Frustrated Crystallization in the Coupled Viscoelastic Phase

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Frustrated Crystallization in the Coupled Viscoelastic Phase Separation Weichao Shi,† Xu-Ming Xie,‡ and Charles C. Han*,† †

Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Science and Materials, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China ‡ Department of Chemical Engineering, Tsinghua University, Beijing 100084, China

ABSTRACT: The interplay between crystallization and phase separation has been intensively studied recently. In this study, we extended the research into a dynamically asymmetric blend composed of amorphous poly(methyl methacrylate) (PMMA) and crystalline poly(ethylene oxide) (PEO). The large dynamic asymmetry induces network stress in concentration growth. We find that crystallization is seriously frustrated when it couples with a simultaneous viscoelastic phase separation. In a single quench experiment, normal spherulites grew in a limited temperature range when crystallization was faster, while crystallization was frustrated at deep quenches when phase separation was faster. In a double quench experiment, crystallization was more difficult to occur after the prior phase separation at a higher temperature. The calorimetric results indicated that both melting temperatures and enthalpies of crystallization decreased in the coupled viscoelastic phase separation. We propose that it is the network stress in the concentration growth that leads to the frustration of crystallization.

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INTRODUCTION Crystalline materials cover a large portion of polymer family, and the phase transition of crystallization has been intensively studied.1−7 For polymer blends, since most polymer mixtures are thermodynamically immiscible, therefore the dual transitions of crystallization and phase separation often occurs interactively. Revealing the mechanism of the coupled two competing phase transitions could help controlling the morphology of the materials and may lead to optimized structures and properties. For the liquid−liquid phase separation, polymer systems are usually difficult to reach the final equilibrium state because of large viscosity. For the liquid−solid phase transition of crystallization, the morphology is frozen as soon as the liquid/melt crystallizes. When these two transitions take place simultaneously, there could possibly be a large variety of pattern formations.8−12 Here we note that the competing dynamic pathway plays the key role in the final pattern formation. As a prerequisite, all phase transitions proceed in the framework of thermodynamics. When phase separation (with an upper critical solution temperature, for example) couples with crystallization, there are typically two kinds of phase diagrams. The type 1 phase diagram is that phase separation region locates fully beneath the equilibrium melting line of crystallization. This type of phase diagram has rarely been investigated and lacks a quantitative determination of the phase boundary.13−15 The type 2 © 2012 American Chemical Society

phase diagram is that phase separation region locates partially above and partially below the equilibrium melting line of crystallization. The upper part of the phase diagram can be well determined, and some typical systems (PEH/PEB, PS/PCL, PCL/PEG) have been reported before.8,16,17 Versatile morphologies are determined under the combined effect of thermodynamics and dynamic pathway. We may give a short review of the current research in the framework of the type 2 phase diagram (Figure 1).2,16 It should be pointed out that this schematic phase diagram is drawn based on an implicit assumption: crystallization and phase separation occur individually not interactively. Strictly speaking from a thermodynamic point of view, the phase diagram of the coupled phase transitions in polymer blends should not be different from that in metals or small molecules. There are several good calculation papers on this topic.18−22 However, the compromise has to be made because of dynamic factors in practical experiment, as will be illustrated later. There are typically three dynamic lines: line BCD indicates the melting line of crystallization, line HAG is the phase separation binodal line, and the cyan curve is the spinodal line which represents the thermodynamic unstable limit. Point A corresponds Received: July 29, 2012 Revised: September 26, 2012 Published: October 11, 2012 8336

