Understanding of Transient Rheology in Step Shear and Its Implication

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Thermodynamics, Transport, and Fluid Mechanics

Understanding of transient rheology in step shear and its implication to explore nonlinear relaxation dynamics of interphase in compatible polymer multi-microlayered systems Huagui Zhang, Khalid Lamnawar, and Abderrahim Maazouz Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00972 • Publication Date (Web): 21 May 2018 Downloaded from http://pubs.acs.org on May 21, 2018

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Industrial & Engineering Chemistry Research

Understanding of transient rheology in step shear and its implication to explore nonlinear relaxation dynamics of interphase in compatible polymer multi-microlayered systems

Huagui Zhanga, Khalid Lamnawarb*, Abderrahim Maazouzb,c a

School of Chemical and Process Engineering, University of Leeds, LS2-9JT, Leeds, United Kingdom b

Université de Lyon, F-69361, Lyon, France; CNRS, UMR 5223, Ingénierie des Matériaux Polymères, INSA Lyon, F-69621, Villeurbanne, France c

Hassan II Academy of Science and Technology, Rabat, Morocco

Corresponding authors: K. Lamnawar: E-mail: [email protected]

ABSTRACT In the industry of polymer coextrusion processing, efforts are being made towards a better control of multilayer flow stability that is governed by the interface/interphase between neighbouring layers, the understanding of which is considerably inadequate. This study aims to explore the relaxation dynamics of polymer chains located in the interphase between two compatible polymer melts based on transient rheology in step shear experiments, an area that is often overlooked without justification. Firstly, transient rheology was investigated based on pure polymers of poly(methyl methacrylate) (PMMA) and poly(vinylidene fluoride) (PVDF) melts, focusing on a feature of abrupt stress decline observed in the transient period after a large step shear. This feature is considered to be the phenomenological onset of rheological nonlinearity (e.g. stress damping) commonly observed in the long-time window of a relaxation for an entangled polymer. From molecular viewpoint, the nonlinearity onset is a result of polymer chain disentanglement under a large flow as interpreted based on a refined version of Doi-Edwards tube model and Wang’s force imbalance theory, etc. A decreased entanglement number of polymer chains, either by decreasing molar mass in the melts or by reducing polymer concentration in solutions, was demonstrated to accelerate the onset of the rheological nonlinearity. In particular, a noticeable stress break-off in transient period can be

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observed upon large deformations in the solutions due to their very weak entanglements. Secondly, large step shears were given to PMMA/PVDF bilayer-structured melts and a new model has been developed to determine the relaxation behaviour of the interphase triggered between the layered polymers. Similar to the solutions, an abrupt stress decline was observed in the transient period for the interphase upon a large step deformation, indicating an analogous entanglement weakness of the interphase to the solution. Hence, a close correlation can be established between the interphase and the pure melts and solutions based on their transient rheology and a concept that the polymer chain entanglements can be weakened either by solvent dilution or by blending with dissimilar chains.

1. INTRODUCTION In the past decades, multiphase polymer systems such as blends and multilayer structures have received a lot of attentions from both academic and industry communities thanks to their great value of applications in broad fields1-3. During the blending or the multi-layered structuring, the interface and the interphase (i.e. a physicochemical affinity triggered between neighboring phases) plays an irreplaceable role in transferring the stress between the neighboring phases to bridge them together. More importantly, in coextrusion process of multi-microlayered polymer structures, the processing is often challenged by the interfacial flow instability such as severe waved defects and encapsulations, etc. due to the properties difference between layered polymers. Presence of a robust interphase between neighboring layers has been demonstrated to be useful in controlling the interfacial flow instability3. The response of the interphase under extreme conditions (e.g. relaxation dynamics in large and fast flows) that are commonly encountered during the coextrusion process still remains as an open question. Fundamental understandings and knowledge on the interphase are needed to better control the interfacial instability. Step shear, one of the most important rheological experiment, has been widely used as a vital tool to study nonlinear stress relaxation not only for pure viscoelastic liquids, but also for multiphase polymer systems where the interface/ interphase is involved4-6. However, a comprehensive physical conceptual framework for nonlinear rheology of pure polymers has not yet been fully established, let alone the multiphase polymer systems. In particular, due to its structure complexity, the stress relaxation of the


