Supporting Information for. Tunable Multiscale Nanoparticle Ordering by Polymer Crystallization

Transcription

1 Supporting Information for Tunable Multiscale Nanoparticle Ordering by Polymer Crystallization Dan Zhao, Vianney Gimenez-Pinto, Andrew M. Jimenez, Longxi Zhao, Jacques Jestin 1, Sanat K. Kumar 1, Brooke Kuei, Enrique D. Gomez, Aditya Shanker Prasad, Linda S. Schadler, Mohammad M. Khani, Brian C. Benicewicz 1 correspondence to: jj2721@columbia.edu, sk2794@columbia.edu 1

2 Estimation of the PEO long period from the XRD data. The estimation of the long period ( ) from the XRD data is based on Scherrer s equation, 1 following the procedure described in our previous paper. 2 Briefly, we first measure the, using SAXS, the lamellar thickness (, ) is then given by:, =,, Where, is the PEO crystallinity from DSC. From here, for the nanocomposite samples can be estimated by: =, / Where is the full width at half maximum of the XRD diffraction peak (here we used the peak of 2 = 19.42, corresponding to the (120) reflection of the monoclinic lattice). Following that, the of the nanocomposites is: = / Modeling of modulus reinforcement. The improvement in the Young s modulus for the case of the ordered and disordered samples (i.e. 58ºC-7d vs. RT quench) can also be understood in the following two ways. (i) Using the Guth and Gold equation, 3 = (1+2.5Φ +14.1Φ ) Where and are the storage modulus of neat PEO and the 20 wt% nanocomposite, respectively. Φ is the volume fraction of the silica core plus the PMMA brush. The effective filler volume fraction contributing to the mechanical reinforcement can be estimated to be ~0.144 and ~0.208 for the cases where the NPs are well dispersed ( disordered ) and organized into sheets ( ordered ), respectively. This suggests that effectively there are more particles in the ordered sample contributing to the mechanical reinforcement than that in the disordered one. This can be reconciled by the fact that in the former case a large fraction of particles are excluded into the interlamellar regions, thus providing larger reinforcements to the amorphous phase of the crystalline PEO. (ii) We have also analyzed these data using the Halpin-Tsai equation, 4 = [ + (Φ +Φ )] Φ +Φ + Where Φ is the volume fraction of PEO, is the modulus of the nanofiller and is an empirical parameter, which is related to the geometry and volume fraction of the fillers. We first estimate the modulus of the grafted particle using the rule of mixtures, i.e., =Φ +Φ 2

3 Where Φ and Φ are the volume fractions of the silica and PMMA in the grafted particle respectively. =70 GPa and =2.5 GPa are used for the modulus of the silica and PMMA. With known values of,, Φ and Φ, we can estimate to be ~2.6 and ~9.8 respectively for the disordered and ordered samples. We know that, for spherical nanofillers, =2+40Φ 2 This agrees reasonably well with the value we obtained above for the well-dispersed system. In the case where NPs are organized into sheets, we can estimate the aspect ratio ( / ) of the sheets to be ~5 according to the following relation, =2( / )+40Φ Note that this relation is only valid for system-spanning oriented plates. But in our case, we know that the sheets are only locally, anisotropically organized within the spherulites while randomly oriented on a larger length scale. Thus the real size of the sheets formed in our system could be significantly larger. Calculation of fracture toughness. We have used two different methods to characterize the fracture toughness of the resulting materials, i.e., strain energy release rate ( ) and the work of fracture. In the former case, we first calculated the stress intensity factor ( ) according to the relations below, where is the sample thickness, is the support span length and is the maximum load. Note that was estimated following the protocols suggested in ASTM standard D = 10 ( ) / ( )= (1 )( ) 2(1+2 )(1 ) / Following that, was determined by the relation below, where is the Young s modulus and is the Poisson s ratio. Note that here we only report the normalized by that of the respective neat polymer assuming addition of NPs does not significantly alter the Poisson s ratio of the base material. = (1 ) We also stress that, according to ASTM standard D , the sample dimension under study does not strictly follow plane strain criteria, as given by,, ( )>2.5 3

