Frictional coefficient polymers

The spreading rate of a polymer droplet on a surface has been measured (363,364). The diffusion constant was at least an order of magnitude smaller than that of the bulk. The monomer—surface friction coefficient for polystyrene has been measured on a number of surfaces and excellent... 

Poly acetals are highly crystalline polymers. The number of repeating units ranges from 500 to 3,000. They are characterized by high impact resistance, strength, and a low friction coefficient. 

In this equation, % is a proportionality factor known as the bead-solvent friction coefficient which purports to account in some kind of average way for the complex molecular interactions as the polymer segments (schematized by the bead) move about in the solvent. Following Stokes law of drag resistance, this friction coefficient is usually given as = 67trisa, with a equal to the bead radius. 

FIGURE 26.14 The friction coefficients of the four gum polymers of Figure 26.13 plotted as function of log flxv. (Data from Heinz, M. and Grosch, K.A., ACS Spring Meeting, St Antonio, 2005.)... 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

The frictional coefficient varies with concentration, but at infinite dilution it reduces to the coefficient (/o) for an isolated polymer molecule moving through the surrounding fluid unperturbed by movements of other polymer molecules (see Chap. XIV). At finite concentrations, however, the motion of the solvent in the vicinity of a given polymer molecule is affected by others nearby binary encounters (as well as ones of higher order) between polymer molecules contribute also to the observed frictional effects. The influence of these interactions will persist to very low concentrations owing to the relatively large effective volume of a polymer molecule, to which attention has been directed repeatedly in this chapter. Since the sedimentation con-stant depends inversely on the frictional coefficient, s must also depend bn concentration. 

Of major importance is the fact that the specific character of polymer chains of a given type enters the relationship (17) only through the effective size of one of its beads as indicated by the ratio f/970. Even the effect of this factor vanishes when the total internal resistance to flow is sufficiently large. Hence, in this limit, which will include nearly all actual cases of interest (see Sec. 4), the molecular frictional coefficient should depend only on the size /s and not otherwise on the nature of the polymer. Accordingly, we choose to let... 

According to Eq. (18), the high polymer molecule should exhibit the frictional coefficient of an equivalent sphere (compare Eq. 15) having a radius proportional to the root-mean-square end-to-end distance (r ) (or to (s ) / ). Similarly, according to Eq. (23) its contribution to the viscosity should be that of an equivalent sphere (compare Eq. 16) having a volume proportional to (r ) / In analogy with Eq. (17 ), we might write... 

Theory presented earlier in this chapter led to the expectation that the frictional coefficient /o for a polymer molecule at infinite dilution should be proportional to its linear dimension. This result, embodied in Eq. (18) where P is regarded as a universal parameter which is the analog of of the viscosity treatment, is reminiscent of Stokes law for spheres. Recasting this equation by analogy with the formulation of Eqs. (26) and (27) for the intrinsic viscosity, we obtain ... 

Frictional coefficient for an element, or bead, of the polymer chain (Chap. XIV). 

Figure 8.16 shows the principal components of a coefficient of friction tester. Polymer samples in the form of thick sheets or molded plaques are attached to the base and a sled with standard dimensions, weight, and surface properties is drawn over the surface. The load beam measures the force required to initiate movement and sustain motion at a given rate of crosshead travel. Thin films can be taped to the sled and drawn across a contact surface that has known properties. 

Table 4 Monomeric Friction Coefficients of Selected Polymers...

Today it is claimed that the surface fluorination of polymers using F2 gas mixtures enhances a wide range of properties, e.g., low permeability to nonpolar liquids4 improved permselectivity,5-6 excellent wettability and adhesion,7 low friction coefficient (especially for elastomers),8 and chemical inertness.9 Obviously, these properties depend on the chemical composition ofthe fluorinated layer, which in turn is determined by the chemical structure ofthe base polymer, the composition of the F2 gas mixture, and the fluorination parameters. 

Each submolecule will experience a frictional drag with the solvent represented by the frictional coefficient /0. This drag is related to the frictional coefficient of the monomer unit (0- If there are x monomer units per link then the frictional coefficient of a link is x(0- If we aPply a step strain to the polymer chain it will deform and its entropy will fall. In order to attain its equilibrium conformation and maximum entropy the chain will rearrange itself by diffusion. The instantaneous elastic response can be thought of as being due to an entropic spring . The drag on each submolecule can be treated in terms of the motion of the N+ 1 ends of the submolecules. We can think of these as beads linked... 

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 ... 

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