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interface/interphase in a multi-layered structure, has neither been reasonably extracted from that of the whole multiphase system nor been well understood7. Typically, a stress relaxation measurement is carried out by recording the decay of shear stress σ(t) as a function of time on a tested liquid subject to a sudden shear deformation γ0. The measured stress is universally expressed in terms of relaxation modulus G(γ0,t) with G (γ 0 , t ) = σ (t ) γ 0 . When the γ0 is small enough, the G(γ0,t) becomes strain-independent, being named as linear relaxation modulus G(t). In the case of large γ0, the G(γ0,t) was found to be separable above a characteristic time, tc, into a strain-dependent function h(γ0), the so-called damping function, and a timedependent function, the linear relaxation modulus G(t), i.e.:

G(γ 0 , t) = G(t)h(γ 0 )

(1)

Obviously, the damping function h(γ0) is an important parameter that can simply describe the degree of rheology nonlinearity (i.e. the vertical reduction of relaxation modulus, the so-called ‘strain softening’ or the ‘stress damping’) upon large deformations8. The characteristic time tc that defines the onset of the time-strain separability is predicted to have a same order to the Rouse relaxation time τR according to the original tube model of Doi-Edwards(DE)9. The DE tube model has gained success in predicting linear viscoelasticity of entangled polymers with a scenario treating the interchain interactions (e.g. the entanglements) stemming from neighboring chains around a test polymer chain as an effective tube that forces the chain diffuse curvilinearly along it. However, the use of the tube model for nonlinear rheology, based on chain orientation and chain stretching under large flow, still remains challenging. For instance, a number of experimental observations show that the tc is close to the order of the tube disengagement time, τd, i.e. the longest reptation relaxation time τrep rather than τR, the predicted time of the model. This problem can be rectified only by introducing a Convective Constraint Release (CCR)10,11 mechanism to the tube model, which reduces the effectiveness of the infinitely strong entanglement constraint assumption primarily set in the original tube model. The essence of the CCR lies in that continuous flows’ convection accelerates molecular relaxation at a condition of intermediate shear rate, i.e.,1/ < ≪ 1/ , thus the relaxation is described by a



form of = + , where is the flow rate. Moreover, to improve its prediction

accuracy in rheological nonlinearity (i.e. ‘strain softening’), a strain-dependent tube diameter (or, equivalently, the entanglement density) in fast/large flows has been proposed to develop the tube model8 that originally assumed a constant tube diameter. Likewise, the CCR theory has been recently revisited by Ianniruberto and Marrucci12 by incorporating a factor of topological entanglements loss in number (hence change in tube diameter) during fast flows and a concept of disentanglement-re-entanglement for the relaxation process in response to a large step-strain has been developed. In parallel to the DE tube model, Wang and coworkers13-15 outlined a completely different picture by treating the entangled polymer system as a dynamic network whose junctions are formed by localized intermolecular interactions. In their theory, the response of an entangled polymer to external deformation is analyzed from a force balance perspective, including the intermolecular gripping forces fimg caused by chain uncrossability upon external deformation, intrachain elastic retraction force fretract and entanglement force fent associated with the entropic barrier that provides the structural integrity or cohesion of the entanglement network. The imbalance of these forces and the accompanying chain sliding at the entanglement points was asserted to be the molecular mechanism for the macroscopic nonlinearity observed either during startup deformation or after a large stepwise strain. Similar to Wang’s scenario, Sussman and Schweizer16-18 recently have also demonstrated that the entanglement force (tube confining barrier) is finite by postulating a two competing parallel relaxation mechanism under stress: strain dependent reptation and activated transverse barrier hopping (tube breaking). From the aforementioned theories that possess different concepts, a consensus can be drawn regarding the rheological nonlinearity. Upon applying a large external deformation, the polymer entanglements are to be destroyed with a reduction in entanglement number (i.e. tube dilation), or even a full disentanglement (i.e. tube breaking), manifested by an ultrafast relaxation of stress within a short time scale in the same order of the polymer’s terminal relaxation time. After the initial fast relaxation, the entanglement constraints reemerge, resulting in a slower reptative relaxation process at long times as in quiescent relaxation. Same to the immaturity in theory development, the experimental studies on step strain are still far from enough. Most of the previous studies of nonlinear relaxation were 4 Environment ACS Paragon Plus

