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1

Karatrantos, Argyrios, Russell J. Composto, Karen I. Winey, Martin Kröger, and Nigel Clarke. "Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review." Polymers 11, no. 5 (May 14, 2019): 876. http://dx.doi.org/10.3390/polym11050876.

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This review concerns modeling studies of the fundamental problem of entangled (reptational) homopolymer diffusion in melts and nanocomposite materials in comparison to experiments. In polymer melts, the developed united atom and multibead spring models predict an exponent of the molecular weight dependence to the polymer diffusion very similar to experiments and the tube reptation model. There are rather unexplored parameters that can influence polymer diffusion such as polymer semiflexibility or polydispersity, leading to a different exponent. Models with soft potentials or slip-springs can estimate accurately the tube model predictions in polymer melts enabling us to reach larger length scales and simulate well entangled polymers. However, in polymer nanocomposites, reptational polymer diffusion is more complicated due to nanoparticle fillers size, loading, geometry and polymer-nanoparticle interactions.
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2

Cloizeaux, J. des. "Double Reptation vs. Simple Reptation in Polymer Melts." Europhysics Letters (EPL) 5, no. 5 (March 1, 1988): 437–42. http://dx.doi.org/10.1209/0295-5075/5/5/010.

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3

Cloizeaux, J. des. "Double Reptation vs. Simple Reptation in Polymer Melts." Europhysics Letters (EPL) 6, no. 5 (July 1, 1988): 475. http://dx.doi.org/10.1209/0295-5075/6/5/018.

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4

Composto, Russell J., Edward J. Kramer, and Dwain M. White. "Reptation in polymer blends." Polymer 31, no. 12 (December 1990): 2320–28. http://dx.doi.org/10.1016/0032-3861(90)90319-t.

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5

SKOLNICK, JEFFREY, ROBERT YARIS, and ANDRZEJ KOLINSKI. "PHENOMENOLOGICAL THEORY OF POLYMER MELT DYNAMICS." International Journal of Modern Physics B 03, no. 01 (January 1989): 33–64. http://dx.doi.org/10.1142/s0217979289000038.

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A particularly interesting problem in polymer physics is the mechanism by which an individual polymer chain moves in a polymer melt or concentrated polymer solution. The first rather successful model of polymer dynamics was the reptation model of de Gennes which asserts that due to the effect of entanglements a polymer finds itself confined to a tube. Thus, the dominant long wavelength motion of the chain should be slithering out the ends of the tube. In order to examine the validity of the reptation model, a series of dynamic Monte Carlo simulations were performed. Although the simulations are on chains sufficiently long that agreement with the experimentally observed scaling with degree of polymerization n of the self diffusion constant and terminal relaxation time is observed, reptation does not appear to be the dominant mechanism of long distance motion. Rather the motion is isotropic, with the slowdown from dilute solution behavior arising from the formation of dynamic entanglements — rare long lived contacts where a given chain drags another chain through the melt for times on the order of longest internal relaxation time. Motivated by the simulations results, a phenomenological theory for the diffusive and viscoelastic behavior is developed that is consistent with both simulations and experiment and which does not invoke reptation. The major conclusions arising from the theoretical approach are described, and comparison is made with experiment.
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6

Maestro, Armando, Hani M. Hilles, Francisco Ortega, Ramón G. Rubio, Dominique Langevin, and Francisco Monroy. "Reptation in langmuir polymer monolayers." Soft Matter 6, no. 18 (2010): 4407. http://dx.doi.org/10.1039/c0sm00250j.

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7

Schiessel, H., J. Widom, R. F. Bruinsma, and W. M. Gelbart. "Polymer Reptation and Nucleosome Repositioning." Physical Review Letters 86, no. 19 (May 7, 2001): 4414–17. http://dx.doi.org/10.1103/physrevlett.86.4414.

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8

Sackmann, Erich, Josef Käs, and Helmut Strey. "The observation of polymer reptation." Advanced Materials 6, no. 6 (June 1994): 507–9. http://dx.doi.org/10.1002/adma.19940060617.

