Theoretical and Experimental Insights into the Phase Transition of

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Cite This: Ind. Eng. Chem. Res. 2017, 56, 13911-13918

Theoretical and Experimental Insights into the Phase Transition of Rubber/Plastic Blends during Dynamic Vulcanization Zhaoyang Wei,†,‡ Shangqing Li,†,‡ Nanying Ning,†,‡ Ming Tian,*,†,‡ Liqun Zhang,†,‡ and Jianguo Mi*,† †

State Key Laboratory of Organic−Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China

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‡

ABSTRACT: While the phase inversion phenomena in thermoplastic vulcanizates have been extensively investigated, the mechanism underlying the evolution from the sea−island to island−sea phase transition is far from being understood. In this work, such transition of the polyolefin elastomer (POE)/ polypropylene (PP) blend was studied simultaneously by density functional theory and experiments. Before vulcanization, the independent POE and PP phases were mixed into a homogeneous blend. After vulcanization, the microstructure of POE was altered, leading to a metastable state of the blend. Thereafter, the blend decomposed into two new phases. Accordingly, the interfacial density changed with the sea−island morphology transition. According to the nucleation thermodynamics, the predicted nanoparticle size of POE nuclei is in general agreement with our experimental measurement. Thus, this work provides a novel thermodynamic explanation regarding the phase inversion in thermoplastic vulcanizates.

1. INTRODUCTION Thermoplastic vulcanizates (TPVs) are well-known as a group of high-performance thermoplastic elastomers.1−3 Involving the in situ cross-linking of high rubber content and the simultaneous mixing with low thermoplastic content, the dynamic vulcanization (DV) is a reactive blending process above the melting temperature under high shear to realize the phase inversion. This class of polymer blends is of interest in applications ranging from structural components for aerospace to electronics packaging.4−6 The microstructures of TPVs, including particle sizes and morphologies of rubber phase, play a remarkable role in their mechanical properties and processabilities.7−12 Therefore, understanding the molecular origins of these properties is becoming increasingly important for experiments aimed at identifying tailored materials for specific applications. Despite the apparent simplicity of the DV process, TPVs are highly complex and involve many chemical and physical processes. In the past few decades, extensive research has focused on the morphology evolution of TPVs. Some researchers have shown that the cross-linking of rubber phase leads to rapid enhancements of viscosity and shear stress; thus, the continuous rubber phase elongates to balance the interfacial forces and breaks up into a multitude of particles dispersed in the plastic matrix, resulting in the phase inversion.13−21 Recently, we further confirmed that the particles are composed of agglomerates of nanoparticles in an ethylene propylene diene monomer (EPDM)/polypropylene (PP) TPV.22,23 However, the evolution mechanism is far from being understood. From a © 2017 American Chemical Society

thermodynamic point of view, molecular recombination requires only modest thermodynamic cost, which occurs easily. However, the recombination interface involves a large amount of thermodynamic cost. If the interface remains invariant, the cost of interfacial free energy should be compensated by other energy that facilitates the phase separation. The energy cost and compensation grow linearly with the surface area and volume, respectively.24 This viewpoint is very common in the classical nucleation theory, which points out that the formation of a critical nucleus is necessary for the phase separation of supersaturated solutions.25 In order to understand the evaluation from the sea−island to island−sea structure of TPVs, the phase transition should be particularly illustrated. During a DV process, the structure of rubber undergoes variations, which plays a vital role in the phase inversion. Such inversion is a dynamic process accompanied by thermodynamic nucleation and phase transition. Developing a theoretical approach that can capture the essential mechanism of phase transition from a metastable to stable state is an attractive goal. Previous investigations employed the well-known Flory− Huggins theory to interpret the phase behavior in polymer blends.26−29 Good fittings to experimental data were achieved by the proper choice of the empirical Flory−Huggins parameter. However, the theory was restricted as a semiReceived: Revised: Accepted: Published: 13911

August 21, 2017 October 19, 2017 October 20, 2017 October 20, 2017 DOI: 10.1021/acs.iecr.7b03452 Ind. Eng. Chem. Res. 2017, 56, 13911−13918

