Supporting Information for. Dynamics of Architecturally Engineered All- Polymer Nanocomposites

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1 Supporting Information for Dynamics of Architecturally Engineered All- Polymer Nanocomposites Erkan Senses,,,,* Madhusudan Tyagi,, Madeleine Pasco, Antonio Faraone,* NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland USA Department of Materials Science and Engineering, University of Maryland, College Park, MD USA Department of Chemical and Biological Engineering, Koc University, Rumelifeneri Yolu, 34450, Sariyer, Istanbul, Turkey Department of Biology, Rose-Hulman Institute of Technology, Terre Haute, IN USA

2 A. Small-angle neutron scattering The conformation of star polymers in their melt form and theta-solvents can be determined using the Benoit model 1 assuming Gaussian statistics of the arms. In the case of binary polymer mixtures, however, the chains may be swollen or contracted; thus, excluded volume ects need to be incorporated. A generalized star-branched polymer form factor was recently formulated by Hammouda 2 as follows: 1 P ( Q) N P ( Q) N (1 N ) P ( Q) star 2 b sb b b ib Nb (1) where P ( Q ) and P ( Q) sb ib are the form factors corresponding to a single star branch and inter-branch, respectively, and N b is the degree of polymerization for each branch. Single-branch form factor is determined using a generalized Gaussian chain form factor with excluded volume parameter,,

3 Psb ( Q) (, U ) (, U ) 1/2 1/ U 2 U (2) where 2 2 (2 1)(2 1) 6 x 1 U Q R and ( x, U ) exp( t) t dt is the incomplete gamma g U 0 function. The form factor for inter-branch interference is simply calculated by P ( Q, N ) 2 P ( Q, 2 N ) P ( Q, N ) 2. Finally, form factor for star polymer filler, P ( Q), and ib b sb b sb b star for the Debye form factor of the linear PVME matrix, (with R g =4.6 nm and v=1/2) were combined using the random phase approximation (RPA) with respect to their volume fractions. Fitting the data with the RPA model 3 (Figure 1b), the R g values of the single arms were obtained and listed in Table 1. The excluded volume parameters were found to be close to 1/ 3 for all-star polymers (v=0.38 for 7 arms-20kda, v=0.33 for 18-arms- 80kDa and 18 arms-40kda) suggesting the particle-like collapsed nature of the stars while v=0.56 for linear 80 kda indicating their slightly swollen state. The R g of the arms of the stars are found to be (2 to 3) nm while the hydrodynamic sizes of the stars determined by DLS in toluene (a good solvent for PS) are approximately two times the arm size. We have also performed SANS experiments on 18-arms dps (80 kg/mol) in h-toluene and compared the profile from the particles in hpvme (see Supplemental Materials). The

4 size of a single arm in toluene ( 4.7 nm ) is larger than its size in PVME ( 3.3 nm) consistent with small negative enthalpy of mixing for PS-PVME system 4 and good solubility and greater swelling of PS in toluene. 18 arms dps 2 10 in h-pvme I [arb.units] arms dps in h-toluene Q [Å -1 ] Figure S1. Small-angle neutron scattering profiles from 18 arms d-ps stars in h-pvme matrix and in h-toluene. The lines are the fits to the star form factors described in the text.

5 K I [arb.units] K 383 K 363 K 333 K Q [Å -1 ] Figure S2. Small-angle neutron scattering profiles from 18 arms dps stars in hpvme matrix at different temperatures. The lines are the fits to the star form factors described in the text. There is no phase separation in the blends up to at least 423 K. B. Glass-transition, dynamics fragility Figure S3. Glass transition of the PS fillers of different architecture. Differential scanning calorimetry (DSC) traces showing the glass-transition temperature (T g ).

6 For sufficiently high M w, the T g of the star polymers becomes comparable to their linear counterparts as the core region of the star becomes negligible. However, as the chains get shorter the number density of the end groups increases and the T g decreases according to the Flory-Fox equation; 5 thus, for the similar total M w of 80 kg/mol, the 18- arms star has lower T g (by 11 K) compared to the linear counterpart. At the highest functionality (f=18), the stars with shorter and longer arms have nearly identical T g. The broader glass transition for the short-arm star is most likely due to its high polydispersity. Such invariance of the T g between 2.5 kg/mol and 5 kg/mol arm lengths of f=18 is likely due to already dense nature of the latter with core region spanning nearly entirely the whole star molecule. For the same arm length (2.6 kg/mol), the T g of the 7-arms star polymer is close to the value corresponding to a linear polymer with the same arm M w and is 10 K lower than that of 18-arms star. Chremos and Douglas 6 recently suggested that the density of the star molecules increases for short arms and high-f stars and alleviates the enhanced free volume ect introduced by the chain ends. Their simulation suggests that the T g of the stars could increase with functionality when f > 6. This is consistent with the trend we observe between 7-arms and 18-arms stars.