4 Where is the yield strength, which is ~5.5 MPa. 5 However, for ductile materials, the plane strain condition can also be defined by the work of fracture, i.e., 25 Where is the specific essential work of fracture. In this perspective, our samples do satisfy the plane strain conditions. Table S1. Inter-particle surface-to-surface separation ( ) vs. silica loading NP wt% NP vol% silica core vol% h, (nm) a h, ( ) (nm) b a h, = [ / ] / [exp ln ( ) ] Where is the number averaged silica core diameter, =2/ is the maximum random dense packing fraction of spheres, is the silica core volume fraction, is the geometric standard deviation of lognormal distribution for silica core size, is the PMMA grafted layer thickness (~5 nm, estimated from self-consistent mean-field theory). b h, ( ) is derived from the ( ) of each sample according to the relation: h, ( ) = 2 /, where corresponds to the first peak of ( ) and = +2 is the diameter of the silica core plus the PMMA corona. The size of the silica core ( ) was measured by SAXS on 0.1 wt% bare silica NPs (without PMMA brush) in methyl ethyl ketone. From this, we obtained a silica median diameter ( ) of 12.6 nm and lognormal polydispersity of 0.28 ( =exp (0.28) = 1.32). Thus the number averaged silica core size is given by: 6 =exp ln + (ln ) = 13.1 nm 2 4

5 Figure S1. Additional TEM micrographs. TEM micrographs for 20 wt% PMMA-gsilica NPs in 100 kg mol -1 PEO (a) quenched at room conditions, (b) isothermally crystallized at 58 C for 7 days, (c-d) isothermally crystallized at 60 C for 8.5 days and (e) in 46 kg mol -1 PEO isothermally crystallized at 57.5 C for 7 days. (f) High magnification TEM image for 40 wt% PMA-g-silica in 100 kg mol -1 PEO isothermally crystallized at 58 C for 7 days. 5

6 Figure S2. SAXS Data for 100 kg mol -1 PEO loaded with varying amounts of PMMA-g-silica. SAXS intensity ( ) vs. the scattering vector for liquid nitrogen quenched nanocomposites with a NP loading of (a) 10 wt%, (b) 20 wt%, (c) 40 wt%, and (d) 60 wt%. The solid red lines correspond to a polydisperse core-shell form factor with a silica core radius (median size) of 6.3 nm, a polydispersity of 0.28, and shell thickness of 2 nm. (e) The ( ) vs. for nanocomposites with varying NP contents. The solid lines are the Percus-Yevick fits. 6

7 Figure S3. Compare SAXS for the quenched sample and that in the polymer melt. ( ) for 100 kg mol -1 PEO based nanocomposites filled with 20 wt% PMMA-g-silica NPs in the melt (red symbols) at 80 C and that quenched with liquid nitrogen (black symbols). The solid lines are fits to a polydisperse core-shell form factor with the Percus- Yevick structure factor. The fitting parameters are shown in the table below. In the table, is silica core radius, Dispersity is the lognormal dispersity of silica core, d is the shell thickness, is the scattering length density difference between the silica core and the PEO matrix, is the scattering length density between the PMMA shell and the PEO matrix, ( ) is the average hard-sphere inter-particle distance, is the effective hard sphere packing volume fraction. Note that the scattering length density of amorphous and crystalline PEO is distinct, yielding different scattering contrasts between the particle and the matrix in the melt and quenched state. This results in the decrease in the scattering intensity in the quenched sample. 7

8 Figure S4. Arrhenius dependence of time-temperature shift factor log( ) on temperature obtained from linear rheology measurements for PMMA-g-silica in 100 kg mol -1 PEO with a NP loading of (a) 0 wt%, (b) 10 wt%, (c) 20 wt%, (d) 40 wt% and (e) 60 wt%. The red lines correspond to linear fits of the data. Note that, for the neat PEO, the last two points (the upper right of the graph, corresponding to 60 C and 65 C) are not included for the linear fitting, presumably because PEO starts to crystallize during the measurement. The activation energy estimated for neat PEO is ~6.2 kcal mol -1, close to the value reported in the literature (~6 kcal mol -1 ). 7,8 (f) Prediction of the shift factors from the Fox relation, i.e., log(, ) = log(, ) + log(, ), where and are the weight fractions of PMMA and PEO, respectively. This indicates that the system relaxation is an average of the matrix PEO and PMMA grafts. Note that the shift factors for PMMA (presumably attributed to relaxation) are obtained by matching the experimental data for the 60 wt% sample following Fox relation mentioned above. Apparently the relaxation times estimated in this way are slower than the relaxation of PMMA probed by dielectric spectroscopy, 9 which could be attributed to the fact that the PMMA chains are densely packed in the grafted layer as a result of the high grafted density (~0.24 chains/nm 2 ). 8

