Intra- and Interchain Correlations in Polymer Nanocomposites: A

Sep 15, 2016 - (11) In all these previous works, the small-angle neutron scattering (SANS) ..... Within the error bar the polymer Rg is slightly affec...
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Intra- and Interchain Correlations in Polymer Nanocomposites: A Small-Angle Neutron Scattering Extrapolation Method Nicolas Jouault*,† and Jacques Jestin‡ †

Sorbonne Universités, UPMC Univ Paris 06, CNRS, Laboratoire PHENIX, Case 51, 4 place Jussieu, F-75005 Paris, France Laboratoire Léon Brillouin (LLB), CEA Saclay, 91191 Gif-Sur-Yvette, France

‡

S Supporting Information *

ABSTRACT: In this Letter we applied for the first time a small-angle neutron scattering (SANS) extrapolation method to study the influence of nanoparticles (NPs) on polymer chain conformation in polymer nanocomposites (PNCs). This new approach is based on a perfect NP matching thanks to a statistical hydrogenated (H)/ deuterated (D) polymer matrix in which a certain amount of labeled chain (H) is added. The extrapolation to zero H content gives the intrachain structure factor, S1(q), and the interchain correlations, S2(q), the latter not being accessible under the zero average contrast (ZAC) condition preferentially used in the previous studies. We validate the method on well-known silica/polystyrene (PS) PNCs and compare the results with our previous ZAC measurements. The analysis of both S1(q) and S2(q) shows (i) no significant modifications of the radius of gyration Rg of the chain and of the interchain interaction induced by the presence of NPs and more interestingly (ii) the existence of chain domains with lower densities included inside NP clusters as the result of excluded volume effects that create an extra scattering at low q. The extrapolation method unambiguously shows that the unexpected behavior observed at low q comes from the chains and not from the unmatched NPs.

T

where S1(q) and S2(q) are the intrachain and interchain structure factors, respectively; Φ is the total polymer volume fraction; φH and φD are the H and D proportion (with φH + φD = 1); ρH, ρD, and ρsolvent are the scattering length densities (SLDs) of H chains, D chains, and solvent, respectively; and V = NVm is the volume (with N the polymerization degree and Vm the molar volume). If the H/D polymer proportion is chosen equal to the solvent, φHρH + φDρD = ρsolvent, i.e., fulfilling the zero average contrast (ZAC) condition, the scattering intensity is reduced to

he influence of nanoparticles (NPs) on the chain conformation in polymer nanocomposites (PNCs) has been the source of many experimental studies during the last 15 years.1 For spherical NPs, the conclusions are disparate: from chain swelling2,3 or contraction4 to, as in most cases, no significant changes in the conformation.5−10 In the case of anisotropic NPs such as carbon nanotubes (CNTs), no changes have been observed at low concentration, while an important chain swelling is found for high concentration.11 In all these previous works, the small-angle neutron scattering (SANS) technique has been used through a specific chain labeling by deuteration that creates a contrast between the chains within the sample. Then the total chain structure factor ST(q) can be extracted from the measured scattering intensity. However, to directly access the chain conformation in PNCs, one has first to “cancel” the predominant scattering coming from the NPs. An efficient way is to be under the zero average contrast (ZAC) condition primarily used to elucidate the chain conformation in a solvent.12 The scattering intensity I(q) of a mixture of hydrogenated (H) and deuterated (D) chains in a solvent is given by eq 1

I(q) = ϕφHφD(ρH − ρD )2 VS1(q)

(2)

I(q) is only related to the intrachain structure factor S1(q), i.e., the chain form factor that contains information on the conformation of a single chain: the radius of gyration Rg and the persistence length lp can be obtained from the fit of the experimental S1(q). In PNCs, the NPs can be viewed as the solvent in eq 1. So the polymer mixture SLD has to be the same as the NP SLD. Since the NP matching cannot be directly checked under ZAC, an accurate NP SLD determination is required by contrast variation of native NP solution prior to the ZAC measurement. One obvious advantage of the ZAC method is that the chain conformation is directly accessible

I(q) = ϕφHφD(ρH − ρD )2 VS1(q)

Received: June 30, 2016 Accepted: September 9, 2016

+ (φHρH + φDρD − ρsolvent )2 [VϕS1(q) + Vϕ2S2(q)] (1) © XXXX American Chemical Society

