Polymer Nanocomposites

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

Melt Chain Conformation in Nanoparticles/Polymer Nanocomposites Elucidated by the SANS Extrapolation Method: Evidence of the Filler Contribution Anne-Sophie Robbes,†,‡ Fabrice Cousin,*,† Florian Meneau,‡ and Jacques Jestin*,† †

Laboratoire Léon Brillouin, Université Paris-Saclay, CEA Saclay, Cedex 91191 Gif-sur-Yvette, France L’Orme des Merisiers, Synchrotron SOLEIL, PO Box 48, Saint-Aubin, 91192 Gif sur Yvette, France

‡

ABSTRACT: We probe by SANS the conformation of polymer chains of the matrix in various nanocomposites based on the same building blocks, namely spherical magnetic nanoparticles of maghemite (γ-Fe2O3) as fillers and polystyrene (PS) for the matrix. Given that the nanoparticles can be arranged in oriented chains during the processing by an external magnetic field and/or grafted by tethered PS chains with a grafting density of ∼0.15 chains/nm2, very different organizations of the nanofillers were tested according to different particle−polymer interactions: (i) homogeneous isotropic dispersion of aggregates of bare nanoparticles; (ii) chains of bare nanoparticles oriented along one direction over the whole sample; (iii) perfect dispersion of grafted nanoparticles; (iv) homogeneous isotropic dispersion of large aggregates of grafted nanoparticles; and (v) chains of large aggregates of grafted nanoparticles objects oriented along one direction over the whole sample. Measurements were performed by the extrapolation to the zero concentration method made possible by the fact that γ-Fe2O3 has the same neutron scattering length density (SLD) as a deuterated polystyrene, so that the nanoparticles scattering is matched in a deuterated PS matrix, whether they are grafted or not. This robust method enables to check that only the polymer chain form factor is effectively probed in a very accurate way. This allows us to show some deviations of the radius of gyration induced by the nanoparticles: (i) for the case of very weak interaction between the polymer and the bare particles, the radius of gyration is swollen by 16% whatever the filler dispersion and orientation; (ii) for the athermal interaction between grafted particles and polymer, the radius of gyration is either unchanged when particles are individually dispersed or compressed of almost 11% when particles are forming overlapped clusters. Despite the remaining relatively small deviations, this is to our best knowledge the first unambiguous experimental evidence on a single system of the influence of the well-known nanofiller dispersion onto the mean chain conformation in nanocomposites for different polymer−particles interactions ranging from attractive to repulsive.

I. INTRODUCTION One of the main goals toward the understanding of the enhanced mechanical properties of nanocomposites, i.e., polymer melts filled with hard nanoparticles compared to pure melts made of the same polymers, is the experimental determination of the conformation of the chains, whether they are free in the matrix or grafted on the nanofillers. The unique technique to access it experimentally is small-angle neutron scattering (SANS) using labeling tricks based on a mixture of hydrogenated and deuterated polymers to cancel the contribution to the scattering of the fillers. Over these past 15 years there has been a lot of work devoted to such a topic, for chains either at rest or under stretching by numerical simulations1−7 and experimental approaches.8−21 If the case of the chains grafted onto fillers is now well described,22,23 the results concerning the free chains are various, and there are still some pending questions which have been extensively discussed in terms of unperfected matching of the fillers, phase separation between H and D chains, and specific interaction between the polymer and the filler. Indeed, the experimental method that is generally used is the zero averaged contrast method (ZAC) that enables the determination of the chain form factor S1(q) in a © XXXX American Chemical Society

single measurement in contrast conditions chosen such as all amplitude terms coming from the structure factor S2(q) exactly compensate, so that their sum is null. To be successful, the ZAC method requires that the difference of neutron scattering length density (SLD) between the matrix and the fillers is exactly the same throughout the whole sample. Such a condition is sometimes not fulfilled for several possible reasons: formation of aggregates of fillers, specific chain adsorption at the surface of the particle caused by particle−polymer interaction, or local change of the polymer density. In all these cases, this induces an additional confusing scattering contribution on the SANS curve. When the size of the particle is larger than the typical size of the polymer, these contributions remain located at low q and do not actually disrupt the scattering curve on the q-range actually used for the determination of conformation. Their origin, which has only been very recently discussed19 and modeled,21 depends on the strength of interaction between the polymer and the particle. Received: October 31, 2017 Revised: January 24, 2018

A

DOI: 10.1021/acs.macromol.7b02318 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Overview of the structures of the nanocomposites that can be obtained with γ-Fe2O3 nanoparticles and polystyrene (PS) for the matrix. (a) Panorama of the structures from X-rays point of view (from left to right): bare nanoparticles,27 bare nanoparticles aligned by a magnetic field during casting,28 PS-grafted nanoparticles for N/P ≥ 1,23 PS-grafted nanoparticles for N/P ≤ 0.4,23 and aggregates of PS-grafted nanoparticles aligned by a magnetic field during casting.23 (b) Same structures as in (a) but from neutrons point of view. (c) Scale of the SLD’s of the different components of the nanocomposites.

