Functionality of the crosslinks

Care ill choosing the particular polymer to be employed in a frac-turing treatment is needed because some polymers can interfere with the function of the crosslinker. Some of these polymers are also stable to high temperature steam and have been successfully used to treat high temperature steam injection wells. Recent developments in organic polymer formation damage control polymers are discussed in chapter 10 of this book. 

In a network where the crosslinks move affinely to the macroscopic strain, the functionality of the crosslinks is insignificant. The modulus of such, a network only depends on the number of chains, no matter how they are connected (22-27)... 

Telechelic polymers rank among the oldest designed precursors. The position of reactive groups at the ends of a sequence of repeating units makes it possible to incorporate various chemical structures into the network (polyether, polyester, polyamide, aliphatic, cycloaliphatic or aromatic hydrocarbon, etc.). The cross-linking density can be controlled by the length of precursor chain and functionality of the crosslinker, by molar ratio of functional groups, or by addition of a monofunctional component. Formation of elastically inactive loops is usually weak. Typical polyurethane systems composed of a macromolecular triol and a diisocyanate are statistically simple and when different theories listed above are... 

This means that the time for flow-out of the powder becomes shorter with increasing functionality of the crosslinker, with respect to the total cycle time required for reaching satisfactory film properties (mechanical, chemical. Fig. 20, step D). The reduced flow-phase time results in a poorer film surface quality. Moreover, when volatiles are set free as a result of the crosslinking reaction, in this case water, they will cause blister formation after the gel-point. Blister for-... 

In copolycondensation for example, the more reactive monomer is expected to become exhausted more rapidly than the less reactive one. If the functionalities of the polyfunctional crosslinker are more reactive, short chains are formed in the beginning of the reaction and long chains in the end. If we assume equilibrium conditions throughout the reaction, the unreacted functionalities of the crosslinker on different growing trees, with short links in the beginning, are expected to react more likely with each other and as a result a part of the final network may be more crosslinked than the other part. This may eventually lead to phase separation. If the reaction is diffusion-controlled (177), cores with higher crosslinking density may be formed. 

Deuterium NMR is very sensitive to orientational behavior and order there are a number of papers dealing with constrained polymeric networks. For example, 2H NMR (in both, solid state and solution) is used in the study of the orientational order generated in uniaxially strained rubbers as a function of the crosslink density. Two sets of rubbers (model end-linked silicone rubbers and randomly crosslinked diene networks) were investigated directly (on perdeuterated silicone labelled chains) and indirectly, via C6D6 as an NMR probe for diene rubbers 45). 

The functionality of the crosslinks should be known, and constant throughout the geL The functionality is the number of elastically effective network chains which are tied to one given crosslink. 

Conversely, permanent chain entanglements25 act as additional, but not fixed, crosslinks, which are more likely to form when the functionality of the crosslinks is rather high, as it will be seen in a later section of this review. 

If the elastic chains solely connect first neighbor nodules, x2 = 1. If the proportion of chains linking crosslinks which are not first neighbors increases, the value of x2 also increases. The parameter x2 therefore characterizes the degree of interpenetration of the network chains, and it should be related to the proportion of entanglements present in the network. In practice, it can be expected that for networks in which the functionality of the crosslinks is low, entanglements are quite unlikely, and the value of x2 should stay close to unity. 

It should be emphasized that if B is supposed to be equal to zero (or very small), A should contain the functionality of the crosslinks, since it is obvious that /plays a role in the swelling equilibrium. ... 

We shall now try to account for these results, assuming, as we did previously, that within a series of networks the functionality of the crosslinks remains constant an assumption which seems to rest on solid grounds. 

If the functionality of the crosslinks is low, the probability for elastic chains to connect first neighbor crosslinks is close to unity. Consequently there is little interpenetration of the elastic chains and few permanent entanglements are expected. However this does not mean that all first neighbor crosslinks in the gel are connected by elastic chains. 

The elastic modulus in the rubbery state is directly related to ve. It has been proposed that the network stiffness under a mechanical solicitation depends on the functionality of the crosslinks (Duiser and... 

Unrelaxed and relaxed moduli for each transition. Let us recall that, generally, the ratio E (unrelaxed)/ E (relaxed) is higher than 10 for the a transition (it is a decreasing function of the crosslink density), whereas it is generally lower than 2 for secondary transitions where it does not depend directly on crosslink density but rather on the mechanical activity of the corresponding molecular motions. 

This contribution deals with some important aspects of coal structure evaluation using modified Gaussian models. Further clarification of the nature and functionality of the crosslinks is presented, including an analysis of refinements in the mathematical equations for the determination of Mc. Preliminary experimental data of relevance to this analysis are also presented and discussed. 

An increase in the functionality of the crosslinker from 5 (basic system) to 20 does not alter the kinetics but it does affect the relative course of the curve indicating chemical conversion (SiH/SiVi = 2) and network formation (Fig. 8, 9). 

Fig. 1. The particle radius R, as a function of the crosslink density (mol% T units) [9]...

Fig. 3. Fluorescence spectra of dimethylaminobenzoic acid esters in swollen polydimethylsiloxane networks as a function of the crosslinker concentration corresponding [-Si-0H] [-Si-0-C2H5 ratios are drawn in the figure, the intensity is plotted in a.u.

Figure 5-12. Glass transition change in the system poly(styrene-co-divinylbenzene) as a function of the crosslink density. No is the number density (e.g., mmol/cm3) crosslinks, whereas p is the bulk mass density (e.g., g/cm3). The dotted line is the fit of equation (5-29) with the result that kp is 130 10 g/mol. [Adapted from T. G Fox and S. Loshaek, J. Polym. Sci., 15, 371 (1955). Copyright 1955, Wiley Periodicals, Inc., a Wiley Company.]...

Figure 16.1 Water uptake as a function of the crosslinking degree of macronet isoporous and hypercrosslinked sulfonates based on (1-3) linear polystyrene, styrene copolymers with (4) 0.8 and (5) 1% DVB, and crosslinked with (1, 5)...

Now we can calculate non-fractal values and as functions of the crosslinking density (vj using Equation (11.29) and the relationship [107] ... 

Particle density is a function of the crosslinking density in the silicone rubber and is influenced by the... 

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