Insight into the formation of a continuous sheath structure for the PS phase in tri-continuous PVDF/PS/HDPE blends

Abstract

This work reports on the morphology development of ternary percolated co-continuous systems in PVDF/PS/HDPE blends in which PVDF and HDPE form two continuous networks, while the PS forms a continuous sheath structure at the PVDF/HDPE interface. By controlling the relative amounts of PVDF, PS and HDPE, continuity data based on gravimetric solvent extraction clearly demonstrate that a PS volume composition as low as 11% results in a very high level of continuity of about 80%. The evolution of PS phase continuity is further studied by changing the component ratios of HDPE and PS with the PVDF phase concentration held at a constant 44% volume fraction. Scanning electron microscopy as well as optical microscopy is used to clearly illustrate and identify the evolution of the PS phase morphology. The results indicate that with a PS phase concentration increase, the evolution of the PS phase morphology in the ternary blends experiences several distinguished stages: when the PS concentration is less than 4 vol%, the PS phase locates at the PVDF and HDPE interface as dispersed droplets; when the PS concentration increases to 7 vol%, the PS phase forms an incomplete interface between PVDF and HDPE; when the PS concentration reaches 10 vol%, most of the PS has clearly and spontaneously structured itself at the PVDF/HDPE interface forming a uniform layer. Additionally, the self-assembly behavior of the PS droplets and the coalescence behavior of the PS layer on the PVDF/HDPE interface are respectively investigated through online observation using optical microscopy under quiescent annealing at 200 °C. The mechanism of the phase morphology evolution under annealing indicates that the movement of the phase interface and interfacial tension play key roles in the phase relaxation and equilibrium.

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Introduction

The controlled formation of complex morphological multiphase materials is an important area of research in advanced materials science.^1–5 For binary immiscible polymer blends, two broad categories of morphology exist: the matrix/dispersed phase structure and the co-continuous morphology.⁶ Recently, because multi-component polymer blends can demonstrate a wide variety of micro-structured morphologies with multiple interfaces present, more attention has been paid to the ternary polymer blends.^7–10

For ternary polymer blends, complete wetting and partial wetting are two possible broad categories of morphological states. Hobbs et al.¹⁰ employed a modified Harkin’s spreading theory (eqn (1)) to predict whether the morphology of a ternary blend is dominated by complete engulfing or by partial wetting.

λ_BC = γ_AC − γ_AB − γ_BC (1a)

λ_AC = γ_BC − γ_AB − γ_AC (1b)

λ_AB = γ_CB − γ_AC − γ_AB (1c)

where the γ values are the interfacial tensions between the different phases. Each spreading coefficient gives the tendency of one phase to spread and form a continuous layer at the interface of the other two. If λ_BC is positive and the other two negative, then phase B forms a continuous phase between A and C and complete encapsulation is observed. In the case that all three spreading coefficients are negative, partial wetting is observed in which none of the phases locate fully between the two others. For ABC ternary blends displaying complete wetting behavior where λ_BC is positive, four possible morphological hierarchies can be achieved and are shown in Fig. 1. Fig. 1a–c illustrate the typical matrix/core–shell dispersed morphology and matrix/two separate dispersed phases morphology. Subsequently, increasing the concentration of the core phase results in the coalescence of the core phases which leads to the formation of a tri-continuous morphology (shown in Fig. 1d).

Fig. 1 Equilibrium morphologies for an ABC ternary polymer system (a) and (b) matrix/core–shell dispersed phase morphologies; (c) matrix/two separate dispersed phase morphology; (d) tri-continuous phase morphology describes complete wetting.

