Non-entangled Chains Research Articles

Determining Entanglement Molar Mass of Glassy Polyphenylenes Using Mechanochromic Molecular Springs.

Molecular force transduction in tough and glassy poly(meta,meta,para-phenylene) (PmmpP) was investigated as a function of Mn using covalently incorporated mechanochromic donor-acceptor torsional springs based on an ortho-substituted diphenyldiketopyrrolopyrrole (oDPP). Blending oDPP-PmmpP probe chains with long PmmpP matrix chains allowed us to investigate molar-mass-dependent mechanochromic properties for a series of specimens having mechanically identical properties. In the strain-hardening regime, the mechanochromic response (Δλmax,em) was found to be a linear function of the acting stress and fully reversible, making oDPP-PmmpP a real-time and quantitative stress sensor. For entangled and nonentangled probe chains, distinctly different values of Δλmax,em were observed, yielding a critical molar mass of Mc ≈ 11 kg mol-1 for PmmpP. Once physical cross-linking of oDPP in the network of PmmpP was ensured, Δλmax,em was found to be independent of Mn. The resulting value of Mc is in very good agreement with results from rheology.

Non-monotonic effect of additive particle size on the glass transition in polymers.

Effect of small additive molecules on the structural relaxation of polymer melts is investigated via molecular dynamics simulations. At a constant external pressure and a fixed number concentration of added molecules, the variation of the particle diameter leads to a non-monotonic change of the relaxation dynamics of the polymer melt. For non-entangled chains, this effect is rationalized in terms of an enhanced added-particle-dynamics which competes with a weaker coupling strength upon decreasing the particle size. Interestingly, cooling simulations reveal a non-monotonic effect on the glass transition temperature also for entangled chains, where the effect of additives on polymer dynamics is more intricate. This observation underlines the importance of monomer-scale packing effects on the glass transition in polymers. In view of this fact, size-adaptive thermosensitive core-shell colloids would be a promising candidate route to explore this phenomenon experimentally.

Sensing adsorption kinetics through slip velocity measurements of polymer melts.

The evolution over time of the nonlinear slip behavior of a polydimethylsiloxane (PDMS) polymer melt on a weakly adsorbing surface made of short non-entangled PDMS chains densely end-grafted to the surface of a fused silica prism has been measured. The critical shear rate at which the melt enters the nonlinear slip regime has been shown to increase with time. The adsorption kinetics of the melt on the same surface has been determined independently using ellipsometry. We show that the evolution of slip can be explained by the slow adsorption of melt chains using the Brochard-de Gennes's model.

Friction of Polymers: from PDMS Melts to PDMS Elastomers.

The slip behavior of polydimethylsiloxane (PDMS) polymer melts flowing on weakly adsorbing surfaces made of short nonentangled PDMS chains densely end-grafted to silica has been characterized. For high enough shear rates, slip lengths proportional to the bulk fluid viscosity have been observed, in agreement with Navier's interfacial equation and demonstrating that the interfacial Navier's friction coefficient is a local quantity, independent of the polymer molecular weight. Comparing the interfacial shear stresses deduced from these measured slip lengths to available friction stress measured for cross-linked PDMS elastomers, we further demonstrate the local character of the friction coefficient and compare its value to the monomer-monomer friction.

A thermo-viscoelastic-damage constitutive model for cyclically loaded rubbers. Part I: Model formulation and numerical examples

