Anomalous phase separation behavior in dynamically asymmetric LCST polymer blends

Abstract

The interplay of thermodynamic forces and self-generated stresses induced in different compositions, and at different quench depths on the phase behavior of dynamically asymmetric PS/PVME blends are studied. The thermodynamic phase diagram is obtained from dynamic temperature sweep experiments. Phase contrast optical microscopy and rheological measurements including linear viscoelastic behavior and the stress growth behavior are employed to investigate the time evolution of the different phase-separating morphologies. At an intermediate quench depth of 14 °C, in addition to thermodynamically controlled phase separation mechanisms (nucleation and growth, NG, and spinodal decomposition, SD), three different kinds of phase separation behavior are induced by transient gel formation due to self-induced stresses in the early stage of phase separation: (i) conventional viscoelastic phase separation (VPS), (ii) nucleation of aggregate-like PS-rich phase and subsequent formation of a percolated network by coalescence, and (iii) nucleation of an aggregate-like PS-rich phase while the dispersed-matrix morphology is preserved in the later stages of phase separation. While it is generally accepted that VPS occurs at deep quench depths, we observe the VPS mechanism at shallow quench depths which is attributed to dynamic heterogeneity in the phase-separated domains. A dynamic phase diagram which shows the effect of dynamic asymmetry on phase behavior is proposed.

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1. Introduction

Phase separation in complex fluids such as polymers, surfactants, colloids, and biological materials has been the subject of several experimental, theoretical, and numerical studies in recent years.^1–7 Understanding the phase separation mechanisms and controlling the morphological evolution are very important to design various advanced materials with novel mechanical, optical, electrical, and transport properties.^1–4 Phase separation mechanisms have traditionally been classified into (i) nucleation and growth, NG, and (ii) spinodal decomposition, SD. Nucleation and growth are associated with metastability, implying the existence of an energy barrier and the occurrence of large composition fluctuations which results in spherical domains. Spinodal decomposition refers to phase separation under conditions in which the energy barrier is negligible, so even small fluctuations in composition grow and tend to form interconnected phases.⁸

Tanaka^3,9–11 found a new and quite unusual phase separation in dynamically asymmetric mixtures, called viscoelastic phase separation, VPS. Dynamic asymmetry can be induced by either a large size difference or a large difference in glass transition temperature (T_g) between the components of a mixture. The former often exists in polymer solutions, colloidal suspensions, protein solutions, and the latter in polymer blends. In addition to the initial diffusive and the final hydrodynamic regimes, which are known in normal phase separation, NPS (NG and SD), there exists an intermediate viscoelastic regime, where self-generated stresses in the more elastic phase during phase separation is built up. This leads to the induction of a percolating network of the more elastic phase even if it is the minor phase. This percolated network structure coarsens in time via a volume shrinking process and eventually breaks into disconnected domains that can be considered as a disintegration process or phase inversion, as mentioned by Tanaka.¹⁰ The induction of the network structure, volume shrinking process and phase inversion behavior are characteristic features of VPS that cannot be observed in the normal phase separation mechanisms. In addition to the VPS in dynamically asymmetric mixtures, Tanaka reported new phase separation mechanisms such as fracture phase separation (FPS)¹¹ and moving droplet phase (MDP)¹² indicating the complexity of phase behavior of dynamically asymmetric blends.

Recently, there have been increasing numbers of studies on VPS, which mainly focus on morphological development including percolating network formation, volume shrinking process and phase inversion,^9–11,13 the effect of shear on VPS,¹⁴ extending the classical phase separation models for dynamically asymmetric blends,^15,16 and the universality of viscoelastic phase separation in dynamically asymmetric mixtures.¹⁰

Thermodynamic forces (concentration fluctuations) and self-generated stresses induced by dynamic asymmetry are strongly dependant on composition and quench depth.^11,13,17 Predicting the interplay between thermodynamics and self-generated stresses in different compositions and different quench depths, that governs the phase behavior, needs fundamental studies. Most of the experimental and theoretical studies on VPS are carried out for polymer solutions in which dynamic asymmetry is originated from a large size difference.^9,11–14 There are few studies on VPS for polymer blends^10,17 in which dynamic asymmetry is induced by a large difference in T_g. Tanaka observed induction of network patterns in polymer solutions by two different VPS mechanisms,¹⁸ formation of a rather uniform ‘microscopic’ transient gel in the initial stage of phase separation, or formation and aggregation of polymer-rich droplets which leads to the development of a ‘mesoscopic’ network structure. The former is the well-known viscoelastic phase separation which has been discussed extensively in the literature; however, the latter mechanism and its differences with the former one are nearly unexplored.

The mixture of PS and PVME is one of the well-studied systems, which was believed for decades that goes through the normal phase separation with LCST behavior. However, for the first time Tanaka observed that the phase separation of PS/PVME blends takes place by the VPS mechanism at a quench depth of about 20 °C above LCST.¹⁰ Tanaka argued that due to a large difference in the glass transition temperature between PS and PVME (about 125 °C), deep quench leads to a significant difference in the viscoelastic properties of coexisting phases, and thus, VPS controls the phase behavior. In our previous works,^17,19 it was shown that there is a region between NG and SD where the VPS mechanism occurs. Classical theories such as Flory–Huggins and Fredrickson–Larson^17,20 ones fairly distinguish the NG mechanism from the SD one. Since, they cannot predict the VPS mechanism for dynamically asymmetric blends.^17,19

Rheology is a highly sensitive tool to assess morphological changes and has been used to study the correlation between phase-separated morphologies and corresponding rheological behaviors, which involves complex combinations of kinetics, thermodynamics and viscoelasticity. Rheological measurements can provide indirect information about phase-separating morphologies, and thus, phase separation mechanism.^17,19–24

The main objective of this paper is to study the interplay of thermodynamic forces and self-generated stresses induced by dynamic asymmetry in different compositions and quench depths, and its effect on the phase behavior of PS/PVME blend. Most of the experimental and theoretical studies on VPS have been carried out for polymer solutions and colloids in which dynamic asymmetry is originated from a large size difference.^9,11–14 A few studies on VPS in polymer blends proposed that the dynamic asymmetry is induced by a large difference in T_g at deep quench depth.¹⁰ However, we observe VPS mechanism at very shallow quench depth, which needs to be theoretically explained. We also present two new phase separation behaviors (in addition to NG, SD and VPS) due to the dynamic asymmetry of PS/PVME which have not been reported to date: (i) nucleation of aggregate-like PS-rich phase and subsequent formation of percolated network by coalescence, and (ii) nucleation of aggregate-like PS-rich phase while the disperse-matrix morphology is preserved during phase separation. Therefore, it seems that there is a similarity between VPS mechanism in colloids and polymer. Finally for the first time, a dynamic phase diagram which includes the effect of dynamic asymmetry on phase behavior is proposed for the PS/PVME blend in this work.

2. Experimental section

2.1. Materials

A commercial grade of PS (polystyrene) supplied by Tabriz Petrochemical Co. (GPPS grade 1460), and PVME (polyvinyl methyl ether), Lutonal M40, supplied by BASF Co., were used in this study. The basic characteristics of the polymers are listed in Table 1. Considering the chemical sensitivity of PVME, utmost cares were taken to prevent its oxidation. This can also be ensured by a simple visual observation of the blend; the sample should look transparent with a slight yellowish color.²² Thermal gravimetric analysis (TGA) was also performed on PVME using Perkin-Elmer Pyris1 TGA system to be sure about its thermal stability during morphological and rheological analysis.

Table 1 Characterization of PS and PVME used in this study

	Mw (g mol^−1)	Mn (g mol^−1)	Tg (°C)	Supplier
PS	340 000	130 000	95	Tabriz Petrochemical Co.
PVME	110 000	64 000	−32	BASF

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2.2. Sample preparation

The PS/PVME blends were prepared by continuous mechanical mixing of the components in toluene. A small amount of (0.05 wt%) antioxidant (Irganox 1010, Ciba-Geigy Group) was added to the mixture to prevent the thermal oxidation during preparation and measurements. It should be noted that the added antioxidant does not change the glass transition temperature of the blend nor the temperature of the thermally induced phase separation.²⁵

The solvent was evaporated slowly at room temperature for 1 week. Then, the samples were put in a vacuum oven for 4 days at 45 °C. The vacuum was applied slowly to prevent any possible bubble formation. Finally, the full vacuum was applied at 70 °C for 24 h in order to remove the residual solvent remaining in the samples.^22,23 Weighting the samples and checking the value to match asymptotically with the total weight of the components, ensured us the complete evaporation of solvent.

