Universal Scaling Characteristics of Stress Overshoot in Startup Shear of Entangled Polymer Solutions

We have carried out conventional theological measurements to explore the well-known stress overshoot behavior in startup shear of eight entangled polybutadiene solutions. In the elastic deformation regime with (gamma)over dot tau(R)\u3e 1, we have identified universal scaling features associated with the stress maximum sigma(max) for samples of different levels of entanglements per chain ranging from 27, 40 to 64. Specifically, at the moment t(max) of the peak stress sigma(max) where the applied strain is gamma(max) = (gamma)over dott(max): (a) sigma(max) varies linearly with gamma(max), (b) sigma(max) scales with t(max) as sigma(max)similar to(t(max))-1/2. The combination of (a) and (b) yields a striking prediction that gamma(max) similar to(gamma)over dot(1/3). Remarkably, these scaling laws form master curves when the peak stress, strain rate, and peak time are all normalized with the crossover modulus G(c,) reciprocal Rouse time, and Rouse time tau(R), respectively. The dependence of sigma(max) on t(max) and gamma on (gamma)over dot is weaker in the crossover regime with (gamma)over dot tau(R) \u3c 1. Equally noteworthy is the emergence of a super-master curve for the normalized stress sigma-(t)/sigma(max) as a function of the normalized strain (gamma)over dott/gamma(max) at various applied rates in these solutions. The solution with only 13 entanglements per chain exhibits behavior deviating appreciably from the well entangled systems. Strain recovery experiments revealed irreversible deformation (i.e., flow) when the sample is sheared beyond the stress maximum (for (gamma)over dot tau(R)\u3e 1) or when sheared with (gamma)over dot tau(R)\u3c 1 for a period longer than the Rouse relaxation time tau(R). (C) 2008 The Society of Rheology

Steady State Measurements in Stress Plateau Region of Entangled Polymer Solutions: Controlled-Rate and Controlled-Stress Modes

Despite decades of efforts, reliable measurements of nonlinear flow behavior of well-entangled polymers in continuous shear have been challenging to obtain. The present work attempts to accomplish three important tasks: (A) overcome this challenge by adopting a strategy of decoupling theological measurements from the outer meniscus region in a cone-partitioned plate (C/PP) setup; (B) determine whether well-entangled solutions indeed undergo a flow transformation under creep that can be taken to phenomenologically define an entanglement-disentanglement transition (EDT); (C) provide the velocity profiles of such solutions undergoing either controlled-stress or controlled-rate shear by carrying out in situ particle-tracking velocimetric (PTV) measurements. Upon removing any influence of edge fracture and sample loss, we are able to reach steady state during continual shear and elucidate more reliably the nonlinear flow behavior of well entangled polymer solutions with little ambiguity. Three well-entangled solutions with Z=40 entanglements per chain exhibited overlapping continuous and monotonic flow curves both in controlled-rate and controlled-stress modes. The OPP based experiments qualitatively confirm the report by Tapadia and Wang [Macro molecules 37, 9083-9095 (2004)] that at a given applied shear stress the solution evolves over time from a state of high viscosity to that of substantially reduced viscosity, i.e., EDT occurs ubiquitously in absence of any edge effects. These results, made possible by a combination of C/PP and PTV, cause us to reevaluate the objectives of polymer rheology, and are expected to impact the future development in the field of rheometry for entangled polymers and other viscoelastic materials. (C) 2008 The Society of Rheology

Large Amplitude Oscillatory Shear Behavior of Entangled Polymer Solutions: Particle Tracking Velocimetric Investigation

Large amplitude oscillatory shear (LAOS) has been employed widely to probe the nonlinear behavior of complex fluids. Typically, the system undergoing LAOS has been assumed to experience homogeneous shear in each cycle so that material functions can be introduced to analyze the nonlinear dependence of these functions on the amplitude and frequency. Using particle-tracking velocimetric technique, we have carried a more systematic investigation on four different entangled polybutadiene (PBD) solutions with the number of entanglements per chain Z=13, 27, 64 and 119, extending well beyond the initial observations of shear banding in entangled PBD solutions under LAOS [Tapadia , Phys. Rev. Lett. 96, 196001-4 (2006a)]. At strain amplitudes gamma(o)\u3e100% and frequencies higher than the overall chain relaxation rate, we observed, for the three samples with 27 or more entanglements per chain, the development of a thin liquid layer where severe chain disentanglement may have taken place. The thin liquid layer takes most of the imposed deformation, while a significant portion of the sample stays hardly deformed and remains presumably well entangled. When the applied gamma(o) was between 100% and 250%, this liquid layer developed only after some oscillation cycles. For gamma(o)\u3e300%, the disentangled layer formed in the first cycle, a phenomenon analogous to failure of solids under external deformation. The solution with the least entanglements of 13 per chain did not show visible inhomogeneous deformation under LAOS. (C) 2008 The Society of Rheology

