Interphase Structures and Dynamics near Nanofiller Surfaces in

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Interphase Structures and Dynamics near Nanofiller Surfaces in Polymer Solutions Tadanori Koga,*,†,‡ Deborah Barkley,‡ Michihiro Nagao,§,∥ Takashi Taniguchi,⊥ Jan-Michael Y. Carrillo,# Bobby G. Sumpter,# Tomomi Masui,% Hiroyuki Kishimoto,% Maho Koga,& Jonathan G. Rudick,‡ and Maya K. Endoh†

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†

Department of Materials Science and Chemical Engineering and ‡Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States § NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-6102, United States ∥ Center for Exploration of Energy and Matter, Indiana University, Bloomington, Indiana 47408, United States ⊥ Graduate School of Engineering, Department of Chemical Engineering, Kyoto University, Katsura Campus, Nishikyo-ku, Kyoto 615-8510, Japan # Center for Nanophase Materials Sciences and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States % Sumitomo Rubber Industries Ltd., 1-1, 2-chome, Tsutsui-cho, Chuo-ku, Kobe 671-0027, Japan & Department of Biological and Environmental Engineering, Cornell University, Ithaca, New York 14853, United States S Supporting Information *

ABSTRACT: We report the in situ structures and dynamics of hydrogenated polybutadiene (PB) chains bound to carbon black nanoparticle surfaces in polymer solutions composed of deuterated PB and deuterated toluene using small-angle neutron scattering and neutron spin-echo techniques together with molecular dynamics (MD) simulations. The experimental results showed that the swollen bound polymer chains exhibit the collective dynamics (the so-called breathing mode) at polymer concentrations (c) below and above the overlap polymer concentration (c*) (i.e., 0.61 < c/c* < 1.83), where the concentration profiles of the bound polymer remained unchanged with the different c values. Interestingly, the collective dynamics slowed down by a factor of 2 compared to that in pure d-toluene when the chain lengths of the bound polymer and matrix polymer were equal. However, when the free polymer chains were longer than the bound polymer chains, the decrease in collective dynamics was not as significant. MD simulations were performed to explore the interfacial event as a whole. As a result, we found that the matrix polymer chains, whose length is equal to that of the bound polymer, can be accommodated in the bound polymer layer effectively and are “strangulated” by the bound polymer chains, while the longer matrix polymer chains only partly penetrate into the bound chains and the diffusion behavior was hardly affected compared to that in bulk.

I. INTRODUCTION Mechanical reinforcement of polymers by nanoparticles is critical for creating materials for a host of applications.1−6 The reinforcement of mechanical properties by nanoparticles mainly results from the formation of irreversibly bound polymer fractions on the particles, modification of the polymer dynamics in the vicinity of nanoparticles, and the formation of a percolating filler network.7,8 As proposed initially by Stickney and Falb,9 a bound polymer covers the surface of a filler particle with a stable layer of macromolecules via van der Waals force and is thus resistant to dissolution even in a good solvent. There seems to be a consensus that the thickness of the bound polymer layer (BPL) in various polymer nanocomposites is between 1 and 5 nm.10−26 Studies spanning © XXXX American Chemical Society

several decades have shown that a restricted molecular motion near the filler surface due to the bound polymer on nanoparticles is critical for increased resistance to mechanical deformation.9,16,27 It has also been shown that the low-mobility chain fragments at the nanoparticle interface provide adsorption network junctions for the rubber matrix.9,16,27 Additionally, according to a previous computer simulation result,28 even a 1 nm thick interface layer on nanoparticles can reach 30% of the total volume. Hence, the formation of an interphase layer17,21,29,30 between the matrix and BPL is a key Received: July 30, 2018 Revised: October 24, 2018

