network modulus
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2020 ◽  
Vol 40 (9) ◽  
pp. 743-752
Author(s):  
Dietrich Gloger ◽  
Elisabeth Rossegger ◽  
Markus Gahleitner ◽  
Christina Wagner

AbstractProcessing isotactic polypropylene (iPP) from cast film into biaxially oriented polypropylene (BOPP) involves plastic drawing of a semi-crystalline morphology in the melting range of iPP, where the crystal phase is reduced and the polymer has high mobility. The literature claims that plastic drawing in general and at elevated temperatures in particular depends predominantly on the structure of the amorphous entanglement network. We investigated this aspect using laboratory-scale biaxial drawing experiments. Three iPP homopolymer types differing in chain isotacticity and molecular weight distribution were extruded into 200-μm-thick primary sheets using 10 different extrusion settings. The sheets were biaxially drawn on a laboratory stretcher at 157°C and 160°C, recording the respective stress-strain curves. These curves were evaluated according to a rubber elasticity model to obtain the network modulus, GN, of the entanglement network. The effects of iPP type, the extrusion parameters, the resulting cast film properties, and the draw temperature on GN are discussed.


Polymers ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 233 ◽  
Author(s):  
Yasser Zare ◽  
Kyong Yop Rhee

In this paper, we consider the interphase regions surrounding the dispersed and networked carbon nanotubes (CNT) to develop and simplify the expanded Takayanagi model for tensile modulus of polymer CNT nanocomposites (PCNT). The moduli and volume fractions of dispersed and networked CNT and the surrounding interphase regions are considered. Since the modulus of interphase region around the dispersed CNT insignificantly changes the modulus of nanocomposites, this parameter is removed from the developed model. The developed model shows acceptable agreement with the experimental results of several samples. “ER” as nanocomposite modulus per the modulus of neat matrix changes from 1.4 to 7.7 at dissimilar levels of “f” (CNT fraction in the network) and network modulus. Moreover, the lowest relative modulus of 2.2 is observed at the smallest levels of interphase volume fraction ( ϕ i < 0.017), while the highest “ ϕ i ” as 0.07 obtains the highest relative modulus of 11.8. Also, the variation of CNT size (radius and length) significantly changes the relative modulus from 2 to 20.


2007 ◽  
Vol 555 ◽  
pp. 491-496 ◽  
Author(s):  
J. Budinski-Simendić ◽  
M. Ilavsky ◽  
Jan Šomvarsky ◽  
M. Špírková ◽  
Lj. Korugić-Karasz ◽  
...  

The aim of this contribution was to study the rubber elasticity of dry and swollen networks obtained by cyclotrimerization crosslinking reaction of isocyanate groups located at a linear telechelic network precursor. Telechelic diisocyanates were prepared in the undiluted state from 2,4-tolylene diisocyanate, α,ω,dihydroxypoly(oxypropylenes) and different contents of the monool component 2-(2-metoxyetoxy) ethanol. The network synthesis proceeded in a bulk. Detailed network topology was calculated by the theory of branching processes. The equilibrium swelling degree of prepared samples was related to the parameters, which are experimentally accessible for a network arising from an end-linking process using the Flory-Rehner theory. The experimental data for network modulus were compared with those arising from the "affine" model, "phantom’ model" and the model of constrained junctions.


Author(s):  
Burak Erman ◽  
James E. Mark

The classical theories of rubber elasticity presented in chapter 2 are based on a hypothetical chain which may pass freely through its neighbors as well as through itself. In a real chain, however, the volume of a segment is excluded to other segments belonging either to the same chain or to others in the network. Consequently, the uncrossability of chain contours by those occupying the same volume becomes an important factor. This chapter and the following one describe theoretical models treating departures from phantom-like behavior arising from the effect of entanglements, which result from this uncrossability of network chains. The chains in the un-cross-linked bulk polymer are highly entangled. These entanglements are permanently fixed once the chains are joined during formation of the network. The degree of entanglement, or degree of interpenetration, in a network is proportional to the number of chains sharing the volume occupied by a given chain. This is quite important, since the observed differences between experimental results on real networks and predictions of the phantom network theory may frequently be attributed to the effects of entanglements. The decrease in network modulus with increasing tensile strain or swelling is the best-known effect arising from deformation-dependent contributions from entanglements. The constrained-junction model presented in this chapter and the slip-link model presented in chapter 4 are both based on the postulate that, upon stretching, the space available to a chain along the direction of stretch is increased, thus resulting in an increase in the freedom of the chain to fluctuate. Similarly, swelling with a suitable diluent separates the chains from one another, decreasing their correlations with neighboring chains. Experimental data presented in figure 3.1 show that the modulus of a network does indeed decrease with both swelling and elongation, finally becoming independent of deformation, as should be the case for the modulus of a phantom network. Rigorous derivation of the modulus of a network from the elastic free energy for this case will be given in chapter 5. The starting point of the constrained-junction model presented in this chapter is the elastic free energy.


Polymer ◽  
1994 ◽  
Vol 35 (21) ◽  
pp. 4521-4526 ◽  
Author(s):  
S. Dutton ◽  
H. Rolfes ◽  
R.F.T. Stepto

1994 ◽  
Vol 27 (12) ◽  
pp. 3191-3198 ◽  
Author(s):  
Sergei P. Obukhov ◽  
Michael Rubinstein ◽  
Ralph H. Colby
Keyword(s):  

1994 ◽  
Vol 2 (3-4) ◽  
pp. 149-157 ◽  
Author(s):  
H. Rolfes ◽  
R.F.T. Stepto
Keyword(s):  

Polymer ◽  
1992 ◽  
Vol 33 (6) ◽  
pp. 1255-1260 ◽  
Author(s):  
Paolo Lomellini
Keyword(s):  

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