Viscoelastic Functions Research Articles

Interconversion of linearly viscoelastic material functions expressed as Prony series: a closure

Interconversion of viscoelastic material functions is a longstanding problem that has received attention since the 1950s. There is currently no accepted methodology for interconverting viscoelastic material functions due to the lack of stability and accuracy of the existing methods. This paper presents a new exact, analytical interconversion method for linearly viscoelastic material functions expressed as Prony series. The new algorithm relies on the equations of the thermodynamics of irreversible processes used for defining linearly viscoelastic constitutive theories. As a result, interconversion is made possible for unidimensional and tridimensional materials for arbitrary material symmetry. The algorithm has been tested over a broad range of cases and was found to deliver accurate interconversion in all cases. Based on its accuracy and stability, the authors believe that their algorithm provides a closure to the interconversion of linearly viscoelastic constitutive theories expressed with Prony series.

Interconversions between linear viscoelastic functions by using relaxation-creep duality representation

The interconversions between relaxation moduli and creep compliances, including stretch, shear, bulk parts, and the time-dependent Poisson’s ratio, are derived by using the relaxation-creep duality representation. The relaxation-creep duality representation for the viscoelastic functions introduced in this paper is composed of an exponential function that characterizes the relaxation behavior and a complementary one that characterizes the creep behavior. All viscoelastic functions can be represented as the same form. The new sets of coefficients, called the modulating constants, between viscoelastic functions obey the elastic-like interconversions, and do not involve the characteristic times. The relationships of characteristic times between those functions are also derived. These interconversion formulas can then be calculated easily. Three literatures are referenced to calculate the consistency of the viscoelastic functions via the new interconversions introduced in this work. The Young’s relaxation modulus in one literature is not consistent to the shear one in another literature. By assuming a constant bulk modulus, the modified Young’s relaxation modulus and time-dependent Poisson’s ratio that was derived by the new interconversions can meet the measured curves and can be consistent to the shear creep compliance in the literatures. The fitted data from experiments can then be checked via the new mathematical interconversions for the consistency.

Design of lubricating grease formulations using recycled polypropylene from postconsumer films as thickener agent

AbstractThis work deals with the design of lubricating greases formulations based on blends of mineral oil and recycled polypropylene from postconsumer waste, coming from films with inks. In particular, the influence of polymer concentration on the rheological, mechanical, and thermal properties of recycled polymer/oil blends was characterized. From the experimental results obtained, it can be deduced that the evolution of recycled polymer/mineral oil formulations on linear viscoelasticity functions with frequency is quite similar to that found for traditional lithium greases. It is observed that these blends form systems with enhanced “plateau” modulus, G, with respect to industrial standard lubricating greases, which could be represent an important advantage, from an economic and environmental point of view. However, the influence of temperature on linear viscoelasticity functions is more pronounced than that found for traditional greases. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

Fractional viscoelastic models: master curve construction, interconversion, and numerical approximation

We use fractional viscoelastic models that result from the application of fractional calculus to the linear viscoelastic theory to characterize thermorheologically simple linear viscoelastic materials. Model parameters are obtained through an optimization procedure that simultaneously determines the time–temperature shift factors. We present analytical interconversion based on the fractional viscoelastic model between the main viscoelastic functions (relaxation modulus, creep compliance, storage modulus, and loss modulus) and the analytical forms of the relaxation and retardation spectra. We show that the fractional viscoelastic model can be approximated by a Prony series to any desired level of accuracy. This property allows the efficient determination of the fractional viscoelastic model response to any loading history using the well-known recursive relationships of Prony series models.

Incremental homogenization approach for ageing viscoelastic polycrystals

An approximate self-consistent modelling is proposed to estimate the effective viscoelastic response of polycrystals presenting an ageing constitutive behaviour. This approach makes use of the equivalence between the Dirichlet series approximation of the viscoelastic functions and an internal variables formulation. An illustrative application is performed for model 2d polycrystals for which the exact expression of the continuous effective relaxation spectrum is given.