simplified silica−polystyrene system, for which filler/polymer interactions are known to be weak.21 Here, we use this extrapolation to zero concentration method to probe the conformation of polymer chains of the matrix in a series of model magnetic nanocomposites based on the same building blocks, namely spherical magnetic nanoparticles of maghemite γ-Fe2O3 as fillers and polystyrene (PS) for the matrix. Such systems are very powerful from the contrast point of view because the SLD of the maghemite particle (6.86 × 1010 cm−2) is very close to the one of the deuterated PS (6.5 × 1010 cm−2) and very different from the one of the hydrogenated PS (1.41 × 1010 cm−2). This provides a huge potential for the fine structural characterization of these systems by coupling X-rays and neutrons: from the standpoint of small-angle scattering, a sample containing hydrogenated chains and deuterated chains is always a two-component system, but these components are not the same whether we consider the electronic contrast (nanoparticles versus polymer chains) or the neutron contrast (hydrogenated chains versus nanoparticles and deuterated chains). Very nicely, this is obviously the case for bare nanoparticles but remains true for grafted nanoparticles, provided that the grafted PS chains are deuterated (see Figure 1). Moreover, this series of model nanocomposites should allow to determine if the conformation of free chain follows a universal behavior by probing a various range of interesting situations with respect to the structure of fillers and filler/ polymer interface (Figure 1). With bare nanoparticles, the fillers have a reproducible hierarchical structure over several decades of volume fractions. This structure is made of an homogeneous dispersion of open clusters called supraaggregates (SA) of mean radius of ∼80 nm made of dense primary aggregates of 20 nm.27 Owing to their magnetic properties, it is possible to organize them in chains of nanoparticles oriented along one direction over the whole sample with the use of an external magnetic field during the processing of the samples.28 Such peculiar structure is especially interesting for the purpose of the present study as it allows to test a situation where the Rg of the polymer chains is lower than the mean distance between fillers perpendicular to the chains of nanoparticles but larger parallel to them. When nanoparticles are grafted by PS chains (what we successfully obtained with a

When this latter is weak, the extra scattering is due to a modification of polymer density in the vicinity of the particle whereas when it is strong, the extra scattering is due to the presence of an adsorbed polymer layer. Apart from this, all the experiments are converging toward a unified conclusion stating that the mean chain conformation in melt is never modified by the presence of the filler. The single situation for which the ZAC method is very limited concerns the case of nanocomposites made of polymer grafted nanoparticles. Indeed, reaching the ZAC condition in that situation implies that both nanoparticle and grafted polymer corona have the same SLD. If this condition is not naturally fulfilled, it necessitates to graft a random hydrogenated and deuterated copolymer whose SLD is equal to the one of the filler, which can be difficult to perform under controlled and reproducible synthesis conditions. However, polymer grafted nanoparticle is a powerful way to control the polymer−particle interaction and the filler dispersion in nanocomposites.24,25 Thus, probing the melt chain conformation should be very useful in that athermal case (grafted layer prevents adsorption of the bulk chain at the surface of the particles) in comparison with the non-grafted systems where the attractions between the chain and particle always exist, to cover on the same system a wide range of various polymer−particle interactions. An alternative route is to use a robust way known as “the extrapolation to zero concentration” method that enables to decouple the contribution of the form factor and the structure factor within the chain scattering signal in a three-components system made of hydrogenated chains, deuterated chains, and a filler phase. Briefly, the idea is to use a system for which the neutron SLD of the filler phase is similar to the one of the two kinds of chains in order to match its scattering. Then, several samples are made with the same overall concentration of chains but with various contents of hydrogenated chains so as to dilute the signal from these hydrogenated chains until it tends toward that of a single chain. This method has been largely used to study the behavior of polymer in solutions because the SLD of the solvent, i.e., the continuous phase, can easily be adjusted to those of the chain by mixtures of hydrogenated and deuterated solvents.26 It implementation to nanocomposite systems has been recently demonstrated by Jouault et al. in the case of a B