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9

Schaefer, D. W. "Polymer reptation in semidilute solution." Journal of Polymer Science: Polymer Symposia 73, no. 1 (March 8, 2007): 121–31. http://dx.doi.org/10.1002/polc.5070730117.

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10

Scher, Harvey, and Michael F. Shlesinger. "On reptation in polymer melts." Journal of Chemical Physics 84, no. 10 (May 15, 1986): 5922–24. http://dx.doi.org/10.1063/1.449905.

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11

Cule, Dinko, and Terence Hwa. "Polymer Reptation in Disordered Media." Physical Review Letters 80, no. 14 (April 6, 1998): 3145–48. http://dx.doi.org/10.1103/physrevlett.80.3145.

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12

Herman, Michael F., and S. F. Edwards. "A reptation model for polymer dissolution." Macromolecules 23, no. 15 (July 1990): 3662–71. http://dx.doi.org/10.1021/ma00217a020.

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13

Valadez-Pérez, Néstor, Konstantin Taletskiy, Jay Schieber, and Maksim Shivokhin. "Efficient Determination of Slip-Link Parameters from Broadly Polydisperse Linear Melts." Polymers 10, no. 8 (August 12, 2018): 908. http://dx.doi.org/10.3390/polym10080908.

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We investigate the ability of a coarse-grained slip-link model and a simple double reptation model to describe the linear rheology of polydisperse linear polymer melts. Our slip-link model is a well-defined mathematical object that can describe the equilibrium dynamics and non-linear rheology of flexible polymer melts with arbitrary polydispersity and architecture with a minimum of inputs: the molecular weight of a Kuhn step, the entanglement activity, and Kuhn step friction. However, this detailed model is computationally expensive, so we also examine predictions of the cheaper double reptation model, which is restricted to only linear rheology near the terminal zone. We report the storage and loss moduli for polydisperse polymer melts and compare with experimental measurements from small amplitude oscillatory shear. We examine three chemistries: polybutadiene, polypropylene and polyethylene. We also use a simple double reptation model to estimate parameters for the slip-link model and examine under which circumstances this simplified model works. The computational implementation of the slip-link model is accelerated with the help of graphics processing units, which allow us to simulate in parallel large ensembles made of up to 50,000 chains. We show that our simulation can predict the dynamic moduli for highly entangled polymer melts over nine decades of frequency. Although the double reptation model performs well only near the terminal zone, it does provide a convenient and inexpensive way to estimate the entanglement parameter for the slip-link model from polydisperse data.
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14

Russell, T. P., V. R. Deline, W. D. Dozier, G. P. Felcher, G. Agrawal, R. P. Wool, and J. W. Mays. "Direct observation of reptation at polymer interfaces." Nature 365, no. 6443 (September 1993): 235–37. http://dx.doi.org/10.1038/365235a0.

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15

Fyhrie, D. P., and J. R. Barone. "Polymer Dynamics as a Mechanistic Model for the Flow-Independent Viscoelasticity of Cartilage." Journal of Biomechanical Engineering 125, no. 5 (October 1, 2003): 578–84. http://dx.doi.org/10.1115/1.1610019.

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The initial, rapid, flow independent, apparent stress relaxation of articular cartilage disks deformed by unconfined compressive displacement is shown to be consistent with the theory of polymer dynamics. A relaxation function for polymers based upon a mechanistic model of molecular interaction (reptation) appropriately approximated early, flow independent relaxation of stress. It is argued that the theory of polymer dynamics, with its reliance on mechanistic models of molecular interaction, is an appropriate technique for application to and the understanding of rapid, flow independent, stress relaxation in cartilage.
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16

Gustafson, Andrew, and David C. Morse. "A Reptation Model of Slip at Entangled Polymer–Polymer Interfaces." Macromolecules 49, no. 18 (September 14, 2016): 7032–44. http://dx.doi.org/10.1021/acs.macromol.6b00666.

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17

Anderssen, R. S., and M. Westcott. "The molecular weight distribution problem and reptation mixing rules." ANZIAM Journal 42, no. 1 (July 2000): 26–40. http://dx.doi.org/10.1017/s1446181100011573.

