Friction coefficient linear polymers

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 ... 

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]. 

It is not clear why this transition should occur at such a higher level of arm entanglement for polystyrene stars than for other star polymers. This observation is in direct conflict with the standard assumption that through a proper scaling of plateau modulus (Go) and monomeric friction coefficient (0 that rheological behavior should be dependent only on molecular topology and be independent of molecular chemical structure. This standard assumption was demonstrated to hold fairly well for the linear viscoelastic response of well-entangled monodisperse linear polyisoprene, polybutadiene, and polystyrene melts by McLeish and Milner [24]. 

K above their glass transitions. All linear polymer melts have viscosity proportional to molar mass (ry M) for sufficiently short chains, when the data are determined at a constant friction coefficient as opposed to isothermal data. Longer chains have entanglement effects (discussed in Chapter 9) and have The full chain length dependence of... 

Equation (8.136) is tested in Fig. 8.17 (solid curves) and found to describe the molar mass dependence of constant friction coefficient viscosity data for all three of these linear polymers. The critical molar mass Me for entanglement effects in viscosity is always a factor of 2-4 larger than the entanglement molar mass Mg. that was defined in Eq. (7.47). 

Viscosity data for three linear polymers corrected to the friction coefficient of high molar mass polymer at roughly 7 g+ 120K, fit to Eq. (8.137) (curves). Open circles are polyisobutylene (r=50°C) with Mc = 14000 gmoP. filled squares are polybutadiene (7 =25°C) with A/< = 6700gmor open triangles are free radically prepared polystyrene T =217°C), and filled triangles are anionically prepared polystyrene T=2[1 C) with... 

Equation (8.137) is perfectly analogous to Eq. (8.12) for a linear polymer (in both cases (is the friction coefficient of a single monomer). The Rouse... 

Films can be formed from dihydroxydocosanoic acid [23] and appear to be formed as polyesters by intermolecular dehydration to form a network polymer. In contrast, monohydroxydocosanoic acid gives a linear polymer. Coefficients of friction are not exceptionally low, with jx of the order of 0.1, but wear properties are claimed to be comparable or better than those of ZDDP, albeit only in simple FourBall testing. However, this mechanism of film formation may be applicable in very low or zero phosphorus formulations if the mechanisms for film generation are applicable in fully formulated oils. 

Polytetrafluoroethylene (PTFE), also known by its generic DuPont tradename of Teflon, is a linear polymer that has a molecular structure similar to PE, but with all the hydrogen-atoms replaced by fluorine atoms (CE2-CE2) . Since fluorine-atoms prefer contact with fluorine-atoms, while repelling all others, this repulsion reduces the friction coefficient of the system and produces a non-adhesive surface (with self-lubricating properties). The strong C-C and C-F bonds make PTFE chemically inert, with excellent chemical resistance. 

Miyata and Yamaoka [26] used scanning probe microscopy (SPM) to determine the micro-scale friction force of a silicone-treated polymer film surface. PU acrylates cured by an electron beam were used as the polymer films. The micro-scale friction force obtained by SPM was compared with macro-scale data, such as surface free energy determined by the Owens-Wendt method and the macro-scale friction coefficient determined by the ASTM D1894 method [27]. These comparisons showed that a good linear relationship existed between the surface free energy and the friction force, which was insensitive to the nature of the polymer specimens or to the silicone... 

Drag reduction is also obtained in the case of laminar flow of polymer solution, in the limits of usual concentrations, accompanied by a slightly increase of viscosity without to modify the linear equation shear-stress/shear-flow rate. Figure 3.378, the behaviour being typical newtonian one. Figure 3.379. Based on the last Figure a small increase a friction coefficient could be expected but not an important drag reduction as was found. 

Eariy experimental evaluations of the solution properties of branched poly-mers did in fact assume that the and P constants of the standard equations for intrinsic viscosity and frictional coefficient of flexible linear polymers ... 

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