Scanning force microscopy experiments probing micromechanical properties on polymer surfaces using harmonically modulated friction techniques II. Investigations of heterogeneous systems

Applying a high-frequency lateral vibration between tip and sample in a scanning force microscope (SFM), a harmonically modulated lateral (friction) force image can be obtained using lock-in techniques. Harmonically modulated lateral force microscopy (HM-LFM) offers several advantages compared with standard lateral force microscopy (LFM). After a brief investigation of the scan velocity dependence of LFM and HM-LFM, two samples were investigated. First, the surface of a poly(acrylonitrile-co-styrene)/polybutadiene blend (ABS) was used to demonstrate the ability of the new technique to decrease the stick effects of the SFM tip. Second, an interface between two chemically very similar polymers was prepared by melting polypropylene (PP) and poly(propene-block-ethene) (PP-block-PE) films on each other. After cutting, the surface roughness of this sample was very high. It is shown that only HM-LFM clearly resolves the local micromechanical properties without artefacts.     

Scanning force microscopy experiments probing micromechanical properties on polymer surfaces using harmonically modulated friction techniques I. Principles of operation

Applying a high-frequency lateral vibration between the sample surface and the tip of a scanning force microscope (SFM), a harmonically modulated lateral (friction) force image can be obtained using lock-in techniques. The principles of operation are explained, in particular the dramatic decrease of image artefacts generally caused by topography cross-talk and laser beam interference. Flat interfaces between the two immiscible polymers, poly(methyl methacrylate) (PMMA) and polystyrene (PS), are prepared on a sodium chloride single crystal from the melt. These samples are used to evaluate the appropriate model for the tip-sample interaction geometry. The relationship between frictional and normal force does not follow Amonton's law. This shows that a single-asperity interaction between the tip and sample surface can be considered. Using the new technique, local measurements of shear strength and Young's modulus can be performed.     

Molecular dynamics simulation of semirigid polymers

The chain rigidity of poly(p-hydroxybenzoate) was estimated through the theoretical evaluation of its persistence length (L_p). A non-Brownian molecular dynamics (MD) simulation of an isolated chain with 20 monomeric units was performed. The sampled conformational population was analyzed and the orientational correlation function between monomeric units along the chain was calculated. An algorithm based on the worm-like chain model was applied to evaluate the persistence length. The results were compared with those obtained from equilibrium models like the freely-rotating-chain and the rotational-matrix method with fluctuations. Equilibrium models give different results depending on the degree of accuracy used in describing the monomeric unit. The inclusion of thermal fluctuations is crucial to obtain realistic results. These coincide with those given by MD simulation when only nearest-neighbour orientational correlations are taken into account: inclusion of higher-order correlation terms leads to lower values of the persistence length. The origin of this discrepancy was investigated. The MD simulation results are characterized by an overrepresentation of conformations with a short end-to-end distance resulting from an anomalous energy concentration in the first bending mode of the chain. In analogy with previous simulation results from systems characterized by a week coupling amoung their degrees of freedom, failure in the energy equipartition is proposed as a likely explanation of the anomalous dynamical behaviour.     

Inexact inner–outer Golub–Kahan bidiagonalization method: A relaxation strategy

We study an inexact inner–outer generalized Golub–Kahan algorithm for the solution of saddle-point problems with a two-times-two block structure. In each outer iteration, an inner system has to be solved which in theory has to be done exactly. Whenever the system is getting large, an inner exact solver is, however, no longer efficient or even feasible and iterative methods must be used. We focus this article on a numerical study showing the influence of the accuracy of an inner iterative solution on the accuracy of the solution of the block system. Emphasis is further given on reducing the computational cost, which is defined as the total number of inner iterations. We develop relaxation techniques intended to dynamically change the inner tolerance for each outer iteration to further minimize the total number of inner iterations. We illustrate our findings on a Stokes problem and validate them on a mixed formulation of the Poisson problem.