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grafting density close of 0.15 chains/nm2. The final grafted objects formed linear aggregates of 3−4 native maghemite particles, grafted by PS tethered chains of mass equal to Mn = 17 000 g/mol (PDI = 1.8), dispersed in DMAc. The mass of the grafted chains was determined by GPC after cleaving from the maghemite core. The suspensions of PSDgrafted nanoparticles were then mixed with a solution of free PS chains solubilized in DMAc (10% vol) with a PSH/PSD content fixed at 25/ 75% for all samples. The nanocomposites were then processed following the same protocol as for bare nanoparticles. The N/P (calculated using Mn ratio22−24) in the nanocomposite was fixed by the masses of free chains. The particle volume fraction ΦγFe2O3 in the final nanocomposites was fixed by the synthesis conditions. One sample was processed with a magnetic field of 600 G. Two representative cases were probed: N/P = 0.26, with ΦγFe2O3 = 0.5% vol, ΦγFe2O3 = 3% vol without field, and ΦγFe2O3 = 0.5% vol with a magnetic field of 600 G, using free chains with Mw = 123 500 g/mol and Mn = 65 000 g/mol (PDI = 1.9); N/P = 1.2 with ΦγFe2O3 = 3% vol, using free chains with Mw = 33 000 g/mol and Mn = 14 000 g/mol (PDI = 2.8). Both deuterated and hydrogenated chains have been synthesized by NMP (120 °C for 2 h) using PBO as initiator. The mass of all chains was measured by GPC using a standard method. For N/P = 0.26 and N/P = 1.2, pure matrices with 25% PSH/75% PSD were also synthesized for reference. II.2. Small-Angle Experiments. II.2.1. Small-Angle X-ray Scattering. The SAXS experiments were carried out at the SWING beamline of the French Synchrotron SOLEIL. Measurements were performed at an energy of 7 keV (λ = 1.77 Å), with a two-dimensional AVIEX-CCD detector placed at a distance of 6.5 and 1.4 m from the sample. A 3 mm beamstop with a photodiode inserted in its center enables to measure the transmission. The resulting q-range (the scattering vector q, defined by q = 4π sin(θ/2)/λ where θ is the angle between incident beam and scattered beam), spanned from 1.8 × 10−3 to 0.15 Å−1. The scattering of a pure PS matrix, without magnetic nanoparticles, Ipure_PS, was first measured. In order to remove the PS chains contribution in the films, (1 − Φpart)Ipure_PS was subtracted from all the nanocomposite samples. The data reduction has been done by the software Foxtrot. II.2.2. SANS Experiments. SANS measurements were performed at the Institut Laue Langevin on the instrument D11 and at the Laboratoire Léon Brillouin on the instrument PACE. On D11, three configurations were used with a wavelength of 8 Å and sample-todetector distances of 34, 8, and 1.5 m, corresponding to a total q-range of 0.001−0.2 Å−1. On PACE, three configurations were used with a wavelength of 6 Å and sample-to-detector distances of 1 and 3 m and a wavelength of 12 Å and sample-to-detector distances of 4.7 m covering a total q-range of 0.003−0.3 Å−1. All measurements were done under atmospheric pressure and room temperature. Standard corrections for sample volume, neutron beam transmission, empty cell signal subtraction, detector efficiency, subtraction of incoherent scattering, and solvent were applied to get the scattered intensities on absolute scale. The data reduction has been done with the homemade software Pasinet. II.2.3. SAS Pattern Averaging. All the samples cast without magnetic field displayed an isotropic structure, whether measurements were performed in SAXS to probe γ-Fe2O3 nanoparticles or in SANS to probe PS chains of the matrix. The radial averaging was then performed on the entire 2-D detector. All the samples cast under magnetic field displayed an anisotropic structure in SAXS, the anisotropy being more or less pronounced when the same samples were measured by SANS. Anisotropic samples were placed within the incoming beam so that the direction of the applied magnetic field (during the casting) was vertical. All two-dimensional spectra displayed an excess of scattering in the horizontal direction (i.e., transverse to the magnetic field). The radial-averaging of the 2D spectrum was performed inside an angular sector (25°) either along the horizontal direction or along the vertical direction. II.3. Extrapolation to Zero Concentration Method. We recall here the principle of the extrapolation to zero concentration method.

grafting density σ of ∼0.15 chains/nm2 29), the structure of the fillers follow the trends emerging on the main state diagram of grafted object-based nanocomposites.25 At such σ, the dispersion state of the fillers is tuned by the ratio N/P of the molecular mass of the grafted chains N to the mass of free chains P and depends mainly on the interactions between the grafted and the free chains. At low N/P, ramified aggregates of a few tens of grafted objects are obtained while objects are perfectly well dispersed for larger N/P, the threshold N/P* between the two cases being located between 0.4 and 1.23 For N/P < 0.4, the aggregates can be aligned in the direction of the magnetic field when applied during synthesis.23

II. MATERIALS AND METHODS II.1. Sample Preparation. II.1.1. Samples with Bare Nanoparticles. The bare maghemite (γ-Fe2O3) nanoparticles were synthesized according to the Massart method in aqueous media.30 They are roughly spherical and their size follow a log-normal distribution with 9.6 nm (d0 = 9.6 nm; σ = 0.35), as measured by SAXS in dilute regime. The aqueous solvent was then exchanged by dialysis with dimethylacetamide (DMAc), a polar solvent which is also a good solvent for the polystyrene (PS).27 Hydrogenated polystyrene chains (PSH) and deuterated PS chains (PSD) with very close masses were respectively synthesized by classical radical polymerization (90 °C for 4 h) using AIBN as initiator. The mass of all chains was measured by GPC using a standard method: Mw(PSH) ∼ 124 000 g/ mol and Mn(PSH) ∼ 67 000 g/mol (PDI = 1.85); Mw(PSD) ∼ 131 000 g/mol and Mn(PSD) ∼ 65 000 g/mol (PDI = 1.9). Such masses were chosen low enough to prevent phase separation that occur in melts made of mixtures of PSH and PSD chains of very large molecular masses due to the non-null value of χ existing between the chains.31 The PS chains were then dissolved in DMAc (10% vol), the respective amounts (volume fraction) in PSH and PSD being chosen so that five contents were obtained (100% PSH, 75% PSH /25% PSD, 50% PSH/ 50% PSD, 25% PSH/75% PSD, and 100% PSD). The suspension of γFe2O3 nanoparticles previously in DMAc was then mixed with this concentrated solution of PS, the concentration chosen to obtain a filler volume fraction ΦγFe2O3 = 3% vol in the final nanocomposite which corresponds to the overlapping concentration of the particle clusters. The mixtures were gently stirred for 2 h. They were then poured in a rectangular homemade Teflon mold (3 × 5 cm) and let cast in an oven at constant temperature Tcast = 130 °C for 8 days. Tcast is much lower than the boiling point of DMAc (160 °C), which ensures gentle evaporation while the medium becomes viscous enough to slow down the structure evolution. The volume of mixture poured in the mold was adjusted to get nanocomposites films with a thickness of ∼0.1 cm. This yields dry films of 1.5 cm3 (3 cm × 5 cm × 0.1 cm). At the final stage, the residual solvent content inside the film was below 1% vol (0.3% wt determined by thermogravimetric analysis). Two series of samples were cast using exactly the same conditions, except for the use of a magnetic field during casting, one being processed without magnetic field and the other with a constant magnetic field of 600 G. Such magnetic field was imposed by two plates of iron magnetized by a series of permanents NeFeB magnets inserted in the mold. The cartography of the applied field within the mold was done with a Halleffect probe to test its homogeneity, which was very satisfactory: the lowest and upper magnetic fields measured over the whole mold were respectively 585 and 615 G. Finally, a series of five pure matrices of PS with the same PSH/PSD content as used for the samples were processed using the same casting route to serve as reference. II.1.2. Samples with Grafted Nanoparticles. We have used PSDgrafted maghemite nanoparticles whose complete description of synthesis and characterization can be found in our previous work.29 Briefly, bare spherical γ-Fe2O3 nanoparticles (d0 = 8.1 nm; σ = 0.29) dispersed in DMAc were grafted by deuterated PS chains by coupling a “grafting from” approach with a controlled radical polymerization process based on nitroxide-mediated polymerization (NMP). This “multistep” method allowed us to graft deuterated PS chains with C