Generally speaking, continuous morphologies represent the special case where, in an A/B system, both components are fully continuous within the blend. Since this often occurs over a concentration range for binary polymer blends, this is also known as the region of dual phase continuity. By selectively controlling the interface,¹¹ composition,¹² processing temperature,¹³ shear rate¹⁴ and annealing time¹⁵ of the blends, it is possible to control the pore size of the co-continuous network over 2–3 orders of magnitude. In an ABC system, the potential of tri-continuous structures is achieved by locating a phase with a specific characteristic at the interface of the two other continuous phases. Because of the complex interface interaction of the phases and the narrow window of the phase continuous morphology, the formation of this hierarchical multiphase continuous morphology is relatively difficult and only a limited number of works have been published.^6,16–19 For example, Luzinov et al.¹⁶ by employing Harkin’s equation, observed a tri-continuous structure in polystyrene/styrene–butadiene rubber/polyethylene (PS/SBR/PE) ternary blends with SBR as the interfacial phase at a composition ratio of 30/25/45 wt%. They also found that with a constant content of SBR at 25 wt%, it was possible to maintain the tri-continuous structure whenever the PS/PE composition ratio ranged from 40/60 to 60/40. Concerned with the control of the tri-continuous structure in ternary blends, Favis et al. studied a series of complete wetting polymer systems such as PMMA/PS/HDPE,⁶ PLA/PBAT/PBS,¹⁷ and HDPE/PS/PCL,¹⁸ and made significant contributions in the field of polymer morphology evolution. By employing 5 component continuous systems of HDPE/PS/PMMA/PVDF/PANI blends, Favis et al.¹⁹ found that the conductive PANI percolation threshold can be reduced to below 5 vol%. Moreover, by employing the prediction of interfacial tension and controlling the composition of the phases, they developed a tri-continuous structure in which PS was situated at the interface of HDPE and PMMA and in this triple percolated system, a PS volume composition as low as 3% resulted in a PS phase continuity of about 70%, a very high level of continuity for such a small volume fraction of PS.⁷ This instructive work has made the multiphase blends with a tri-continuous structure a candidate to design ultralow percolation threshold systems which are of particular interest in conductive applications.

In the case of the preparation of conductive ternary blends using a tri-continuous structure, both the interphase content and interphase layer thickness influence the percolation threshold. Therefore, the morphology control of tri-continuous structures in ternary blends should be clarified firstly. Ravati et al.¹⁸ reported on the annealing of HDPE/PS/PCL ternary polymer blends with a tri-continuous structure. It was shown that the thickness of the PS interfacial layer had increased from 2.3 μm before annealing to an average size of 112 μm after 30 min annealing.

However, the detailed morphological study of ternary blends demonstrating complete wetting structures is still insufficient, especially for the development from co-continuous morphologies in binary blends to tri-continuous morphologies when the third interphase is added. This paper therefore reports on the development of a tri-continuous morphology in PVDF/PS/HDPE ternary blends. The morphology will be determined through a combination of electron and optical microscopy as well as through the estimation of continuity effects via selective solvent extraction/gravimetry of specific phases. The morphology evolution of the ternary blends with low and high PS phase content was further investigated through an annealing process using an optical microscope equipped with a heating stage.

Experimental

Materials

PVDF (type FR906) powder with an average molecular weight of 3.7 × 10⁵ g mol⁻¹ was obtained from the Shanghai 3F New Materials Company (China). PS (type PG-33) pellets with an average molecular weight of 1.2 × 10⁵ g mol⁻¹ were obtained from the Taiwan Qimei Company. HDPE (type 2911) pellets with an average molecular weight of 1.7 × 10⁵ g mol⁻¹ were obtained from the Fushun Petrochemical Company (China). The detailed information of each component is noted in Table 1.

Table 1 Polymer characteristics

	ρ (g cm^−3) at 25 °C	ρ (g cm^−3) at 200 °C	η0 (Pa s) at 0 s^−1 at 200 °C	η (Pa s) at 50 s^−1 at 200 °C
PVDF	1.6	1.5	585.3	145.1
PS	1.05	0.95	4173.0	240.5
HDPE	0.93	0.85	377.2	187.6

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Sample preparation

All polymers were dried in a vacuum oven for 24 h at 80 °C before blending to minimize the effects of moisture. Various volume ratios of the PS and HDPE pellets with 44 vol% of the PVDF powders were added simultaneously into a Haake torque mixer at 200 °C and 100 rpm for 8 min. The average shear rate was estimated to be γ = 50 s⁻¹ based on the type of mixer. Binary blends of HDPE/PVDF, PVDF/PS and HDPE/PS were prepared using the same procedure. After blending, the blends were quenched in cold water to freeze-in the morphology. Blends were annealed at 200 °C for 0, 5, 10, 15 or 20 min using an optical microscope equipped with a heating stage.

