Origin of mechanical stress and rising internal energy during fast uniaxial extension of SBR melts

Accepted Manuscript Origin of mechanical stress and rising internal energy during fast uniaxial extension of SBR melts Panpan Lin, Jianning Liu, Zhichen Zhao, Zhen-Gang Wang, Shi-Qing Wang PII:

S0032-3861(17)30708-5

DOI:

10.1016/j.polymer.2017.07.041

Reference:

JPOL 19853

To appear in:

Polymer

Received Date: 2 May 2017 Revised Date:

5 July 2017

Accepted Date: 16 July 2017

Please cite this article as: Lin P, Liu J, Zhao Z, Wang Z-G, Wang S-Q, Origin of mechanical stress and rising internal energy during fast uniaxial extension of SBR melts, Polymer (2017), doi: 10.1016/ j.polymer.2017.07.041. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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For Table of Contents only: Origin of mechanical stress and rising internal energy during fast uniaxial extension of polymer melts Panpan Lin, Jianning Liu, Zhichen Zhao, Zhen-Gang Wang and Shi-Qing Wang* 8 -1

Wi =0.34 (1.0 s ) R

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SBR 616K

w (MPa)

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w - mechanic work h - internal energy 1

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h - conformational 2

h (MPa)

q - heat exchange

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Origin of mechanical stress and rising internal energy during fast uniaxial extension of SBR melts Panpan Lin,1 Jianning Liu, 1 Zhichen Zhao, 1 Zhen-Gang Wang2,* and Shi-Qing Wang1,* 1

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Department of Polymer Science University of Akron, Akron, Ohio 44325-3909, United States 2 Division of Chemistry and Chemical Engineering California Institute of Technology, Pasadena, CA

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Abstract: We carry out simultaneous mechanical and IR-thermal-imaging based temperature measurements of SBR melts during uniaxial extension in order to delineate the nature of the observed mechanical responses. Using the first law of thermodynamics, we evaluate the enthalpy change h1 associated with the temperature rise in the extending melt, estimate the heat loss to the surrounding, and conclude that there is an appreciable non-thermal enthalpic buildup h2 = (w − h1 − q) during either adiabatic or isothermal extension. The monotonic increase of h2 with the stretching ratio λ until the onset of inhomogeneous extension or melt rupture reveals that fast melt extension is largely elastic even after yielding in presence of partial chain disentanglement. At high rates, the lock-up of chain entanglement produces such a high level of h2 that is rarely seen in extension of crosslinked rubbers. When melt extension is carried out under isothermal condition, we show that the time-temperature superposition principle (TTS) fails to predict the transient response of a SBR melt at a fixed effective rate involving three temperatures. The failure of the TTS suggests that the terminal chain dynamics show different temperature dependence from the local segmental dynamics that control the transient stress responses.

*

Corresponding author at [email protected] 1

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I. Introduction

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Mechanical behavior of elastomers and rheological responses of entangled polymers have been respectively studied for decades. The classical rubber elasticity theory[1] has actually provided the foundation for dynamics of non-crosslinked concentrated solutions and melts. The first treatment of the mechanical effect of chain entanglement in polymer melts is a transient network model[2] rooted in the framework of the rubber elasticity theory.[3] To observe rubbery-elastic response, entangled polymers need to be deformed at a sufficiently fast rate relative to the dominant relaxation time (e.g., the reptation time τ), i.e., at a high Weissenberg number (which is a product of the deformation rate and τ) Wi >> 1. In absence of crosslinking, affine elastic deformation usually cannot last. For example, in uniaxial extension of an entangled melt, the tensile force or its normalization known as engineering σengr could not grow monotonically without bound unless chain entanglement truly acts like crosslinking. Unlike crosslinked rubbers that can be examined in the zero-rate limit to have isothermal stretching at different temperatures, mechanical responses of entangled melts to large deformation vary with Wi. The zero-rate limit is uninteresting because entanglement has sufficient time to renew by molecular diffusion during slow (Wi << 1) deformation. When Wi >> 1, we must delineate how chain entanglement responds to the external deformation, which is the core question in nonlinear rheology of entangled polymers. Entangled melts are expected to behave like a crosslinked rubber at low strains when entanglement remains intact. What eventually happens to the polymer entanglement depends on the magnitude of Wi. Extensional deformation[4, 5] indicates that chain entanglement partially locks up, causing σengr to grow monotonically until rupture, when Wi well exceeds the ratio (τ/τR),[6-8] i.e., Wi > Wirupture. Such a phenomenon suggests that intermolecular interactions can actually indeed produce point-like entanglement via chain uncrossability. The tube model has been the standard model for polymer rheology including nonlinear behavior of entangled polymers.[9-11] Until recently, it is commonly believed[9, 12] that different responses[4] of entangled melts to startup uniaxial extension can be depicted by the tube model for Wi < Wirupture although the tube model does not contemplate why entanglement may lock up in extension to produce melt rupture. Being a universal theory for both entangled solutions and melts, the tube model is expected to prescribe identical rheological responses of solutions and melts that have the same number of entanglements per chain and are subjected to the same equivalent Hencky rates. Experiments have revealed qualitative differences between solutions and melts, in contradiction with the tube theory.[13-15] Despite the theoretical efforts to make theoretical calculations fit with experiment within the tube model paradigm,[16-18] our understanding remains inadequate. To address the emergent difficulties, it may be necessary consider an alternative framework. We may ask whether breakdown or yielding of the entanglement network can occur during continuous extension when the intrachain entropic retraction force grows to reach the magnitude of the intermolecular grip force.[19] During uniaxial extension along the Z direction, σengr begins to drop when the areal density of active entanglement strands decrease in the XY plane sufficiently fast due to the force imbalance.[19] Such a trend is indicative of an emerging

