Surface segregation in binary polymer mixtures: a lattice model

Investigation of the Effects of Isotopic Labeling at a PS/PMMA Interface Using SIMS and Mean-Field Theory

“…29 For quantitative analysis of the interfacial segregation, we have employed a self-consistent mean-field lattice model (SCMF-L) 18 as derived previously for polymer segregation to polymer surfaces and polymer/substrate interfaces. 19 A cubic lattice was used for all calculations. Because the relaxed chain diameter of dPS-130 (R 0 ) aN 1/2 ≈ 23 nm, where R 0 is the rms end-to-end distance, a is the statistical segment length, and N is the number of segments in a dPS-130 chain) is much greater than the overlap of PS and PMMA at the interface (w 1/2 ) a/(6 ) 1/2 ≈ 1.4 nm for ) 0.038), 16,30 the PMMA layer is treated as an infinitely flat (rigid) substrate.…”

“…13,19,20 Similarly where kT∆ p is the net energetic preference per segment for dPS over hPS at an hPMMA "substrate", and λ 1 is a lattice weighting factor (1/6 for cubic). 18 As shown in eq 3, ∆ p should be proportional to a simple difference in values for dPS/ hPMMA and hPS/hPMMA.…”

“…At 128°C, diffusion-controlled segregation was observed (see Figure 1), implying an energetic gain >kT per dPS chain. Using a self-consistent mean-field lattice model, 18,19 the enthalpic preference for dPS over hPS at the hPS: dPS/hPMMA interface was interpreted using an energetic parameter ∆ p . These results are in complete disagreement with previously reported values for PS/PMMA as a function of isotopic labeling (see Figure 7b), 6 which predict a depletion of dPS at a hPS:dPS/hPMMA interface.…”

Composition depth profiling of polystyrene/poly(vinyl ethyl ether) blend thin films by angle resolved XPS

“…A c c e p t e d M a n u s c r i p t For a binary polymer blend in which one component preferentially segregates to the surface the CDP in the near surface region, expressed in terms of the volume fraction of the surface segregating component, (z), can be described by an empirical hyperbolic tangent function [42]:…”

“…PVEE preferentially segregates to the blend surface and we describe the use of ARXPS to investigate the CDPs of the blend thin films and of SFM to study their surface morphology and hence miscibility. We assume that the CDPs can be modelled by an empirical hyperbolic tangent function [42] described by three floating parameters. These are determined by nonlinear least squares regression, their uncertainties estimated and the curve fit residuals analysed to demonstrate that the hyperbolic tangent CDP is a satisfactory fit to the ARXPS data.…”