Cyclically loaded rubbers exhibit a complex history-dependent response characterized by fatigue-induced stress-softening and hysteresis along with dissipative heating. The coupling between these different inelastic effects usually appearing together is far from being fully established. In this Part I of two-part paper, we present a new thermo-viscoelastic-damage approach, in accordance with the thermodynamic principles, for the prediction of this set of inelastic fatigue phenomena. An interpretation of the underlying physical mechanisms is proposed in which two types of dissipative network rearrangements are considered, i.e. recoverable rearrangements inducing viscoelasticity and unrecoverable rearrangements inducing damage. The recoverable viscoelastic rearrangements are assumed to be induced by the move of entangled and non-entangled free chains superimposed on a purely elastic perfect rubber network. Each population of free chains is considered to be the main source of one aspect of the history-dependent mechanical cyclic features, i.e. stress-softening and hysteresis, respectively. The thermo-mechanical coupling is defined by postulating the existence of a free energy in which two internal state variables are introduced to account for the two types of dissipative network rearrangements. Network thermal kinetics, induced by the dissipative heating, as well as network damage kinetics, induced by the fatigue damage, are defined and used to alter the cyclically loaded perfect rubber network. The proposed constitutive model is implemented into a finite element program and a parametric study is presented via numerical applications on rubber structures in order to analyze the effects of key model parameters on the rubber inelastic fatigue response. A focus is especially made on the respective influence of temperature, viscoelasticity and damage on the rubber softening.

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.

Chain Dynamics in Polymer Melts at Flat Surfaces

We investigate, by extensive molecular dynamics simulations as well as a simplified single-chain model, the influence of steric hindrance on the dynamic properties of nonentangled chains in polymer melt due to confining surfaces. We extend the Rouse model to also include wall effects, using an additional potential that results from the assumption that chain conformations have reflected random-walk statistics, as first advocated by Silberberg. Results for end-to-end vector and Rouse mode correlation functions of chains end-tethered to the surface compare well with those obtained from molecular dynamics simulations of a multichain system using the Kremer–Grest bead–spring model (KG MD). Even though the additional single-chain potential is parameter-free, we show that the accuracy of the model for surface chains is comparable to that of the Rouse model for bulk chains. An analytic dumbbell model accurately describes the longest Rouse mode correlation function of surface-tethered “mushroom” chains immersed in...

Viscoelastic Relaxation of Rouse Chains undergoing Head-to-Head Association and Dissociation: Motional Coupling through Chemical Equilibrium

For nonentangled Rouse chains undergoing head-to-head association and dissociation reaction, the viscoelastic relaxation functions g1(t) and g2(t) were formulated for a case that a given dissociated unimer chain rapidly reassociates with its original partner unimer. The relaxation of the unimer and dimer was essentially determined by ratios ra and rd of the Rouse relaxation time (in the absence of reaction) to the association and dissociation times. For small ra and rd, the reaction was slow so that the unimer and dimer relaxed through respective pure Rouse modes, as naturally expected. However, for most cases in wide ranges of ra and rd, the dimer relaxation was accelerated with increasing rd (>1), and g2 of the dimer was indistinguishable from the pure Rouse relaxation function of the unimer, g1,Rouse. For those cases, g1 of the unimer also coincided with g1,Rouse. These results demonstrate that the motional coupling between the unimer and dimer, occurring through the association/dissociation reaction, strongly affects the relaxation. The Rouse modes of the unimer and dimer were found to split in two series due to this coupling, and new relaxation modes due to the coupling emerged as well. Those new modes largely contribute to g1 and g2 for the cases of ra, rd > 1, thereby compensating the difference between the split modes (involved in gj) and the pure Rouse modes (in g1,Rouse) to provide the unimer and dimer with the superficial coincidence between their gj and g1,Rouse. In addition, in limited cases of moderately small rd, the relaxation of odd modes of the dimer was accelerated by the dissociation but remained still slower than the relaxation of g1,Rouse. For this case, the unimer relaxation was slower than its pure Rouse relaxation (namely, the unimer relaxation was retarded by the reaction), because of the coupling with the dimer odd modes. This result confirmed the significant effect of motional coupling on the relaxation of the unimer and dimer.