9 Figure S5. DSC characterization of the nanocomposites. (a) Heat flow curves of 100 kg mol -1 PEO with varying NP loadings during isothermal crystallization at 55 C. (b) Relative crystallinity ( ) vs. crystallization time for samples in (a). The dashed green lines correspond respectively to ( ) = 1 and ( ) = 0.5. The inset shows ( ) vs. = /( /, / /, ). (c) Avrami plots of the samples in (a). The line has an apparent slope of ~2.5. Effect of NP on polymer crystallization. The heat flow curves of PEO (Figure S5a) show that isothermal crystallization shifts to longer times with increased NP loading. However, the shape of the curves assumes an apparently universal form when plotted against /( /, / /, ), where / is the crystallization half-life (Figure S5b, inset). While the NPs slow down crystallization, they do not appear to affect the underlying thermodynamics or the crystal habit. An Avrami analysis 10 of the rate of crystallization, based on the heat flow curves (Figure S5c), shows that the Avrami exponent, indicative of the crystallization mechanism, is ~2.5 for all loadings. Also XRD shows the same peak positions in the pure PEO and the nanocomposites. 2 These results verify that the PEO crystallization mechanism appears to be unaffected by the NPs. This is consistent with the fact that the Flory-Huggins interaction parameter between PEO and PMMA is close to zero. 11 9

10 Figure S6. Optical microscopy measurements on spherulite growth rate. The spherulite diameter ( ) vs. time ( ) during isothermal crystallization at a series of temperatures for 46 kg mol -1 or 100 kg mol -1 PEO loaded with varying amounts of PMMA-g-silica NPs. The different samples in (a) through (i) are described in each figure. The solid lines are linear fits of vs.. Note that at high crystallization temperatures (e.g., 58 C and 60 C for the 100 kg mol -1 PEO based samples; 57.5 C for the 46 kg mol -1 PEO based ones), pre-seeding at 55 C was used for growth rate measurements, as nucleation barely occurs at these temperatures within a reasonable experimental time scale. 10

11 Table S2. Spherulite growth rate ( m/s) for nanocomposites with varying NP content at different crystallization temperatures Sample ID 50 C 52 C 55 C 56 C 57.5 C 58 C 60 C 100k_0wt% k_10wt% k_20wt% k_40wt% k_0wt% k_20wt%

12 Figure S7. Linear rheology of the nanocomposites in the melt. The linear storage (, black symbols) and loss (, red symbols) modulus vs. the angular frequency at 85 C for 100 kg mol -1 PEO melts filled with PMMA-g-silica NPs of different loadings. As shown here, at 20 wt%, the and are nearly parallel to each other, indicating that it is akin to a critical gel. Going further, at 40 wt%, starts to be larger than at low rates of deformation and tentatively displays a plateau. This suggests the NPs are connected to form a system-spanning network, thus making the material solid-like. 12

13 Figure S8. XRD Analysis. The long period ( ) or the interparticle separation distance (h ) vs. the NP weight percent for PMMA-g-silica NPs in 100 kg mol -1 PEO quenched from melt at room conditions. The black diamonds are s probed by XRD while the red diamonds denote the average interparticle spacing measured by SAXS (Table S1). 13

14 Figure S9. SAXS Analysis for samples crystallized at 52 C. Variation of (a) the extracted from the peak of ( ) and (b) the inter-particle separation distance (2 / ) with NP content for PMMA-g-silica NPs in 100 kg mol -1 PEO crystallized at 52 C for a varying amount of time, as indicted inside the graph. The dashed lines in (a) are fits of vs. NP vol% ( ) according to a power-law relation, ~. The results of the fits are (quenched) = Φ ; (4h) = Φ ; (1d) = Φ As expected, in the case of the uniform particle dispersion, i.e., the quenched samples, the power exponent is close to 1/3 while upon isothermal crystallization at 52 C, the system becomes strongly non-homogeneous, as indicated by the large values of the power exponents. Also notably, in (b) the inter-surface separation for the 60 wt% sample after 1d crystallization becomes negative, which presumably indicates the polymer brushes of neighboring particles start to overlap. 14

15 Figure S10. SANS Data on nanocomposites loaded with PMMA-g-silica NPs. Small angle neutron scattering data on 20 wt% PMMA-g-silica NPs in 100 kg mol -1 PEO. (a) and (b) are 2-D scattering patterns for samples crystallized at 52 C and 58 C for 7 days, respectively. (c) ( ) and (d) ( ) vs. for these two samples, with the black and red symbols corresponding to crystallization at 52 C and 58 C, respectively. 15

16 Figure S11. USAXS/SAXS data for nanocomposites loaded with PMMA-g-silica NPs. (a) Ultra-small angle X-ray scattering intensity ( ) vs. scattering vector for 20 wt% PMMA-g-silica NPs in 100 kg mol -1 PEO isothermally crystallized at 58 C for varying periods of time. (b) SAXS ( ) vs. for 20 wt% PMMA-g-silica NPs in 46 kg mol -1 PEO isothermally crystallized at 57.5 C for varying periods of time. 16