Physical characterization and rheological behavior of polyurethane/poly(ϵ‐caprolactone) blends, prepared by solution blending using dimethylacetamide

AbstractBlending effects of thermoplastic polyurethane based on polycaprolactone diol, PU (PCL diol), and poly (ϵ‐caprolactone) (PCL) on the rheological properties and morphological behavior of the solvent‐cast blends were investigated by parallel plate rheometer. The amount of PCL was varied from 20 to 50% by weight. Fourier transform infrared (FTIR) results showed existence of hydrogen bonding in PU/PCL blends. From FTIR, we also found the increase of PCL composition tends to reduction of intermolecular hydrogen bonding and enhancing of microphase separation in blends. Differential scanning calorimetry (DSC) indicated that these blend systems are partially miscible. Based on rheological characterization, decrease can be seen in the moduli, zero shear viscosity and plateau modulus of blends, as compared with net PU. Using Cole‐Cole plots and composition dependencies of η0 and the other viscoelastic functions expressed variation of morphology of blends due to increase of PCL content. Frequency sweep tests on PU/PCL (80/20) at five temperatures showed validity of time‐temperature superposition in this blend. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Synthesis and characterization of isocyanate‐functionalized PVA‐based polymers with applications as new additives in lubricant formulations

AbstractThis work deals with the incorporation of reactive isocyanate groups into polymer additives, which could be potentially used to modify the rheological properties of lubricating greases by reinforcing the role of traditional thickening agents. Thus, a batch of partially protected poly(vinylalcohol) (PVA) copolymers was successfully synthesized. Some of their OH groups were blocked as tetrahydropyranyl (THP) ethers (PVA–THP), while the spare hydroxyl groups were further functionalized with NCO pendant groups by reaction with 1,6‐hexamethylene diisocyanate, leading to several isocyanate‐functionalized PVA‐based polymers (PVA–THP–NCO), which were tested as rheology modifiers of lithium lubricating greases. The highest protection degree of hydroxyl groups achieved as THP‐ether was 58.5% and the recovered polymers were isolated with excellent yields (close to 90% in most cases). NCO‐functionalized PVA‐based polymers (PVA–THP–NCO) exerted a significant rheological modification in lithium 12‐hydroxystearate lubricating greases, increasing the values of the linear viscoelastic functions. The influence of the degree of protection and later functionalization of PVA on the rheological properties of PVA–THP–NCO‐additivated lubricating greases is discussed. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Influence of Oral Administration of Soybean Peptide on Water Content of the Stratum Corneum, Transepidermal Water Loss and Skin Viscoelasticity

Soybean Peptide (SP) increases collagen content in fibroblasts, but no previous studies have investigated the effects of SP on skin properties such as water content of the stratum corneum, Transepidermal Water Loss (TEWL) and skin viscoelasticity. Thus, we orally administered SP to ultraviolet (UV)-irradiated mice in order to investigate the effects on skin. Hairless mice were irradiated with a daily dose of 22.3 J/cm2 of UVA and a 20% aqueous solution of SP or Collagen Peptide (CP) was administered via oral gavage to achieve a daily dose of 2 mg/g. UVA radiation and oral samples were administered for 25 consecutive days. Water content of the stratum corneum and TEWL were measured daily and skin viscoelasticity was measured every other week. Skin was collected and prepared as frozen sections after the conclusion of the study for use in histological observation with hematoxylin and eosin staining. Oral administration of SP and CP to UVA-irradiated mice resulted in no significant differences in body weight in any of the groups. Water content of the stratum corneum and TEWL improved over time in all groups. TEWL recovered more quickly in the SP group than the CP group. Skin viscoelasticity improved in all groups. The values in the SP group were almost identical to those in the normal group, which did not receive UVA irradiation or oral treatment. Histological observations revealed suppression in UVA-induced epidermal thickening in the SP group. The findings of this study indicate that oral administration of CP and SP improves the barrier function of skin and skin viscoelasticity in UV-irradiated mice.

