Chains interchain interaction

The excluded volume is not limited to a pair of monomers on the same chain (intrachain interaction). It exists equally for a pair of monomers on different chains (interchain interaction). At higher concentrations, the interchain interaction is the dominant part of the excluded volume effect. 

The highly conductive class of soHds based on TTF—TCNQ have less than complete charge transfer (- 0.6 electrons/unit for TTF—TCNQ) and display metallic behavior above a certain temperature. However, these soHds undergo a metal-to-insulator transition and behave as organic semiconductors at lower temperatures. The change from a metallic to semiconducting state in these chain-like one-dimensional (ID) systems is a result of a Peieds instabihty. Although for tme one-dimensional systems this transition should take place at 0 Kelvin, interchain interactions lead to effective non-ID behavior and inhibit the onset of the transition (6). 

In the previous section we assumed that disorder results in random fluctuations of the order parameter around some average value A<). Such an approach is, essentially, a mean field treatment of the lattice. It requires sufficiently strong interchain interactions, whose role is to establish a coherence between the phases of the order parameter in different chains. 

While for strong interchain interactions large deviations of the order parameter from its average value are unlikely, for weak interactions the minimal-energy lattice configuration of disordered chains contains a finite density of kinks and anti-... 

Basically, the first approach to correlate the polyimide chain organization to the monomer structure was to take into consideration the electron affinity of the anhydride and the ionization potential of the diamine,10 as shown in Fig. 5.3. The strongest interactions between the polymeric chain are expected when the polyimide is prepared with the dianhydride having the highest electron affinity and die diamine with the lowest ionization potential. The strongest interchain interaction leads to high Tg and low solubility. 

Later we will describe both oxidation and reduction processes that are in agreement with the electrochemically stimulated conformational relaxation (ESCR) model presented at the end of the chapter. In a neutral state, most of the conducting polymers are an amorphous cross-linked network (Fig. 3). The linear chains between cross-linking points have strong van der Waals intrachain and interchain interactions, giving a compact solid [Fig. 14(a)]. By oxidation of the neutral chains, electrons are extracted from the chains. At the polymer/solution interface, positive radical cations (polarons) accumulate along the polymeric chains. The same density of counter-ions accumulates on the solution side. 

In polyelectrolyte solutions, the counterion condensation on linear polyelectrolyte chains is known to occur when the charge density along the chain exceeds the critical value [40]. Our work indicates the existence of a critical value for the separation distance between chains, where the interchain interaction changes drastically, most likely due to the transition in the binding mode of the counterions (see Fig. 13). Many peculiar forms of behavior, which are often interpreted by the cluster formation or the interchain organization of polyelectrolytes, have been reported for high concentrations of aqueous polyelectrolytes... 

The introduction of bulky side chains that contain adamantyl groups to poly(p-phenylenevinylene) (PPV), a semiconducting conjugated polymer, decreases the number of interchain interactions. This action will reduce the aggregation quenching and polymer photoluminescence properties would be improved [93]. 

Whatever is the mechanism of interchain interactions to form a three dimensional network, the basis is the formation of a cooperative junction whose stability depends on the specific energy of the linkages and the number of units cooperatively bound, as well as the number of chains involved. 

Turning to polymers giving thermodynamically stable mesophases we must assume that, since we have described bundles as an inherent structural feature of undercooled polymer melts, such structures should occur, at least in principle, also in such systems, to the extent that attractive interchain interactions which account for bundle formation play a significant role. On the other hand, rigorously speaking Class II mesophases are entropy-stabilized and inter-chain... 

The phantom network behaviour corresponding to volumeless chains which can freely interpenetrate one through the other and thus to unrestricted fluctuations of crosslinks should be approached in swollen systems or at high strains (proportionality to the Mooney-Rivlin constant C-j). For suppressed fluctuations of crosslinks, which then are displaced affinely with the strain, A for the small-strain modulus (equal to C1+C2) approaches unity. This situation should be characteristic of bulk systems. The constraints arising from interchain interactions important at low strains should be reflected in an increase of Aabove the phantom value and no extra Gee contribution to the modulus is necessary. The upper limit of the predicted equilibrium modulus corresponds therefore, A = 1. 

The above considerations apply to isolated polymer chains in solution, i.e. at very low polymer concentrations or volume fractions, < >p (i.e. in the limit < >p - 0). As p increases, interchain interactions becom important. Indeed, at a critical polymer concentration, interchain overlap begins, and beyond a second critical concentration, the chains are so overlapped... 

The interchain interaction of dipole moments collinear to the chain axes decays exponentially with the interchain distance (see Eq. (2.2.11)) and has no contribution descending by the power law y2 in Eq. (3.3.6). Summation over lattice sites and interchain distances involves the Riemann zeta-function... 

Many studies on side-chain modifications in PF were initially based on the idea of excimer formation, resulting in the green emission during LED operation or in solid-state PL on annealing PF films. This resulted in several proposed strategies for the design of fluorene side-chain homopolymers, where bulky substituents at position 9 of the fluorene moiety should sterically prevent (hinder) interchain interaction and thus improve the stability of blue emission. 

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