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Figure 2. Conformation of free chains from the extrapolation to zero concentration method for pure matrix: (a) SANS measurements for the different PSH/PSD ratios normalized by φH, except for the 100%PSD sample that is in absolute units; (b) normalized form factor S1(q) obtained from extrapolation fitted by a Debye function (Gaussian chain form factor) and compared with the 25%PSH measurement; (c) same data as in (b) using the Kratky representation. The full gray lines correspond to the Debye fitting (eq 11). deuterated chains, kD = 0, as for the case of the present paper where deuterated chains are PSD chains and where the continuous phase is made of γ-Fe2O3 nanofillers; hence

First, let us write the expression of the scattering of a mixture with two kinds of chains in a continuous phase:

I(q ⃗) (cm−1) =

n

1 V

n

∑ ∑ kikjeiq ⃗·(ri⃗− rj⃗) i

where ki = bi − bcont v

vi

cont

I(q) (cm−1) = kH 2SHH(q)

(1)

j

The total volume fraction of chains in the continuous phase is the sum of the volume fractions of the two types of chains, ΦT = ΦH + ΦD. Since hydrogenated and deuterated chains are perfectly identical except for the value of b (in particular, vH = vD = vpol), it follows that

is the “contrast length” between one repeat

unit of scattering length bi (in cm) and molar volume vi and an elementary scatterer of the continuous phase (bcont, vcont). For the sake of simplicity, let us first consider the case where all polymer chains are labeled in the same way with respect to the continuous phase; i.e., for all i, we have ki = kpol. The intensity simply writes

I(q) (cm−1) = k pol 2Spol − pol(q)

SHH(q) = ΦHS1(q) + ΦH 2S2(q)

(2)

where Spol−pol(q) is the scattering of the polymer chains (in cm ). It is now useful to separate in Spol−pol(q) the respective contributions to the scattering arising from correlations between monomers of the same chain, i.e., the form factor, to the ones arising from correlations between monomers from different chains, i.e., the structure factor. When all chains have the same mass with N repeat units and when there are nH chains in the sample, eq 1 can be rewritten like ⎛ npol npol N N ⎞ α β 1 k pol 2⎜⎜∑ ∑ ∑ ∑ eiq ⃗·( ri⃗ − r j⃗ )⎟⎟ V ⎝∝ β i j ⎠

I(q) (cm−1) = kH 2(S1(q) + ΦHS2(q)) ΦH

(3)

The scattered intensity is thus the sum of (npolN) terms, with npolN2 coming from intrachain correlations and (npol − 1)npolN2 (≈ npol2N2) from interchain correlations: ⎛ ⎞ N N β α α α 1 k pol 2⎜⎜n pol ∑ eiq ⃗·( ri⃗ − r j⃗ ) + n pol 2 ∑ eiq ⃗·( ri⃗ − r j⃗ )⎟⎟ V ⎝ ⎠ i,j i,j,α≠β

III. RESULTS AND DISCUSSION III.1. Pure Matrix. Prior to the actual experiments on nanocomposites that contain fillers, we have checked the principle of the extrapolation to zero concentration method with a reference series of pure melts containing various contents of PSH (0%, 25%, 50%, 75%, and 100% vol). In a pure melt of deuterated and hydrogenated chains, provided that there are no fluctuations at large scale, it can be demonstrated that the structure factor S2(q) equals the form factor S1(q), and thus that the scattering reduces to (see eq 9)

(4) This equation enables to define the form factor S1(q) and the structure factor S2(q) and can be expressed as a function of volume fraction of n pol chains Φpol (∝ V ): I(q) (cm−1) = k pol 2(Φpol S1(q) + Φpol 2S2(q))

(5)

Let assume now that the chains are labeled in two different ways. In practice, we use hydrogenated chains (ki = kH) and deuterated chains (ki = kD). The scattering becomes: I(q) (cm−1) = kH 2SHH(q) + 2kHkDSHD(q) + kD2SDD(q)

(9)

Thus, if one measures several samples with various contents of hydrogenated chains but an overall constant amount of polymer chains, it enables to “dilute” the labeled chains that give rise to the scattering without changing the structure factor. The contribution from S2(q) to the scattering decreases with such dilution and the signal progressively tends toward S1(q). Ultimately, at infinite dilution, S1(q) would be directly measured because only one chain would be probed (see Figure 3a). In practice, we will experimentally measure the scattering of a given system at four different compositions in PSH/PSD of the matrix (25% PSH, 50% PSH, 75% PSH, and 100% PSH). According to eq 11, for each q value, the four intensities will be linear as a function of ΦH, and the extrapolation to ΦH = 0 will provide the value of S1(q).