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AbstractMixing rules model how the physical properties of a polymer, such as its relaxation modulus G(t), depend on the distribution w(m) of its molecular weights m. They are of practical importance because, among other things, they allow estimates of the molecular weight distribution (MWD) w(m) of a polymer to be determined from measurements of its physical properties including the relaxation modulus. The two most common mixing rules are “single” and “double” reptation. Various derivations for these rules have been published. In this paper, a conditional probability formulation is given which identifies that the fundamental essence of “double” reptation is the discrete binary nature of the “entanglements”, which are assumed to occur in the corresponding topological model of the underlying polymer dynamics. In addition, various methods for determining the MWD are reviewed, and the computation of linear functionals of the MWD motivated and briefly examined.
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18

des Cloizeaux, J. "Polymer melts: a theoretical justification of double reptation." Journal de Physique I 3, no. 1 (January 1993): 61–68. http://dx.doi.org/10.1051/jp1:1993112.

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19

Duan, Xiaoli, Qingxin Tang, Jie Qiu, Yanhua Niu, Zhigang Wang, and Wenping Hu. "Polymer reptation for molecular assembly of copper phthalocyanine." Applied Physics Letters 95, no. 11 (September 14, 2009): 113301. http://dx.doi.org/10.1063/1.3216040.

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20

Nam, Gimoon, Albert Johner, and Nam-Kyung Lee. "Reptation of a semiflexible polymer through porous media." Journal of Chemical Physics 133, no. 4 (July 28, 2010): 044908. http://dx.doi.org/10.1063/1.3457999.

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21

Buhot, Arnaud. "Viscosity and Renewal Time of Polymer Reptation Models." Macromolecules 43, no. 21 (November 9, 2010): 9155–59. http://dx.doi.org/10.1021/ma1015402.

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22

Hess, W. "Self-diffusion and reptation in semidilute polymer solutions." Macromolecules 19, no. 5 (September 1986): 1395–404. http://dx.doi.org/10.1021/ma00159a019.

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23

Marmonier, M. F., and L. Leger. "Reptation and Tube Renewal in Entangled Polymer Solutions." Physical Review Letters 55, no. 10 (September 2, 1985): 1078–81. http://dx.doi.org/10.1103/physrevlett.55.1078.

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24

Semenov, A. N., and M. Rubinstein. "Dynamics of strongly entangled polymer systems: activated reptation." European Physical Journal B 1, no. 1 (January 1998): 87–94. http://dx.doi.org/10.1007/s100510050155.

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25

Rotstein, N. A., S. Prager, T. P. Lodge, and M. Tirrell. "Simultaneous reptation and constraint release in polymer melts." Theoretica Chimica Acta 82, no. 5 (1992): 383–96. http://dx.doi.org/10.1007/bf01113939.

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26

KAWASAKI, KYOZI. "A NOTE ON THE MODE COUPLING THEORY OF POLYMER MELT DYNAMICS." Modern Physics Letters B 04, no. 14 (August 10, 1990): 913–16. http://dx.doi.org/10.1142/s0217984990001124.

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The mode coupling theory of polymer melt dynamics put forward recently by Schweizer is combined with the curvilinear displacement invariance of the potential energy. The resulting equation of motion of a tagged polymer chain is shown to be consistent with the reptation picture when the matrix surrounding the tagged chain is frozen.
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27

SHIWA, YASUHIRO. "THEORY OF POLYMER RELAXATION TIMES IN SEMI-DILUTE SOLUTIONS." International Journal of Modern Physics B 09, no. 01 (January 10, 1995): 57–67. http://dx.doi.org/10.1142/s0217979295000045.

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The explicit crossover behavior of the longest relaxation time for the dilute and semi-dilute polymer solutions is presented. Gradual reduction of the excluded-volume and the hydrodynamic interaction due to screening is taken into account along with the entanglement effect. The result reveals a continuous approach to a reptation-like asymptote with increasing concentration.
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28

Mohorič, Aleš, Gojmir Lahajnar, and Janez Stepišnik. "Diffusion Spectrum of Polymer Melt Measured by Varying Magnetic Field Gradient Pulse Width in PGSE NMR." Molecules 25, no. 24 (December 9, 2020): 5813. http://dx.doi.org/10.3390/molecules25245813.

