Network structure quantitative characterization

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. 

Static H Multiple Quantum (MQ) NMR spectroscopy, on the other hand, has shown the ability to more reliably quantitatively characterize elastomer network structure and heterogeneities (14-19). H MQ NMR methods allow for the measurement of absolute residual dipolar couplings (cooperative dynamics without interference from magnetic susceptibility and field gradients which complicate relaxation measurements (13, 14, 20,21). It has previously been shown that the residual dipolar couplings are directly related to the dynamic order parameter, Sb, and the crosslink density (1/N)(P) ... 

Epoxy thermosets are typical densely cross-linked polymer materials. They are used in a wide variety of practical applications and thus have been studied extensively. However, the quantitative dependence of physical properties, such as strength, stiffness, and fracture toughness, on network microstructure are largely undetermined. This can be attributed, in part, to the lack of adequate techniques for characterizing densely cross-linked network structure. Several microstructiu e variables that have been studied with some success are (1) cross-link density,... 

Precipitation of the growing polymer from the initial solution of styrene and DVB in an inert diluent during crosshnking copolymerization results in the formation of a two-phase heterogeneous network, in which one phase is presented hy the highly crosshnked and rigid polymer, while the rejected diluent forms another phase. After removing the diluent, permanent voids remain in the copolymer beads. The total pore volume, and the inner surface area, S, are the major characteristics of the porous structure these are intimately related to pore size and pore size distribution. These parameters determine the practical apphcation frelds of the polymeric adsorbent resins therefore, a precise quantitative characterization of resin porosity becomes an important task. 

Because of their known structures, such model elastomers are now the preferred materials for the quantitative characterization of rubberlike elasticity. The properties of PDMS networks have been of interest to a variety of groups. " Such specific cross-linking reactions are also useful in the preparation of some of the liquid-crystalline elastomers,discussed in chapter 3. 

It is possible to characterize this non-Gaussian limited extensibility more quantitatively in a number of ways. The first involves the interpretation of limited chain extensibility in terms of the configurational characteristics of the PDMS chains making up the network structure. The upturn in modulus generally begins at approximately 60-70% of maximum chain extensibility. " This value is approximately twice that estimated previously- from stress-strain isotherms of elastomers that may have been undergoing strain-induced crystallization. 

Problem 3.20 The structure of a three-dimensional random network may be described quantitatively by two quantities the density of crosslinking designated by the fraction e of the total structural units engaged in crosslinkages and the fraction / of the total units which occurs as terminal units or free chain ends (i.e., which are coimected to the structure by only one bond). Alternative quantities, such as the number (mole) N of primary molecules and the number (mole) v of crosslinked units, in addition to M and Me, de ned above, are also used to characterize a random network structure. Relate N and v to these other quantities. 

The efficient utilization of any polymeric material requires a detailed molecular understanding of its unique properties. In its most useful form, such information consists of quantitative relationships between the physical properties of interest and the structural characteristics of the material that determines them. In the case of elastomeric materials, the molecular feature of surpassing importance is the interlinking or cross-linking of the polymer chains into a macroscopic, three-dimensional network structure ". Such networks can not be molecularly dispersed in a solvent, and the usual solution characterization techniques can not be applied to obtain the required structural information. For this reason, it has been exceedingly difficult to obtain reliable structure-property relationships for elastomeric materials ... 

Modulus data on crosslinked systems would seem to offer the most direct method for studying entanglement effects. Certainly, from the standpoint of molecular modeling, the advantages of equilibrium properties are clear. However, the structural characterization of networks has proven to be very difficult, and without such characterization it is almost impossible to separate entanglement contributions from those of the chemical crosslinks alone. Recent work suggests, however, that these problems are not insurmountable, and some quantitative results are beginning to appear. 

In terms of practical application, expert systems overlap with systems for deriving and applying quantitative structure-activity relationship (QSAR) models or equations, and with systems using artificial neural networks (ANN) or genetic algorithms. The expert systems described in this chapter are characterized by their use of a generalized store of knowledge. 

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