Distribution of Segmental Mobilities in Network Polymers

Abstract

All solid polymers are present in three dimentional network structure because their molecular chains aggregate with various junctions e.g. chemical crosslinking, chain entanglement and other intermolecular couplings. It is probable that the macroscopic properties of polymers are dependent on the nature of the network structure even when no regularity exists in the mode of the aggregation and the system is completely amorphous. Descriptions of the network structure so far presented has been done solely in terms of the network density. However, the network structure may also depends on local packing geometry of molecular chain which includes many junctions. An essential feature of network structure is the restriction of segmental motion by the network junction. In the case of flexible chain molecule, this restriction may be effective in certain length of chains around the junction point. Segmental mobilities are then distributed along a molecular chain which passes through several junctions. To characterize the network structure, a new concept of the distribution of segmental mobilities is introduced. This concept will be found to be valid so as to apprehend systematically the volume effect of network density and some aspects of viscoelasticity.A simple relation between specific volume v and the network density ρ is deduced assuming that the restriction is localized near the junction point, v=βalnρ0/ρ (1)ρ0 being a constant. The parameter β is unity above the glass temperature Tg, and a depends on the decrement of free volume accompanied by an increase in ρ. In several crosslinked polymers, a takes a value ranging 0.02 to 0.04 which is in reasonable agreement with the previous estimation of fractional free volume of polymers. Below the glass temperature, β depends on the distribution of free volume along the chain taking values between zero and unity according to the uniform distribution and the extreme localization, respectively. Assuming that the segmental mobilities are a function of free volume alone, β can be regarded as a measure of distribution of segmental mobilities. Dependence of β on the structure of chain unit is studied on crosslinked styrene copolymers. It is found that β takes a lower value in the case of higher styrene content, reflecting the rotation hindrance of the rigid styrene sequence. From equation (1) one can derive an expression of the dependence of Tg on ρ.Tg-a/Δα(1-β)lnKρ (2)where K is a constant and Δα is the difference of the thermal expansion coefficient above and below the glass temperature. Equation (2) is found to hold for several crosslinked systems.As for the viscoelasticity, response of a modified ladder model is studied by an analog computer. Larger resistive values are assinged to terminal elements according to the concept of distribution of segmental mobilities. The shape of tanδ curve becomes mare symmetric when the localization of restriction due to network junction is pronounced. Since experimental tanδ curves of polymers are usually symmetric, it can be concluded that the localization of the restriction is a universal feature of network polymers provided the model was an adequate one. The ratio of the resistive values of terminal elements to that of middle elements has a marked effect on the steepness of viscoelastic dispersion. The dispersion becomes much steeper, increasing this ratio which is considered to correspond to increasing β. Practical examples may be found in copolymer systems of two components, one of which is more flexible having a higher value of β. Tobolsky has reported that the slopes of relaxation modulus become steeper when the concentration of butadiene is increased in styrene butadiene copolymers