A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

Superensembles of linear viscoelastic models of polymer melts

The idea of incorporating multiple models of linear rheology into a superensemble, to forge a consensus forecast from the individual model predictions, is investigated. The relative importance of the individual models in the so-called multimodel superensemble (MMSE) was inferred by evaluating their performance on a set of experimental training data, via nonlinear regression. The predictive ability of the MMSE model was tested by comparing its predictions on test data that were similar (in-sample) and dissimilar (out-of-sample) to the training data used in the calibration. For the in-sample forecasts, we found that the MMSE model easily outperformed the best constituent model. The presence of good individual models greatly enhanced the MMSE forecast, while the presence of some bad models in the superensemble also improved the MMSE forecast modestly. While the performance of the MMSE model on the out-of-sample training data was not as spectacular, it demonstrated the robustness of this approach.

Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Viscoelastic properties of high pressure and heat induced tofu gels

Tofu gels were rheologically examined to determine their storage or elastic (G′) and loss or viscous (G″) moduli as a function of frequency within their linear viscoelastic limits. The tofu gels were made using either glucono-δ-lactone (GDL) or calcium sulphate (CaSO4·2H2O), followed by either heat treatment (heated soymilk at 97 °C prior to coagulation and subsequently held at 70 °C for 60 min, HT) or high pressure treatment (400 MPa at 20 °C for 10 min, HP). The overall moduli values of the GDL gels and CaSO4·2H2O gels of both physical treatments were similar, each gave frequency profiles expected for weak viscoelastic materials. However, although both temperature and high pressure treatments could be used to produce tofu gels, the final products were not the same. Pressure formed gels, despite having a higher overall “consistency” (increasing values of their moduli), had a proportionately higher contribution from the loss modulus (increased tan δ). Differences could also be observed using confocal scanning laser microscopy. While such treatment may give rise to differing systems/structures, with new or modified organoleptic properties, the more “open” structures obtained by pressure treatment may well cause processing difficulties if subsequent reworking or moulding is required.

Viscoelastic properties of high pressure and heat induced tofu gels

Tofu gels were rheologically examined to determine their storage or elastic (G') and loss or viscous (G '') moduli as a function of frequency within their linear viscoelastic limits. The tofu gels were made using either glucono-delta-lactone (GDL) or calcium sulphate (CaSO4 center dot 2H(2)O), followed by either heat treatment (heated soymilk at >= 97 degrees C prior to coagulation and subsequently held at 70 degrees C for 60 min, HT) or high pressure treatment (400 MPa at 20 degrees C for 10 min, HP). The overall moduli values of the GDL gels and CaSO4 center dot 2H(2)O gels of both physical treatments were similar, each gave frequency profiles expected for weak viscoelastic materials. However, although both temperature and high pressure treatments could be used to produce tofu gels, the final products were not the same. Pressure formed gels, despite having a higher overall "consistency" (increasing values of their moduli), had a proportionately higher contribution from the loss modulus (increased tan delta). Differences could also be observed using confocal scanning laser microscopy. While such treatment may give rise to differing systems/structures, with new or modified organoleptic properties, the more "open" structures obtained by pressure treatment may well cause processing difficulties if subsequent reworking or moulding is required. (c) 2007 Elsevier Ltd. All rights reserved.

Comparing tube models for predicting the linear rheology of branched polymer melts

The hierarchical and "bob" (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent alpha and the factor p(2) which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.

Effects of variation in the palm stearin: palm olein ratio on the crystallisation of a low-trans shortening

Changes in the theological properties during crystallisation and in the crystal size and morphology of blends containing rapeseed oil with varying percentages of palm stearin (POs) and palm olein (POf) have been studied. The crystals formed from all three blends were studied by confocal laser scanning microscopy, light microscopy and environmental scanning electron microscopy, which revealed the development of clusters of 3-5 individual elementary "spherulites" in the early stages of crystallisation. The saturated triacylglycerol content of the solid crystals separated at the onset of crystallisation was much greater than that in the total fat. Fat blends with a higher content of palm stearin had a more rapid nucleation rate when observed by light microscopy, and this caused an earlier change in the rheological properties of the fat during crystallisation. Using a low torque amplitude (0.005 Pa, which was within the linear viscoelastic region of all samples studied) and a frequency of 1 Hz, the viscoelastic properties of melted fat during cooling were studied. All samples, prior to crystallisation, showed weak viscoelastic liquid behaviour (G '', loss modulus >G', storage modulus). After crystallisation a more "solid like" behaviour was observed (G' similar to or greater than G ''). The blend having the highest concentration of POs was found to have the earliest onset of crystallisation (27% w/w POs; 12 mins, 22% w/w POs; 13.5 mins, 17% w/w POs, 15 mins, respectively). However, there were no significant differences in the time to the point when G' became greater than G' among the three blends. (c) 2006 Elsevier Ltd. All rights reserved.

