Supporting Information for Effect of. Polymer/Solid and Polymer/Vapor. Instantaneous Interfaces on the Interfacial

Transcription

1 Supporting Information for Effect of Polymer/Solid and Polymer/Vapor Instantaneous Interfaces on the Interfacial Structure and Dynamics of Polymer Melt Systems Selemon Bekele and Mesfin Tsige Department of Polymer Science, The University of Akron, Akron, Ohio S1

2 1. The ITIM method The ITIM 1, method of interface reconstruction uses a spherical probe of a certain radius which is moved towards the surface of interest from a certain distance above or below the surface until it first touches an atom of the system. The probe needs to have the proper size in order to properly scan the surface. The choice of the appropriate probe radius is achieved by determining the number of interfacial molecules for different values of the radius. A value of. Å was used in our simulation N(R) R (Å) Figure S1: Number of interfacial atoms versus probe radius determined by the ITIM method of interface reconstruction. Density profiles relative to instantaneous surfaces reconstructed using the grid based (GIP) 3,4 method by finding the position of the atom with the maximum z-component in each grid 3 ) 3 PMMA LF, 5 K PS LF, 5 K 4 3 ρ (g/cm Z(Å) Figure S: Mass density profiles relative to an instantaneous interface constructed using the grid based (GIP) method. (Left) Mass density profile of a PMMA film relative to an instantaneous PMMA/vapor surface. (Right) Mass density profile of a PS film relative to an instantaneous PS/graphite (left peaks) and PS/vapor (right peak) surfaces. S

3 3. Mean-squared displacement on a linear scale for polystyrene atoms at the PS/vapor and PS/graphite interfaces 4 3 PS/vapor PS/bulk PS/graphite ) (Å 4 3 K r PMMA bulk K PMMA bulk Figure S3: Mean squared displacement at T = 5 K (left) and T = (right) for polystyrene atoms at the PS/vapor and PS/graphite interfaces, and those in the PS bulk. 4. Wave vector (i.e. q) dependent surface height correlation functions Figures S4 and S5 show the q dependent correlations functions in terms of the intermediate self scattering function F (q, t) = cos( q z) in the range.3 Å 1 <= q <=.7 Å 1 for the PS/vapor and PMMA/vapor surfaces. z = z(t) z() where z(t) is the z coordinate of a point on the surface. The range of q values considered is dictated by the length of the simulation (low q value) in which the correlation decays well below the value 1/e and the noise level in the data (high q value). Qualitatively, the data show that the fast surface S3

4 modes decay over a time scale of ten to hundreds of picoseconds while the slow ones seem to survive well into the nanoseconds. While the relaxation gets faster with increasing q for both systems, the PMMA appears to relax slowly as compared to PS for the same temperature. A full quantitative study of the relaxation times as a function of q and temperature will be addressed in future work since it requires more data be recorded to boost statistics, the simulation time extended and additional temperatures included. In addition, the lateral simulation box dimensions need to be enlarged in order to probe the modes with q <.3 Å 1 where surface capillary waves essentially dominate. The statistics for the short wavelength fast modes also needs to be improved to be able to test the how small in length scale one can go to have continuum models still describe data in the large q regime. 4a. Surface height correlation functions for the PS/vapor interface at T = 56 K and at T = 5K F(q,t) q=.3 Å q=.4 Å q=.5 Å q=.6 Å q=.7 Å F(q,t) K q=.3 Å q=.4 Å q=.5 Å q=.6 Å q=.7 Å Figure S4: Wave vector dependent surface height correlation functions for the PS/vapor interface are shown in terms of the intermediate self scattering function at T = (Left) and at T = 5 K (Right). Lines are fits to the KWW function. S4

5 4b. Surface height correlation functions for the PMMA/vapor interface at T = F(q,t) q=.3 Å q=.4 Å q=.5 Å q=.6 Å q=.7 Å Figure S5: Wave vector dependent surface height correlation functions for the PMMA/vapor interface is shown in terms of the intermediate self scattering function at T =. Lines are fits to the KWW function. 5. Wave vector ( q) dependent Relaxation time The mean relaxation times ( τ ) obtained from the KWW fits shown in Figures S4 and S5 decrease with increasing q. The value of τ at T = for the PMMA/vapor interface is approximately an order of magnitude larger than that for the PS/vapor interface, indicating that the relaxation of PMMA/vapor interface is quite slower than that of the PS/vapor interface at the same temperature. The values of τ at T = for the PS/vapor interface are expected to be lower than that at T = 5 K. However, the data do not show a consistently lower value at the higher temperature. The value of τ at q =.3 Å 1 at T = is even larger than the corresponding value of τ at T = 5 K. Considering the small lateral size of the PS film and the insufficient amount of data available presently, much may not be said about the significance of the difference. A fully quantitative study of the q dependence of the surface dynamics will be the subject of future work. S5

6 <τ> (ns) q (Å ) Figure S6: Relaxation time as a function of wave vector ( q) 6. Conformational tensor components for PS chains with both ends in the interfacial regions Table S1: Conformational tensor components for chains with both ends satisfying z z surf < 6Å. Owing to symmetry in the x- and y-directions, it is expected that C xx = C yy and thus we report the components parallel (C ) and perpendicular (C = C zz ) to the substrate System T C C zz PS/graphite 5 K PS/vapor 5 K References (1) Pártay, L. B.; Hantal, G.; Jedlovszky, P.; Vincze, A.; Horvai, G. A new method for determining the interfacial molecules and characterizing the surface roughness in computer simulations. Application to the liquid vapor interface of water. J. Comput. Chem. 8, 9, () Pártay, L. B.; Horvai, G.; Jedlovszky, P. Molecular level structure of the liquid/liquid interface. Molecular dynamics simulation and ITIM analysis of the water-ccl 4 system. Phys. Chem. Chem. Phys. 8, 1, S6

7 (3) Jorge, M.; Cordeiro, M. N. D. S. Intrinsic Structure and Dynamics of the Water/Nitrobenzene Interface. J. Phys. Chem. C 7, 111, (4) Jorge, M.; Cordeiro, M. N. D. S. Molecular Dynamics Study of the Interface between Water and -nitrophenyl Octyl Ether. J. Phys. Chem. B 8, 11, S7