR. Moreover, we observe the linearly increasing graft density with square root of time up to 0.8 chains/nm2. In order to investigate the formation mechanism of the dynamic polymer brush in detail, we simulated the change of graft density as a function of time by introducing the following model. In the model, the copolymers diffuse with diffusion coefficient, D, discretely in multilayers as shown in Figure 8. In the early stage of brush formation, the increasing rate of graft density should be controlled by the amount of block copolymer arriving at the interface. It was assumed that diffusion of copolymers follows Fick’s law: F = −D(Cj − Cj − 1)/l

(1)

where F is the flux of the block copolymer, D is the diffusion coefficient of the block copolymer, Cj is the concentration of the block copolymer in the jth layer, and l is the thickness of each layer. For this simulation, the total thickness of the film was set to 200 nm, the thicknesses of the films used in NR and QCM experiments. The concentration of block copolymers was set to 10 wt %, the experimentally used value. The film was divided into 100 layers, and therefore l = 2 nm, and the additional polymer brush layer was placed independently. We assumed that initially block copolymers are homogeneously

Figure 9. Schematic diagram of hopping diffusion of block copolymer in PDMS matrix. E

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Macromolecules diffusion of micelles; however, Yokoyama et al.42 reported that when block copolymers are embedded in a high molecular weight polymer matrix, the diffusion of micelles do not occur and diffusion of block copolymer is dominated by the hopping diffusion. In this study, cross-linked PDMS was used as a matrix; therefore, the diffusion of micelles does not occur. Consequently, the block copolymers diffuse by hopping between micelles and reach the water interface to form dynamic polymer brush as schematically drawn in Figure 9.

(2) Jeon, S. I.; Lee, J. H.; Andrade, J. D.; De Gennes, P. G. ProteinSurface Interactions in the Presence of Polyethylene Oxide. I. Simplified Theory. J. Colloid Interface Sci. 1991, 142, 149−158. (3) Halperin, A. Polymer Brushes That Resist Adsorption of Model Proteins: Design Parameters. Langmuir 1999, 15, 2525−2533. (4) Pavey, K. D.; Olliff, C. J. SPR Analysis of the Total Reduction of Protein Adsorption to Surfaces Coated with Mixtures of Long- and Short-Chain Polyethylene Oxide Block Copolymers. Biomaterials 1999, 20, 885−890. (5) Unsworth, L. D.; Sheardown, H.; Brash, J. L. Protein Resistance of Surfaces Prepared by Sorption of End-Thiolated Poly(ethylene Glycol) to Gold: Effect of Surface Chain Density. Langmuir 2005, 21, 1036−1041. (6) Vincent, B. The Effect of Adsorbed Polymers on Dispersion Stability. Adv. Colloid Interface Sci. 1974, 4, 193−277. (7) Genz, U.; D’Aguanno, B.; Mewis, J.; Klein, R. Structure of Sterically Stabilized Colloids. Langmuir 1994, 10, 2206−2212. (8) Jaquet, B.; Wei, D.; Reck, B.; Reinhold, F.; Zhang, X.; Wu, H.; Morbidelli, M. Stabilization of Polymer Colloid Dispersions with pHSensitive Poly-Acrylic Acid Brushes. Colloid Polym. Sci. 2013, 291, 1659−1667. (9) Joanny, J. F. Lubrication by Molten Polymer Brushes. Langmuir 1992, 8, 989−995. (10) Klein, J. Shear, Friction, and Lubrication Forces Between Polymer-Bearing Surfaces. Annu. Rev. Mater. Sci. 1996, 26, 581−612. (11) Kobayashi, M.; Terayama, Y.; Hosaka, N.; Kaido, M.; Suzuki, A.; Yamada, N.; Torikai, N.; Ishihara, K.; Takahara, A. Friction Behavior of High-Density poly(2-Methacryloyloxyethyl Phosphorylcholine) Brush in Aqueous Media. Soft Matter 2007, 3, 740−746. (12) Mansfield, T. L.; Iyengar, D. R.; Beaucage, G.; McCarthy, T. J.; Stein, R. S.; Composto, R. J. Neutron Reflectivity Studies of EndGrafted Polymers. Macromolecules 1995, 28, 492−499. (13) Koutsos, V.; van der Vegte, E. W.; Pelletier, E.; Stamouli, A.; Hadziioannou, G. Structure of Chemically End-Grafted Polymer Chains Studied by Scanning Force Microscopy in Bad-Solvent Conditions. Macromolecules 1997, 30, 4719−4726. (14) Koutsos, V.; van der Vegte, E. W.; Hadziioannou, G. Direct View of Structural Regimes of End-Grafted Polymer Monolayers: A Scanning Force Microscopy Study. Macromolecules 1999, 32, 1233− 1236. (15) Ejaz, M.; Yamamoto, S.; Ohno, K.; Tsujii, Y.; Fukuda, T. Controlled Graft Polymerisation of Methyl Methacrylate on Silicon Substrate by the combined used of the Langmuir-Blodgett and Atom Transfer Radical Polymerization Techniques. Macromolecules 1998, 31, 5934−5936. (16) Husseman, M.; Malmström, E. E.; McNamara, M.; Mate, M.; Mecerreyes, D.; Benoit, D. G.; Hedrick, J. L.; Mansky, P.; Huang, E.; Russell, T. P.; Hawker, C. J. Controlled Synthesis of Polymer Brushes by ≪Living≫ Free Radical Polymerization Techniques. Macromolecules 1999, 32, 1424−1431. (17) Ma, H.; Davis, R. H.; Bowman, C. N. Novel sequential photoinduced living graft polymerization. Macromolecules 2000, 33, 331−335. (18) Inutsuka, M.; Yamada, N. L.; Ito, K.; Yokoyama, H. High density polymer brush spontaneously formed by the segregation of amphiphilic diblock copolymers to the polymer/water interface. ACS Macro Lett. 2013, 2, 265−268. (19) Perahia, D.; Wiesler, D. G.; Satija, S. K.; Sinha, S. K.; Milner, S. T. Neutron Reflectivity of End-Grafted Polymers: Concentration and Solvent Quality Dependence in Equilibrium Conditions. Phys. Rev. Lett. 1994, 72, 100−103. (20) Retsos, H.; Terzis, A. F.; Anastasiadis, S. H.; Anastassopoulos, D. L.; Toprakcioglu, C.; Theodorou, D. N.; Smith, G. S.; Menelle, A.; Gill, R. E.; Hadziioannou, G.; et al. Mushrooms and Brushes in Thin Films of Diblock Copolymer/homopolymer Mixtures. Macromolecules 2002, 35, 1116−1132. (21) Hoshino, T.; Tanaka, Y.; Jinnai, H.; Takahara, A. Surface and Interface Analyses of Polymer Brushes by Synchrotron Radiation. J. Phys. Soc. Jpn. 2013, 82, 021014.