7 In the dynamically asymmetric polymer blends, the Fox equation 7 often fails to explain the T g of the components. It is understood that a component (A) is locally enriched by its own monomer kind due to the connectivity of monomers along the chain, thus experiences larger ective concentration (, A ) at the length scale of a Kuhn segment ( 1 nm) compared to the average A, A, A self, A (1 self, A ) A concentration in the bulk ( ). 8 is determined by where self, A is the self-concentration of monomer A. The ective glass-transition of the component A can then be determined by the well-known Fox equation, 1 T T (1 ) T g. A, A g, A, A g, B using the locally ective volume fractions and the bulk T g values of the components A and B. For PVME and PS, self, PVME and, self PS are estimated to be 0.25 and 0.22, respectively. For the 20 % PS in the blends used in this work, the ective T g s in the linear PS-PVME blends are estimated to be 258 T g. PVME K ; 281 K and T 287 K. Since the DSC traces represent average behavior of Tg. PS 3KD g. PS 80KD the samples, T g of the components may not be obtained directly, rather, broader T g s are the norm for most blend systems. 8 We report on the mobility of the h-pvme matrix from the glassy state to the melt state using elastic neutron scattering (ENS) experiments. Furthermore, we performed quasielastic neutron scattering experiments well above the ective T g s of the components as well as the calorimetric T g s,, T T T g, PS g, PVME, where, the dynamic confinement ect 9 of the glassy high-t g PS chains on the segmental motions of the low-t g PVME matrix is negligible. Table S1. Glass transition temperatures of the composites and the pure components measured by DSC. We determined the breath of the transitions from the onset points where the deviations from glass and liquid lines on the DSC traces is shown on Figure 3a of the main text. Samples T g,dsc (K) Breath of transition (K)

8 hpvme matrix ± hpvme-dps linear 3kD ± hpvme-dps linear 80kD ± hpvme-dps 7-arms 20kD ± hpvme-dps 18-arms 80kD ± C. Quasielastic neutron scattering Table S2. Elementary Rouse rates of PVME at 363 K in the neat form and in the composites with PS of various architectures. Nanocomposites Wl 4 (Å 4 /ns) h-pvme (matrix only) ± 27.5 h-pvme/ d-ps linear -3K 40.4 ± 6.5 h-pvme/ d-ps linear -80K 46.3 ± 3.9 h-pvme/ d-ps 18 arm- 40K 49.0 ± 8.3 h-pvme/ d-ps 18 arm - 80K 44.3 ± 9.4 h-pvme/ d-ps 7 arm - 20K 42.6 ± 6.4 Table S3. Elementary Rouse rates of PVME at 393 K in the neat form and in the composites with PS of linear and star architectures. Nanocomposites Wl 4 (Å 4 /ns) h-pvme (matrix only) 333 ± 35 h-pvme/ d-ps linear -80K 171 ± 48 h-pvme/ d-ps 18 arm - 80K 222 ± 53

9 a S( Q, ) /S( Q, ) max Q = 3.6 nm -1 b Q = 13.6 nm -1 MSD [nm 2 ] E [ ev] Q = 3.6 nm /2 t [ns 1/2 ] Figure S4. (a) Representative QENS spectra (at Q = 3.6 nm -1 and Q = 13.6nm -1 ) for the neat h- PVME (black squares), and the composites with h-pvme and linear d-ps (80 kg/mol) (brown triangles) and h-pvme and star d-ps (88 kg/mol) (red circles). (b) The mean-squaredisplacements (at Q=3.6 nm -1 ) in the Rouse scaling, t 1/2, showing the linear dependence from which the elementary Rouse rates are calculated and given in Table 3. D. Neutron spin-echo spectroscopy Table 4. Elementary Rouse rates and the reptation tube sizes of PVME determined from neutron spin echo at 393 K in the neat form and in the composites with PS of various architectures. Note that the relative trend of Wl 4 parameters among the three samples are consistent with the QENS results although the obtained values differ. Wl 4 NSE Nanocomposites (Å 4 /ns) d (nm) h-pvme (matrix only) 1870 ± ± 0.92 h-pvme/ d-ps linear -80K 990 ± ± 0.16 h-pvme/ d-ps 18 arm - 80K 1420 ± ± 0.35 Finally, we note that both in neutron backscattering and neutron spin-echo spectroscopy experiments, the PS chains are deuterated, therefore, made invisible to the neutrons. In

