Constraint release in entangled binary blends of linear polymers: a molecular dynamics study

We present extensive molecular dynamics simulations of the dynamics of diluted long probe chains entangled with a matrix of shorter chains. The chain lengths of both components are above the entanglement strand length, and the ratio of their lengths is varied over a wide range to cover the crossover from the chain reptation regime to tube Rouse motion regime of the long probe chains. Reducing the matrix chain length results in a faster decay of the dynamic structure factor of the probe chains, in good agreement with recent neutron spin echo experiments. The diffusion of the long chains, measured by the mean square displacements of the monomers and the centers of mass of the chains, demonstrates a systematic speed-up relative to the pure reptation behavior expected for monodisperse melts of sufficiently long polymers. On the other hand, the diffusion of the matrix chains is only weakly perturbed by the diluted long probe chains. The simulation results are qualitatively consistent with the theoretical predictions based on constraint release Rouse model, but a detailed comparison reveals the existence of a broad distribution of the disentanglement rates, which is partly confirmed by an analysis of the packing and diffusion of the matrix chains in the tube region of the probe chains. A coarse-grained simulation model based on the tube Rouse motion model with incorporation of the probability distribution of the tube segment jump rates is developed and shows results qualitatively consistent with the fine scale molecular dynamics simulations. However, we observe a breakdown in the tube Rouse model when the short chain length is decreased to around N-S = 80, which is roughly 3.5 times the entanglement spacing N-e(P) = 23. The location of this transition may be sensitive to the chain bending potential used in our simulations.

Neutron-mapping polymer flow: Scattering, flow visualization, and molecular theory

Flows of complex fluids need to be understood at both macroscopic and molecular scales, because it is the macroscopic response that controls the fluid behavior, but the molecular scale that ultimately gives rise to rheological and solid-state properties. Here the flow field of an entangled polymer melt through an extended contraction, typical of many polymer processes, is imaged optically and by small-angle neutron scattering. The dual-probe technique samples both the macroscopic stress field in the flow and the microscopic configuration of the polymer molecules at selected points. The results are compared with a recent tube model molecular theory of entangled melt flow that is able to calculate both the stress and the single-chain structure factor from first principles. The combined action of the three fundamental entangled processes of reptation, contour length fluctuation, and convective constraint release is essential to account quantitatively for the rich rheological behavior. The multiscale approach unearths a new feature: Orientation at the length scale of the entire chain decays considerably more slowly than at the smaller entanglement length.

Constriction flows of monodisperse linear entangled polymers: Multiscale modeling and flow visualization

We explore both the rheology and complex flow behavior of monodisperse polymer melts. Adequate quantities of monodisperse polymer were synthesized in order that both the materials rheology and microprocessing behavior could be established. In parallel, we employ a molecular theory for the polymer rheology that is suitable for comparison with experimental rheometric data and numerical simulation for microprocessing flows. The model is capable of matching both shear and extensional data with minimal parameter fitting. Experimental data for the processing behavior of monodisperse polymers are presented for the first time as flow birefringence and pressure difference data obtained using a Multipass Rheometer with an 11:1 constriction entry and exit flow. Matching of experimental processing data was obtained using the constitutive equation with the Lagrangian numerical solver, FLOWSOLVE. The results show the direct coupling between molecular constitutive response and macroscopic processing behavior, and differentiate flow effects that arise separately from orientation and stretch. (c) 2005 The Society of Rheology.

Hierarchical modeling of entangled polymers

We demonstrate that it is possible to link multi-chain molecular dynamics simulations with the tube model using a single chain slip-links model as a bridge. This hierarchical approach allows significant speed up of simulations, permitting us to span the time scales relevant for a comparison with the tube theory. Fitting the mean-square displacement of individual monomers in molecular dynamics simulations with the slip-spring model, we show that it is possible to predict the stress relaxation. Then, we analyze the stress relaxation from slip-spring simulations in the framework of the tube theory. In the absence of constraint release, we establish that the relaxation modulus can be decomposed as the sum of contributions from fast and longitudinal Rouse modes, and tube survival. Finally, we discuss some open questions regarding possible future directions that could be profitable in rendering the tube model quantitative, even for mildly entangled polymers

