Linear polymers curves

Fig. 19. Generalized modulus—temperature curves for polymeric materials showing the high modulus glassy state, glass-transition regions for cured and uncured polymers, plateau regions for cross-linked polymers, and the dropoff in modulus for a linear polymer.

Synthetic polymers TSK-GEL GMPWxi TSK-GEL GSOOOPWxl G3000PWxl Large pore size, low adsorption, linear calibration curve... 

Ketten-glied. n. link (or member) of a chain, -isomerie, /. chain isomerism, -kokken, m.pl. streptococci, -linie,/. catenary (curve), -moldktil, n. chain molecule, linear molecule, -polymer, n. chain polymer, linear polymer, -rad, n. sprocket wheel, -reaktion, /. chain reaction, -trieb, m. chain drive. 

The shape of the pore size distribution curve strongly depends on the molecular weight distribution of the linear polymer. The narrowest pore size distributions were obtained with the linear polymers having the lowest polydisper-sity indices. 

Distribution curves calculated for several values of / are shown in Fig. 56. Values of p have been adjusted to give the same number average (see Eq. 23), which also locates the maxima in the curves very nearly at the same abscissa value. The sharpening of the curves with increase in / is evident. The curve for /= 1, corresponding to the most probable distribution, is included for comparison. Even for /=2, which represents the linear polymer prepared by condensing... 

The log Mn vs. count calibration curve is shown on Figure 5. This is a fairly linear calibration curve, but it covers only a relatively narrow molecular weight range of 145,000 to 317,000 g/mole. Although we have sought to prepare higher MW samples for this purpose, we inadvertently obtained polymers with bimodal MWD s and did not use them for this calibration. 

EXAFS (Extended X-ray Absorption Fine Structure) measurements using synchrotron radiation have been successfully applied to the determination of structural details of SCO systems and have been particularly useful when it has not been possible to obtain suitable crystals for X-ray diffraction studies. Perhaps the most significant application has been in elucidating important aspects of the structure of the iron(II) SCO linear polymers derived from 1,2,4-triazoles [56]. EXAFS has also been applied to probe the dimensions of LIESST-generated metastable high spin states [57]. It has even been used to generate a spin transition curve from multi-temperature measurements [58]. 

A detailed investigation of the polymerization of this monomer in a series of solvents has shown, however, that the auto-accelerated character of the reaction is not related to the precipitation of the polymer. Thus, linear conversion curves and atactic polymers are obtained if the monomer is diluted in such nonassociating solvents as toluene, n-hexane, carbon tetrachloride and chloroform, in spite of the precipitation of the polymer, whereas, both auto-acceleration and syndiotacticity persist for fairly high dilutions in water, methanol and dioxane even under conditions where the reaction medium turns homogeneous (4). 

While the calibration curve is strictly valid only for the Linear PIBs, it was assumed that it provides sufficiently accurate Mjj information for three-arm star products as well. This assumption was corroborated by determining the Mns of select liquid three-arm PIBs by GPC and VP0 The Mns were within experimental error. Evidently PIB calibration curves prepared with linear polymers can also be used for Mn determination of three-arm products also in the low molecular weight (<10,000) range. H NMR spectra were taken by a Varian T-60 Spectrometer using concentrated (v20% by weight) carbon tetrachloride solutions and TMS standard. 

Another very special feature of these polymers is the relationship between molecular weight and melt viscosity. For linear polymers, the increase in melt viscosity with molecular weight is linear with a transition to a 3.4 power law when the molecular weight reaches the critical mass for entanglements, M. For hyperbranched polymers, the increase in viscosity follows a different curve it is less pronounced and levels off at higher molecular weights [117] (Fig. 11). 

Fig.3. G (co) and G"(co) for monodisperse linear polymers of PI, PB and PS. The curves have been shifted so that the plateau moduli and terminal times coincide. The dashed line indicates the Doi-Edwards prediction for G"((o) in the absence of path-length fluctuations...

Fig. 17. Damping functions in shear from the tube model for linear polymers (lowest curve) and various branched architectures. In the cases of comb and tree, the lower curves give the case of the structure with four levels of branching, the upper the limit of large structures hatched area covers published results on LDPE...

This theory clearly predicts that the shape of the polymer length distribution curve determines the shape of the time course of depolymerization. For example Kristofferson et al. (1980) were able to show that apparent first-order depolymerization kinetics arise from length distributions which are nearly exponential. It should also be noted that the above theory helps one to gain a better feeling for the time course of cytoskeleton or mitotic apparatus disassembly upon cooling cells to temperatures which destabilize microtubules and effect unidirectional depolymerization. Likewise, the linear depolymerization kinetic model could be applied to the disassembly of bacterial flagella, muscle and nonmuscle F-actin, tobacco mosaic virus, hemoglobin S fibers, and other linear polymers to elucidate important rate parameters and to test the sufficiency of the end-wise depolymerization assumption in such cases. 

In several cases the melt viscosity of a series of lightly-branched polymers has been determined as a function of MW, and compared with that of linear polymers, and it has been found or may be deduced from the published data that there is a cross-over molecular weight, below which the branched polymer is less viscous, but above which it more viscous, than the linear polymer of equal MW. This behaviour is observed with some comb-shaped polystyrenes (35) and poly(vinyl acetate)s (59, 89), star polybutadienes (57, 58, 123), and randomly-branched polyethylenes (56,61). Jackson has found (141) that if the ratio ZJZC of the number of chain atoms at the cross-over point, Zx, to the number at the kink in the log 0 — logM curve, Zc, [as given in Ref. (52)], is plotted against nb, the number of branches, a reasonable straight line is obtained, as in Fig. 5.1. 

The value of the MW exponent for the low shear-rate melt viscosity, usually accepted as 3.4—3.5 for linear polymers, has been called in question for PE. Schreiber and Bagley (164) reported a value of 4.22 for linear PE Porter and Johnson (165) had earlier reported values up to 8 for LDPE. For branched polymers an effect of this kind could be due to the effect mentioned in Section 5, in which a cross-over point is found on a log-log plot of viscosity vs. MW when linear and slightly branched polymers are compared, since the curve for the branched polymers must be steeper than that for the linear ones near the cross-over point. 

Mendelson and co-workers (56) have studied the extrapolated zero shear-rate melt viscosities of linear HDPE and branched LDPE found that while the LDPE fractions could have either lower or higher viscosities than linear polymers of the same MW, results for the LDPE fractions could be reduced to the same curve by taking not Mw but gMw as the independent variable, where... 

Figure 7.5—Determination of molecular mass. The use of a calibration curve made with standards of known molecular masses. It should be noted that the calibration curve is linear over a wide range of masses due to the use of a mixture of stationary phases. (Reproduced by permission of Polymer Lab.) The bottom right figure shows the geometry assumed by a linear polymer in solution (figure from PSS).

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