Some remarks on the dynamics of polymer melts

The Challenges Facing the Current Paradigm Describing Viscoelastic Interactions in Polymer Melts

Staudinger taught us that macromolecules were made up of covalently bonded monomer repeat units chaining up as polymer chains. This paradigm is not challenged in this paper. The main question raised in polymer physics remains: how do these long chains interact and move as a group when submitted to shear deformation at high temperature when they are viscous liquids? The current consensus is that we need to distinguish two cases: the deformation of "un-entangled chains" for macromolecules with molecular weight, M, smaller than Me, "the entanglement molecular weight", and the deformation of "entangled" chains for M > Me. The current paradigm stipulates that the properties of polymers derive from the statistical characteristics of the macromolecule itself, the designated statistical system that defines the thermodynamic state of the polymer. The current paradigm claims that the viscoelasticity of un-entangled melts is well described by the Rouse model and that the entanglement issues raised when M > Me, are well understood by the reptation model introduced by de Gennes and colleagues. Both models can be classified in the category of "chain dynamics statistics". In this paper, we examine in detail the failures and the current challenges facing the current paradigm of polymer rheology: the Rouse model for un-entangled melts, the reptation model for entangled melts, the time-temperature superposition principle, the strain-induced time dependence of viscosity, shear-refinement and sustained-orientation. The basic failure of the current paradigm and its inherent inability to fully describe the experimental reality is documented in this paper. In the discussion and conclusion sections of the paper, we suggest that a different solution to explain the viscoelasticity of polymer chains and of their "entanglement" is needed. This requires a change in paradigm to describe the dynamics of the interactions within the chains and across the chains. A brief description of our currently proposed open dissipative statistical approach, "the Grain-Field Statistics", is presented.

Nonlinear Extensional Rheology of Poly(n-alkyl methacrylate) Melts with a Fixed Number of Kuhn Segments and Entanglements per Chain

Molecular theories for dynamics of entangled polymers are based on both the number of Kuhn segments per entanglement N_e and the number of entanglements per chain N/N_e. Extensive studies have shown that, for polymer chains in the solutions or melts, linear viscoelasticity can be properly normalized, whereas the nonlinear extensional rheological properties cannot be normalized when N/N_e is kept the same. The failure of the latter normalization has been attributed to a difference in N_e. Nevertheless, nonlinear rheological studies are lacking for a suitable model system with fixed N_e and N/N_e. In this study, we identify poly(n-alkyl methacrylate)s with the number of carbons per alkyl group below seven as a model system. We find that the degree of the transient strain hardening during extensional flow strengthens with increasing the size of the alkyl group even when N_e and N/N_e are kept the same, which is attributable to the weaker friction reduction when the main backbones are more separated.

The combination of neutron spin echo and dielectric spectroscopy to examine tube dilation

The polymer dynamics in blends of long and short chains spans several decades in time and the understanding of the effect of the short chains on the relaxation mechanism of the long chains due to constraint release requires the combination of microscopic and macroscopic techniques. While the longtime dynamics can be accessed by mechanical or dielectric spectroscopy (DS), its relation to the microstructural details requires the application of theoretical models. In contrast, neutron spin echo (NSE) measures directly the dynamic structure factor reflecting the process of constraint removal at the molecular scale. Here the comparison of NSE and DS results in a model blend of short and long polyisoprene enables the exploration of the entire time regime showing that constraint release leads to a dilation of the confining tube. We show the description of the dynamic tube dilation using a simple model in which the time controlling the tube dilation for the long chain is the terminal time of the short chain.

Diffusion Spectrum of Polymer Melt Measured by Varying Magnetic Field Gradient Pulse Width in PGSE NMR

The translational motion of polymers is a complex process and has a big impact on polymer structure and chemical reactivity. The process can be described by the segment velocity autocorrelation function or its diffusion spectrum, which exhibit several characteristic features depending on the observational time scale—from the Brownian delta function on a large time scale, to complex details in a very short range. Several stepwise, more-complex models of translational dynamics thus exist—from the Rouse regime over reptation motion to a combination of reptation and tube-Rouse motion. Accordingly, different methods of measurement are applicable, from neutron scattering for very short times to optical methods for very long times. In the intermediate regime, nuclear magnetic resonance (NMR) is applicable—for microseconds, relaxometry, and for milliseconds, diffusometry. We used a variation of the established diffusometric method of pulsed gradient spin-echo NMR to measure the diffusion spectrum of a linear polyethylene melt by varying the gradient pulse width. We were able to determine the characteristic relaxation time of the first mode of the tube-Rouse motion. This result is a deviation from a Rouse model of polymer chain displacement at the crossover from a square-root to linear time dependence, indicating a new long-term diffusion regime in which the dynamics of the tube are also described by the Rouse model.