2.3. Rheological measurements

All the rheological measurements were performed by a stress/strain controlled rheometer, UDS 200, Paar Physica. The experiments were carried out using parallel plates geometry with 25 mm diameter and 1 mm gap. All the experiments were carried out under a continuous flow of nitrogen gas around the sample pan, and a fresh sample was used for each measurement.

The following small amplitude oscillatory shear experiments were carried out in the linear viscoelastic region, as was verified by preliminary amplitude sweep tests: (i) isochronal dynamic temperature sweep was carried out to detect the onset of the phase separation by measuring storage and loss moduli at a fixed frequency of 0.05 Hz (which was found to be small enough to lie in the terminal region in agreement with literature data^22,23), and a uniform heating rate (0.5 °C min⁻¹)^7,17,23,26 at a certain strain (1%). (ii) Dynamic time sweep experiments were performed in the two-phase region at a fixed frequency of 1 rad s⁻¹ and a given strain of 5% to investigate the phase separation kinetics. According to the Kim et al. rheological measurements with these conditions can sensitively detect the early stage of phase separation.²⁴ (iii) Isothermal dynamic frequency sweep experiments were carried out at strain of 1% and temperature of 110 °C to study the linear viscoelastic properties. For samples at the two phase region, measurements were performed after various preheat times at 110 °C to induce desired phase-separated morphologies.

To study stress growth behavior of PS/PVME blends, start-up of simple shear flow were applied on samples at shear rate of 0.2 s⁻¹ and temperature of 110 °C. For samples at the two-phase region, measurements were carried out after various preheat times at 110 °C to have desired phase separated morphologies.

2.4. Optical microscopy (OM)

Samples for optical microscopy were prepared similarly. However, the thickness of samples for OM was approximately 25–30 μm. This is considerably thicker than the critical thickness (5–8 μm thin films) found by Reich and Cohen²⁷ above which, there is no dependence of the phase behavior on the film thickness and substrate. The phase contrast optical microscopy (Leica DMRX) was used to investigate the morphological changes at different quench depths. Samples were placed in a hot stage sample holder (Linkam LTS350) which was controlled by the hot stage controller (Linkam CI 94). Fresh nitrogen gas was circulated in the heating chamber of OM to avoid any possible thermal degradation. A CCD camera mounted directly on the microscope was used to record the evolution of blends structure in real time.

3. Results and discussions

3.1. Phase diagram and morphological observation

To obtain the phase diagram of PS/PVME blends, isochronal dynamic temperature sweep test, which has become one of the most reliable and widely used methods^{7,17,22,23,26,28} was carried out for various compositions. The typical variation of elastic (G′) and loss moduli (G′′) versus temperature for the 40/60 PS/PVME blend sample is shown in the Fig. 1a. The temperature where G′ starts to increase in the temperature sweep curve is assigned as the binodal temperature for the corresponding composition.²⁸ Obtaining the phase separation temperature of PS/PVME blend by rheological measurements has been explained comprehensively in our previous works^17,19,23 and the references therein.

Fig. 1 (a) Temperature dependence of storage modulus, G′, and loss modulus, G′′, for the PS/PVME 40/60 blend at frequency f = 0.05 Hz, strain 1%, and a heating rate of 0.5 °C min⁻¹. (b) Determination of spinodal temperature as described in the text for PS/PVME 40/60 blend. (c) Phase diagram of studied PS/PVME blend determined from rheological measurements: binodal temperature (○), spinodal temperature (●). Also, the average T_g's of the blend is shown (□). Solid and dashed lines are guides to the eye.

Ajji and Choplin²⁰ extended the Fredrickson and Larson's theory²⁹ for block copolymer melts near the order–disorder transition to determine the concentration fluctuation contribution to the shear stress for near-critical polymer mixtures. Kapnistos et al.²² quantified this effect and showed that spinodal curve can be obtained from rheological measurements. They found the following scaling for polymer mixtures in the vicinity of phase separation temperature:

This scaling has been successfully applied to LCST and UCST polymer blends by Kapnistos et al.²² and Vlassopoulos et al.,³⁰ respectively.

Fig. 1b shows typical representation of ((G′′)²/(G′T))^2/3 versus 1/T data for the 40/60 blend. The slop of curve in the linear region, which is corresponding to the one-phase region near the phase separation temperature, is taken and the inverse of the intercept with the 1/T axis gives the reciprocal of the spinodal temperature, T_s.

Fig. 1c shows the obtained thermodynamic phase diagram of PS/PVME blend which exhibits a lower critical solution temperature (LCST) with the critical point located at temperature of about T_c ≈ 96 °C and weight fraction of PS/PVME 20/80. The calorimetric glass transition temperature (T_g), reported in ref. 31, is also shown in the phase diagram.

Increasing heating rate²² or frequency³² of rheological measurements could lead to higher measured phase separation temperatures. However, low heating rates (below 0.5 °C min⁻¹) and low frequencies^{7,17,22,23,26,33,34} (as used in this work) provide reliable phase diagram compared to that obtained by static methods, such as laser light transmission,³³ DSC,^23,33 turbidity temperature measurements^23,33,34 and optical micrographs of morphology development.¹⁷ The polydispersity of polymers can also change the phase separation temperature.^35–37 Increase in the polydispersity index enlarges the phase separation area and shifts the LCST to lower temperatures. The polydispersity effect weakens with the increase of molecular weight. Li et al.³⁷ observed that in PS/PVME blend polydispersity did not change the composition of the critical blend, while the phase separation temperature of samples with monodispersed PS was at most 3 °C higher than the ones with highly polydispersed PS.

The optical microscopy observations during the phase separation of PS/PVME blends shown in Fig. 2 were carried out at various regions of the phase diagram at 110 °C that corresponds to a quench depth (distance from the critical temperature) of ΔT = 14 °C (ΔT = T − T_c where T and T_c denote the measuring and the critical temperatures, respectively). The T_g − T_b, where T_b is the binodal temperature, cannot be considered as quench depth in the studied system since the blends T_g is far below the phases separation temperature, or in other words, all samples are in non-glassy state.

Fig. 2 Optical micrographs indicating time evolution of the phase-separating morphologies for PS/PVME blends with different compositions at 110 °C: (a) 40/60: (a₁) 6 h, (a₂) 7 h, (a₃) 8 h, (a₄) 10 h; (b) 30/70: (b₁) 2 h, (b₂) 4 h, (b₃) 7 h, (b₄) 10 h; (c) 15/85: (c₁) 2 h, (c₂) 4 h, (c₃) 6 h, (c₄) 9 h; (d) 10/90: (d₁) 2 h, (d₂) 3 h, (d₃) 4 h, (d₄) 5 h; (e) 5/95: (e₁) 1 h, (e₂) 2 h, (e₃) 3 h, (e₄) 5 h; (f) 3.5/96.5: (f₁) 2 h, (f₂) 4 h, (f₃) 5 h, (f₄) 6 h. All the scale bars correspond to 30 μm.

For the PS/PVME 40/60 blend, spherical PVME-rich domains nucleate and grow up in size (Fig. 2a), which indicates that it is located in the PS-rich metastable region of the phase diagram at the measuring temperature.

For the 30/70 blend, a highly interconnected structure is developed in the early stages of phase separation as a characteristic of spinodal decomposition (Fig. 2b). A considerable free energy is stored in the co-continuous morphology due to the presence of highly curved interface between the two phases, which is not in thermodynamic equilibrium and will break up into droplet-matrix morphology at later stages. For the 30/70 blend after about 3 h, the interconnected structure breaks up into droplet-matrix morphology. At longer times, droplets grow dramatically with a broad size distribution. Similar behavior is observed for 20/80 blend in which SD mechanism controls the phase behavior.