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c. A single quench to the metastable region, to study either the liquid−liquid nucleation phenomenon (path 4 or 6) or the coupled liquid−liquid nucleation and crystallization (path 5). In the dynamically symmetric case, the nucleation phenomena in paths 4 and 6 are not much different, but the mechanism may be different in the the dynamically asymmetric case. The nucleation of the fast component in the matrix of the slow component is usually frustrated because of viscoelastic depression.36,37 In path 5, there is competition between liquid−liquid nucleation for phase separation and crystallization. Currently, it is argued that crystal nucleation is assisted by a preceding mesomorphic phase.4,38 Then it is reasonable to check this idea in this condition. d. A direct quench to point I to study crystallization in the melt-miscible region. The crystallization is usually consisted of a regular arrangement of crystallizable molecules while expelling the amorphous ones. So there is amorphous-rich region at the growth front, and the phase transition may be different from that in the original melt. A slow crystallization may induce phase separation at the growth front when point I is only slightly above the binodal line (dashed line CG).8 e. A special case (path 7) to study the real simultaneous crystallization and phase separation on thermodynamic sense. Strictly speaking, the competition of the dual phase transitions completely arises from the dynamic factors. The thermodynamics of crystallization overwhelms that of phase separation in the concentration region over ϕ*, and the opposite case occurs in the lower concentration regions. In the framework of thermodynamics, the pattern formation is mainly the result of dynamic competition between crystallization and phase separation. There are two fundamental problems: the effect of crystallization on phase separation and, the contrary case, the effect of phase separation on crystallization. It was found that in the PS/PCL blend the slow growth of PCL spherulites induced nucleation of PS-rich droplets at the growth front.8 Recently, we found in a PEO/PMMA blend that the initial growth of spherulites enhanced spinodal decomposition and led to concentric alternating PEO-/PMMA-rich ring structures.13−15 The recent research of the effect of phase separation on crystallization was focused on the coupled spinodal decomposition and crystallization. Most experiments were carried out in dynamically symmetric blends (such as polyolefin blends: PEH/PEB, PP/PEOc, and so on).9,10,16,17 A common opinion is that the ability of crystallization is assisted in the unstable phase separation state and decreases as phase separation prolongs. The optimal nucleation sites are found mostly located at the interface.39 Although this counterintuitive opinion is confirmed over and over again, the physical origin is still under debate. One opinion focuses on the thermodynamics40 and the other on dynamic factors.41,42 In the process of spinodal decomposition, the crystalline component-rich phase becomes more and more concentrated, which should assist crystallization more on thermodynamic sense intuitively. This discrepancy indicates some other factors may lead to even stronger crystallization ability before the complete phase separation. The thermodynamic opinion considers the interface boundary may play as nucleation

Figure 1. Schematic representation of the experimental procedures which can be applied in the type 2 phase diagram.

to the critical point. The binodal line can be usually determined through cloud point under optical microscopy or scattering techniques.23 The spinodal line can be determined through an extrapolation to the infinite fluctuation point, usually using random phase approximation under neutron scattering.24,25 The determination of the equilibrium melting point in the miscible region is usually carried out using the extrapolation of Hoffman− Weeks or Gibbs−Thomson equations.2,3,26 When it intersects with binodal line and reaches the phase separation region, the equilibrium melting line cannot be easily measured. The binodal line and the equilibrium melting line intersect at point C. The line CD is drawn as a horizontal line under the assumption that every step of phase transitions proceeds slowly enough to get the equilibrium conditions. However, this assumption is problematic because the concentration growth in spinodal decomposition does not reach the coexisted concentration from the very beginning. The actual spinodal decomposition consists of diffusive growth in the initial stage and hydrodynamic coarsening in the late stage.27−32 So it remains a future challenge to obtain a valid determination of the equilibrium solid−liquid transition line in the phase separation region. In the type 2 phase diagram, we can usually study the following cases: a. The critical phenomenon nearby point A (path 1).33 b. A single quench to the unstable region, either to get single spinodal decomposition (path 2) or to get the coupled crystallization and spinodal decomposition (path 3). We should note that the coexisted concentration in path 2 is directed by the binodal curve, but the situation is different in path 3. If phase separation dynamics is much faster than crystallization, then the coexisted concentration is still predicted by the binodal curve and crystallization proceeds laterally in the phase-separated domains.8,16,17 If the crystallization is much faster than phase separation, then the amorphous component will mostly be trapped within the interlamellar or interfibrillar regions. The phase separation may be smeared or totally covered.8,16,17 A double-quench experiment may also be applied to study the effect of phase separation on crystallization.34 Usually the first step is carried out in the single phase separation region for a certain time, and then a second step is followed in the crystallizable region. One problem should be noted in this case is that a secondary phase separation may also proceed at the second quench in the well-phase-separated domains (E, F). To minimize this effect, the second quench is often applied at the optimal crystallization temperature, corresponding to the largest growth rate of crystallization.35 8337

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T0m,b is the equilibrium melting temperature of a given blend, Tm0 is the equilibrium melting temperature of the neat crystalline polymer, Ni (i = 1 corresponds to the amorphous component and i = 2 the crystalline one) is the degree of polymerization, Viu is the molar volume of the repeating units, ϕi is the volume fraction, and χ is the interaction parameter. The contribution from the entropy is very small and is usually neglected. So the melting point depression is mainly the result of attractive interaction between crystalline polymer and diluents in miscible conditions. In immiscible conditions where χ > 0, the melting point should be even higher than the equilibrium temperature, which is quite questionable. We note that the application of Nishi−Wang equation in immiscible conditions is implicitly under the prerequisite that crystallization should be much faster than phase separation. The usual procedure to obtain melting point depression in miscible blend is to consider limited lamellar thickness via the Hoffman−Weeks extrapolation before considering thermodynamic effects in the Nishi−Wang equation. In addition, a very crude estimation on interaction parameter can be achieved in this procedure. Of course, the relationship between melting temperature Tm,b and equilibrium melting temperature T0m,b in polymer blends also follows the Gibbs−Thomson relationship:

