Friction coefficient Translation coefficients

In the limit of infinite dilution the friction coefficient can be related to the single particle translational diffusion coefficient... 

To simulate the particle-particle collision, the hard-sphere model, which is based on the conservation law for linear momentum and angular momentum, is used. Two empirical parameters, a restitution coefficient of 0.9 and a friction coefficient of 0.3, are utilized in the simulation. In this study, collisions between spherical particles are assumed to be binary and quasi-instantaneous. The equations, which follow those of molecular dynamic simulation, are used to locate the minimum flight time of particles before any collision. Compared with the soft-sphere particle-particle collision model, the hard-sphere model accounts for the rotational particle motion in the collision dynamics calculation thus, only the translational motion equation is required to describe the fluid induced particle motion. In addition, the hard-sphere model also permits larger time steps in the calculation therefore, the simulation of a sequence of collisions can be more computationally effective. The details of this approach can be found in the literature (Hoomans et al., 1996 Crowe et al., 1998). 

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. 

W. G. Miller, University of Minnesota, Minnesota In vlsco elastic studies the monomeric friction coefficient is used to describe motion. The same parameter Is used to look at translational diffusion of solvent and Its concentration dependence. Is there any relationship between this parameter and your three bond motion or Is the correlation length way too long ... 

Combining the above descriptions leads to a picture that describes the experimentally observed concentration dependence of the polymer diffusion coefficient. At low concentrations the decrease of the translational diffusion coefficient is due to hydrodynamic interactions that increase the friction coefficient and thereby slow down the motion of the polymer chain. At high concentrations the system becomes an entangled network. The cooperative diffusion of the chains becomes a cooperative process, and the diffusion of the chains increases with increasing polymer concentration. This description requires two different expressions in the two concentration regimes. A microscopic, hydrodynamic theory should be capable of explaining the observed behavior at all concentrations. 

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... 

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