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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.
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29

Klein Wolterink *, J., and G. T. Barkema. "Polymer diffusion in a lattice polymer model with an intrinsic reptation mechanism." Molecular Physics 103, no. 21-23 (November 10, 2005): 3083–89. http://dx.doi.org/10.1080/00268970500208682.

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30

Öttinger, Hans Christian. "Coarse-graining of wormlike polymer chains for substantiating reptation." Journal of Non-Newtonian Fluid Mechanics 120, no. 1-3 (July 2004): 207–13. http://dx.doi.org/10.1016/j.jnnfm.2003.12.006.

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31

Langeloth, Michael, Yuichi Masubuchi, Michael C. Böhm, and Florian Müller-Plathe. "Reptation and constraint release dynamics in bidisperse polymer melts." Journal of Chemical Physics 141, no. 19 (November 21, 2014): 194904. http://dx.doi.org/10.1063/1.4901425.

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32

Aalberts, Daniel P., and J. M. J. Van Leeuwen. "Dynamic symmetry breaking in a model of polymer reptation." Electrophoresis 17, no. 6 (1996): 1003–10. http://dx.doi.org/10.1002/elps.1150170607.

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33

FALLER, ROLAND, MATHIAS PÜTZ, and FLORIAN MÜLLER-PLATHE. "ORIENTATION CORRELATION IN SIMPLIFIED MODELS OF POLYMER MELTS." International Journal of Modern Physics C 10, no. 02n03 (May 1999): 355–60. http://dx.doi.org/10.1142/s0129183199000267.

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We investigate mutual local chain order in systems of fully flexible polymer melts in a simple generic bead-spring model. The excluded-volume interaction together with the connectivity leads to local ordering effects which are independent of chain length between 25 and 700 monomers, i.e. in the Rouse as well as in the reptation regime. These ordering phenomena extend to a distance of about 3 to 4 monomer sizes and decay to zero afterwards.
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34

von Meerwall, Ernst D. "Pulsed and Steady Field Gradient NMR Diffusion Measurements in Polymers." Rubber Chemistry and Technology 58, no. 3 (July 1, 1985): 527–60. http://dx.doi.org/10.5254/1.3536078.

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Abstract Some twenty years after the development of the steady and pulsed gradient spin-echo NMR methods of measuring self-diffusion, these techniques are now maturing and experiencing a surge of interest, much of it concentrated on polymer systems. The methods are briefly reviewed here, together with the most important results in polymers, with particular concentration on work described within the last few years. The research is divisible into three categories: diffusion of diluent and penetrant molecules in rubbery high polymers, diffusion of polymer molecules in dilute and semidilute solutions with liquid solvents, and diffusion of macromolecules dissolved in concentrated solutions or melts of equivalent or different polymers of arbitrary molecular weight. The review includes the main theoretical interpretations of the experiments, particularly the free-volume theory in its various forms and power-law behaviors postulated by recent refinements of tube/reptation and scaling theory. This article represents an updated elaboration of an earlier review.
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35

SCHAUSBERGER, A., G. SCHINDLAUER, and H. JANESCHITZ-KRIEGL. "POLYMER MELT RHEOLOGY: ON THE EVALUATION OF THE REPTATION MODEL." Chemical Engineering Communications 32, no. 1-5 (January 1985): 101–15. http://dx.doi.org/10.1080/00986448508911644.

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36

Richter, D., L. Willner, A. Zirkel, B. Farago, L. J. Fetters, and J. S. Huang. "Polymer Motion at the Crossover from Rouse to Reptation Dynamics." Macromolecules 27, no. 25 (December 1994): 7437–46. http://dx.doi.org/10.1021/ma00103a029.

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37

Semenov, A. N. "Concentration fluctuations and reptation dynamics in polymer solutions and melts." Physica A: Statistical Mechanics and its Applications 171, no. 3 (March 1991): 517–53. http://dx.doi.org/10.1016/0378-4371(91)90300-2.

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38

Рыжов, В. А., В. В. Жиженков, and Н. Г. Квачадзе. "Особенности локальной динамики и ориентационного состояния жесткоцепных жидкокристаллических полимеров." Физика твердого тела 61, no. 2 (2019): 381. http://dx.doi.org/10.21883/ftt.2019.02.47141.218.

