Tubes Monte Carlo simulations with

A. Milchev, W. Paul, K. Binder. Polymer chains confined into tubes with attractive walls A Monte Carlo simulation. Macromol Theory Simul 5 305-323, 1994. 

Since currently available HAPD s are of small diameter, we masked a 2 photomultiplier tube to investigate the dependence of the photoelectron yield on detector area. A masked PMT (with sensitive area 18 mm in diameter) gave 5.4 0.2 photoelectrons or 0.68 0.03 pe/cm with the n = 1.032 aerogel sample. The observed spectrum is shown in Figure 4.15. These results are well-reproduced by a detailed Monte Carlo simulation. We are thus confident that it is possible to extrapolate with results taken with HAPD s of the current size to larger area devices. 

A polymer chain with repulsive interactions between the segments confined into a cylindrical pore has been studied by Monte Carlo simulations by Milchev et al. [115]. Besides the equilibrium conformation of the molecules in the confined geometry, the time-dependent mean-square displacements of the segments was also studied. It is shown fliat relaxation times scaling with hP- as well as hP play a role in the reptative motion of the chain in these tubes. 

Below we will come back to the reptation model in context with the dynamics of polymers confined in tube-like pores formed by a solid matrix. For a system of this sort the predictions for limits (II)de and (III)de (see Table 1) could be verified with the aid of NMR experiments [11, 95] as well as with an analytical formalism for a harmonic radial potential and a Monte Carlo simulation for hard-pore walls [70]. The latter also revealed the crossover from Rouse to reptation dynamics when the pore diameter is decreased from infinity to values below the Flory radius. 

The theoretical background of the confinement effect in (artificial) tubes was recently examined in detail with the aid of an analytical theory as well as with Monte Carlo simulations [70]. The analytical treatment referred to a polymer chain confined to a harmonic radial tube potential. The computer simulation mimicked the dynamics of a modified Stockmayer chain in a tube with hard pore walls. In both treatments, the characteristic laws of the tube/reptation model were reproduced. Moreover, the crossover from reptation (tube diameter equal to a few Kuhn segment lengths) to Rouse dy-... 

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