Fundamental Investigation of Polymer Dynamics with Dielectric and Viscoelastic Methods

This paper briefly summarizes two representative examples of investigation of fundamental polymer dynamics with dielectric and viscoelastic methods: 1) Entangled dynamics of flexible polymers: For type-A polymers having the electrical dipoles parallel along the chain backbone, the entanglement dynamics is differently reflected in the dielectric and viscoelastic relaxation functions. A simple relationship between these functions was deduced for the case of full dynamic tube dilation (full-DTD). This full-DTD relationship was found to hold experimentally for monodisperse linear chains, but not for branched (star and Cayley-tree) chains and linear/linear blends. A refined relationship, referred to as partial-DTD, was developed by taking into account the time necessary for constraint release equilibration. This partial-DTD relationship was found to valid for the linear, branched, and blend systems. 2) Effect of carbon dioxide (CO2) on polymer dynamics: Pressurized CO2 dissolves into polymers to exhibit a plasticizing effect. Dielectric tests revealed that the local dynamics of polymer chains was accelerated by pressurized CO2 without changing relaxation mode distribution. This unusual plasticizing effect of pressurized CO2 for the local dynamics was attributed to extraordinary fast diffusion of CO2 compared to the segmental motion of the polymer chain. The concentration fluctuation of the polymers, being responsible for the relaxation mode broadening usually observed for plasticized polymer systems, is smeared by the fast CO2 molecules in the time scale of segmental motion. In contrast, pressurized CO2 behaves just as an ordinary solvent for the slow, global dynamics of polymer chains.

Influence of some processing variables on the rheological properties of lithium lubricating greases modified with recycled polymers

This work deals with the effect that some processing variables and type of mineral lubricating oil (naphthenic and paraffinic) used exert on the rheological properties of lubricating greases modified with recycled polymers. In particular, the optimisation of recycled polymer addition at different lubricating grease processing stages and cooling profiles were studied. The influence of processing variables was evaluated by performing small-amplitude oscillatory shear (SAOS), viscous flow and thermal analysis tests. From the experimental results obtained, it may be concluded that the addition of recycled polymer significantly increases the values of linear viscoelasticity functions, especially when added immediately after the saponification reaction, during the heating stage, or at the beginning of the cooling stage (180°C). A combined stepwise cooling ramp, first at a high rate and then at a low rate, is more effective to achieve higher values of the rheological functions than the application of constant cooling rates in the final processing stage. The values of the rheological functions decrease as base oil viscosity increases and increase when using a naphthenic instead of a paraffinic oil of similar viscosity.

Effect of polymer molecular weight on the structural properties of non aqueous ethyl cellulose gels intended for topical drug delivery

Abstract The structural properties of five ethyl cellulose polymers (EC) in mixture with the non aqueous solvent of propylene glycol dicaprylate (PGD) have been investigated with a view to facilitating topical drug delivery. Total concentration of the polymer varied from 12 to 20% (w/w) and its weight average molecular weight was in the range of 64–223 kDa. Experimental techniques utilised were small-deformation dynamic oscillation in shear, attenuated total reflectance Fourier transform infrared spectroscopy (ATR FTIR) and wide-angle X-ray diffraction. The nature of the time and temperature dependence on viscoelastic functions of all samples could be treated with the Chambon and Winter criterion allowing determination of the critical gelation temperature in relation to polymer concentration and molecular weight. A further refinement of this school of thought allowed correlation between the viscoelastic relaxation exponent and fractal dimensions in thermally treated EC/PGD matrices. Tangible evidence on the packing arrangements of the ethyl cellulose network and the molecular nature of its interaction with the non aqueous solvent as a function of polymer concentration and molecular weight was provided by X-ray diffraction and infrared studies.

Effect of using Erythritol as a Sucrose Replacer in Making Spanish Muffins Incorporating Xanthan Gum

Spanish muffins are sweet, high-calorie baked products which are highly appreciated for their good taste and soft texture. The aim of this work was to evaluate the suitability of erythritol and of its combination with xanthan gum and double quantities of leavening agent for replacing sucrose in Spanish muffins and to understand their functionality in a muffin system. The linear viscoelastic properties of the batter during heating, its specific gravity and bubbles, muffin weight loss during baking and muffin bubbles, height, volume, and instrumental texture were studied. Both erythritol and sucrose increase in the temperature at which the viscoelastic functions increased with temperature. In comparison with the reduced sucrose muffins, the use of erythritol increased the number of air bubbles in the batter. The height of the muffins also increased in the presence of erythritol when compared to the corresponding reduced sucrose muffins, although the volume did not. Erythritol was not effective in diminishing the increased hardness associated with sucrose reduction, but the combination of erythritol with xanthan gum and a double quantity of leavening agent significantly improved the muffin volume (from 94 cm3 for 100% erythritol formulation to 108 cm3 for 100% erythritol–xanthan double-leavening agent formulation) and significantly decreased the hardness (from 75 N for 100% erythritol formulation to 25 N for 100% erythritol–xanthan double leavening agent formulation).