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

Stimulating dormancy release and emergence of annual ryegrass (Lolium rigidum) seeds using short-term hydrated storage in darkness

Experiments were performed to determine whether the dormancy release effect of hydrated storage in darkness (dark-stratification) is common amongst annual ryegrass populations and has the potential to occur under field conditions. Dormant seeds from all populations tested (22) became sensitive to light during dark-stratification, enabling them to germinate when subsequently exposed to light. Under controlled temperature (25/15degreesC), light (12-h photoperiod), and hydration (solidified agar-water) conditions, more seeds germinated by 28 days if the first 14 days were in darkness followed by exposure to light for 12 h per day than if they were exposed to light throughout or darkness throughout. Constraint over the conditions imposed during dark-stratification and germination was gradually reduced to investigate whether the dormancy release effect was diminished. Dark-stratification was effective in promoting germination when performed under natural diurnal temperatures, and burial in moist soil provided suitable conditions for dark-stratification to occur. The surface of moist soil, with natural diurnal temperatures and sunlight, was suitable for germination of dark-stratified seeds. Dark-stratification is a quick and effective means to enhance the sensitivity of dormant annual ryegrass seeds to light, enabling the majority of the population to germinate. However, large quantities of light are required to promote germination of dark-stratified seeds, so buried seeds must be moved to the soil surface to allow exposure to adequate light for germination.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model

For data assimilation in numerical weather prediction, the initial forecast-error covariance matrix Pf is required. For variational assimilation it is particularly important to prescribe an accurate initial matrix Pf, since Pf is either static (in the 3D-Var case) or constant at the beginning of each assimilation window (in the 4D-Var case). At large scales the atmospheric flow is well approximated by hydrostatic balance and this balance is strongly enforced in the initial matrix Pf used in operational variational assimilation systems such as that of the Met Office. However, at convective scales this balance does not necessarily hold any more. Here we examine the extent to which hydrostatic balance is valid in the vertical forecast-error covariances for high-resolution models in order to determine whether there is a need to relax this balance constraint in convective-scale data assimilation. We use the Met Office Global and Regional Ensemble Prediction System (MOGREPS) and a 1.5 km resolution version of the Unified Model for a case study characterized by the presence of convective activity. An ensemble of high-resolution forecasts valid up to three hours after the onset of convection is produced. We show that at 1.5 km resolution hydrostatic balance does not hold for forecast errors in regions of convection. This indicates that in the presence of convection hydrostatic balance should not be enforced in the covariance matrix used for variational data assimilation at this scale. The results show the need to investigate covariance models that may be better suited for convective-scale data assimilation. Finally, we give a measure of the balance present in the forecast perturbations as a function of the horizontal scale (from 3–90 km) using a set of diagnostics. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

The role of convective parameterization in the simulation of a cyclone over the South Atlantic

Numerical simulations are carried out to examine the role of the Kuo and Kain-Fritsch (KF) cumulus parameterization schemes and dry dynamics on a cyclone development, in a weak baroclinic atmosphere, over subtropical South Atlantic Ocean. The initial phase of the cyclone development is investigated with a coarse horizontal mesh (75 km) and when the cyclone reaches the mature stage two different horizontal resolutions are used (75 and 25 km). The best performance simulation for the cyclone initial phase occurs when the Kuo convective scheme is applied, and this may be attributed to a greater diabatic warming in the troposphere. On the other hand, the dry simulation is not capable of simulating the correct location and intensity of the cyclone in its initial phase. During the mature phase, a cyclone over deepening occurs in the Kuo scheme experiment associated with larger latent heat release in a deep vertical column. The presence of downdraft currents in the KF scheme, which acts to cool and dry the lower levels, is essential to stabilize the atmosphere and to reproduce the nearest observation cyclone deepening rate. The largest cyclone deepening is found in the Kuo scheme high resolution experiment. This suggests that the KF convective scheme is less sensitive to the horizontal grid resolution. It was also revealed that the diabatic processes are crucial to simulate the observed features of this marine cyclone over subtropical region.

