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Strain accelerated mesophase separation during nonlinear stress relaxation of olefin multiblock copolymer
Accepted Manuscript Strain accelerated mesophase separation during nonlinear stress relaxation of olefin multiblock copolymer Zhijun Nie, Wei Yu PII:
S0032-3861(17)30319-1
DOI:
10.1016/j.polymer.2017.03.053
Reference:
JPOL 19549
To appear in:
Polymer
Received Date: 29 December 2016 Revised Date:
24 February 2017
Accepted Date: 19 March 2017
Please cite this article as: Nie Z, Yu W, Strain accelerated mesophase separation during nonlinear stress relaxation of olefin multiblock copolymer, Polymer (2017), doi: 10.1016/j.polymer.2017.03.053. 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.
β=2 β=1
104
β=0
102
135oC
Olefin block copolymer γ=0.1 γ=3
150oC
phase separated <154oC
165oC 180oC
100
300 s 2700 s 5100 s 7500 s 9900 s
10-2 -4
10
10-6 10-2
10-1
γ=5 γ=3 (homogeneous, >154oC) 100
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106
101
102
103
AC C
EP
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Time (s)
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G(t, γ)*10β (Pa)
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104
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Strain accelerated mesophase separation during nonlinear stress relaxation of olefin multiblock copolymer Zhijun Nie, Wei Yu*
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Advanced Rheology Institute, Department of Polymer Science and Engineering, State Key Laboratory for Metal Matrix Composite Materials, Shanghai Key Laboratory of Electrical
Insulation and Thermal Ageing, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
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Abstract
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The nonlinear relaxation behavior of olefin multiblock copolymers subjected to step shear strains has been investigated. Compared to homogeneous polymer, a two-step relaxation behavior was identified in olefin multiblock copolymers, with the faster one for the chain relaxation and the slower one for the domain relaxation. It is
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found that the domain relaxation has stronger strain dependence than the chain relaxation. Large repeated step strains can cause longer relaxation process of domains
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as compared to the single step strain test. The prolonged domain relaxation and nearly constant relaxation plateau modulus are ascribed to the coarsening of domain as well
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as the increase of the volume fraction of domains, which indicates the accelerated mesophase separation of olefin multiblock copolymer under large strains.
*
Corresponding author. Email: [email protected] 1
ACCEPTED MANUSCRIPT 1. Introduction It is well known that block copolymers comprising two or more chemically distinct monomer blocks tend to undergo microphase separation due to the
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incompatibility of distinct blocks [1, 2]. The microphase separation is influenced by the block length, the interaction between blocks and the volume fraction of a block according to various experiments [1-4] and mean field theory [5, 6]. Recent studies by
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rheology have further revealed that the number of blocks and the polydispersity in
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molecular weight also affect the phase separation behavior [7, 8]. As compared to the monodispersed diblock copolymer, much shorter block length can induce phase separation in polydispersed multiblock copolymers [8] and the domain size (~100 nm) is much larger than that diblock copolymers (~15-25 nm) [7], which is known as the
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mesophase separation [9-11]. Although there are lots of work focused on the micro(meso-) phase separation behavior of block copolymers, the effect of flow remains far
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unrevealed [12-14]. In contrast, it has been found that shear flow is able to induce mixing or de-mixing of partially miscible polymer blends [15-19]. Possible reasons
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for lacking of such knowledge in block copolymers are the fast kinetics and much smaller domain sizes in the phase separation of block copolymers, which make the real time investigation difficult. Among all the techniques to characterize the phase behavior of block copolymer, rheology has almost no requirements on the materials properties like refractive index and electron density, and has the advantage of online measurement especially under flow field. Moreover, it is very sensitive to the concentration fluctuation [20, 21], 2
ACCEPTED MANUSCRIPT which make it a feasible method to study the phase separation of polymer blends and block copolymers. The linear viscoelastic properties of polymers, as normally measured by small amplitude oscillatory shear, is useful in analyzing the relaxation
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processes of different microstructures. However, it is only meaningful when the total deformation is quite small or very slow, which limits its application in detection of the phase transition under quiescent condition. For larger or more rapid deformations, the
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response to an imposed deformation not only depends on the magnitude of the
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deformation, but also depends on the rate and the kinematics of the deformation. In other words, the response to an imposed deformation is no longer a material property but also depends on the history of deformation [22]. Nonlinear rheological properties may not only represent the nonlinear mechanical responses of microstructures, but
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also involve the change of structures.
The step shear strain experiment is frequently used to investigate the nonlinear
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response of polymer [23]. An experimental phenomenon is that the stress relaxation following a step strain satisfies time-strain separability (TSS) at sufficient long time.
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In such case, the nonlinear relaxation moduli G ( t , γ ) can be expressed as G ( t , γ ) = G ( t ) h (γ ) , where G(t ) is the linear relaxation moduli and h(γ ) is the
damping function [24]. Subtle variations in structure or architecture might lead to obvious distinction for the damping function. Numerous studies have been performed on star polymers [25], H-polymers [26], pom-poms [27], comb polymers [22, 28, 29] and other architectures [30-32]. The damping behavior of star polymers, H-polymers, comb polymers exhibited less strain softening than the universal Doi-Edwards 3
ACCEPTED MANUSCRIPT damping function [22, 26, 28, 29, 33, 34] , which is ascribed to the hierarchical relaxation mechanism [34]. Moreover, the hierarchical relaxation mechanism involving the chain relaxation and the domain relaxation is also found in polymer
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blend [35, 36]. For block copolymers, in addition to the segmental relaxation and chain relaxation in homogeneous state, the relaxation in heterogeneous state also involves
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that of the domain structures. We have found recently that the mechanical responses
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of domain relaxation can be greatly enhanced in large amplitude oscillatory shear [37]. It indicates that nonlinear rheological behaviors can be good candidates to study the flow effect on the phase separation of block copolymers. In this work, we will focus our attention on the nonlinear relaxation behavior after step shear strains and try to
copolymers.
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uncover the effect of shear on the mesophase separation of polydispersed multiblock
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2.1. Materials
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2. Experimental Section
The Olefin Multiblock Copolymers (OBCs) synthesized via the chain-shuttling
technology were provided as pellets by Dow Chemical Company [38, 39]. In the past decade, the OBCs [7-9, 37] and relevant blends [40-42] have been the focus of considerable research stemming from the significant technological applications that are crucially depend on their distinctive mesophase separation behavior and the crystallization properties. In this work, six low octene content olefin block 4
ACCEPTED MANUSCRIPT copolymers OBCs are selected. Typical information on molecular structure is given in Table 1. The octene content (C8) and block structure of OBCs were determined by 13C NMR, the molecular weight (Mw) and polydispersity index (PDI=Mw/Mn) were
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measured by high temperature gel permeation chromatography (GPC). More details can be found in our previous publications [8, 37, 43]. These six OBCs are labelled as Hx/Mx/Lx, where H/M/L denotes the relatively high/medium/low content of hard
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block, and the subscripts x are numbers that increase with the molecular weight (MW).
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The difference between the octene content in hard block and soft block (∆C8) is similar in all six samples, which implies similar interaction between hard block and soft block in these samples. Then, the phase separation behavior is mainly determined by the molecular weight and the hard block content [8].