substrate to induce heterogeneous crystallization. Although the crystalline component-rich phase becomes concentrated, the heterogeneous effect becomes less as interfacial area decreases. The dynamic opinion postulates concentration fluctuation may induce local conformational ordering to assist crystallization. The fluctuation strength decreases as phase separation prolongs. In the conventional studies of phase separation, component molecules have nearly equal mobility and usually relax much faster than concentration growth. However, the more typical case is that the component molecules have unmatched dynamics, that is, the dynamic asymmetry. The fast component responses to a perturbation immediately, while the slow component falls behind. This induces an internal network stress mainly sustained by the slow component and the network stress will feed back to mediate the molecular diffusion. This is known as stress-diffusion coupling.33,43−45 So it leads to the central issue of the present study that how crystallization will proceed when it is coupled with the viscoelastic phase separation in dynamically asymmetric blends? We deliberately build up dynamic asymmetry by employing a slow amorphous component of poly(methyl methacrylate) (PMMA) and a fast crystalline component of poly(ethylene oxide) (PEO). The large dynamic asymmetry arises from about 180 °C apart of glass transition temperatures.

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⎛ 1 2σ ⎞ 0 ⎜⎜1 − ⎟⎟ Tm,b = Tm,b Lc,b ΔHm0 ⎠ ⎝

THEORETICAL BACKGROUND Polymer crystals usually grow into stacked layers. The growth in the extensional direction is limited because of chemical connection, which leads to melting point depression of crystals. The Gibbs−Thomson equation gives the classical description:1−3 Tm =

1 2σ ⎞ ⎟ − Lc ΔHm0 ⎠ ⎝

Suppose the interfacial energy does not alter upon blending; then melting temperature decrease in blends from pure polymer is expressed like47

⎛

Tm0⎜1

0 ΔTm = Tm − Tm,b = (Tm0 − Tm,b )+

(1)

Accordingly, the difference in melting point is composed of two parts: one arises from thermodynamic depression (the first term) and the other mainly lamellar thickness.

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(2)

(3)

For constant β, there is a linear relationship between Tm and Tc. T0m is usually obtained through extrapolation when Tm = Tc. Thermodynamics of crystallization is different for the crystalline component in polymer blends and in neat melt. By considering Flory−Huggins description of free energy, the thermodynamic contribution to melting point depression is revealed by Nishi−Wang equation:46 1 0 Tm,b

−

EXPERIMENTAL SECTION

Materials. PMMA and PEO were purchased from Aladdin Reagent Inc. and Alfa-Aesar Chemcal Co., respectively. The weight-average molecular weight for PMMA and PEO are 100 and 24 kg/mol, which were determined by gel permeation chromatography. The polydispersity for PMMA and PEO are 1.78 and 1.52, respectively. The materials were used after purification. The glass transition temperatures of PMMA and PEO were found to be about 116 and −60 °C, respectively, using a differential scanning calorimeter (DSC, TA Q2000) at a heating rate of 10 °C/min. Film Preparation. PMMA and PEO were dissolved in chloroform with 5% of polymer by total weight. The solution was stirred at room temperature over 24 h and then casted on a clean glass plate. The solvent was quickly evaporated at 60 °C (humidity 1) of the primary critical nuclei Lmin, then ⎤ ⎡ 2σT 0 1 m ⎥ Lc = βLmin = β ⎢ ⎣ ΔHm0 Tm0 − Tc ⎦

(5)

⎤ ⎛ 1 1 1⎞ R V2u ⎡ ln ϕ2 2 ⎥ ⎢ = − + − ϕ + χϕ ⎜ ⎟ 1 ⎥ N1 ⎠ 1 ΔHm0 V1u ⎢⎣ N2 Tm0 ⎝ N2 ⎦ R V2u ≅− χϕ 2 ΔHm0 V1u 1 (4) 8338

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RESULTS AND DISCUSSION Phase Diagram and Dynamic Melting Line. The phase diagram is presented in Figure 2. The glass transition