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collapse of the entanglement network.[7, 8, 20] Depending on Wi, we expect the strain-induced disentanglement to produce two different forms of strain localization.[4, 7] Since the concept of yielding, first suggested by Maxwell and Nguyen,[21] is still rather unfamiliar in the literature on polymer melt rheology, additional studies need to be carried out to further delineate the nature of the stress response of entangled melts to startup uniaxial extension. Specifically, to gain further insights into the nature of the mechanical response of entangled melts, it would be useful to determine what processes are involved during fast extension, in terms of the various emergent forms of the energy. We would like to know whether and how much of the deformation is still elastic after yielding, e.g., after the peak in σengr during startup extension. Such information is expected to give us more clues about the physics behind the specimen breakup during continuous melt stretching. In the present work we carry out in situ temperature measurement of an extending melt using an IR camera and analyze the state of deformation in terms of the first law of thermodynamics. Such simultaneous rheometric and thermal observations reveal that even for Wi < Wirupture there is a monotonic increase in one component h2 of the enthalpy density during homogeneous extension of styrene-butadiene copolymer (SBR) melts in the post-yield regime. For Wi > Wirupture, the stretched specimen can store h2 that is nearly half of the total mechanical work w. We are not aware of previous studies that reveal the emergence of such significant h2 during melt stretching. Based on one SBR melt (SBR153K) with high Tg, we also go to low enough temperature to avoid application of high rates that produce adiabatic stretching and confirm that there is a breakdown of the time-temperature superposition (TTS) principle.[22] In other words, it is found that TTS is invalid to predict the transient rheological responses of entangled polymers to startup extension at sufficiently high Wi. Specifically, at the same RouseWeissenberg number WiR (product of the Hencky rate and Rouse relaxation time), we found SBR153K to yield, i.e., to have its σengr showing a non-monotonic variation with the stretching ratio λ at room temperature but to lose its ability to yield, i.e., σengr growing monotonically with λ until melt rupture at a lower temperature of 9.5 oC. This paper is organized as follows. Section II provides a theoretical analysis to show how the mechanical stress and the potential enthalpy h2 can be delineated in terms of experimental observables. Experimental results are presented in Section III to show how the simultaneous mechanical and thermal measurements allow us to elucidate where the mechanical energy is spent. Further discussion is given in Section IV before the Conclusion Section V. II. Theoretical analyses

In this work we aim to determine the state of deformation during startup uniaxial extension of polymer melts. Specifically, by in situ monitoring the specimen's temperature, we can capture the build-up of internal potential energy as a function of time or stretching ratio λ. Under constant pressure P, it is more convenient to work with the enthalpy H defined as H=U+PV, where U is the internal energy and V the volume of the system. The first law of thermodynamics[23] in the form of rate per unit volume can be written as
ℎ⁄
 =
⁄
 +
 ⁄
,

(1) 3

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where the left-hand side is the change of enthalpy density h = H/V,
⁄
 represents the heat exchange with the surrounding, and dw/dt the rate of non-PV work density. For uniaxial extension the mechanical power density is given by
 ⁄
 =  =  .

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(2)

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⁄
 +
ℎ ⁄
 =  − 2  −  ⁄

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Here is the true stress,  the Hencky strain rate, and  the time derivative of λ. Because chain dynamics are usually temperature dependent, rheological measurements of polymeric liquids should desirably be carried out under isothermal condition so that the applied rate can be regarded as constant during rate-controlled experiments. In all extensional setups, the heat exchange is realized by immersing the specimen either in air[24] or in a liquid[25] and can be expressed in terms of the convection heat transfer coefficient a so that eq 1 can rewritten as (3)

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where D is the thickness of the sheet-like specimen, Ta is the ambient temperature, and Ts is the surface temperature, which is expected to be slightly lower than the interior temperature T by an amount that depends on the specimen's thickness D. A justification is provided in Supplementary Materials for this approximation. Because the difference between T and Ts is small, the remaining analysis takes Ts to be T. Here we have separated the enthalpy into two contributions h = h1 + h2, with dh1/dt given by 
⁄
. In eq 3,  represents density,  is specific heat capacity and T is the temperature of specimen. See further discussion in the Supplementary Materials. The last term on the right-hand-side of eq 3 is accurate for sheet-like specimens. Upon integration of eq 3 over time, and taking the undeformed state at the initial temperature as the reference, we find h2 to be determined by ℎ =  − ℎ + 

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where

(4a)

h1 = ρcp(T − Ta).

(4b)

Here we have taken cp to be approximately constant, i.e., hardly varying with temperature T and stretching ratio λ. It is shown in Supplementary Materials that this may be a good approximation. The heat inflow q can be estimated by monitoring the specimen's temperature as =−

% 2 [ ′ &

−  ]⁄ $ 
′ ,

(5)

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with Ta being the ambient temperature, the instant specimen thickness D(t) being related to its initial value D0 as D0exp(− t/2). The work density w is given by the following integration w(λ)=

' ′
′  

.