Sample code L01
MW
PDI
(kg/mol)
fhard
total C8
TMST o
Mesophase
(wt%)
(mol%)
( C)
separation
79.8
1.97
11.0
13.7
163.5
Very weak
126.5
2.06
11.0
14.0
>205
Strong
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L02
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Table 1. Molecular Parameters of Olefin Multiblock Copolymers
61.7
1.83
25.0
11.7
153.8
Very weak
M02
82.6
2.15
25.0
12.0
160.4
Medium
M03
156.6
1.97
25.0
11.5
>215
Very strong
77.6
1.92
35.0
9.6
154.0
Medium
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M01
H01
2.2. Measurements
All rheological measurements were performed on OBCs melts using a
strain-controlled rotational rheometer (ARES-G2, TA Instruments). Stainless steel cone-plate geometries with diameter of 25 mm were used. The disk-like samples with thickness about 1 mm were made by compression molding at 180°C under a pressure 5
ACCEPTED MANUSCRIPT of 10 MPa. In order to evaluate thermal stability of OBCs, dynamic time sweeps were performed at 1 rad/s. The storage moduli of OBCs stay constant and deviate from the initial value no more than 5% up to the time for the subsequent rheological
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measurements. For M01, it can keep thermal stability more than 10 hours at 135°C and 2 hours at 180°C. For other OBCs, the duration time of thermal stability is longer than M01. In order to evaluate linear strain range of OBCs, dynamic strain sweeps
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were performed at 1 rad/s. It is found that the linear strain range depends on the
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molecular weight of OBCs. For M03, the storage moduli stays constant when the strain is up to 0.3. For other OBCs, the linear strain range is even larger. Step shear strain experiments were performed on OBCs melts within a temperature range of 135∼180 °C. Samples were allowed to equilibrate for at least 5
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min before collecting data. The time required to impose nonlinear shear strains varied from 0.05 s for the lower molecular weight OBCs to 0.8 s for the highest molecular
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weight polymer. In each case, the terminal relaxation time of materials exceeded strain imposing times by at least more than one order of magnitude, indicating that it
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is appropriate to consider the imposed deformation a step strain. Rest time, which is 8~10 times of the terminal relaxation time, were provided for stress relaxation between successive step shear strain measurements to minimize history effects on stress relaxation measurements. The samples were subjected to different step strains ranging from 10 to 800% to investigate the strain dependence of the stress relaxation behaviors. All step strain tests were repeated for at least three times to ensure the repeatability of the data. 6
ACCEPTED MANUSCRIPT 3. Results and Discussion 3.1. Time-Temperature Superposition The step shear strain experiment is frequently used to investigate the linear and
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the nonlinear responses of polymers [22-24, 29, 44]. When the step strain ( γ ) is small enough, the influences of temperature and molecular weight on the linear relaxation
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modulus G ( t ) help to understand the phase separation behavior under quiescent condition. Time-temperature superposition (TTS) and time-molecular weight
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superposition (TMS) [37] were applied on different OBC samples, and the superposed relaxation moduli can be seen in Fig. 1. It is seen that a clear entanglement plateau is absent although the molecular weights of OBCs are well above the entanglement molecular weight (Me). This is ascribed to the short terminal relaxation time.
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According to the tube model, the reptation time can be estimated as τ d = 3Z 3τ e , with Z the number of entanglement, and τ e the equilibrium time of segment. We may
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estimate the reptation time using the constants of polyethylene, although the copolymerization of small amount of octene (~10-14 mol%) may slightly alter the
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equilibrium time and the entanglement molecular weight. For PE at 430K, τ e is about 10-8s [45]. For OBCs with molecular weight ranging from about 60K to 150K, the reptation time is about 0.005s to 0.07s. Because the entanglement plateau appears at times shorter than the reptation time and such time regime is out of the experimental time window of stress relaxation, the entanglement plateau is unable to seen in the present experiments.
7
ACCEPTED MANUSCRIPT Actually, information from Fig. 1 are exactly the same as those from the plot using dynamic moduli [8, 37]. The success of TTS implies that mesophase transition is extremely weak in OBCs with low molecular weight (M01, L01). Faint failure of
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TTS can be seen in OBCs with higher molecular weight (M02). As molecular weight increases further, evident failure of TTS indicates possible inhomogeneity in OBCs, such as L02, M03. What’s more, failure of TTS is also found in OBCs with higher
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hard block (H01). TMS can eliminate the effect of MW on the terminal relaxation,
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and helps to compare samples with different MWs. It has been reported that the zero shear viscosity and the terminal relaxation time of OBCs in homogeneous state depend on the weight average molecular mass through a power law with the scaling exponent about 3.4 [32]. The molecular weight shift factor aM is defined as
)
n
from the power law dependence of terminal relaxation time on
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a M = ( M w M w , ref
the weight average molecular weight. n is the power law exponent, which is 3.4 for OBCs [8]. The failure superposition of G ( t ) in high MW samples at long time
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further indicates the presence of slow relaxation process due to the heterogeneous
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structures. Therefore, the relaxation process of heterogeneous OBCs can be reasonably decomposed into the chain relaxation and the domain relaxation, while only chain relaxation exists in homogeneous OBCs.
8
ACCEPTED MANUSCRIPT 105
strain=0.1
103 102 1350C1500C1650C1800C
101
M01 M02 M03 L01 L02 H01
100 10-1 -1 10
100
101
102
103
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aMaTt (s)
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G(t) (Pa)
104
Figure 1. Relaxation moduli G(t) versus shifted time for different OBCs. aT is the temperature
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shift factor with the reference temperature Tref = 135 oC. aM is the molecular weight shift factor with the molecular weight of M03 as the reference molecular weight, Mw, ref = Mw, M03. The strain (=0.1) lies in the linear viscoelastic regime of all samples.
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As step strain increases, an experimental observation in the rheological behavior of homogeneous polymer melts is that the nonlinear relaxation modulus G ( t , γ ) satisfies
the time-strain
separability (TSS)
at
sufficient
long
time,
i.e.,
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G ( t , γ ) = G ( t ) hchain (γ ) when t > λk , where hchain (γ ) is the damping function of
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chain relaxation [24]. For heterogeneous block copolymer melts, the relaxation of the chain and the domain are both strain dependent. Whether the strain dependence of chain relaxation and domain relaxation are the same or not is important for the applicability of TSS. As shown in Fig. 2, the ratio G ( t , γ ) hchain ( γ ) becomes more or less irrespective of the applied strain in homogeneous OBC (M01), indicating the success of TSS. However, the TSS becomes invalid in heterogeneous OBCs. For example, in L02 and H01, the superposition of G ( t , γ ) hchain ( γ ) under different 9
ACCEPTED MANUSCRIPT strains can only be seen in short time regime, which corresponds to the relaxation of chains. Failure of superposition of G ( t , γ ) hchain ( γ ) are clear at longer time. It indicates that the strain dependencies of the chain relaxation and the domain
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relaxation in nonlinear modulus are different, i.e., the damping function of chain relaxation hchain ( γ ) and domain relaxation hdomain ( γ ) are different. The fact that TSS fails via either increasing the hard block fraction (from L01 to M02 and H01) or
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increasing the molecular weight (from M01 to M03, from L01 to L02) is reminiscent
OBCs. 7
106 105 4
10
103 102 1
0.1 0.5 1 2 3 4 5 8
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G(t, γ)/hchain(γ) (Pa)
10
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of the similar effects in mesophase separation of OBCs on the failures of TTS in
10
100
10-1 10-2
10-1
H01
M01
100
101
102
103
Time (s)
EP
10-3 10-2
L02
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Figure 2. The reduced relaxation moduli of H01 (at 135 °C) and L02 (at 180 °C) after applying TSS. For comparison, the reduced relaxation moduli of M01 (at 135 °C) is also given. Moduli of L02 have been shifted by two orders of magnitude vertically to avoid overlapping.
