Molecular extensions

Fig. 21. Microhardness values parallel and perpendicular to the axial direction of oriented CEPE as a function of molecular extension 14 ...

If the preceding analysis of hydrodynamic effects of the polymer molecule is valid, K should be a constant independent both of the polymer molecular weight and of the solvent. It may, however, vary somewhat with the temperature inasmuch as the unperturbed molecular extension rl/M may change with temperature, for it will be recalled that rl is modified by hindrances to free rotation the effects of which will, in general, be temperature-dependent. Equations (26), (27), and (10) will be shown to suffice for the general treatment of intrinsic viscosities. 

Diffusion and sedimentation measurements on dilute solutions of flexible chain molecules could be used to determine the molecular extension or the expansion factor a. However, the same information may be obtained with greater precision and with far less labor from viscosity measurements alone. For anisometric particles such as are common among proteins, on the other hand, sedimentation velocity measurements used in conjunction with the intrinsic viscosity may yield important information on the effective particle size and shape. ... 

When calculating the potential of mean force along a fluctuating coordinate r, we can at best observe r (e.g., the instantaneous molecular extension), but we do not set it explicitly. Therefore, r is no longer an externally controlled coupling parameter, and Jarzynski s identity does not immediately apply. However, as was shown in [3], an extension produces the desired result. 

As determined from X-ray diffraction measurements, the unit cell of crystalline PET is triclinic with a repeat distance of 1.075 nm along the major axis [5, 6], This corresponds to >98 % of the theoretical extended length of the monomer repeat unit [6], There is very little molecular extensibility remaining in a PET crystal, resulting not only in a high modulus but also a relatively short extension range over which the crystal can be extended and still recover elastically. The density of the crystalline structure is 1.45 g/ml, or about 9% higher than the amorphous structure [3],... 

Single molecule pulUng experiments can be described with the formalism developed in Section lll.C.l. In the simplest setting the configurational variable C corresponds to the molecular extension of the complex (handles plus inserted molecule) and the control parameter X is either the force/measured in the bead or the molecular extension of the system, x. For small enough systems the thermodynamic equation of state is dependent on what is the variable that is externally controlled [87]. In the actual experiments, the assumption that either the force or the extension is controlled is just an approximation. Neither the molecular extension nor the force can be really controlled in optical tweezers [88]. For example, in order to control the force a feedback mechanism must operate at aU times. This feedback mechanism has a time delay response so the force is never really constant [89, 90]. By assuming that the force is constant. 

In general, neither the force nor the molecular extension can be controlled in the experiments so definitions in Eqs. (96), (98), and (99) result in approximations to the true mechanical work that satisfy Eqs. (40) and (41). The control parameter in single molecule experiments using optical tweezers is the distance between the center of the trap and the immobilized bead [88]. Both the position of the bead in the trap and the extension of the handles are fluctuating quantities. It has been observed [94—96] that in pulhng experiments the proper work that satisfies the FT includes some corrections to Eqs. (97) and (99) mainly due to the effect of the trapped bead. There are two considerations to take into account when analyzing experimental data. 

Figure 4.9 (a) Molecular orientation without high molecular extension, (b) Molecular orientation with high molecular extension. 

Figure 3.18 Elastic spring force versus molecular extension for the Warner spring, for the freely jointed chain (which is described by the inverse Langevin function), and for the linear spring. (From Tanner, copyright 1985 by Oxford University Press, Inc. Used by permission of Oxford University Press, Inc.)...

The deformation of long chain polymer molecules has always been of great industrial interest as more value can be placed on a material that has improved properties. Molecular extension, or alternatively molecular orientation, is of particular interest as it can enhance mechanical properties of an otherwise weak polymer. Oriented materials are inherently anisotropic. These anisotropic regions can be found directly in semicrystalline polymers where chains organize themselves into crystalline domains. 

This is not necessarily the case at the molecular level where the efficiency of permanent chain extension can be influenced by factors like chain relaxation, topological restraints, chain size and distribution, dissipation of frictional heat, chain repeating structure, and chain slippage. An expression that accounts for chain slippage and provides a measure of true molecular extension has been proposed by Porter et al. ... 

Lengths in the coarse-grained model can be identified with a real system by matching the characteristic molecular extension, Re(m) of one species with the experimental value. This quantity is conserved by the representation and is an example of an invariant quantity [41] mentioned in the introduction. In a generic model, these quantities are the only parameters that convey a specific physical information, establishing relevance with the energy, length and time scales of the real systems. 

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