Continuous relaxation and retardation spectrum method for viscoelastic characterization of asphalt concrete

This paper presents a simple and practical approach to obtain the continuous relaxation and retardation spectra of asphalt concrete directly from the complex (dynamic) modulus test data. The spectra thus obtained are continuous functions of relaxation and retardation time. The major advantage of this method is that the continuous form is directly obtained from the master curves which are readily available from the standard characterization tests of linearly viscoelastic behavior of asphalt concrete. The continuous spectrum method offers efficient alternative to the numerical computation of discrete spectra and can be easily used for modeling viscoelastic behavior. In this research, asphalt concrete specimens have been tested for linearly viscoelastic characterization. The linearly viscoelastic test data have been used to develop storage modulus and storage compliance master curves. The continuous spectra are obtained from the fitted sigmoid function of the master curves via the inverse integral transform. The continuous spectra are shown to be the limiting case of the discrete distributions. The continuous spectra and the time-domain viscoelastic functions (relaxation modulus and creep compliance) computed from the spectra matched very well with the approximate solutions. It is observed that the shape of the spectra is dependent on the master curve parameters. The continuous spectra thus obtained can easily be implemented in material mix design process. Prony-series coefficients can be easily obtained from the continuous spectra and used in numerical analysis such as finite element analysis.

Curing of epoxy/carbon nanotubes physical networks

AbstractA melt‐mixing procedure has been used to disperse multi‐walled carbon nanotubes (MWCNT) in an epoxy matrix. According to dynamic viscoelastic results, a physical network is formed for carbon nanotube concentrations of 0.3 weight per cent (wt%) and above. The temperature activated curing process is followed analyzing the evolution of the dynamic viscoelastic functions and the dielectric loss with time. Curing process from a physical to a chemical network is monitored. The presence of MWCNT accelerates curing, even when the rheological percolation is not reached (absence of physical network). Several hypotheses are considered to explain this result. Electrical conductivity decreases during cure, so lower electrical conductivities are found for cured MWCNT/epoxy samples than for dispersions: this is explained by a distortion of nanotubes physical network and a reduction of the ionic conductivity contribution of the liquid phase. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers

Formulation of new biodegradable lubricating greases using ethylated cellulose pulp as thickener agent

The influence of cellulose pulp ethylation processing conditions has been evaluated to design suitable renewable and biodegradable lubricating greases from cellulose pulp-based gel-like dispersions. Ethyl/glucose molar ratio (E/G) has a positive effect on the ethyl groups degree of substitution (DS). Gel-like biodegradable dispersions of cellulose pulp in castor oil have been prepared by adding ethylated cellulose samples differing in the substitution degree to modify the rheological properties of castor oil. The rheology of ethyl cellulose/castor oil binary systems is highly influenced by DS. The linear viscoelastic functions and consistency are very similar to those found in traditional lithium lubricating greases.

Properties of protein powder prepared from Cape hake by-products

Cape hake protein powder (HPP) was prepared by alkaline extraction, isoelectric precipitation and freeze drying. It contained 90% protein, 0.53% fat, and 1.44% ash. HPP showed high levels of Na, K, Ca and Mg but lower than in hake mince. The protein profile of HPP was similar to the raw material.The surface hydrophobicity and sulfhydryl group content of HPP were identical to those of the proteins before freeze-drying. The HPP had higher fat absorption capacity, lower emulsifying and foaming capacity than soy protein concentrate, pea protein isolate and egg white powder. The gel strength of HPP was medium (44.8 Nxmm) and was increased by addition of transglutaminase.Gels with different HPP concentrations showed a typical pattern of myofibrillar protein networks with a thermo-reversible behavior. The structure of emulsions prepared with HPP showed increasing complexity as the protein level increased. An increase in the magnitude of the viscoelastic functions and an increment in the magnitude of the zero shear rate limiting viscosity with increasing HPP content were observed.