Article

Industrial & Engineering Chemistry Research

the Haake Rheomix under the conditions of 170 °C and 100 rpm. Meanwhile, the blend decomposed into two new phases. 2.3. Interfacial Tension Measurement. To determine the surface tension (γ), the contact angles for the samples in the form of films were measured using a Kruss instrument (model DCAT21; Germany). The interfacial tension (γ12) between PP and POE was therefore calculated from the harmonic mean equation15

empirical model because the effect of polymer chain conformation was overlooked. In the present work, the phase transition and interfacial evolution in polyolefin elastomer (POE)/PP TPV were investigated using the classical three-dimensional density functional theory (3D-DFT).30−33 Meanwhile, the corresponding experiments were conducted to assess the predicted results. In general, POE has a relatively simple structural feature, which is particularly suitable for theoretical characterization and could serve as an excellent benchmark for the phase transition of TPVs. We aimed to (i) understand the molecular origin of the observed POE nanoparticles through their microstructure evolution and (ii) predict the variations of interfacial tension as well as the critical nucleation size. Seeking out a reasonable expression for the grand potential based on different interfacial microstructures depending on different interactions between POE and PP is the key issue of the DFT approach. Through minimization of the grand potential, the interfacial structures and properties were evaluated to decipher the phase inversion mechanism. Meanwhile, the biphasic morphology and actual sizes of rubber nanoparticles were observed in experiments. Finally, the theoretical predictions were tested with the experimental values to assess the reliability of the DFT model.

γ12 = γ1 + γ2 −

Table 1. Characteristics of the Materials Used polymer property

density (g/cm3) MFI (g/10 min) Tm (°C) octene content (wt %) Mooney viscosity ML (1 + 4) 125 °C grade supplier

POE

γ1d + γ2d

−

4γ1pγ2p γ1p + γ2p

(1)

where γ1 and γ2 represent the surface tensions of POE and PP, respectively. γd and γp are the associated nonpolar and polar components. At high temperatures, the values of γd and γp were calculated from the χ value, which is the ratio of γp to γ and does not change with temperature (χ = γp/γ, dχ/dT = 0).15,16 2.4. Morphology Investigation. The morphologies of the samples were observed using a peak force atomic force microscopy (PF-AFM) instrument (Nanoscope IIIa, Bruker Corporation, Karlsruhe, Germany). First, the samples were polished using a cryo-ultramicrotome (Leica EM UC7; Wetzlar, Germany) at −130 °C to obtain a flat surface for AFM characterization. The size of the individual POE rubber particles was also observed by the PF-AFM. The dynamically vulcanized POE/PP TPV was dissolved in hot xylene for 96 h. The solvent was refreshed every 24 h to wash off the dissolved PP. The obtained product was coated onto a clean coverslip using a spin coater (KW-4A; China). The obtained sample was then observed using PF-AFM. The POE particle size was counted with the Image-Pro Plus 4.5 software.

2. EXPERIMENTAL SECTION 2.1. Materials. Two types of commercially available polymers were used and are listed in Table 1. Dicumyl

a

4γ1dγ2d

PP

0.86 0.5b  27 33

0.91 0.5c 159  

Engage8150 DuPont Dow Elastomers Co., Ltd. (United States)

HP500D DOW Co., Ltd. (China)

3. THEORETICAL SECTION Within the 3D-DFT framework, the interactions between different sites in POE and PP molecules were described by the universal MARTINI force field,34 in which the groups of four or three units were represented by a single coarse-grained (CG) bead. For the ethylene and octene contents, we applied standard 4-to-1 mapping. For the propene content, however, we applied 3-to-1 mapping because the CH2 groups can be shared by the adjacent CG beads. Therefore, a POE molecule was described using a series of bonded C1 beads. Meanwhile, a PP molecule was simplified into a series of bonded SC1 beads.34,35 Figure 1 shows the coarse-grained POE and PP. The POE and PP chains were composed of 200 C1 and 200 SC1 beads, respectively. Our calculations revealed that once the chain length reached 200, the effect of the chain length on the polymer structure was trivial. The pairwise nonbonded interactions were given by the Lennard-Jones (LJ) potential. As a consequence, the united intermolecular potentials were calculated by summing the pair potentials

a MFI, melt flow index; Tm, melting point. bAt 190 °C and 2.16 kg. cAt 230 °C and 2.16 kg.