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CONCLUSION The kinetics of the dynamic polymer brush formation was measured by NR and QCM. In the NR measurement, the later stage of formation kinetics in the brush regime (graft density above 0.29 chains/nm2) was measured and the brush structure as a function of time was analyzed quantitatively. In order to measure the kinetics in the early stage, QCM was employed. In the QCM experiment, the crossover from mushroom to brush regime as well as crossover from viscous to elastic brushes which occurred at around 10 and 20 s, respectively, were successfully measured. The dynamic polymer brush formation is rapid and, therefore self-repairing time is also expected to be rapid. In order to understand the brush formation kinetics, the graft density change as a function of time was simulated by diffusion controlled segregation model. The simulation revealed that grafting rate is dominated by diffusion of block copolymers until the graft density reaches 0.80 chains/nm2 with the diffusion coefficient of D ≈ 2 × 10−18 m2/s. The abnormally slow diffusion can be explained by hopping diffusion of block copolymers between micelles and to the water interface.

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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.7b00636. Figures S1−S3 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(H.Y.) Phone +81-4-7136-3766; e-mail [email protected]. ORCID

Hideaki Yokoyama: 0000-0002-0446-7412 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by JSPS KAKENHI Grant 15H03862. This work was partially supported by ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan). The neutron reflectometry experiments were performed using SOFIA at JPARC with the support from the S-type (2009S08, 2014S08) and general use (2015A0253) research project of KEK. This work was performed under the approval of the Photon Factory, KEK (Proposal No. 2015G716, 2015G073).

