Polymer clusters visualization

As will be shown, model systems for cells employing lipids or composed of polymers have been in existence for some time. Model systems for coccolith-type structures are well known on the nanoscale in inorganic and materials chemistry. Indeed, many complex metal oxides crystallize into approximations of spherical networks. Often, though, the spherical motif interpenetrates other spheres making the formation of discrete spheres rare. Inorganic clusters such as quantum dots may appear as microscopic spheres, particularly when visualized by scanning electron microscopy, but they are not hollow, nor do they contain voids that would be of value as sites for molecular recognition. All these examples have the outward appearance of cells but not all function as capsules for host molecules. 

In binary solutions - in the case under consideration, water sorbed in a polymer - non-random mixing is also described as clustering. For this case, the cluster size is rarely, if ever, sufficient to produce visual opacity, and the evidence for the phenomenon is found in peculiarities of the sorption isotherm. 

Compression molded samples of poly(vinyl acetate) also showed a mild temperature dependence in equilibrium absorption. The amount of water went from 4% at 23°C to 6% at 70°C. This polymer was the only one we tested that formed clustered water while stored Isothermally at room temperature. This clustering was obtained after 17h. as confimed by DSC and could be seen visually as a whitening of the polymer. 

In our opinion, the main advantage of real-space methods is the simplicity and intuitiveness of the whole procedure. First of all, quantities like the density or the wave-functions are very simple to visualize in real space. Furthermore, the method is fairly simple to implement numerically for 1-, 2-, or 3-dimensional systems, and for a variety of different boundary conditions. For example, one can study a finite system, a molecule, or a cluster without the need of a super-cell, simply by imposing that the wave-functions are zero at a surface far enough from the system. In the same way, an infinite system, a polymer, a surface, or bulk material can be studied by imposing the appropriate cyclic boundary conditions. Note also that in the real-space method there is only one convergence parameter, namely the grid-spacing. 

In normal Euclidian space the fractal dimension is equivalent to the normal space dimension, as it must. The most well-known fractal is the linear Gaussian polymer chain, and we see immediately that it is characterized by dfo = 2, - whereas for the self-avoiding chain the mean field value dfo = 5/3 is found at once. The cluster in the classical Flory-Stockmayer theory is characterized by a fractal dimension of 4 as visualized by R 1/425,26 another example consider the percolation cluster. The number of monomers in a volume is given by... 

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