peroxide (DCP) was used as the cross-linking agent, which was purchased from Akzo Nobel Polymer Chemicals. A commercially available pentaerythritol tetrakis 3-(3,5-ditert-butyl-4hydroxyphenyl) propionate (1010) was applied as the antioxidant. Cyclohexane and xylene were purchased from Beijing Chemical Works, China. 2.2. Preparation of the Samples. The POE/PP TPV was prepared by melt mixing PP with POE in a Haake internal mixer (Haake Rheomix 600 OS, Thermo Fisher Scientific, America) equipped with two counter-rotating rotors. First, the two composites of POE and PP with the mass ratio of 60/40 were fed into a two-roll mill at 180 °C. At the initial stage, they formed an inhomogeneous premix. After long time mixing, the premix was transformed to a homogeneous blend. Meanwhile, antioxidant 1010 (0.35 wt % based on the POE) was added to prevent PP from aging. The sample with addition of DCP (1.5 wt % based on the POE) was then transferred to another tworoll mill at ambient temperature. Finally, the blend was fed into

⎧ 12 6⎤ ⎡ ⎪∑ 4εαα ′⎢⎜⎛ σαα ′ ⎟⎞ − ⎜⎛ σαα ′ ⎟⎞ ⎥ r ≥ σαα ′ ⎝ r ⎠⎦ U (r) = ⎨ ⎣⎝ r ⎠ ⎪ r < σαα ′ ⎩∞

(2)

where εαα′ and σαα′ are LJ potential parameters. The levels of interactions between different CG sites are given in Table 2. The cross-interaction parameters were estimated using the mixing rules with εαα′ = εαεα′ and σαα′ = (σα + σα′)/2. The grand potential Ω[{ρα(r)}] of polymer blend system can be expressed as 13912

DOI: 10.1021/acs.iecr.7b03452 Ind. Eng. Chem. Res. 2017, 56, 13911−13918

Article

Industrial & Engineering Chemistry Research F att[{ρα (r)}] = kBT ∑

∫ (ρα (r){F1[ρα̅ (r)] + F2[ρα̅ (r)]})dr

α

(7)

where the expressions of F1[ρ̅α(r)] and F2[ρ̅α(r)] can be given by the first-order mean spherical approximation expansion38 ⎡ ⎛ F1[ρα̅ (r)] = − 2πρα̅ (r)β∑ ∑ xαx α′εαα′⎢k1, αα′⎜⎜G0, αα′(z1, αα′)e z1, αα′R αα′ ⎢⎣ ⎝ α α′ ⎛ 1 + z1, αα′R αα′ ⎞ ⎟⎟ − k 2, αα′⎜⎜G0, αα′(z 2, αα′)e z 2, αα′R αα′ 2 z1, αα′ ⎠ ⎝ ⎤ 1 + z 2, αα′R αα′ ⎞ 3 ⎟⎟⎥ + 8πρα̅ (r)β∑ ∑ xαx α′εαα′R αα − ′Iαα′, ∞ z 2,2 αα′ ⎠⎥⎦ α α′ −

3 − 8πρα̅ (r)β∑ ∑ xαx α′εαα′g0, αα′(R αα′)R αα ′Iαα′,1 α

Figure 1. United atoms to CG maps of POE and PP (red and blue circles). C1 and SC1 are standard CG types.

