Elasticity, single-molecule

FIGURE 6 Relaxation of a A-DNA molecule when the maximum extent of stretching is in the Gaussian region. Qualitative sketch based on experimental results presented elsewhere. (From Schroeder, Babcock, Shaqfeh et al. [72].) 

The utility of such measurements in the area of rubberlike elasticity is illustrated in the following section. 

In other experiments on this same system, the DNA chains were in fact stretched close to the Umits of their extensibility [70]. The results for this more complicated case are shown schematically in Fig. 7. At the higher elongations, the chains are clearly in the non-Gaussian region, as evidenced by a much 

Although such studies are inherently very interesting, it should be noted that they are not directly relevant to the many unresolved questions in the area of rubberlike elasticity that involve the interactions among the chains making up an elastomeric network. 

GTreloar, The Physics of Rubber Elasticity, Clarendon Press, Oxford, 1975. 

---

Keywords AFM Desorption Inherent elasticity Macromolecules Mechanochemistiy Molecular motor Non-covalent interactions Polymer models QM calculations Single-molecule elasticity SMFS Supramolecular chemistry Supramolecular polymer Water rearrangement... 

VII. Enthalpic and Entropic Contributions to Rubber Elasticity Force-Temperature Relations Vtn. Direct Determination of Molecular Dimensions IX. Single-Molecule Elasticity References... 

Tskhovrebova et al., 1997] Tskhovrebova, L., Trinick, J., Sleep, J., and Simmons, R. Elasticity and unfolding of single molecules of the giant protein titin. Nature. 387 (1997) 308-312... 

Elastic tunneling spectroscopy is discussed in the context of processes involving molecular ionization and electron affinity states, a technique we call orbital mediated tunneling spectroscopy, or OMTS. OMTS can be applied readily to M-I-A-M and M-I-A-I -M systems, but application to M-A-M junctions is problematic. Spectra can be obtained from single molecules. Ionization state results correlate well with UPS spectra obtained from the same systems in the same environment. Both ionization and affinity levels measured by OMTS can usually be correlated with one electron oxidation and reduction potentials for the molecular species in solution. OMTS can be identified by peaks in dl/dV vs bias voltage plots that do not occur at the same position in either bias polarity. Because of the intrinsic... 

The take-home message here is that conductivity measurements in single-molecule junctions are difficult to analyze without the support of quantum mechanical calculations that include the metal electrodes. This is very much the domain of specialists, and the simple rules discussed for analyzing elastic tunneling spectra in other junction types generally do not apply for metal-single-molecule-metal junctions. 

The model of a reacting molecular crystal proposed by Luty and Eckhardt [315] is centered on the description of the collective response of the crystal to a local strain expressed by means of an elastic stress tensor. The local strain of mechanical origin is, for our purposes, produced by the pressure or by the chemical transformation of a molecule at site n. The mechanical perturbation field couples to the internal and external (translational and rotational) coordinates Q n) generating a non local response. The dynamical variable Q can include any set of coordinates of interest for the process under consideration. In the model the system Hamiltonian includes a single molecule term, the coupling between the molecular variables at different sites through a force constants matrix W, and a third term that takes into account the coupling to the dynamical variables of the operator of the local stress. In the linear approximation, the response of the system is expressed by a response function X to a local field that can be approximated by a mean field V ... 

S. Cocco, J. Marko, and R. Monasson, Theoretical models for single-molecule DNA and RNA experiments from elasticity to unzipping. C. R. Phys. 3, 569-584 (2002). 

Suppose we imagine a single molecule bouncing back and forth across a surface between two restraining barriers. If we define the direction of this motion to be the x direction and the velocity of the molecule to be vx, then the change in momentum at each collision (if we assume they are elastic) is... 

Earlier studies of positron-molecule elastic scattering did not involve such detailed descriptions of the scattering process as do the variational and R-matrix formulations. Instead, the interaction between the positron and the molecule was represented by a relatively simple model potential, and the positron wave function F(r 1) was assumed to satisfy the equivalent single-particle Schrodinger equation... 

Single-molecule theories originated in early polymer physics work (45) to describe the flow behavior of very dilute polymer solutions, which are free of interpolymer chain effects. Most commonly, the macromolecular chain, capable of viscoelastic response, is represented by the well-known bead-spring model or cartoon, shown in Fig. 3.8(a), which consists of a series of small spheres connected to elastic springs. 

---