Why is understanding glassy polymer mechanics so difficult?

In this Perspective, I describe recent work on systems in which the traditional distinctions between (i) unentangled versus well‐entangled systems and (ii) melts versus glasses seem least useful, and argue for the broader use in glassy polymer mechanics of two more dichotomies: systems which possess (iii) unary versus binary and (iv) cooperative versus noncooperative relaxation dynamics. I discuss the applicability of (iii–iv) to understanding the functional form of strain hardening. Results from molecular dynamics simulations show that the “dramatic” hardening observed in densely entangled systems is associated with a crossover from unary, noncooperative to binary, cooperative relaxation as strain increases; chains stretch between entanglement points, altering the character of local plasticity. Promising approaches for future research along these lines are discussed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.     

Polymers coalesced from their cyclodextrin inclusion complexes: What can they tell us about the morphology of melt‐crystallized polymers?

Cyclodextrins (CDs) are cyclic polysaccharides with nano‐size, largely hydrophobic cavities, and exteriors covered with hydrophilic hydroxyl groups, making them water soluble. Threading and filling their cavities with polymer chains produces noncovalently bonded crystalline inclusion compounds (ICs). In this study, we formed fully covered, stoichiometric ICs between guest poly(L ‐lactic acid), poly(ε‐caprolactone), and nylon‐6 chains and host α‐CD. Coalesced samples of all three polymers were obtained after appropriately removing the stacked α‐CD host channels from their ICs. Distinct differential scanning calorimetriy (DSC) thermograms were observed for as‐received and coalesced samples, with the coalesced samples crystallizing faster at higher temperatures from their melts, and this distinction was maintained even after extensive, long‐time melt‐annealing (hours, days, and weeks). We believe this is due to the largely unentangled chains with extended conformations that are more densely packed in the initially coalesced samples. When small amounts (～2 wt %) of the coalesced polymers are used as self‐nucleating agents for their as‐received samples, the resulting self‐nucleated samples show DSC thermograms similar to those of the neat coalesced polymers, including their long‐time stability to melt‐annealing. Coalesced polymers, whether neat or in samples they self‐nucleate, may conserve their organization in the melt (largely extended and unentangled chains) for long periods, because the process of entangling the many chains influenced by a single initially extended unentangled coalesced chain, after it randomly coils, is extremely sluggish. By contrast, in melt‐crystallized or solution‐cast samples, polymer chains generally become fully randomly coiled, interpenetrate, and entangle after being heated and held in their melts for comparatively much shorter times. For example, we have recently observed (DSC) that ultra high molecular weight, gel‐spun spectra polyethylene (PE) fibers^® did not conserve or retain any memory of their as‐spun and highly drawn semicrystalline morphology even after spending as little as 2 min in the melt. As a consequence of the comparison to the behavior of coalesced polymer melts, we believe that polyethylene chains in Spectra fibers^® must be at least intimately dispersed within their crystalline regions, and likely partially coiled and entangled in their noncrystalline regions, thereby facilitating their rapid transformation into a full entanglement network of randomly coiling chains in the melt. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Spatial displacement correlations in polymeric systems

The spatial correlations of the monomer displacements are studied via molecular-dynamics simulations of a melt of fully flexible, unentangled polymer chains with different length, interacting potential, density, and temperature. Both the scalar and the vector characters of the correlations are considered and their extension quantified in terms of suitable dynamical correlation lengths. Displacements performed at both short, i.e., vibrational, and long times, i.e., comparable to the structural relaxation time, are investigated. On both time scales the spatial correlations are modulated according to the radial distribution function g(r) to an extent which is determined by the character of the correlations, the time scale of the displacements and the structural slowing down. The spatial correlations of the short-time displacements have clear directional character. The modulus correlations of the long-time displacements are more marked, especially for sluggish states. Analogous findings are found by experiments on colloids. By inspecting the dynamical heterogeneities of states with slowed-down dynamics, it is observed that fast monomers exhibit correlations which are stronger and more differing from the bulk than the slow ones. It is shown that states with identical average vibrational monomer displacement exhibit identical spatial correlations of the monomer displacements pertaining to the subsets of the fast and the slow monomers characterizing both the short-time and the long-time dynamical heterogeneities.     

