Ktisis Cyprus University of Technologyhttps://ktisis.cut.ac.cyThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 25 Nov 2020 11:02:46 GMT2020-11-25T11:02:46Z5081- Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube modelhttps://ktisis.cut.ac.cy/handle/10488/15838Title: Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model
Authors: Stephanou, Pavlos S.; Baig, Chunggi; Tsolou, Georgia; Mavrantzas, Vlasis G.; Kröger, Martin
Abstract: The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static (statistical) properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics (MD) trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability ψ (s,t) that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time. The computed ψ (s,t) curves account directly for both of these phenomena, as well as for contour length fluctuations, since all of them are automatically captured in the atomistic simulations. Linear viscoelastic properties such as the zero shear rate viscosity and the spectra of storage and loss moduli obtained on the basis of the obtained ψ (s,t) curves for three different polymer melts (polyethylene, cis-1,4-polybutadiene, and trans-1,4-polybutadiene) are consistent with experimental rheological data and in qualitative agreement with the double reptation and dual constraint models. The new methodology is general and can be routinely applied to analyze primitive path dynamics and chain reptation in atomistic trajectories (accumulated through long MD simulations) of other model polymers or polymeric systems (e.g., bidisperse, branched, grafted, etc.); it is thus believed to be particularly useful in the future in evaluating proposed tube models and developing more accurate theories for entangled systems. © 2010 American Institute of Physics.
Tue, 30 Mar 2010 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/158382010-03-30T00:00:00Z
- Assessment of the Tumbling-Snake Model against linear and nonlinear rheological data of bidisperse polymer blendshttps://ktisis.cut.ac.cy/handle/10488/15784Title: Assessment of the Tumbling-Snake Model against linear and nonlinear rheological data of bidisperse polymer blends
Authors: Stephanou, Pavlos S.; Kröger, Martin
Abstract: We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the academic case of a monodisperse sample. Here, we extend these studies and provide the stationary solutions of the tumbling-snake model both analytically, for small shear rates, and via Brownian dynamics simulations, for a bidisperse sample over a wide range of shear rates and model parameters. We further show that the tumbling-snake model bears the necessary capacity to compare well with available linear and non-linear rheological data for bidisperse systems. This capacity is added to the already documented ability of the model to accurately predict the shear rheology of monodisperse systems.
Tue, 01 Jan 2019 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/157842019-01-01T00:00:00Z
- Tumbling-snake model for polymeric liquids subjected to biaxial elongational flows with a focus on planar elongationhttps://ktisis.cut.ac.cy/handle/10488/15787Title: Tumbling-snake model for polymeric liquids subjected to biaxial elongational flows with a focus on planar elongation
Authors: Stephanou, Pavlos S.; Kröger, Martin
Abstract: We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.
Fri, 16 Mar 2018 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/157872018-03-16T00:00:00Z
- Solution of the complete Curtiss-Bird model for polymeric liquids subjected to simple shear flowhttps://ktisis.cut.ac.cy/handle/10488/15820Title: Solution of the complete Curtiss-Bird model for polymeric liquids subjected to simple shear flow
Authors: Stephanou, Pavlos S.; Kröger, Martin
Abstract: The complete kinetic theory model for concentrated polymer solutions and melts proposed by Curtiss and Bird is solved for shear flow: (a) analytically by providing a solution for the single-link (or configurational) distribution function as a real basis spherical harmonics expansion and then calculating the materials functions in shear flow up to second order in the dimensionless shear rate and, (b) numerically via the execution of Brownian dynamics simulations. These two methods are actually complementary to each other as the former is accurate only for small dimensionless shear rates where the latter produces results with increasingly large uncertainties. The analytical expansions of the material functions with respect to the dimensionless shear rate reduce to those of the extensively studied, simplified Curtiss-Bird model when ϵ' = 0, and to the rigid rod when ϵ' = 1. It is known that the power-law behavior at high shear rates is very different for these two extremal cases. We employ Brownian dynamics simulation to not only recover the limiting cases but to find a gradual variation of the power-law behaviors at large dimensionless shear rates upon varying ϵ'. The fact that experimental data are usually located between these two extremes strongly advocates the significance of studying the solution of the Curtiss-Bird model. This is exemplified in this work by comparing the solution of this model with available rheological data for semiflexible biological systems that are clearly not captured by the original Doi-Edwards or simplified Curtiss-Bird models.
Mon, 28 Mar 2016 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/158202016-03-28T00:00:00Z
- Communication: Appearance of undershoots in start-up shear: Experimental findings captured by tumbling-snake dynamicshttps://ktisis.cut.ac.cy/handle/10488/15792Title: Communication: Appearance of undershoots in start-up shear: Experimental findings captured by tumbling-snake dynamics
Authors: Stephanou, Pavlos S.; Schweizer, Thomas; Kröger, Martin
Abstract: Our experimental data unambiguously show (i) a damping behavior (the appearance of an undershoot following the overshoot) in the transient shear viscosity of a concentrated polymeric solution, and (ii) the absence of a corresponding behavior in the transient normal stress coefficients. Both trends are shown to be quantitatively captured by the bead-link chain kinetic theory for concentrated polymer solutions and entangled polymer melts proposed by Curtiss and Bird, supplemented by a non-constant link tension coefficient that we relate to the nematic order parameter. The observed phenomena are attributed to the tumbling behavior of the links, triggered by rotational fluctuations, on top of reptation. Using model parameters deduced from stationary data, we calculate the transient behavior of the stress tensor for this “tumbling-snake” model after startup of shear flow efficiently via simple Brownian dynamics. The unaltered method is capable of handling arbitrary homogeneous flows and has the promising capacity to improve our understanding of the transient behavior of concentrated polymer solutions.
