Contour length critical

Takahashi et al.67) prepared ionene-tetrahydrofuran-ionene (ITI) triblock copolymers and investigated their surface activities. Surface tension-concentration curves for salt-free aqueous solutions of ITI showed that the critical micelle concentration (CMC) decreased with increasing mole fraction of tetrahydrofuran units in the copolymer. This behavior is due to an increase in hydrophobicity. The adsorbance and the thickness of the adsorbed layer for various ITI at the air-water interface were measured by ellipsometry. The adsorbance was also estimated from the Gibbs adsorption equation extended to aqueous polyelectrolyte solutions. The measured and calculated adsorbances were of the same order of magnitude. The thickness of the adsorbed layer was almost equal to the contour length of the ionene blocks. The intramolecular electrostatic repulsion between charged groups in the ionene blocks is probably responsible for the full extension of the... 

The influence of the degree of polymerization and contour length respectively, on the critical concentrations are given in Table 8 for PDADMAC. 

Figure 2.5 Critical volume fractions < i below which a solution of poly(benzyl-L-glutamate) is fully isotropic (O) and 2 above which the solution is fully liquid crystalline ( ) as functions of the number of peptide residues N in the chain. The molecular contour length is roughly 1.5N A. (From Robinson et al. 1958, reproduced by permission of The Royal Society of Chemistry.)...

Assuming that the tightly bound counterions move in a square well potential [69] with a length of L (its upper value is the polyion contour length), Ookubo et al. [25] calculated from the critical frequency of LF relaxation the diffusion constant of these ions Dl... 

Rory [29] proposed a lattice theory that accommodates chain flexibility in liquid-crystalline polymers in a later version. The critical concentration for mesophase formation depends for freely jointed rods on the aspect ratio of the individual Kuhn segment, that is, instead of the contour length, the axial ratio of is used for the calculation. The critical volume fraction of the polymer V is determined by the aspect ratio x, and Eq. (8) was derived as... 

Since A"(ni<) begins to depart from zero at ni< near unity, it follows from eq 4.6 that the theoretical critical contour length Lc for the onset of the excluded-volume effect on chain dimensions is approximately given by... 

Comparing with eq 4.2, we see that Lc is at least one order of magnitude smaller than the experimentally estimated critical contour length Lc. This pronounced difference does not seem attributable to the fact that eq 4.6 is correct only to first order in z. ... 

Transport coefficients of actual polymers should also show die onset of the excluded-volume effect at certain critical contour lengths. It is interesting to study how such lengths can be estimated experimentally and what relations exist between them and Lc or Lc. However, these problems remain almost unexplored. 

To test the theories quantitatively, careful measurements on well-characterized fractions of polymer are required. The contour length, persistence length and chain diameter may be found from dilute solution measurements on fractions in a given solvent. The critical concentrations for mesophase formation in the same solvent may be calculated from the contour length, persistence length and chain diameter by means of the theories for freely jointed or worm-like chains mentioned above. Results have been reported for... 

Contacts, 19-2-19-3, 19-6-19-10, 19-17, 19-19, 19-23-19-24, 19-29, 19-31, 19-39 Contour length, 9-24, 9-25-9-26 Conventional thin films, 7-20 Cooperativity, 18-7-18-8 Coplanarity, 9-23 Copolymerization, 8-13-8-14 Copolymers, 20-13, 20-22, 20-34-20-44 Core-excited states, 21-7 Corrosion, 18-6-18-7, 18-29 Cotton effect, 3-9-3-12 Coulomb blockade transport, 16-15-16-18 Coulomb-blockade (CB), 16-15-16-18, 16-21 Critical regime, 16-5, 16-9 Crossed metallic SWNT, 16-11 Cross-linking, 7-32, 7-34-7-35, 8-12-8-13, 8-34-8-38, 9-17, 9-18... 

Such a framework can be applied straightforward to the other copolymers with complex structures such as multiblock copolymer or star-block copolymer. The critical point is to rebuild the partition functions of the polymer chain with different chain structures. For miktoarm star polymer, the expression of partition calculation g,(r,i) and gj(r, 5) is the same as in Equation 15.12. But the contour length variable s in Equations 15.12 and 15.13 is from 0 to/j ifi is the average volume fraction of the th component in the system i represents A, B, and C and i +/b +/c = ) Meanwhile, the initial condition is g,.(r,0)=l and g ir,0) = gBir,fB)gc(rJc) ... 

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