(6)

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Thus, from the rheometric measurements and in situ temperature reading of the extending specimen, we can measure h2. III. EXPERIMENTAL A. Materials and sample preparation

Table 1. Microstructures of SBR melts Styrene (%) 20 22 22 26

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SBR325K SBR616K SBR1M SBR153K 6

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Butadiene (%) 80 78 78 74

Vinyl content in butadiene (%) 53 38 29 70

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Samples

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Four nearly monodisperse styrene-butadiene random copolymer (SBR) with different molecular weights were used in this work. They were provided by Dr. Xiaorong Wang at Bridgestone Americas Center for Research and Technology. Their microstructures are listed in Table 1. The basic linear viscoelastic properties of these SBR are also obtained from small amplitude oscillatory shear (SAOS) measurements using an ARES-LS rotational rheometer (TA Instrument). Specifically, Figure 1(a) to 1(d) are storage and loss moduli G' and G" of the four SBR, from which we identify the terminal relaxation time τ as the reciprocal of the crossover frequency ωc as listed in Table 2 along with other pertinent parameters including the Rouse time τR.

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Figure 1a

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Figure 1b

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SBR 325K

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Figure 1c Figure 1d Figure 1 Small amplitude oscillatory shear measurements of (a) SBR325K at 25 oC, (b) SBR616K at 25 oC, (c) SBR1M at 25 oC and (d) SBR153K at 30 oC. The storage and loss modulus, G' and G", are represented by circles and squares, respectively. Also plotted is the viscosity (triangles) on the left Y-axis. The vertical lines denote the Hencky rates used to carry out melt extension in the present study.

Table 2. Viscous characteristics of SBR melts.

from Ref.[26]. from Ref. [8]. d from Ref.[22]. c

Mw/Mn 1.36 1.12 1.23 1.05 1.1

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Mn (kg/mol) 325 616 1068 153 2000

Gpl (MPa) 0.76 0.88 0.85 0.53 0.22

Z 152 276 510 37 154

τ (s) 714 920 11000 1280 8851

τR (s) 1.0 0.34 7.2 12.5 19

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Sample SBR325K (25 oC)a SBR616K (25 oC)b SBR1M (25 oC)c SBR153K (30 oC)d PS2M (150 oC) a from Ref.[7] .

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Note: the Rouse relaxation time τR was calculated from the zero-shear viscosity[27] as () = 6+, -⁄.  /+0 ⁄+, .1 for SBR325K, SBR616K and SBR153K. For SBR1M, τR was calculated from Doi-Edwards formula as () = (⁄33.

To prepare specimens for uniaxial extension, SBR melts were placed between two Mylar films and pressed into thin sheets for a sufficient long time, e.g., 10τ. Rectangular-shaped samples were cut by a razor blade involving typical thickness H0 ranging from 0.5 mm to 1.0 mm. The present study also carried out melt extension of monodisperse polystyrene with molecular weight equal to 2000 kg/mol. PS was molded into dog-bone shaped specimens where the thin dimensions were 10 mm × 2.9 mm × 1.0 mm. B. Apparatus

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All uniaxial extension experiments on SBR were carried out by either a Physica MCR 301 rotational rheometer (Anton Paar) at room temperature or an advanced rheometric expansion system (ARES)-LS rotational rheometer at low temperatures. A first generation SER fixture was mounted on either of the two rheometers to perform melt extension. In situ temperature measurements were taken by an infrared (IR) camera (FLIR SC325) with a recording rate of 60 Hz. To reduce the air cooling effect, a box, made with thermal insulation materials, was applied to cover SER fixture to reduce the air convection. All room-temperature measurements involved the use of this box except for the data in Figures 10 to 12.

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Melt extension of PS employed an Instron 5543 with an environment chamber at a constant crosshead speed of 1000 mm/min at 150 oC. After stretched to different elongation ratios of λ = 5, 6, 7, 8, respectively, the samples were quickly quenched by spray of icy water to preserve the melt-stretching effect. Instead of in situ temperature measurements, we examined the post-stretch by annealing melt-stretched PS in a custom-made heater with temperature controller, where the specimen was mounted on the Instron so that any retractive stress could be measured during the annealing. IV. RESULTS

To evaluate eq 5, we directly determine the value of air convection heat transfer coefficient a in these expressions by heating up with hot air blower a sheet-like specimen of SBR1M with length of 18 mm, width of 3 mm and thickness of D = 0.40 mm and using the infrared (IR) camera to record the temperature decrease as a function time due to the air cooling. The temperature drop due to air cooling can be predicted according to the expression  6

 −   whose solution is given by

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6<0=

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=

(7)

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where Ti is the initial temperature. The detailed procedure for the specific heat cp for all SBR samples characterized by Differential scanning calorimetry (DSC) to ensure the weak temperature dependence of cp is included in the Supporting Information. For the SBR melt, we have ρ = 933 BC⁄DE and  FG/ 1+ = 2070 K⁄BC ∙ M. Two pairs of the values for Ti and Ta were involved. In absence of a blowing fan, Ti = 68 oC and Ta = 25 oC. With the fan, we had Ti = 78 oC and Ta = 25 oC. By fitting the temperature data in Figure 2 to eq 7, we obtain the decay time constant (ρcpD/2a) to be 5.6 and 15.1 s respectively, depending on whether a fan is used or not to accelerate the cooling. Therefore, we find a to be 26 and 69 K⁄D ∙ M  respectively from the upper and lower curves in Figure 2, which are within the expected range.