For the PS/PVME 15/85 blend, PVME-rich major phase nucleates in the minor PS-rich phase in the early stages of phase separation and grows in size (Fig. 2c). The PS-rich matrix becomes network like with the growth of PVME-rich phase and at longer times, phase inversion occurs, leading to the break-up of PS-rich network into disconnected domains in PVME-rich matrix. This behavior is a characteristic of VPS that takes place in mixtures having largely different viscoelastic properties known as dynamically asymmetric mixtures.¹⁰ In dynamically asymmetric mixtures, thermodynamically favored growth of concentration fluctuations occurs in the early stage. The enhancement of concentration fluctuations makes the PS-rich phase much more elastic than the PVME-rich one, which increases the dynamic asymmetry. When the volume deformation rate induced by phase separation becomes faster than the stress relaxation rate, the elastic stresses are built up in the PS-rich phase (the more elastic minor phase). The elastic stresses prevent rapid growth of composition fluctuations leading to formation of a network of PS molecules (transient gel).¹³ This stage is called the frozen period, which is a unique feature of viscoelastic phase separation. In dynamically asymmetric mixtures, domain growth induces elastic stresses in the higher viscoelastic component during phase separation. Therefore, the resultant stresses mainly cancel the stress originating from the surface tension thereby preserving the continuity of more elastic phase even when it is in the minority.^10,38 In the late stage of VPS when the volume of each phase approaches the thermodynamically favorable state, domain growth slows down that weakens the resulting stress fields. Consequently, the interfacial force starts to play a dominant role competing with the elastic forces. Thus, the network structure becomes unstable in the reduced stress fields, and the interconnectivity of minor phase breaks into droplet-matrix morphology that is the thermodynamically favorable due to a lower interfacial energy.

Decrease in the volume fraction of the PS-rich phase in PS/PVME 15/85 blend with time can be observed in the optical micrographs. Since the phase separation pattern is essentially two dimensional, we can obtain the volume fraction from the area fraction.¹¹ The PS-rich phase covers almost 80% of the total picture in the early stages of phase separation. However, volume fraction of PS-rich phase decreases to about 20% in the late stage of phase separation, which is due to the volume shrinking process of the PS-rich phase by the diffusional transport of PVME from the PS-rich phase to the PVME-rich one through the phase boundary.¹⁰ This result violates the well-accepted opinion on the late stage of phase separation, which states that the two phases are almost in equilibrium with constant volume fraction after the formation of a sharp interface. Volume shrinking process is a unique characteristic of VPS which is very similar to the bulk phase separation process of a chemical gel.¹⁰

It should be mentioned that the initial stage of phase separation for the samples phase separating by VPS is similar to SD, where the osmotic force, Π, causes the diffusional motion of the molecules and the usual growth of concentration fluctuations. In the dynamically asymmetric mixtures, such thermodynamic diffusion induces the stress, σ, in the component with the higher relaxation time. According to the dynamic equation, osmotic and elastic forces have the opposite directions with each other (Π − σ):¹⁶

where v_p and v_s are the average velocity of the polymer (here the component with higher T_g) and solvent (here the component with lower T_g), respectively, v is the average velocity of the mixture, ρ₀ is the density, η is the viscosity and ζ is the friction constant. For the sample in the SD region, the strong concentration fluctuations cancel the self-generated stresses and phase separation proceeds in the thermodynamic driven way. However, the initial growth of concentration fluctuations is significantly suppressed for samples in VPS region leading to formation of transient gel.

An unusual phase behavior is observed for the 10/90 blend sample, where aggregate-like PS-rich phase nucleates in the early stages of phase separation (Fig. 2d). It seems that the 10/90 blend is located in a transition region where the interplay between viscoelasticity and thermodynamics, as formulated in eqn (2), determines the phase behavior. According to the viscoelastic phase separation theory, the self-induced stresses decrease considerably as the volume fraction of the slower component decreases¹⁶ leading to a weaker transient gel in the early stage of phase separation. In other words, phase separation in the early stage of 10/90 blend tends to proceed via VPS mechanism by formation of a transient gel of PS molecules which is weak due to the low concentration of PS-rich phase. With phase separation thermodynamics overcomes the viscoelasticity and NG controls the phase behavior. However, spherical shape cannot be consequently recovered, because the self-generated stresses extremely slow down the shape relaxation process. This is consistent with numerical simulations showing that noncircular dispersed phase nucleates at low concentrations of the slow component in the dynamically asymmetric mixtures.³⁸ Supplementary evidences will be provided in Rheology section. At later stages, aggregates coalesce and a thin percolating network of the minor PS-rich phase is formed. Network structure coarsens and the length scale of percolated network increases with phase separation which breaks up into disconnected PS-rich domains in the late stage of phase separation. The network formation of minor phase and the phase inversion phenomena are characteristics of VPS mechanism.^3,10,11

Notice that the VPS behavior of 10/90 blend is essentially different from the 15/85 one. In the former, VPS is induced by the coalescence of minor phase, while in the latter VPS is directly originated from a transient gel in the early stage of phase separation; thus, we will call them “coalescence induced viscoelastic phase separation” (C-VPS) and “transient gel induced viscoelastic phase separation” (TG-VPS), respectively. The TG-VSP is the well-known viscoelastic phase separation which has been studied extensively in the literature.^{9–11,13–16} However, C-VPS mechanism and its differences from TG-VPS one are unexplored.

In addition to the difference in the initial mechanism of network structure formation, the pattern evolution during the phase separation is also different in the two types of VPS mechanisms as seen in optical micrographs. For C-VPS the volume fraction of the PS-rich phase is nearly constant, which is similar to the normal phase separation after the formation of sharp interface. Coarsening proceeds by expelling the PVME-rich regions trapped in the PS-rich strands to minimize the total free energy. For the network to thicken, however, some thin (weak) stretched parts of the network breaks up. According to the simulation results,³⁹ the stress is concentrated selectively on the thinner parts, which are in a high-energy state, and eventually breaks them up. Consequently, the network structure relaxes into a lower metastable energy state. In the case of TG-VPS, however, the volume fraction of PS-rich phase decreases steeply by diffusion of mainly PVME molecules from the PS-rich phase to the PVME-rich one, which results in the growth of the PVME-rich domains and formation of a thin percolating network of the PS-rich phase.

The importance of the self-generated stresses is clear as the backbone of network is stretched before their breakup in both C-VPS and TG-VPS [Fig. 2c and d]. Note that the branches of network meet at a junction with an angle about 120° since the local mechanical force balance condition should be satisfied in this 2D phase separation (as mentioned the thickness of sample is much smaller than the scale of strands during the phase separation).⁴⁰

Fig. 2e shows morphology development for the 5/95 blend where the aggregate-like PS-rich phase nucleates in the early stages of phase separation. This indicates the similarity of early stage of phase separation between the 5/95 and 10/90 blends. Aggregate-like structure transforms to spheres under the interfacial tension action in the late stage of phase separation. Due to the lower volume fraction of the PS-rich phase for the 5/95 blend, interaction of aggregates does not take place to form a network structure like 10/90 blend. According to the lever rule,¹⁷ the volume fraction of PS-rich dispersed phase is about 8% and 16% in 5/95 and 10/90 blends, respectively. In binary polymer blends, with the morphology of monodisperse spherical droplets in the matrix, the percolation threshold is about φ = 0.156 and is higher for a polydisperse system.⁴¹ The morphology development of the 5/95 blend, in which chain-like aggregates form during the phase separation with preserving disperse-matrix morphology, is different from the normal NG mechanism (NNG) where droplets nucleate and grow in spherical shape. We call the phase separation mechanism of 5/95 blend “aggregating NG” (ANG). Since the ANG is also originated from self-generated stresses in the more elastic phase, it can be considered as a VPS mechanism. When the weight fraction of PS is further decreased to 3.5%, conventional NG mechanism, (NNG), is observed (Fig. 2f). PS-rich droplets nucleate in the PVME-rich matrix and grow in spherical shape without formation of an aggregate structure.