Interfacial tension measurement

The interfacial tension for the pairs of polymers in this study was determined using the rheological behavior of their respective blend. The data were analyzed using Gramespasher and Meissner’s analyses²⁰ following the procedures reported elsewhere.²¹ The results concerning the interfacial tensions are listed in Table 2. These interfacial tension data are used to calculate the spreading coefficients:

λ_AB = γ_BC − γ_AC − γ_BA (2)

where γ represents the interfacial tension for the various polymer pairs and sub-indexes. A, B and C refer to each component. The spreading coefficient, λ_AB, is defined as the tendency of component (A) to encapsulate or spread onto component (B) in a matrix of component (C). A positive value of one of the spreading coefficients such as λ_AB demonstrates a complete wetting morphology (two-phase contact) in which phase A spreads and forms a complete layer at the interface of phases B and C. Three negative spreading coefficients indicate a partial wetting behavior in which none of the three spread at the interface of the other phases and all three meet along a common line of three-phase contact. The calculated results are listed in Table 3. For the ternary blends of PVDF/PS/HDPE, it is predicted that the PS phase should be completely spread between the PVDF and HDPE phases to form a complete wetting structure.

Table 2 Interfacial tension for the polymer pairs at 200 °C

Polymer pairs	Interfacial tension (mN m^−1)
PVDF/PS	4.7
PS/HDPE	3.4
HDPE/PVDF	11.9

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Table 3 Spreading coefficients for the ternary PVDF/PS/HDPE systems at 200 °C

	Spreading coefficient (mN m^−1)
λ(PS/HDPE)	3.8
λ(PVDF/PS)	−13.2
λ(HDPE/PVDF)	−10.6

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Selective solvent extraction

Samples of 0.3–0.5 g were immersed in a large volume of xylene and stirred gently at room temperature to selectively extract the PS component until the samples reached a constant weight. After the extraction procedure the samples were dried in the vacuum oven at a temperature of 80 °C for one day and the mass of the samples was determined. A gravimetric method was used to calculate the extent of the continuity of the PS phase, using the simple equation:⁶in this equation, m_initial is the initial mass of the sample, m_final is the final mass of the sample and m_initial(A) is the initial mass of polymer A contained in the sample before the selective extraction, calculated by its mass proportion based on the sample.

Morphology characterization

For the optical microscopy observations, 20 μm thick specimens were prepared using a microtome. The morphologies of these thin sections were examined using an Olympus BX51 polarizing optical microscope (Olympus Co., Tokyo, Japan) under both bright field and crossed-polar conditions. For the SEM observations, the cryogenically fractured surface was directly coated with a thin layer of gold and observed at an accelerating voltage of 20.0 kV using a JEOL JSM-5900LV scanning electron microscope (SEM, JEOL, Japan).

Quantitative analysis of the dispersed morphology was performed using the image analysis of Image-Pro Plus 6. At least 300 dispersed domains were measured by manually tracing the phase boundaries to estimate the number-average diameter (d_n) for each sample. Corrections to the particles size were performed using the Schwartz–Saltykov method.²²

Results and discussion

Co-continuity window in the PVDF/HDPE blends

In order to form a tri-continuous structure in the PVDF/PS/HDPE ternary blends, the co-continuity window in the PVDF/HDPE blends is first investigated. Fig. 2 presents the phase continuity of both components in the PVDF/HDPE blends measured using selective solvent extraction as a function of the volume fraction of PVDF. It can be seen that the HDPE component is continuous for the PVDF up to 60 vol%, whereas the PVDF component is continuous for the HDPE above 35 vol%. Therefore, the co-continuity window for the PVDF/HDPE blends is PVDF of 35–60 vol%. Likewise, the inset polarized micrographs show that the dispersed PVDF phase type structure is converted to a continuous type structure through an increase in the PVDF composition. This conclusion was reached by considering the crystallization temperature of the materials as they cooled on the hot stage of the light microscope and then comparing that temperature to the crystallization temperatures of the neat materials. Pure PVDF and HDPE spherulites form at 146 °C and 115 °C. Such crystallization temperatures correspond to the DSC cooling run and crystalline peaks obtained for PVDF and HDPE (not shown here).

Fig. 2 Continuity of both components in the PVDF/HDPE blends as a function of PVDF concentration; the inset polarized micrographs were obtained at 140 °C using POM (PVDF displays bright view while HDPE displays dark view).

