Perspective: Single polymer mechanics across the force regimes

Abstract

I review theoretical and experimental results on the force-extension response of single polymers, with a focus on scaling pictures of low-force elastic regimes, and recent measurements of synthetic and biological chains that explore those regimes. The mechanical response of single polymers is an old theoretical problem whose exploration was instigated by the curious thermomechanical behavior of rubber. Up until the 1990s, the main utility of those calculations was to explain bulk material mechanics. However, in that decade, it became possible to directly test the calculations through high-precision single-chain stretching experiments (i.e., force spectroscopy). I present five major single-chain elasticity models, including scaling results based on blob-chain models, along with analytic results based on linear response theory, and those based on freely jointed chain or worm-like chain structure. Each model is discussed in terms of the regime of force for which it holds, along with the status of its rigorous assessment with experiment. Finally, I show how the experiments can provide new insight into polymer structure itself, with particular emphasis on polyelectrolytes. C 2015 AIP Publishing LLC. [http://dx

Single polymer dynamics for molecular rheology

“…However, single molecule pulling experiments on ssDNA showed a qualitatively different response, such that x ∼ ln f in the high-force regime [38]. It was found that this unusual behavior arises due to polyelectrolyte or charge effects for flexible polymers in the high-force regime, supported by scaling theory [71] and simulations of the stretching of flexible polyelectrolytes under high force [72,73].…”

Exact solution for the force-extension relation of a semiflexible polymer under compression

“…The linear response χ(T, F = 0) of the semiflexible polymer to the compression force can also be obtained exactly by expanding the full solution in Eqs. (26), (27), and (28) to second order in the force. For a clamped polymer we use the expansions of the Mathieu functions for ϕ 0 = ϕ L = 0 and the corresponding eigenvalues up to second order in the deformation parameter q from Refs.…”

“…Due to their semiflexibility, biopolymers show a peculiar response to external forces [20][21][22], where the static and dynamic properties are dominated by their enthalpic elasticity, but conformational entropy still plays a significant role. Experimental techniques such as optical [23,24] and magnetic tweezers [25], transmission electron microscopy [26], and (atomic) force spectroscopy [19,27] have been used to quantify the mechanical properties in terms of force-extension relations [28]. These capture the nonlinear effects emerging in the stretching and buckling of semiflexible polymers such as DNA [29][30][31], actin [32], and synthetic carbon nanotubes [26], but also single molecules such as titin [33], which is an important component in striated muscle tissues, and collagen [34], present in, e.g., skin and bones.…”

Counting the ions surrounding nucleic acids

“…Beyond their biological significance, NAs are of interest to polymer physicists as models of strong polyelectrolytes (10). …”