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ORAL PRESENTATION
Session: 2 Multiscale modeling and molecular simulations
(scheduled: Monday, 08:50 )
Primitive Path Identification and Entanglement Statistics in Polymer Melts: Results from a Direct Topological Analysis on Atomistically Detailed Polyethylene Models
K. Foteinopoulou1,2, N.Ch. Karayiannis1,2, V.G. Mavrantzas1,2, M. Kröger3
1 Department of Chemical Engineering, University of Patras, GR 26504, Greece
2 FORTH-ICE/HT, Patras GR 26504, Greece
3 ETH Zurich, Polymer Physics, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland
A large number of well equilibrated atomistic configurations of linear, strictly monodisperse polyethylene (PE) melts of molecular length ranging from C78 to C1000, obtained with the Double Bridging Monte Carlo algorithm, have been subjected to a detailed topological analysis with the Z code [Kröger, Comp. Phys. Comm., 2005]. The code constructs primitive paths that connect the two ends of a polymer chain (which in all cases are considered as fixed in space) geometrically under the constraint of no chain crossability, such that the multiple disconnected (coarse-grained) path has minimum contour length. When applied to a given, dense polymer configuration in 3-d space, it allows us to obtain the primitive path (PP) and the related number and positions of entanglements (kinks) for all chains in the simulation box, and extract information about the topological structure (the primitive path network) hidden in bulk PE. Results will be presented for the distribution and mean values of the number of entanglements per chain, the entanglement length, the tube diameter, the Kuhn step length and the contour length [1]. In particular, our analysis demonstrates that with increasing chain length, the entanglement molecular length reaches a plateau value characteristic of entangled polymeric behavior, which for the PE systems analyzed here comes out to be about 60 carbon atoms. We further validate recent predictions [Schieber, J. Chem. Phys., 2003] about the shape of the distribution of number of strands in a chain at equilibrium. At the same time we show, that the number of entanglements obtained by assuming random walk statistics [Everaers et al., Science, 2004] deviates significantly from these predictions which we regard as a clear sign of evidence that the direct counting of entanglements and related quantities, as proposed here, offers advantages for a quantitative analysis of the statistical nature of entanglements in polymeric systems. © IWNET 2006
[1] K. Foteinopoulou, N.Ch. Karayiannis, V.G. Mavrantzas, M. Kröger, Macromolecules 39, 4207 (2006) »
ORAL PRESENTATION
Session: 4 Complex fluid deformation and rheology: Theories and thermodynamic relationships
(scheduled: Tuesday, 11:10 )
Thermodynamics of Non-Isothermal Polymer Flows: Experiment, Theory and Simulation
T.C. Ionescu1, B.J. Edwards1, D.J. Keffer1, V.G. Mavrantzas2
1 Department of Chemical Engineering, University of Tennessee, Knoxville, TN 37996-2200, USA
2 Department of Chemical Engineering, University of Patras, Patras GR 26504, Greece
We provide a critical evaluation of the so-called ''Theory of Purely Entropic Elasticity'', which states that the free energy change of a flowing, non-isothermal viscoelastic fluid is entirely due to entropic effects, and contains no contributions due to elastic energy changes. Our investigation consists of both theoretical and experimental parts. In the theoretical part, we perform non-equilibrium Monte Carlo simulations to calculate both the energetic and entropic contributions to the free energy of the material under uniaxial elongational flow. This results in measurable energetic effects at higher strain rates, and these effects increase as temperature decreases. Experimentally, we measured the heat capacity at constant volume of LDPE under steady-state shear and uniaxial elongational flow conditions, and calculated the conformational contribution to this quantity. According to the Theory of Purely Entropic Elasticity, the conformational contribution to the heat capacity should be negligible, however, significant non-vanishing contributions are measurable at high strain rates. Results are qualitatively consistent between theory and simulation. © IWNET 2006
ORAL PRESENTATION
Session: 2 Multiscale modeling and molecular simulations
(scheduled: Monday, 08:00 )
Atomistic simulation of polymers with a non-linear molecular architecture: Calculation of branch point friction and chain reptation time of an H-shaped polyethylene melt
N.Ch. Karayiannis1,2, V.G. Mavrantzas1,2
1 Department of Chemical Engineering, University of Patras, GR 26504, Greece
2 Institute of Chemical Engineering and High-Temperature Chemical Processes (FORTH-ICE/HT), Patras GR 26504, Greece
A hierarchical simulation strategy is presented for simulating structure and dynamics in polymers characterized by a non-linear molecular architecture, such as the H-shaped macromolecules [1]. First, a novel Monte Carlo (MC) algorithm is employed to generate well equilibrated atomistic configurations of these highly non-linear chain structures. The new algorithm is built around state-of-the-art chain connectivity altering moves, like the end-bridging and double-bridging, and is many orders of magnitude more efficient than Molecular Dynamics (MD) in equilibrating these systems, even if multi-step time integration schemes are incorporated in the MD algorithm. In a second step, the equilibrated structures generated by the new MC algorithm are used as initial configurations in detailed NPT MD simulations of H-shaped polyethylene (PE) melts for very long times, on the order of microseconds. In our simulations, the average number of carbon atoms in the backbone has ranged from 48 up to 300 corresponding to both unentangled and entangled crossbars, while the average branch length was kept relatively small (it ranged from 24 up to 50 carbon atoms) corresponding always to unentangled arms. The MD simulation results provide convincing evidence for the different relaxation mechanisms exhibited by an H-polymer melt: the fast relaxation due solely to arm breathing (on the order of a few ns, for an H_300_50 melt), and the slow branch point diffusion which is accompanied by a sluggish backbone diffusion due to reptation (on the order of a few μs, for an H_300_50 melt). They have further demonstrated that the center-of-mass diffusivity in an H-polymer follows faithfully that of branch points, thus validating from first-principles the main assumption of the McLeish-Larson pom-pom theory that all friction in an H-molecule is concentrated at the branch points. For the longest H-polymers studied, logarithmic plots of the msd of the inner crossbar segments against time were seen to exhibit the four different regimes predicted by the reptation theory of Doi-Edwards for entangled linear polymer melts, with corresponding exponents remarkably close to those of the theory. This allowed us to extract the characteristic relaxation times τe, τR, and τd for each one of the simulated systems and their effective tube diameter. © IWNET 2006
[1] N.Ch. Karayiannis and V.G. Mavrantzas, Macromolecules 38, 8583 (2005).