When PMMA content was over 10%, we cannot observe any crystallization indication in the dynamic calorimetric measurement. Therefore, we present the crystallization is confined into a very small region in the phase diagram. In the previous studies, a type 1 phase diagram was obtained by employing a small molecular weight of PMMA (Mw = 15 kg/mol) and PEO (Mw = 20 kg/mol).14 We reported very slight melting point depression which lied between 65 and 70 °C in the large melt-miscible region. As the molecular weight of PEO is not much different in this study, the melting phenomenon should not be different under the assumption that there is no interaction between crystallization and phase separation. However, the experimental results actually indicate that viscoelastic phase separation does strongly affect crystallization. We will give detailed investigations and explanation on crystallization in the following sections. Single Quench Experiment. To start with, we will show the strong crystallization ability of a neat PEO. We prepared PEO melt on a hot stage and then quickly transferred it to another hot stage which was kept at −60 °C. Although the glass transition of PEO is about −60 °C, we observed a very quick growth of PEO spherulites and regular Maltese cross (Figure 4). The strong ability of crystallization led PEO crystallize quickly before the sample reached −60 °C under the limitation of heat transfer. When only 2% of PMMA was introduced into the system, in contrast, the situation became different (Figure 5). At 40 °C, crystallization took place slowly with irregular shapes and finally stopped growing when phase separation occurred in the outer regions. Crystals cannot fill the whole space, and we note that crystallization cannot occur in the phase-separated regions even after a long time of annealing. At the intermediate temperatures (−40 to 30 °C), regular spherulites with Maltese cross grew quickly in the sample and covered the whole space. At −50 °C, crystallization and phase separation occurred simultaneously. Regular spherulites only covered a part of the space, and small irregular crystallites emerged in the phase-separated domains. Even at −60 °C, we still observed the dual phase transitions because of slow heat transfer. Phase separation occurred first with all crystallites growing in the well-phaseseparated domains. Here we show that the crystallization of PEO is seriously affected by even such a minor introduction of PMMA of 2%. When the PMMA content was increased to 5%, more variations of patterns can be formed under the interplay between crystallization and phase separation. At a shallow quench (40 °C), crystallization dominated the initial stage and the role of phase separation emerged laterally (Figure 6). Compact spherulites grew initially with long fibrillars in the radial direction. As spherulites grew larger, there was apparent concentration growth in other regions. Then, small crystal stacks grew at the growth front and finally stopped growing. Spherulites cannot cover the full space at last. Phase transition dynamics became fast at lower temperatures, and morphology can be fixed in a short time. At 30 °C, compact spherulites grew with smooth surface (Figure 7a). Between −20 and 20 °C, we got compact sperulites with rippling surfaces (Figure 7b,c). We will discuss this structure later. At −30 °C, crystallization and phase separation occurred simultaneously (Figure 7d). Compact spherulites with wavy surfaces cannot cover the whole sight, and the other regions were occupied by phase-separated domains (similar to Figure 6d). At −40 °C, phase separation became dominating,

Figure 2. Phase diagram of the PEO/PMMA blend in this study. The blue squares indicate the phase separation boundary; the gray circles indicate the glass transition temperatures; the red triangles indicate the dynamic melting points of PEO.

temperatures were measured by DSC with a heating rate of 10 °C/min. Because of nearly 180 °C apart of glass transition temperatures between PMMA and PEO, the glass transition curve has strong concentration dependence. The phase separation binodal line was measured under optical microscopy. Because of the large contrast in molecular weights, the phase boundary is highly asymmetric. The critical weight fraction is estimated around 0.2 and critical temperature about 135 °C. The phase separation dynamics can be largely mediated with respect to concentration and temperature. By decreasing the content of PEO, the phase transition dynamics slows down drastically. For a certain composition (PEO content at 0.9, for example), the phase separation dynamics is anomalous at different temperatures. Phase separation dynamics is fast at high temperatures (above 100 °C) while there is a long “frozen” period before fast concentration growth at intermediate temperatures (near room temperatures). At very deep quenches (−30 to −50 °C), the phase separation returns to be fast again because of the thermodynamic dominance. The detailed phase separation dynamics was reported in details in a recent paper.48 Strictly speaking, a thermodynamic equilibrium melting line for PEO cannot be obtained in this study because crystallization and phase separation overlap in a large temperature range. Instead, we determined a dynamic melting line by DSC (Figure 3). The samples were quenched from the miscible state to −70 °C with a cooling rate of 10 °C/min and then followed by a heating rate of 10 °C/min in a reversed procedure. We can monitor the heat flow in the crystallization and melting processes. The ability of crystallization was strong for neat PEO, corresponding to high crystallization/melting temperature and large enthalpy. But crystallization became difficult as soon as PMMA was introduced into the system. When PMMA content reached 7%, there was no apparent crystallization in the cooling run but a cold crystallization emerged in the heating run. We note that crystallization/melting temperature as well as enthalpy decreased dramatically as PMMA content increased. 8339

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Figure 3. Calorimetric measurements of the crystallization/melting behavior in PEO/PMMA blends with 10 °C/min cooling/heating rate.

