Topology limitation

There is also another topological limit on C H ratio. Physisorption proceeds only in the monolayer above the boiling point of hydrogen, and the adsorption must follow the Langmuir isotherm. Hence, the storage capacity depends on the pressme of Hj gas above the carbon surface at a fixed temperatme. It is also greatly limited by available SSA of carbon phase as provided by porous stmctme. 

It should be pointed out that the topological limit cannot be removed by a simple temperature rise as is the case in reactions controlled by glass transition. 

The reaction can be truly adiabatic for a wide range of experimental conditions. It initiates in the kinetic region and reaches a limit of 94-96 % conversion, which corresponds to the topological limit for these systems 5>14, l617-5169). The reaction kinetics is well described by the adopted mechanism 51,69 and the resulting experimental kinetic and thermodynamic reaction parameters are similar to those obtained in isothermal experiments. 

Due to the lattice rigidity, some of the umeacted groups cannot find their reaction partners and remain unreacted this is called the topological limit of the reaction. A few of these groups can also form monocycles (cf. also Section 2.VII.4 of Ref. This topological limit was confirmed by some experiments, some other authors claim, however, that they can reach 100 % reaction. An accurate determination of the few unreacted groups in the rigid structure is, however, not an easy task. 

In conclusion, it can be said that the theory can well describe the development of the gel structure. The correlation between the equilibrium modulus and sol fraction is very good so that the sol fraction can alternatively be used for determination of the concentration of EANC s if an accurate and precise determination of conversion meets with difficulties. It is to be recalled here that the Gaussian rubber elasticity theory does not apply to highly crosslinked networks of usual stoidiiometric systems. When a good theory is available, the calculated value of taking possibly into account the topological limit of the reaction will be ne ed. 

Topological limit of the reaction 24 Torsion pendulum (TP) 88 Torsional braid analysis (TBA) 88 Transesterification 48... 

Geometrical and topological limitations on the structures of molecules and crystals... 

Figure 3.11 Conversion versus temperature transformation diagram showing conditions under which gelation, vitrification and chemical degradation take place, as well as restriction arising from topological limitations for novolac epoxy resin cured with DDS. Reprinted with permission from RA. Oyanguren and R.J.J. Williams,/owmia/ of Applied Polymer Science, 1993, 47,1361 1993,...

The concept of an ultimate conversion lower than 100% is reasonable in view of steric restrictions in a highly crosslinked network. Oleinik has reported an ultimate conversion of 92% in a diepoxide-diamine stem. This ultimate conversion value is attributed to topological limitations and is consistent with computer simulations Hale reports an experimental ultimate conversion of less than 85% for a 1 1 stoichiometry ECN-phenolic cresol novolac (PCN) system which is similar to the one in this study. The lower ultimate conversion seen in the ECN-PCN stem is in agreement with greater steric hindrances arising from the cresol pendant group. The topological constraints on the ultimate conversion will increase as functionahty of the reactive molecules also increases. 

Conflict Analysis in Top-down Bus Synthesis. The top-down bus synthesis method uses 2-bus models with fixed topologies. Since the fixed topologies limit the parallelism of the system, not all control sequences synthesized by the code scheduler are feasible. The inner loop of the code scheduler is a hardware conflict analysis algorithm that determines if two sets of microoperations conflict when packed into a control state. For top-down bus S5mthesis, interconnection conflicts are determined as follows ... 

In this case, the topological limit of the bifurcating periodic motion as —> — 0 contains no equilibrium point, but a periodic trajectory of the saddle-node type which disappears when e < 0. The trajectory is a simple saddle-node in the sense that it has only one multiplier, equal to 1, and the first Lyapunov value is not equal to zero. 

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