A

DOI: 10.1021/acs.macromol.8b01615 Macromolecules XXXX, XXX, XXX−XXX

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coated-CB” fillers were dispersed in pure d-toluene (degree of deuteration of 99.8%, Cambridge Isotope Laboratories, Inc., Cambridge, MA) or dPB/d-toluene solutions for the SANS and NSE experiments. By use of transmission electron microscopy, the thicknesses of the BPL were estimated to be 4.5 ± 0.5 nm for hPB35k and 7.0 ± 0.5 nm for hPB115 K, respectively36 (Figure S1). These thicknesses correspond to 0.75Rg,PB and 0.63Rg,PB (Rg,PB is the radius of polymer gyration in the melt), respectively, and are in good agreement with theoretical prediction.40 Hereafter we assign the CB filler covered with the BPL layer as “BPL-coated CB”. As mentioned above, the scattering length density of d-toluene (SLDd‑toluene = 5.7 × 10−4 nm−2) is nearly identical to that of the CB filler (SLDCB = 6.0 × 10−4 nm−2) or dPB (SLDdPB = 6.0 × 10−4 nm−2). The volume fraction of the BPL-coated CB fillers in the polymer solutions was fixed to 1.8% to make the CB particles isolated in the polymer solution.36 Three different polymer concentrations (c < c*, c ≅ c*, and c > c*), where c* is the overlap concentration (c* = 0.063 g/cm3 for dPB35k and c* = 0.034 g/cm3 for dPB115k41), were prepared. Before the neutron scattering experiments, the BPL-coated CB fillers were dispersed in solution using an ultrasonic bath, and the stability of the BPL-coated CB fillers in the polymer solutions for at least 30 days was confirmed by SANS experiments. Techniques. Neutron Scattering Experiments. SANS and NSE experiments were performed at the National Institute of Standards and Technology Center for Neutron Research (NCNR). The details of the instruments have been described elsewhere.42−45 The BPLcoated CB/d-toluene solutions were filled in custom-made titanium cells with quartz windows available for the SANS and NSE experiments. SANS measurements were taken at four different sample-to-detector distances, 1, 4, 13, and 15.5 m, using the NG730m SANS instrument.41 The wavelength (λ) of the incident beam was 0.6 and 0.81 nm. The scattered intensity was azimuthally averaged and corrected for the background of the cell, the electronic noise, and sensitivity of the detector and then stitched together to an observed q range of 0.01−5.6 nm−1, where q is the magnitude of the scattering vector defined by q = (4π/λ) sin(θ/2), where θ is the scattering angle. The incoherent scattering was estimated based on the established method previously reported by Shibayama and coworkers46 (see the Supporting Information for details). The temperature for the samples was set to 25 °C. NSE measurements were performed on the CHRNS-NSE instrument at 25 °C. The wavelength of the incident beam was 0.8 nm. Measurements were taken at three different detector positions to cover nine different q values for each sample spanning from 0.47 to 1.43 nm−1 or spanning from 0.51 to 1.47 nm−1, depending on the actual measurements of the polarization of the respective samples. The Fourier time range was covered from 70 ps to 40 ns. The NSE data were reduced by using the software DAVE,45 and normalized intermediate scattering functions were calculated for each sample. Transmission Electron Microscopy (TEM) Experiments. The extracted BPL-coated CB fillers were first characterized by TEM. The BPL-coated CB were dispersed in toluene, and droplets of the solution were placed on TEM grids (Nisshin EM Corporation, Japan) and the grids were completely dried. These grids were visualized using a Hitachi H-7100 transmission electron microscope (TEM). A large number of TEM images were taken, and the diameter of the fillers and the thickness of the bound polymer layer were statistically characterized using an image processing software (ImageJ). Thermogravimetric Analysis (TGA). The extracted BPL-coated CB filler was further characterized by TGA (TGA Q500, TA Instruments). The specimen was burned in TGA at a heating rate of 50 °C/ min. PB is expected to decompose at a temperature of about 200 °C, while the CB filler does not burn off within this temperature range. Based on the TGA experiments, the weight percentages of the BPL were determined to be 7.8% for hPB35k and 10.3% for hPB115k. It is possible to estimate the thickness of the BPL on the basis of the weight percentage of the bound polymer layer.16 Assuming that the BPL-coated CB fillers are spherical and the density of the bound rubber is the same as in bulk (0.91 g/cm3), the thickness of the BPL was estimated to be 2.2 nm for hPB35k and 3.1 nm for hPB115k.