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focused on a long time window and on damping function, with the transient period where the actuation of a ‘step’ strain is detectable overlooked19-22. Indeed, a finite rise time, t0, is needed in practice to actuate a prescribed strain since the moving rheometer components and the fluid have inertia and cannot be accelerated in terms of a perfect step function23. To avoid the imperfect strain history appeared therefrom, the experimental data in the transient period are often deliberately omitted using a "rule of thumb" of skipping the data before 10t0, which however was demonstrated to be invalid for the materials that have a relaxation time in the same order of magnitude to the strain actuation time t024. Certainly, some few researchers like Archer and coworkers25-27 have shed lights into the initial short time (e.g. < 0.01s) period and have reported the observation of an obvious rapid G(γ0,t) decline. In addition, by virtue of particle tracking velocimetric (PTV) technique, Wang and coworkers28-30 recently observed within the transient period some macroscopic motions either at the sample/wall interfaces(i.e. wall slip) or in the sample interior (i.e. internal yielding) during step shears based on entangled polymer melts25 and solutions.26 They ascribed the observed macroscopic failure to be a result of the structural breakup of entanglement network and argued that to be the reason of the widely observed strain softening13, 29, 30. As to the sample preference for the stress relaxation measurements, both the entangled polymer melts and the polymer solutions are available, while the use of melts for high shear rates/deformation measurements are readily limited by flow instabilities such as the edge fracture2. For the solutions, the solvent dilution reduces the stresses and thus defers the edge instabilities. Moreover, the solution offers ease to vary entanglement density by simply changing the polymer concentration. It is worth noticing that nuance has been reported in the nonlinear viscoelasticity between the concentrated solutions and the melts especially in the extensional flow as a result of their subtle distinctions in entanglement characteristics and in monomeric friction31, 32. The present study firstly deals with the transient period of step strain experiments and its relevance to the onset of rheological nonlinearity based on PVDF, PMMA melts and PMMA solutions. Afterwards, the effect of entanglement density on transient rheology is studied by varying molar mass of the polymer in melts and by varying concentration of the polymer in solutions whereby states are changed from marginal entanglement to full entanglement. Furthermore, focuses are given to the step strain



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experiments of PMMA/PVDF layered polymer melts and a rheological model has been developed for the relaxation behavior of the interphase. The obtained relaxation data of the interphase show a great similarity to the solutions especially within the transient period, manifesting an analogue between them on the entanglement weakness. In a word, this study sketches a central line from revealing mechanism of rheological nonlinearity within transient period to looking into entanglement density effect thereof providing hints for the relaxation of the interphase in layered structures.

2. EXPERIMENTAL 2.1 Materials: Poly (methyl methacrylate) (PMMA) and poly(vinylidene fluoride) (PVDF) were supplied by ARKEMA. Dimethylformamide(DMF) of analysis grade was supplied from Sigma-Aldrich. In particular, PMMAs with different molar masses were investigated in the present study. Main material characteristics of these polymers are listed in Table 1. Note that the difference in the glass transition temperature Tg of the PMMAs, or more exactly, the inverse relation of Tg with weight-averaged molecular weight (Mw) of PMMA as shown in Table1, is associated with the difference in tacticity of the PMMAs, which has been demonstrated in our earlier study33,

34

. A

higher amount of the syndiotactic triads in PMMA-1 than PMMA-4 corresponds to a higher Tg. More information of the polymers' characterization could be found in our earlier work33, 34. Table 1.Characteristics of the investigated polymers Tc a

(oC)

Tg a (oC)

Tm a (°C)

Mwb (kg/mol)

Mw/Mnb

Ea c (KJ/mol)

Kynar 720/ARKEMA

136

-42

170

210

2.0

59

PMMA-1

V825T/ ARKEMA

—

114

—

95

2.1

169

PMMA-2

V825T/ ARKEMA

—

112

—

100

1.9

160

PMMA-3d

Homemade

—

107

—

119

2.5

160

PMMA-4

V046/ ARKEMA

—

102

—

137

2.0

157

Samples

Trademark/ Supplier

PVDF


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a

The crystallization temperature Tc, glass transition temperature Tg and melting temperature Tm were measured in our laboratory by a TA Instruments Q20 DSC at a heating and cooling rate of 10 ºC/min under N2. bdetermined in our laboratory by size exclusion chromatography (SEC) with tetrahydrofuran (THF) as the eluent for PMMA and dimethyl formamide(DMF) for PVDF. c energy of activation of the viscous flow (Ea) obtained from lnη0 plotted versus 1/T within a temperature range of 180 ºC

Understanding of Transient Rheology in Step Shear and Its Implication

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