Stress relaxation in symmetric ring-linear polymer blends at low ring fractions

We combine linear viscoelastic measurements and modelling in order to explore the dynamics of blends of the same-molecular-weight ring and linear polymers in the regime of the low volume fraction (0.3 or lower) of the ring component. The stress relaxation modulus is affected by the constraint release (CR) of both rings and linear components due to the motion of linear chains. We develop a CR-based model of ring-linear blends that predicts the stress relaxation function in the low fraction regime of ring component in excellent agreement with experiments. Rings trapped by their entanglements with linear chains can only relax by linear-chain-induced constraint release, resulting in much slower relaxation of rings than of linear chains. The relative viscosity η ( ϕ R * ) / η L of the blend with respect to the linear melt viscosity η _L at ring overlap volume fraction ϕ R * increases proportionally to the square root of ring molecular weight M w , R . Our experimental results clearly demonstrate that it is possible to enhance the viscosity and simultaneously the structural relaxation time of linear polymer melts by adding a small fraction of ring polymers. These results not only provide fundamental insights into the physics of the CR process but also suggest ways to fine-tune the flow properties of linear polymers by means of adding rings.

Clustering of Entanglement Points in Highly Strained Polymer Melts

Polymer melts undergoing large deformation by elongation are studied by molecular dynamics simulations of bead-spring chains in melts. By applying a primitive path analysis to strongly deformed polymer melts, the role of topological constraints in highly entangled polymer melts is investigated and quantified. We show that the overall, large scale conformations of the primitive paths (PPs) of stretched chains follow affine deformation while the number and the distribution of entanglement points along the PPs do not. Right after deformation, PPs of chains retract in both directions parallel and perpendicular to the elongation. Upon further relaxation we observe a long-lived clustering of entanglement points. Together with the delayed relaxation time this leads to a metastable inhomogeneous distribution of topological constraints in the melts.

Chain Retraction in Highly Entangled Stretched Polymer Melts

We use computer simulations to study the relaxation of strongly deformed highly entangled polymer melts in the nonlinear viscoelastic regime, focusing on anisotropic chain conformations after isochoric elongation. The Doi-Edwards tube model and its Graham-Likhtman-McLeish-Milner (GLaMM) extension, incorporating contour length fluctuation and convective constraint release, predict a retraction of the polymer chain extension in all directions, setting in immediately after deformation. This prediction has been challenged by experiment, simulation, and other theoretical studies, questioning the general validity of the tube concept. For very long chains we observe the initial contraction of the chain extension parallel and perpendicular to the stretching direction. However, the effect is significantly weaker than predicted by the GLaMM model. We also show that the first anisotropic term of an expansion of the 2D scattering function qualitatively agrees to predictions of the GLaMM model, providing an option for direct experimental tests.

Consequences of Grafting Density on the Linear Viscoelastic Behavior of Graft Polymers

The linear viscoelastic behavior of poly(norbornene)-graft-poly(±-lactide) was investigated as a function of grafting density and overall molar mass. Eight sets of polymers with grafting densities ranging from 0 to 100% were synthesized by living ring-opening metathesis copolymerization. Within each set, the graft chain molar mass and spacing between grafts were fixed, while the total backbone length was varied. Dynamic master curves reveal that these polymers display Rouse and reptation dynamics with a sharp transition in the zero-shear viscosity data, demonstrating that grafting density strongly impacts the entanglement molar mass. The entanglement modulus (G_e) scales with inverse grafting density (n_g) as G_e ∼ n_g^1.2 and G_e ∼ n_g⁰ in accordance with scaling theory in the high and low grafting density limits, respectively. However, a sharp transition between these limiting behaviors occurs, which does not conform to existing theoretical models for graft polymers. A molecular interpretation based on thin flexible chains at low grafting density and thick semiflexible chains at high grafting density anticipates the sharp transition between the limiting dynamical regimes.