New Theoretical Considerations in Polymer Rheology: Elastic Breakdown of Chain Entanglement Network

Recent experimental evidence has motivated us to present a set of new theoretical considerations and to provide a rationale for interpreting the intriguing flow phenomena observed in entangled polymer solutions and melts [P. Tapadia and S. Q. Wang, Phys. Rev. Lett. 96, 016001 (2006); 96, 196001 (2006); S. Q. Wang , ibid. 97, 187801 (2006)]. Three forces have been recognized to play important roles in controlling the response of a strained entanglement network. During flow, an intermolecular locking force f(iml) arises and causes conformational deformation in each load-bearing strand between entanglements. The chain deformation builds up a retractive force f(retract) within each strand. Chain entanglement prevails in quiescence because a given chain prefers to stay interpenetrating into other chains within its pervaded volume so as to enjoy maximum conformational entropy. Since each strand of length l(ent) has entropy equal to k(B)T, the disentanglement criterion is given by f(retract)\u3c f(ent)similar to k(B)T/l(ent) in the case of interrupted deformation. This condition identifies f(ent) as a cohesive force. Imbalance among these forces causes elastic breakdown of the entanglement network. For example, an entangled polymer yields during continuous deformation when the declining f(iml) cannot sustain the elevated f(retract). This opposite trend of the two forces is at the core of the physics governing a cohesive breakdown at the yield point (i.e., the stress overshoot) in startup flow. Identifying the yield point as the point of force imbalance, we can also rationalize the recently observed striking scaling behavior associated with the yield point in continuous deformation of both shear and extension. (c) 2007 American Institute of Physics

Nonquiescent Relaxation in Entangled Polymer Liquids After Step Shear

Large step shear experiments revealed through particle tracking velocimetry that entangled polymeric liquids display either internal macroscopic movements upon shear cessation or rupturelike behavior during shear. Visible inhomogeneous motions were detected in five samples with the number of entanglements per chain ranging from 20 to 130 at amplitudes of step strain as low as 135%

Meta‐Analysis of Genome‐wide Linkage Studies in BMI and Obesity

Objective: The objective was to provide an overall assessment of genetic linkage data of BMI and BMI‐defined obesity using a nonparametric genome scan meta‐analysis. Research Methods and Procedures: We identified 37 published studies containing data on over 31,000 individuals from more than >10,000 families and obtained genome‐wide logarithm of the odds (LOD) scores, non‐parametric linkage (NPL) scores, or maximum likelihood scores (MLS). BMI was analyzed in a pooled set of all studies, as a subgroup of 10 studies that used BMI‐defined obesity, and for subgroups ascertained through type 2 diabetes, hypertension, or subjects of European ancestry. Results: Bins at chromosome 13q13.2‐ q33.1, 12q23‐q24.3 achieved suggestive evidence of linkage to BMI in the pooled analysis and samples ascertained for hypertension. Nominal evidence of linkage to these regions and suggestive evidence for 11q13.3‐22.3 were also observed for BMI‐defined obesity. The FTO obesity gene locus at 16q12.2 also showed nominal evidence for linkage. However, overall distribution of summed rank p values <0.05 is not different from that expected by chance. The strongest evidence was obtained in the families ascertained for hypertension at 9q31.1‐qter and 12p11.21‐q23 (p < 0.01). Conclusion: Despite having substantial statistical power, we did not unequivocally implicate specific loci for BMI or obesity. This may be because genes influencing adiposity are of very small effect, with substantial genetic heterogeneity and variable dependence on environmental factors. However, the observation that the FTO gene maps to one of the highest ranking bins for obesity is interesting and, while not a validation of this approach, indicates that other potential loci identified in this study should be investigated further.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/93663/1/oby.2007.269.pd