3.2. Decomposition of the relaxation modulus In order to further study the relaxation behavior of domains, the nonlinear relaxation modulus G ( t , γ ) of heterogeneous OBCs was separated into two parts,
G ( t , γ ) = Gchain ( t , γ ) + Gdomain ( t , γ ) , where the subscripts “chain” and “domain” stand 10
ACCEPTED MANUSCRIPT for the fast relaxation of the chain and the slow relaxation of the domain. For OBCs with phase separation temperature lies in the temperature range of experiments (such as H01 in Fig. 3), the nonlinear modulus Gchain ( t , γ ) of chain relaxation in the
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heterogeneous regime can be obtained from the nonlinear relaxation modulus in the homogeneous state (above TMST) using TTS. The nonlinear modulus Gdomain ( t , γ ) of domain relaxation can be obtained by subtracting Gchain ( t , γ ) from the measured
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modulus G ( t , γ ) . For OBCs with phase separation temperature out of the
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experimental temperature range (such as L02 and M03), the nonlinear responses of chain relaxation cannot be obtained directly from their homogeneous state. Since the chain relaxation of the low molecular weight sample with the same hard block content (such as L01 and M01) is believed to own the same character of high molecular
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weight sample regardless of the effect of MW, Gchain ( t , γ ) of L02 (or M03) can be obtained from Gchain ( t , γ ) of L01 (or M01) using TMS. Details of decomposition of highly phase separated samples (L02 and M03) can be found in Fig. S1-S4 of
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supporting information.
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It is necessary to point out that such treatment might not be applicable in monodispersed di- or tri-block copolymers, whose domain size (~15-25 nm) is much smaller than that of OBCs (~100 nm) [7]. The former is comparable to the radius of gyration (Rg) of polymer, and the relaxation behavior is definitely conformation dependent. Since the junctions between different blocks are more or less localized at the interface and the blocks would behave as tethered chains (for the end block) and/or loop/bridge chains (for the middle blocks), all having the constraint at the 11
ACCEPTED MANUSCRIPT block ends. In this case, direct using the relaxation of bulk chains with two free ends would be largely inaccurate, which is the reason to adopt the arm relaxation process in literatures [14]. In OBCs, the domain size is much larger than Rg of polymer. It means
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that the domains contain not only those chains tethered on the interface, but also large amount non-tethered chains. This is similar to the copolymer compatibilized polymer blend, where relaxations of polymer chains inside domains are similar to those in the
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bulk. Therefore, the change of chain conformation is ignored due to their minor
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contribution, and take the relaxation moduli in homogeneous state to approximate the relaxation moduli from components in heterogeneous state.
105
Gtotal(t,γ)
104
101 100 10-1 10-2 10-3 -2 10
0.1 0.5 1 2 3 4 5 8
10-1
Gdomain(t,γ)
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102
EP
G (t,γ) (Pa)
103
Gchain(t,γ)
100
101
102 10-2
100
101
Time (s)
102 10-1
100
101
102
103
Time (s)
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Time (s)
10-1
Figure 3. Nonlinear relaxation moduli and their decompositions of H01 at 135°C. Gchain ( t , γ ) is obtained from the nonlinear relaxation moduli in homogeneous state (180oC) using TTS.
3.3. Damping function of OBCs It is apparent that the domain relaxation takes much longer time than the chain relaxation. Moreover, a plateau is visible in Gdomain ( t , γ ) (Fig. 3), with the decreasing plateau value and increasing relaxation time as the strain increases. Such behavior is 12
ACCEPTED MANUSCRIPT similar to that in polymer blends with droplet-matrix morphology [35, 36]. Actually, the mesophase separated domain structure of multiblock olefin copolymers (OBCs) had been discussed in details in our previous articles [8, 37], where the morphology
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has been confirmed by AFM to be spherical droplets [37]. Therefore, the damping function of domain relaxation cannot be obtained from the same definition as chain relaxation. Instead, we suggest to use the following definition to obtain hdomain ( γ ) ,
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i.e., Gdomain ( t , γ ) = Gdomain ( tτ domain ( γ ) ) hdomain ( γ ) . The damping function hchain ( γ ) and
hdomain ( γ ) of OBCs at 135°C can be seen in Fig. 4. By comparing the damping
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functions hchain ( γ ) and hdomain ( γ ) , we find that the domain relaxation has stronger strain dependence than the chain relaxation. Moreover, both damping functions are very similar for different homogeneous OBCs or different heterogeneous OBCs,
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implying that the molecular weight, hard block content, and the extent of phase separation of OBCs have very weak influences on the damping functions. By comparing with the model predictions on damping functions, we found that the chain
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damping function of OBCs shows weaker strain dependence than the Doi-Edwards
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model prediction [24, 46], and much close to the PSM model [47]. It might be related to the multiblock chain architecture and polydispersity in molecular weight distribution. For domain relaxation, the Yu-Bousmina model [48] is used to calculate the domain damping function. It is found that hdomain ( γ ) of OBCs is close to the prediction when the viscosity ratio is close to 4. One possible reason is that the block distributions might be different among chains with different molecular weight, i.e., the hard block content might be higher in longer chain. The other possible reason is the 13
ACCEPTED MANUSCRIPT long chain has higher tendency to phase separate as compared to the short chains. Both reasons may result in higher viscosity of hard block enriched domains.
10-1
hdomain(γ)
L01 M01 M02 DE model PSM model FBN model
H01 L02 M03 YB model (p=4) YB model (p=3)
10-1
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hchain(γ)
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hchain(γ), hdomain(γ)
100
100
101
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Strain
Figure 4. The damping function hchain ( γ ) and hdomain ( γ ) of OBCs at 135°C. For chain relaxation, the lines are the prediction of the Doi-Edwards (DE) model without the independent alignment assumption [24, 46] (solid, h(γ ) = 1 (1 + αγ ) with 2
h(γ ) = 6 (4 + γ 2 + 4 + γ 2 ) )
and
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(dash,
the
PSM
α = 4 15 ), the FBN model [49] model
[47]
(short
dash,
h(γ ) = 1 (1 + αγ 2 ) with α = 5 39 ), respectively. For domain relaxation, the lines are the
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prediction of the Yu-Bousmina (YB) model [48] with viscosity ratio p=3 (dash dot dot) and p=4
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(dash dot), respectively.
3.4. Strain accelerated mesophase separation Having the knowledge of domain relaxation in heterogeneous OBCs, it is
interesting to see if strain could affect the phase separation of multiblock copolymer. Therefore, repeated step strains were applied on OBCs in heterogeneous state. The nonlinear relaxation behavior of H01 sample subjected to repeated step strains is illustrated in Fig. 5. For each experiment, the sample is annealed at specified 14
ACCEPTED MANUSCRIPT temperature for 300s, then step strain was applied and the sample was allowed to relax for 2400s. After that, same step strain was applied again and the sample relaxed for 2400s. Such process was repeated for 5 times. When the step strain is small
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enough ( γ = 0.1 ), it was found that the relaxation modulus of H01 does not change in the repeated step strain. The same situation was also found when the strain is large ( γ = 3 ) but the temperature lies in the homogeneous regime (165 oC and 180 oC). It
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implies that the effect of annealing on the domain relaxation process of H01 cannot be
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revealed under quiescent condition (actually in the linear viscoelastic region), and also the domain relaxation process is not affected by the annealing time in homogeneous regime even under large step strains. It is also seen that the relaxation process at 150oC, which is slightly lower than phase transition temperature TMST (about 154oC
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[8]), is also not influenced by the step strains. It may be explained by the weak thermodynamic driving force (small quench depth ∆T = TMST − T = 4o C ) for phase separation at 150oC. At higher quench depth ( T = 135o C and ∆T = 19 o C ) and
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higher step strains ( γ > 0.1 ), it can be seen that the relaxation moduli exhibit similar
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behavior in the first step of chain relaxation. However, in the second step of domain relaxation, the plateau becomes more and more obvious and the relaxation time gets longer with the increasing repeated times of step strains. Moreover, larger repeated step strain causes stronger effect on the increase of the domain relaxation time. Actually, when the quench depth increases further ( ∆T > 25o C for L02 at T = 180o C in Fig. 5b), the effect of nonlinear step strains can hardly be observed
again due to the fast phase separation resulting from the strong thermodynamic 15
ACCEPTED MANUSCRIPT driving force. It is necessary to mention that nonlinear stress relaxation was adopted here to detect the structural change. The method is different from those in linear viscoelastic
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regime, but may share some common features. For example, both Winter’s criterion (for detection the structural change far above Tg) [50, 51] and Struik’s protocol (for physical aging below Tg) [52, 53] require the measurement time much smaller than
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the annealing (or aging) time so that the annealing (or aging) process itself will not
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influence the mechanical responses. As show in Fig. 5, the domain relaxation time increases from about 40s to about 300s under strain 5. During these periods, the change of relaxation time due to coarsening is expected to be smaller than 3% according to the dependence of domain relaxation time on annealing time.
