Simple Reptation Research Articles

Crossover time in relative fluctuations characterizes the longest relaxation time of entangled polymers

In entangled polymer systems, there are several characteristic time scales, such as the entanglement time and the disengagement time. In molecular simulations, the longest relaxation time (the disengagement time) can be determined by the mean square displacement (MSD) of a segment or by the shear relaxation modulus. Here, we propose the relative fluctuation analysis method, which is originally developed for characterizing large fluctuations, to determine the longest relaxation time from the center of mass trajectories of polymer chains (the time-averaged MSDs). Applying the method to simulation data of entangled polymers (by the slip-spring model and the simple reptation model), we provide a clear evidence that the longest relaxation time is estimated as the crossover time in the relative fluctuations.

Interplay between Dewetting and Layer Inversion in Poly(4-vinylpyridine)/Polystyrene Bilayers

We investigated the morphology and dynamics of the dewetting of metastable poly(4-vinylpyridine) (P4VP) thin films situated on top of polystyrene (PS) thin films as a function of the molecular weight and thickness of both films. We focused on the competition between the dewetting process, occurring as a result of unfavorable intermolecular interactions at the P4VP/PS interface, and layer inversion due to the lower surface energy of PS. By means of optical and atomic force microscopy (AFM), we observed how both the dynamics of the instability and the morphology of the emerging patterns depend on the ratio of the molecular weights of the polymer films. When the bottom PS layer was less viscous than the top P4VP layer (liquid-liquid dewetting), nucleated holes in the P4VP film typically stopped growing at long annealing times because of a combination of viscous dissipation in the bottom layer and partial layer inversion. Full layer inversion was achieved when the viscosity of the top P4VP layer was significantly greater (>10⁴) than the viscosity of the PS layer underneath, which is attributed to strongly different mobilities of the two layers. The density of holes produced by nucleation dewetting was observed for the first time to depend on the thickness of the top film as well as the polymer molecular weight. The final (completely dewetted) morphology of isolated droplets could be achieved only if the time frame of layer inversion was significantly slower than that of dewetting, which was characteristic of high-viscosity PS underlayers that allowed dewetting to fall into a liquid-solid regime. Assuming a simple reptation model for layer inversion occurring at the dewetting front, the observed surface morphologies could be predicted on the basis of the relative rates of dewetting and layer inversion.

A differential formulation of thermal constraint release for entangled linear polymers

We present a new differential formulation of the thermal constraint release phenomenon for linear entangled polymers. This new formulation predicts a relaxation modulus identical to that predicted by the double reptation theory of Tsenoglou [C. Tsenoglou, Viscoelasticity of binary polymer blends, ACS Polym. Prepr. 28 (1987) 185–186] or Des Cloizeaux [J. Des Cloizeaux, Double reptation vs simple reptation in polymer melts, J. Europhys. Lett. 5 (1988) 437–442] for both monodisperse and polydisperse systems. Additionally, we discuss a simple approximation of our approach as well as its possible use for building simple constitutive equations that account for constraint release in a polydisperse environment.

Dielectric and viscoelastic normal-mode relaxation in entangled, polydisperse cis-polyisoprene melts

We investigate the effects of polydispersity on dielectric and viscoelastic normal-mode relaxation of cis-polyisoprene melts above entanglement. Measured dielectric and mechanical spectra and relaxation moduli of polydisperse samples are compared to the predictions of models combining either simple reptation, double reptation or des Cloizeaux’ time-dependent-diffusion single-chain autocorrelation functions (ACF) to linear or nonlinear (Tsenoglou) mixing rules. The blending rules are tested by employing experimental data, thereby eliminating uncertainties associated with the experimental molecular weight distribution (MWD) and choice of specific forms for the ACFs. Predictions from the various models based on the MWD from size exclusion chromatography are compared to the experimental data as well. We find that dielectric spectra are satisfactorily captured by a linear mixing rule, but quantitative description of the rheology requires the use of the nonlinear (Tsenoglou) mixing rule. The single-chain ACF of reptation with a 3.7 power-law dependence of the relaxation time on molecular weight accurately predicts both dielectric and viscoelastic spectra. The double reptation ACF, while being inadequate in the dielectric case, gives viscoelastic predictions that are nearly identical to those obtained with the simple reptation ACF. The des Cloizeaux ACF fails in the dielectric case and is less satisfactory than simple or double reptation in the viscoelastic case. This limited evidence indicates that the ACFs for end-to-end vector reorientation (dielectric relaxation) and entanglement ‘‘dissolution’’ (viscoelastic relaxation), although both originating in chain reptation, reflect different mechanisms.