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T(t) - Ta = (Ti - Ta)exp[-2at/(Dρcp)]

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a = 26 J/m .K (without fan) 1 2

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a = 69 J/m .K (with fan) 120

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Fig. 2 Fig. 3 Figure 2 Experimental data from IR thermal imaging camera in agreement with eq 7 both in absence (circles) and presence (squares) of a fan, where the straight lines are the fit to eq 7, corresponding to having a = 26 and 69 respectively.

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Figure 3 Four IR thermal images showing the temperature rise upon uniaxial extension of SBR616K at a Hencky rate of 1.0 s-1. The color scheme on the right refers to the temperature in the unit of Celsius (oC). A. Adiabatic melt stretching A.1 Regime of Necking (yielding)

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Although melt extension has been studied to characterize processing behavior of polyethylene since 1970s, it has rarely been shown whether there is any significant internal energy buildup that is not associated with temperature rise. Traditionally, entangled melts have not been treated as transient solids although a few early studies[28-30] had reported melt rupture. We can obtain more valuable information about the nature of the rheological response of entangled melts to extensional deformation if we experimentally determine how the internal energy h2 builds up according to eq 4a.

SBR616K

1.0 s , Wi =0.34

2.5

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o

T = 25 C

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Figure 4 Figure 5 Figure 4 Engineering stress σengr (circles) as a function of the stretching ratio λ during melt extension of SBR616K at a Hencky rate of 1.0 s-1 at Ta = 25 oC. Also plotted is the corresponding temperature increase ∆T above Ta (squares) as a function of λ. 8

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Figure 5 Mechanical work density w (circles) and stored enthalpy density h2 (diamonds) as well as h1 (squares) and heat loss q (triangles) as a function of λ. Since q is negligibly low relative to w, the test is essentially adiabatic.

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At modest Hencky rates, i.e., around 1 to 10 s-1 under room temperature, several SBR melts show a significant temperature increase during melt stretching to suggest that such melt extension experiments were hardly isothermal.[31] To have isothermal extension, it would be necessary to immerse the stretching specimen in a circulating liquid as done in early experiments.[25] Figure 3 shows four IR thermal images of SBR616K at different stages of the startup uniaxial extension at a Hencky rate of 1.0 s-1. The measurable temperature increase allows us to examine how polymer entanglement responds to fast extensional deformation. Figure 4 shows a pronounced peak in the engineering stress σengr for SBR616K. In other words, the stress monotonically grows until reaching the peak that we have identified as the yield point.[19] Here we only show the data involving homogeneous deformation. Also plotted in Figure 4 is the temperature change (squares) according to the reading from the IR camera. Clearly, such a rheometric test is far from isothermal. Therefore it is not a truly constant-rate experiment because the effective rate, measured in terms of the Weissenberg number Wi = εɺ τ[T(λ)], varies with λ as T varies. One way to depict the nature of the rheological response is to evaluate the total mechanical work density w according to eq 6 and the enthalpy density h2 according to eq 4a. Figure 5 shows that h2 keeps growing, along with w, during the startup stretching before necking becomes visible. Here h1 in eq 4a and eq 4b is evaluated according to the measured value of cp, provided in the Supplementary Materials, and the data of (T − Ta) in Figure 4.

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To illustrate the universality of the findings in Figure 4 and 5, we also carried out uniaxial extension of SBR325K at a Hencky rate of 3.0 s-1 in the necking regime. The stress (circles) and the corresponding temperature rise (squares) are shown in Figure 6(a). Moreover, Figure 6(b) confirms the behavior observed in Figure 5.

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Figure 6 (a) Engineering stress σengr (circles) as a function of the stretching ratio λ during melt extension of SBR325K at a Hencky rate of 3.0 s-1 at Ta = 25 oC. Also plotted is the corresponding temperature increase ∆T above Ta (squares) as a function of λ. (b) 9

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Mechanical work density w (circles) and stored enthalpy density h2 (diamonds) as a function of λ for SBR325K at a Hencky rate of 3.0 s-1. A.2 Melt rupture

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At higher Hencky rates, i.e., N7O = () is much larger than unity, entangled melts only undergoes partial yielding, evidenced by monotonic increase of σengr during startup extension until melt rupture.[4, 7] For example, at a Hencky rate of 6.0 s-1 SBR1M is beyond the yield-torupture transition (YRT) as shown in terms of the stress vs. strain curve in Figure 7(a). The upturn of σengr indicates true strain hardening as discussed before.[32] Figure 7(b) shows that the absolute values of h2 as a function of λ in this rupture regime. As a second case of such strain hardening leading to melt rupture, Figure 8(a) and 8(b) present the results of startup extension of SBR153K at a Hencky rate of 4.0 s-1. It is interesting to note that the buildup of h2 is even higher than that observed in Figure 7(b).