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The diversity in the relaxation behaviors of H01 after repeated step strains at 135°C should be mainly ascribed to the increased contribution of interface due to
EP
phase separation. For monodispersed di- or tri-block copolymers, the equilibrium structure can be readily accessed, but it is not the case for OBCs. In fact, as shown in
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Fig. 5, the domain relaxation time increases with the annealing time, and such process can be accelerated by shear flow. Such phenomena is in contrast to the monodispersed di- or tri-block, but somewhat similar to polymer blends. Therefore, these findings indicate that there is probably no equilibrium structure in OBCs. Since the emulsion models [48, 54, 55] have been adopted to describe the domain contribution of OBCs in the nonlinear oscillatory shear [37] and in the damping function of the nonlinear stress relaxation above, the concept of emulsion rheology will be used here to 16
ACCEPTED MANUSCRIPT understand the mesophase separation of multiblock copolymer. According to the emulsion models, the stress (or the plateau modulus of domain relaxation) is determined by the domain size as well as the volume fraction of domains [56]. Higher
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volume fraction or smaller domain size results in higher plateau modulus of domain relaxation. The relaxation time is mainly related to the size of domains, and larger domains will relax slower. Other factor like interfacial tension is regarded as constant,
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and will not be considered here. It has been reported that the plateau modulus of
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domain relaxation decreases and the relaxation time increases with the increase of annealing time in polymer blends [35], which is ascribed to coarsening of domain size during annealing. However, in olefin block copolymer, the relaxation time increases while the plateau modulus of domain relaxation keeps nearly unchanged during the
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repeated step strains. This is due to the accelerated phase separation of H01 under repeated step strains, which results in coarsening of domain as well as the increase of the volume fraction of domains. The opposite effects of domain size and volume
EP
fraction on the plateau modulus cancel out and result in apparent constant plateau
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modulus during repeated step strain. 5
10
104 2
10
β=2
-2
G(t, γ) (Pa)
β=4
γ=0.1
10-1 10
β=6
γ=1
10-3 10-4 -5
γ=3
10
-6
10
104 10
3
10
2
10
1
135oC 150oC 165oC
100
180oC
10-1
10-7 10-8
300 s 2700 s 5100 s 7500 s 9900 s
L02,180oC
105
1
10
100
7
106
3
10
G(t, γ)/10β (Pa)
10
β=0
γ=5
(a) T=135oC
-9
10
10
-1
10
0
1
10
10
Time (s)
2
3
10
10-2 10
(b) γ=3
-3
10
-1
0
10
10
1
10
2
Time (s) 17
ACCEPTED MANUSCRIPT Figure 5. The nonlinear relaxation behavior of H01 after annealing at 135°C for different times subjected to various strains (a) and the nonlinear relaxation behavior of H01 at different temperatures with step strain of 3 (b). For comparison, the nonlinear relaxation behavior of L02 at
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180°C with step strain of 3 is also given. Moduli in (a) and Moduli of L02 in (b) have been shifted vertically to avoid overlapping.
Since the domain relaxation time depends mainly on the domain size, its
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evolution during the repeated step strains can be used to quantify the effect of strain in
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acceleration of the phase separation. The relaxation time can be determined by fitting the domain relaxation modulus Gdomain ( t , γ ) with multiple exponential decay functions. Usually, two or three modes of exponential function are enough, and the longest relaxation time is taken as the characteristic domain relaxation time
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τ domain ( γ ) . Variation of τ domain ( γ ) with annealing time for H01 during repeated step strains at 135°C is presented in Fig. 6a. Moreover, control tests were performed with
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the same thermal history but only one step strain at specified time. The characteristic relaxation time of control tests are shown as hollow symbols in Fig. 6a, which are
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almost constant at small strain and increases more slowly with annealing time at higher strain. A power law dependency is clearly seen between τ domain ( γ ) and the α annealing time ( τ domain (γ ) ~ tanneal ). It is noticed that the power law exponent α is
almost zero either when the strain is small or when the temperature is in the homogeneous regime. We also find that the power law exponents in the repeated step strain tests are higher than those in control tests. It means that annealing process alone can cause further phase separation, and large strain can accelerate such process. The 18
ACCEPTED MANUSCRIPT power law exponent increases with the step strain, and reaches a constant as strain increases (Fig. 6b). We would stress that both the phase separation under quiescent process and the strain accelerated phase separation are not detectable in linear
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viscoelastic regime. Actually, such understanding extends our findings in previous work [8] that the effect of annealing on dynamic moduli is negligible, but the discernible effect of annealing on crystallization indicates the development of phase
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separation during annealing. The accelerated phase separation under large strain may
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also indicate that olefin block copolymers could be a blend of homopolymer and block copolymer, which has been reported by Wang et al. [57].
(a)
1
10
3
Coarsening exponent, α
2
10
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τdomain(γ) (s)
0.5
0.1 1 1 3 3 5 5
4
10
10
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Annealing time (s)
τ domain ( γ )
0.3
0.2
0.1
(b)
0.0 0
1
2
3
4
5
6
strain
(a) and the coarsening exponent (b) for H01
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Figure 6. The domain relaxation time
0.4
after annealing at 135°C for different time subjected to various strains. The hollow symbols in (a) and (b) stand for the domain relaxation after annealing for certain time without repeated step strains.
4. Conclusion In this work, the nonlinear relaxation behavior of olefin multiblock copolymers subjected to step shear strains has been investigated. Due to the mesophase separation, 19
ACCEPTED MANUSCRIPT failure of time-temperature superposition and time-strain separability as the molecular weight or hard block fraction increases is found using the nonlinear relaxation moduli. Compared to homogeneous polymer, a two-step relaxation behavior was identified in
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olefin multiblock copolymers, namely a fast relaxation reflecting the chain relaxation and a slower one for the domain relaxation. It is found that the domain relaxation has stronger stain dependence than the chain relaxation as indicated from the damping
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functions hchain ( γ ) and hdomain ( γ ) . The relaxation process of olefin multiblock
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copolymers is independent of the annealing time under quiescent condition, and also the relaxation process is not affected by the annealing time in homogeneous regime even under large step strains. However, Large strain can accelerate mesophase separation of olefin multiblock copolymer, resulting in increases of the relaxation
domains.
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Acknowledgement
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time due to the coarsening of domain as well as the increase of the volume fraction of
The authors thank the support from the National Natural Science Foundation of
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China (No. 21474063 and No. 51625303) and the National Basic Research Program of China (973 Program 2011CB606005).
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23
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Strain accelerated mesophase separation during nonlinear stress relaxation of olefin multiblock copolymer Zhijun Nie, Wei Yu*
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Advanced Rheology Institute, Department of Polymer Science and Engineering, State Key Laboratory for Metal Matrix Composite Materials, Shanghai Key Laboratory of Electrical
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Insulation and Thermal Ageing, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
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Highlights
1. Failures of time-temperature superposition and time-strain separability were revealed from the nonlinear relaxation moduli due to mesophase separation
copolymers
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2. A two-step relaxation mechanism was identified in olefin multiblock
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3. Mesophase separation of olefin multiblock copolymer could be accelerated
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by shear strain
*
Corresponding author. Email: [email protected]
S0032-3861(17)30319-1
DOI:
10.1016/j.polymer.2017.03.053
Reference:
JPOL 19549
To appear in:
Polymer
Received Date: 29 December 2016 Revised Date:
24 February 2017
Accepted Date: 19 March 2017
Please cite this article as: Nie Z, Yu W, Strain accelerated mesophase separation during nonlinear stress relaxation of olefin multiblock copolymer, Polymer (2017), doi: 10.1016/j.polymer.2017.03.053. 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.