the samples were etched by acetone to remove amorphous PMMA on the surface. We should stress that this kind of pattern is different from the concentric alternating structure which has been reported in our previous studies.13−15 The latter was the result of crystallizationenhanced phase separation at the growth interface, which led to alternating crystalline-/amorphous-rich rings. The undulating surfaces in this study are the result of fast interior mass transport and slow surface relaxation. Quick growth of spherulites is in need of fast transport of PEO at the growth front. The high mobility of PEO chains ensures the continuous growth of spherulites. But the slow entangled PMMA chains may not respond fast enough in the PEO-poor region near the growth front. The internal network stress may lead to mechanical instability of the surface.51,52 This interpretation is supported by a continuous capture of the growth kinetics under optical microscopy (Figure 9). We noticed that there were already folded surfaces ahead of the growth front. If the growth of spherulites is slow (at higher temperatures) or the internal network stress is small enough (with smaller amount of PMMA), the undulation of the surface is not induced with crystal growth. When the content of PMMA is increased to 10% in the blend, crystallization cannot take place easily. We did not capture any crystallization when the sample was kept at 30 °C for as long as 6 days (Figure 10). Only phase separation took place slowly as revealed by phase-contrast optical microscopy. At even deeper quenches (−40 °C), still only phase separation took place without macroscopic crystallization. In the single quench experiment, crystallization and concentration growth are both slow at high temperatures; crystallization dominates the whole process at intermediate temperatures, while phase separation dominates the low-temperature region. We note

Figure 4. Crystallization of neat PEO when the melt was transferred to a hot stage which was kept at −60 °C. Picture (a) was taken under phase-contrast optical microscopy and (b) under polarized optical microscopy.

and small crystallites grew in the well-phase-separated domains (Figure 7e). At −50 °C, however, we observed phase separation in the phase-contrast optical microscopy but did not get macroscopic information on crystallization (Figure 7f). At even lower temperatures (below −60 °C), the sample seems in the glassy state already. In this set of experiments, crystallization dominates in the higher temperature regions and phase separation overwhelms under deep quenches at lower temperatures. We find crystallization is seriously frustrated as soon as phase separation intervenes. There were concentric-like structures in the intermediate temperature region (between −20 and 20 °C). Under polarized optical microscopy, there were alternating bright and dark bands, which was very similar to banded spherulites.49,50 However, it has nothing to do with screwed lamellar growth but only a surface phenomenon. We observed undulating surfaces directly under SEM (Figure 8). But flat surfaces appeared when 8340

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Double Quench Experiment. Here we would like to check whether it is really true that crystallization is frustrated by viscoelastic phase separation. We employed a double quench method to test this idea. The PMMA/PEO blend (PEO content 0.95) was first annealed at 70 °C for 20 h to obtain a well-phase-separated structure, and then the sample was quenched to lower temperatures to crystallize. Phase transitions were monitored by optical microscopy (Figure 11). After 20 h of annealing at 70 °C, we found well-phaseseparated structures in the blend. When the second quench was applied to the sample at higher temperatures (above 30 °C), we did not observe the occurrence of crystallization. At 30 °C, dendritic crystals were observed growing slowly in the blend. The crystal cannot cover the full space and was finally trapped by a very bright region at the growth front. At 0 °C, very loose spherulites were observed growing in the phase-separated PEOrich domains. The bright PMMA-rich phase was totally intercalated within the spherulites. The growth rate of spherulites was estimated about 20 μm/min. At −30 °C, spherulites cannot grow but small crystallites appeared in the well-phase-separated domains. At −50 °C, the contrast between phase-separated domains were enhanced under phase-contrast optical microscopy, while there was no indication of macroscopic crystallization under polarized optical microscopy. At 30 °C, we found there was a bright region trapping the crystal growth. We would like to investigate the kinetic process to reveal the nature of this bright region. In Figure 12, a dendritic crystal grew irregularly in the sample with faster rates at four arms. As crystal grew, some regions became turbid white and depressed crystal growth in those directions. Finally, the whole crystal was totally trapped by the white layer. This phenomenon is quite similar to a predicted result in a simulation work.21 The crystal growth is normally consisted by a regular arrangement of crystallizable molecules at the growth front and a repulsion of amorphous ones to outside regions. As crystals grow larger, the amorphous region becomes even thicker at the growth front. In this case, the bright region in Figure 12 was no doubt the PMMA-rich phase. In addition, we think that the relaxation of PMMA molecules is not fast enough and may lead to some internal stress. Therefore, we propose that the brightness was more or less under the effect of stress-optical coupling as in a cross-linked rubber.53

Figure 5. Phase transition of PEO/PMMA blend (PEO weight fraction 0.98) after annealing at (a) 40, (b) 0, (c) −30, (d) −50, and (e) −60 °C. Pictures in the left column were taken under phasecontrast optical microscopy and the right column under polarized optical microscopy.

crystallization is seriously frustrated as soon as phase separation occurs.