10 the backscattering, the scattering intensity is dominated by the self-motion of H-atoms in the PVME at time scales ranging from 100 ps to 1 ns. Neutron spin echo spectroscopy covers the dynamic range up to 100 ns. The QENS experiments were performed at 363 K (and additionally at 393 K) while NSE was performed at 393 K. The T g values of the PS fillers range from 354 K to 365 K as given in Table 1 in the main text. Therefore, for the experiments performed at 363 K (near the T g of PS), the segmental relaxation time of PS is on the order seconds which is out of the experimental timescale for the neutrons (nanoseconds). For the experiments performed at 393 K, we estimated the elementary Rouse rate using the viscosity value of PS reported in an earlier work performed at 443 K 10 as follows: Using the given Williams-Landel-Ferry (WLF) shift factors, the viscosity of PS at 393 K is estimated to be 10 8 Pa-s. The reptation time at 393 K is then estimated from τ d = η o G o = = 1000 s (where G o is the entanglement modulus of PS). The elementary Rouse is then estimated using the relation Wl 4 (PS,T = 393 K) = 3N3 l τ d π 2 d 2 Å 4 /ns. 11 Here, l= 0.68, d=8.5 nm as reported by Fetters et al. 12 and N=1300 (as in ref 10). Comparing the Wl 4 numbers for PVME at the same temperature (given in Table S3), PS

11 is 5 orders of magnitude slower than PVME, which makes PS essentially frozen compared to PVME. References: 1. Benoit, H., On the Effect of Branching and Polydispersity on the Angular Distribution of the Light Scattered by Gaussian Coils. J. Polym. Sci., Part A: Polym. Chem. 1953, 11, Hammouda, B., Form Factors for Branched Polymers with Excluded Volume. J. Res. Natl. Inst Stan 2016, 121, Hammouda, B., Probing Nanoscale Structures-the Sans Toolbox. National Institute of Standards and Technology Yurekli, K.; Karim, A.; Amis, E. J.; Krishnamoorti, R., Phase Behavior of Ps Pvme Nanocomposites. Macromolecules 2004, 37, Jr., T. G. F.; Flory, P. J., Second Order Transition Temperatures and Related Properties of Polystyrene. I. Influence of Molecular Weight. J. Appl. Phys. 1950, 21, Chremos, A.; Douglas, J. F., Communication: When Does a Branched Polymer Become a Particle? J. Chem. Phys. 2015, 143, Hiemenz, P. C.; Lodge, T. P., Polymer Chemistry. CRC press: Lodge, T. P.; McLeish, T. C. B., Self-Concentrations and Effective Glass Transition Temperatures in Polymer Blends. Macromolecules 2000, 33, Colmenero, J.; Arbe, A., Segmental Dynamics in Miscible Polymer Blends: Recent Results and Open Questions. Soft Matter 2007, 3, Liu, S.; Senses, E.; Jiao, Y.; Narayanan, S.; Akcora, P., Structure and Entanglement Factors on Dynamics of Polymer-Grafted Nanoparticles. ACS Macro Lett. 2016, 5, Richter, D.; Monkenbusch, M.; Arbe, A.; Colmenero, J., Neutron Spin Echo in Polymer Systems. In Neutron Spin Echo in Polymer Systems, Springer: 2005; pp Fetters, L.; Lohse, D.; Colby, R., Chain Dimensions and Entanglement Spacings. In Physical Properties of Polymers Handbook, Springer: 2007; pp

Polymer Dynamics. Tom McLeish. (see Adv. Phys., 51, , (2002)) Durham University, UK

Polymer Dynamics. Tom McLeish. (see Adv. Phys., 51, , (2002)) Durham University, UK Polymer Dynamics Tom McLeish Durham University, UK (see Adv. Phys., 51, 1379-1527, (2002)) Boulder Summer School 2012: Polymers in Soft and Biological Matter Schedule Coarse-grained polymer physics Experimental