2

I(q) (cm−1) =

(8)

with S1(q) and S2(q) concerning all hydrogenated and deuterated chains, as defined in eqs 4 and 5. Finally, whatever the hydrogenated chains’ content, the intensity is written as

−3

I(q) (cm−1) =

(7)

(6)

I(q) (cm−1) = kH 2S1(q)ΦH(1 − ΦH)

where SHH(q) is the scattering of the hydrogenated chains, SDD(q) the scattering of the deuterated chains, and SHD(q) is the cross-term. In the particular case where the scattering length density of the continuous phasecommonly the solvent but here the nanoparticle filler in the particular case of nanocompositesmatches the one of the

(10)

Only S1(q) is then measured, the maximum of scattering being obtained for a ratio of 50%/50% H-chains/D-chains.32 Experimentally, the scattering curves for the 25% PSH, 50% PSH, and 75% PSH present exactly the same features: the D


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Figure 3. Conformation of free chains from the extrapolation to zero concentration method for samples containing bare nanoparticles. (a) Principle of the measurement, γ-Fe2O3 nanoparticles and PSD chains are shown in red, PSH chains in blue. (b) SANS measurements for the different PSH/PSD ratios normalized by ΦH, except for the 100% PSD sample that is in absolute units. (c) Normalized form factor S1(q) obtained from extrapolation fitted by a Debye function (Gaussian chain form factor full gray line with error bars) and compared with the normalized 25% PSH measurement. (d) Same data as in (c) in the Kratky representation.

characteristic q−2 decay of the Gaussian behavior of the chains at large q, the Guinier plateau at low q, and an upturn at very low q with a scattering decay around q−3 (Figure 2a). This last scattering arises from the presence of microcracks within the samples. On the 100% PSH and 100% PSD sample only the microcracks signal is present. This spurious signal is especially marked at 100% PSD because PSD (6.5 × 1010 cm−2) is much more contrasted to air for neutrons than PSH (SLD = 1.41 × 1010 cm−2). The extrapolated curve and the 25% PSH are shown in Figures 2b and 2c in the Kratky representation Iq2 vs q. To determine the radius of gyration of the chain, we used the same method developed in ref 11. In order to obtain the absolute values of the intensity, and as a result the form factor of the chain S1(q), we normalized all the scattering curves by the product of the contrast term Δρ2 by the volume of the chain Vchain, the chain volume fraction φH(1 − φH), and the volume fraction of the particles (1 − Φpart). For the pure matrix, Δρ2Vchain = 513 cm−1, as calculated from the molecular mass Mw = 124 000 g/mol determined by GPC and using a density of PS of 1.04 g/mol. As expected, S1(q) tends to 1 at low q. Except the low q part, the extrapolated curve can be perfectly modeled by the Debye function that describes the form factor of a Gaussian chain of gyration radius Rg: PDebye(q) =

2 2 2 (q 2 R g 2 − 1 + e − q R g ) 2 2 (q R g )

2

measurements with neutrons, we have checked by SAXS that the structure of fillers is similar to what we obtained in previous papers with Rmean = 8.1 nm and ΦγFe2O3 = 3% vol,27,28 as described in the Introduction. The features of such SAXS scattering curves are exactly similar to the ones measured by SANS on the 100% PSH samples because the system contains only two componentsnanoparticles and matrixfrom the contrast point of view in both cases. Moreover, we have checked by SAXS prior to the neutrons measurements that the structural organization of the nanoparticles is perfectly reproducible from one sample to another within a given series. III.2.2. Conformation of Chains: Nanocomposites Processed without a Magnetic Field. Figure 3b shows the scattering spectra I(q)/φH obtained for the series of samples at ΦγFe2O3 = 3% vol processed without a magnetic field. Their intensity is larger by almost 2 orders of magnitude than that of a witness sample realized with the 100% PSD matrix, enabling to verify that the extinction of the signal arising from the nanoparticles is almost perfect. As for the pure matrices scattering, there are strong upturns at very low q (typically below 0.003 Å−1) on all the spectra which are due to the presence of microcracks within the samples. These upturns are even more pronounced than for the pure matrices because the amount of microcracks increases with the fillers concentration. This spurious signal cannot be subtracted in a consistent way for the whole set of samples because its intensity depends both on the contrast between the matrix and the air and on the number and the structure of the microcrackstwo parameters that may vary from sample to another in a noncorrelated manner. Apart from these microcracks, the features of the scattering curves exemplify nicely the principle of the zero concentration method. Starting from the nanocomposite made with 100% PSH matrix whose scattering only arises from structure of fillers, the progressive introduction of deuterated chains makes appear the signal of the polymeric chains at the expense of the nanoparticles that disappears concurrently. This results in the decrease of the signal at small q arising from the nanoparticles aggregates which is accompanied by a change of

(11)

Indeed, the PS is very flexible (persistence length lp ∼ 10 Å33), so that the deviation from the q−2 behavior due to the intrinsic rigidity of chains that occurs for q > 6/πlp ∼ 0.2 Å−1 is out of the q-scale actually probed in our experiments. The value obtained for Rg is 103 ± 7 Å with Rg as the single fitting parameter of the eq 11 (the prefactor of the intensity is set to 1). As shown in Figure 2c, the extrapolated curve superimpose perfectly with the 25% PSH measurement normalized by (1 − φH)Δρ2V) as well as the fitting calculation. That means that the 25% H is diluted enough to directly determine the form factor. III.2. Nanocomposite with Bare Nanoparticles. III.2.1. Structure of Fillers. Prior to the conformation E