element in reinforcement.31−34 The structure and dynamics of the interphase are expected to be different from either the BPL or matrix phase and may vary depending on the distance from the BPL.14,35 However, a detailed molecular scale description about the interphase remains a challenge because the interphase has no well-defined border with the bulk polymer. Previously, we studied the structure and dynamics of a physically adsorbed hydrogenated polybutadiene (PB) layer formed on a carbon black (CB) filler in deuterated toluene (dtoluene, a good solvent for PB) using small-angle neutron scattering (SANS) and neutron spin-echo (NSE) experiments.36 A novel aspect of CB along with its practical importance is that the scattering length density (SLD) is nearly identical to that of a deuterated solvent, allowing “(nearly) contrast matched” SANS/NSE experiments to label the BPL of hPB selectively. The SANS results revealed that the BPL in the good solvent is composed of two regions regardless of molecular weights of hPB: the inner unswollen region of ≈0.5 nm thickness and outer swollen region where the polymer chains display a parabolic profile with a diffuse tail. At the same time, the NSE results demonstrated that the dynamics of the swollen bound chains exhibit collective dynamics which can be explained by the so-called “breathing mode”.37 In this paper, we extend the aforementioned contrastmatched neutron scattering experiments by adding chemically identical polymer chains to a good solvent (in a semidilute regime). In addition, to further explore the interfacial event, we performed molecular dynamics (MD) simulations and aimed to quantify the density distributions of the matrix polymer chains near the BPL regime as well as the bound chains. The experimental and computational results highlight the roles of chain lengths of the matrix polymer in the interphase structures and dynamics near the filler surface.

II. EXPERIMENTAL SECTION Materials. To provide the detailed nanometer-scale descriptions at the polymer/filler interface, we used simplified industrial PB/CB nanocomposites, i.e., a spherical bare CB filler (the mean diameter is 86 ± 40 nm36) with mostly nonfused aggregates (Asahi Carbon Co., Japan) and monodisperse hydrogenated PB (hPB) and deuterated PB (dPB). The molecular characteristics of the polymers are listed in Table 1. The radius of gyration of the pure CB fillers was Rg,CB = 49 ±

Table 1. Characteristics of Polymers Used in This Study sample code

polymer

Mw (103 g/mol)

Mw/Mn

supplier

hPB35k dPB35k

hydrogenated PB deuterated PB

34600 35000

1.05 1.03

hPB115k dPB115k

hydrogenated PB deuterated PB

115000 118000

1.10 1.03

Polymer Source Sumitomo Rubber Polymer Source Polymer Source

1 nm based on small-angle X-ray scattering results.36 The error bars used in this paper represent ±1 standard deviation. This is about 1.5 times larger than that of the primary CB particles (Rg,TEM = 33 nm),36 suggesting that ∼3 (= (Rg,CB/Rg,TEM)3) CB primary particles are fused together into the aggregates on the basis of the volume consideration.38,39 The preparation of the BPL on the CB filler has been described elsewhere.36 Briefly, the CB filler was compounded into the hPB35k or hPB115k using a Banbury mixer. The solvent leaching with toluene was repeated at room temperature for several days until the weight of the CB filler with the insoluble rubber component (i.e., BPL) remained unchanged. The resultant “BPL B

DOI: 10.1021/acs.macromol.8b01615 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules These values are a factor of ∼2 smaller than those estimated from the TEM results. However, the former assumption is not appropriate for the present CB fillers fused together (see Figure S1). Furthermore, as mentioned above, the thicknesses of the bound layer in the dry state obtained from TEM are in good agreement with the theoretical prediction.40 We therefore believe that the disparate results obtained with TEM and TGA are attributed to an underestimate of the true bound layer thickness based on TGA measurements, as claimed by Kumar and co-workers.22 Molecular Dynamics (MD) Simulations. As previously reported,47 an implicit solvent coarse-grained MD simulations of bead−spring polymers is adequate in describing the chain conformations of the adsorbed polymer chains in contact with impenetrable attractive substrates (representing CB) in a polymer solution matrix. Because the size of the CB fillers by far exceeds the BPL thickness (as will be discussed later), the simulation box was treated as a slab configuration where it has periodic boundary conditions in both x- and y-axes but not in the z-axis. An attractive substrate, made up of Lennard-Jones beads arranged in a hexagonal closed pack lattice, is placed such that it serves as a boundary at z = 0. Details of the simulations are described in the Supporting Information. Note here that all units are in the reduced units, where σ is the diameter of a Lennard-Jones bead, energy is scaled in kBT or the thermal energy, m is the mass of a bead, and τ is the characteristic time.