3.2. Rheology

3.2.1. Linear viscoelastic behavior. Fig. 3 shows dynamic moduli, G′ and G′′, and tan δ as a function of frequency at different phase separation times for PS/PVME blends. tan δ as a function of frequency can be used as a tool to differentiate the liquid-like behavior from solid-like one. At low frequencies, the slope of tan δ curve against frequency is negative for the systems with liquid-like behavior and positive for the solid-like ones.⁴²

Fig. 3 Dynamic moduli and tan δ for PS/PVME blends as a function of frequency at different phase separation times at 110 °C with the compositions: (a) 40/60, (b) 30/70, (c) 15/85, (d) 10/90, (e) 5/95, and (f) 3.5/96.5.

For the PS/PVME 40/60 blend which is located in PS-rich metastable region, G′ decreases with time (corresponding to increasing the droplet size) (Fig. 3a) and dynamic moduli exhibits a power law behavior at low frequencies (G′ ∝ ωⁿ, G′′ ∝ ω^m) in which m and n increase with phase separation. For PS/PVME 3.5/96.5 blend which is located at PVME-rich metastable region of phase diagram, in contrast to the 40/60 blend, morphology evolution increases G′ at low frequencies with a terminal behavior, G′ ∝ ω² and G′′ ∝ ω¹ (Fig. 3f). The loss modulus, G′′, is greater than the storage modulus, G′, over the whole frequency range for both compositions and the slope of tan δ plots at low frequencies is negative at different phase separation times indicating a fluid-like behavior for samples with droplet-matrix phase separation (i.e. 3.5/96.5 and 40/60 blends), regardless of matrix phase (PS-rich and PVME-rich).

As explained in our previous work,¹⁷ the observed behavior of respectively decreasing and increasing G′ at low frequencies by phase separation time for 40/60 and 3.5/96.5 blends can be explained in terms of experimentally accessible frequency range. For 3.5/96.5 blend, G′′ nearly does not change with phase separation since PVME, which exhibits viscous behavior at 110 °C, dominates the loss behavior of the blend.

For the PS/PVME 30/70 blend (Fig. 3b) after 5 min from the onset of phase separation, G′ is higher than G′′ at low frequencies indicating rheologically solid-like behavior with weak dependence of moduli on ω (the scaling behavior of approximately G′ ∝ ω^0.4 and G′′ ∝ ω^0.3). The tan δ versus ω plot indicates that in the early stages of phase separation (i.e. samples with 5 and 20 min annealing), the slope of curve in the low frequency zone is positive indicating a solid-like behavior. This can be attributed to the interconnections of the strands of coexisting phases that can behave as strong anchor point to hinder the flow. At later stages, the slopes of curves become negative indicating dominance of liquid-like behavior. The large deviation from terminal behavior in the early stages of phase separation can be attributed to the highly interconnected structure and high interfacial area induced by spinodal decomposition, which gives rise to dynamic moduli at low frequencies.

According to the Doi–Ohta theory,⁴³ the elastic modulus is proportional to the interfacial area for co-continuous morphology;⁴⁴ thus, high interfacial area induced in the early stages of SD leads to a large increase in the elastic modulus. In addition, interconnectivity in a network structure gives rise to the elastic modulus according to the rubber elasticity theory.⁸ Dynamic moduli during SD decreases with time and its dependence on frequency increases as was observed by Polios et al.³¹ The change of G′ by phase separation time is more noticeable than G′′ due to the fact that the stress induced by the phase separation is mostly of elastic origin.²²

The interconnected structure of SD could be assumed as a physical network structure.⁴⁵ Since the elastic behavior of the network is an increasing function of the number of interconnections per unit volume, which decreases during the coarsening process, G′ decreases by SD phase separation. In addition, coarsening of the structure decreases the interfacial area, and thus, the storage modulus. After about 3 h from the onset of SD phase separation, morphology evolution leads to breakup of co-continuous structure into droplet-matrix morphology, thereafter the decrease of G′ during the phase separation is only a consequence of interfacial area reduction.

For the PS/PVME 15/85 blend in which TG-VPS controls the phase behavior, it can be seen that in the early stages of phase separation, G′ is higher than G′′ at low frequencies with weak dependence on ω and the scaling behavior of approximately G′ ∝ ω^0.23 and G′′ ∝ ω^0.4 (Fig. 3c). The tan δ versus ω plot shows that in early stages of phase separation (i.e. samples with 5 and 20 min annealing), the slope at law frequency region is positive indicating a solid-like behavior. Such solid-like behavior confirms the formation of PS-rich transient gel in the early stage of VPS that hinders the flow. Storage modulus increases in low frequency region with phase separation time up to 20 min after the onset of phase separation due to the concentration fluctuations (will be discussed in the next section). However, due to the volume shrinking process, the network interconnectivity and interfacial area, and thus, storage modulus, decrease by time.

For the PS/PVME 10/90 blend which exhibits C-VPS phase separation mechanism, solid-like behavior, G′ > G′′, is observed in the early stages of phase separation (after 5 min annealing). The dependence of dynamic moduli on ω at low frequencies is weak with the scaling behavior of approximately G′ ∝ ω^0.22 and G′′ ∝ ω^0.7 (Fig. 3d). The tan δ versus ω plot shows a positive slope, and thus solid-like behavior, at law frequency region in the early stages of phase separation. The observed rheological response strongly supports the concept of the formation of transient gel in the early stages of phase separation. It can be seen that the G′ increases with phase separation up to 20 min probably due to the concentration fluctuations (as will be discussed in the next section). At later stages, the transient gel collapses and aggregates of PS-rich phase are formed. Interfacial area and consequently G′ decrease due to the coarsening of phase separated domains by time.

Fig. 3e shows the dynamic moduli as a function of frequency at different phase separation times for PS/PVME 5/95 blend in which ANG controls the phase behavior. At different phase separation times, G′ < G′′ is observed over the whole frequency range and the low frequency slope of tan δ versus ω plot is negative. It can be seen that PS/PVME 5/95 sample after 5 min annealing exhibits a deviation from the terminal behavior with the scaling properties of G′ ∝ ω^1.4 and G′′ ∝ ω^0.92. The deviation confirms the formation of a transient network of PS molecules in the early stages of phase separation. However, this transient network is weaker than the one formed in PS/PVME 10/90 due to the limited connectivity of fewer PS chains. It can be seen that the G′ increases with phase separation up to 1 h probably due to the concentration fluctuations. Aggregate-like structure relaxes to the spherical shape under the interfacial tension action in the late stage of phase separation, and G′ approaches the terminal behavior at low frequencies, G′_{PS/PVME 5/95}(4 h) ∝ ω^1.86. G′′ nearly does not change with phase separation because of the low concentration of PS in the blend.

3.2.2. Kinetics of phase separation by rheology. To investigate the phase separation kinetics under different mechanisms (NG, SD, and VPS), isothermal time sweep experiments were carried out as described in the Experimental section. The results are normalized to steady state value to have a proper comparison among samples as shown in Fig. 4. Time evolution behavior of the storage modulus can provide valuable information on the evolution of the morphological changes over time.

Fig. 4 Time evolution of the storage modulus at frequency of 1 rad s⁻¹ and given strain of 5% strain for PS/PVME blends at temperature of 110 °C.

It can be seen that for the PS/PVME blends, G′ initially increases and after passing through a maximum subsequently decreases consistent with the prediction of time-dependent Ginzburg–Landau (TDGL) theory.²¹ The initial increase is due to the combination effects of enhanced concentration fluctuations and induced interfacial area in the early stages of phase separation.^17,46 In the NG region, critical nuclei are formed by the concentration fluctuations. For the samples in the SD and VPS regions, abrupt growth of concentration fluctuations creates a highly interconnected structure and a transient gel, respectively. At later stages, domains coarsen, the interfacial area per unit volume decreases, and thus, G′ decreases.

It can be seen that the phase separation kinetics of samples phase separating by NG (40/60 and 3.5/96.5 blends) and ANG (5/95 blend), is slower than those phase separating by SD and VPS, because the domain growth in NG region is controlled by the chain diffusion and coalescence process which are much slower than spinodal concentration fluctuations or volume shrinking process.^17,46 The 15/85 blend that exhibits TG-VPS process shows the fastest phase separation kinetics, where G′ dramatically decreases with phase separation time reflecting the fast growth of the PVME-rich domains by volume shrinking process.

