Force Versus Extension Behavior in the Good Solvent Regime

2 Force Versus Extension Behavior in the Good Solvent Regime 

In cf = 3 dimensions, a useful interpolation formula between both regimes is  

The various crossover predictions and the numerical evidence that we have obtained for these crossovers are described in detail in two long papers [20, 22] here we show only two examples that illustrate the crossover from the linear response to the Pincus regimes, both in d = 2 and d = 3 dimensions (Fig. 4). We stress that the widely used interpolation formula for the force versus extension curve quoted in Eq. (2) does not include the Pincus regime. 

We emphasize that these deviations from the Kratky-Porod model that occur for semiflexible polymers both in equilibrium and in their response to stretching forces, were not properly noticed in most of the experiments. However, in analyzing data one normally does not have strictly monodisperse chains, and neither p nor L are independently known both parameters are usually used as adjustable fitting parameters. Because fp depends on d, and is also affected by solvent conditions, and for strongly stretched real chains other effects (related to the local chemical structure of the effective monomeric units) come into play, this failure is not surprising. However, some of the confusion over the actual values of p that 

The problem of understanding the persistence length and its consequences is also taken up by Butt et al. [26] for bottle-brush polymers, there is the challenging problem of understanding how their stifliiess depends oti the grafting density and degree of polymerization of the grafted side chains. 

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