BPL(hPB115k)-coated CB on the basis of the assumption of l = Rg,BR − Rg,CB. After fitting the SANS data to the UF equation, the excess scattering at high q, seen in the deviation from the power law scattering with the slope of about −4, was evaluated by subtracting the contributions calculated by the UF equation from the observed scattering. The detailed procedure has been described elsewhere.36 A representative result is shown in Figure 2a. It should be noted that the excess scattering is the

III. RESULTS AND DISCUSSION NSE and SANS Data. Figure 1 shows the SANS profiles for the BPL(hPB115k)-coated CB in dPB115k/d-toluene solution

Figure 1. SANS profiles for the BPL(hPB115k)-coated CB fillers in the dPB115k/d-toluene solution with the three different polymer concentrations. Note the incoherent scattering intensity is subtracted from the data, and the SANS curves for c/c* = 0.61 and c/c* = 1.83 are vertically shifted by 1 and 2 orders of magnitude, respectively, for clarity. The error bars represent ±1 standard deviation and are smaller than the sizes of the symbols.

Figure 2. SANS and NSE results for the BPL(hPB35k)-coated CB in dPB115k/d-toluene at c/c* = 1.83: (a) Excess scattering (open symbols, I(q,0)) after subtraction of the filler scattering calculated by eq S4. The closed circles represent to the calculated I(q,0) at the three different q values used for the fitting shown in (b). (b) Measured I(q,t)/I(q,0) (symbols) at the three different q values (q = 0.65 (red), 0.94 (blue), and 1.47 nm−1 (green)). The error bars represent ±1 standard deviation. The solid lines correspond to the best fits of the breathing model (eq 3). (c) The volume fraction profile of the BPL vs the distance (z) from the CB surface obtained from the best fit of the breathing model.

with three different polymer concentrations (c): c/c* = 0, 0.61, and 1.83. Because distinct scattering maxima from a core−shell type form factor are not seen, we instead utilized the unified (UF) equation48 for structural analysis of the BPL(hPB115k)coated CB fillers with further consideration of an interfacial root-mean-square roughness (σr) between the BPL-coated CB and d-toluene.49 The detailed analysis on the basis of the UF equation has been described elsewhere,36 and the details of the fitting are summarized in the Supporting Information. The radii of gyration of the BPL-coated CB fillers (Rg,BR) for the BPL(hPB35k)-coated CB and BPL(hPB115k)-coated CB were determined to be 57 ± 5 and 60 ± 5 nm, respectively, based on the best fits of the UF equation to the SANS profiles. The thicknesses of the swollen BPL (l) are then approximated to be 8 nm for the BPL(hPB35k)-coated CB and 11 nm for the

sum of two contributions of the BPL: the static structure factor of the BPL, S(q), and density fluctuations in the BPL that is the origin of the collective dynamics. This will later be discussed in further detail. Representative normalized intermediate dynamic structure factors (i.e., I(q,t)/I(q,0)) of the BPL(hPB35k)-coated CB nanoparticles in dPB115k/d-toluene solutions at 25 °C are shown in Figure 2b. From Figure 2b and Figure S2, it can be seen that the I(q,t)/I(q,0) functions are not completely relaxed at the Fourier times of up to 40 ns. However, the qdependence of the plateau-like behavior implied that the polymer chains are still in motion in the solution.30 Hence, it is obvious that the overall dynamic structure factors cannot be described by segmental chain dynamics in a solvent, such as the Rouse model50 and the Zimm model.51,52 It should also be noted that the hydrodynamic radius (RH) was estimated to be C

