Session D45: Polymer Melts & Solutions II

Visco-elasticity of bottlebrush polymer melts: Pushing the lower limit of the entanglement modulus

Without swelling in a solvent, it is challenging to obtain materials with a modulus below \textit{ca}.10$^{5}$ Pa, which is dictated by chain entanglements. Here we analyze the densely grafted molecular brush architecture to create solvent-free neat polymer melts and elastomers with plateau moduli down to hundred Pa. Such materials are theorized to behave as linear chains with rescaled dimensions of the entanglement strand due to the increase in both width and persistence length of polymer bottlebrushes. This simple rescaling leads to a prediction that entanglement modulus decreases with the degree of polymerization (DP) of the sidechains to the -1.5 power. Experimental evidence gives a remarkably close power of -1.38 $\pm$ 0.05 with moduli in the hundreds of Pascals for long sidechains with DP$\cong $100. The experimental data have been fit using a combination of the Rouse relaxation and double reputation models lending further evidence that bottlebrush polymer behave as linear polymers with large entanglement weights and longer persistence lengths. With the addition of crystallizable block it will be possible to control the crosslinking density and design ultrasoft shapememory materials for use in mechanically sensitive applications.   

First-Passage Time in Entangled Star Polymers Melts

For a single star polymer in a melt of extremely long linear chains, the stress of star polymer relaxes by arm-retraction in which the star arms explore new configurations by withdrawing along their tubes and stretching out towards a new direction. Pearson and Helfand proposed that the arm in the tube can be represented as a harmonic spring with an applied thermal tension such that the arm-end feels an entropic force if it fluctuates away from its equilibrium position. We have investigated the first-passage(FP) time of the destruction of tube segments by representing the arm as a one-dimensional Rouse chain. In contrast, we found that the disengagement of a tube segment is getting faster with more Rouse modes added in, which means the FP problem has to be modelled by a multi-dimensional Kramer's problem. We found a new way of solving the multi-dimensional FP problem by projecting the problem along the most probable trajectory termed ``minimal action trajectory'' and correcting it by entropy term. In addition, we performed direct and forward-flux simulations of Rouse chains of different lengths. A good agreement between the analytical calculations and simulations was achieved for both discrete and continuous Rouse chains.   

Simplified tube models for entangled supramolecular polymers

This presentation describes current efforts investigating non-linear rheology of entangled, supramolecular polymeric materials. We describe two recently developed models: 1) We have developed a simplified model for the rheology of entangled telechelic star polymers. This is based on a pre-averaged orientation tensor, a stretch equation, and stretch-dependant probability of detachment of the sticker. In both linear and non-linear regimes, we produce maps of the whole parameter space, indicating the parameter values for which qualitative changes in response to flow are predicted. Results in the linear rheology regime are consistent with previous more detailed models (van Ruymbeke et al. Macromolecules, 43, 4401-4411, 2010) and are in qualitative agreement with experimental data. 2) Using the same modelling framework, we investigate entangled linear polymers with stickers along the backbone. We use a set of coupled equations to describe the stretch between each stickers, and use equations similar to our star model for attachment/detachment of the sticky groups. This model is applicable to industrial polymers such as entangled thermoplastic elasomers, or functionalised model linear polymers.   

Fingerprinting the Non-linear Response of Three Arm Star Polystyrene by Mechanical Spectral Hole Burning, Lissajous-Bowditch Loops, and Fourier Transform Rheology

It is well known that large amplitude oscillatory shear (LAOS) has become a powerful tool to fingerprint the nonlinear response of polymers and other complex fluids. In a recent work, Nabila and McKenna [J. Rheol. 58(1), 43-62, 2014] used the mechanical spectral hole burning (MSHB) which was developed in our labs, along with Lissajous-Bowditch (LB) curves and Fourier transform rheology (FTR) methods to characterize the nonlinearity of linear polystyrene solutions. They observed a linear relationship between the horizontal hole intensity and the square of pump strain amplitude. The similar quadratic dependence was found for the third harmonics from FTR. However, the origins are not same for these two signatures. In the current work, the nonlinearity of polymers with more complicated molecular structure, such as three arm star polystyrene, will be studied by these three methods. The concentration dependence of the fingerprinting will also be discussed.   

Breakup dynamics of Non-Newtonian droplets in microfluidic devices: From necking to Rupture

It has been shown that addition of small amounts of polymers to a Newtonian fluid can exhibit non-Newtonian behavior in extensional flows. For instance, polymeric fluids produce strong filament thinning called necking when subjected to extensional flows. Coiled polymeric chains are expected to be stretched in this exponential necking regime. These stretched long chains induce elastic stress that resist the capillary forces trying to break the filament apart. Still, the molecular picture behind filament thinning and rupture of polymeric threads in extensional flow conditions is unknown. In this work, we study breakup and filament thinning of micro-droplets containing polymeric suspensions by using micro-fluidic devices. To reveal the underlying mechanism of thinning and rupture of polymeric filament, conformation of DNA suspensions were visualized in different flow conditions. Experiments have been done on both dilute and concentrated polymeric solutions. These new results allow us to pinpoint the molecular mechanism behind filament thinning and flow instabilities in strong extensional flows of polymeric fluids.\\[4pt] [1] Y. Wang, P. E. Boukany, S.Q. Wang, X. Wang, Physical review letters 99 (23), 237801, (2008)\\[0pt] [2] P. E. Boukany, et al., ``Molecular imaging of slip in entangled DNA solution'' Physical review letters 105 (2), 027802 (2010).   