β=2 β=1
104
β=0
102
135oC
Olefin block copolymer γ=0.1 γ=3
150oC
phase separated <154oC
165oC 180oC
100
300 s 2700 s 5100 s 7500 s 9900 s
10-2 -4
10
10-6 10-2
10-1
γ=5 γ=3 (homogeneous, >154oC) 100
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106
101
102
103
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EP
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Time (s)
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G(t, γ)*10β (Pa)
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104
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Strain accelerated mesophase separation during nonlinear stress relaxation of olefin multiblock copolymer Zhijun Nie, Wei Yu*
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Advanced Rheology Institute, Department of Polymer Science and Engineering, State Key Laboratory for Metal Matrix Composite Materials, Shanghai Key Laboratory of Electrical
Insulation and Thermal Ageing, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
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Abstract
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The nonlinear relaxation behavior of olefin multiblock copolymers subjected to step shear strains has been investigated. Compared to homogeneous polymer, a two-step relaxation behavior was identified in olefin multiblock copolymers, with the faster one for the chain relaxation and the slower one for the domain relaxation. It is
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found that the domain relaxation has stronger strain dependence than the chain relaxation. Large repeated step strains can cause longer relaxation process of domains
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as compared to the single step strain test. The prolonged domain relaxation and nearly constant relaxation plateau modulus are ascribed to the coarsening of domain as well
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as the increase of the volume fraction of domains, which indicates the accelerated mesophase separation of olefin multiblock copolymer under large strains.
*
Corresponding author. Email: [email protected] 1
ACCEPTED MANUSCRIPT 1. Introduction It is well known that block copolymers comprising two or more chemically distinct monomer blocks tend to undergo microphase separation due to the
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incompatibility of distinct blocks [1, 2]. The microphase separation is influenced by the block length, the interaction between blocks and the volume fraction of a block according to various experiments [1-4] and mean field theory [5, 6]. Recent studies by
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rheology have further revealed that the number of blocks and the polydispersity in
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molecular weight also affect the phase separation behavior [7, 8]. As compared to the monodispersed diblock copolymer, much shorter block length can induce phase separation in polydispersed multiblock copolymers [8] and the domain size (~100 nm) is much larger than that diblock copolymers (~15-25 nm) [7], which is known as the
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mesophase separation [9-11]. Although there are lots of work focused on the micro(meso-) phase separation behavior of block copolymers, the effect of flow remains far
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unrevealed [12-14]. In contrast, it has been found that shear flow is able to induce mixing or de-mixing of partially miscible polymer blends [15-19]. Possible reasons
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for lacking of such knowledge in block copolymers are the fast kinetics and much smaller domain sizes in the phase separation of block copolymers, which make the real time investigation difficult. Among all the techniques to characterize the phase behavior of block copolymer, rheology has almost no requirements on the materials properties like refractive index and electron density, and has the advantage of online measurement especially under flow field. Moreover, it is very sensitive to the concentration fluctuation [20, 21], 2
ACCEPTED MANUSCRIPT which make it a feasible method to study the phase separation of polymer blends and block copolymers. The linear viscoelastic properties of polymers, as normally measured by small amplitude oscillatory shear, is useful in analyzing the relaxation
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processes of different microstructures. However, it is only meaningful when the total deformation is quite small or very slow, which limits its application in detection of the phase transition under quiescent condition. For larger or more rapid deformations, the
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response to an imposed deformation not only depends on the magnitude of the
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deformation, but also depends on the rate and the kinematics of the deformation. In other words, the response to an imposed deformation is no longer a material property but also depends on the history of deformation [22]. Nonlinear rheological properties may not only represent the nonlinear mechanical responses of microstructures, but
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also involve the change of structures.
The step shear strain experiment is frequently used to investigate the nonlinear
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response of polymer [23]. An experimental phenomenon is that the stress relaxation following a step strain satisfies time-strain separability (TSS) at sufficient long time.
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In such case, the nonlinear relaxation moduli G ( t , γ ) can be expressed as G ( t , γ ) = G ( t ) h (γ ) , where G(t ) is the linear relaxation moduli and h(γ ) is the
damping function [24]. Subtle variations in structure or architecture might lead to obvious distinction for the damping function. Numerous studies have been performed on star polymers [25], H-polymers [26], pom-poms [27], comb polymers [22, 28, 29] and other architectures [30-32]. The damping behavior of star polymers, H-polymers, comb polymers exhibited less strain softening than the universal Doi-Edwards 3
ACCEPTED MANUSCRIPT damping function [22, 26, 28, 29, 33, 34] , which is ascribed to the hierarchical relaxation mechanism [34]. Moreover, the hierarchical relaxation mechanism involving the chain relaxation and the domain relaxation is also found in polymer
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blend [35, 36]. For block copolymers, in addition to the segmental relaxation and chain relaxation in homogeneous state, the relaxation in heterogeneous state also involves
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that of the domain structures. We have found recently that the mechanical responses
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of domain relaxation can be greatly enhanced in large amplitude oscillatory shear [37]. It indicates that nonlinear rheological behaviors can be good candidates to study the flow effect on the phase separation of block copolymers. In this work, we will focus our attention on the nonlinear relaxation behavior after step shear strains and try to
copolymers.
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uncover the effect of shear on the mesophase separation of polydispersed multiblock
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2.1. Materials
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2. Experimental Section
The Olefin Multiblock Copolymers (OBCs) synthesized via the chain-shuttling
technology were provided as pellets by Dow Chemical Company [38, 39]. In the past decade, the OBCs [7-9, 37] and relevant blends [40-42] have been the focus of considerable research stemming from the significant technological applications that are crucially depend on their distinctive mesophase separation behavior and the crystallization properties. In this work, six low octene content olefin block 4
ACCEPTED MANUSCRIPT copolymers OBCs are selected. Typical information on molecular structure is given in Table 1. The octene content (C8) and block structure of OBCs were determined by 13C NMR, the molecular weight (Mw) and polydispersity index (PDI=Mw/Mn) were
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measured by high temperature gel permeation chromatography (GPC). More details can be found in our previous publications [8, 37, 43]. These six OBCs are labelled as Hx/Mx/Lx, where H/M/L denotes the relatively high/medium/low content of hard
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block, and the subscripts x are numbers that increase with the molecular weight (MW).
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The difference between the octene content in hard block and soft block (∆C8) is similar in all six samples, which implies similar interaction between hard block and soft block in these samples. Then, the phase separation behavior is mainly determined by the molecular weight and the hard block content [8].