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Macromolecules ∼70 nm by assuming a rigid spherical shape of the BPL(hPB35k)-coated CB fillers (RG/RH = 0.77). The calculated decay for the diffusion is then up to 0.6 at q = 1.5 nm−1 and t = 40 ns. Hence, as seen in Figure 2, this is a negligible contribution comparing to the observed decay for the BPL(hPB35k)-coated CB fillers. Instead, as previously demonstrated for the BPL-coated CB nanoparticles in pure d-toluene, it was assumed that the fast decay and slow tail is attributed to collective motions53,54 of the bound polymer chains, the so-called breathing mode determined by the balance of the restoring force due to the osmotic pressure gradient and a viscous force exerted on a polymer.53 The breathing mode is considered to be a relaxation mode of a temporal elastic polymer network (via physical entanglements among polymer chains) through a matrix solvent against thermal agitation. The dynamic structure factor for the collective dynamic response of adsorbed chains was explicated by De Gennes52 and corroborated experimentally by Farago and co-workers.54 We used the same formulated dynamic structure factors in a good solvent, accounting for the breathing mode. More details have been summarized elsewhere.36 To quantify the NSE data based on the breathing mode, we approximated the planar sample geometry, since the size of the CB filler exceeds the BPL thickness (≈8 nm for hPB35K and ≈11 nm for hPB115 K even in the solvent36). Hence, the equation for a local displacement u(z,t) for the adsorbed chains along the normal (z) direction of the surface can be given by54 6πη ∂u ∂ ij ∂u y jjE(z) zzz = 2 ∂z k ∂z { ξ ∂t

The static structure factor S(q) is found by assuming a BPL on a flat substrate with a polymer concentration profile, ϕ(z), in the direction normal to the substrate surface (Figure 2c). S(q) can be then calculated by L

S(q) = |∫ ρ0 ϕ(z) exp(iqz) dz|2 , where L is the cutoff thick0 ness of the swollen pseudobrush layer and ρ0 is the difference in contrast of the polymer and solvent. Taking previous experimental21,56,57 and computational58 results into account, a two-layer model with inclusion of a less swollen adsorbed layer next to the filler surface was adopted: l ϕa , 0 ≤ z < z1 o o o o o o ϕ(z ; z1 , L) = o m ϕm[1 − (z /L)2 ] , z1 ≤ z < L o o o o o 0, L≤z n

where ϕa is the polymer segment volume fraction of the adsorbed layer, and ϕm is the extrapolated volume fraction to z = 0 from the pseudobrush part. Additionally, we introduced a tail of a parabolic function to fit the data by convoluting eq 5 with a normalized Gaussian function.59 Then, this ϕ(z) was applied as a first approximation and then refined in simultaneous fits of the excess scattering (i.e., I(q,0)) and I(q,t)/I(q,0) data using a nonlinear least-squares data fitting to optimize the two unknown parameters (E0, γ) and ϕ(z). As a result of the best fits (Figure 2a and Figure S7), it was found that the two-layer model (Figure 2c) fits the SANS and NSE data reasonably well (the solid lines in Figures 2a and 2b), as previously discussed.36 The best fits imply that the inner region of z1 = 0.5 nm does not contain any solvent (ϕa = 1), while the polymer chains in the outer region are expanded parabolically with zmax = 7.5 ± 1.0 nm and ϕm = 0.64 ± 0.05 (Figure 2c) for the BPL (hPB35k)-coated CB regardless of the polymer concentrations. The best-fit results for the BPL (hPB115k)-coated CB samples gave us nearly identical ϕ(z) profiles to those of the BPL (hPB35k)-coated CB except for zmax = 11.0 ± 1.0 nm: the inner unswollen layer of ≈0.5 nm thick along with ϕm = 0.64 ± 0.05 regardless of the polymer concentrations (see Table 2). The independence of ϕ(z) with the different polymer concentrations is also indicated by the MD results, as will be discussed later. We also found that E0, which is related to the chain elasticity and is predicted to be on the order of 1,55 is nearly identical (E0 = 0.20 ± 0.09) for all the polymer solutions. According to the molecular theory of rubber elasticity, the stiffness of rubber depends on the number density of “strands” between two neighboring entanglement points.60 If that would be the case,