α′

F2[ρα̅ (r)] = − πρα̅ (r)β∑ ∑ xαx α′εαα′[k1, αα′(G1, αα′(z1, αα′)e z1, αα′R αα′) α′

α

Table 2. CG Potential Interaction Parameters34,35 site

σ (Å)

ε (kJ/mol)

C1 SC1

4.7 4.3

3.5 2.6

Ω[{ρα (r)}] = kBT ∑

− k 2, αα′(G2, αα′(z 2, αα′)e α

∫ ρα (r)μα dr

α

(3)

Iαα′,1 =

ρα̅ (r) =

(4)

(10)

∑ ∫ ρα′(r′)ωααatt′(|r − r′|)dr′

(11)

att att att with the weight function ωαα ′(r) = uαα′(r)/ ∫ uαα′(r)dr . Here, att uαα′(r) is the LJ attractive interaction potential between any two sites of species α and α′. Chain connectivity is considered as a series of bonding segments by providing a label to each segment and allowing the segments to be exclusively integrated with their particular matching segments.40 Therefore, the contribution of chain connectivity to the free-energy functional is presented as follows

(5)

where Φhs[nm (r)] is the free-energy density, which stems from the modified fundamental measure theory37 and includes both the scalar and vector contributions

N

⎡ n1n2 − n V1·n V2 Φhs[nm(r)] = ⎢ −n0 ln(1 − n3) + ⎢⎣ 1 − n3 +

12 6 3 1 ⎛ σαα′ ⎞ 1⎛ σ ′⎞ 2⎛ σ ′⎞ ⎜ ⎟ − ⎜ αα ⎟ + ⎜ αα ⎟ 9 ⎝ Dαα′ ⎠ 3 ⎝ Dαα′ ⎠ 9 ⎝ Dαα′ ⎠

α′

where three terms on the right-hand side represent hard-sphere repulsion, dispersive attraction, and chain connectivity, respectively. The contribution of hard-sphere repulsion can be described by the fundamental measure theory36

∫ dr Φhs[nm(r)]

(9)

where xα is mole fraction of component α, z1,αα′ = 2.9637/σαα′, and z2,αα′ = 14.0167/σαα′. G0 and G1 are the radial distribution functions at hard-sphere contact. The details of calculation of F1[ρ̅α(r)] and F2[ρ̅α(r)] can be seen elsewhere.38,39 The weighted density ρ̅α(r) is defined as

F ex[{ρα (r)}] = F hs[{ρα (r)}] + F att[{ρα (r)}]

F hs[{ρα (r)}] = kBT

α′

12 6 1 ⎛ σαα′ ⎞ 1 ⎛ σαα′ ⎞ Iαα′, ∞ = ⎜ ⎟ − ⎜ ⎟ 9 ⎝ Dαα′ ⎠ 3 ⎝ Dαα′ ⎠

where Fex[{ρα(r)}] is the excess free-energy contributions. α denotes a site in polymer molecules; kB is the Boltzmann constant, and T is the temperature. μα represents the bulk chemical potential of component α. The excess free energy is presented as follows

+ F chain[{ρα (r)}]

)]

with

α

+ F [{ρα (r)}] − kBT ∑

z 2, αα′R αα′

3 − 4πρα̅ (r)β∑ ∑ xαx α′εαα′g1, αα′(R αα′)R αα ′Iαα′,1

∫ dr ρα (r)[ln(ρα (r)) − 1]

ex

(8)

∫ dr′ ∑ ρα (r′)×

F chain[{ρα (r)}] = kBT

α=1

⎛ ⎞ X α(r′) ∑ ⎜ln XAα(r′) − A + 1 ⎟ ⎝ 2 2⎠ A ∈Γ(α)

3 n32 ⎞ n2 − 3n2 n V2 ·n V2 ⎤ 1 ⎛ ⎥ ⎜n3 ln(1 − n3) + ⎟ ⎥⎦ 36π ⎝ (1 − n3)2 ⎠ n3 3

(12)

where the first summation is for the overall segments α and the second one is for the overall association sites on segment α as Γ(α); the variable XαA stand for the fraction of segments α that are not bonded at association site A. The details of the above functional derivatives can be seen elsewhere.41,42 In fact, more association schemes, in which polymer molecules may involve

(6)

where nm(r) represents the weighted densities with m = 0, 1, 2, 3, V1, V2. The details of nm(r) can be found in the literature.37 For the attractive contribution, Fatt[{ρα(r)}] can be described using the weighted density approximation method38 13913