Tri-continuous morphology in the PVDF/PS/HDPE ternary blends

Ternary PVDF/PS/HDPE blends with tri-continuous structures were prepared based on the co-continuity region found for the PVDF/HDPE binary blends. Moreover, Harkin’s spreading theory for the ternary PVDF/PS/HDPE blend shows a positive spreading coefficient of λ_PS/HDPE with a value of 3.8 mN m⁻¹. It predicts complete wetting with the PS phase located at the interface of PVDF and HDPE. Experimental observations of the location of the phases will be discussed in more detail below. Fig. 3 shows the phase morphology of the PVDF/PS/HDPE ternary blend with a composition ratio of 44/20/36 vol%. The SEM image of the PVDF/PS/HDPE blend in Fig. 3a displays a total continuous structure of the different phases. In order to distinguish the phases, the PS is etched by xylene and uniform cracks pervading entirely throughout the sample (shown in Fig. 3b) can be clearly seen, in contrast to Fig. 3a. In this case, the gravimetric solvent extraction results reveal a 96 ± 2% continuity for PS. The EDS data of the other two areas in this sample are given. According to Fig. 3c, C and F atoms can be seen in one of the phases while the other phase only shows C atoms. This demonstrates that the PVDF phase and HDPE phase can be accurately distinguished. Fig. 3d shows the polarized optical microscope (POM) image obtained at room temperature. It can be noted that the PVDF (bright white domains, corresponding to the crystalline structure) and HDPE phases (in dark yellow) appear as the main components and are separated by a thin PS layer (notice the black domains corresponding to the amorphous phase). The tri-continuous structure with the PS located at the interface between PVDF and HDPE is verified again.

Fig. 3 The tri-continuous structure of the PVDF/PS/HDPE (44/20/36 vol%) ternary blend (a) SEM micrograph of cryo-fractured surfaces, (b) SEM micrographs of cryo-fractured surfaces with PS etched by xylene, (c) EDS spectra of the areas marked by a white square and red triangle in b, (d) crystalline structure of the sample under polarized optical microscopy after cooling down the temperature to the crystalline temperature of the phases.

Continuity curves of ternary PVDF/PS/HDPE, binary HDPE/PS and PVDF/PS blends

The presence of a PS layer at the interface of the co-continuous PVDF/HDPE blends significantly reduces the PS volume fraction required for its percolation and continuity development as compared to classical binary HDPE/PS and PVDF/PS blends. Continuity data based on gravimetric solvent extraction clearly demonstrate this effect and are shown in Fig. 4. It can be seen that in this complete wetting triple phase system, a PS volume composition as low as 11 vol% results in a PS phase continuity of about 80%, a very high level of continuity for such a small volume fraction of PS. Moreover, the PS layer continuity increases with increasing PS volume content, reaching an apparent maximum value of approximately 95%.

Fig. 4 Continuity of PS phase as a function of PS concentration in PVDF/PS/HDPE, HDPE/PS and PVDF/PS blends using the solvent dissolution technique (PVDF was held at a constant content of 44 vol% in the PVDF/PS/HDPE blends).