Polymer relaxation and stretching dynamics in semi-dilute DNA solutions: a single molecule study

In this work, we study polymer relaxation and stretching dynamics in semi-dilute DNA solutions using single molecule techniques. Using this approach, we uncover a unique scaling relation for longest polymer relaxation time that falls in the crossover regime described by semi-flexible polymer solutions, which is distinct from truly flexible polymer chains. In addition, we performed a series of step-strain experiments on single polymers in semi-dilute solutions in planar extensional flow using an automated microfluidic trap. In this way, we are able to precisely control the flow strength and the amount of strain applied to single polymer chains, thereby enabling direct observation of the full stretching and relaxation process in semi-dilute solutions during transient start-up and flow cessation. Interestingly, we observe polymer individualism in the conformation of single chains in semi-dilute solutions, which to our knowledge has not yet been observed. In addition, we observe the relaxation data can be explained by a multi-exponential decay process after flow cessation in semi-dilute solutions. Overall, our work reports key advance in non-dilute polymer systems from a molecular perspective via direct observation of dynamics in strong flows.   

Optical Nanodozers

Experiment, simulation and scaling analytics are converging on a comprehensive picture regarding the equilibrium behaviour of nanochannel confined semiflexible, self-avoiding chains. Yet, strongly non-equilibrium behaviour of confined polymers is largely unexplored from either an experimental or theoretical point of view. Combining optical trapping and nanofluidics, we have developed a ``nanodozer'' assay for quantifying confined polymer dynamics. An optical trap is used to slide a nanosphere at a fixed velocity along a nanochannel. The trapped bead acts as a permeable gasket, letting fluid escape but preventing the polymer from passing. As the sliding bead comes in contact with a nanochannel extended DNA, the molecule is dynamically compressed, undergoing transient dynamics characterized by a traveling concentration ``shockwave'' before reaching a final steady state with a ramp-like concentration profile. Remarkably, these strongly non-equilibrium measurements can be quantified via a simple nonlinear convective-diffusion formalism and yield insights into the local blob statistics, allowing us to conclude that the compressed nanochannel confined chain exhibits mean-field behaviour.   

Shear and normal forces in charged polymer brushes

We present the results of molecular dynamics simulations of steady shear between a pair of opposing charged polymer brushes in the osmotic-brush regime and compare the results with predictions of scaling models. Using the monomer and counterion density profiles, we have verified different regimes in the diagram of states of compressed polyelectrolyte brushes predicted by the scaling model of Zhulina \textit{et al }[Macromolecules, 2014]. Our simulation results for the normal forces of compressed polyelectrolyte brushes are in excellent agreement with predictions of the scaling model. However, our results for the dependence of the shear forces on the separation between brushes are only in qualitative agreement with the predictions of the scaling model. The dependence of the interpenetration length on the separation of polyelectrolyte brushes exhibits a maximum instead of the plateau predicted by the scaling model for the partially interpenetrated brushes. Our simulation results confirm that our implicit solvent simulations of polyelectrolyte brushes that ignore hydrodynamics interaction are in agreement with the scaling predictions that include hydrodynamic interaction because of screening of hydrodynamic interaction and long range electrostatic interactions on the correlation length scale.   

A Molecular Mechanism of viscoelasticity in aligned polyethylene

The key observed property of aligned polyethylene is its viscoelastic behaviour, which is traditionally fitted with Maxwell models [1]. Although these empirical models are successful at reproducing the mechanical response of the material, they fail to capture the underlying molecular mechanisms that lead to the observed viscoelastic behaviour. We explain the observed viscoelastic behaviour in terms of the formation, interaction and movement of solitons, and relate these molecular mechanisms to the semi-crystalline microstructure of the material. Using Molecular Dynamics we demonstrate the following results: (a) The formation of solitons from interfaces between crystalline and amorphous regions (b) The transfer of tensile load between molecular chains (c) the pile-up of solitons in a molecular chain that allows the concentration of stress at particular points (d) The disassociation of solitons into $\pi$-twistons at 300K.\\[4pt] [1] H Van der Werff and AJ Pennings. Tensile deformation of high strength and high modulus polyethylene fibers. Colloid and polymer science, 269(8):747--763, 1991.   

