Entropic spring constant

We can take the Rouse term l/ ke 02rm/0m2 (ke = 3kBT//2) entropic spring constant) into consideration formally, if we define the element Tnm of the Oseen tensor as Tnm = E/ . The equation of motion (13) thus becomes... 

K(R),Kg Entropic spring constant, (7.41), spring constant for a Rouse segment, (7.55). 

The coefficient of proportionality 3kTj Nb ) is the entropic spring constant of an ideal chain. It is easier to stretch polymers with larger numbers of monomers N, larger monomer size b, and at lower temperature T. The fact... 

The entropic spring constant and the friction coefficient of a Kuhn segment are given by... 

This result states that there is an entropic spring term in the free energy that penalizes deviations of the mean size m from the mean size in the parent distribution. The spring constant is inversely proportional to the variance in the parent distribution thus if the parent is narrower, it is harder to move away from the parental mean size [64]. However, as indicated above, the CLT is not... 

This identifies an effective spring constant for the polymer, namely 3T/2R. This spring like behaviour is purely an entropic effect. 

The entropic force inside each tube segment is linear with the spring constant k=3kBT/ Nj/). 

Rubber bands are entropic springs. Experiments show that the retractive force / of polymeric elastomers as a function of temperature T and expansion H is approximately given by f(T,C) = aT ( - tn) where a and l ) are constants. 

Notice how this entropic spring force is linearly related to the extension the extended polymer behaves like a classical Hookean spring. The formula can be easily seen as a form of Hooke s law, yielding a spring constant k of... 

The enthalpic contribution becomes important at higher forces when chemical bonds are extended and deformed. To a first approximation, this can be accounted for by an additional linear stretching term, which contains the Kuhn or persistence length, the polymer length, and a Hookean spring constant as fit parameters. Here one has to assume that the restoring force can be separated into an entropic and an enthalpic contribution. For a review, see Reference 79. 

As seen in Chapter 3, the force constant on the harmonic spring is of entropic origin. The spring forces on bead 1 and bead 2, denoted by Fi and F2, respectively, are given by... 

The first one is an entropic term where we assume that the polymer behaves like a spring with constant q, where is the radius of an ideal chain when no interactions are present. The second term is the interaction energy in which v is the excluded volume interaction, discussed for linear chains. Except for the presence of N, this is very similar to what we considered for chains. The presence of this factor is due... 

The result implies that a sequence behaves like a spring, showing a linear relation between force and extension. The force constant is proportional to the absolute temperature T, as is characteristic for forces of entropic origin. Note furthermore that 6r decreases on increasing the size of the sequence. 

This in an interesting result. It tells us that this entropic force increases linearly with the distance between the two end-groups, just as if they were connected by a mechanical spring. The stiffness constant, denoted 6, increases with temperature and decreases with an increasing size of the chain. 

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