These observations are in agreement with the power-law scaling relationship, R ∝ t^m, proposed experimentally and theoretically for domain growth, where R is the characteristic domain size. The exponent m is dependent on the coarsening mechanism which is known to be 1/3, 1 and 1.5 for the NG,^47,48 SD⁴⁹ and TG-VPS¹⁰ mechanisms, respectively. As the C-VPS mechanism for polymer blends is reported for the first time in this work, there is no theory for the prediction of its domain size growth. However, Fig. 4 implies that phase separation kinetics for C-VPS is to some extent slower than SD, m < 1.

Another noticeable parameter in the Fig. 4 is the height of peak which can be used as a measure of the excess energy induced by concentration fluctuations in the early stages of phase separation. As seen, the maximum in the SD is much higher than the ones in the NG region, due to the considerable free energy storage at the interface between the two phases of highly interconnected co-continuous morphology. Therefore, the microstructure is not in the thermodynamic equilibrium and will break up into the droplet-matrix morphology in the late stage. The maximum for the 10/90 sample that exhibits C-VPS behavior is in the order of the one induced by SD. This supports the idea of formation of a transient gel in the early stage of phase separation for 10/90 blend. The 15/85 blend that has TG-VPS behavior exhibits the most pronounced peak with height about 2 times of the samples in the SD and C-VPS regions.

3.2.3. Transient shear flow behavior. In start-up shear flow experiments, a constant shear rate is imposed on a sample that is initially at rest and equilibrium. In the nonlinear regime, the microstructure of samples changes by deformation, and therefore, the measured stress provides indirect information about the morphology. It is known that shear flow can induce mixing or demixing depending on the magnitude of the imposed shear rate.³⁴ However, in this work the stress overshoot in the start-up experiments occurs within the first 20 s of the measurements and the selected shear rate, 0.2 s⁻¹, is too low to affect the phase diagram.³⁴ At such low strains, the effect of phase separation on the morphology is insignificant (mixing/demixing process is negligible), and the observed nonlinear behavior is mainly due to the initial induced morphology.⁵⁰

Fig. 5 shows the results of normalized transient shear stress in start-up shear flow experiments for the PS/PVME blends at different phase separation times. For the 40/60 blend, a stress overshoot typical of nonlinear viscoelastic behavior is observed at small strains, followed by a steady state region (Fig. 5a). The stress overshoot is due to the deformation of PVME-rich droplets into an ellipsoid with the major axis oriented with an angle θ with respect to the flow direction. For small deformations, θ is close to 45°, while for large ones, θ, becomes smaller than 45° and the deformed droplet becomes more oriented in the flow direction.⁵¹ With increasing phase separation time for the 40/60 blend, which corresponds to an increase in droplet size, the magnitude of the stress overshoot increases. This is due to the tendency of larger droplets to be more deformed and then be oriented toward the flow direction.¹⁷

Fig. 5 Normalized stress growth at a shear rate of 0.2 s⁻¹ for the PS/PVME blends at different phase separation times at 110 °C for different compositions: (a) 40/60, (b) 30/70, (c) 15/85, (d) 10/90, (e) 5/95 and (f) 3.5/96.5.

The 30/70 blend sample, located in an unstable region, exhibits a strong stress overshoot in the early stage of phase separation and in contrast to the 40/60 blend sample, the stress overshoot decreases with phase separation (Fig. 5b). The strong overshoot of 30/70 sample in the early stages of phase separation can be attributed to the stretching and/or orientation of highly interconnected structure with a large interfacial area.⁵⁰ According to the Doi–Ohta theory,⁴³ a higher interfacial area induces a larger stress overshoot for co-continuous structure. Therefore, the decrease in the stress overshoot for samples with longer annealing in the spinodal decomposition regime can be explained by the decrease in the interconnectivity and interfacial area due to the coarsening process.

The 15/85 blend exhibits a strong overshoot at the onset of phase separation which decreases with phase separation time (Fig. 5c). The pronounced stress is due to the percolated network structure of the viscoelastic phase-separating sample. According to the dynamic equations derived based on the time dependent Ginzberg–Landau model, the strong overshoot of a percolated network induced during VPS is mainly due to the network deformation under shear. In other words, the PS-rich phase behaves like a percolated gel that mainly supports the applied stress.¹⁴ The volume shrinking of the PS-rich phase during the TG-VPS over time leads to a decrease in the interconnectivity, and thus, the stress overshoot magnitude.

In addition, at different phase separation times the initial overshoot is followed by a shoulder and a slow decay to steady state. Similar behavior is observed in wormlike micelles^52,53 and polymeric bicontinuous microemulsions.⁵⁰ The shoulder can be attributed to the flow induced phase separation⁵⁰ which is not possible due to the low shear rate in this study,³⁴ and/or the loss (relaxation) of orientation.⁵² The decay of stress toward an ultimate steady-state value has been modeled by using a stretched exponential equation:^50,52,53

where α is 2, σ_m is the stress corresponding to the shoulder, σ_p is the ultimate steady-state value and τ is the longest relaxation time. This equation was derived by using a nucleation and one-dimensional growth model in which there is a shear-induced anisotropic growth of a nematic phase from the isotropic phase.⁵² Although this model may not be appropriate in details for our system due to the absence of shear banding, it fits reasonably well the shoulder in the stress growth behavior. As results of fitting, τ is obtained 35, 24 and 22 s for the samples after 5 min, 3 h and 7 h annealing, respectively. The considerably higher value of τ in the early stage of phase separation can be another indication of transient gel formation.

The overshoot of the PS/PVME 10/90 blend which has C-VPS behavior increases with phase separation up to a maximum at about 30 min of phase separation (Fig. 5d). The initial increase is due to the concentration fluctuations which lead to the stronger structure consistent with the linear viscoelastic results. In the later stages, the transient gel collapses and aggregate-like PS-rich phase nucleates, and forms a network of the minor PS-rich phase through coalescence. The development of overshoot observed for this sample by time up to ∼30 min supports the concept of transient gel formation in the early stages of phase separation.

A weak stress overshoot, which varies slightly with phase separation, is observed for PS/PVME 5/95 blend at different phase separation times due to the low concentration of dispersed PS-rich phase (Fig. 5e). The overshoot is slightly larger for the sample after 1 h annealing because of the concentration fluctuations that lead to the stronger structure in agreement with linear viscoelastic results. No stress overshoot can be observed for 3.5/96.5 blend at different phase separation times (Fig. 5f) due to the very low volume fraction of almost undeformable PS-rich droplets in PVME-rich matrix.

Overall, the results demonstrate that the stress growth behavior upon start-up of shear flow similar to the linear viscoelastic one is strongly dependent on the morphology of the sample and correlates well with the evolution of the phase-separating morphologies.

3.3. The effect of quench depth on phase behavior

The effect of quench depth on the phase behavior of PS/PVME blends was also examined in this work by studying (i) a shallower quench (ΔT = 4 °C) and (ii) a deeper quench (ΔT = 29 °C). Accordingly, we propose a complete phase diagram for PS/PVME blend in Fig. 6 including viscoelastic effects.

Fig. 6 The dynamic phase diagram of PS/PVME blends which shows different types of phase separation occurring at each region: (A) NNG, (B) SD, (C) TG-VPS, (D) C-VPS, (E) ANG, and (F) NNG. The blue and yellow colors indicate respectively PS-rich and PVME-rich phases in the typical morphologies shown next to the phase diagram.

In this section, we focus on the quench depth dependence of VPS and the ANG mechanisms which are rarely explored. Fig. 7 and 8 shows the morphology development of PS/PVME blends in C, D, E and, F regions of the obtained phase diagram at two different quench depths.