受限状态聚合物熔体的分子动力学模拟

用粗粒化的分子动力学(MD)模拟方法从分子层次研究了受限于粗糙壁内的聚合物熔体的动力学性质. 结果表明, 对于链长较短的受限聚合物熔体体系, 随着膜厚的增加, 体系内部高分子链的松弛时间逐渐减少; 然而对于链长较长的受限体系, 聚合物链的松弛时间随着膜厚的增加先减少后增加. 推测这种由于链长的变化所引起的动力学性质的差异源自受限熔体内聚合物链聚集状态的改变, 并且通过考察交叠参数对这种改变进行了分析. 结果表明, 在膜厚增加的过程中, 决定受限状态高分子长链松弛机理的因素逐渐从受限效应转变成为链间的缠结效应.     

Viscoelasticity and primitive path analysis of entangled polymer liquids: from F-actin to polyethylene

We combine computer simulations and scaling arguments to develop a unified view of polymer entanglement based on the primitive path analysis of the microscopic topological state. Our results agree with experimentally measured plateau moduli for three different polymer classes over a wide range of reduced polymer densities: (i) semidilute theta solutions of synthetic polymers, (ii) the corresponding dense melts above the glass transition or crystallization temperature, and (iii) solutions of semiflexible (bio)polymers such as F-actin or suspensions of rodlike viruses. Together, these systems cover the entire range from loosely to tightly entangled polymers. In particular, we argue that the primitive path analysis renormalizes a loosely to a tightly entangled system and provide a new explanation of the successful Lin-Noolandi packing conjecture for polymer melts.     

On a quantity describing the degree of chain entanglement in linear polymer systems

In the present paper we define a quantity which describes how strong a polymer system is entangled. In MD computer simulations we apply this definition to samples of polymer melts which were generated with a specific large-scale structure, as characterized by their radius of gyration, end-to-end distance and the “degree” of mutual entanglement of the chains. The quantities mentioned above are monitored over the relaxation of the samples towards equilibrium.     

A highly coarse-grained model to simulate entangled polymer melts

We introduce a highly coarse-grained model to simulate the entangled polymer melts. In this model, a polymer chain is taken as a single coarse-grained particle, and the creation and annihilation of entanglements are regarded as stochastic events in proper time intervals according to certain rules and possibilities. We build the relationship between the probability of appearance of an entanglement between any pair of neighboring chains at a given time interval and the rate of variation of entanglements which describes the concurrence of birth and death of entanglements. The probability of disappearance of entanglements is tuned to keep the total entanglement number around the target value. This useful model can reflect many characteristics of entanglements and macroscopic properties of polymer melts. As an illustration, we apply this model to simulate the polyethylene melt of C(1000)H(2002) at 450 K and further validate this model by comparing to experimental data and other simulation results.     

New Light on Old Wisdoms on Molten Polymers: Conformation,Slippage and Shear Banding in Sheared Entangled and Unentangled Melts

The flow of viscoelastic materials is usually interpreted as resulting from intramolecular properties. Typically, the non‐linear flow behaviour and sluggish relaxation dynamics in entangled polymers are interpreted by a disentanglement process. This molecular interpretation has never been validated by direct observation. We report here on in situ observations of polymer melts under steady‐state shear flow using neutron scattering and particle tracking velocimetry. It is shown that the chains remain largely undeformed under steady‐state shear flow whereas wall slippage and shear‐banding are identified in both entangled and unentangled polymer melts. These observations are of prime importance; they reveal that the flow mechanism and its viscoelastic signature reflect a collective effect and not properties of individual chains.

     

Mobility of Spherical Probe Objects in Polymer Liquids

We use scaling theory to derive the time dependence of the mean-square displacement ?Δr(2)? of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (?Δr(2) (t)? ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (?Δr(2) (t)? ~ t(1/2)) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τ(e) of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τ(e)) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τ(rep). At longer times t > τ(rep), the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.     

Communication: effects of stress on the tube confinement potential and dynamics of topologically entangled rod fluids

A microscopic theory for the effect of applied stress on the transverse topological confinement potential and slow dynamics of heavily entangled rigid rods is presented. The confining entanglement force localizing a polymer in a tube is predicted to have a finite strength. As a consequence, three regimes of terminal relaxation behavior are predicted with increasing stress: accelerated reptation due to tube widening (dilation), relaxation via deformation-assisted activated transverse barrier hopping, and complete destruction of the lateral tube constraints corresponding to microscopic yielding or a disentanglement transition.     