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Figure 4. Comparison of SAXS and SANS 2D spectra obtained on the series where bare nanoparticles have been aligned by a magnetic field. (a) SAXS measurements and corresponding schematic structure. γ-Fe2O3 nanoparticles are shown in black and PS chains in white. (b) SANS measurements and corresponding schematic structure. γ-Fe2O3 nanoparticles and PSD chains are shown in red and PSH chains in blue.

slope at intermediate and large q, from the q−4 decay of the form factor of the spherical nanoparticles at 100% PSH to a q−2 decay law at 25% PSH, characteristic of a signal of a Gaussian chain. For this 25% PSH sample, a Guinier plateau is reached between 0.003 and 0.01 Å−1. In between, at 50% PSH or 75% PSH, the intermediate value of the decaying slope at large q shows that both fillers and chains have a significant contribution to the scattering at such PSH/PSD ratio, as depicted in the scheme in Figure 3a. The scattering curve extrapolated from samples with the four different contents in hydrogenated chains is shown in Figure 3c. The low q part of the extrapolated curve is in practice not usable because the scattering from the microcrays perturbs the sample signal to allow a proper extrapolation. It has to be noted that all scattering curves intersect exactly at a given qintersect (0.008 Å−1) when normalized by Δρ2Vchain = 513 cm−1 corresponding to the same molecular weight than for the pure matrix. In principle, this means that S2(q) is null at qintersect, so that the value of S1(q) can be obtained with great confidence for such scattering vector. We have thus considered that the whole extrapolated scattering curve is usable for q > qintersect. As for the pure matrix, we superimposed the extrapolated curve with the normalized 25% H (red curve in Figure 3c). Beyond the qintersect, both curves superimposed quasi-perfectly as previously meaning that even for the filled samples, the 25% H is diluted enough to directly determine the S1(q). However, we can observe that the low q plateau do not reach the expected value of 1 for the normalized intensity: both red and blue

curves are below of about 20−30%. This is more clear with the Kratky (Figure 3d) representation for which the value of the high q plateau (around 1.5 × 10−4 Å−2) is below the ones of the pure matrix as shown in Figure 2.c where the plateau value is around 1.9 × 10−4 Å−2. As a direct consequence, the fitting of the Rg with the Debye function gives us a significant larger value of Rg = 119 ± 7 Å, considering the same range of error bars. We can observe a bump on the curves above the qintersect that can be attributed to an indirect contribution of the interparticle structure factor. However, the presence of this contribution does not influence the determination of the radius of gyration which is fixed at high q by the value of the plateau in the Kratky representation after normalization. III.2.3. Conformation of Chains: Nanocomposites Processed with a Magnetic Field of 600 G. Figure 4 compares the SAXS and SANS 2D spectra of the four PSH/PSD contents of the series of samples at ΦγFe2O3 = 3% vol processed under magnetic field during casting. In these samples, the nanoparticles have been organized in anisotropic aggregates oriented in average along one specific direction by the magnetic field.28 While all SAXS spectra are similar and highly anisotropic, the anisotropy decreases gradually within SANS spectra when increasing the amount of deuterated chains up to become completely isotropic for the sample containing 25% of hydrogenated chains. This qualitatively shows that the alignment of the nanoparticles in chains along one direction did not induce any alignment of the polymeric chains. It is thus an elegant and visual experimental demonstration of the F


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Figure 5. Chain conformation determined from the sample at 25% of H chains containing 3% vol of particles for the sample aligned perpendicular to the magnetic field in normalized log−log (a) and in Kratky representation (b) and for the sample aligned parallel to the magnetic field in normalized log−log (c) and in Kratky representation (b). The full gray lines are fits from Debye model with errors bars.

Figure 6. Conformation of free chains containing grafted objects for a grafted to free chain length ratio N/P = 0.26 in normalized log−log representation: (a) pure matrix and grafted particles at 0.5% vol, (b) grafted particles at 0.5% vol under magnetic field at 600 G, (c) grafted particles at 3% vol and in Kratky representation, (d) pure matrix and grafted particles at 0.5% vol, (e) grafted particles at 0.5% vol under magnetic field at 600 G, and (f) grafted particles at 3% vol. Gray solid lines are fits with the Debye model.

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Macromolecules

Figure 7. Conformation of free chains containing grafted objects for a grafted to free chain length ratio N/P = 1.2 for the pure matrix and the grafted particles at 3% vol in the normalized log−log representation (a) and in the Kratky representation (b). The full gray lines are the fits by the Debye model.