Fig. 7 Optical micrographs indicating time evolution of the phase-separating morphologies for PS/PVME blends with different compositions at temperature of 100 °C: (a) 15/85: (a₁) 2 h, (a₂) 6 h, (a₃) 7 h, (a₄) 11 h; (b) 10/90: (b₁) 2 h, (b₂) 3 h, (b₃) 7 h, (b₄) 9 h; (c) 5/95: (c₁) 1 h, (c₂) 3 h, (c₃) 8 h, (c₄) 9 h; (d) 3.5/96.5: (d₁) 4 h, (d₂) 6 h, (d₃) 9 h, (d₄) 12 h. All the black scale bars correspond to 30 μm.

Fig. 8 Optical micrographs indicating time evolution of the phase-separating morphologies for PS/PVME blends with different compositions at temperature of 125 °C: (a) 15/85: (a₁) 30 min, (a₂) 1 h, (a₃) 105 min, (a₄) 3 h; (b) 10/90: (b₁) 30 min, (b₂) 1 h, (b₃) 90 min, (b₄) 3 h; (c) 5/95: (c₁) 2 h, (c₂) 4 h, (c₃) 6 h, (c₄) 9 h; (d) 3.5/96.5: (d₁) 45 min, (d₂) 90 min, (d₃) 3 h, (d₄) 9 h. All the black scale bars correspond to 30 μm.

Tanaka argued that VPS occurs at deep quenches where the large composition difference between the two coexisting phases causes a large T_g difference between them.¹⁰ However, TG-VPS and C-VPS take place in shallow quench depth of 4 °C for the 15/85 and 10/90 blends, respectively. According to the phase diagram, the phase-separated PS-rich and PVME-rich phases at this temperature contain 32% PS and 2% PS, respectively. The calorimetric T_g's of PS-rich and PVME-rich phases are also estimated to be −14 °C and −27 °C, respectively, taken from the midpoint of heat capacity change in the DSC curve. Interestingly such a weak dynamic asymmetry (only 13 °C difference in the T_g of the phase separated domains) induces VPS. We attribute the observed phenomena to the dynamic heterogeneity in the PS-rich phase. Traditionally, a single mobility and relaxation time are considered for both components of a miscible blend which implies a single glass-transition for both components. However, recent studies indicate the presence of intrinsic mobility difference for the components in the dynamically asymmetric miscible blends (known as dynamic heterogeneity) which causes a different effective T_g for each component.^54,55 This means that PS and PVME chains in PS-rich phase have different T_g's from the measured calorimetric ones. Therefore, in contrast to a single glass-transition for both components of a miscible blend considered by Tanaka,¹⁰ the effective glass transition temperatures, T_geff, in the phase separated domains should be considered to study the effect of dynamic asymmetry on VPS. T_geff of each component of a miscible blend can be obtained as follows:⁵⁵

T_g1eff(ϕ₁) = T_g2 + (T_g1 − T_g2)[(1 + K₁)ϕ_1eff − (K₁ + K₂)ϕ_1eff² + K₂ϕ_1eff³] (4)

where T_g1eff is the T_geff of polymer 1; T_g1 and T_g2 are the glass transitions of pure polymers 1 and 2, respectively; K₁ and K₂ are −0.707 and 0.462 for PS/PVME blend, respectively;⁵⁵ and ϕ_1eff is the effective local concentration of polymer 1 in the blend which can be obtained from following equation:⁵⁴

ϕ_1eff = ϕ_s + (1 − ϕ_s)ϕ₁ (5)

where ϕ_s is the self-concentration term whose magnitudes for PS and PVME are 0.27 and 0.25, respectively.⁵⁴ Using the above equations, T_geff of PS chains in PS-rich phase is obtained 2 °C which is 16 °C higher than calorimetric T_g of the PS-rich phase. The effective T_g of both components in the PVME-rich phase are nearly equal to the calorimetric T_g, −27 °C, due to the low PS content.⁵⁴ According to the above analysis, the difference between T_g of the PVME chains in the PVME-rich phase (the fast phase) and PS chains in the PS-rich phase (the slow component in the slow phase), which is about 29 °C, can provide the dynamic asymmetry required for VPS. This calculation shows the possibility of VPS mechanism even at shallow quench depths in dynamically asymmetric polymer blends as a result of a large difference in the T_g of the individual components. In other words, the conventional idea that VPS only occurs at deep quench depths may be true for polymer solutions in which dynamic asymmetry is induced by the large size difference between the components of a mixture. As mentioned in the Introduction, there is no study in the literature on the temperature dependence of VPS in polymer blends to compare the results with.

Tanaka observed a transition from VPS to fracture phase separation (FPS) in the polymer solutions with increasing the quench depth.¹¹ FPS can be regarded as a special case of VPS. In FPS, the self-generated stresses during the shrinkage eventually lead to crack formation. The cracks grow with time similar to the mechanical fracture process. However, we have not observed FPS for the PS/PVME blend in the studied range of temperatures in this work.

As seen in optical micrographs, volume shrinking increases sharply for the TG-VPS mechanism by increasing the temperature due to the stronger thermodynamic driving force for the phase separation under deep quench. The volume shrinking dynamics during phase separation, (ϕ − ϕ_eq.)/(ϕ₀ − ϕ_eq.),¹⁰ is plotted against the phase separation time t in Fig. 9a for 15/85 blend at different quench depths. Here ϕ_eq. and ϕ₀ are the initial and the final equilibrium values of the volume (area) fraction, ϕ, of the PS-rich phase at time t respectively, which is estimated by image analysis. Since the phase separation pattern is essentially two dimensional, we can obtain the volume fraction from the area fraction.¹⁰

Fig. 9 (a) Volume shrinking kinetics of PS/PVME 15/85 sample, the inset shows characteristic time of the volume shrinking (τ) as a function of phase separation temperature (T) for PS/PVME 15/85 sample. The continuous lines show the exponential fitting of data. (b) Phase inversion time as a function of phase separation temperature (T).

The curves can be divided into two regimes: the elastic regime in the early stages of phase separation, and the final hydrodynamic regime in the late stage. Only in the elastic regime the volume fraction steeply decreases with time. As seen, the volume shrinking dynamic is strongly temperature dependent, and the PS-rich volume fraction sharply decreases with time at high quench depth. The change in volume fraction can be fitted by (ϕ − ϕ_eq.)/(ϕ₀ − ϕ_eq.) ∝ exp(−t/τ), where τ is the characteristic time of volume shrinking.¹¹ The volume shrinking dynamic becomes faster with increasing temperature as seen in the temperature dependence of τ plotted in Fig. 9a inset. Note that the volume shrinkage is negligible in C-VPS mechanism.

The phase inversion (disruption of the network like structure) time obtained from OM for TG-VPS and C-VPS mechanisms at different quench depths are shown in Fig. 9b. The network is persistent for longer times in both C-VPS and TG-VPS at shallower quench depths. The decrease in phase inversion time with increase of temperature can be attributed to the increase of interfacial tension and also the faster kinetics of phase separation with increase of quench depth. According to Helfand and Tagami scaling, α ∝ χ^1/2T (ref. 56) (where α is interfacial tension, χ is Flory–Huggins polymer–polymer interaction parameter and T is the temperature), with increase of quench depth in LCST blends, both T and χ increase, and thus, interfacial tension increases. There is often a competition between self-generated stresses and interfacial tension in the elastic regime of VPS. The self-generated stresses largely cancel the stress originated from the interfacial tension, thereby preserving the continuity of more elastic phase even when it is in the minority.

Fig. 6 and 8 shows that at temperatures higher than 125 °C, ANG disappears. At deeper quench depths, the strong concentration fluctuations cancel the self-generated stresses and phase separation proceeds via thermodynamic driven way (NNG mechanism). At binodal region, spherical PS-rich domains are nucleated and grow in size without formation of chain like aggregates. In general, three different mechanisms are known for coarsening of droplets in phase separating mixtures.