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REFERENCES

(1) Milner, S. T. Polymer Brushes. Science 1991, 251, 905−914. F

DOI: 10.1021/acs.macromol.7b00636 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules (22) Domack, A.; Prucker, O.; Rühe, J.; Johannsmann, D. Swelling of a Polymer Brush Probed with a Quartz Crystal Resonator. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1997, 56, 680−689. (23) Himmelhaus, M.; Bastuck, T.; Tokumitsu, S.; Grunze, M.; Livadaru, L.; Kreuzer, H. J. Growth of a Dense Polymer Brush Layer from Solution. Europhys. Lett. 2003, 64, 378−384. (24) Inutsuka, M.; Tanoue, H.; Yamada, N. L.; Ito, K.; Yokoyama, H. Dynamic Contact Angle on a Reconstructive Polymer Surface by Segregation. RSC Adv. 2017, 7, 17202−17207. (25) Shoji, Y.; Ishige, R.; Higashihara, T.; Kawauchi, S.; Watanabe, J.; Ueda, M. Synthesis and liquid crystalline behavior of laterally substituted polyimides with siloxane linkages. Macromolecules 2010, 43, 8950−8956. (26) Nakajima, Y.; Shimada, S. Hydrosilylation Reaction of Olefins: Recent Advances and Perspective. RSC Adv. 2015, 5, 20603−20616. (27) Yamada, N. L.; Torikai, N.; Mitamura, K.; Sagehashi, H.; Sato, S.; Seto, H.; Sugita, T.; Goko, S.; Furusaka, M.; Oda, T.; Hino, M.; Fujiwara, T.; Takahashi, H.; Takahara, A. Design and Performance of Horizontal-Type Neutron Reflectometer SOFIA at J-PARC/MLF. Eur. Phys. J. Plus 2011, 126, 1−13. (28) Mitamura, K.; Yamada, N. L.; Sagehashi, H.; Torikai, N.; Arita, H.; Terada, M.; Kobayashi, M.; Sato, S.; Seto, H.; Goko, S.; Furusaka, M.; Oda, T.; Hino, M.; Jinnai, H.; Takahara, A. Novel Neutron Reflectometer SOFIA at J-PARC/MLF for in-Situ Soft-Interface Characterization. Polym. J. 2013, 45, 100−108. (29) Yamada, N. L.; Mitamura, K.; Sagehashi, H.; Torikai, N.; Sato, S.; Seto, H.; Furusaka, M.; Oda, T.; Hino, M.; Fujiwara, T.; Kobayashi, M.; Takahara, A. Development of Sample Environments for the SOFIA Reflectometer for Seconds-Order Time-Slicing Measurements. JPS Conf. Proc. 2015, 8 (036003), 1−6. (30) Nelson, A. Co-Refinement of Multiple-Contrast neutron/X-Ray Reflectivity Data Using MOTOFIT. J. Appl. Crystallogr. 2006, 39, 273−276. (31) https://www.ncnr.nist.gov/resources/activation/. (32) http://www.g8kbb.co.uk/html/n2pk_vna.html. (33) Johannsmann, D.; Reviakine, I.; Richter, R. P. Dissipation in Films of Adsorbed Nanospheres Studied by Quartz Crystal Microbalance (QCM). Anal. Chem. 2009, 81, 8167−8176. (34) Tellechea, E.; Johannsmann, D.; Steinmetz, N. F.; Richter, R. P.; Reviakine, I. Model-Independent Analysis of QCM Data on Colloidal Particle Adsorption. Langmuir 2009, 25, 5177−5184. (35) Johannsmann, D. The Quartz Crystal Microbalance in Soft Matter Research, 1st ed.; Springer International Publishing: Basel, 2015. (36) Linegar, K. L.; Adeniran, A. E.; Kostko, A. F.; Anisimov, M. A. Hydrodynamic Radius of Polyethylene Glycol in Solution Obtained by Dynamic Light Scattering. Colloid J. 2010, 72, 279−281. (37) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: Oxford, 2003. (38) Tanoue, H.; Yamada, N. L.; Ito, K.; Yokoyama, H. Quantitative Analysis of Polymer Brush Formation Kinetics Using Quartz Crystal Microbalance: Viscoelasticity of Polymer Brush. Langmuir 2017, 33, 5166−5172. (39) Rittig, F.; Karger, J.; Papadakis, C. M.; Fleischer, G.; Stepanek, P.; Almdal, K. Self-diffusion investigations on a series of PEP-PDMS diblock copolymers with different morphologies by pulsed field gradient NMR. Phys. Chem. Chem. Phys. 1999, 1, 3923−3931. (40) Yokoyama, H.; Kramer, E. J. Self-Diffusion of Asymmetric Diblock Copolymers with a Spherical Domain Structure. Macromolecules 1998, 31, 7871−7876. (41) Yokoyama, H.; Kramer, E. J.; Rafailovich, M. H.; Sokolov, J.; Schwarz, S. A. Structure and Diffusion of Asymmetric Diblock Copolymers in Thin Films: A Dynamic Secondary Ion Mass Spectrometry Study. Macromolecules 1998, 31, 8826−8830. (42) Yokoyama, H.; Kramer, E. J.; Hajduk, D. A.; Bates, F. S. Diffusion in mixtures of asymmetric diblock copolymers with homopolymers. Macromolecules 1999, 32, 3353−3359.

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DOI: 10.1021/acs.macromol.7b00636 Macromolecules XXXX, XXX, XXX−XXX