Abstract 
There is an intimate relationship between the molecular structure of industrial
polymers, their rheological properties and their final processing and mechanical properties.
The tube model of Doi, Edwards and de Gennes (Doi and Edwards, 1986; de Gennes, 1971)
enables a molecular understanding of this relationship. The linear rheology data of linear and
star polymers can be quantitatively predicted by adaptations of the original tube model. All
parameters can be determined selfconsistently from the chemistry except for the dilution
exponent α and friction parameter p2 whose exact values are still being debated (van
Ruymbeke et al., 2012). However, the inherent problems of the tube model theory arise with
predictions of complex branched structures and with predictions of these polymers in complex
nonlinear shear and extensional flows. One of the reasons for this is due to the uncertainty
related to relaxation mechanisms such as constraint release. Moreover, it is also a problem of
obtaining welldefined mondisperse branched polymers, accurate characterization of the
branching structure and developing reliable nonlinear flow experiments where experimental
artificats are avoided. This is the exact goal of this work, to combine welldefined anionic
synthesized polymers, stateoftheart characterization tools such as TGIC and systematic
rheological studies in both the linear and nonlinear regime in order to validate and improve
existing current tube model theories.
More specifically, our study focuses on the determination of the physical origin of
chain stretch in complex branched polymers. We use the Sentmanat Extensional Rheometer
fixed to a strain controlled rheometer to perform uniaxial extensional rheology. Uniaxial
extensional rheology is difficult to measure in experimental setups but is a crucial experiment
for introducing chain stretch. We investigate three types of architecture from order of
branching complexity: linear, H, comb polymers. The uniaxial extensional rheology of linear
polymers is highly rate dependent and the onset rate of experimental strain hardening (the
macroscopic consequence of chain stretch) is equivalent to the theoretical prediction of the
inverse Rouse time. Moreover, even linear polymers will stretch considerably under high
deformations until they reach finite extensibility. The molecular dynamic picture becomes
more complicated when introducing two or more branch points and two or more relaxation
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times. We study H polymers, which have been anionically synthesized by (Roovers, 1984)
and characterized recently by stateoftheart TGIC. We discover that due to the hierarchical
relaxation scheme of the H polymer, there is a greater degree of chain stretch and an earlier
onset rate. We determine that as the experimental extensional rate is increased, the chain
stretch is increased until it is no longer entropically favourable to do so, and branch point
withdrawal occurs. Contrary to linear polymers, the maximum stretch is independent of stretch
rate and only depends on architecture such that λ=q where q is the number of arms on each
branch point. This can be explained by the simple rationale that the backbone segment is not
free to relax until the branches have full retracted (McLeish and Larson, 1998). When
increasing the number of entanglements of the arms and backbone of the H polymer, the effect
of chain stretch is magnified. Moreover, we study welldefined comb polymers (Roovers,
1979) with long molar mass of backbone Mb and rather short arm ends. When doubling the
number of entanglements of the arms systematically while keeping the Mb constant, the onset
of chain stretch occurs at earlier rates. This can be rationalized by accounting for the effect of
dynamic tube dilution and extra drag from the arms that results in an effectively slower stretch
relaxation time. We modify the original differential pompom model of (McLeish and Larson,
1998) with the recently added modification to include drag strain coupling (Blackwell et al.,
2000) by specifying the coupling of stretch between adjacent backbone segments. The model
is validated successfully by comparison with a wide variety of combs (with different
molecular features) and a wide range of extensional rates. At high rates, the maximum stretch
condition is reached and branch point withdrawal occurs, when arms are first oriented and
then withdrawn into the stretched backbone tube segments, first from the free ends and then
gradually progressing towards the center. By studying the internal dynamics of the backbone
segments, we discover that at this maximum stretch condition, the central backbone segment
has a stretch factor equal to λ=ns/2 and that the stretch factor decreases by a value of 1 at each
adjacent backbone segment. At these high rates, the addition of drag strain coupling
smoothens the transition to maximum stretch and allows for better predictions.
Moreover, our study focuses on the effects of the environment on the reptation and
fluctuations of model H and comb polymers. By systematically varying the length of the
linear chains, we study the acceleration factor related to the arm and backbone relaxation
times. The acceleration factor has a strong dependence on the length of the linear chains. The
shorter the chains, or the larger the difference between the relaxation times of the linear
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matrix and the branched polymer, the more enhanced is the acceleration factor. For the study
of bidisperse linear blends, there is the StruglinksyGraessley parameter which is often
invoked to explain the transition from static dilution of the short linear chains in a dilated tube
to reptation in a skinny tube. There is no similar interpretation for blends of branched
polymers and linear chains. We model the SAOS data using the Time Marching Algorithm
by estimating a priori whether the linear polymer would be taken as a theta solvent or whether
the reptation occurs in a skinny tube. The criterion for this estimation is based on the
relaxation timescale separation between the linear matrix and the H or comb. In addition, the
BOB model is used to model the SAOS data of the mixtures and is shown to match the data
moderately well. The second diluted plateau modulus is overpredicted, indicating that the full
dilution is not taken into account.
