Elastically active network

In POLYM the output data of KINREL are used with compositional information to calculate the number and mass average molecular masses (Rn and Rm, respectively) and number and end-group average functionalities (fp and fg> respectively) in the pre-gel region in all stages. In addition, the network characteristics such as sol fraction, mj, and the number of elastically active network chains per monomer (5), Ng, are calculated in the post-gel regime of stage 3. 

For imperfect epoxy-amine or polyoxypropylene-urethane networks (Mc=103-10 ), the front factor, A, in the rubber elasticity theories was always higher than the phantom value which may be due to a contribution by trapped entanglements. The crosslinking density of the networks was controlled by excess amine or hydroxyl groups, respectively, or by addition of monoepoxide. The reduced equilibrium moduli (equal to the concentration of elastically active network chains) of epoxy networks were the same in dry and swollen states and fitted equally well the theory with chemical contribution and A 1 or the phantom network value of A and a trapped entanglement contribution due to the similar shape of both contributions. For polyurethane networks from polyoxypro-pylene triol (M=2700), A 2 if only the chemical contribution was considered which could be explained by a trapped entanglement contribution. 

To obtain accurate values of the sol, thin specimens (1 mm) in one study (13) were kept in the solvent for six weeks in another study (14), thin specimens were extracted for more than 18 days in Soxhlet extractors. When the present experimental data were obtained (6), there was little interest in knowing the sol fraction accurately. However, as discussed subsequently, to compute the extent of the curing reactions and the concentration of elastically active network chains, the sol fraction must be known accurately. 

Polymer networks are formed from functional precursors by covalent bond formation [1], As a result, molecular weights and polydispersity increase and the system passes through a critical point, the gel point. At this point, an infinite structure (molecule) is formed for the first time. Beyond the gel point, the fraction of the infinite structure (the gel) increases at the expense of finite (soluble) molecules (the sol). The sol molecules become gradually bound to the gel and eventually all precursor molecules can become a part of the gel - the network. This is not always the case for different reasons sometimes sol is still present after all functional groups have reacted. In passing from the gel point to the final network not only the gel fraction increases, but also the network becomes denser containing increasing amounts of crosslinks and strands between them called elastically active network chains. 

Figure 5.4 Schematic representation of sol and a part of the gel DC dangling chains, EANC elastically active network chains, EAC elastically active crosslinks...

Figure 5.5 Calculated dependence of weight fractions of various substructures in the crosslinking system of H3 + I2 type on the initial molar ratio of H-groups to l-groups, ah (a polyurethane system) DC - dangling chains, BC - backbone chains, S - sol (backbone chains are elastically active network chains without dangling chains)...

Note 2 A model network is not necessarily a perfect network. If a non-linear polymerization is used to prepare the network, non-stoichiometric amounts of reactants or incomplete reaction can lead to network containing loose ends. If the crosslinking of existing polymer chains is used to prepare the network, then two loose ends per existing polymer chain result. In the absence of chain entanglements, loose ends can never be elastically active network chains. 

Note 4 Loose ends and ring structures reduce the concentration of elastically active network chains and result in the shear modulus and Young s modulus of the rubbery networks being less than the values expected for a perfect network structure. 

Using the values of the modulus G, measured just after preparation (X = 1), one can determine the concentration of elastically active network chains (EANC), vd, related to the dry state... 

The concentrations of elastically active network chains related to the dry state vd series A-F were [26] vd = 3.6, 5.7, 6.3, 7.1, 10.9 and 15.2 x 10 5 molcm 3 (structure formation at high dilution in the system. Using vd values together with other molecular parameters, the dependences of y vs ip 2 were calculated and both the extent of the collapse, A, and the critical value,... 

Gordon, M., Kucharuk,S., Ward,T. C. The statistics of elastically active network chains and the efficiency of crosslinking in rubbers. Collection Czech. Chem. Commun. 35,3252-3264 (1970). 

According to the theory of rubber elasticity, the elastic response of molecular networks is characterized by two mechanisms. The first one is connected with the deformation of the network, and the free energy change is determined by the conformational changes of the elastically active network chains. In the early theories, the free energy change on deformation of polymeric networks has been completely identified with the change of conformational entropy of chains. The molecular structure of the chains... 

In the following, we will briefly outline the use of the link p.g.f. (l.p.g.f.) for the calculation of the gel point in /-functional polycondensation without and with cyclization including the f.s.s.e. In Chapter II, section 2.2 we will consider an application in connection with the number of elastically active network chains in random polycondensates or in a collection of randomly crosslinked chains. 

Assuming that no internal elastic chains are activated, the concentration of elastically active network chains per unit mass, ve, may be calculated... 

The mass fraction of material pertaining to elastically active network chains (EANC) is obtained from Eq. (3.34). 

The presence of hard clusters affects mechanical properties. The major problem is the way to define elastically active network chains (EANC) and crosslinks (Chapter 3, Fig. 3.3). It has been demonstrated that hard clusters must be considered as multifunctional crosslinks (fc = 6 in Fig. 7.6a) while macrodiol chains behave as EANC. 

Figure 14.6 Destruction of elastically active network chains resulting from a chain scission in the case of tetrafunctional (a) and trifunctional nodes (b). 

In the case of unsaturated polyesters, nondegraded samples made from a prepolymer of molar mass M and a styrene mass fraction s have a chain-ends concentration b = [2(1 — s)/M]p, where p is the density. If ve is the actual concentration of elastically active network chains, an ideal network would be obtained by welding each chain end to another one, leading to... 

Fig. 13.84c, known as the Smith failure envelope, is of great importance because of its independence of the time scale. Moreover, investigations of Smith, and Landel and Fedors (1963,1967) proved that the failure envelope is independent of the path, so that the same envelope is generated in stress relaxation, creep and constant-rate experiments. As such it serves a very useful failure criterion. Landel and Fedors (1967) showed that a further generalisation is obtained if the data are reduced to ve, i.e. the number of elastically active network chains (EANCs). The latter is related to the modulus by... 

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