The morphology of the PVDF/PS/HDPE ternary blends after blending

SEM observation for the development of tri-continuous morphology with PS content increase. Fig. 5 shows the morphology of the PVDF/PS/HDPE ternary blends with different volume fractions after extracting PS with xylene. As an overview from the images, the blends display a matrix/dispersed phase morphology when the PS content is less than 10 vol% (Fig. 5a–c) while the morphology changes into a tri-continuous morphology when the PS content is more than 12 vol% (Fig. 5d–f). For the tri-continuous morphology samples, it is clearly seen that the extracted PS phase forms a uniform crack, located at the interface of PVDF/HDPE that spreads entirely throughout the sample. However, for the matrix/dispersed phase morphology samples, large PVDF droplets uniformly disperse in the HDPE matrix while the PS phase forms small dispersed droplets around the PVDF particles due to the lower PS concentration. More microstructures of the PVDF/PS/HDPE blends with a low PS content are shown in Fig. 6. Fig. 6 exhibits the morphologies for samples with 4 and 7 vol% PS in OM and SEM micrographs. For the OM observations, although the phases can be recognized from the interfacial-angles, phase identification is also confirmed by the cooling temperature of the particular phase as it cools from the melt. This method requires that two important conditions be respected. Firstly, for a ternary blend, at least two components should be semi-crystalline with different crystallinity temperatures (shown in Fig. 2), and secondly, the crystallinity of the phases should not influence each other (confirmed in Fig. 3d). Fig. 6a shows that at a 44/4/52 vol% composition, the resulting morphology consists of PS droplets located at the PVDF/HDPE interface with a fraction remaining in the HDPE phase. Their affinity for the HDPE side of the PVDF/HDPE interface is expected since the PS/HDPE has a interfacial tension of 3.2 mN m⁻¹ which is lower than 4.9 mN m⁻¹ for the PS/PVDF. When the PS content increases to 7 vol%, the PS droplets coalesce into a layer that partly covers the PVDF phase (shown in Fig. 6b). Fig. 6c and d give the further SEM observations of these ternary blends with 4 vol% and 7 vol% PS respectively. In order to enhance the phase contrast of the samples, PVDF and PS were successively extracted using DMF and xylene before the SEM testing. Self-assembly of the PS droplets into a perfectly close-packed droplet array at the PVDF/HDPE interface can be clearly seen in Fig. 6c. Remarkably, when highly concentrated at the interface, the PS droplets coalesce into a partial layer at the interface (in Fig. 6d) and tend to form a uniform layer at higher PS content which has been proved by the above results (in Fig. 5d–f). This highly organized microstructure evolution is induced by the complete wetting of the PVDF/HDPE interface by the PS phase.

Fig. 5 SEM micrographs of the morphology evolution of the PVDF/PS/HDPE blends at various compositions, (a) 44/4/52 vol%; (b) 44/7/49 vol%; (c) 44/10/46 vol%; (d) 44/12/44 vol%; (e) 44/15/41 vol%; and (f) 44/20/36 vol%. (The PVDF is held constant at 44 vol% and the PS phase is extracted by xylene in all samples.)

Fig. 6 Optical micrographs of PVDF/PS/HDPE at different composition ratios (a) 44/4/52 vol% and (b) 44/7/49 vol%; SEM micrographs of PVDF/PS/HDPE at (c) 44/4/52 vol% and (d) 44/7/49 vol% composition ratios. (Optical micrographs were taken at 200 °C using optical mode, SEM images were taken after the PVDF and PS phases were etched by DMF and xylene.)

The mechanism of morphology evolution for the PVDF/PS/HDPE blends during mixing. For all the ternary samples we studied, the concentration of the PVDF phase was held at 44 vol% and only the volume fraction of PS to HDPE changed. In all the cases, the volume fraction of PVDF based on the two major phases (PVDF and HDPE) changes from 46% to 55% which is still within the co-continuous window. However, the PVDF phase morphology changes from dispersed droplets to a continuous region with increasing PS content. Moreover, the number average diameter of the PVDF phase as a function of PS content in the ternary blends is analyzed in Fig. 7. Compared with the PVDF/HDPE binary blends, the introduction of the PS phase led to a decrease of the PVDF phase size from 123 ± 10 μm to 21 ± 0.7 μm, subsequently the PVDF phase size increases with increasing PS content and reaches a maximum value of 176 ± 12 μm with a PS content of 12 vol%. This PS content also presents the phase inversion of the PVDF/PS/HDPE blends. With continuous increase of the PS content, the PVDF size decreases monotonously. How does one explain this morphology evolution during mixing? Two factors that can have a major impact on the evolution of the phase morphology in polymer blends are (1) the effect of interfacial tension on the interfacial equilibration when PS is introduced and (2) the variation of viscoelasticity when the components composition changes.

Fig. 7 PVDF phase number average diameter as a function of PS concentration in the PVDF/PS/HDPE ternary blends (PVDF has a constant content of 44 vol%). The blue dash line represents the phase inversion according to Fig. 4 and 5.

