Peterlin model

Consequently, we will follow the example of Mills et al. (29) who recently presented the first measurements of local solvent concentration using the Rutherford back-scattering technique. They analyzed the case of 1,1,1-trichloroethane (TCE) diffusing into PMMA films in terms of a simpler model developed by Peterlin 130-311, in which the propagating solvent front is preceded by a Fickian precursor. The Peterlin model describes the front end of the steady state SCP as ... 

Now let me try to get some insists into molecular mechanisms of the mechanic fracture in polymers 73). The l teilin model was originally proposed in ex]danation of the mechano-radical formatirm in the hi y stretched fibre. However, one can apply the Peterlin model to the fracture ptenomena in crystalline polymers, because large deformations proceed always in advance of a mechanical fracture. Thus, the tie molecules are assumed to be only parts vtdiich are broken in the case of destmction of bulk polymers. The fact that no mechano-radical is formed from the polymer having no tie mdecules even after the milling supports the interpretation mentioned ove. However, for amorjdious pd[ymers such as PMMA and PB, formation of the mechano-radkals is not attributed to the ruptures of the tie molecules, becau% neither the crystalline parts nor frie tie molecule exist in an amorphous polymer and no particular part of the polymer, on which the applied stress is concentrated, can be assumed in the amorphous polymer. It was found that the polymer chains are ruptured even in the case of an amorphous polymer, like PMMA, PB, and other elastomers, as mentioned in the Section III. The medianism other than the Peterlin model is needed to explain the bond scissions of polymer chains in the amorphous pdymers. 

Fig. 7. Models (oversimplified) of highly oriented hbres (a) Peterlin model (b) Morgan model (c) possible erack path (Morgan model) (d) Northolt model.

After the biaxial stretching the crystallites transform to the febrile structure according to the Peterlin Model... 

Peterlin, A. Molecular model of internal viscosity. Rheol. Acta 12,496-502 (1973). 

Numerous studies of the structure and properties of drawn crystalline polymers have led to the microfibrillar model of fibrous morphology177 179 180. According to Peterlin 179) and Prevorsek et al. 180), the long and thin microfibrils are the basic elements of the fibrous structure. The microfibrils consist of alternating folded chain crystallites and amorphous regions. The axial connection between the crystallites is accomplished by intrafibrillar tie-molecules inside each microfibril and by inter-fibrillar tie-molecules between adjacent microfibrils. 

The other approach concerns the analysis of models of oriented crystalline polymers 7,8172). For the Peterlin-Prevorsek model, the expression for px can be represented as... 

A similar model by Peterlin illustrates a method of turbulence suppression by mechanical interference. One end of the macromolecule lies in the core of a microvortex and the other outside this strains the intermediate section causing molecular exten-... 

Peterlin A (1970) Molecular model of drag reduction by polymer solutes Nature 227 598... 

The internal viscosity force is defined phenomenologically by equations (2.26) formulated above. Various internal-friction mechanisms, discussed in a number of studies (Adelman and Freed 1977 Dasbach et al. 1992 Gennes 1977 Kuhn and Kuhn 1945 Maclnnes 1977a, 1977b Peterlin 1972 Rabin and Ottinger 1990) are possible. Investigation of various models should lead to the determination of matrices Ca/3 and Ga and the dependence of the internal friction coefficients on the chain length and on the parameters of the macromolecule. 

Finally, the dotted curve in Fig. 13 traces the relation between v and vs for rigid prolate ellipsoids of revolution [see Peterlin (16) or Frisch and Simha (6 )] with axial ratio proportional to molecular weight. This curve lies very far from those for flexible molecules except for very low values of the axial ratio p. This seems to exhaust the available information of the type represented by Fig. 13. In connection with the behavior of DNA and perhaps other naturally occurring macromolecules, it would be interesting to have calculations for rods with one or two or at most a small number of flexible joints, such as might correspond to almost completely helical structures [see Section III D]. In spite of the absence of theories for this and possibly other relevant molecular models, it is often possible to arrive at useful indications of conformation by comparing the experimental data with Fig. 13. 

The theory of non-Newtonian viscosity for ellipsoidal particles was first explicitly stated by Kuhn and Kuhn (1945), using Peterlin s distribution function (Peterlin, 1938) and Jeffery s hydrodynamic treatment (Jeffery, 1922-1923) [Eq. (10)]. More elegant treatments have recently been developed by Saito (1951), using the same ellipsoidal model, and also by Kirkwood and his co-workers (Kirkwood, 1949 Kirkwood and Auer, 1951 Kirkwood and Plock, 1956 Riseman and Kirkwood, 1956) for rodlike particles. The equivalence of the three theories has also been demonstrated by Saito and Sugita (1952). The general solution of Eq. (10) for the viscosity increment, v, can be expressed in the form... 

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