Figure 6. Phase transition of PEO/PMMA blend (PEO weight fraction 0.95) annealed at 40 °C. Pictures in the upper row were focused on the center of a growing spherulite and the bottom row on the growth front. Pictures (a) (d) were taken under phase-contrast optical microscopy, (b) and (e) under polarized optical microscopy, and (c) and (f) were observed under SEM with amorphous PMMA etched by xylene. 8341

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Figure 7. Phase transition of PEO/PMMA blend (PEO weight fraction 0.95) annealed at (a) 30, (b) 0, (c) −20, (d) −30, (e) −40, and (f) −50 °C. Pictures in the first and third columns were taken under phase-contrast optical microscopy and second and fourth columns under polarized optical microscopy.

Figure 8. Surface morphology in PEO/PMMA blend (PEO weight fraction 0.95) observed under scanning electron microscopy. The samples were annealed at 0 °C. (b) was etched by acetone before observation.

Figure 9. Crystallization of PEO/PMMA blend (PEO weight fraction 0.95) annealed at 0 °C. The pictures were taken consequently within 1 min under phase-contrast optical microscopy.

Figure 10. Phase transition of PEO/PMMA blend (PEO weight fraction 0.9) after annealing at 30 °C for 6 days. Picture (a) was taken under phase-contrast optical microscopy and (b) under polarized optical microscopy.

Figure 11. Double quench experiment of PEO/PMMA blend (PEO weight fraction 0.95). The sample was annealed at (a) 70 °C for 20 h and then quenched to (b) 30, (c) 0, (d) −30, and (e) −50 °C. Pictures in the left column were taken under phase-contrast optical microscopy and right column under polarized optical microscopy.

In this set of experiment, we validate our hypothesis that crystallization is frustrated by the coupled viscoelastic phase separation using double quench experiment. In comparison with the single quench experiment, the crystallization ability becomes even more frustrated in the well-phase-separated

conditions. We will further investigate the frustration using calorimetric measurements. Calorimetric Measurement. In the single quench experiment, the PMMA/PEO blend (PEO content 0.95) was annealed at each crystallization temperature for 1 h before 8342

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Figure 12. Double quench experiment of PEO/PMMA blend (PEO weight fraction 0.95). The sample was annealed first at 70 °C for 20 h and then quenched to 30 °C for (a) 100, (b) 180, (c) 320, and (d) 600 min.

Figure 13. Calorimetric measurements of PEO crystal melting in PEO/PMMA blend (PEO content 0.95) for single quench experiments. The samples were annealed at given temperatures for 1 h before heating with a rate of 10 °C/min.

Figure 14. Calorimetric measurements of PEO crystal melting in PEO/PMMA blend (PEO content 0.95) for double quench experiments. The samples were annealed at different temperatures for 1 h after phase separation at 70 °C for 20 h.

the heating process in DSC (Figure 13). There was nearly no melting enthalpy for nucleation-controlled crystallization at 50 °C. In the intermediate temperature region for crystallization (between 40 and −10 °C), the melting temperature and enthalpy did not decrease too much. For crystallization at −30 °C, there were double peaks in the melting curve: one located at about 20 °C and the other at 40 °C. For crystallization at −50 °C, there was first a cold crystallization at about −30 °C and then followed by two small melting peaks at higher temperatures. Compared with direct morphology observations under optical microscopy (Figure 7), we propose that the higher melting peak corresponds to the melting of compact spherulites and the lower peak to the melting of small irregular crystallites in phase-separated domains. In the double quench experiment, the melting temperature and enthalpy showed sharp decrease (Figure 14), in contrast to the single quench experiment. For 1 h of annealing above 30 °C, there was no indication of crystal melting in the heating process. For crystallization at even lower temperatures (between −30 and 20 °C), there were double melting peaks which indicated two kinds of crystals with different stability. As crystallization temperature lowered, more crystal melted at lower temperatures. For crystallization at −50 °C, there was apparent cold crystallization in the heating process before the subsequent double melting peaks. By comparing the exothermic and endothermic heat, we found they were nearly equal. This indicated that there

was almost no crystallization at −50 °C, and the melting peaks corresponded to the cold crystallization in the heating procedure. Furthermore, we can compare the calorimetric results in this study with two more polymer systems (Figure 15). For melting of crystallization in neat PEO, the melting temperatures were high and enthalpies large. When PEO was blended with 5% of small molecular weight of PMMA (Mw = 15 kg/mol), the blend showed thermodynamic miscibility in a large temperature range. We found that there was only slight drop of melting temperatures and enthalpies. In comparison, there were dramatic drop of calorimetric property in the current study. At the lower temperature crystallization took place, the larger drop was observed in the melting process. Frustrated Crystallization and Melting Depression. In dynamically symmetric blends, there are possibly three factors in phase separation that affect the coupled crystallization: fluctuation, interfacial area, and concentration.40−42 Fluctuation and interfacial area enhance crystallization ability, and the effect decreases as phase separation proceeds. In the very late stage of phase separation, crystallization is mainly determined by the concentration in the well-phase-separated crystalline-rich domains. In this dynamically asymmetric PEO/PMMA blend, we confirm that crystallization is frustrated when it couples with viscoelastic phase separation. Now we come to the essential question: what leads to the frustration? 8343