According to the results listed in Table 2, PVDF/HDPE interfacial tension is 11.9 mN m⁻¹ which is much larger than that of PVDF/PS and HDPE/PS. Also, PS has a much higher zero shear viscosity compared with PVDF and HDPE. The phenomenon that PVDF phase size decreases when PS is introduced in the PVDF/HDPE blends can be explained by means of the capillary number eqn (4):²³

where the capillary number Ca is a comparison between the viscous forces and the interfacial tension,^24,25 R is the radius of the droplet, γ is the interfacial tension, η_m is the viscosity of the matrix, and α is the shear rate during mixing. For our blend systems, the calculated Ca values increase about 3.7 times when the PS phase is added which means an enhanced tendency for phase break up, thus leading to the decrease of the PVDF phase size. The subsequent increase of the PVDF phase size when the PS content is lower than 12 vol% in the ternary blends is mainly caused by a concentration effect. It is well known that in a matrix/dispersed phase morphology blend, with the content of the minor phase increasing, the size of the dispersed droplets will enlarge due to the coalescence of adjacent droplets.²⁶ In our ternary blend system, the morphology consists of a HDPE matrix, a PVDF dispersed phase and PS dispersed phase when the content of PS is lower than 12 vol%. The volume fraction of PVDF based on the HDPE and PVDF phases changes from 46% to 50% with the PS concentration increasing, thus resulting in the increase of the PVDF dispersed phase size.

The tri-continuous morphology with the PS layer located at the interface of PVDF and HDPE is achieved when the PS content reaches 12 vol% which is consistent with its thermodynamic equilibrium morphology. Therefore, the change of viscosity of the blends is mainly responsible for the size decrease of PVDF and it can be explained by the follow eqn (5):²⁷

τ = η_mα (5)

where τ is the shear stress, η_m is the viscosity of the matrix, and α is the shear rate during mixing. On account of the preset conditions of constant mixing parameters (mixing time, temperature and screw speed), a higher mixing energy input is provided for the more viscous materials; high shear stresses are exerted by the highly viscous matrix phase leading to a better droplet break-up and less coalescence.²⁸ Also Taylor²⁹ observed that when the radius of the drop was great enough or when the rate of distortion was high, the drops break up. He developed eqn (6), which is an expression for determining the size of the largest drop that exists in a fluid undergoing distortion at any rate:where R is the radius of the droplet, γ is the interfacial tension, η_m and η_d is the viscosity of the matrix and dispersed phase respectively, and α is the shear rate during mixing. For the PVDF/PS/HDPE ternary blends with a tri-continuous morphology, the γ between each two phases is constant, α is 50 s⁻¹ for all the samples, and only the viscosity of the system increases with the PS phase increasing because of its higher viscosity (shown in Table 1), causing the decrease of the PVDF phase size.

The self-assembly behavior of the PS droplets on the PVDF/HDPE interface during melt annealing

For the PVDF/PS/HDPE blends with a low PS content, the morphology consists of PS droplets located at the HDPE/PVDF interface without complete wetting behaviors against the prediction of interfacial tension. In order to better investigate the microstructure equilibrium behavior and better visualize the blend’s structure, quiescent annealing was carried out. Quiescent annealing allows the interfacial forces to dominate and leads to the phase morphology at a thermodynamic steady state.^9,30

The morphology evolution of PVDF/PS/HDPE with a composition ratio of 44/4/52 vol% can be determined from Fig. 8. Before annealing (Fig. 8a), the first observed phenomenon is partial and complete exclusion of PS from the PVDF/HDPE interface and HDPE regions, respectively. During annealing, the growth of the PVDF phase and PS droplet phase at the PVDF/HDPE interface is obviously seen from Fig. 8b–e. Additionally, after 20 min annealing, the number of PS droplets in the HDPE regions largely decreases compared to the 0 min annealing image of Fig. 8a. The difference is striking and a divergence emerges for the PS droplet size during quiescent annealing as demonstrated in Fig. 9. It is clearly noticed that the size of PS at the interface is increasing with annealing while the size of PS in the HDPE regions is barely changed. Table 4 lists the calculated sizes of the different phases. It is found that the average diameter increases from 11.2 ± 2.5 to 29 ± 2.4 μm for the PS droplets at the PVDF/HDPE interface after 20 min of annealing time, as compared to an almost constant value of 4.8 μm for the PS droplets in the HDPE region for the same annealing time. How do the large differences of two types of PS droplet morphology happen in the PVDF/PS/HDPE blends under the same annealing conditions?