aggregates. This specific behavior probably originates from the fact that the mass of free chains we used is lower than the entanglement mass of polymer matrix (equal to 18 000 g/mol for PS). For such N/P ≥ 1, measurements on very close systems have demonstrated that the chains of the grafted corona have a Gaussian behavior.24 The bulk conformation measurements with grafted objects are shown in Figure 6 for the grafted to free chain length ratio N/P = 0.26 (0.5% vol of particles without and with magnetic field of 600 G and 3% vol of particles) and in Figure 7 for N/P = 1.2 (3% vol of particles) and compared with the reference pure matrices. All curves were normalized by the product (1 − φH)(1 − Φpart)VchainΔρ2 for the given corresponding molecular mass of the H chains respectively equal to Mw = 108 800 g/mol for N/P = 0.26 and Mw = 19 400 g/mol for N/P = 1.2. The volume of the grafted brush is taken into account for the calculation of the particle volume fraction. As expected, the normalized S1(q) plateau tends to 1 when q tends to zero, and the corresponding value of molecular masses determined by GPC is in good agreement with the normalization factors Mw = 123 500 g/mol for N/P = 0.26. We can notice a small discrepancy between the normalization value and those determined by GPC, Mw = 33 000 g/mol for N/P = 1.2. We believe that this deviation is mainly due to the very high polydispersity index of the matrix chains (PDI = 2.8) used for this case that increased the uncertainty, especially for the GPC measurement. For the sample at N/P = 0.26 casted in the presence of magnetic field, the 2D spectrum was perfectly isotropic, so an isotropic averaging was used. It appears that all scattering curves share the same classical features of a Gaussian chain, i.e., a q−2 decay at large q and the Guinier plateau at low q. At very low q, there are some slight differences depending on the N/P. At N/P = 0.26 (Figure 6), the scattering of the ΦγFe2O3 = 0.5% vol sample superimposes with those of the pure matrix, except a slight upturn at very low q that we assign to microcracks scattering, as for the case of the bare nanoparticles. At 0.007 Å−1, the upturn is more marked and is of the same magnitude whether a magnetic field was applied or not during the casting, the 2D spectra being perfectly isotropic in the first case. As for the case of the bare nanoparticles, we assess these additional scattering to microcracks, whose number increases

principle of extrapolation to zero concentration. It also proves that the measurement at 25% of PSH chains is almost similar to that of the extrapolated scattering curve, similarly to what is observed in the isotropic and for the pure matrix case. A proper refined extrapolation of the chain form factor is displayed in Figure 5 performed either in the horizontal direction or in the vertical direction, i.e., parallel (Figure 5a,b) or perpendicular (Figure 5c,d) to the magnetic field applied during processing. From the analysis of the scattering curves, we obtained radius of gyration Rg∥ = 120 ± 7 Å for the chain form factor aligned parallel to the magnetic field and Rg⊥ = 116 ± 7 Å for the chain form factor aligned perpendicular to it. These values are very close to the one obtained for the isotropic sample (discussion below) and allowed us to conclude that the amount of polymer chains trapped between particles inside the chain-like cluster perpendicular to the field direction should be certainly very low. III.3. Nanocomposites Containing Grafted Nanoparticles. As the measurements with the extrapolation to zero concentration method are very expensive in quantity of nanoparticles because samples have to be duplicated, we have decided to perform the measurements on nanocomposites filled by nanoparticles grafted by a deuterated corona only on samples containing 25% PSH chains. We assume that the signal comes only from the form factor of chains as demonstrated previously for the case of bare nanoparticles. The nanostructure of the fillers has already been fully described in a previous paper23 on the basis of a combination of TEM and SAXS measurements. We recall here only their main features. For N/ P = 0.26, the grafted objects are organized in an homogeneous dispersion of dense compact aggregates having a Nagg of ∼50 and an inner fractal dimension Df of 2.6, the grafted chains of the corona being partially collapsed. When processed under magnetic field, these dense aggregates align themselves in chainlike objects. For N/P = 1, the grafted objects are perfectly dispersed and have a homogeneous distribution within the sample. Finally, at N/P = 1.2, the structure is intermediate between the two other cases. Indeed, there are still isolated and well-dispersed grafted objects as for N/P = 1, but they coexist with some large open ramified aggregates. These additional large aggregates are in limited number because the mean aggregation number Nagg is ∼10, which is an average between the two coexisting populations of isolated objects and H


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Macromolecules with the particle volume fraction ΦγFe2O3. In Figure 6a, the radius of gyration obtained for the pure matrix matches perfectly the one obtained for the filled sample with 0.5% vol of grafted particles Rg = 92 ± 6 Å. In Figure 6b, one can see that this value is slightly reduced to Rg = 88 ± 6 Å when we applied the magnetic field. In Figure 6c, the value is even more reduced to Rg = 83 ± 6 Å when we increase the particle loading from 0.5% to 3% vol. When grafted objects are almost well dispersed for N/P = 1.2, the behavior is clear-cut. In that case, the scattering curve of the sample containing the grafted objects superimposes exactly with those of the pure matrix even for 3% vol of particles. It can be fitted by the Debye model with a similar gyration radius Rg of 45 ± 4 Å. The discrepancy observed between the molecular mass value used for normalization and the one deduced from GPC measurement is due to the high PDI of the polymer. III.4. Discussion. The reliability of the method presented here is based on a combination of several parameters. The first important point of the present study is that the extrapolation method is very robust to determine the chain form factor in the presence of fillers in nanocomposites without any possible ambiguous imperfect matching of the filler. Except the spurious scattering from the microcracks which always exists for nanocomposites prepared by casting, we demonstrated that we can extract the extrapolation signal from the single polymer chain without and with nanoparticles for different particles dispersion. The method has been previously demonstrated by Jouault et al.21 Here thanks to the specific versatility of the extrapolation method, we extend the method to different situations of particles−polymer interactions ranging from attractive to repulsive: from very weak interaction with the bare particles up to the entropically favorable (athermal) interaction with the grafted particles. We also demonstrated that the sample containing 25% of H chains superimposes always perfectly to the extrapolated signal, meaning that this case is diluted enough to directly determine the chain form factor. By achieving a very accurate absolute normalization of the scattering curves taking into account the exact volume fraction of the fillers and mass of the matrix chains, we were able to determine the radius of gyration of the polymer chain without any assumptions and any other fitting parameter. This determination is completed by a perfect knowledge of the filler morphology for the different grafted and bare particle cases previously analytically modeled with a combination of SAXS and TEM.23,27,28 Let us now discuss the results which are summarized in Figure 8 that shows the radius of gyration determined in the presence of particles divided by the radius of gyration for the corresponding pure polymer as a function of the different situations probed: (i) left side of the plot, bare particles without and with magnetic field; (ii) right side of the plot, grafted particles for two particles loading, two grafted to free chain length ratio, without and with magnetic field. One can observe a significant increase of the radius of gyration (almost 16%) for the bare particles that can be explained by the very weak interaction between the particles and the polymer. As mentioned in the Introduction and described in ref 27 the nanoparticles are forming multiscale aggregates with a two-step structure. The formation of large scale clusters called supraaggregated (SA) of mean size R ∼ 80 nm made from primary aggregates results from a strong repulsive interaction between fillers and polymer.

