Molecular graph intersection

To investigate this issue, we start from the concept of the molecular reaction graph, and particularly the binary relations defined within this framework, i.e. the union U, and the intersection n, and the set-theoretical difference J of the edge sets of two graphs. 

Fig. 24 shows the results obtained for the D-8 solution-silicon oil system in a methylated quartz capillary, r = 3.6 pm. Interface tension of silicon oil (molecular mass 2400, viscosity >/2 = 21 cPs) in contact with bulk D-8 solution is equal to yo = 2.5 mN/m [37]. Three methylated quartz capillaries were prefilled with the silicon oil. The v(AF) dependencies are obtained in the same way as for the solution-air system. Positive values of flow rates, v > 0, correspond to displacement of silicon oil by D-8 solution. The inverse case, when D-8 solution was displaced by oil, corresponds to negative v values. As seen from Fig. 24, to displace oil one needs to overcome the dynamic capillary counterpressure of oil, = ly 2 cos 0r//-. The intersection point of the linear part of the graph at v > 0, shown by an arrow, gives yi2 cos 0r = 10 mN/m. 

Fig. 4. Phase diagram for the solutions of a polystyrene sample with broad molecular weight distribution (My, = 346 kg/mol and Mn = 210 kg/mol) in cyclohexane 12) w is the mass fraction of polymer. Full circles cloud points, full line cloud point curve, dashed lines binodal curves (connecting the end points of the tie lines) referring to the different constant overall polymer concentrations indicated in the graph. A closed binodal curve is only observed for critical overall composition, it intersects the cloud point curve in the critical point depicted as an asterisk.

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