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ACS Macro Letters within a single measurement. However, imperfect NP matching4,5 or additional effects like preferential H or D adsorption9,13 usually perturbate the low q scattering signal and can interfere with the correct interpretation of the results, suggesting that the ZAC condition is not fulfilled locally when the NP size is in the same order of magnitude as the chain size. Here we report an alternative SANS approach, never used previously for PNCs, that separates the scattering intensity I(q) into a S1(q) and S2(q) by the specific labeling and extrapolation method. We validate it on a widely studied silica/polystyrene (PS) PNC5,6,8 by comparing the results with our previous ZAC measurements.6 This new approach relies on a statistical H/D PS matrix (Mw = 170 000 g/mol with Mw/Mn = 1.74, the synthesis has been detailed elsewhere6) that contrast-matches the silica NPs. The H/D matrix plays the role of the solvent in eq 1, and a given volume fraction of H PS, ϕH (Mw = 138 000 g/mol with Mw/Mn = 1.05 purchased from Polymer Source), is introduced. In that condition the scattering intensity I(q) is I(q) = (ρH − ρH/Dmatrix )2 VS1(q) ϕH + ϕ(ρH − ρH/Dmatrix )2 VS2(q)

(3)

−2

where ρH = 1.43 × 10 cm and ρH/D matrix are the SLDs of the H/D matrix that contrast-matched the silica (= 3.41 × 1010 cm−2). Figure 1 shows a schematic representation of the 10

Figure 1. Schematic representation of the SANS extrapolation method. The dashed circles represent the matched NPs and the blue lines the hydrogenated (H) polymer chains. The green background represents the H/D matrix that contrast-matched the NPs.

Figure 2. (a) Normalized scattering intensities I(q)/ϕH (with ϕH of 25%, 50%, and 70% v/v) and the extrapolation to ϕH → 0 (red circles). The H/D matrix intensity is also plotted for comparison (black crosses). The intrachain structure factor S1(q) is shown in the inset. (b) Kratky representation q2S1(q) as a function of q. The black continuous line represents the best fit using the Debye formula. In the inset is shown the interchain correlation S2(q), which is equal to the opposite of S1(q), as expected for the polymer melt.

extrapolation method. One has to measure the scattering intensity I(q) for different ϕH. The S1(q) and S2(q) can be then obtained separately using eq 3: the extrapolation for each q value to ϕH = 0 gives S1(q), and the slope gives S2(q). We first checked this approach on neat PS (i.e., without NPs) and used three different ϕH: 25%, 50%, and 70% v/v. SANS measurements were performed on D11 spectrometer at Institut Laue Langevin (ILL, Grenoble, France, see details in SI). Figure 2a shows the normalized scattering intensities I(q)/ ϕH and the extrapolation to ϕH → 0 (red circles), which are typical for an ideal Gaussian PS chain with a q−2 dependence at high q.14,15 The pure H/D matrix is also plotted for comparison (the upturn at low q is due to crazes). The extrapolated curve is then normalized by Δρ2V = 86.4 cm−1 to get S1(q) (inset in Figure 2a), and, as expected, S1(q) tends to 1 at low q. Figure 2b shows the Kratky plot, q2S1(q), as a function of q. In this representation, for a Gaussian chain, the plateau value at high q is equal to 2/Rg2. Here one finds a Rg of 10.0 ± 0.9 nm, in good agreement with the expected value (Rg = 0.0275*Mw0.5 = 10.2 nm).14 Finally the fit of q2S1(q) by the Debye function, (2/ x2)(exp(−x) − 1 + x) (with x = q2Rg2), using a Rg of 10.0 nm nicely reproduces the data (continuous black line in Figure 2b).

Note that the extrapolated S1(q) is similar to the one obtained under the ZAC condition6 (see Figure S1 in Supporting Information, SI), confirming the validity of the extrapolation method. Contrary to the ZAC condition, the extrapolation method also provides the interchain correlation S2(q), i.e., correlations between monomers belonging to different chains. For unfilled polymer melt, chains are supposed ideal; i.e., the interaction between monomers can be neglected.15 Here, there is no demixing between the H/D matching matrix and the H chains, which is consistent with the low H/D Flory−Huggins parameter, χ, for 138 kg/mol PS (χ = 1.4 × 10−4). In these conditions the S2(q) is equal to the opposite of S1(q)16 as shown in the inset of Figure 2b. From the analysis of the neat PS we can conclude that the extrapolation method is validated for the determination of the chain conformation in the melt. We now turned to PNCs filled with 5% v/v of silica NPs. The colloidal silica NPs with a mean radius RNP of 6.1 nm (purchased from Nissan Chemicals) were initially dispersed in dimethylacetamide (DMAc). PNCs were prepared by mixing NP solution with a polymer solution containing the matching polymer (statistical H/D PS) and different amounts of H 1096

