Translational friction coefficient

In the presence of a sieving media the motion of the ions is impeded by a frictional force (Ff). The frictional force is dependent on the translational friction coefficient (f) ... 

Hydrodynamic properties, such as the translational diffusion coefficient, or the shear viscosity, are very useful in the conformational study of chain molecules, and are routinely employed to characterize different types of polymers [15,20, 21]. One can consider the translational friction coefficient, fi, related to a transport property, the translational diffusion coefficient, D, through the Einstein equation, applicable for infinitely dilute solutions ... 

The theoretical prediction of these properties for branched molecules has to take into account the peculiar aspects of these chains. It is possible to obtain these properties as the low gradient Hmits of non-equilibrium averages, calculated from dynamic models. The basic approach to the dynamics of flexible chains is given by the Rouse or the Rouse-Zimm theories [12,13,15,21]. How-ever,both the friction coefficient and the intrinsic viscosity can also be evaluated from equilibrium averages that involve the forces acting on each one of the units. This description is known as the Kirkwood-Riseman (KR) theory [15,71 ]. Thus, the translational friction coefficient, fl, relates the force applied to the center of masses of the molecule and its velocity... 

This result is appHcable to semi-dilute and concentrated solutions [21], and is also useful to check many simulations that do not include HI. For non-draining chains, introducing Gaussian statistics in Eq. (35), and transforming the summations over a large number of units in Eq. (34) into integrals, the translational friction coefficient can finally be written as [ 15]... 

Since the rigid-body approximation gives only an upper bound for the translational friction coefficient and viscosity, MC values of the viscosity for ideal star... 

The translational friction coefficient ft of the polymer chain at infinitely dilute solutions is calculated by equating the net force acting on the chain, — and —fR, where R is the net drift velocity of the center of mass of the chain... 

Using and S, the translational friction coefficient and the electrophoretic mobility can be calculated by simply replacing G by in the respective formulas. Before we proceed to do this, we present the collective dynamics of monomer density and counterions. 

Chapter D is concerned with intrinsic viscosity and translational friction coefficient. Published data for the molecular-weight dependence of these quantities of polypeptides in helieogenic solvents and helix-breaking solvents are summarized, and the variations of these quantities during the helix-coil transition are described. 

This chapter summarizes important data for intrinsic viscosity and translational friction coefficient of polypeptides. The first half of the chapter discusses the data obtained in helicogenic solvents and in helix-breaking solvents. It is actually a supplement to the review article by Benoit et al. (61), in which such data published by 1967 were surveyed critically. The second half of the chapter is concerned with the helix-coil transition region. The context here is largely descriptive because of the lack of relevant theory. 

The translational friction coefficient S can be determined from the measurement of s0 or D0 by making use of the relations (63)... 

Available experimental data for translational friction coefficients of polypeptides are still meager, but those obtained so far in helicogenic solvents display one feature in common plots of s0 or D0M against InM are virtually linear over a wide range of M, as illustrated in Fig. 25 (80, 81). Thus, from such data alone we may conclude that the molecular helices are essentially rigid up... 

As far as we are aware, only a few experimental results are available for the translational friction coefficient of polypeptides in the helix-coil transition region, and our discussion about it cannot but be very incomplete. Figure 33, taken from the work of Okita et al. (13) on the system PHPG-aqueous methanol, shows the dependence of the reduced sedimentation coefficient [s0] on the helical fraction. Here [s0] is defined as s0ri0/( 1 — i>g0), with and Q0 being the... 

Teller, D. C., Swanson, E. and De Haen, C. 1979. The translational friction coefficient of proteins. Methods EnzymoL 61 (Part H), 103-124. 

Stokes-Einstein Relationship. As was pointed out in the last section, diffusion coefficients may be related to the effective radius of a spherical particle through the translational frictional coefficient in the Stokes-Einstein equation. If the molecular density is also known, then a simple calculation will yield the molecular weight. Thus this method is in effect limited to hard body systems. This method has been extended for example by the work of Perrin (63) and Herzog, Illig, and Kudar (64) to include ellipsoids of revolution of semiaxes a, b, b, for prolate shapes and a, a, b for oblate shapes, where the frictional coefficient is expressed as a ratio with the frictional coefficient observed for a sphere of the same volume. 

In recent years, cyclic polymers (also referred to as polymer rings or macrocycles) became easier to prepare. By a number of different approaches and advances in cyclization techniques, a wide range of novel cyclic polymers have been prepared in good yields [10]. In contrast to linear polymers, cyclic polymers are topologically distinct species, and all monomer units of cyclic polymers are chemically and physically equivalent. This equivalence is due to the fact that their properties are not affected by the nature of the end groups, since cyclic polymers have no chain ends. They include the radius of gyration, intrinsic viscosity, translational friction coefficient, critical solution temperature, refractive index, density, dipole moment, glass transition temperature, and surface property [11]. 

A difference in volume between cyclic and linear polymers leads to different solution properties of the cyclic polymers compared to the linear polymers, such as higher GPC elution volume [233], lower intrinsic viscosity [234], lower translational friction coefficient [235], neutron scattering functions more rapid decrease of second virial coefficient with molecular weight [236], and higher critical solution temperature [237]. 

According to the Einstein relation, the diffusion coefficient is inversely proportional to the translational friction coefficient / at infinite dilution by the expression... 

Particle scattering factors and translational friction coefficients of microcap-sulcs with different shapes are summarized in Table 1. 

TABLE 1 Part icle Scattering Factor and Translational Friction Coefficient of Microcupsule... 

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