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Figure 7 (a) Engineering stress σengr (circles) as a function of stretching ratio λ of SBR1M at a Hencky rate of 6.0 s-1 at Ta = 25 oC. Also plotted is the corresponding temperature increase ∆T above Ta (squares) as a function of λ. (b) Mechanical work density w (circles) and stored enthalpy density h2 (diamonds) as a function of λ.

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Figure 8 (a) Engineering stress σengr (circles) as a function of stretching ratio λ during melt extension of SBR153K at a Hencky rate of 4.0 s-1 at Ta = 25 oC. Also plotted is the corresponding temperature rise (squares). (b) Mechanical work density w (circles) and stored enthalpy density h2 (diamonds) as a function of λ. 10

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B. Isothermal extension at low temperatures

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In the four cases examined in the preceding sections, the melt stretching is adiabatic because of the high tensile stresses and fast extensional rates. Air cooling is rather ineffective for these tests that were carried out in a chamber to minimize air circulation. For such tests to be isothermal, the second term on the right-hand-side (RHS) of eq 3 must be larger than the first term on the RHS of eq 3, which is the mechanical power density dw/dt. Using a fan to increase air convection around the extending SBR melt, we can approach isothermal testing condition for SBR153K whose nonlinear rheological responses show up at rather low rates. Indeed, with a = 69 W/m2K for a specimen of initial thickness D0 = 0.5 mm, qɺac =2a∆T/D ~ 0.14λ1/2 MPa/s provided that the specimen has a temperature rise of 0.5 oC. If the applied rate εɺ = 0.0792 s-1, i.e., WiR = 3.6 for SBR153K, we can expect σengr ~ 1 MPa so that dw/dt = 0.0792λ MPa according to eq 2, which is comparable or lower than qɺac until high stretching ratios. Such an

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estimate is conservative because not all of w turns into heating up the specimen. For example, h2 keeps building up according to Figure 5 and Figure 6b. To confirm that the quasi-isothermal condition is achieved for SBR153K in the regime of yielding at room temperature, we carry out in situ temperature measurement during extension. Using a fan to increase air cooling, we measured the temperature change to be within 0.5 oC as shown in Figure 9. According to the temperature dependence of the chain dynamics shown in Figure 10, the effective rate, i.e., WiR indeed stays near 3.35. 25

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Figure 9 Temperature change T (left Y-axis) as a function of λ, where the smooth curve is an average reading of the temperature, along with the corresponding effective rate WiR (right Y-axis) as a function of λ, during melt stretching of SBR153K at a Hencky rate of 0.0792 s-1 at room temperature with an initial thickness D0=0.6 mm with a fan. Figure 10 Rouse relaxation time τR of SBR153K as a function of temperature. This dependence presents equivalent information as the WLF shift factor aT. It is actually obtained using aT from the SAOS measurements at the different temperatures from 0 to 90 oC. 11

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Even without a fan, the extension at a rate as low as 0.1 s-1 was not far from isothermal. Specifically, with an eventual temperature rise of 1.5 oC, the actual WiR decreases only by 20 %. The response is ultimately determined by the stretching rate, i.e., the value of WiR. Figure 11 shows that up to a significant stretching ratio of ca. five, the buildup of h2 is similar although the applied WiR varies from 3.35 to 50. Because of the yielding to be shown in Figure 12, h2 cannot grow sharply with increasing λ at WiR ~ 3-4, in contrast to the upturn in h2 at WiR = 50 that results in rupture.

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Figure 11 Figure 12 Figure 11 Non thermal part of the enthalpy change density h2 as a function of stretching ration  of SBR153K under different conditions: (1) WiR=50 at 25.0 oC (circles in red); (2) WiR=3.35 at 24.2 oC with a fan to take heat away (diamonds in green); (3) WiR=3~4 at 24.5 oC without a fan blowing (squares in blue). Figure 12 Engineering stress σengr as a function of stretching ratio  of SBR153K under different conditions: (1) at a Hencky rate of 0.00081 s-1 at 9.5 oC (circles in red); (2) at a Hencky rate of 0.006374 s-1 at 15 oC (squares in blue); (3) at a Hencky rate of 0.00594 s-1 at 15.0 oC (half-filled squares in blue); (4) at a Hencky rate of 0.0792 s-1 at temperature range from 24.1 to 24.5 oC (diamonds in green). The numbers in brackets show the range of effective rate WiR with consideration of temperature rise during deformation.

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C. Breakdown of time-temperature superposition

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The YRT can take place over a rather narrow range of rate.[4, 7] If the testing condition can be assured to be isothermal, this transitional characteristic can be exploited to examine whether the principle of time-temperature superposition (TTS) holds during transient response to startup melt extension.[22] The preceding subsections indicate the poor air cooling efficiency leading to adiabatic stretching. Specifically, according to the theoretical analysis given in Section II, the extensional stress and rates are too high for air cooling to be effective in the fast extensional deformation of these SBR melts at room temperature. However, for the sluggish SBR153K, the melt extension at 0.0792 s-1 at room temperature is slow enough to allow approximate thermal equilibration between the stretching specimen and the surrounding air so that the applied WiR stays around 3.35 as shown in Figure 9. At WiR = 3.35, SBR153K undergoes yielding at room temperature as shown by the diamonds in Figure 12.