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ACS Macro Letters chains (25%, 50%, or 70% v/v). The polymer/NP solution is then stirred during 2 h, poured into Teflon molds, cast and annealed at 130 °C during 8 days. Small-angle X-ray scattering (SAXS, ID-02 at ESRF, Grenoble, France, see SI for details) on dry PNCs revealed that the NPs arrange in nonconnected fractal aggregates.17 An aggregate form factor has been used to fit the data with the aggregation number Nagg and the fractal dimension Df as parameters, as described elsewhere.17 From these two values, a spherical aggregate radius, Ragg = Nagg1/DfRNP, and a compactness, κ = Nagg(RNP/Ragg)3, are calculated. Table 1 Table 1. Structural Parameters of the Silica Aggregates Obtained by SAXS (Nagg, Df) and of the Polymer Chain Obtained by SANS (Rg)a 5% v/v

extrapolation

ZAC

Nagg Df Ragg (nm) κ ϕagg Rgchain (nm) polymer SLD (× 1010 cm−2) polymer density (g·cm−3)

14 1.89 25 0.20 0.25 10.3 2.75 0.88

9 1.85 20 0.26 0.19 9.2 2.98 0.95

a

Data related to the ZAC measurements have been published elsewhere.6 They are used here for comparison with the extrapolation method. Figure 3. (a) Normalized scattering intensities I(q)/ϕH (with ϕH of 25%, 50%, and 70% v/v) and the extrapolation to ϕH → 0 (red circles) for 5% v/v filled PNCs. (b) Intrachain structure factor S1(q) obtained by the extrapolation method. The black continuous lines correspond to the best fit composed of an aggregate and a polymer chain (Debye function) form factors (see main text for details). The inset in (b) shows the scattering intensity of the H/D matrix containing 5% v/v of silica NPs compared to the unfilled H/D matrix.6

lists the values obtained for both methods: extrapolation and ZAC. The aggregate sizes are slightly different between the two methods. We attribute this small variation to possible changes during the sample preparation.18 Figure 3a shows the normalized scattering intensities I(q)/ ϕH (with ϕH of 25%, 50%, and 70% v/v) and the extrapolation to ϕH → 0 (red circles) for 5% v/v filled PNCs. The corresponding S1(q) obtained by normalizing the scattering intensity I(q) by Δρ2V of the chain is shown in Figure 3b. The S1(q), larger than 1 at low q, indicates the existence of an extra contribution different from the classical chain scattering. To investigate its origin and its effect on the polymer Rg we hypothesize that the S1(q) can be expressed as a sum of two form factors S′1(q), one from the polymer chain and one from an extra contribution that will be detailed below (assuming no correlations between these two contributions) S1(q) = ϕextS′1,ext (q) + ϕchainS′1,chain (q)

contribution does not come from unmatched aggregates. The perfect NP matching has been checked and confirmed by the scattering intensity of the H/D matrix filled with 5% v/v of silica NPs: as highlighted in the inset of Figure 3b, the signal is low and constant, similar to the unfilled H/D matrix. We hypothesize that the local polymer density around the aggregates, i.e., its SLD, is decreased due to the excluded volume effect. We consider a composite spherical object composed of silica aggregate and some PS chains, as depicted by the scheme in Figure 3b. This low q region is then fitted using a polydisperse sphere form factor whose parameters are the radius R, the polydispersity σ, and the SLD of the sphere. Since R is known from the SAXS data (= 25 nm), the best fit is obtained for σ = 0.34 and a SLD of 2.89 × 1010 cm−2. Note that the fitting has been performed on the extrapolated I(q)/ϕH to determine the SLD. The SLD reflects the composition and density of the sphere according to SLDsphere = ϕSiO2SLDSiO2 + ϕpolymerSLDpolymer, where ϕSiO2 is the volume fraction of SiO2 inside the sphere, i.e. the compactness κ; and SLDSiO2 is the SLD of pure SiO2 (= 3.41 × 1010 cm−2). Then, we extract the SLD of the polymer inside the sphere, SLDpolymer, equal to 2.75 × 1010 cm−2. In principle, ϕH tends to 0 in the extrapolated curve, and the polymer SLD should be equal to the one of the matching matrix (i.e., 3.41 × 1010 cm−2). This is not the case here because the SLD is lower, suggesting a decrease in the polymer density. Assuming a H/D composition of 60.9/39.1, we

(4)

At high q the chain scattering S′1,chain dominates and can be fitted by a Debye function whose only parameter is the Rg of the chain (ϕchain is a fixed value equal to1 − ϕext, with ϕext = ϕagg, see below): one found a Rg of 10.3 nm, giving a Rg/Rg,0 of 1.03 (with Rg,0 = 10.0 nm). Within the estimated experimental error bar of 10%, we can conclude that the chain conformation is not affected by the presence of the NPs, in good agreement with previous studies.5,6,8 This is the first important message of this paper. At low q the S1(q) is dominated by an extra contribution, S′1,ext. Previously, similar extra scattering contributions were attributed to bound chain layers at the NP surface for individual NP dispersion: adsorbed chains have an SLD different from the bulk, creating a SANS contrast.9,13 However, the system here is more complex due to NP aggregation and fractal aggregates: the S1(q) cannot be fitted with a simple core/shell model accounting for the bound layer. Additionally, this extra 1097