Sample code L01
MW
PDI
(kg/mol)
fhard
total C8
TMST o
Mesophase
(wt%)
(mol%)
( C)
separation
79.8
1.97
11.0
13.7
163.5
Very weak
126.5
2.06
11.0
14.0
>205
Strong
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L02
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Table 1. Molecular Parameters of Olefin Multiblock Copolymers
61.7
1.83
25.0
11.7
153.8
Very weak
M02
82.6
2.15
25.0
12.0
160.4
Medium
M03
156.6
1.97
25.0
11.5
>215
Very strong
77.6
1.92
35.0
9.6
154.0
Medium
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M01
H01
2.2. Measurements
All rheological measurements were performed on OBCs melts using a
strain-controlled rotational rheometer (ARES-G2, TA Instruments). Stainless steel cone-plate geometries with diameter of 25 mm were used. The disk-like samples with thickness about 1 mm were made by compression molding at 180°C under a pressure 5
ACCEPTED MANUSCRIPT of 10 MPa. In order to evaluate thermal stability of OBCs, dynamic time sweeps were performed at 1 rad/s. The storage moduli of OBCs stay constant and deviate from the initial value no more than 5% up to the time for the subsequent rheological
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measurements. For M01, it can keep thermal stability more than 10 hours at 135°C and 2 hours at 180°C. For other OBCs, the duration time of thermal stability is longer than M01. In order to evaluate linear strain range of OBCs, dynamic strain sweeps
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were performed at 1 rad/s. It is found that the linear strain range depends on the
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molecular weight of OBCs. For M03, the storage moduli stays constant when the strain is up to 0.3. For other OBCs, the linear strain range is even larger. Step shear strain experiments were performed on OBCs melts within a temperature range of 135∼180 °C. Samples were allowed to equilibrate for at least 5
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min before collecting data. The time required to impose nonlinear shear strains varied from 0.05 s for the lower molecular weight OBCs to 0.8 s for the highest molecular
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weight polymer. In each case, the terminal relaxation time of materials exceeded strain imposing times by at least more than one order of magnitude, indicating that it
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is appropriate to consider the imposed deformation a step strain. Rest time, which is 8~10 times of the terminal relaxation time, were provided for stress relaxation between successive step shear strain measurements to minimize history effects on stress relaxation measurements. The samples were subjected to different step strains ranging from 10 to 800% to investigate the strain dependence of the stress relaxation behaviors. All step strain tests were repeated for at least three times to ensure the repeatability of the data. 6
ACCEPTED MANUSCRIPT 3. Results and Discussion 3.1. Time-Temperature Superposition The step shear strain experiment is frequently used to investigate the linear and
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the nonlinear responses of polymers [22-24, 29, 44]. When the step strain ( γ ) is small enough, the influences of temperature and molecular weight on the linear relaxation
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modulus G ( t ) help to understand the phase separation behavior under quiescent condition. Time-temperature superposition (TTS) and time-molecular weight
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superposition (TMS) [37] were applied on different OBC samples, and the superposed relaxation moduli can be seen in Fig. 1. It is seen that a clear entanglement plateau is absent although the molecular weights of OBCs are well above the entanglement molecular weight (Me). This is ascribed to the short terminal relaxation time.
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According to the tube model, the reptation time can be estimated as τ d = 3Z 3τ e , with Z the number of entanglement, and τ e the equilibrium time of segment. We may
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estimate the reptation time using the constants of polyethylene, although the copolymerization of small amount of octene (~10-14 mol%) may slightly alter the
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equilibrium time and the entanglement molecular weight. For PE at 430K, τ e is about 10-8s [45]. For OBCs with molecular weight ranging from about 60K to 150K, the reptation time is about 0.005s to 0.07s. Because the entanglement plateau appears at times shorter than the reptation time and such time regime is out of the experimental time window of stress relaxation, the entanglement plateau is unable to seen in the present experiments.
7
ACCEPTED MANUSCRIPT Actually, information from Fig. 1 are exactly the same as those from the plot using dynamic moduli [8, 37]. The success of TTS implies that mesophase transition is extremely weak in OBCs with low molecular weight (M01, L01). Faint failure of
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TTS can be seen in OBCs with higher molecular weight (M02). As molecular weight increases further, evident failure of TTS indicates possible inhomogeneity in OBCs, such as L02, M03. What’s more, failure of TTS is also found in OBCs with higher
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hard block (H01). TMS can eliminate the effect of MW on the terminal relaxation,
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and helps to compare samples with different MWs. It has been reported that the zero shear viscosity and the terminal relaxation time of OBCs in homogeneous state depend on the weight average molecular mass through a power law with the scaling exponent about 3.4 [32]. The molecular weight shift factor aM is defined as
)
n
from the power law dependence of terminal relaxation time on
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a M = ( M w M w , ref
the weight average molecular weight. n is the power law exponent, which is 3.4 for OBCs [8]. The failure superposition of G ( t ) in high MW samples at long time
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further indicates the presence of slow relaxation process due to the heterogeneous
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structures. Therefore, the relaxation process of heterogeneous OBCs can be reasonably decomposed into the chain relaxation and the domain relaxation, while only chain relaxation exists in homogeneous OBCs.
8
ACCEPTED MANUSCRIPT 105
strain=0.1
103 102 1350C1500C1650C1800C
101
M01 M02 M03 L01 L02 H01
100 10-1 -1 10
100
101
102
103
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aMaTt (s)
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G(t) (Pa)
104
Figure 1. Relaxation moduli G(t) versus shifted time for different OBCs. aT is the temperature
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shift factor with the reference temperature Tref = 135 oC. aM is the molecular weight shift factor with the molecular weight of M03 as the reference molecular weight, Mw, ref = Mw, M03. The strain (=0.1) lies in the linear viscoelastic regime of all samples.
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As step strain increases, an experimental observation in the rheological behavior of homogeneous polymer melts is that the nonlinear relaxation modulus G ( t , γ ) satisfies
the time-strain
separability (TSS)
at
sufficient
long
time,
i.e.,
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G ( t , γ ) = G ( t ) hchain (γ ) when t > λk , where hchain (γ ) is the damping function of
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chain relaxation [24]. For heterogeneous block copolymer melts, the relaxation of the chain and the domain are both strain dependent. Whether the strain dependence of chain relaxation and domain relaxation are the same or not is important for the applicability of TSS. As shown in Fig. 2, the ratio G ( t , γ ) hchain ( γ ) becomes more or less irrespective of the applied strain in homogeneous OBC (M01), indicating the success of TSS. However, the TSS becomes invalid in heterogeneous OBCs. For example, in L02 and H01, the superposition of G ( t , γ ) hchain ( γ ) under different 9
ACCEPTED MANUSCRIPT strains can only be seen in short time regime, which corresponds to the relaxation of chains. Failure of superposition of G ( t , γ ) hchain ( γ ) are clear at longer time. It indicates that the strain dependencies of the chain relaxation and the domain
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relaxation in nonlinear modulus are different, i.e., the damping function of chain relaxation hchain ( γ ) and domain relaxation hdomain ( γ ) are different. The fact that TSS fails via either increasing the hard block fraction (from L01 to M02 and H01) or
SC
increasing the molecular weight (from M01 to M03, from L01 to L02) is reminiscent
OBCs. 7
106 105 4
10
103 102 1
0.1 0.5 1 2 3 4 5 8
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G(t, γ)/hchain(γ) (Pa)
10
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of the similar effects in mesophase separation of OBCs on the failures of TTS in
10
100
10-1 10-2
10-1
H01
M01
100
101
102
103
Time (s)
EP
10-3 10-2
L02
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Figure 2. The reduced relaxation moduli of H01 (at 135 °C) and L02 (at 180 °C) after applying TSS. For comparison, the reduced relaxation moduli of M01 (at 135 °C) is also given. Moduli of L02 have been shifted by two orders of magnitude vertically to avoid overlapping.
