Comments on C. Roselieb's "Simulation of Wessling Model for Network Formation in Dispersions"
B. Wessling
ZIPPERLING KESSLER & Co.
The above work [1] is very helpful for analyzing and understanding my recently developed simulation model. Moreover, his analysis and the development of a new model helps to stimulate more productive discussion, even though not all of his statements are correct from the experimental [2] and theoretical [3] standpoint of view. The following aspects should be considered:
Flocculation in real systems does really take place in a 2- dimensional space, as the dispersed phases arrange themselves in very thin monolayers ("seams").
C. Roselieb's model with a triangular arrangement of the sites will probably be more appropriate to describe the real systems, compared to the program which was available for me.
His analysis program is extremely helpful, as it does quantitatively show how dynamic the system is and how it oscillates between different structures which are more or less developed (i .e., lead to a higher or lower conductivity, higher or lower impact strength, etc.).
The SEM pictures documented earlier [2] show, that a very high portion of the particles is not integrated in the network, but exists as singular isolated dispersed particles ("dead ends") or in groups ("clusters"). So the analysis of my previous model with 40 % "clusters" in the best case is not unrealistic, and a value of 57 % particles arranged in chains in the best iteration step seems quite correct.
Ageing (tempering) experiments [2] have shown that rearrangement of structures is occuring with temperature and time, preferably in molten stage. However, such a process does not occur in a short time scale, but obviously in the scale of minutes or hours. We have found, that an improvement by one order of magnitude in resistance takes about 30 minutes. On the other hand, an SEM picture is made in about 10- 2 seconds.
The non-equilibrium theory developed for these systems [3] shows, that the formation of a network chain does occur with a slight, but significant gain of energy (so it will occur "deliberately", exotherm and exergon). The energy gain is about 10- 5 Nm/mol, quite a lot for such a process. This means, that structures with more "chains" are energetically preferred and hence more stable!
A perfect simulation model would be one which can account for energy differencies, too. Both of our models, my first one and the new one by C. Roselieb, do not contain any energy parameter.
From experimental and theoretical considerations it is not at all necessary, but it even seems unappropriate to ask for a "stable" network. I fully agree, that a structure is basically rearranged completely after no more than 3 generations in my model. I am convinced that this is the case in real systems, too. This is also a character of all dissipative structures in the world, too:
in turbulent flow, water molecules being members of the turbulent structures or members of the laminar parts do constantly interchange
cells building our own body are constantly exchanged, and e.g. your skin seems to stay the same for all time, but is completely exchanged after less than 7 years.
This is why I do not agree, that a model needs to lead to stable structures. If a model allows for oscillation and rearrangement of particles, then it is suitable enough for desciribing the real systems. We should not make the mistake to believe, that the model "is like" the real system itself - energetic and interfacial interaction parameters are much more complex in reality. The models developed up to now are capable of giving more insight in the behaviour of heterogeneous polymer systems. They can not "explain" them, only model.