Simple linear asymmetrical complexes of silver(I): NC-Ag-NH3 and Br-Ag-NH3

The compounds Ag(CN)(NH3) and Ag(Br)(NH3) are remarkable in that they form solids containing the simple molecular units NC-Ag-NH3 and Br-Ag-NH3, rather than extended solids, and are the first examples of simple linear asymmetric complexes of silver(I).

Facile strategies for the synthesis and crystallization of linear trinuclear nickel(II)-Schiff base, complexes with carboxylate bridges: Tuning of coordination geometry and magnetic properties

Three new linear trinuclear nickel(II) complexes, [Ni-3(salpen)(2)(OAc)(2)(H2O)(2)]center dot 4H(2)O (1) (OAc = acetate, CH3COO-), [Ni-3(salpen)(2)(OBz)(2)] (2) (OBz=benzoate, PhCOO-) and [Ni-3(salpen)(2)(OCn)(2)(CH3CN)(2)] (4) (OCn = cinnamate, PhCH=CHCOO-), H(2)salpen = tetradentate ligand, N,N'-bis(salicylidene)-1,3-pentanediamine have been synthesized and characterized structurally and magnetically. The choice of solvent for growing single crystal was made by inspecting the morphology of the initially obtained solids with the help of SEM study. The magnetic properties of a closely related complex, [Ni-3(salpen)(2)(OPh)(2)(EtOH)] (3) (OPh = phenyl acetate, PhCH2COO-) whose structure and solution properties have been reported recently, has also been studied here. The structural analyses reveal that both phenoxo and carboxylate bridging are present in all the complexes and the three Ni(II) atoms remain in linear disposition. Although the Schiff base ligand and the syn-syn bridging bidentate mode of the carboxylate group remain the same in complexes 1-4, the change of alkyl/aryl group of the carboxylates brings about systematic variations between six- and five-coordination in the geometry of the terminal Ni(II) centres of the trinuclear units. The steric demand as well as hydrophobic nature of the alkyl/aryl group of the carboxylate is found to play a crucial role in the tuning of the geometry. Variable-temperature (2-300 K) magnetic susceptibility measurements show that complexes 1-4 are antiferromagnetically coupled (J = -3.2(1), -4.6(1). -3.2(1) and -2.8(1) cm(-1) in 1-4, respectively). Calculations of the zero-field splitting parameter indicate that the values of D for complexes 1-4 are in the high range (D = +9.1(2), +14.2(2), +9.8(2) and +8.6(1) cm(-1) for 1-4, respectively). The highest D value of +14.2(2) and +9.8(2) cm(-1) for complexes 2 and 3, respectively, are consistent with the pentacoordinated geometry of the two terminal nickel(II) ions in 2 and one terminal nickel(II) ion in 3. (C) 2009 Elsevier Ltd. All rights reserved.

Linear amplification of marginally neutral baroclinic waves

Baroclinic wave development is investigated for unstable parallel shear flows in the limit of vanishing normal-mode growth rate. This development is described in terms of the propagation and interaction mechanisms of two coherent structures, called counter-propagating Rossby waves (CRWs). It is shown that, in this limit of vanishing normal-mode growth rate, arbitrary initial conditions produce sustained linear amplification of the marginally neutral normal mode (mNM). This linear excitation of the mNM is subsequently interpreted in terms of a resonance phenomenon. Moreover, while the mathematical character of the normal-mode problem changes abruptly as the bifurcation point in the dispersion diagram is encountered and crossed, it is shown that from an initial-value viewpoint, this transition is smooth. Consequently, the resonance interpretation remains relevant (albeit for a finite time) for wavenumbers slightly different from the ones defining cut-off points. The results are further applied to a two-layer version of the classic Eady model in which the upper rigid lid has been replaced by a simple stratosphere.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Decadal predictability of the Atlantic Ocean in a coupled GCM: forecast skill and optimal perturbations using Linear Inverse Modelling

The decadal predictability of three-dimensional Atlantic Ocean anomalies is examined in a coupled global climate model (HadCM3) using a Linear Inverse Modelling (LIM) approach. It is found that the evolution of temperature and salinity in the Atlantic, and the strength of the meridional overturning circulation (MOC), can be effectively described by a linear dynamical system forced by white noise. The forecasts produced using this linear model are more skillful than other reference forecasts for several decades. Furthermore, significant non-normal amplification is found under several different norms. The regions from which this growth occurs are found to be fairly shallow and located in the far North Atlantic. Initially, anomalies in the Nordic Seas impact the MOC, and the anomalies then grow to fill the entire Atlantic basin, especially at depth, over one to three decades. It is found that the structure of the optimal initial condition for amplification is sensitive to the norm employed, but the initial growth seems to be dominated by MOC-related basin scale changes, irrespective of the choice of norm. The consistent identification of the far North Atlantic as the most sensitive region for small perturbations suggests that additional observations in this region would be optimal for constraining decadal climate predictions.