Shear and extensional rheology of entangled polymer melts: Similarities and differences

This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities have recently been identified for both step strain and startup continuous deformation, including elastic yielding, i.e., chain disentanglement after cessation of shear or extension, and emergence of a yield point during startup deformation that involves a deformation rate in excess of the dominant molecular relaxation rate. At a sufficiently high constant Hencky rate, uniaxial extension of an entangled melt is known to produce window-glass-like rupture. The present study provides evidence against the speculation that chain entanglements tie up into "dead knots" in constant-rate extension because of the exponentially growing chain stretching with time. In particular, it is shown that even Instron-style tensile stretching, i.e., extending a specimen by applying a constant velocity on both ends, results in rupture. Yet, in the same rate range, the same entangled melt only yields in simple shear, and the resulting shear banding is clearly not a characteristic of rupture. Thus, we conclude that chain entanglements respond to simple shear in the manner of yielding whereas uniaxial extension is rather effective in causing some entanglements to lock up, making it impossible for the entanglement network to yield at high rates.     

Static and dynamic properties of computer simulated melts of multiarm polymer stars

Cooperative motion algorithm (CMA) is applied to simulate properties of polymer stars in dense systems which are considered as representations of polymer melts. Effects of arm number and arm length of stars on static and dynamic properties of model systems are analysed. Static properties are characterised by star sizes and their spatial correlations. Dynamic properties describing arm orientation relaxation and translational motion of stars are presented. Results indicate strong ordering effects for multiarm stars in the melt and suggest that the terminal relaxation of star melts can alternatively be controlled by arm orientation relaxation or by cooperative star translations depending in the two parameters of star structure i.e. arm length and arm number.     

Chain dimensions and entanglement spacings in dense macromolecular systems

In this article, we reexamine and extend a relationship proposed earlier between entanglement density and chain dimensions in polymer melts. The power-law equation presented in the earlier work, relating the entanglement molecular weight M_e, melt chain density ρ, and the packing length p is tested with additional polymer species. Now included are additional polydienes and their hydrogenated derivatives, the isotactic forms of polypropylene and polystyrene, the essentially syndiotactic form of poly(methyl methacrylate), along with poly(tetrafluoroethylene), poly(vinylmethyl ether), various poly(methacrylates), and polymeric sulfur. We find that within experimental uncertainties, M_e/ρ and p are related through an equation (M_e/ρ = 218p³) that is insensitive to temperature (25°C ≤ T ≤ 380°C) and which seems to be universal for flexible Gaussian chains in the melt state. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1023–1033, 1999     

Dynamics of entangled supramolecular polymer networks in presence of high‐order associations of strong hydrogen bonding groups

Dynamics of entangled polymer chains in the melt state are deliberately excluded in most of the studies on supramolecular polymer networks by utilizing nonentangled precursor chains. Relaxation of the system mainly depends on the dissociation of the associative groups in latter case and nonentangled chains deliver nothing to resist afterward. Conversely, in an entangled system, relaxation of polymer chains and dissociation of associative groups can occurred parallel. Supramolecular networks based on an entangled precursor polymer with different levels of strong associating ureidopyrimidinone (UPy) groups are synthesized to screen the corresponding effects on the dynamics of the system. Binary‐associated UPy groups phase separate into collective assemblies by stacking and form high‐order, needle‐like domains at higher UPy contents. Relaxation of polymer chains is significantly hindered due to the trapping of polymer segments between UPy stacks. Above a certain threshold of UPy content (~4 mol%), the plateau level and final relaxation time of networks show a significant jump, which is attributed to the onset of high‐order association of UPy groups.     

Monte Carlo simulations of the polymer glass transition: From the test of theories to material modeling

We present results on the glass transition in polymer melts using Monte Carlo simulations of the bond fluctuation lattice model. There are two questions we address in this work. What is the temperature dependence of the entropy density in such a model polymer melt and how well is it described by theories like the Gibbs-DiMarzio theory of the glass transition? And to what degree is one able to map the Hamiltonian of such an abstract lattice model onto a specific polymer material and use it to model the large scale and long time properties of a realistic polymer melt?     

Communication: Fast and local predictors of the violation of the Stokes-Einstein law in polymers and supercooled liquids

The violation of the Stokes-Einstein (SE) law is investigated in a melt of linear chains by extensive molecular-dynamics simulations. It is found that the SE breakdown is signaled (with 5% uncertainty) by the monomer mean-square displacement on the picosecond time scale. On this time scale the displacements of the next-next-nearest neighbors are uncorrelated. It is shown that: (i) the SE breakdown occurs when is smaller than the breadth of the distribution of the square displacements to escape from the first-neighbors cage, (ii) the dynamical heterogeneity affects the form of the master curve of the universal scaling between the structural relaxation and .