Ion Beam Analysis of Diffusion in Polymer Melts

Two ion beam depth profiling methods have been used to measure the diffusion of polymer chains of molecular weight M into a matrix of polymer of molecular weight P. In the first the displacement xm of Au markers at the original interface of a diffusion couple between polystyrene with P=2×107 and a thin film of PS with M<P is measured using Rutherford backscattering spectrometry. From this modern version of the Kirkendall effect we find x=0.4t8(D*t) 0 5, where D* the tracer diffusion coefficient of the M chains at 174°C, is found to be D*=O.007M−2cm2/sec, in good agreement with the D*=DR expected for the reptation mechanism. Forward recoil spectrometry, a technique in which the energies of recoiling deuterons are detected, is used to obtain concentration profiles, and hence D*, of deuterated PS M-chains diffusing into a hydrogenated PS P-chain matrix. When P>>M, D*=0.008M−2, in good agreement with the marker data. When P<P*(M) however D*; increases greatly as P decreases; P* increases slowly with increasing M. The results are predicted quantitatively by D*=DR+DCR, where DCR=0.10Me2/(Mp 3 ) describes the diffusion of the M-chain by release of its topological constraints (by diffusion of the surrounding P-chains) and Me is an entanglement molecular weight. D* for self-diffusion (M=P) is dominated by reptation except for M's close to Me.

Polymer-Polymer Interdiffusion

Interdiffusion of polymer chains plays an important role in establishing good adhesion at polymer interfaces as well as in the kinetics of phase separation and mixing in polymer blends. Reptation, a process in which a given linear chain crawls along a primitive path defined by the topological constraints due to the surrounding chains, is thought to be the most important diffusion mechanism. A reptating chain of Volecular weight M should have a tracer diffusion coefficient given by D =DR =Do M−2, where D depends on the Rouse mobility of the chain and an entang ement molecular weight, Me. Because the topological constraints are assumed to be fixed, DR is independent of the molecular weight P of the polymer into which the M-chains are diffusing. In principle however if M is large enough and P is small enough the M-chain can diffuse by rearrangement of the P-chains surrounding it, a process called constraint release. The D for this process, DCR= αCRDoMe2/(MP3), where αCR is a constant approximately equal to 13, increases strongly with decreasing P. Recent experimental results, which give evidence for both reptation and constraint release, will be reviewed. These results have important implications for the diffusion of nonlinear polymer chains, e.g. stars and rings.

Do deviations from reptation scaling of entangled polymer melts result from single- or many-chain effects?

By studying the relaxation of small amounts of short entangled "probe" chains in a high molecular weight matrix, we show that the deviations from reptation scaling of the longest relaxation time are not as much dominated by single-chain effects (usually referred to as contour length fluctuations or CLF) as assumed by current mesoscopic models but also originate to a very significant extent from mutual chain relaxation effects. This result is in fact consistent with literature data on tracer and self-diffusion. Moreover, tube theories also overpredict the influence of CLF on the plateau modulus. Improved theories, simulations, and careful experiments are urgently needed to resolve this important question.

DNA electrophoresis in polymer solutions: Ogston sieving, reptation and constraint release

The electrophoresis of long polyelectrolytes is considered theoretically, with special attention to duplex DNA. We first discuss quantitative approaches to determine unambiguously the entanglement properties of polymer solutions. Following an idea proposed by Grossman and Soane, we then assume that the "mesh" size of the solution plays the role of a dynamic "pore size" in order to apply theories for gel electrophoresis. In the framework of the Ogston model, we predict that duplex DNA up to 1 kb or more should be separable in dilute (i.e. nonentangled) solutions of high molecular weight polymers. In an entangled solution, and for DNA larger than the pore size, we use a recently developed fluctuation-reptation model to predict the range of sizes in which separation should be possible as a function of electric field E and pore size zeta b. For zeta b larger than the Kuhn length of DNA, we predict a separation up to a size N*scaling as E-1 zeta b-1. For zeta b smaller than the Kuhn length, two different regimes are expected. For small electric fields (typically of the order of 10 V/cm), N*should be proportional to E-1 zeta b-3/2, whereas for high electric fields such as encountered in capillary electrophoresis, we expect that N*is proportional to E-2/5 zeta b-12/5. These predictions are qualitatively different from earlier ones. Finally, we demonstrate that the finite lifetime of the "pores" in an entangled solution (as opposed to a gel) may lead to a new migration mechanism by constraint release, which is not size-dependent.(ABSTRACT TRUNCATED AT 250 WORDS)

The Interdiffision of Polymers

In contrast to interdiffusion in simple liquids, interdiffusion of polymeric chains is dominated by their intertanglement and their large size. These properties profoundly reduce both the molecular mobilities and the role of entropy in driving the mixing. The resulting diffusional processes have only recently been studied. Such studies reveal a wide spectrum of behavior ranging from accelerated interdiffusion (for strongly compatible chains) to its suppression below the critical point for phase separation. Effects that are still poorly understood include the initial disposition at interfaces of the chains' ends (through which diffusion proceeds by reptation) and the need for cooperative motion, which can strongly magnify local friction.