(1)

where E(z), η, and ξ are the osmotic compressibility, the effective viscosity of a matrix, and the correlation length (i.e., a blob size),55 respectively. Based on the scaling theory for semidilute solutions,55 the relations ξ = kz and E(z) = E0kBT/ ξ3 (k and E0 are numerical constants and kB is the Boltzmann constant) are given. As for the time decay, eq 1 has a solution of a simple exponential:54 u(z , t ) = un(z) exp( −t /τn)

(2)

In addition, because of the boundary conditions, eq 1 is a Sturm−Liouville boundary value problem with eigenvalues, E0 kBT 1/τn = 6πη Λ ((Λn = anb + e (n = 1, 2, ...and a, b, and e k (z )3 n max

are constants), and eigenfunctions un(z) for the displacement.36 zmax corresponds to the maximum height of the BPL including the tail. The intermediate dynamic structure factor with a mode n, In(q,t), depends on the density fluctuation, δρ = d(ϕ(z)un(z,t))/dz, and I(q,t)/I(q,0), which is given by the summation of contributions In(q,t) from mode n (n ≤ 10 in the present case), is given by the same protocol established previously:54 ∞

Table 2. Fitting Results for the SANS/NSE Data

2

S(q) + ∑n E Λ q 2̃ |(ϕ|un)|2 exp( −γE0 Λ nt ) I (q , t ) 0 n = ∞ 2 I(q , 0) S(q) + ∑n E Λ q 2̃ |(ϕ|un)|2 0

n

(3)

where γ =

kBT/(6πηkzmax3).

(ϕ|un) =

∫0

1

(ϕ|un) represents

ϕ(z)̃ un(z)e ̃ iqz̃ ̃ dz ̃

(5)

(4)

BPL

matrixa

c/c*

hPB115k hPB115k hPB115k hPB115k hPB35k hPB35k hPB35k hPB35k hPB35k

d-toluene dPB115k dPB115k dPB115k d-toluene dPB35k dPB115k dPB115k dPB115k

0 0.61 1.10 1.83 0 1.10 0.61 1.10 1.83

γ 0.032 0.017 0.016 0.014 0.099 0.046 0.089 0.065 0.071

± ± ± ± ± ± ± ± ±

0.006 0.001 0.001 0.001 0.007 0.005 0.015 0.010 0.011

zmax (nm)

ϕm

11.0 11.0 11.0 11.0 7.5 7.5 7.5 7.5 7.5

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

a

The matrix is either the pure solvent or polymer solution composed of the polymer and d-toluene with the given concentration.

with q̃ = qzmax and z̃ = z/zmax. D

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gain associated with the penetration of the mobile free chains in the brush that is not able to compensate for the elastic deformation of the grafted chains. However, in the present case, it is challenging to extract the lone contribution of the deuterated polymer chains dissolved in d-toluene within the BPL (i.e., little neutron contrasts between them) experimentally. MD Results. To overcome this difficulty and further understand the interfacial phenomenon, molecular dynamics simulations were performed. Because the effect of chain entanglements between the BPL and free polymer chains is not significant, as mentioned above, the simulation systems were simplified by choosing Nfree, NBPL < Ne (the critical entanglement length, Ne = 85).62 An image showing how the simulation box was prepared is shown in Figure S3, where the final step (step 4) illustrates the initial configuration of the production simulation runs. A set of simulations without the bounding substrates was also performed and used to determine the bulk properties of the polymers such as the overlap concentration, c*, and diffusion coefficient, D (see Figure S4). The reported values and error bars in the present simulation results are the average and one standard deviation, respectively, of three independent simulation runs. Because of the presence of the attractive substrate, a polymer adsorbed on the planar substrate via physisorption, forming a thin bound polymer layer (i.e., a Guiselin brush).63 Here this layer is referred as a BPL, and its degree of polymerization is NBPL. Figure 4 and Figure S9 show the monomer density distributions of the BPL for NBPL = 20 and Nfree = 20 and NBPL = 20 and Nfree = 80. The density profile of the BPL in the range of c/c* is qualitatively in good agreement with the experimental results shown in Figure 2c. In addition, the results indicate that the monomer distributions of the bound

the data suggests no increase in entanglements between the bound polymer and free polymer chains with the given c values for the two different BPL-coated CB fillers. However, it should be noted that the volume fraction of the bound polymer chains in the entire system is estimated to be