Nonlinear Stress Relaxation of Scarcely Entangled Chains in Primitive Chain Network Simulations

Polymeric liquids exhibit a crossover from the nonentangled to entangled behavior on an increase of the molecular weight M. For example, it has been established that the zero-shear viscosity h0(M ) of non-entangled low-M chains is proportional to M as described by Rouse model, whereas h0(M ) of well-entangled high-M chains is proportional to M a with a = ~ 3.4. 2) Not only for the linear viscoelastic property, the crossover has been observed also for nonlinear viscoelasticity, specifically in the shear damping function h(g), where g is a magnitude of step shear strain. h(g ) is insensitive to M and close to the Doi-Edwards (DE) prediction for high-M chains. This universal damping behavior was classified by Osaki as the type-A behavior. In contrast, the g dependence of h(g) considerably weakens with decreasing M when M is below a critical value ~ 2Me (with Me being the entanglement molecular weight), as reported by Takatori et al. and Inoue et al. for polystyrene (PS) solutions and by Vega et al. for polystyrene (PS) melts. This weak damping was classified by Osaki as the type-B behavior. A couple of theoretical attempts has been made for explaining the origin of type-B damping behavior. Kapnistos et al. have reported a weak damping of h(g ) for scarcely entangled polymer deduced from their slip-spring model where a Rouse chain is confined in a tube shaped parabolic potential. The confinement is realized by some springs having one end anchored in space and the other end connected to the chain. The spring end connected to the chain slides along the chain backbone to mimic the entanglement. Kapnistos et al. reported that if the number of slip-springs on the chain, which reflects the number of entanglement per chain, is decreased, the strain dependence of h(g) is weakened. Since there is no damping in the limit of free Rouse chain, it is rather natural that the strain dependence of h(g ) becomes weaker when the number of springs on the chain becomes smaller. They discussed that their simulation results are consistent with those for comb polymers with a small number of backbonebackbone entanglements. Another explanation of the type-B behavior was given by Kharlamov et al. They derived the distribution function of the end-to-end vector of a whole chain Ree after the chain contraction along the primitive path, and then calculated the stress from the second moment of Nonlinear Stress Relaxation of Scarcely Entangled Chains in Primitive Chain Network Simulations

Dependency of non-homogeneity energy dispersion on absorbance line-shape of luminescent polymers

In this paper, we study the importance of the non-homogeneity energy dispersion on absorption line-shape of luminescent polymers. The optical transition probability was calculated based on the molecular exciton model, Franck–Condon states, Gaussian distribution of non-entangled chains with conjugate degree n, semi-empirical parameterization of energy gap, electric dipole moment, and electron-vibrational mode coupling. Based on the approach of the energy gap functional dependence 1/n, the inclusion of the non-homogeneity energy dispersion 1/n2 is essential to obtain good experimental data agreement, mainly, where the absorption spectra display peaks width of about 65meV. For unresolved absorption spectra, such as those observed for a large number of conjugated polymers processed via spin-coating technique, for example, the non-homogeneity energy dispersion parameterization is not significant. Results were supported by the application of the model for poly (p-phenylene vinylene) films.

Slow Dynamics in Homopolymer Liquids

Dynamic physical properties of homopolymer liquids relax through global motion of the polymer chains over their dimension. This motion is affected by a variety of factors. For high molecular weight (M) chains, the entanglement retards the global motion to affect the properties. This entanglement effect changes with the chain architecture as well as the molecular weight distribution. The effect of the chain architecture on the global chain dynamics is found also for non-entangled low-M chains as well. This article gives a very brief summary of the experimental facts and molecular interpretations for these effects.

On the dynamics and disentanglement in thin and two-dimensional polymer films

We present results from molecular dynamics simulations of strictly two-dimensional (2D) polymer melts and thin polymer films in a slit geometry of thickness of the order of the radius of gyration. We find that the dynamics of the 2D melt is qualitatively different from that of the films. The 2D monomer mean-square displacement shows a $t^{8/15}$ power law at intermediate times instead of the $t^{1/2}$ law expected from Rouse theory for nonentangled chains. In films of finite thickness, chain entanglements may occur. The impact of confinement on the entanglement length $N_\mathrm{e}$ has been analyzed by a primitive path analysis. The analysis reveals that $N_\mathrm{e}$ increases strongly with decreasing film thickness.