Rheology of new green lubricating grease formulations containing cellulose pulp and its methylated derivative as thickener agents

This work is focused on the development of gel-like formulations, potentially applicable as biodegradable lubricating greases obtained by dispersing eucalyptus Kraft cellulose pulp, or its methylated derivative, in an ethyl cellulose/castor oil medium. The effects that concentration and weight ratio of the different cellulosic derivatives exert on the rheological properties, thermal resistance and mechanical stability of these oleogels were studied. The evolution of linear viscoelasticity functions with frequency was very similar to that found for traditional lubricating greases. In general, linear viscoelastic functions increase with Kraft cellulose pulp or methylcellulose concentrations and ethyl cellulose/Kraft cellulose pulp weight ratio. However, the relative elasticity of gel-like dispersions based on ethyl cellulose/Kraft cellulose pulp is not affected by the composition of these thickener blends, which allows the application of an empirical superposition method to obtain generalized master curves for describing the viscoelastic response of these formulations. On the contrary, the relative elasticity of methylcellulose-based gel-like dispersions depends on the composition of methylated cellulose pulp/ethyl cellulose blends. An Arrhenius-type equation can be used to quantify the linear viscoelastic functions thermal dependence of these gel-like dispersions. Moreover, formulations prepared using Kraft cellulose pulp/ethyl cellulose blends show appropriate mechanical stabilities to be used as bio-lubricating greases.

Novel foods with microalgal ingredients – Effect of gel setting conditions on the linear viscoelasticity of Spirulina and Haematococcus gels

Microalgae represent an alternative and innovative source of natural ingredients that can be used in the development of novel food products. Biologically active compounds (e.g. carotenoids) are naturally encapsulated within microalgal cells, being able to resist harsh technological conditions involved in food technology processes. The aim of this work was to study the effect of adding Haematococcus pluvialis and Spirulina maxima microalgal biomass on the linear viscoelastic behaviour of vegetarian food gels prepared from pea protein, κ-carrageenan and starch. The gelation process was monitored in situ through dynamic oscillatory measurements, under different thermal profile conditions. Increasing temperature (70–90°C, 5min) resulted in more structured gels, while the effect of time (5–30min, at 90°C) was less pronounced. The effect of heating and cooling rates on gel setting was also studied. Haematococcus gels were highly structured and less dependent on gel setting conditions. Spirulina gels presented lower values of viscoelastic functions than the control (gel matrix without microalgae), but this was overcome when using lower heating/cooling rates.

The sources of inelastic behavior of Glass Fibre/Vinylester non-crimp fabric [±45]s laminates

The non-linear and time-dependent stress—strain response of NCF [±45]s laminates in tension is studied. Testing methodology is suggested to separate and quantify the effect of damage development, non-linear viscoelastic effects, and viscoplasticity on the inelastic response. This is achieved by decomposition of viscoelastic and viscoplastic response, both of them being affected by microdamage accumulated during the service life. Material model based on Schapery’s work on viscoelasticity and Zapas viscoplastic function with added damage terms is presented and used. Simulation is performed and validated with constant stress rate tensile tests, identifying the non-linear viscoelasticity and viscoplasticity as the major sources of the non-linear response.

Computational optimization of characteristics for composites of viscoelastic components

The problem of describing of the viscoelastic properties of composite materials that consist of more than one viscoelastic component is studied. It is supposed that the viscoelastic properties of the components are known. The difficulty in the application of the mixture theory arises in the cases when the properties are described by integral operators with different integral kernels. This difficulty is avoided by the approximations of the viscoelastic operators in the stress–strain relations. A method is proposed to obtain appropriate approximations that reduce all the viscoelastic operators to a general kernel using rational approximations of their Laplace transforms. The proposed method allows for the reduction of the approximation error for related operators. Examples are given for the adjustment of viscoelastic functions in the cases of increase and decrease of functions parameter.