Network structure models

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. 

Development and Application of Network Structure Models to Optimization of Bake Conditions for Thermoset Coatings... 

In order to answer these questions, the kinetic and network structure models were used in conjunction with a nonlinear least squares optimization program (SIMPLEX) to determine cure response in "optimized ovens ". Ovens were optimized in two different ways. In the first the bake time was fixed and oven air temperatures were adjusted so that the crosslink densities were as close as possible to the optimum value. In the second, oven air temperatures were varied to minimize the bake time subject to the constraint that all parts of the car be acceptably cured. Air temperatures were optimized for each of the different paints as a function of different sets of minimum and maximum heating rate constants. 

A network structure model has been developed from which a parameter that correlates well with physical measures of paint cure can be calculated. This model together with a kinetic model of crosslinking as a function of time and temperature has been used to evaluate the cure response of enamels in automotive assembly bake ovens. It is found that cure quality (as measured by the number and severity of under and overbakes) is good for a conventional low solids enamel. These results are in agreement with physical test results. Use of paints with narrower cure windows is predicted to result in numerous, severe under and over bakes. Optimization studies using SIMPLEX revealed that narrow cure window paints can be acceptably cured only if the bake time is increased or if the minimum heating rate on the car body is increased. 

AL Delcher, S Kasif, HR Goldberg, WH Hsu. Protein secondary structure modelling with probabilistic networks. Intelligent Systems m Molecular Biology 1 109-117, 1993. 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

The number of neurons to be used in the input/output layer are based on the number of input/output variables to be considered in the model. However, no algorithms are available for selecting a network structure or the number of hidden nodes. Zurada [16] has discussed several heuristic based techniques for this purpose. One hidden layer is more than sufficient for most problems. The number of neurons in the hidden layer neuron was selected by a trial-and-error procedure by monitoring the sum-of-squared error progression of the validation data set used during training. Details about this proce-... 

Chapter 8 describes a number of generalized CA models, including reversible CA, coupled-map lattices, quantum CA, reaction-diffusion models, immunologically motivated CA models, random Boolean networks, sandpile models (in the context of self-organized criticality), structurally dynamic CA (in which the temporal evolution of the value of individual sites of a lattice are dynamically linked to an evolving lattice structure), and simple CA models of combat. 

Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

Explicit forms for the stress tensors d1 are deduced from the microscopic expressions for the component stress tensors and from the scheme of the total stress devision between the components [164]. Within this model almost all essential features of the viscoelastic phase separation observable experimentally can be reproduced [165] (see Fig. 20) existence of a frozen period after the quench nucleation of the less viscous phase in a droplet pattern the volume shrinking of the more viscous phase transient formation of the bicontinuous network structure phase inversion in the final stage. 

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