Electrostatics effects on normal load capacity of two like-charge hydrogels

In mammalian joints, an effective lubrication mechanism is maintained under extremely high pressures due to charged polymeric structures coating the surfaces of the relatively moving tissues. Equally low frictional forces are also observed experimentally in the shear motion of polyelectrolyte gel and brush bilayers. The lubrication capabilities of these systems are attributed to either a polymer-free zone, separating the bilayers or hydration layers that can dissolve polymeric segments. Previous hypothesis have stated that the separation zone should decrease the polymer-polymer physical contact, and hence, result in only viscous friction of the liquid filling this layer. In this study, using extensive Molecular Dynamics simulations and analytical tools, we investigate the separation zone under compression at high electrostatic strengths. We show that Coulombic interactions significantly change the thickness of the separation zone as well as the normal pressure that a hydrogel bilayer can support upon strain-control deformations. We observe that under high pressures the separation zone completely disappears. As a result, the number of polymer-polymer contacts increases. We speculate that the frictional forces between polymer segments can reduce the efficiency of the lubrication   

Entangled Polymer-Nanocomposites: Dynamics and phase stability

Polymer nanocomposites (PNCs) prepared by incorporating nanoparticles (NPs) in polymer hosts, have been reported to exhibit unusual mechanical, dynamical, and glassy features when the particle size approaches the random coil dimensions of the host polymer, even at low NP content. By taking advantage of favorable enthalpic interactions between particle-tethered and high-molecular weight host polymer molecules, we show by means of small-angle X-ray scattering that it is possible to create model PNCs in which spherical NPs are uniformly dispersed in polymeric hosts. Using these materials as model systems for studying polymer dynamics, we find that even at low concentrations, NPs profoundly alter a host polymer's dynamics on all timescales. On short timescales, NPs slow-down fast segmental motions and lowers the glass transition temperature of the host. On intermediate timescales where entanglement and tube dynamics are typically observed in entangled melts, NPs hasten the onset of these effects, leading to an early transition to reptation behavior. On long timescales, NPs lead to an earlier than expected onset of tube escape. This latter behavior appears correlated with previous reports of viscosity reductions in entangled PNCs, but in reality would only be experimentally observable in systems where nanoparticles do not also slow-down segmental scale motions of their polymer host.   

Slip-spring model of entangled rod-coil block copolymers

Understanding the dynamics of rod-coil block copolymers is important for optimal design of functional nanostructured materials for organic electronics and biomaterials. Recently, we proposed a reptation theory of entangled rod-coil block copolymers, predicting the relaxation mechanisms of activated reptation and arm retraction that slow rod-coil dynamics relative to coil and rod homopolymers, respectively. In this work, we introduce a coarse-grained slip-spring model of rod-coil block copolymers to further explore these mechanisms. First, parameters of the coarse-grained model are tuned to match previous molecular dynamics simulation results for coils, rods, and block copolymers. For activated reptation, rod-coil copolymers are shown to disfavor configurations where the rod occupies curved portions of the entanglement tube of randomly varying curvature created by the coil ends. The effect of these barriers on diffusion is quantitatively captured by considering one-dimensional motion along an entanglement tube with a rough free energy potential. Finally, we analyze the crossover between the two mechanisms. The resulting dynamics from both mechanisms acting in combination is faster than from each one individually.   

Influence of Asymmetric Chain Dynamics on the Viscoelastic Response of Block Copolymers Near the Order-Disorder Transition

Composition fluctuations in the disordered state profoundly influence block copolymer phase behavior near the order-disorder transition. Although the first experimental evidence of composition fluctuations highlighted a rheological feature, a complete understanding of the influence of fluctuations on rheology has remained elusive. For example, a rheological fingerprint of fluctuations is absent in many reports in the literature for various diblock copolymer systems. Here, we present work elucidating how differences in the individual block-relaxation times of a block copolymer influence the ability to probe composition fluctuations using rheology. This work resolves a long-unanswered question pertaining to the ability to measure composition fluctuations, and aids in understanding low-frequency scaling for both the dynamic elastic and loss moduli.   

Hierarchical assembly of block copolymer micelles into reversible networks: MC simulations

The rapid development of nanoscience has considerably expanded the range of building blocks for complex self-assembled nanostructure formation, which show great potential for numerous advanced applications. We apply Monte Carlo simulations to gain understanding of molecular mechanism of self-assembly of nanostructures formed by diblock copolymer micelles interconnected by means of metal-ligand complexation. These systems exhibit interesting chemical and mechanical stimuli-responsive behavior and possess two levels of self-assembly: 1) self-assembly of diblock copolymers into micelles and 2) reversible inter-micelle bridging by coordination bonding between metal ions and ligands attached to the corona of nanoparticles, which is responsible for the network viscoelastic properties. Using MC simulations we investigate the effect of metal-ligand complexation on diblock-copolymer micelle formation and vice versa. We analyze the extent of intra- and inter-micelle loops and bridges formed by metal-ligand complexation in relation to the degree of crosslinking and elastic properties of the network. The effect of polymer concentration, hydrophilic block length, metal to oligomer ratio and type of complexation (2:1 or 3:1) on equilibrium properties of reversible networks will be discussed.