Fig. 8 Morphology evolution of the PVDF/PS/HDPE 44/4/52 vol% blend as a function of annealing time (a) 0 min, (b) 5 min, (c) 10 min, (d) 15 min and (e) 20 min at 200 °C using OM.

Fig. 9 Number average diameter d_n of the PS droplets at the interface and in the HDPE region for the PVDF/PS/HDPE 44/4/52 vol% blend as a function of annealing time.

Table 4 Number average diameter d_n of the different phases in the PVDF/PS/HDPE 44/4/52 vol% blend

Annealing time (min)	dn (PS at the interface, μm)	dn (PS in the HDPE regions, μm)	dn (PVDF phases, μm)
0	11.2 ± 2.5	4.3 ± 1.8	97.1 ± 10.6
5	19.9 ± 3.2	4.8 ± 1.4	103.4 ± 10.1
10	23.3 ± 2.1	5.2 ± 0.6	110.3 ± 9.8
15	25.1 ± 1.9	5.1 ± 1.4	117.7 ± 8.7
20	29.8 ± 24	4.9 ± 1.7	125.8 ± 11.2

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In order to understand the change of PS droplet size at the PVDF/HDPE interface and HDPE regions during annealing, it is necessary to consider the factors that influence the phase relaxation and evolution such as viscoelastics,⁹ inertial effects,²³ interfacial motion³⁰ and interfacial forces.³¹ Actually the kinetics related to interfacial motion and the role of interfacial forces are the two key factors to control the evolution of the phase morphology during quiescent annealing. The interfacial motion ability of the different polymer pairs is firstly investigated in each binary blend during quiescent annealing. The phase coalescence rates can be used as a simple standard to measure the ability of interfacial motion.^32–34 Therefore, the PVDF phase size in PVDF/HDPE and the PS phase size in PVDF/PS or HDPE/PS were calculated and the results are shown in Fig. 10.

Fig. 10 Number average diameter d_n of the PVDF phase size in PVDF/HDPE and the PS phase size in the PVDF/PS and HDPE/PS blends as a function of annealing time (the lines represent the best linear fitting of each curve).

Clearly, significant differences in coalescence rates are observed for different blends. Here we define a parameter K, which means the increment of phase size per unit time, to represent the coalescence rates. The linear fitting data reveal that K of PVDF/HDPE has the largest value of 29.8 compared to 16.9 for PVDF/PS and 4.7 for the HDPE/PS blends. These results mean the ability of PVDF/HDPE’s interfacial motion > PVDF/PS > HDPE/PS. Therefore, for the PVDF/PS/HDPE blends, during annealing, the fast coalescence rates of the PVDF/HDPE domains cause the overall PVDF/HDPE interfacial area to decrease, which has been demonstrated in other research.^33,35–37 This signifies a movement of the PVDF/HDPE interface, which can trap PS droplets located in the HDPE phase while moving, increasing the number of PS droplets at the PVDF/HDPE interface. Since the PS droplets are more thermodynamically stable when located at the PVDF/HDPE interface, more and more PS droplets will be trapped on the interface during annealing. Because of a higher interface area, this trapping effect is significant at initial annealing. With the decrease of the PVDF/HDPE interface, the trapped PS droplets on the interface are forced to come into contact and coalesce, thus resulting in a size increase of the PS droplets. This morphology evolution is illustrated in Fig. 11. Moreover, because HDPE/PS has an inferior interfacial motion ability and combining the above analysis, this is why the size of the PS droplets in the HDPE regions barely increases during annealing (shown in Fig. 10).

Fig. 11 Schematic map showing the morphology evolution of the PVDF/PS/HDPE 44/4/52 vol% blend during annealing at 200 °C. The gray region represents PVDF, the red region represents HDPE and the black droplets are PS. The white arrows in part (a) indicate the movement of the PVDF/HDPE interface, (b) the PS droplets in the HDPE phase are trapped on the PVDF/HDPE interface due to the movement of the PVDF/HDPE interface and (c) the trapped PS droplets on the interface are forced to come into contact and coalesce, caused by the decrease of the PVDF/HDPE interface.

The coalescence behavior of the PS layer on the PVDF/HDPE interface during melt annealing

With the concentration of the PS phase increasing, the coalescence of the PS phases on the PVDF/HDPE interface leads to the formation of a tri-continuous morphology.