Figure 8. Summary of the normalized radius of gyration for (i) bare particles (left) and (ii) grafted particles (right) as a function of particles loading, applied magnetic field, and grafted to free chain length ratio N/P. Top: sketches illustrating the different chain conformations.

We calculated in ref 27 the effective volume fraction occupied by the supra-aggregates ΦSA as a function of particle volume fraction, and we obtained ΦSA = 0.8 for 3% vol of particles and ΦSA = 1.3 for 5% vol of particles loading. Considering that threshold of overlapping of the supraaggregates is achieved for ΦSA = 1, we choose experimental conditions for which clusters concentration was very close to such threshold in order to create a high level of confinement for the polymer chain. For that situation, the accessible free space available for the chain is strongly reduced. Thus, in order to minimize the energy, the chains have to be swollen to explore the free volume and avoid the fillers. Orienting the fillers with an external magnetic field does not improve or reduce this swollen effect. This is different from what was obtained by Jouault et al.,21 who did not observe a modification of the radius of gyration in the case of silica/PS system with a weak interaction. However, the repulsion between the silica and the PS is smaller than for the maghemite particles, as demonstrated by the fact that only a single stage of aggregation of the filler into the polymer matrix occurred for such silica/PS system. In addition, the particles loading used by the authors, 5% vol, was far away from the overlapping and/or the percolation threshold of the silica clusters. The degree of confinement for the polymer chains was thus significantly lower. When moving to grafted particles, the interactions between the filler and the free chains changed dramatically: owing to the mixing entropy, free and grafted chains are entangled in various situations depending of the grafted to the free chain length ratio: a large entanglement for N/P = 1.2 that gives rise to a good dispersion of the nanoparticles and a low entanglement for N/P = 0.26 that provokes the formation of clusters as a result of the partial collapse of the grafted brush.22 When the loading particles are almost well dispersed at low content, there is no specific balance of the interaction that could induce a modification of radius of gyration with respect to the pure polymer one, in accordance with what we measure for N/P = I


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Macromolecules

The manuscript was written through contributions of A.S.R., J.J., and F.C. All authors have given approval to the final version of the manuscript.

1.2: the grafted brush prevents any specific adsorption of the bulk chain at the surface of the particle. All the conformation remains accessible for the chains in the free space remaining between the well-dispersed fillers. This result is agreement with the results of Jouault et al.20 obtained for well dispersed silica in a favorable interacting polymer (PMMA). On the contrary, when the chains of the grafted brush are partially collapsed, the chains of the matrix are still interacting with the clusters by entanglement even if the distance between the cluster is larger than the chain size.23 They feel the long-range volume compression of the fillers and have to collapse to minimize the energy. If the particle loading is too low (0.5% vol), the level of confinement is not large enough to compress the chain, whether the clusters of fillers are isotropic or organized in chains under magnetic field. But when the loading content is increased up to 3% vol loading, this results in a decrease of almost 11% of the radius of gyration. Comparable influence of the filler on the chain conformation has already been observed previously,8,12 namely, a decrease of 10−20% of the radius of gyration. However, these result have usually been obtained for a given single case of polymer−filler interaction and under unperfected filler contrast matching condition or unclear characterization of the filler dispersion, as discussed by the authors themselves in their papers.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the ILL for the neutron beam allocation and especially Ralf Schweins for his help on the D11 spectrometer.

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IV. CONCLUSION We have shown here that the use of the extrapolation method enables to highlight some small deviations of the mean chain bulk conformation of the polymer in the presence of fillers in nanocomposites which are directly related to the filler dispersion and thus driven by the polymer filler interactions: a swelling of the chain for bare particles induced by the topological constrains imposed by the particles clusters when the particle filler interaction is weak, a nonmodified conformation for well-dispersed grafted particles when the polymer filler interaction is favored, and a volume compression of the entangled chain when grafted particles are forming clusters. We believe that this is the very high accuracy of the extrapolation method that enabled to detect these small deviations by comparison to the usual ZAC method that usually suffers from limitations due to unperfect filler matching conditions. These experimental evidence relying the impact of the filler organization with the interaction onto the polymer chain open new readings in the understanding of the polymer contribution on the macroscopic mechanical properties of the nanocomposite materials.

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AUTHOR INFORMATION

Corresponding Authors

*(J.J.) E-mail [email protected]. *(F.C.) E-mail [email protected]. ORCID

Fabrice Cousin: 0000-0001-7523-5160 Jacques Jestin: 0000-0001-7338-7021 Present Address

F.M.: LNLS Brazilian Synchrotron Light Laboratory, Rua Giuseppe Máximo Scolfaro, 10.000, Polo II de Alta Tecnologia de Campinas, Campinas, São Paulo, Brazil 13083-100. Author Contributions

J.J. and F.C. have designed the experiments. A.S.R. has prepared all the samples. All the authors have performed the experiments and participated in the analysis and interpretation of the results. J


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