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densities of POE in the POE-poor phase, respectively. The averaged density was obtained by integrating the density distribution in the nucleation region. The initial droplet density profile can be written as

multiple segments or multiple sites, may lead to more complex polymer structures.43 Here the multiple associating segments of POE were determined by the degree of cross-linking as follows: (1) Measure the volume swell ratio Q in the experiment. The details of measurement of Q can be seen our previous study.23 (2) Estimate the molecular weight Mc between the cross-links using the Flory−Rehner equation.44 (3) Calculate the multiple associating segments with n = Mn/Mc, where Mn is the number average molecular weight of PEO. The equilibrium density profiles can be obtained by ∂Ω/ ∂ρα(r) = 0. Then, the Euler−Lagrange equation can be generalized as

⎧ 0 ≤ r ≤ R0 ρ ⎪ rich ρ (r ) = ⎨ ⎪ρ ⎩ super r > R 0

for the iteration calculations. Here R0 is the initial radius of the nucleus, ρrich is the bulk density of POE in POE-rich phase. In order to avoid the influence of the edge effect, the interfacial densities were calculated on a 3D grid of 256 × 256 × 256 points. The grid spacing was set as 0.1σ in each direction. The outmost site of the surface was arranged in the z coordinate of the polymer surface sites and was located at the point where z = 0. The traditional Picard-type iterative method was employed to calculate the density profiles. For the description of interfacial density distributions in the theoretical model, the external force fields given by the pure PP and POE/PP blend were constructed using molecular dynamics simulations to mimic the real surfaces. In these simulations, all molecule parameters were derived from the MARTINI force field.34,35 More importantly, the force field parameters and contents of POE and PP in the simulations and theoretical calculations were exactly the same to ensure their consistency. First, the elongated polymer chains with extremely low density were placed in a large periodic box to obtain the initial configuration. Then a uniform dispersion could be obtained by running the NVT ensemble for a long time. The system was then compressed to the actual density by the NPT ensembles. At atmospheric pressure, the NVT simulations run for at least 6 ns to ensure system balance. Finally, the structural information of equilibrated system was collected by running of (10−20) × 106 NVT simulation steps at 443 K. During all simulation runs, 1.0 fs was chosen as the time step for the multiple time step integrator.45 A Nose−Hoover thermostat at the coupling frequency of 0.02 fs−1 was used to perform the isothermal calculations. The pressure was controlled by the Nose−Hoover barostat.46 A SHAKE algorithm was used to constrain the bond lengths.47 As a consequence, the external force fields could be represented as the slices of the equilibrium systems.

ρα (r) = ⎛ δ(F hs[{ρα (r)}] + F att[{ρα (r)}] + F chain[{ρα (r)}]) ⎞ ⎟⎟ exp⎜⎜βμα − β δρα (r) ⎝ ⎠ (13)

The interfacial tension γ of POE−PP was calculated from the grand potential, which can be written as Ω[ρ(r)] − Ω(ρb ) ΔΩ = (14) A A where Ω(ρb) is the grand potential of the bulk phase and A is the interfacial area. According to the liquid−liquid phase equilibrium thermodynamics, the chemical potential of each component has to be the same in different phases. For a binary mixture, the equations for calculating the chemical potentials can be written as γ=

⎛ ∂μ ⎜ 1 ⎛ dμ ⎞ ⎜ ∂P ⎜ 1⎟ = ⎜ ⎜ dμ ⎟ ⎝ 2 ⎠ ⎜ ∂μ2 ⎜ ∂P ⎝

∂μ1 ⎞ ⎟ ∂y1 ⎟ ⎛ dp ⎞ ⎟=⎜ ⎟ ∂μ2 ⎟ ⎜⎝ dy1⎟⎠ ∂y1 ⎟⎠

(16)