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is larger for small NPs: assuming that the NPs are welldispersed in the polymer matrix, they concluded that the shell contribution has an important impact on the scattering intensity. Here, the extra scattering is more pronounced in the extrapolated curve, compared to the ZAC one. The aggregate compactness κ appears to be an important parameter: the lower κ (the more “open” aggregate) the larger the extra scattering. The polymer density is more affected by large fractal aggregates. In summary, we presented a new SANS approach to investigate the polymer chain conformation in PNCs based on a clear NP matching and an extrapolation method. Despite a low q extra scattering, the Rg of the chain can be unambiguously analyzed and is not modified in the presence of NPs, in agreement with ZAC results.6 The extrapolation method also provides novel information with the determination of the S2(q), not possible under ZAC. Here again the presence of NPs does not affect the interaction between monomers, the chains remaining ideal, as expected for the polymer melt. More importantly the extrapolation method clearly shows that the extra scattering at low q is attributed to the chains and not to unmatched NPs. Here we explain it by a decrease in polymer density around the silica aggregates, modifying its SLD and creating a SANS contrast. The refined description of the polymer chain properties (conformation, density) in PNCs is essential for further understanding and predictions of the macroscopic properties of the materials.

estimated the polymer density inside the sphere to be equal to 0.88 g/cm3, corresponding to 19% lower than the bulk density (= 1.09 g/cm3). Such a description of the S1(q) enables us to reproduce correctly the experimental data. One can notice that depletion is visible in the intermediate q range. The observed “hole” in the experimental S1(q) comes from the crossover of the I(q)/ϕH data at intermediate q (see Figure 3a) and has no physical origin. The same fitting strategy has been used for the ZAC data, and the total fit, shown in Figure S2 with the results reported in Table 1, perfectly reproduces the data. Within the error bar the polymer Rg is slightly affected by the presence of the NPs (Rg/ Rg,0 = 0.92, i.e., 8% decrease) within a range comparable to the one obtained from the extrapolation method: the presence of the NP does not modify significantly the mean chain conformation. The low q behavior is explained by a 13% decrease in polymer density (= 0.95 g/cm3) in the vicinity of silica aggregates. This result is also in line with the one obtained from the extrapolation method. Finally, the S2(q) of the 5% v/v filled sample has also been extracted. Since the “aggregate” scattering dominates at low q we only focus on the high q region, where the chain scattering dominates (see Figure 4). In

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications Web site. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.6b00500. Complementary SANS and SAXS data(PDF)

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Figure 4. Intra- (S1(q), red circles) and interchain (-ϕS2(q), blue squares) correlations for 5% v/v filled PNC. As expected for polymer melt, S1(q) = −ϕS2(q) in the q-range where the chain scattering dominates.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (N.J.). Notes

The authors declare no competing financial interest.

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this q-range, S1(q) = −ϕS2(q) as expected for polymer melt: the presence of NPs does not affect the intersegmental correlation at this scale, and the chain behavior remains ideal. Interestingly the extrapolation method unambiguously gives a quantitative novel insight into the unexpected behavior at low q observed in recent ZAC SANS studies. Contrary to the ZAC in which the good NP matching cannot be directly checked, the use of a statistical H/D matching matrix clearly shows that the extra scattering is not due to an imperfect NP matching. The origin of such extra scattering has been discussed recently under the ZAC condition. Banc et al.9 proposed that a local H/D deviation from the ZAC condition due to preferential H (or D) adsorption around the NPs creates a SANS contrast. Similarly, the low q extra contribution observed in well-dispersed silica/ PMMA PNCs has been fitted assuming the existence of a polymer-bound layer surrounding the NPs.13 In this paper the extra contribution comes from the decrease in polymer density around silica aggregates. The common feature in all these studies is a local change in polymer behavior (adsorption or excluded volume), modifying the polymer SLD. In their model, Banc et al.9 observed that the amplitude of the extra scattering

ACKNOWLEDGMENTS The authors thank François Boué (LLB, CEA Saclay). We also acknowledge the European Synchrotron Radiation Facility (ESRF, Grenoble, France) and the Institut Laue Langevin (ILL, France) for beam time allocation and Ralf Schweins for his help during the SANS experiment.

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