Orientational anisotropy for Rouse eigenmodes during creep and recovery process

The Rouse model is a well established model for nonentangled polymer chains and its dynamic behavior under step strain has been fully analyzed in the literature. However, to the knowledge of the authors, no analysis has been made for the orientational anisotropy for the Rouse eigenmodes during the creep and creep recovery processes. For completeness of the analysis of the Rouse model, this anisotropy is calculated from the Rouse equation of motion. The calculation is simple and straightforward, but the result is intriguing in a sense that respective Rouse eigenmodes do not exhibit the single Voigt-type retardation. Instead, each Rouse eigenmode has a distribution in the retardation time. This behavior, reflecting the interplay among the Rouse eigenmodes of different orders under the constant stress condition, is quite different from the behavior under rate-controlled flow (where each eigenmode exhibits retardation/relaxation associated with a single characteristic time).

Simulation of diffusion and relaxations of non-dilute star chains

Star polymer chains with 12 arms in a good solvent have been investigated using a dynamic Monte Carlo algorithm with the bond fluctuation model in the dilute, semidilute and concentrated regimes. We have characterized the self-diffusion coefficient and different relaxation modes of individual chains. We discuss the variation of the results with the arm length (or number of beads) and concentration. The ratio of diffusion coefficient of a star to that of a homologous linear chain is shown to increase progressively with concentration for overlapped non-entangled chains. It is also observed that diffusion and elastic relaxation of individual arms are more sensitive to the chains overlapping than global rotation or disentanglement between arms.

GLASS TRANSITION IN THIN POLYMER FILMS: A MOLECULAR DYNAMICS STUDY

A melt of nonentangled polymer chains confined between two smooth and purely repulsive walls is studied for various film thicknesses D and temperatures. The dynamics of the supercooled films is qualitatively identical to that of the bulk, but the walls lead to faster relaxation. To quantify this observation we analyze the data by the mode-coupling theory (MCT) of the glass transition. We find that the critical temperature of MCT, Tc(D), decreases with D and that T - Tc(D) is a relevant temperature scale. The static structure factor and dynamic correlation functions at intermediate times coincide with bulk behavior when compared to the same T - Tc(D).

Melt viscosities of lattice polymers using a Kramers potential treatment

Kramers relaxation times τK and relaxation times τR and τG for the end-to-end distances and for center-of-mass diffusion are calculated for dense systems of athermal lattice chains. τK is defined from the response of the radius of gyration to a Kramers potential which approximately describes the effect of a stationary shear flow. It is shown that within an intermediate range of chain lengths N the relaxation times τR and τK exhibit the same scaling with N, suggesting that N-dependent melt-viscosities for nonentangled chains can be obtained from the Kramers equilibrium concept.

Structure and dynamics of thin polymer films: a case study with the bond-fluctuation model

This paper reports Monte Carlo simulation results of a polymer melt of short, non-entangled chains which are embedded between two impenetrable walls. The melt is simulated by the bond-fluctuation lattice model under athermal conditions, i.e. only excluded volume interactions between the monomers and between the monomers and the walls are taken into account. In the simulations, the wall separation is varied from about one to about 15 times the bulk radius of gyration Rg. The confinement influences both static and dynamic properties of the films: Chains close to the walls preferentially orient parallel to it. This parallel orientation decays with increasing distances from the wall and vanishes for distances larger than about 2Rg. Strong confinement effects are therefore observed for film thicknesses D≲4Rg. The preferential alignment of the chains with respect to the walls suppresses reorientations in perpendicular direction, whereas parallel reorientations take place in an environment of high monomer density. Therefore, they have a relaxation time larger than that of the bulk. On the other hand, the influence of confinement on the translation motion of the chains parallel to the walls is very weak. It almost coincides with the bulk behavior even if D≈1.5Rg. Despite these differences between translational and reorientational dynamics, their behavior can be well reproduced by a variant of Rouse theory which only assumes orthogonality of the Rouse modes and determines the necessary input from the simulation.

