Polymer network model

Thus it is clear that the understanding of physical models for reactive processed polymers is less mature than that for network polymer models. However, it is also very clear that useful models that characterize both network and reactively processed polymers require concurrent chemical and physical models. The experimental techniques and models for network and reactive polymers will now be examined in detail in the remaining chapters. 

The purpose of this case study was to develop a simple neural network based model with the ability to predict the solvent activity in different polymer systems. The solvent activities were predicted by an ANN as a function of the binary type and the polymer volume frac-... 

The thermodynamic point of view developed in this review and in our original works with regard to the behavior of SAH in laboratory experiments and in soil models can pave, in our opinion, the most rational way for achieving the optimal results. Based on the existing theory of network polymers, this concept is undoubtedly open to further improvement that would expand its prognostic potentialities. 

The final physical properties of thermoset polymers depend primarily on the network structure that is developed during cure. Development of improved thermosets has been hampered by the lack of quantitative relationships between polymer variables and final physical properties. The development of a mathematical relationship between formulation and final cure properties is a formidable task requiring detailed characterization of the polymer components, an understanding of the cure chemistry and a model of the cure kinetics, determination of cure process variables (air temperature, heat transfer etc.), a relationship between cure chemistry and network structure, and the existence of a network structure parameter that correlates with physical properties. The lack of availability of easy-to-use network structure models which are applicable to the complex crosslinking systems typical of "real-world" thermosets makes it difficult to develop such correlations. 

See also Biodegradable polymer networks Filled silicone networks Interpenetrating networks (IPNs) Model silicone networks Monodisperse model networks ... 

Dendrimers represent a model for compact multifunctional precursor of polymer networks. Polymer networks prepared by crosslinking of dendrimers were suggested several years ago [64]. Since then, some experimental work has been performed, but there are still many points in structural interpretation of network formation and network properties that are not well understood. 

Now, the question arises to what extent the thermodynamic information on the low-molecular-weight model compounds can be applied to real epoxy-amine network polymers. A clear answer to this question is given by a direct comparison of the... 

An illustrative description of the ineffective cycles is provided by the network polymer random model8,187>. The model is underlied by a conception of the network polymer structure as a combination of the accidentally associated cycles with a certain distribution by size. Scheme (27) illustrates the first members of a series of cyclic structures formed by reaction of the diepoxides with diamines (the notation i, j means a ring composed of i diepoxide and j diamine units)... 

In building mathematical models of product formation in a mold it is possible to treat a polymeric material as motionless (or quasi-solid), because the viscosity grows very rapidly with the formation of a linear or network polymer thus, hydrodynamic phenomena can be neglected. In this situation, the polymerization process itself becomes the most important factor, and it is worth noting that the process occurs in nonisothermal conditions. 

A partially reacted polymer network is modeled as a random solution of reacted functionalities with a concentration equal to conversion (4>i = x, Tg = Tg00, Acpi(Tg00) =Acpco), and unreacted functionalities with a concentration equal to (1 — x) (<1) = 1 — x, Tgi — Tg0, Acpi(Tgo) = Acp0). Substituting in Eq. (4.8) with... 

The most important result is that the nonbonded interactions make a significant contribution to the deviatoric stress via the mechanism of anisotropic steric shielding. This mechanism is not present in network scale models in which polymer chains appear as threads without structure. 

Higgs, P. G. and Ball, R. C. 1990. A reel-chain model for the elasticity of biopolymer gels, and its relationship to slip-link treatments of entanglements, in Physical Networks. Polymers and Gels, eds. W, Burchard and S. B. Ross-Murphy, Chapter 15, Elsevier Applied Science Publishers, Barking, England. 

There has been much work on the development of physicochemical models for network polymers and reactive polymers, and a brief summary is provided here. 

Data on the fractal forms of macromolecules, the existence of which is predetermined by thermodynamic nonequilibrium and by the presence of deterministic order, are considered. The limitations of the concept of polymer fractal (macromolecular coil), of the Vilgis concept and of the possibility of modelling in terms of the percolation theory and diffusion-limited irreversible aggregation are discussed. It is noted that not only macromolecular coils but also the segments of macromolecules between topological fixing points (crosslinks, entanglements) are stochastic fractals this is confirmed by the model of structure formation in a network polymer. 

---