In this part, the coalescence behavior of the PS interfacial layer in ternary PVDF/PS/HDPE is studied during annealing. Fig. 12a illustrates the tri-continuous structure of the PVDF/PS/HDPE blend. It shows that most of the PS phase has formed a continuous layer located at the PVDF/HDPE interface. There are still some PS droplets embedded in the HDPE regions which are caused by the lower interfacial tension of HDPE/PS than that of PVDF/PS. Also a minority of PVDF/PS core–shell dispersed droplets (shown by the black circle in Fig. 12) can be found in the HDPE regions. During annealing, these core–shell droplets tend to be trapped by the large region phases because of the movement of the phase interface, thus resulting in the increase of phase size. Fig. 12f shows the sample after 30 min annealing and the thickness of the PS layer has increased from 5.3 ± 0.8 μm before annealing to 14.2 ± 1.2 μm after 30 min annealing.

Fig. 12 Morphology evolution of PVDF/PS/HDPE 44/15/41 vol% blend as a function of annealing time (a) 0 min, (b) 5 min, (c) 10 min, (d) 15 min, (e) 20 min and (f) 30 min at 200 °C using OM.

Quantification of the thickness of the PS layer as a function of annealing time is shown in Fig. 13. The growth rate for the thickness of the PS layer shows a clear linear relationship with annealing time with a relative value of 0.3 μm min⁻¹. The quantitative linear growth of the phase thickness with time for the interfacial layer in this tri-continuous ternary blend suggests a similar mechanism to the co-continuous binary blend systems.³⁸ Yuan et al.¹⁵ proposed that the driving force for the coarsening process under static annealing is a result of capillary pressure and showed that the linear coarsening growth rate is dependent on the interfacial tension between phases, the viscosity ratio of the phases and the zero-shear viscosity of the matrix. The interfacial layer growth rate in our tri-continuous system however, is significantly lower than the coarsening rates in the binary co-continuous case (shown in Fig. 10). The reason for the very low growth rate in the completely wet tri-continuous ternary case is due to the fact that the confinement effect of the PS layer on the movement between the PVDF and HDPE interface. The PS phase has a very large zero shear viscosity of 4173.0 Pa s compared with 377.2 Pa s for PVDF and 585.3 Pa s for HDPE and the PS phase located at the PVDF/HDPE interface will tune the interfacial tension of the phase interfaces which makes for a more thermodynamically stable structure.

Fig. 13 The thickness of the PS layer in the PVDF/PS/HDPE 44/15/41 vol% blend as a function of annealing time.

Conclusions

In this work, the morphology development of PVDF/PS/HDPE ternary blends after melt mixing and during quiescent annealing is studied. The Harkin’s spreading theory indicates that the PS phase is spread over the PVDF/HDPE interface, forming a complete wetting structure. It has been found that the PS phase can form a continuous sheath structure at the PVDF/HDPE interface when its concentration reaches 11 vol%. With the PS concentration increasing, the PS phase morphology in the ternary blends experiences several distinguished stages: when the PS concentration is less than 4 vol%, the PS phase locates at the PVDF and HDPE interface as dispersed droplets; when the PS concentration increases to 7 vol%, the PS phase forms an incomplete interface between PVDF and HDPE; when the PS concentration reaches 10 vol%, most of the PS has clearly and spontaneously structured itself at the HDPE/PMMA interface forming a uniform layer. The self-assembly behavior of the PS droplets on the PVDF/HDPE interface during annealing is caused by an interface trap effect induced by the decrease of the interface area. This can be well understood from Harkin’s spreading theory and the coarsening of the PVDF/HDPE co-continuous structure. The interfacial coalescence of the PS layer reveals that the thickness of the PS layer has increased from 5.3 ± 0.8 μm before annealing to 14.2 ± 1.2 μm after 30 min annealing. The growth rate for the thickness of the PS layer shows a lower value of 0.3 μm min⁻¹ which is caused by the confinement effect of the PS layer on the movement between the PVDF and HDPE interface.

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (contract no. 51273219, 51573106 and 5142106), the National Key Basic Research Program of China (973 Program, no. 2012CB025902), the Fundamental Research Funds for the Central Universities (no. 2013SCU04A03) and the Foundation of State Key Laboratory of Polymer Materials Engineering (grant no. sklpme2014-3-12).

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