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Figure 13 Temperature rise ∆T calculated from eq 3 with dh2/dt=0, as a function of stretching ratio  for SBR153K with an initial thickness D0=0.6 mm at two different temperatures of 9.5 oC (red circles) and 15.0 oC (blue squares) with the same effective rate WiR=3.35. Figure 14 The initial IR temperature change ∆T as a function of stretching ratio for three types of SBR melts: (1) SBR616K at a Hencky rate of 1.0 s-1 (green diamonds); (2) SBR1M at a Hencky rate of 6.0 s-1 (blue squares); (3) SBR325K at a Hencky rate of 3.0 s1 (red circles). The inset plots the temperature change ∆T as a function of σengr. It also includes SBR153K at a Hencky rate of 4.0 s-1 (black triangles).

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To have WiR = 3.35 at 15 oC, the applied Hencky rate should be 0.00594 s-1, much lower than the rate at room temperature so that the corresponding mechanical power is much lower. We can quantitatively estimate an upper bound for the temperature increase during such an extension using eq 3. This is an upper bound because our estimate sets the second term of the left-hand-side to be zero. Taking a conservative value of  = 50 N ⁄D ∙ M  for the force oven and D0 = 0.6 mm, the temperature increase is not expected to exceed 0.1 oC as shown in Figure 13 so that WiR would range between 3.25 and 3.35. Yet, the stress response is visibly stronger as shown in Figure 12 relative to that at room temperature (diamonds in Figure 12). Figure 13 also presents the estimated temperature rise of ca. 0.025 oC when SBR153K is subjected to startup extension under 9.5 oC at 0.0081 s-1, i.e., WiR = 3.35. Figure 12 shows that strain hardening and melt rupture in circles at 9.5 oC. Such strain hardening is absent at 15 oC at a higher even rate of 0.0637 s-1 (than 0.00594 s-1) as shown by the open squares in Figure 12 although WiR exceeds 3.35. The comparison between the stress responses of SBR153K at these three temperatures in Figure 12 under comparable values of WiR = 3.35 unambiguously suggests a breakdown of the TTS. In other words, at the same WiR, SBR153K shows typical yielding behavior with a pronounced peak in σengr at room temperature, nearly losing the peak at 15 oC and clearly undergoing strain hardening and inevitable rupture at 9.5 oC. V. Discussions 13

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Time-temperature superposition principle (TTS) is known to work well for quiescent chain dynamics for a large number of polymers.[33, 34] For some polymers where terminal chain and segmental dynamics may have different temperature dependence, TTS has been found to be invalid when the linear-response viscoelastic characterization covers both segmental and terminal chain dynamics.[35, 36] If nonlinear steady-state rheological behavior depends on terminal chain dynamics, e.g., depending on the value of Wi or WiR,[37] and TTS has been observed to apply, e.g., at steady-state.[38] Here the failure of TTS is revealed by examining whether the critical condition for the yield-to-rupture transition can be specified by a common effective rate (Wi or WiR). When melt rupture[7] occurs the conventional picture of any transient Gaussian-chain network model[2] breaks down: The lifetime of the network junctions diverges at sufficiently high rates. Similarly, the tube model[9, 12] does not anticipate the "permanent" nature of chain entanglement during fast melt extension that produces melt rupture. The lock-up of chain entanglement leading to the melt rupture is expected to arise from chain uncrossability associated with excluded volume interactions. Segmental dynamics dictate whether the intermolecular uncrossability is effective in producing chain entanglement. The observed TTS seems to suggest that the local segmental dynamics have different temperature dependence from that of terminal chain dynamics.

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The experimental results in IV.A and IV.B indicate that the ability to monitor the temperature of a stretching melt provides useful insights into the nature of the nonlinear responses of entangled melts to fast extension. According to our current understanding, the homogeneous melt extension becomes impossible because the entanglement network eventually breaks down via chain disentanglement.[7, 8, 20] Strain localization in tensile extension is inevitable because the load-bearing elements, e.g., the active strands in entanglement network are arranged in series along the stretching axis. We interpret the monotonic growth of the enthalpy change h2 as evidence of ongoing overall chain stretching during startup melt extension until the termination at melt rupture. To evaluate h2 from eq 4a, we have estimated h1 of eq 4b using the measured value of cp from differential scanning calorimetry, which shows that cp can be treated as constant, as discussed further in the Supplementary Materials.

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Figure 15 Stored enthalpy density h2 as a function of the mechanical work density w for the four SBR melts stretched with different effective rates: (1) SBR153K with WiR=50 (black triangles); (2) SBR1M with WiR=43 (blue squares); (3) SBR325K with WiR=3.0 14

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(red circles); (4) SBR616K with WiR=0.34 (green diamonds). The diagonal line indicates the limit of h2 = w. At the highest effective rate WiR = 50, there appears to be more viscous dissipation to slow down the buildup of h2, which is plausible and reasonable.

