Polymers with thickness constraint

Ground-State energy per monomer mm//V of tubelike polymers with nine monomers as a function of the global radius of curvature constraint p (solid line). For comparison, the energy curve of the perfect a-helix is also plotted (dashed line). The inset shows that for a small interval around p 0.686, the ground-state structure is perfectly o -helical. Also depicted are side and top views of putative ground-state conformations for various exemplified values of p. For the purpose of clarity, the conformations are not shown with their natural thickness. From [243]. 

Proteins form the most prominent class of polymers, where different types of secondary structures occur, typically within the same molecule. It is therefore useful to extend the homopolymer model employed in the previous section by introducing two types of monomers which can be hydrophobic or polar. For this purpose, we will now combine the already introduced and for the line-like heteropolymers in Chapter 8 extensively studied AB model with the thickness constraint. 

The stresses near the root of a notch are extremely complex and the stress analysis becomes exceedingly difficult when the strain is large, as is the case when yield or failure is imminent. A sharp notch causes constraints and introduces a state of triaxial tension behind the root of the notch (5). This state of stress is consistent with LeGrand s observation of the growth of a flaw behind a notch in a bar of polycarbonate (4). A blunt notch causes constraints when the thickness of the specimen is large. Such a notch can also introduce a state of triaxial tension. While it is desirable to investigate the behavior of polymers in a well-defined state of triaxial tension, it is difficult to accomplish experimentally. However, as we demonstate below, a state of plane strain is relatively easy to produce. The relationship between plane strain and brittleness of plastics is the subject of our investigation. 

Unambiguous determination of the conditions under which slippage occurs requires a technique able to measure the velocity of the fluid in the immediate vicinity of the solid wall over a thickness comparable to the size of a polymer chain, i.e. a few tens of nanometers. Classical laser Doppler velocimetry does not meet this requirement even if it allows for the determination of velocity profiles which clearly reveal a non-zero velocity within typically a few 10 pm from the wall. We have developed a new optical technique. Near Field Velocimetry (N.F.V.) [14], which combines Evanescent Wave Induced Fluorescence (E.WF.) [27] and Fringe Pattern Fluorescence Recovery After Photobleaching (F.P.F.R.A.P.) [28]. The former technique gives the spatial resolution normal to the solid wall, while the latter one enables the determination of the local velocity of the fluid. A major constraint of the technique is that it needs polymer molecules labelled with an easily photobleachable fluorescent probe. 

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