The evaporation–condensation mechanism (EC), or Ostwald ripening. In this mechanism, the bigger droplets grow at the expense of smaller ones by diffusion of material through the continuous phase into the larger droplets driven by the difference in Laplace pressure. This mechanism is also known as Lifshitz–Slyozov–Wagner (LSW) mechanism.⁴⁷

The Brownian-coagulation mechanism (BC), where the droplets move freely without any interaction due to the Brownian motion and coalesce upon collision with each other. This mechanism is also known as Binder–Stauffer (BS) mechanism.⁴⁸

Collision induced collision (CIC) which was proposed by Tanaka.^57,58 There are three different kinds of CIC. Interdroplet collision and the resulting shape relaxation directly induce hydrodynamic flow which leads to another collision (CIC via flow). A collision process causes a strong diffusion field around the resultant droplet which induces strong attractive interactions between the resultant droplet and the surrounding droplets. This leads to the subsequent collisions. In other words, a droplet formed through collision is more susceptible to the subsequent collisions (CIC via diffusion). Moreover, the shape of droplets changes during coalescence, which may result in touching other droplets in the close proximity to induce further collision (geometrical CIC). Both interdroplet and hydrodynamic interactions are ignored in BC and EC mechanisms.

The thermal diffusion coefficient, D₀, of a droplet of radius a in a fluid with viscosity η at temperature T can be expressed as:⁵⁹

where k_B is the Boltzmann constant. Moreover, the time t_D for a particle to diffuse on a distance equal to its radius, a, is equal to:

Optical microscopy shows that the PS-rich droplets grow mainly by coalescence process. Calculations based on eqn (6) and (7) show that the time needed for the PS-rich droplets to move a distance equal to their size is about 10 h at 125 °C, which means that Brownian motion is too slow to affect the coalescence process here. Therefore, CIC mechanism controls coarsening behavior in binodal region as also evidenced by OM observations. It should be noted that when the droplet number density is high, the driving force for initial transportation of droplets and inducing collisions is the gradient of concentration. When two droplets are in close proximity, the concentration gradient is smaller in the interdroplet region. This leads to the formation of iso-concentration lines, which induces a strong attractive interaction between the droplets and accelerates the interdroplet collisions.⁵⁹

3.4. Fractal behavior analysis

It is of particular interest to study the topological characteristics of aggregates and network structures by using the fractal dimension, d_f.⁶⁰ The smaller the d_f, the more porous and less compact the structure will be.⁶¹ In order to have a deeper insight into the structural properties of the observed anomalous phase separation mechanisms, ANG, TG-VPS and C-VPS, we studied the fractal behavior of the phase separating morphologies induced by these mechanisms. The fractal dimensions were estimated based on image analysis of the OM micrographs, using ImageJ software⁶² which has been widely used to calculate the fractal dimension⁶³ by applying the box counting method. Note that a fractal dimension equal to 2 (maximum fractal dimension) in two-dimensional space corresponds to a network that completely spans the matrix space, while a fractal dimension of 1 corresponds to a straight line in 2D space.

Fig. 10 shows the time evolution of two-dimensional d_f. The fractal dimension of the 15/85 blend is very high in the early stages of phase separation, which is due to the continuous and large PS-rich network induced by VPS. Volume shrinking process decreases the compactness of the network with phase separation leading to a large decrease of d_f in the late stage of phase separation.

Fig. 10 Fractal dimension versus phase separation time for the blends containing 5, 10 and, 15% PS at 110 °C.

The d_f of 10/90 blend is small in the early stages of phase separation due to the initial disperse-matrix morphology. However, d_f increases with phase separation due to the formation of aggregates and after passing through a maximum decreases. The maximum is the point that the network structure is formed by coalescence of PS-rich aggregates. The subsequent decrease of d_f indicates coarsening of the network structure. The d_f is small for 5/95 sample at different phase separation times since a network structure does not form during the phase separation. However, with phase separation the aggregate size becomes larger by coalescence up to 30 min from onset of phase separation which corresponds to the maximum in Fig. 10.

As mentioned, the fractal dimension in the samples is calculated from the optical micrographs. Therefore, the length scale of network that is considered in the calculations is in the order of phase separating domains (in the order of ∼0.5 μm). In other words, we believe that the rheological responses, particularly in TG-VPS, C-VPS and ANG, are mainly influenced by molecular level networks at early stages of phase separation which cannot be observed by OM. The molecular network weakens by phase separation, while the phase separating domains grow. Therefore, while the fractal dimension of molecular network after formation in the early stage (30 min) decreases, the fractal dimension of phase separating domains increases up to the maximum in Fig. 10. After the maximum the fractal dimension decreases, because the interfacial energy overcomes the viscoelasticity, and thus, the phase separating domains start to break up.

The fractal nature of the colloidal clusters and interconnected networks commonly displays two types of particle/cluster aggregation behavior:^64,65 (i) diffusion-limited cluster aggregation (DLCA), which results in a fast gelation with rather open network structure (with two-dimensional d_f about 1.45 (ref. 65)); and (ii) reaction-limited cluster aggregation (RLCA), which yields slow aggregation with a more compact and dense structure (with two dimensional d_f about 1.6 (ref. 65)).

The d_f of 15/85 sample in the early stages of phase separation is much higher than the one induced in the RLCA mechanism indicating a very compact network structure. With phase separation, the structure becomes similar to the one induced by DLCA. For the 10/90 blend, aggregate structure induced in the early stages of phase separation is similar to the DLCA one. However, the maximum d_f for the network structure induced in this composition is also higher than the RLCA one. d_f decreases with phase separation and the structure becomes similar to the one induced by DLCA at later stages. The induced aggregates in 5/95 blend (the maximum point) has a structure similar to the one induced by RLCA.

It should be noticed that gelation phenomena in many systems including colloids can be classified as a viscoelastic phase separation. A strong attraction between molecules or particles results in formation of fractal clusters that can ultimately span the system as a 3D network, even if their volume fraction is close to zero.⁶⁶ Many important attraction mechanisms that drive gelation are short-range, like van der Waals forces and depletion attraction.⁶⁶ A transient network formed by strong interaction tends to shrink in a poor-solvent to further lower the free energy of system. However, the connectivity of network in such transient-gel resists the shrinking and generates the mechanical stress.¹³ In polymer blends with very different T_gs (such as PS/PVME blend), the phase rich in the slow component has a lower relaxation time than the characteristic deformation rate induced by phase separation; therefore, it behaves like an elastic body leading to formation of transient gel.¹⁰ Molecular weight and PDI of polymer blend components can influence the relaxation time, and thus, the dynamic asymmetry and transient gel formation. For example, increasing the M_w and PDI of slow component in polymer blends could promote the transient gel formation to induce TG-VPS, C-VPS and ANG, instead of SD and NNG behaviour. By studying the phase behavior of PS/PVME blends of various molecular weights and polydispersities, one can study the possibility of proposing a universal dynamic phase diagram which remains an open subject for future investigation.

4. Conclusion

We studied the interplay of thermodynamic forces and self-generated stresses induced by dynamic asymmetry in different compositions and quench depths, and its effect on the phase behavior of PS/PVME blend. We observed a rich variety of phase-separated morphologies, droplet, network, co-continuous, and aggregate structures with respect to the temperature and concentration. At intermediate quench depth of 14 °C, in addition to thermodynamically controlled phase separation mechanisms (nucleation and growth, NG, and spinodal decomposition, SD), three different kinds of phase separation mechanisms were induced as a result of self-generated stresses in the early stage of phase separation: (i) transient gel induced viscoelastic phase separation (TG-VPS), where the major PVME-rich phase nucleates in the minor PS-rich phase in the early stages of phase separation and grows in size; (ii) aggregate-like PS-rich phase nucleates in the early stages of phase separation, and forms a percolating network of the minor PS-rich phase through coalescence at later stages (C-VPS); and (iii) nucleation of aggregate-like PS-rich phase while the disperse-matrix morphology is preserved in the later stages of phase separation (ANG). Rheological behavior of phase-separating PS/PVME blends consistently correlated with the evolution of the corresponding phase separating morphologies and used to quantify different phase separation mechanisms. Time sweep experiments of elastic modulus, G′, showed that the TG-VPS exhibits the fastest phase separation kinetics. While it was generally accepted that VPS occurs at deep quench depth, we observed VPS mechanism at shallow quench depth due to the dynamic heterogeneity in the phase separated domains. We developed a dynamic phase diagram which includes the effect of dynamic asymmetry on phase behavior of PS/PVME blend. The results showed that that studying the phase behavior of dynamically asymmetric polymer blends involves complex combinations of thermodynamics and viscoelasticity. The fractal behavior of different phase-separating morphologies was investigated and the results were analyzed by the theories of diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA).

