Polymers single-chain mechanics

Force Spectroscopy of Polymers Beyond Single Chain Mechanics... 

In the above examples the size of the chain can be measured by considering the number of automobile collisions that result from the first accident, or the number of fission reactions which follow from the first neutron capture. When we think about the number of monomers that react as a result of a single initiation step, we are led directly to the degree of polymerization of the resulting molecule. In this way the chain mechanism and the properties of the polymer chains are directly related. 

As for further analysis, curve fitting against the worm-like chain (WLC) model was conducted and indicated as a solid line in Figure 21.4. The model describes single polymer chain mechanics ranging from random-coil to fully extended forms, as follows ... 

Recently a very detailed study on the single chain dynamic structure factor of short chain PIB (M =3870) melts was undertaken with the aim to identify the leading effects limiting the applicability of the Rouse model toward short length scales [217]. This study was later followed by experiments on PDMS (M =6460), a polymer that has very low rotational barriers [219]. Finally, in order to access directly the intrachain relaxation mechanism experiments comparing PDMS and PIB in solution were also carried out [186]. The structural parameters for both chains were virtually identical, Rg=19.2 (21.3 A). Also their characteristic ratios C =6.73 (6.19) are very similar, i.e. the polymers have nearly equal contour length L and identical persistence lengths, thus their conformation are the same. The rotational barriers on the other hand are 3-3.5 kcal/mol for PIB and about 0.1 kcal/mol for PDMS. We first describe in some detail the study on the PIB melt compared with the PDMS melt and then discuss the results. 

The mechanical properties of the polymers were tested in bulk as well to correlate with the single chain nanomechanical studies. Polymer samples were cast into thin films and subjected to stress-strain analysis. Figure 10.4 shows the comparison of... 

The electrical conductivity of a material is a macroscopic solid-state property since even in high molecular-weight polymers there is not just one conjugated chain which spans the distance between two electrodes. Then it is not valid to describe the conductivity by the electronic structure of a single chain only, because intra- and interchain charge transport are important. As with crystalline materials, some basic features of the microscopic charge-transport mechanism can be inferred from conductivity measurements [83]. The specific conductivity a can be measured as the resistance R of a piece of material with length d and cross section F within a closed electrical circuit,... 

The conductivity is a solid-state phenomenon, and, as pointed out already, conductivity is not a single chain phenomenon. The band-gap description of a conjugated chain is a one-dimensional model. Additionally, considerably interchain charge transport is necessary to describe a metal-like behavior in the highly doped three-dimensional sample and further transfer mechanisms across the polymer chains have to be discussed. What one actually needs to know in explaining conductivity of organic polymers is how the charge transport proceeds... 

The size of the problem is enormous. For the properties of polymers that are governed only by single chain behavior the number of degrees of freedom is exceedingly large. Application of sophisticated statistical mechanics methods is required to study these properties. 

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