Simple model of trapping electrophoresis with complicated transient dynamics.

A simple reptation model of DNA trapping gel electrophoresis is shown to lead to surprisingly complicated transient dynamics. The DNA has a big neutral object attached to one of its ends; electrophoretic migration is thus slowed by trapping when it occurs in random gels. The detrapping process is thermally driven and its dependence upon the instantaneous molecular conformation gives rise to anomalous transport properties in our computer simulations. The electric field affects the molecular conformations and thus modifies the nature of the transient dynamics in nontrivial ways. The phenomenon is analyzed in terms of a directed walk through a periodic lattice of traps with a broad release time distribution. For large molecular sizes, we estimate that it is actually impossible to reach the steady state in an (experimentally) reasonable period of time.

‘‘Lakes–straits’’ model of field-inversion gel electrophoresis of DNA

We replace the tube in the simple reptation model of the gel electrophoresis of DNA by a chain of open spaces, ‘‘lakes,’’ connected by narrow ‘‘straits.’’ We also allow loops of DNA to ‘‘overflow’’ out of the sides of the lakes under the pull of the electric field; a method of estimating the frequency of such overflows is developed based on Kramers’ theory of diffusion over a barrier. We study this model under both steady-field and inverting-field conditions. With small fields it explicitly gives an improved form of the simple-reptation formula, distinguishing between the contour length of the chain of lakes and the contour length of the DNA chain within them. With higher fields it is necessary to use computer simulation to integrate the equations of motion. For long chains the results show a very pronounced antiresonance, that is, a minimum, in the dependence of mobility on cycle period with cyclically reversing fields, in semiquantitative agreement with recent experiments. The antiresonance arises from the development of conformations shaped like the Greek letter lambda, Λ, with two arms both pulled in the direction of the field and high tension in the chain near the vertex. Under these conditions the chain moves very slowly, but when the field inverts the lambda appears as a V, and the high tension causes the chain to move rapidly toward the vertex. The antiresonance appears when the timing of the field cycle matches the time of lambda formation, so that the fast motion in the short, backward part of the cycle nearly cancels the slow motion in the long, forward part. The period of the antiresonance is proportional to the time needed for the chain to traverse its own length in steady field; the dimensionless proportionality constant appears to have a value of 0.4±0.1 both in our simulations and in experiments from the literature over a variety of conditions.

Self-diffusion of polystyrene in solution 2. Discussion of experimental results on the basis of the reptation mechanism and entanglements

The expressions for polymer self-diffusion in semidilute solutions, theoretically derived from the reptation mechanism, the blob concept and scaling considerations, are discussed and compared against experimental data from the authors' investigations and the literature. In the nonentangled (from viscoelastic data) semidilute solution, the experimentally observed concentration and molar mass exponents are in fair agreement with those derived theoretically. However, a quantitative estimation shows that the experiments cannot be explained by reptation. Experiments with polymer mixtures also give strong evidence against reptation. It is concluded, that in the nonentangled semidilute solution, the polymer self-diffusion is more complicated than simple reptation. This is also supported by recently observed long-range density fluctuations or cluster formation in this concentration region detected by scattering techniques and NMR-PFGT. In the entangled semidilute solution, the self-diffusion data are in accordance with the reptation mechanism; reptation being within a tube having approximately 20 blobs between entanglements.

Morphology dynamics of block copolymer systems

The approach to polymer morphology dynamics developed in our previous paper (Physica 143A (1987) 349) is applied to block copolymer systems. The combination of the reptation idea and the incompressibility requirement introduces correlations among reptative motions, where polymer ends as well as junction points play important roles. Diffusive motion of smooth deformations of the lamellar structure is derived. The domain wall equation of motion is also derived in the strong segregation limit. However, there are some difficulties in the simple reptation model in this limit which are also discussed. Finally, consequences of certain ways of relaxing the strict incompressibility requirement are discussed.