Fusion of cross-linked polymers

Chain units that are involved in forming intermolecular cross-links require special attention as far as crystallization is concerned. When a sufficient number of intermolecular cross-links are imposed on a collection of linear polymer chains, a three-dimensional network structure reaching macroscopic dimensions is developed. Such structures are termed infinite networks. According to theory (1,2) the initial formation of a network occurs when the fraction of cross-linked units p exceeds a critical value pc that is expressed as 

In contrast to other types of structural irregularities, chain units involved in intermolecular cross-linkages act in a unique manner since they actually join together portions of different chains. There is, therefore, the distinct possibility that the cross-linked units could be restricted from participating in the crystallization for steric reasons. In addition, the fact that a network structure is formed can lead 

In the theoretical treatment for the formation of networks, it is customary to assume that the points of cross-linkage are randomly distributed over the complete volume of the sample. It is not necessary, however, to make any restrictive assumptions with regard to the disposition of the polymer chains at the time of network formation. Networks are commonly formed from randomly coiled chains. However, this represents a special case among several possibilities. Networks can also be formed from either deformed systems or systems where the chains are in ordered or partially ordered array when the cross-links are introduced. Theory has shown(4) that properties of a network are strongly influenced by the nature of the chain arrangement when the cross-links are introduced. Therefore, in discussing the properties of networks in general, and their crystaflization behavior in particular, careful distinction must be made as to their mode of formation. 

A network in the liquid or amorphous state can be given a quantitative descrip-tion(4,9,10) by defining a chain as that portion of the molecule which traverses from one cross-linked unit to a succeeding one. It is convenient to characterize each chain by a vector r which connects the average position of its terminal units, namely, the cross-linked units. The number of chains v must be equal to the number of intermolecularly cross-linked units. If No is the total number of chain units in the network, then p is equal to v/No. The network can then be characterized by the number of chains and their vectorial distribution. When the network is deformed, a common assumption made is that the chain vector distribution is altered directly as the macroscopic dimensions. An affine transformation of the average position of the coordinates of the cross-links occurs. It is also usually assumed that the individual chains obey Gaussian statistics. 

A reference state for the network is conveniently taken as one wWchjepre nts the isotropic network with mean-square vector components, xl = yl = 

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The process of polyethylene oxidation is characterized by struc-turii - the formation of cross-linked structures [12]. Structuring is usually manifested at increased temperatures. Thus, the oxidation of a fusion of polyethylene at 180°C leads to the accumulation of insoluble products after 30 hr, about 50% of them accumulate after 61 hr, 90% after 150 hr, 100% by weight. Under the conditions of structuring, the viscosity of the polymer first drops rapidly during the oxidation process, and then rises as insoluble structures accumulate. 

If the network structure is such that the crystallization of the cross-linked units is not restricted, AH and A5 can be taken to be independent of the fraction of units cross-linked. Under these conditions, A5 is identified with the entropy of fusion of the pure non-cross-linked polymer, and the ratio of A5 to AH is identified with the equilibrium melting temperature of the pure polymer. If, however, steric requirements are such that cross-linked units are excluded from the crystalline regions, an alteration will occur in these quantities. The presence of cross-linked units in the molten phase and not in the crystalline phase results in an increase in A 5 (when compared with the non-cross-linked polymer) of an amount Rp per mole of chain units. The melting temperature must accordingly be depressed for this reason, as long as AH is unaffected by the presence of cross-links. 

Radiation resistance of polymer materials is of critical importance when the materials are applied in radiation environments. To y rays or electron beams, the radiation resistance is well studied, especially by JAERI [113] and CERN [114]. Polymeric materials will be applied for space or a fusion reactor as constructing or insulating materials. The materials are subjects to in-conventional radiation such as protons, heavy ions, and neutrons having high LET to materials. With this fact, radiation resistance to high LET radiation would be different from that to low LET radiation. However, the underlying radiation chemical effects that cause deterioration are cross-linking and/or main chain scission, therefore microscopic and macroscopic effects have a close correlation with each other. 

The greater stability of the crystalline state of networks formed from unoriented but crystalline chains compared with networks formed from amorphous polymers, can be explained in the same way as for networks formed from axially oriented natural rubber. Although prior to network formation the crystallites are randomly arranged relative to one another, portions of chains are still constrained to lie in parallel array. The cross-linking of the predominantly crystalline polymer cannot, therefore, involve the random selection of pairs of units. The units that can be paired are limited by the local chain orientation imposed by the crystalline structure. An increase in the isotropic melting temperature of such networks would therefore be expected. It can be concluded that orientation on a macroscopic scale is not required for partial order in the liquid state to develop. Concomitantly a decrease in the entropy of fusion will result, which reflects the increase in molecular order in the melt. This is an important concept that must be kept in mind when studying the properties of networks formed in this manner. This conclusion has important implications in studying the properties of networks formed from unoriented crystalline polymers. 

A characteristic property of amorphous polymers is the ability to sustain large strains. For cross-linked three-dimensional networks the strain is usually recoverable and the deformation process reversible. The tendency toward crystallization is greatly enhanced by deformation since chains between points of cross-linkages are distorted from their most probable conformations. A decrease in conformational entropy consequently ensues. Hence, if the deformation is maintained, less entropy is sacrificed in the transformation to the crystalline state. The decrease in the total entropy of fusion allows crystallization, and melting, to occur at a higher temperature than would normally be observed for the same polymer in the absence of any deformation. This enhanced tendency toward crystallization is exemplified by natural rubber and polyisobutylene. These two polymers crystallize very slowly in the absence of an external stress. However, they crystallize extremely rapidly upon stretching. 

Extrapolated melting temperatures as a function of extension ratio, 110 repeating units between successive cross-links, the melting temperature at extension ratio 1.0 is 333.5 K, heat of fusion 8.37 kJ/mol. Data by W. R. Krigbaum, J. V. Dawkins, G. H. Via, and Y. I. Balta,/. Polymer ScL, Part A-2, 4, 475 (1966). 

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