3.2. Decomposition of the relaxation modulus In order to further study the relaxation behavior of domains, the nonlinear relaxation modulus G ( t , γ ) of heterogeneous OBCs was separated into two parts,
G ( t , γ ) = Gchain ( t , γ ) + Gdomain ( t , γ ) , where the subscripts “chain” and “domain” stand 10
ACCEPTED MANUSCRIPT for the fast relaxation of the chain and the slow relaxation of the domain. For OBCs with phase separation temperature lies in the temperature range of experiments (such as H01 in Fig. 3), the nonlinear modulus Gchain ( t , γ ) of chain relaxation in the
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heterogeneous regime can be obtained from the nonlinear relaxation modulus in the homogeneous state (above TMST) using TTS. The nonlinear modulus Gdomain ( t , γ ) of domain relaxation can be obtained by subtracting Gchain ( t , γ ) from the measured
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modulus G ( t , γ ) . For OBCs with phase separation temperature out of the
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experimental temperature range (such as L02 and M03), the nonlinear responses of chain relaxation cannot be obtained directly from their homogeneous state. Since the chain relaxation of the low molecular weight sample with the same hard block content (such as L01 and M01) is believed to own the same character of high molecular
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weight sample regardless of the effect of MW, Gchain ( t , γ ) of L02 (or M03) can be obtained from Gchain ( t , γ ) of L01 (or M01) using TMS. Details of decomposition of highly phase separated samples (L02 and M03) can be found in Fig. S1-S4 of
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supporting information.
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It is necessary to point out that such treatment might not be applicable in monodispersed di- or tri-block copolymers, whose domain size (~15-25 nm) is much smaller than that of OBCs (~100 nm) [7]. The former is comparable to the radius of gyration (Rg) of polymer, and the relaxation behavior is definitely conformation dependent. Since the junctions between different blocks are more or less localized at the interface and the blocks would behave as tethered chains (for the end block) and/or loop/bridge chains (for the middle blocks), all having the constraint at the 11
ACCEPTED MANUSCRIPT block ends. In this case, direct using the relaxation of bulk chains with two free ends would be largely inaccurate, which is the reason to adopt the arm relaxation process in literatures [14]. In OBCs, the domain size is much larger than Rg of polymer. It means
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that the domains contain not only those chains tethered on the interface, but also large amount non-tethered chains. This is similar to the copolymer compatibilized polymer blend, where relaxations of polymer chains inside domains are similar to those in the
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bulk. Therefore, the change of chain conformation is ignored due to their minor
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contribution, and take the relaxation moduli in homogeneous state to approximate the relaxation moduli from components in heterogeneous state.
105
Gtotal(t,γ)
104
101 100 10-1 10-2 10-3 -2 10
0.1 0.5 1 2 3 4 5 8
10-1
Gdomain(t,γ)
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102
EP
G (t,γ) (Pa)
103
Gchain(t,γ)
100
101
102 10-2
100
101
Time (s)
102 10-1
100
101
102
103
Time (s)
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Time (s)
10-1
Figure 3. Nonlinear relaxation moduli and their decompositions of H01 at 135°C. Gchain ( t , γ ) is obtained from the nonlinear relaxation moduli in homogeneous state (180oC) using TTS.
3.3. Damping function of OBCs It is apparent that the domain relaxation takes much longer time than the chain relaxation. Moreover, a plateau is visible in Gdomain ( t , γ ) (Fig. 3), with the decreasing plateau value and increasing relaxation time as the strain increases. Such behavior is 12
ACCEPTED MANUSCRIPT similar to that in polymer blends with droplet-matrix morphology [35, 36]. Actually, the mesophase separated domain structure of multiblock olefin copolymers (OBCs) had been discussed in details in our previous articles [8, 37], where the morphology
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has been confirmed by AFM to be spherical droplets [37]. Therefore, the damping function of domain relaxation cannot be obtained from the same definition as chain relaxation. Instead, we suggest to use the following definition to obtain hdomain ( γ ) ,
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i.e., Gdomain ( t , γ ) = Gdomain ( tτ domain ( γ ) ) hdomain ( γ ) . The damping function hchain ( γ ) and
hdomain ( γ ) of OBCs at 135°C can be seen in Fig. 4. By comparing the damping
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functions hchain ( γ ) and hdomain ( γ ) , we find that the domain relaxation has stronger strain dependence than the chain relaxation. Moreover, both damping functions are very similar for different homogeneous OBCs or different heterogeneous OBCs,
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implying that the molecular weight, hard block content, and the extent of phase separation of OBCs have very weak influences on the damping functions. By comparing with the model predictions on damping functions, we found that the chain
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damping function of OBCs shows weaker strain dependence than the Doi-Edwards
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model prediction [24, 46], and much close to the PSM model [47]. It might be related to the multiblock chain architecture and polydispersity in molecular weight distribution. For domain relaxation, the Yu-Bousmina model [48] is used to calculate the domain damping function. It is found that hdomain ( γ ) of OBCs is close to the prediction when the viscosity ratio is close to 4. One possible reason is that the block distributions might be different among chains with different molecular weight, i.e., the hard block content might be higher in longer chain. The other possible reason is the 13
ACCEPTED MANUSCRIPT long chain has higher tendency to phase separate as compared to the short chains. Both reasons may result in higher viscosity of hard block enriched domains.
10-1
hdomain(γ)
L01 M01 M02 DE model PSM model FBN model
H01 L02 M03 YB model (p=4) YB model (p=3)
10-1
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hchain(γ)
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hchain(γ), hdomain(γ)
100
100
101
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Strain
Figure 4. The damping function hchain ( γ ) and hdomain ( γ ) of OBCs at 135°C. For chain relaxation, the lines are the prediction of the Doi-Edwards (DE) model without the independent alignment assumption [24, 46] (solid, h(γ ) = 1 (1 + αγ ) with 2
h(γ ) = 6 (4 + γ 2 + 4 + γ 2 ) )
and
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(dash,
the
PSM
α = 4 15 ), the FBN model [49] model
[47]
(short
dash,
h(γ ) = 1 (1 + αγ 2 ) with α = 5 39 ), respectively. For domain relaxation, the lines are the
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prediction of the Yu-Bousmina (YB) model [48] with viscosity ratio p=3 (dash dot dot) and p=4
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(dash dot), respectively.
3.4. Strain accelerated mesophase separation Having the knowledge of domain relaxation in heterogeneous OBCs, it is
interesting to see if strain could affect the phase separation of multiblock copolymer. Therefore, repeated step strains were applied on OBCs in heterogeneous state. The nonlinear relaxation behavior of H01 sample subjected to repeated step strains is illustrated in Fig. 5. For each experiment, the sample is annealed at specified 14
ACCEPTED MANUSCRIPT temperature for 300s, then step strain was applied and the sample was allowed to relax for 2400s. After that, same step strain was applied again and the sample relaxed for 2400s. Such process was repeated for 5 times. When the step strain is small
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enough ( γ = 0.1 ), it was found that the relaxation modulus of H01 does not change in the repeated step strain. The same situation was also found when the strain is large ( γ = 3 ) but the temperature lies in the homogeneous regime (165 oC and 180 oC). It
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implies that the effect of annealing on the domain relaxation process of H01 cannot be
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revealed under quiescent condition (actually in the linear viscoelastic region), and also the domain relaxation process is not affected by the annealing time in homogeneous regime even under large step strains. It is also seen that the relaxation process at 150oC, which is slightly lower than phase transition temperature TMST (about 154oC
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[8]), is also not influenced by the step strains. It may be explained by the weak thermodynamic driving force (small quench depth ∆T = TMST − T = 4o C ) for phase separation at 150oC. At higher quench depth ( T = 135o C and ∆T = 19 o C ) and
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higher step strains ( γ > 0.1 ), it can be seen that the relaxation moduli exhibit similar
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behavior in the first step of chain relaxation. However, in the second step of domain relaxation, the plateau becomes more and more obvious and the relaxation time gets longer with the increasing repeated times of step strains. Moreover, larger repeated step strain causes stronger effect on the increase of the domain relaxation time. Actually, when the quench depth increases further ( ∆T > 25o C for L02 at T = 180o C in Fig. 5b), the effect of nonlinear step strains can hardly be observed
again due to the fast phase separation resulting from the strong thermodynamic 15
ACCEPTED MANUSCRIPT driving force. It is necessary to mention that nonlinear stress relaxation was adopted here to detect the structural change. The method is different from those in linear viscoelastic
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regime, but may share some common features. For example, both Winter’s criterion (for detection the structural change far above Tg) [50, 51] and Struik’s protocol (for physical aging below Tg) [52, 53] require the measurement time much smaller than
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the annealing (or aging) time so that the annealing (or aging) process itself will not
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influence the mechanical responses. As show in Fig. 5, the domain relaxation time increases from about 40s to about 300s under strain 5. During these periods, the change of relaxation time due to coarsening is expected to be smaller than 3% according to the dependence of domain relaxation time on annealing time.