Acknowledgements

We thank Mrs Tahereh Samaee Yekta for her assistance in carrying out the morphological observations of this work.

References

1. K. Asadi, H. J. Wondergem, R. S. Moghaddam, C. R. McNeill, N. Stingelin, B. Noheda, P. W. M. Blom and D. M. de Leeuw, Adv. Funct. Mater., 2011, 21, 1887–1894.
2. M. Shin, H. Kim, J. Park, S. Nam, K. Heo, M. Ree, C. S. Ha and Y. Kim, Adv. Funct. Mater., 2010, 20, 748–754.
3. H. Tanaka, Adv. Mater., 2009, 21, 1872–1880.
4. Y. Iwashita and H. Tanaka, Nat. Mater., 2006, 5, 147–152.
5. X. Y. Ye, F. W. Lin, X. J. Huang, H. Q. Liang and Z. K. Xu, RSC Adv., 2013, 3, 13851–13858.
6. J. Zhang, T. Li, Z. Hu, H. Wang and Y. Yu, RSC Adv., 2014, 4, 442–454.
7. P. Xavier and S. Bose, J. Phys. Chem. B, 2013, 117, 8633–8646.
8. L. H. Sperling, Introduction to Physical Polymer Science, John Wiley & Sons, Hoboken, New Jersey, 2006.
9. H. Tanaka, Phys. Rev. Lett., 1993, 71, 3158–3161.
10. H. Tanaka, Phys. Rev. Lett., 1996, 76, 787–790.
11. T. Koyama, T. Araki and H. Tanaka, Phys. Rev. Lett., 2009, 102, 065701.
12. H. Tanaka, Macromolecules, 1992, 25, 6377–6380.
13. T. Koyama and H. Tanaka, Europhys. Lett., 2007, 80, 68002.
14. T. Imaeda, A. Furukawa and A. Onuki, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2004, 70, 051503.
15. H. Tanaka, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1997, 56, 4451–4462.
16. J. Zhang, Z. Zhang, H. Zhang and Y. Yang, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2001, 64, 051510.
17. J. K. Yeganeh, F. Goharpey and R. Foudazi, Macromolecules, 2010, 43, 8670–8685.
18. H. Tanaka, T. Koyama and T. Araki, J. Phys.: Condens. Matter, 2003, 15, S387–S393.
19. J. K. Yeganeh, F. Goharpey and R. Foudazi, RSC Adv., 2012, 2, 8116–8127.
20. A. Ajji and L. Choplin, Macromolecules, 1991, 24, 5221–5223.
21. Z. L. Zhang, H. D. Zhang, Y. L. Yang, I. Vinckier and H. M. Laun, Macromolecules, 2001, 34, 1416–1429.
22. M. Kapnistos, A. Hinrichs, D. Vlassopoulos, S. H. Anastasiadis, A. Stammer and B. A. Wolf, Macromolecules, 1996, 29, 7155–7163.
23. A. Gharachorlou and F. Goharpey, Macromolecules, 2008, 41, 3276–3283.
24. J. K. Kim, H. W. Son, Y. Lee and J. Kim, J. Polym. Sci., Part B: Polym. Phys., 1999, 37, 889–906.
25. J. Kim, T. K. Kwei and E. M. Pearce, Chem. Eng. Commun., 1992, 116, 105–116.
26. J. Sharma and N. Clarke, J. Phys. Chem. B, 2004, 108, 13220–13230.
27. S. Reich and Y. J. Cohen, J. Polym. Sci., Polym. Phys. Ed., 1981, 19, 1255–1267.
28. F. Zou, X. Dong, W. Liu, J. Yang, D. Lin, A. Liang, W. Li and C. C. Han, Macromolecules, 2012, 45, 1692–1700.
29. G. H. Fredrickson and R. G. Larson, J. Chem. Phys., 1987, 86, 1553–1560.
30. D. Vlassopoulos, A. Koumoutsakos, S. H. Anastasiadis, S. G. Hatzikiriakos and P. Englezos, J. Rheol., 1997, 41, 739–755.
31. I. S. Polios, M. Soliman, C. Lee, S. P. Gido, K. S. Roher and H. H. Winter, Macromolecules, 1997, 30, 4470–4480.
32. R. Zhang, H. Cheng, C. Zhang, T. Sun, X. Dong and C. Han, Macromolecules, 2008, 41, 6818–6829.
33. K. E. Mabrouk and M. Bousmina, Rheol. Acta, 2006, 45, 877–889.
34. K. E. Mabrouk and M. Bousmina, Polymer, 2005, 46, 9005–9014.
35. J. Yang, Z. Sun, W. Jiang and L. An, J. Phys. Chem. B, 2002, 106, 11305–11314.
36. J. Yang, Z. Sun, W. Jiang and L. An, J. Chem. Phys., 2002, 116, 5892–5900.
37. L. Li, Y. Huang and Q. Yang, J. Macromol. Sci., Part B: Phys., 2011, 50, 2140–2149.
38. T. Taniguchi and A. Onuki, Phys. Rev. Lett., 1996, 77, 4910–4913.
39. H. Tanaka and T. Araki, Europhys. Lett., 2007, 79, 58003.
40. H. Tanaka and Y. Nishikawa, Phys. Rev. Lett., 2005, 95, 078103.
41. J. L. Jorgensen and L. A. Utracki, Makromol. Chem., Macromol. Symp., 1991, 48–49, 189–209.
42. M. Joshi, B. S. Butola, G. Simon and N. Kukaleva, Macromolecules, 2006, 39, 1839–1849.
43. M. Doi and T. Ohta, J. Chem. Phys., 1991, 95, 1242–1248.
44. I. Vinckier and H. M. Laun, J. Rheol., 2001, 45, 1373–1385.
45. I. Vinckier and H. M. Laun, Macromol. Symp., 2000, 149, 151–156.
46. Y. H. Niu and Z. G. Wang, Macromolecules, 2006, 39, 4175–4183.
47. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids, 1961, 19, 35–50.
48. K. Binder and D. Stauffer, Phys. Rev. Lett., 1974, 33, 1006–1009.
49. E. D. Siggia, Phys. Rev. A, 1979, 20, 595–605.
50. K. Krishnan, W. R. Burghardt, T. P. Lodge and F. S. Bates, Langmuir, 2002, 18, 9676–9686.
51. P. H. P. Macaubas, N. R. Demarquette and J. M. Dealy, Rheol. Acta, 2005, 44, 295–312.
52. J. F. Berret, Langmuir, 1997, 13, 2227–2234.
53. S. Lerouge and J. P. Decruppe, Langmuir, 2000, 16, 6464–6474.
54. T. P. Lodge and T. C. B. McLeish, Macromolecules, 2000, 33, 5278–5284.
55. E. Leroy, A. Alegra and J. Colmenero, Macromolecules, 2002, 35, 5587–5590.
56. E. Helfand and Y. Tagami, J. Chem. Phys., 1972, 56, 3592–3601.
57. H. Tanaka, Phys. Rev. Lett., 1994, 72, 1702–1705.
58. H. Tanaka, J. Chem. Phys., 1997, 107, 3734–3737.
59. H. Tanaka, J. Chem. Phys., 1995, 103, 2361–2364.
60. W. Wang and Y. Chau, Soft Matter, 2009, 5, 4893–4898.
61. R. G. Larson, The Structure and Rheology of Complex Fluids, Oxford University Press, New York, 1999.
62. Freeware from the National Institutes of Health, http://rsbweb.nih.gov/ij/.
63. N. E. Kurland, J. Kundu, S. Pal, S. C. Kundu and V. K. Yadavalli, Soft Matter, 2012, 8, 4952–4959.
64. M. Y. Lin, M. H. Lindsay, D. A. Weitz, R. C. Ball, R. Klein and P. Meakin, Nature, 1989, 339, 360–362.
65. J. Stankiewicz, M. A. C. Vilchez and R. H. Alvarez, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1993, 47, 2663–2668.
66. P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino and D. A. Weitz, Nature, 2008, 453, 499–503.

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