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The temperature increase during the near-adiabatic extension in the initial dominantlyelastic deformation regime before yielding, has the same origin as that observed in rateindependent stretching of crosslinked rubbers. For crosslinked rubbers, the standard interpretation is that the mechanical energy causes "molecular agitation"[3] so that the internal kinetic energy increase. Figure 14 is analogous to the classical data of Joule[39] and JamesGuth,[1] which were presented as Figure 2.10 in Treloar's book.[3] The initial temperature dip indicates that the internal kinetic energy has turned into the other form of internal energy. We note that this interpretation is consistent with Chauveau's view expressed on p. 453 in Ref. [40] that the initial temperature drop was due to a change in dimensions of the intermolecular spaces. This interpretation differs from the one given on p. 39 in Ref. [3] that "the initial cooling effect corresponds to positive entropy of deformation". Well beyond the initial response, the temperature increase can be rather significant, as shown in the inset of Figure 14 as function of the emergent engineering stress σengr. Below the YRT, as is the case discussed in IV.A.1, the temperature still increases when σengr saturates or slightly declines. Beyond the yield point, i.e., when the data start to turn vertical in the inset of Figure 14, there can be significant viscous dissipation upon disentanglement when chains slide past one other, interacting by friction. A fully developed flow state would involve all strands constantly slide past one another without any additional chain stretching. This does not occur under the condition of Wi >> 1 in a global melt stretching experiment of well entangled melts until the onset of necking. Such a conclusion is consistent with the previous interpretations.[7, 20] When a melt is well entangled, it appears improbable for chain entanglement to "sort out", i.e., to disentangle, uniformly in a macroscopic specimen during uniaxial extension. Above the YRT in the melt rupture regime, the rapid temperature rise is accompanied by the growing σengr. Here the internal kinetic energy increase associated with the temperature rise is merely one feature. The other characteristic is that h2 continues to grow strongly with λ. Throughout the explored range of Hencky rates, we indeed observe a significant amount of change in the enthalpy, i.e., in h2 that is not directly related to the temperature rise of the specimen. As shown in Figure 15, h2 is an appreciable fraction of the mechanical work w, even below the YRT, i.e., for WiR < 1. Above the YRT, a great deal of the work resulted in an increase of h2 (reaching nearly half of w) when the chain entanglement locks up to act like permanent crosslinks. Unlike typical extension of crosslinked rubbers, we are able to stretch these SBR melts at the high rates to far greater extensions. In other words, we have observed an unprecedented amount of enthalpic buildup during melt stretching, which is unfamiliar according to any textbook knowledge.[3] Such significant internal energy increase appears to have rarely been reported in the literature.[41] Since it rises strongly with the stretching ratio λ, h2 should be due to chain stretching. Taking the monomeric mass of SBR to be m = 70 g/mol and mass density to be ρ = 900 kg/m3, when h2 reaches 15 MPa as shown in Figure 14, on the average, the enthalpy storage hm 15

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tensile stress (MPa)

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rubber elasticity 2

=G (λ−1/λ )

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pl

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per monomer is hm = h2(m/ρ) = 1.17 kJ/mol. According to the literature, there are many conformational states in 1,4-polybutadiene that require a significant amount of energy to reach, ranging from below 1 kJ/mol to well above 10 kJ/mol.[42] Similarly, the barrier between trans and gauche states in PS is as high 15 kJ/mol.[43, 44] Therefore, it seems plausible that the observed level of enthalpic increase on the order of hm ~ 1 kJ/mol arises from conformational changes produced by the melt extension. The emergence of these high energy states of chain conformation supports the idea that entanglements indeed act like crosslinks and segmental distortions can take place in entanglement strands although the equilibrium segmental relaxation times are much faster than the reciprocal stretching rate. It is plausible that with ongoing fast melt extension entanglement strands can become increasingly strained as long as the entanglements survive. Correspondingly the segmental distortion increases to store more internal energy.

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Fig 16 (a) Engineering stress as a function of the tensile "strain" (λ−1/λ2) for meltstretching of PS at 150 oC at a constant crosshead speed 1000 mm/min, to stretching ratios λ = 5, 6, 7, and 8 respectively. (b) Tensile stress curve observed during annealing at 90 oC of the four melt-stretched PS.

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In search for the mechanism to store internal energy h2, we performed melt stretching of PS melt at 150 oC and quenched the melt-stretched PS sufficiently fast to room temperature in order to retain the molecular deformation. As shown in Figure 16(a), the rheological behavior resembles that observed for SBR325 melt stretching in Figure 6(a). In absence of crosslinking, the stress response is much weaker than the limit given by the rubber elasticity formula. Nevertheless, there is striking evidence shown in Figure 16(b) that internal stress of intrachain origin may be trapped at some segmental level. Specifically, when we brought melt-stretched PS to 90 oC where the PS is in its glassy sate, the specimen shows considerable retractive stress despite the thermal expansion that first caused the specimen to bend between the two clamps of the Instron. Such elastic yielding[45] shows that deformed polymer chains can cause intersegmental repacking in the glassy state, leading to imbalance between intersegmental and intrachain interactions . Macroscopic retractive stress suggests that chain tension has caused activation of the glassy state. Thus, the observed elastic yielding behavior in Figure 16(b) is consistent with or in support of the notion that melt-stretching of well-entangled polymers can result in significant intern energy buildup, as inferred from the data presented in the preceding section.