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The diversity in the relaxation behaviors of H01 after repeated step strains at 135°C should be mainly ascribed to the increased contribution of interface due to
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phase separation. For monodispersed di- or tri-block copolymers, the equilibrium structure can be readily accessed, but it is not the case for OBCs. In fact, as shown in
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Fig. 5, the domain relaxation time increases with the annealing time, and such process can be accelerated by shear flow. Such phenomena is in contrast to the monodispersed di- or tri-block, but somewhat similar to polymer blends. Therefore, these findings indicate that there is probably no equilibrium structure in OBCs. Since the emulsion models [48, 54, 55] have been adopted to describe the domain contribution of OBCs in the nonlinear oscillatory shear [37] and in the damping function of the nonlinear stress relaxation above, the concept of emulsion rheology will be used here to 16
ACCEPTED MANUSCRIPT understand the mesophase separation of multiblock copolymer. According to the emulsion models, the stress (or the plateau modulus of domain relaxation) is determined by the domain size as well as the volume fraction of domains [56]. Higher
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volume fraction or smaller domain size results in higher plateau modulus of domain relaxation. The relaxation time is mainly related to the size of domains, and larger domains will relax slower. Other factor like interfacial tension is regarded as constant,
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and will not be considered here. It has been reported that the plateau modulus of
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domain relaxation decreases and the relaxation time increases with the increase of annealing time in polymer blends [35], which is ascribed to coarsening of domain size during annealing. However, in olefin block copolymer, the relaxation time increases while the plateau modulus of domain relaxation keeps nearly unchanged during the
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repeated step strains. This is due to the accelerated phase separation of H01 under repeated step strains, which results in coarsening of domain as well as the increase of the volume fraction of domains. The opposite effects of domain size and volume
EP
fraction on the plateau modulus cancel out and result in apparent constant plateau
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modulus during repeated step strain. 5
10
104 2
10
β=2
-2
G(t, γ) (Pa)
β=4
γ=0.1
10-1 10
β=6
γ=1
10-3 10-4 -5
γ=3
10
-6
10
104 10
3
10
2
10
1
135oC 150oC 165oC
100
180oC
10-1
10-7 10-8
300 s 2700 s 5100 s 7500 s 9900 s
L02,180oC
105
1
10
100
7
106
3
10
G(t, γ)/10β (Pa)
10
β=0
γ=5
(a) T=135oC
-9
10
10
-1
10
0
1
10
10
Time (s)
2
3
10
10-2 10
(b) γ=3
-3
10
-1
0
10
10
1
10
2
Time (s) 17
ACCEPTED MANUSCRIPT Figure 5. The nonlinear relaxation behavior of H01 after annealing at 135°C for different times subjected to various strains (a) and the nonlinear relaxation behavior of H01 at different temperatures with step strain of 3 (b). For comparison, the nonlinear relaxation behavior of L02 at
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180°C with step strain of 3 is also given. Moduli in (a) and Moduli of L02 in (b) have been shifted vertically to avoid overlapping.
Since the domain relaxation time depends mainly on the domain size, its
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evolution during the repeated step strains can be used to quantify the effect of strain in
M AN U
acceleration of the phase separation. The relaxation time can be determined by fitting the domain relaxation modulus Gdomain ( t , γ ) with multiple exponential decay functions. Usually, two or three modes of exponential function are enough, and the longest relaxation time is taken as the characteristic domain relaxation time
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τ domain ( γ ) . Variation of τ domain ( γ ) with annealing time for H01 during repeated step strains at 135°C is presented in Fig. 6a. Moreover, control tests were performed with
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the same thermal history but only one step strain at specified time. The characteristic relaxation time of control tests are shown as hollow symbols in Fig. 6a, which are
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almost constant at small strain and increases more slowly with annealing time at higher strain. A power law dependency is clearly seen between τ domain ( γ ) and the α annealing time ( τ domain (γ ) ~ tanneal ). It is noticed that the power law exponent α is
almost zero either when the strain is small or when the temperature is in the homogeneous regime. We also find that the power law exponents in the repeated step strain tests are higher than those in control tests. It means that annealing process alone can cause further phase separation, and large strain can accelerate such process. The 18
ACCEPTED MANUSCRIPT power law exponent increases with the step strain, and reaches a constant as strain increases (Fig. 6b). We would stress that both the phase separation under quiescent process and the strain accelerated phase separation are not detectable in linear
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viscoelastic regime. Actually, such understanding extends our findings in previous work [8] that the effect of annealing on dynamic moduli is negligible, but the discernible effect of annealing on crystallization indicates the development of phase
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separation during annealing. The accelerated phase separation under large strain may
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also indicate that olefin block copolymers could be a blend of homopolymer and block copolymer, which has been reported by Wang et al. [57].
(a)
1
10
3
Coarsening exponent, α
2
10
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τdomain(γ) (s)
0.5
0.1 1 1 3 3 5 5
4
10
10
EP
Annealing time (s)
τ domain ( γ )
0.3
0.2
0.1
(b)
0.0 0
1
2
3
4
5
6
strain
(a) and the coarsening exponent (b) for H01
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Figure 6. The domain relaxation time
0.4
after annealing at 135°C for different time subjected to various strains. The hollow symbols in (a) and (b) stand for the domain relaxation after annealing for certain time without repeated step strains.
4. Conclusion In this work, the nonlinear relaxation behavior of olefin multiblock copolymers subjected to step shear strains has been investigated. Due to the mesophase separation, 19
ACCEPTED MANUSCRIPT failure of time-temperature superposition and time-strain separability as the molecular weight or hard block fraction increases is found using the nonlinear relaxation moduli. Compared to homogeneous polymer, a two-step relaxation behavior was identified in
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olefin multiblock copolymers, namely a fast relaxation reflecting the chain relaxation and a slower one for the domain relaxation. It is found that the domain relaxation has stronger stain dependence than the chain relaxation as indicated from the damping
SC
functions hchain ( γ ) and hdomain ( γ ) . The relaxation process of olefin multiblock
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copolymers is independent of the annealing time under quiescent condition, and also the relaxation process is not affected by the annealing time in homogeneous regime even under large step strains. However, Large strain can accelerate mesophase separation of olefin multiblock copolymer, resulting in increases of the relaxation
domains.
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Acknowledgement
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time due to the coarsening of domain as well as the increase of the volume fraction of
The authors thank the support from the National Natural Science Foundation of
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China (No. 21474063 and No. 51625303) and the National Basic Research Program of China (973 Program 2011CB606005).
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ACCEPTED MANUSCRIPT
Strain accelerated mesophase separation during nonlinear stress relaxation of olefin multiblock copolymer Zhijun Nie, Wei Yu*
RI PT
Advanced Rheology Institute, Department of Polymer Science and Engineering, State Key Laboratory for Metal Matrix Composite Materials, Shanghai Key Laboratory of Electrical
SC
Insulation and Thermal Ageing, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
M AN U
Highlights
1. Failures of time-temperature superposition and time-strain separability were revealed from the nonlinear relaxation moduli due to mesophase separation
copolymers
TE D
2. A two-step relaxation mechanism was identified in olefin multiblock
EP
3. Mesophase separation of olefin multiblock copolymer could be accelerated
AC C
by shear strain
*
Corresponding author. Email: [email protected]