(15)

where dμi (i = 1, 2) means the differential of μi. The iteration method for obtaining the phase equilibrium at given temperature and pressure is as follows: (1) Set the premix as 1.0 mol, and the mole quantity of POE-rich phase is LPOE‑rich = 0.995. (2) Assume different mole fractions of POE in POErich and PP-rich phases (xPOE and yPOE) to satisfy zPOE = xPOELPOE‑rich + yPOE(1 − LPOE‑rich), where zPOE is the constant mole fraction of POE in the premix. (3) Substitute the two values into eq 15, and solve the equation to obtain new x′POE and yPOE ′ . (4) Repeat step 3, and estimate the chemical potentials of POE and PP in the two phases. (5) Evaluate the POE‑rich −3 chemical potentials. If μPOE‑rich − μPP‑rich − POE POE > 10 , or μPP PP‑rich −3 μPP > 10 , set a new mole quantity of POE-rich phase with Lnew POE‑rich = LPOE‑rich − 0.005. (6) Perform the iteration procedure −3 including the steps of 2, 3, and 4 until μPOE‑rich − μPP‑rich POE POE < 10 POE‑rich PP‑rich and μPP − μPP < 10−3. Accordingly, the phase equilibrium at given temperature and pressure are determined. Then change the temperature to obtain a new equilibrium. As such, the temperature−composition phase diagram is finally determined. According to nucleation thermodynamics, nucleation occurred under a supersaturated condition. A growing embryo should overcome its free-energy barrier before reaching a stable state. When the free energy reaches its maximum, the droplet size is defined as the critical size (dc), and the maximum is the energy barrier. The supersaturation ratio can be defined as S = ρsuper/ρpoor, where ρsuper and ρpoor denote the averaged and bulk

4. RESULTS AND DISCUSSION The initial morphology of the premix was first determined, at which PP (denoted as island) was dispersed in POE (denoted as sea). Figure 2 shows the spatial density profile of POE on the PP surface to display the interfacial microstructure. The POE molecules display pronounced and disordered packing on the PP surface. The strongest interactions, which were ascribed to the close rows of the PP chains, resulted in the highest peaks at the slots of the surface. On the other hand, one can see that both ordered and disordered voids were dispersed on the rough PP surface. These voids were induced by the synergistic effect of chemical characteristics and topological structures. When the POE molecules were in contact with the PP matrix, some of the voids were occupied by POE molecules because their sizes were approximately equal. Because of the similarity in the chemical structure of POE and PP, they can form a compatible blend.48,49 From the thermodynamics point of view, the molecular weight of POE increases with the vulcanization of POE, which reduces the mixing entropy and leads to the phase decomposition.2 Figure 3 13914


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temperature (LCST). The vertical dashed line indicated the mole fraction of POE in the homogeneous blend in the current experiment. At the experimental temperature of phase separation, the POE-rich phase (denoted as island) and the PP-rich phase (denoted as sea) were formed. Therefore, the composition of the two phases was determined based on the requirement of equal chemical potential and pressure in the coexistent phases. After phase separation at 443 K, the initial sea−island morphology in the premix had been transferred to the new island−sea morphology. Accordingly, the newly interfacial microstructure was determined. Structure analysis is an effective tool to interpret a wide range of interfacial phenomenon. Figure 4 shows the corresponding density distributions of the sea (PPrich) on the island (POE-rich) surface. One can immediately see the obvious multilayer adsorptions of POE and PP in the POE-rich region. The density distributions close to the interface are high peaks, which can be attributed to the enhancement of interfacial adsorption. Outside the interface, the density distributions vary from peak to trough, implying the transformation of local adsorption−desorption. The comparison of the panels a and b of Figure 4 implies that more adsorption peaks emerge in Figure 4a, because the attractions of POE−POE are stronger than those of POE−PP. The above density fluctuations correlate to interfacial energy or interfacial tension, which was calculated by eq 14. It is unambiguous that the variations of density profiles, including the height and width of the fluctuations, affect the interfacial tension. Table 3 presents the experimental and calculated

Figure 2. Two-dimensional cut of the spatial density distribution of the sea (POE) on the island (PP) surface. The distribution is cut at y = 0.