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AbstractProton magnetic resonance (PMR) spectra and terahertz IR spectra of Vectra A950 fibers and granules and Armos fibers before and after heat treatment were obtained and analyzed in order to understand the molecular mobility mechanisms that ensure the self-organization and restructurization of these rigid-chain liquid-crystal polymers, as well as their similarity and difference. It is shown that large-scale thermal (quasi-segmental) mobility in such LC polymers is due to the reptation of macromolecules with respect to each other and the conformational transitions necessary for the motion of chains in them are the result of random accumulation of displacements that occur during local bending and torsional-vibrational movements in the links of polymer chains according to the Bresler–Frenkel mechanism.
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39

Thimm, Wolfgang, Christian Friedrich, Dieter Maier, Michael Marth, and Josef Honerkamp. "Determination of Molecular Weight Distributions from Rheological Data: An Application to Polystyrene, Polymethylmethacrylate and Isotactic Polypropylene." Applied Rheology 9, no. 4 (August 1, 1999): 150–57. http://dx.doi.org/10.1515/arh-2009-0010.

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Abstract Based on a recently introduced generalized mixing rule, which contains the results of the reptation and double reptation model as special cases, it is possible to determine the molecular weight distribution (MWD) from rheological data. By evaluating data from bimodal PS-mixtures Maier et al. (1998) have shown how the MWD can be estimated from the relaxation shear modulus, G(t), using an inversion method. Thimm et al. (1999) derived an analytical relation between the relaxation time spectrum and the MWD, which is able to reproduce the result of Maier et al. (1998) with less computational effort. In this article we compare both methods by evaluating data from three different series of polymer mixtures: Polystyrene (PS), Polymethylmethacrylate (PMMA) and isotactic Polypropylene (iPP). We compare the MWD obtained from rheological data with results from size exclusion chromatography (SEC) and discuss differences.
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40

Consolati, Giovanni, Dario Nichetti, Francesco Briatico Vangosa, and Fiorenza Quasso. "BEYOND THE SPHERICAL APPROXIMATION: ELONGATED FREE VOLUME HOLES IN RUBBERS: A POSITRON ANNIHILATION STUDY." Rubber Chemistry and Technology 92, no. 4 (October 1, 2019): 709–21. http://dx.doi.org/10.5254/rct.19.80452.

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ABSTRACT The free volume fraction, a key parameter for the understanding of mechanical and transport properties of polymers, has been evaluated in a fluoroelastomer and a cis-polyisoprene rubber by means of positron annihilation lifetime spectroscopy and dilatometry. The evaluation showed that the assumption of elongated holes allows one to get a very good agreement between the free volume fraction experimentally determined and the theoretical expectation based on the lattice-hole model. On the other hand, systematic discrepancies are found using the spherical approximation. Moreover, the average hole size is found to be correlated to the effective bond length leff, a parameter connected to reptation motions and largely independent of the polymer structure. The result sheds some light on conformational statistics for the most flexible linear polymers that approach Gaussian chain behavior.
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41

Von Seggern, J., S. Klotz, and H. J. Cantow. "Reptation and constraint release in linear polymer melts: an experimental study." Macromolecules 24, no. 11 (May 1991): 3300–3303. http://dx.doi.org/10.1021/ma00011a039.

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42

Viovy, Jean-Louis, and Thomas Duke. "DNA electrophoresis in polymer solutions: Ogston sieving, reptation and constraint release." Electrophoresis 14, no. 1 (1993): 322–29. http://dx.doi.org/10.1002/elps.1150140155.

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43

Zheng, X., B. B. Sauer, J. G. Van Alsten, S. A. Schwarz, M. H. Rafailovich, J. Sokolov, and Michael Rubinstein. "Reptation Dynamics of a Polymer Melt near an Attractive Solid Interface." Physical Review Letters 74, no. 3 (January 16, 1995): 407–10. http://dx.doi.org/10.1103/physrevlett.74.407.