Modeling of deep-convective

Deep convection by pyro-cumulonimbus clouds (pyroCb) can transport large amounts of forest fire smoke into the upper troposphere and lower stratosphere. Here, results from numerical simulations of such deep convective smoke transport are presented. The structure, shape and injection height of the pyroCb simulated for a specific case study are in good agreement with observations. The model results confirm that substantial amounts of smoke are injected into the lower stratosphere. Small-scale mixing processes at the cloud top result in a significant enhancement of smoke injection into the stratosphere. Sensitivity studies show that the release of sensible heat by the fire plays an important role for the dynamics of the pyroCb. Furthermore, the convection is found to be very sensitive to background meteorological conditions. While the abundance of aerosol particles acting as cloud condensation nuclei (CCN) has a strong influence on the microphysical structure of the pyroCb, the CCN effect on the convective dynamics is rather weak. The release of latent heat dominates the overall energy budget of the pyroCb. Since most of the cloud water originates from moisture entrained from the background atmosphere, the fire-released moisture contributes only minor to convection dynamics. Sufficient fire heating, favorable meteorological conditions, and small-scale mixing processes at the cloud top are identified as the key ingredients for troposphere-to-stratosphere transport by pyroCb convection.

Auxin And Physical Constraint Exerted By The Perianth Promote Androgynophore Bending In Passiflora Mucronata L. (passifloraceae).

The androgynophore column, a distinctive floral feature in passion flowers, is strongly crooked or bent in many Passiflora species pollinated by bats. This is a floral feature that facilitates the adaptation to bat pollination. Crooking or bending of plant organs are generally caused by environmental stimulus (e.g. mechanical barriers) and might involve the differential distribution of auxin. Our aim was to study the role of the perianth organs and the effect of auxin in bending of the androgynophore of the bat-pollinated species Passiflora mucronata. Morpho-anatomical characterisation of the androgynophore, including measurements of curvature angles and cell sizes both at the dorsal (convex) and ventral (concave) sides of the androgynophore, was performed on control flowers, flowers from which perianth organs were partially removed and flowers treated either with auxin (2,4-dichlorophenoxyacetic acid; 2,4-D) or with an inhibitor of auxin polar transport (naphthylphthalamic acid; NPA). Asymmetric growth of the androgynophore column, leading to bending, occurs at a late stage of flower development. Removing the physical constraint exerted by perianth organs or treatment with NPA significantly reduced androgynophore bending. Additionally, the androgynophores of plants treated with 2,4-D were more curved when compared to controls. There was a larger cellular expansion at the dorsal side of the androgynophores of plants treated with 2,4-D and in both sides of the androgynophores of plants treated with NPA. This study suggests that the physical constraint exerted by perianth and auxin redistribution promotes androgynophore bending in P. mucronata and might be related to the evolution of chiropterophily in the genus Passiflora.

Fluoride release profile of a nanofilled resin-modified glass ionomer cement

The present study aimed to compare the fluoride (F-) release pattern of a nanofilled resin-modified glass ionomer cement (GIC) (Ketac N100 - KN) with available GICs used in dental practice (resin-modified GIC - Vitremer - V; conventional GIC - Ketac Molar - KM) and a nanofilled resin composite (Filtek Supreme - RC). Discs of each material (n=6) were placed into 4 mL of deionized water in sealed polyethylene vials and shaken, for 15 days. F- release (μg F-/cm²) was measured each day using a fluoride-ion specific electrode. Cumulative F- release means were statistically analyzed by linear regression analysis. In order to analyze the differences among materials and the influence of time in the daily F- release, 2-way ANOVA test was performed (α=0.05). The linear fits between the cumulative F- release profiles of RC and KM and time were weak. KN and V presented a strong relationship between cumulative F- release and time. There were significant differences between the daily F- release overtime up to the third day only for GICs materials. The daily F- release means for RC were similar overtime. The results indicate that the F- release profile of the nanofilled resin-modified GIC is comparable to the resin-modified GIC.