Effect of Branching

This behavior can be understood qualitatively in ter as of the tube model for topological constraints, as pointed out by de Gennes the presence of a branch strongly inhibits the reptation of a molecule along its contour, and motions must be accomplished by tube reorganization. The critical molecular weight for onset of this behavior would be expected to depend on the branch length i.e.. 

Logarithmic plot of steady-flow viscosity at 379° K against weight-average molecular weight for polybutadienes circles, linear squares, three-arm star triangles, four-arm star. (Kraus and Gruver. ) Reproduced, by permission, from the Journal of Polymer Science. 

M/f Me- An approximate theory for the viscosity enhancement due to branching has been presented by Graessley. gome cases, the viscosity of a polymer of very high molecular weight has been observed to be infinite (at small stresses), despite the absence of a cross-linked network as evidenced by complete solubility this behavior is probably due to extensive branching which completely inhibits the ability of a molecule to escape from its constraints. 

The onset of non-Newtonian flow occurs at a lower shear rate for branched than for linear polymers of the same molecular weight,so that at high shear rates the apparent viscosity jj may be lower for a branched polymer even when M fMc-This corresponds to a relatively large value for the characteristic time r,. 

It has been observed by Graessley that equation 21, and presumably also equation 20, holds also for branched polymers. Since both jjo and are enhanced by branching when the branches are long enough to entangle, it follows that the terminal relaxation time ti is greatly increased, corresponding to the increase in Tq which is apparent in the onset of non-Newtonian viscosity. 

In order to parameterize the data into a descriptive model, the combined data sets of viscosity and shear rate relationship for linear and linear-branched PLA are fitted to the Carreau—Yasuda model. The form of the model used is given by (Lehermeier and Dorgan 2001)  

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Comparing Eqs. (2.68) and (2.70) suggests that the effect of branching on t might be an exponential increase with the length of the side chain, provided that the entanglement mechanism is operative for both the branched and unbranched samples being compared ... 

Criticize or defend the following proposition In dilute solutions, branching affects viscosity only inasmuch as the branched molecule has a more compact shape. At higher concentrations, the effect of branching is closer to a bulk effect. 

The effect of branching is to increase the number of chain ends and, therefore, free volume, which decreases Tg. Conversely, crosslinking ties together separate molecules, decreases the number of loose ends, and raises Tg. Copolymers show different effects on T, depending on the microstructure... 

As is the case in the polyolefins, the polymethacrylates with branched side chains have higher softening points and are harder than their unbranched isomers. The effect of branching of Vicat Softening point is shown in Table 75.5.> ... 

Two types of well defined branched polymers are acessible anionically star-shaped polymers and comb-like polymers87 88). Such macromolecules are used to investigate the effect of branching on the properties, 4n solution as well as in the the bulk. Starshaped macromolecules contain a known number of identical chains which are linked at one end to a central nodule. The size of the latter should be small with respect to the overall molecular dimensions. Comb-like polymers comprise a linear backbone of given length fitted with a known number of randomly distributed branches of well defined size. They are similar to graft copolymers, except that backbone and branches are of identical chemical nature and do not exhibit repulsions. 

On the basis of the analyses carried out it can be maintained that the presence of branching or an aliphatic cycle increases AIT. The analysis does not allow differentiation between the effects of branching or cyclization. The AIT averages of the linear, branched and cyclic compounds are respectively 364 10°C, 437 17 C and424 irc. 

Branching in the polymer chain affects the relationship between retention and molecular weight.83 Universal calibration has been used with some success in branched polymers, but there are also pitfalls. Viscosimetry84-91 and other instrumental methods have proved to be useful. A computer simulation of the effects of branching on hydrodynamic volume and the detailed effects observable in GPC is available in the literature.92 93 In copolymer analysis, retention may be different for block and random copolymers, so universal calibration may be difficult. However, a UV-VIS detector, followed by a low-angle light-scattering (LALLS) detector and a differential... 

Figure 2 Effect of branch frequency on glucan conformation. Conformational characterization of glucans was carried out as described in the experimental section. Curdlan is a linear p(l-3)linked glucan Yeast glucan has a 30% P(l-6) branch frequency and PGG-R glucan has a 50% p(l-6) branch frequency. The Congo Red-single/triple helix complex absorption maxima are indicated.

Allylic trifluoromethyl groups that are of the type CF3CR=C appear at higher field than those of the CF3CH=C type, which is consistent with our knowledge of the effect of branching on chemical shift (Scheme 5.34). 

Figure 17 Effect of branching on the secondary nucleation and linear growth rates from the work of Lambert and Phillips [58]. The effect of branching on the Regime l-ll transition can also be seen. Reprinted with permission from Lambert and Phillips [58]. Copyright 1994, American Chemical Society.

Table 6 Schematic representation of the effects of branching and molecular weight on the crystallization kinetics and the appearance of the Regimes in crystallization...

The qualitative agreement between theory and experiment is very good.24 The DE approach can be used to provide qualitative information on the effects of branching. In order for a simple unbranched polymer to relax an applied strain we have seen there are two relaxation processes, a... 

G. Bellucci, C. Chiappe, F. Marioni, M. Benetti, Regio- and Enantioselectivity of the Cytosolic Epoxide Hydrolase-Catalysed Hydrolysis of Racemic Monosubstituted Alkyloxiranes ,./. Chem. Soc., Perkin Trans. 1 1991, 361 - 363 G. Bellucci, C. Chiappe, L. Conti, F. Marioni, G. Pierini, Substrate Enantioselection in the Microsomal Epoxide Hydrolase Catalyzed Hydrolysis of Monosubstituted Oxiranes. Effects of Branching of Alkyl Chains ,./. Org. Chem. 1989, 54, 5978 - 5983. 

These differences are of special value for an estimation of the effects of branching. 

Generalized ratios of the four differently defined radii can be written. By this manipulation the molar mass dependence is widely eliminated, and the effects of branching becomes more evident. See Table 2. 

In earlier experiments the effect of branching on the second virial coefficient was not seriously considered because the accuracy of measurements were not sufficient at that time. With the refinements of modern instruments a much higher precision has now been achieved. Thus A2 can also now be measured with good accuracy and compared with theoretical expectations. The second virial coefficient results from the total volume exclusion of two macromolecules in contact [3,81]. Furthermore, this total excluded volume of a macromolecule can be expressed in terms of the excluded volume of the individual monomeric units. In the limit of good solvent behavior this concept leads to the expression [6,27] as shown in Eq. (24) ... 

The final chapter develops the most modern insights in the relation between the rheological properties and the large scale architecture of polymers. Indeed, the largest effects of branching are encountered in their melt relaxation properties. In the absence of reptation, which dominates relaxation processes in Hnear polymers, a rich variety of other relaxation processes becomes apparent. The control ot the melt properties of polymers by means of their long-chain branch architecture will continue to lead to new industrial applications. 

Effects of Branching and Cross-Linking on Poiymer Properties... 

Antec 96. Volume II. Conference proceedings. Indianapolis, 5th-10th May 1996, p.1941-7. 012 EFFECT OF BRANCHED STRUCTURE ON THE CELL MORPHOLOGY OF EXTRUDED POLYPROPYLENE FOAMS. I. CELL NUCLEATION... 

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