Interchain distances

Firstly, we focus on cofacial dimers formed by stilbene molecules in such conformations, the amplitude of interchain interactions is expected to be maximized [57], Table 4-1 collects the INDO/SCl-calculated transition energies and intensities of the lowest two excited states of stilbene dimers for an interchain distance ranging from 30 to 3.5 A. 

Figure 4-6. Evolution of the INDO/SCI-calculalcd. splitting between the lowest two oplieal transitions of cofacial dimers formed by two PPV chains as a function of the inverse number of bonds (1/u) along the conjugated backbone of the oligomer. The theoretical results are reported for interchain distances of 4 A (open circles) and C> A (tilled circles).

The photoinduced absorption and the electrical characteristics of the conjugated LPPP show that the optoelectrical properties are strongly dependent on charge carrier traps in the bandgap. From aromatic molecular crystals it is known that impurities and structural imperfections form localized states [34]. LPPP forms homogeneous and dense films with a mean interchain distance of about 20 A and ncgligi-... 

Table 4-1. INDO/SCI-calculalcd iransilion energies, intensities, and Cl dcscriplions of llie lowest two excited stales (S and S2, respectively) of a cofacial dimer formed by Iwo stilbene molecules for various interchain distances.

Interchain distance Excilcd sluic Transition energy (cV) Intensity (arb. units) Cl deseriplion... 

Figure 4-5. lNDO/SCl-calculalcd transition energies of the lowest two optical transitions of a cofacial dimer formed by two slilhcnc molecules as a function of interchain distance. The horizontal line refers to the transition energy of the isolated molecule. Note that the upper value reported at 3.S A corresponds to the transition to the fifth excited stale, which provides the lowest intense absoiption feature. 

Figure 4-9. INDO/SCI-simulalcd absorption and emission spectra of two slilbene molecules with a huge interchain distance (solid lines) and those of a cofacial dimer formed by two slilbene chains separated by 4 A (dolled lines).

In summary, over a large range of interchain distances, the most stable species photogenerated in the lowest excited stale of clusters formed by identical molecules are excitons mostly with an intrachain character. The calculations also show that po-laron-pairs, also referral to as interchain excitons (corresponding to a positive polar-... 

Introduction of bulky lateral substituents on monomer units to increase interchain distance and prevent close packing in polymer crystal. The use of unsymmetrically substituted monomers, resulting in a random distribution of head-to-head and head-to-tail structures in polymer chains, further helps in disrupting regularity. Some examples of substituent effects are given in Table 2.16. 

FIG. 13 Schematic drawing of possible binding modes of counterions to polyelectrolyte chains. Counterions loosely bind and form a cloud around the polyelectrolyte chains when the interchain distance (d) is greater than 2.4 0.5 nm, while they strongly bind to form nearly neutral polyelectrolytes at smaller distances d < 2.4 0.5 nm). 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

According to Hess, the relative strength of the entanglement friction can be related to the more microscopic parameter q , describing the range of the true interchain interaction potential. A value of q 1 = 7 A, close to the average interchain distance of about 4.7 A, is obtained. 

Table 3.6 Characteristic interchain distance, R, of polypyrrole with cycloalkyl rings fused to the pyrrole moiety...

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... 

Fig. 1.2 Richness of dynamic modulus in a bulk polymer and its molecular origin. The associated length scales vary from the typical bond length ( A) at low temperatures to interchain distances ( 10 A) around the glass transition. In the plateau regime of the modulus typical scales involve distances between entanglements of the order of 50-100 A. In the flow regime the relevant length scale is determined by the proper chain dimensions...

The time needed by a proton to move as far as the average interchain distance dchain ... 

Thus, the application of the Bragg s equation to the scattering peak at20 = 18 and applying a correction of 20% yields an interchain distance ca 6A. As a function of the degree of sulpho-nation and relative humidity, this distance appears to be constant. 

The overall increase in the total integrated Cls level intensity as a function of reaction time is readily interpreted in terms of a cross linking mechanism since the number of carbon atoms per unit area increases in the surface regions consequent upon the decrease in interchain distance on crosslinking. Indeed the kinetic scheme... 

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