ORAL PRESENTATION
Session: 7 Applications to complex materials: glasses, micelles, colloids, blends, interfaces
(scheduled: Thursday, 11:10 )
Atomistic molecular dynamics simulation of the temperature and pressure dependences of local and terminal relaxations in cis-1,4-polybutadiene
G. Tsolou, V.G. Mavrantzas
1 Department of Chemical Engineering, University of Patras, GR 26504, Greece
2 Institute of Chemical Engineering and High-Temperature Chemical Processes (FORTH-ICE/HT), Patras GR 26504, Greece
We have explored features of local and terminal relaxation in cis-1,4-polybutadiene (cis-1,4-PB) over a wide range of temperature and pressure conditions by conducting atomistic molecular dynamics simulations (MD) with a united atom model on a 32-chain C128 cis-1,4-PB system [1]. Segmental relaxation was analyzed in terms of the dipole moment time autocorrelation function (DACF) of the simulated polymer. By Fourier transforming the DACF, the dielectric spectrum was computed and the validity of the time-temperature and time-pressure superposition principles were checked to decide for the appearance or not of additional relaxation mechanisms at low enough temperatures or high enough pressures. The relative contribution of thermal energy and volume to segmental relaxation was also calculated and evaluated in terms of the ratio QV/QP [2]. In contrast to experimental studies in other polymers [3], our results support that, in the temperature and pressure range studied, segmental and chain relaxations are influenced similarly by pressure and temperature variations. Further information about the dynamics of the intermediate chain segments has been extracted through the calculation of the dynamic structure factor. Current efforts focus on the determination of characteristic relaxation times in cis-1,4-PB and their variation with density or temperature and pressure, separately. © IWNET 2006
[1] G. Tsolou, V.A. Harmandaris, V.G. Mavrantzas, Macromol. Theory Simul. 15, 381 (2006).
[2] G. Tsolou, V.A. Harmandaris, V.G. Mavrantzas, J.Chem.Phys. 124, 084906 (2006).
[3] G. Floudas, T. Reisinger, J. Chem.Phys. 111, 5201 (1999).
POSTER PRESENTATION
Tuesday, 15:40, Panel No. 4
Structure and dynamics of polyethylene melts bearing short chain branches frequently spaced along their backbone as revealed from atomistic simulations
V. Dimitriadis1, N. Karayiannis1, V.G. Mavrantzas1, E. Chiotellis2, D. Mouratides2, C.D. Kiparissides2
1 Department of Chemical Engineering, University of Patras & FORTH-ICE/HT, Patras GR 26504, Greece
2 Department of Chemical Engineering, Aristotle University of Thessaloniki & CPERI-CERTH, Thessaloniki 54124, Greece
Based on the molecular architecture of the constituent chains polyethylene (PE) is usually classified as HDPE (High Density PE), LLDPE (Linear Low Density PE), and LDPE (Low Density PE). HDPE consists of linear chains resulting from the catalytic reaction of pure ethylene monomers, LLDPE consists of chains bearing short branches sparsely distributed along their main backbone and LDPE consists of chains with densely packed branches of variable length that may carry additional arms thus creating a complex, dendritic-like structure. LDPE and other well-defined polymers with several kinds of molecular architecture are nowadays synthesized by metallocene and other single-site catalysts through anionic living polymerization techniques by employing organolithium initiators. Also, dangling branches are considered in general as ''long'' or ''short'' if their length longer or shorter, respectively, than the characteristic molecular length between entanglements, Ne, which for PE is around C70. In this work, we will present results for the effect of short chain branching (SCB) on the volumetric, structure, conformational and dynamic properties of PE obtained from detailed atomistic MC and MD simulations with two families of PE microstructures: the first corresponded to a total of 142 carbon atoms per chain (MW = 1990 g/mol) and the second to a total of 320 carbon atoms per chain (MW = 4482 g/mol). We will show that short-chain branched (SCB) PE melts are characterized by significantly smaller dimensions than linear PE melts of the same total chain length under the same temperature and pressure conditions, due to the more symmetric arrangement of their material around the chain center-of-mass. In contrast, SCB and linear PE melts of the same chain length exhibit practically identical volumetric properties, suggesting that the differences recorded at temperatures below their melting point in the densities of the ''LLDPE'' and ''HDPE'' end-products of PE are due to their totally different degrees of crystallinity. We will also show that short-chain branching causes a decrease in the chain self diffusion coefficient compared to the value exhibited by the linear melt of the same total chain length by a factor which can range from 10 up to 40% depending on the molecular characteristics of the simulated system (branch length, branching frequency, and total chain length). © IWNET 2006
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and Kleanthi for IWNET 2006