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phase separation is the result of transient entanglement of the slow component. To consider nucleation and growth in dynamically asymmetric blends, Onuki proposed that the Gibbs−Thomson equation should be modified by including the network stress at the interface.37 We follow his approach and apply it within the kinetic crystallization theory. Then the equilibrium condition at the melting point of crystallization is gcLc + 2σ + σn = ga Lc

(7)

where gc and ga are Gibbs free energies of a monomer in the perfect crystal and in the melt, Lc corresponds to the thickness of the equilibrium crystal at the temperature, and σn is the normal component of network stress at the interface. In the viscoelastic model for phase separation in dynamically asymmetric blends, Tanaka proposed the network stress coupled with concentration growth for component k should be43,57 t

∫−∞ dt′[GS(k)(t − t′)κij(k)(t′)

σij⃡ (k)(t ) =

+ G B(k)(t − t ′)(∇·υk (t ′))δij]

(8)

(k) where κ(k) + ∇jυ(k) − 2/3δij∇·υk and GS and GB are ij = ∇iυj i shear modulus and bulk modulus, respectively. In the very asymmetric blends (gels or polymer solutions), the network stress is mainly sustained by the slow component. The σn associated with the network stress in eq 7 is37

σn =

∑

n⃡ ·σ ⃡ (k)· n⃡ (9)

k = 1,2

With a linear approximation, the driving force for crystallization is ga − gc ≅ (T0m − Tm)ΔH0m/T0m. So the modified Gibbs− Thomson equation yields the melting point as

Figure 15. Calorimetric measurements of PEO crystal melting at different conditions. One corresponds to the melting of neat PEO. PEO/PMMA (M) corresponds to the blends of PEO with small molecular weight of PMMA (Mw = 15 kg/mol), which is in miscible conditions. PEO/PMMA (I) corresponds to the direct quench in this study, which is in the immiscible condition. PEO/PMMA (I, DQ) corresponds to the double quench in this study.

⎛ 2σ + σn ⎞ ⎟ Tm = Tm0⎜1 − LcΔHm0 ⎠ ⎝

(10)

The network stress applied onto the crystal plays the same role as additional surface tension. The situation returns to usual Gibbs−Thomson relationship when the effect of network stress vanishes. Provided that crystallization is independent and under the assumption that Lc = β′Lmin (β′ is a constant), then the Hoffman−Weeks relationship is still available with some modifications

In conventional systems with dynamic symmetry, component molecules show high mobility and response immediately to a driving force. So there is concentration fluctuation, diffusive growth, and coarsening in the phase separation process. In dynamically asymmetric blends, an internal stress can be produced by even a small perturbation if the stress relaxation time of one component is long.33,43−45 This transient stress mainly arises from entanglements of the slow component, which acts like a transient network. In the viscoelastic phase separation, the internal network stress is closely coupled with concentration growth. So we propose that the frustrated crystallization also results from the network stress in viscoelastic phase separation. To verify our postulation, we first consider an ultimate case in cross-linked gels.33 The crystallization ability of crystallizable solvent in a gel is usually frustrated.54 Also, the crystallization is dramatically depressed if the crystalline polymer is cross-linked.55 If the cross-linking density is very high in the network, the crystallization may be totally prohibited.56 These phenomena indicate that crystallization is frustrated by random stress. The network stress in gels usually results from permanent junction points. In contrast, the network stress in viscoelastic

⎛ ⎛ 2σ + σn ⎞ 2σ + σn ⎞ Tm = Tm0⎜1 − ⎟ ⎟ + Tc⎜ 2σβ′ ⎠ ⎝ ⎝ 2σβ′ ⎠

(11)

We can still get an equilibrium melting temperature when Tm = Tc. But the modified relation shows a larger slope when the network stress intervenes. The experimental data seem to follow the tendency in this crude interpretation. In another point of view, the equilibrium melting temperature seems to show drastic drop in the presence of network stress. Similar to eq 6, we can attribute the melting point depression to three factors: thermodynamic depression, lamellar thickness, and network stress in addition. Then, we consider the kinetics of nucleation and crystal growth. Because of the larger interfacial energy, the nucleation barrier becomes larger. Accordingly, the nucleation rate drops with an exponential factor exp[(−2σnσlT0m)/(kTcΔH0m(T0m − Tc))], where σl associates with lateral surface energy. The 8344