Table 3. Interfacial Tensions of POE/PP Blend γ (mN/m)

Figure 3. Temperature−composition phase diagram of vulcanized POE (1) and PP (2) at constant pressure. The vertical dashed line denotes the mole fraction of POE in the blend. xPOE is the mole fraction of POE in the POE-rich phase, and yPOE is the mole fraction of POE in the PP-rich phase.

species

theory

experiment

POE/PP (premixed) POE/PP (vulcanized)

0.47 0.34

0.50 ± 0.05 

results. For the premixed system, the calculated value generally agrees with the experimental one, which indicates that the theory provides quantitatively reasonable descriptions of the interfacial microstructures and properties of the POE/PP blend. Figure 5 shows the experimental phase images of POE/PP blend. The lighter and darker regions represent the POE and PP phases, respectively. The initial sea−island morphology in the premix can be observed in Figure 5a. As expected, the

presents the calculated temperature−composition phase diagram for the vulcanized POE/PP at constant pressure. In descending order of temperature, the POE/PP blend revealed a complex phase behavior involving a lower critical solution

Figure 4. Two-dimensional cuts of the spatial density distributions of the sea (PP-rich phase) containing POE (a) and PP (b) on the island (POErich phase) surface. The distributions are cut at y = 0. 13915


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Figure 6b displays the calculated excess free-energy curve during the formation of POE-rich droplets. It is shown that the size of POE-rich droplets is 22 nm. In general, the theoretical prediction is consistent with the experimental results. The reason lies in the fully homogeneous mixing, such that the thermodynamic bases of the theoretical and experimental phase transitions are the same. The differences between the theoretical prediction and experiment measurement could be caused by (a) the lack of detail of the topologic structures due to the coarse-grained disposal of various groups and (b) the coalescence of nanoparticles during the DV process. Figure 5. AFM phase images of the POE/PP blend taken of (a) premixed and (b) dynamically vulcanized samples. The lighter and darker regions represent the POE and PP phases, respectively.

5. CONCLUSION The 3D-DFT calculations and AFM measurements were combined to investigate the phase separation of POE/PP blend during DV. The phase equilibrium and interfacial properties were quantitatively predicted to illustrate the morphology transition from sea−island to island−sea in the blend. The results indicate that the phase transition is induced by thermodynamic driving force which is developed during the dynamic cross-linking process. In other words, the dynamic cross-linking causes the microstructure variations of POE, which results in the reduced interfacial tension and finally the liquid−liquid phase transition. The observed POE nanoparticles nucleated into new phases, and the nucleus size was demonstrated by the 3D-DFT approach. The agreement between the theory and experiment enables a fundamental understanding of the phase inversion of the TPV.

inhomogeneous PP domains, including large or small PP regions, were dispersed in the POE matrix. In Figure 5b, one can see a new island−sea structure after the DV disposal, indicating the occurrence of liquid−liquid phase decomposition. Because the POE-rich domains were dispersed in the PPrich phase, and some PP crystals were located in the crosslinked POE phase, the morphology of the TPV product was quite complex.50 Figure 6 displays the formed POE nuclei from the theoretical calculations and experimental measurements. The size was determined using the interfacial density distributions. During the nucleation process, a droplet that is growing in size should overcome its free-energy barrier before reaching a stable state in the system. The critical size (dc) was defined as the droplet size at the point where the free energy needed for the formation of POE-rich droplet is maximum. When an embryo has a size less than the critical value, any increase of the size is accompanied by additional free-energy consumption, which means the embryo would shrink. On the other hand, when an embryo has a size greater than the critical value, any increase in size is accompanied by the depressed free-energy, and the embryo grows. Figure 6a shows an AFM image of the POE/PP sample, which was coated on a coverslip. To characterize the individual POE-rich nanoparticle, the PP content was washed off with hot xylene. The lighter and darker regions represent the glass substrate and the cross-linked POE-rich phase, respectively. The minimum size of the POE-rich nanoparticles is 20 nm.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Ming Tian: 0000-0002-4820-7372 Liqun Zhang: 0000-0002-8106-4721 Jianguo Mi: 0000-0002-6355-783X Notes

The authors declare no competing financial interest.

Figure 6. (a) AFM phase image of the dissolved POE/PP blend. (b) Dimensionless free-energy barrier of the growing POE-rich droplets. 13916


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ACKNOWLEDGMENTS The financial support from the National Basic Research Program of China (Grant No. 2015CB654700 (2015CB674704)) and the National Natural Science Foundation of China (Nos. 51525301 and 51521062) is gratefully acknowledged. We also express our sincere thanks to the CHEMCLOUDCOMPUTING of Beijing University of Chemical Technology.

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