Fri, 28 Apr 2017 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/157922017-04-28T00:00:00Z
- From intermediate anisotropic to isotropic friction at large strain rates to account for viscosity thickening in polymer solutionshttps://ktisis.cut.ac.cy/handle/10488/15786Title: From intermediate anisotropic to isotropic friction at large strain rates to account for viscosity thickening in polymer solutions
Authors: Stephanou, Pavlos S.; Kröger, Martin
Abstract: The steady-state extensional viscosity of dense polymeric liquids in elongational flows is known to be peculiar in the sense that for entangled polymer melts it monotonically decreases - whereas for concentrated polymer solutions it increases - with increasing strain rate beyond the inverse Rouse time. To shed light on this issue, we solve the kinetic theory model for concentrated polymer solutions and entangled melts proposed by Curtiss and Bird, also known as the tumbling-snake model, supplemented by a variable link tension coefficient that we relate to the uniaxial nematic order parameter of the polymer. As a result, the friction tensor is increasingly becoming isotropic at large strain rates as the polymer concentration decreases, and the model is seen to capture the experimentally observed behavior. Additional refinements may supplement the present model to capture very strong flows. We furthermore derive analytic expressions for small rates and the linear viscoelastic behavior. This work builds upon our earlier work on the use of the tumbling-snake model under shear and demonstrates its capacity to improve our microscopic understanding of the rheology of entangled polymer melts and concentrated polymer solutions.
Mon, 14 May 2018 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/157862018-05-14T00:00:00Z
- Non-constant link tension coefficient in the tumbling-snake model subjected to simple shearhttps://ktisis.cut.ac.cy/handle/10488/15791Title: Non-constant link tension coefficient in the tumbling-snake model subjected to simple shear
Authors: Stephanou, Pavlos S.; Kröger, Martin
Abstract: The authors of the present study have recently presented evidence that the tumbling-snake model for polymeric systems has the necessary capacity to predict the appearance of pronounced undershoots in the time-dependent shear viscosity as well as an absence of equally pronounced undershoots in the transient two normal stress coefficients. The undershoots were found to appear due to the tumbling behavior of the director u when a rotational Brownian diffusion term is considered within the equation of motion of polymer segments, and a theoretical basis concerning the use of a link tension coefficient given through the nematic order parameter had been provided. The current work elaborates on the quantitative predictions of the tumbling-snake model to demonstrate its capacity to predict undershoots in the time-dependent shear viscosity. These predictions are shown to compare favorably with experimental rheological data for both polymer melts and solutions, help us to clarify the microscopic origin of the observed phenomena, and demonstrate in detail why a constant link tension coefficient has to be abandoned.
Tue, 07 Nov 2017 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/157912017-11-07T00:00:00Z
- Understanding dynamics in binary mixtures of entangled cis- 1,4-polybutadiene melts at the level of primitive path segments by mapping atomistic simulation data onto the tube modelhttps://ktisis.cut.ac.cy/handle/10488/15960Title: Understanding dynamics in binary mixtures of entangled cis- 1,4-polybutadiene melts at the level of primitive path segments by mapping atomistic simulation data onto the tube model
Authors: Baig, Chunggi; Stephanou, Pavlos S.; Tsolou, Georgia; Mavrantzas, Vlasis G.; Kröger, Martin
Abstract: We study dynamics in bidisperse melts of linear cis-1,4-polybutadiene composed of probe and matrix chains at the level of the segment survival probability function ψ(s,t) which is computed directly in the course of long atomistic molecular dynamics simulations [Stephanou et al. J. Chem. Phys. 2010, 132, 124904]. By controlling precisely the matrix chain length and composition, the effect of contour length fluctuations (CLFs) and constraint release (CR) on melt dynamics is quantified. Our study shows that (a) the values of the static topological properties of the probe chains (e.g., the average value of their primitive path (PP) contour length and its fluctuation) remain unaltered in the different matrices, but (b) their dynamical properties (including ψ(s,t) and its average over all segments s, ψ(t), the time autocorrelation function of the PP contour length, and the time autocorrelation function of the chain end-to-end vector) vary significantly from matrix to matrix. As the length of the matrix chains decreases, the functions ψ(s,t) and ψ(t) describing the reptation relaxation of the probe chains are found to decrease more rapidly. Furthermore, the relaxation of longer probe chains is seen to be delayed as the concentration of shorter matrix chains decreases. Overall, our direct computational study proves that CR is the dominant relaxation mechanism in melts of long and short cis-1,4-polybutadiene chains accounting for the majority of differences observed in their relaxation dynamics in different environments (since CLFs appear to be unaffected by compositional differences); as a result, it has a profound effect on the linear viscoelastic properties of the melt, such as the spectra of storage and loss moduli. By further analyzing the mean-square displacement of atomistic segments in the different matrices, we find that while the tube diameter is constant in the mixtures with MS ≤ Me where MS is the molecular weight of short chains and Me the entanglement molecular weight, it gradually increases in the mixtures with MS < Me. How the simulation results compare with laboratory measurements on melts of bidisperse polymers reported in the literature is also discussed. © 2010 American Chemical Society.
Tue, 12 Oct 2010 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/159602010-10-12T00:00:00Z