Effective monomer length

The radius R is dependent on the solvent. Where the polymer is represented as an ideal, freely jointed chain, no account is taken of the effect of the solvent. This represents the borderline case between a poor and good solvent. Here, each link is in a random direction with respect to its neighbors and the end-to-end distance is proportional to aN where a is the effective monomer length. This distance is much smaller than the molecular length aN and is characteristic of the molecular radius R. For the more common case of a chain in a good solvent, excluded volume effects must be considered, and where this volume is of the order of it can be shown that (de Gennes 1979, 1990)... 

Fig. 1). A polymer chain is made of effective monomers joined by bonds. A bond corresponds to the end-to-end distance of a group of 3-5 successive chemical bonds and can fluctuate in some range. It is represented by vectors 1 of the set P(2,0,0),P(2,1,0),P(2,1,1),P(3,0,0), and P(3,l,0) which guarantee that intersections of the polymer chain with other chains, or with itself, are virtually impossible. All lengths are here measured in units...

As has already been emphasized in Fig. 1.1, there is the further problem of connecting the mesoscopic scale, where one considers length scales from the size of effective monomers to the scale of the whole coils, to still much larger scales, to describe structures formed by multichain heterophase systems. Examples of such problems are polymer blends, where droplets of the minority phase exist on the background of the majority matrix, etc. The treatment of... 

Rouse behavior observed on PI homopolymer melts has to be modified if the labelled (protonated) PI species are replaced by diblock copolymers of proto-nated PI and deuterated polystyrene (PS) [46]. The characteristic frequency Q(Q) is slowed down considerably due to the presence of the non-vanishing X-parameter. Thus, the reduction is stronger at smaller Q-values or at larger length scales than in the opposite case. In addition, as a minor effect, Q(Q) becomes dependent on both friction coefficients per mean square monomer length, //2, valid for PI and for PS. 

Here a0 is a constant called the effective bond length of the chain, and as(z) is a dimensionless quantity called the linear expansion factor of the chain. The latter depends on long-range interactions between pairs of monomer units and chain length through the so-called excluded-volume parameter z. For details of these quantities characterizing the dimensions of random-coil polymers, the reader is referred to a recently published book by Yamakawa (40). At this place we simply note that as tends to unity in the absence of excluded-volume effect. 

While the octamer 331 has Xmax = 458 nm, electrochemically generated poly(3-alkyl-a-thiophene)s have a noticeable smaller 7max value of 430-440 nm in solution. These data support the notion that the effective conjugation length in conjugated thiophene polymers may only be 6-7 monomer units long. 

Fig. 9. Phase diagram ofthe thin film with surface parameters p O.2, g=-0.5 plotted in the plane of variables % 1, for polymers of chain length N=100 and for three choices of film thicknesses D=20 (diamonds), D=60 (crosses) and D=100 (squares). Broken curve shows the bulk phase diagram of the underlying Flory-Huggins model for comparison. Remember that lengths are measured in units of the size b of an effective monomer. From Flebbe et al. [58]...

The Sj-Sj annihilation rate constant was determined in the following manner. First, the concentration of the excimer was obtained by dividing the observed absorbance by its extinction coefficient and by the effective cell length where the Sj<-Sp absorbance at 266nm was 1. In addition, in pure liquid benzene as well as in solution, there exists rapid equilibrium between monomer and excimer, of which time constants of association and dissociation are in the order of a few ps °. Hence, the sum of the monomer and excimer concentrations obtained by the equilibrium constant at each temperature was used as the concentration of the excited singlet species for the analysis. Although this assumption may affect to some extent the accuracy of the obtained rate constant, the error of this estimation would not depend upon the temperature. 

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