Cross-linking Density in IPNs

In spite of many investigations of the structure and properties of IPNs, the questions connected to the network density in IPNs still have no answers. Meanwhile, the effective network density is one of the most important characteristics of any network, including IPNs. To study IPN properties, first of aU it is necessary to compare its density with the densities of the constituent networks. To calculate the effective cross-linking density it is necessary to know the usual physical densities of both networks, which are used in the following calculations. 

Usually two methods of estimating the effective cross-linking density are used. The first is based on elasticity theory. It computes the concentration of the cross-links in the network from the value of the elastic modulus and the polymer density according to the equation  

Meanwhile, chain entanglements in IPNs play a very important role in the processes of their microphase separation, by preventing it, which early has not been taken into account. Nevertheless, this method was used in many works. One example is the study of the sequential IPNs based on copolymers of styrene and DVB [107] for various ratios of constituent networks wi and W2. The value of Ve was compared with the density of the cross-Hnks in net- 

The second method of computing the cross-Unking density is based on the well-known Flory-Huggins theory, and was initially used in some works by Frisch, Frisch, and Klempner [9,108,109]. 

To determine Vg of a homogeneous (swollen) polymer network, the equi-libriiun modulus is measured in shear, compression, or extension [31, 111]. The stress in uniaxial extension/compression mode is equal to 

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Temperature dependencies of loss modulus G" and tan S usually show sharp maxima at the glass transition temperatures that correspond to the cooperative movement of the segments of polymer chains. Low-temperature maxima are ascribed to the movements of short fragments of the main chain or of the side groups. The equilibrium elastic modulus oo could be an important characteristic of the cross-linking density in IPNs and may be presented as consisting of two parts ... 

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