Glassy dynamics of simulated polymer melts: Coherent scattering and van Hove correlation functions

Whereas the first part of this paper dealt with the relaxation in the β-regime, this part investigates the final relaxation (α-relaxation) of a simulated polymer melt consisting of short non-entangled chains in the supercooled state above the critical temperature of ideal mode-coupling theory (MCT). The temperature range covers the onset of a two-step relaxation behaviour down to a temperature merely 2% above . We monitor the incoherent intermediate scattering function as well as the coherent intermediate scattering function of both a single chain and the melt over a wide range of wave numbers q. Upon approaching the coherent α-relaxation time of the melt increases strongly close to the maximum q max of the collective static structure factor Sq and roughly follows the shape of Sq for q q max. For smaller q-values corresponding to the radius of gyration the relaxation time exhibits another maximum. The temperature dependence of the relaxation times is well described by a power law with a q-dependent exponent in an intermediate temperature range. Deviations are found very close to and far above , the onset of which depends on q. The time-temperature superposition principle of MCT is clearly borne out in the whole range of reciprocal vectors. An analysis of the α-decay by the Kohlrausch-Williams-Watts (KWW) function reveals that the collective KWW stretching exponent and KWW relaxation time show a modulation with Sq. Furthermore, both incoherent and coherent KWW times approach the large-q prediction of MCT already for q > q max. At small q, a q-3 power law is found for the coherent chain KWW times similar to that of recent experiments.

Structure and Dynamics of Hairy Spherical Colloids in a Matrix of Nonentangled Linear Chains

We describe the structure and dynamical behavior of a homogeneous mixture of hairy nanospheres, i.e., polyorganosiloxane microgels grafted with polystyrene chains, and linear polystyrene chains. Previously, it has been found that such mixtures are only homogeneous if the molecular weight of the polymer hairs is at least as large as that of the linear matrix chains. Otherwise, the depletion mechanism typical for most colloid−polymer mixtures leads to a phase separation. It indicates that the length of the polymer hairs with respect to the length of the matrix chains has an important effect on structure and dynamics of the colloid−polymer blends. Here we demonstrate that if the chains are much shorter than the hairs, the colloidal hair corona is strongly swollen by the matrix polymer, leading to a long-range soft interparticle repulsion (“wet brush”). If hairs and chains are comparable in length, the corona shows much less volume swelling, leading to a short-range repulsive potential similar to hard-sphere systems (“dry brush”). As a consequence, wet brush mixtures exhibit a liquid−solid transition, as identified by dynamic mechanical measurements, at much lower particle weight fraction in comparison to dry brush systems. These studies are compared with our recent work on copolymer micelles with corona and matrix chains of much higher molecular weight.

Dynamics of a supercooled polymer melt above themode-coupling critical temperature: cage versus polymer-specificeffects

This paper reports results of molecular dynamics simulations for aglassy polymer melt consisting of short, non-entangled chains. Thetemperature region studied covers the supercooled state of the meltabove the mode-coupling critical temperature. The analysis focuseson the interplay of simple-liquid and polymer-specific effects. Onecan clearly distinguish two regimes: a regime of small and one of largemonomer displacements. The first regime corresponds to motion of amonomer in its local environment. It is dominated by the cage effectand well described by the idealized mode-coupling theory. Thesecond regime is governed by the late-β/early-α process.In this regime the connectivity of the monomers begins tointerfere with the cage dynamics and finally becomes dominant. Themonomer displacement is compared with simulation results for abinary Lennard-Jones mixture to highlight the differences which areintroduced by the connectivity of the particles.