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44

Arrighi, Valeria, and Julia S. Higgins. "Local Effects of Ring Topology Observed in Polymer Conformation and Dynamics by Neutron Scattering—A Review." Polymers 12, no. 9 (August 21, 2020): 1884. http://dx.doi.org/10.3390/polym12091884.

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The physical properties of polymers depend on a range of both structural and chemical parameters, and in particular, on molecular topology. Apparently simple changes such as joining chains at a point to form stars or simply joining the two ends to form a ring can profoundly alter molecular conformation and dynamics, and hence properties. Cyclic polymers, as they do not have free ends, represent the simplest model system where reptation is completely suppressed. As a consequence, there exists a considerable literature and several reviews focused on high molecular weight cyclics where long range dynamics described by the reptation model comes into play. However, this is only one area of interest. Consideration of the conformation and dynamics of rings and chains, and of their mixtures, over molecular weights ranging from tens of repeat units up to and beyond the onset of entanglements and in both solution and melts has provided a rich literature for theory and simulation. Experimental work, particularly neutron scattering, has been limited by the difficulty of synthesizing well-characterized ring samples, and deuterated analogues. Here in the context of the broader literature we review investigations of local conformation and dynamics of linear and cyclic polymers, concentrating on poly(dimethyl siloxane) (PDMS) and covering a wide range of generally less high molar masses. Experimental data from small angle neutron scattering (SANS) and quasi-elastic neutron scattering (QENS), including Neutron Spin Echo (NSE), are compared to theory and computational predictions.
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45

Mayeed, M. S., and T. Kato. "Modeling Replenishment of Ultrathin Liquid Perfluoropolyether Z Films on Solid Surfaces Using Monte Carlo Simulation." Journal of Nanoscience 2014 (April 6, 2014): 1–9. http://dx.doi.org/10.1155/2014/104137.

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Applying the reptation algorithm to a simplified perfluoropolyether Z off-lattice polymer model an NVT Monte Carlo simulation has been performed. Bulk condition has been simulated first to compare the average radius of gyration with the bulk experimental results. Then the model is tested for its ability to describe dynamics. After this, it is applied to observe the replenishment of nanoscale ultrathin liquid films on solid flat carbon surfaces. The replenishment rate for trenches of different widths (8, 12, and 16 nms for several molecular weights) between two films of perfluoropolyether Z from the Monte Carlo simulation is compared to that obtained solving the diffusion equation using the experimental diffusion coefficients of Ma et al. (1999), with room condition in both cases. Replenishment per Monte Carlo cycle seems to be a constant multiple of replenishment per second at least up to 2 nm replenished film thickness of the trenches over the carbon surface. Considerable good agreement has been achieved here between the experimental results and the dynamics of molecules using reptation moves in the ultrathin liquid films on solid surfaces.
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46

Zimm, Bruno H., and Oscar Lumpkin. "Reptation of a polymer chain in an irregular matrix: diffusion and electrophoresis." Macromolecules 26, no. 1 (January 1993): 226–34. http://dx.doi.org/10.1021/ma00053a035.

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47

Faller, Roland, and Florian Müller-Plathe. "Chain Stiffness Intensifies the Reptation Characteristics of Polymer Dynamics in the Melt." ChemPhysChem 2, no. 3 (March 16, 2001): 180–84. http://dx.doi.org/10.1002/1439-7641(20010316)2:3<180::aid-cphc180>3.0.co;2-z.

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48

Reiter, G., and U. Steiner. "Measurements of polymer diffusion over small distances. A check of reptation arguments." Journal de Physique II 1, no. 6 (June 1991): 659–71. http://dx.doi.org/10.1051/jp2:1991197.

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49

Canpolat, Murat, Ayşe Erzan, and Önder Pekcan. "Reptation of a polymer chain by conformal transitions in the entangled regime." Physical Review E 52, no. 6 (December 1, 1995): 6904–7. http://dx.doi.org/10.1103/physreve.52.6904.

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Schulz, M., R. G. Winkler, and P. Reineker. "Reptation of polymer chains: A combined Monte Carlo and molecular-dynamics study." Physical Review B 48, no. 1 (July 1, 1993): 581–84. http://dx.doi.org/10.1103/physrevb.48.581.

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