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usually shown like a “bell”-shaped curve between melting temperature and glass transition temperature. Nucleation dominates the high-temperature region, and diffusion dominates at low temperatures. Then there are two types of relationship between crystal growth and concentration growth. If the concentration growth rate is faster than crystal growth in the full temperature range, then crystallization proceeds laterally in the phase-separated domains. This case often appears when the upper critical solution temperature is very high beyond the melting curve. In this study, it seems that crystallization is faster in a temperature range between T1 and T2, while phase separation dominates the higher and lower temperature regions so that crystallization is frustrated by network stress. Compared with experimental data, T1 is near around 40 °C and T2 −30 °C for the blend with 5 wt % of PMMA. Here we should point out that the network stress stays only transiently (although relatively long in the study). It is usually built up by molecular diffusion in the early stage of phase separation and relaxes slowly in the late stage. So the effect of network stress on crystallization changes as phase separation proceeds. When crystallization is much faster than phase separation, the crystallization is less affected before network stress is induced. Under a single deep quench or a double quench, the effect from the network stress is remarkable for a certain period. In some conditions, crystallization seems to be fully prohibited. After a sufficiently long time, however, the internal network stress may be relaxed so that crystallization can take place slowly. For example, when PMMA weight fraction is 10%, we did not observe apparent crystallization after 6 days of annealing (Figure 10), but we did capture crystallization after 4 months. Until present, one essential problem still leaves unsettled in viscoelastic phase separation: the network stress cannot be determined experimentally. Quantitative description of the network stress is only given in simulation works.59,60 We propose that the network stress may be estimated indirectly with eqs 10 and 11. In addition, the molecular dynamics is another challenging problem.61,62 In an intuitive picture, there are typically three kinds of interactions in the this blend: PMMA−PMMA, PMMA−PEO, and PEO−PEO. What is the exact motion of the molecular dynamics for each component, especially when there is large dynamic asymmetry?63,64 We believe that much more experimental and theoretical effort is needed on these topics.

growth rate under network stress expressed in a simplified form is then G∼

0 ⎛ (2σ + σ )T 0 ⎞ 1 Tm − Tc n m ⎟ exp⎜ − 0 0 τ0 Tc ⎝ (Tm − Tc)ΔHm ⎠

(12)

There are two factors leading to the depression of growth rate. The thermodynamic reason is closely related with network stress and the induced shifting of equilibrium melting temperature. The other lies in the mobility. In eq 12, the Vogel−Fulcher relation gives τ0 ∼ exp[B/(ϕg − ϕ)], where B is a positive constant and ϕg the glassy fraction.58 So we point out that growth rate in dynamically asymmetric blends is severely affected by the unmatched glass transition temperatures between two components. By considering the network stress, the frustrated crystallization in this study can be explained qualitatively. First, we consider concentration dependence. We found crystallization was difficult to take place when the amount of PMMA was over 10%. Larger PMMA concentration indicates larger network stress under even a small perturbation. In addition, the uprising glass transition curve impedes the mobility even more. Together, they give the concentration-dependent frustration on crystallization. Second, we consider the temperature dependence. As network stress is initiated by concentration growth in phase separation, the dynamic path way has a large effect on crystallization ability. If crystallization takes place prior to phase separation, the effect from network stress is small. The role of the network stress is important in the contrary case. We show the competition between crystal growth and initial phase separation with respect to temperature in a schematic picture (Figure 16).

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CONCLUSION In this study, we investigated the interplay between crystallization and phase separation in a dynamically asymmetric blend. In contrast to the assisted crystallization in dynamically symmetric blends, crystallization seems to be frustrated by the coupled viscoelastic phase separation with large dynamic asymmetry. After detailed investigations in single quench, double quench, and calorimetric experiments, we propose that the frustration is the result of network stress produced by the concentration growth. The effect of the network stress is more important when viscoelastic phase separation dynamics is ahead of crystallization.

Figure 16. Schematic representation of competition between crystal growth rate (bell-like curve) and concentration growth rate from phase separation (curves 1 and 2).

The growth rate in the initial stage of viscoelastic phase separation can be expressed as33 R(q) = −2q2M[(χs − χ ) + κq2](1 + ξ 2q2)−1

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(13)

where q is the wave vector, M the mobility, χ the interaction parameter, κ the interfacial tension, and ξ the viscoelastic length. Under shallow quenches, the concentration growth is usually depressed in the viscoelastic length so that the dynamics is slow in the initial stage. However, the growth rate is dominated by thermodynamics at very deep quenches. This part of work has been given in a separate paper.48 The growth rate of crystallization is

AUTHOR INFORMATION

Corresponding Author

*Phone +86 10 82618089; Fax +86 10 62521519; e-mail [email protected]. Notes

The authors declare no competing financial interest. 8345

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ACKNOWLEDGMENTS This work is supported by the National Basic Research Program of China (973 Program, 2012CB821503) and National Natural Science Foundation of China (No. 50930003).

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