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In passing, we make a cautionary remark. Strictly speaking, the enthalpy h2 of eq 4 is a state function that can only be defined at equilibrium. For the present viscoelastic melts, our measurements simply adopt eq 4 to show that the right-hand-side of eq 4 is positive and can actually be a significant fraction of the mechanical work w. In other words, apart from the increased kinetic internal energy associated with the observed temperature rise and any heat exchange with the surrounding, a sizable fraction of the input mechanical work appears to have been stored as internal energy (enthalpy) in the form of higher energy states of the chain conformations. Finally, some additional comments are in order. Our demonstration of the TTS breakdown requires us to maintain isothermal condition during extension. SBR153K is the only sample that has a sufficiently long Rouse relaxation time at room temperature for us to probe the temperature dependence of the yielding-to-rupture transition (YRT) using sufficiently low Hencky rates. Only at such low rates, air cooling is effective enough to ensure an efficient heat exchange between the sample and the surrounding and maintain the sample temperature. To study the other samples would require the tests to be carried out in a low-temperature chamber, to which our IR imaging camera could be applied to verify isothermal condition. We have not carry out such tests. It also remains unknown whether the TTS failure would occur similarly upon startup simple shear. The current demonstration of the TTS failure in melt extension is clear because we examined how the response changes from yielding to rupture at the same WiR where the rheological characteristics differ remarkably. Unless a similar YRT exists as a function of the applied rate in simple shear, any TTS failure may be less obvious. Currently, no suitable shear rheometric apparatus is available to apply high shear stress without edge fracture. Yet high strain is necessary to explore whether an entangled melt can also avoid complete yielding and behave like a crosslinked rubber upon startup simple shear as it does in startup uniaxial extension, beyond a threshold value of WiR. It is beyond the scope of the present study to make a parallel investigation on the validity of the TTS for nonlinear transient responses in simple shear. Finally, it remains unclear whether the observed TTS breakdown is due to the specificity of the SBR microstructure, i.e., due to the "glassy" blocks of styrene in the random copolymer of SBR. Unpublished data on polystyrene melts appear to indicate that the TTS does break in the same sense, i.e., showing different transient stress responses at a common value of WiR. We also note that according to the literature[46] pure PS does not show observable failure of the TTS under equilibrium until the temperature is close to T/Tg = 1.06. Since polybutadiene hardly shows any TTS breakdown, SBR is not expected to show any visible failure of the TTS in equilibrium at T/Tg = 1.06. Interestingly, Figure 12 indicates that we can observe a failure of TTS at significantly higher temperatures (e.g., 15 oC corresponding to T/Tg = 1.095). Currently it is unclear that whether or not the observed failure at such higher temperatures is related to the high sensitivity afforded by the method to examine the critical condition for the YRT. VI. Conclusions The present work applied IR thermal imaging to monitor the temperature rise in fast uniaxial extension of SBR melts. Without immersing the specimens in a cooling and circulating liquid to obtain quick heat removal, the typical tests of these melts are found to be essentially adiabatic. Informed by simultaneous mechanical and IR thermal measurements, we found that 17

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the extension is largely elastic until the onset of strain localization well after yielding, i.e., after the tensile force has begun to decline. Specifically, we observe that a fraction of the enthalpy, h2, increases monotonically despite significant ongoing chain disentanglement. Thus, the in situ temperature reading during uniaxial extension of SBR melts reveals continuing chain stretching of the surviving entanglement strands in the collapsing entanglement network up to the onset of tensile strain localization. This conclusion is consistent with the previous assertion that in global uniaxial extension yielding of the entanglement network through disentanglement results in termination of uniform extension and a fully-developed flow state is not accessible during startup extension with Wi > 1. Clearly, the same temperature-measurement-based analysis should be applied to any measurements that claim to report steady flow properties of entangled melts in uniaxial extension, including those in the literature that were based on filament stretching rheometry.

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At sufficiently high rates, the internal energy buildup can be as much as half of the total mechanical work when the entanglement locks up to prevent complete yielding of the entanglement network, as shown in Figure 15. This observation of remarkable storage in the form of intrachain elastic energy occurs because of the considerable stretching that the specimens are able to sustain. It appears that such capacity of an entangled melt to store energy has not been previously discussed.

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Using one of the four SBR melts with a rather high glass transition temperature Tg, we are able to perform isothermal melt stretching by applying sufficiently low Hencky rates. In such a limit, air convection can be a sufficiently effective cooling mechanism. Under this circumstance, we have examined the principle of time-temperature superposition (TTS) that usually holds for nonlinear rheological investigations in steady flow. At a given fixed effective rate, specifically, at WiR = 3.35, we find the SBR153K to undergo yielding until necking at room temperature but to suffer melt rupture at 9.5 oC, revealing an impressive breakdown of the TTS as shown in Figure 12. This observed failure of TTS has far-reaching implications concerning our current theoretical framework for nonlinear rheology of entangled polymers and is expected to simulate further future work on both experimental and theoretical sides.

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Acknowledgment This work is, in part, supported by the Polymers program at the National Science Foundation (DMR-1105135). SQW acknowledges a conversation with G. Hamed on rubber elasticity. We thank Dr. S.Z.D. Cheng and Xueyan Feng for assistance with the DSC measurements presented in the Supplementary Materials. For Table of Contents only: Origin of mechanical stress and rising internal energy during fast uniaxial extension of polymer melts Panpan Lin, Jianning Liu, Zhichen Zhao, Zhen-Gang Wang and Shi-Qing Wang*

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Highlights: • Melt stretching can store significant internal energy and cause conformational distortion at the bond level. • Transient rheological response to startup extension does not follow the timetemperature superposition. • Quenched samples after melt stretching show a different glassy state with reduced energy barrier to permit emergence of retractive stress below Tg.