17 Figure S12. Estimation of the PEO long period from SAXS data. (a) ( ) vs. for neat 100 kg mol -1 PEO crystallized at various conditions, either quenched at room conditions or isothermally crystallized, e.g. 60C 8.5d indicates one that had been isothermally crystallized at 60 C for 8.5 days. (b) The same data plotted as ( ) vs.. (c) The long period extracted from the first peak in ( ) for neat PEO crystallized at various conditions. Table S3. The fitting results of the SANS/VSANS data in Figure 2B in the main text a d and ϕ eff are the Percus-Yevick structure factor parameters. and are the radius of the interlamellar and the radius of gyration of the interfibrillar clusters. is the mass fractal of the interfibrillar aggregates. 17

18 Figure S13. SANS data for nanocomposites loaded with PMA-g-silica NPs. ( ) vs. for PMA-g-silica in 100 kg mol -1 PEO with a NP loading of (a) 10wt%, (b) 20wt%, (c) 40wt% and (d) 60wt%. ( ) vs. for the same samples with a NP loading of (e) 10wt%, (f) 20wt%, (g) 40wt% and (h) 60wt%. Note that in each graph, the black symbols represent the quenched sample at room conditions while the red symbols correspond to the one that had been isothermally crystallized at 58 C for 7 days. (i) Replot ( ) vs. for all loadings that had been crystallized at 58 C for 7 days. From the second lower peak, we estimate the average inter-layer center-to-center distance is ~71 nm and ~94 nm respectively for the 40 wt% and 60 wt% samples. 18

19 Simulations The schematics of simulation model for anisotropic NP ordering is shown in Figure 3A of the main text. Simulation box is orthorhombic with an aspect ratio of Crystal growth modeled as an infinite-pillar moving with velocity. Boundary conditions are periodic in the x-, y-axis and fixed in the z-axis. For simplicity, we do not consider localization of particles in the interspherulitic zone, as before mentioned. We can safely use G as crystallization speed in the interfibrillar direction given that our system crystalizes in a regime where g ~ G according to Lauritzen-Hoffmann theory. 12 Figure S14 shows the equilibrium distance d between crystal and particles ahead of the front for different crystallization speeds. Particle ordering occurs in a regime with larger d values, while the observed plateau with increasing G corresponds with a fully dispersed state, as engulfment becomes dominant in the system. Figure S14. Numerical Study: Average particle location relative to growing front. Fitted equilibrium distance between crystal and NPs ahead of front vs.. Here, interlamellar space is 1.1 ; Hamaker constant is -0.4ε. is calculated by fitting the timeseries of < z NP z front >, averaged within a 2.0 cut-off, to a constant. As expected, d increases with smaller crystallization rates. Note that d has the same scale as the NP radius. 19

20 Figure S15. Optical Microscopy for fully developed spherulites. Comparing the size and morphology of spherulites formed in the four materials in Figure S16. (a) neat PEO fast, (b) 20 wt% fast, (c) neat PEO slow and (d) 20 wt% slow. Note the difference in the scale bars in (a)/(b) and (c)/(d). As shown here, the size and morphology of the spherulites are quite comparable for samples crystallized at identical conditions. 20

21 Table S4. Compare the crystallinity of the four materials in Figure S16 21

22 Figure S16. The loss modulus and angle from DMTA measurements. (a) The loss modulus ( ) and (b) loss angle (tan ) for four materials (either neat PEO or 20 wt% PMMA-g-silica NPs in 100 kg mol -1 PEO) as measured by DMTA at room temperature, namely neat PEO crystallized at ambient conditions ( fast ), neat PEO crystallized at 58 C for 7 days ( slow ), a 20 wt% loading sample crystallized at room conditions ( fast ), and that crystallized at 58 C for 7 days ( slow ). Note that in either case, the neat and nanocomposite samples are crystallized at identical conditions. 22

23 Figure S17. The stress intensity factor from 3-point bending tests. The stress intensity factor ( ) for the four materials shown in Figure S16. These tests were performed on samples with a ligament length ~ 3 mm. For each material, at least three specimens were measured. 23

24 Figure S18. SEM Micrographs. SEM micrographs of the fracture surfaces for the four materials shown in Figure S16: (row 1) neat PEO fast, (row) 20 wt% fast, (row 3) neat PEO slow and (row 4) 20 wt% slow. The scale bar and magnification is the same for images in the same column, as indicated inside the graph. 24

25 Figure S19. Work of fracture for specimens with varying ligament length. The specific work of facture ( ) as a function of the ligament length ( ) for the four materials shown in Figure S16. The figures (a)-(d) describe the specific samples considered. The red lines are linear fits to the data, yielding comparable essential and nonessential work of fracture for all the four materials tested. 25

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