Effect of Composition Asymmetry on the Phase Separation and

Ashok Kumar Dasmahapatra. Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati - 781039, Assam, India. J. Phys. Chem...
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Effect of Composition Asymmetry on the Phase Separation and Crystallization in Double Crystalline Binary Polymer Blends: A Dynamic Monte Carlo Simulation Study Ashok Kumar Dasmahapatra* Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati - 781039, Assam, India S Supporting Information *

ABSTRACT: Polymer blends offer an exciting material for various potential applications due to their tunable properties by varying constituting components and their relative composition. Our simulation results unravel an intrinsic relationship between crystallization behavior and composition asymmetry. We report simulation results for nonisothermal and isothermal crystallization with weak and strong segregation strength to elucidate the composition dependent crystallization behavior. With increasing composition of low melting B-polymer, macrophase separation temperature changes nonmonotonically, which is attributed to the nonmonotonic change in diffusivity of both polymers. In weak segregation strength, however, at high enough composition of B-polymer, A-polymer yields relatively thicker crystals, which is attributed to the dilution effect exhibited by B-polymer. When B-polymer composition is high enough, it acts like a “solvent” while A-polymer crystallizes. Under this situation, A-polymer segments become more mobile and less facile to crystallize. As a result, A-polymer crystallizes at a relatively low temperature with the formation of thicker crystals. At strong segregation strength, the dilution effect is accompanied by the strong A−B repulsive interaction, which is reflected in a nonmonotonic trend of the mean square radius of gyration with the increasing composition of the B-polymer. Isothermal crystallization also reveals a strong nonmonotonic relationship between composition and crystallization behavior. Two-step, compared to one-step, isothermal crystallization yields better crystals for both polymers.

1. INTRODUCTION Polymer blends (a mixture having two or more polymers)1,2 possess superior properties over pure polymer for a wide range of modern applications, such as nanoelectronics,3 polymerbased light emitting diodes4 (LEDs), and medical appliances.5 In most of the cases, constituting components are chemically dissimilar and hence phase separate via macrophase separation, which may be overcome by addition of a suitable compatibilizer to bring miscibility. The extent of phase separation dictates the overall morphological development, influencing various properties of the resultant blend. A miscible binary blend shows a single glass transition temperature6−14 (Tg), whereas an immiscible blend shows two Tg’s, corresponding to the respective components.15,16 Blends with one crystallizable component have been studied extensively to understand miscibility pattern, phase behavior, and crystallization characteristics. The crystallization behavior of binary blends with two crystallizable components is challenging due to the complexity arising from the interplay between macrophase separation driven by mutual immiscibility and crystallization. Usually, the high melting component (HMC) crystallizes first and forms a crystalline domain, which creates confinement for the crystallization of the low melting component (LMC), which crystallizes in the confined © 2017 American Chemical Society

space created during the crystallization of HMC. In most of the cases, the crystal domains are separated from each other, but in some cases, interpenetrating17−21 and mixed crystals are observed.22 Mutual miscibility plays a pivotal role in determining phase behavior and morphological development in binary blends. Close proximity in the melting points of the components usually facilitates forming a miscible blend, exhibiting a single Tg6−14 and interpenetrating spherulites.17−19 However, this is not always true. For example, poly(ethylene oxide) (PEO) and poly(ε-caprolactone) (PCL) have melting points close to each other (Tm ∼ 70 °C), even though they produce immiscible blends.23 The molecular weight of the constituting components also influences miscibility. For example, in the blend of poly(3hydroxybutyrate) (PHB) (Tm: 176 °C) and poly(L-lactic acid) (PLLA),24 high molecular weight (MW) PLLA (Tm: 176 °C) produces an immiscible blend, whereas low MW (Tm: 123 °C) produces a miscible blend. Therefore, the extent of interaction between the components plays a major role in deciding the mutual miscibility. Immiscible blends usually show two distinct Received: March 19, 2017 Revised: May 14, 2017 Published: May 23, 2017 5853

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The Journal of Physical Chemistry B glass transition temperatures (Tg’s) for individual components; however, the values of Tg are influenced by the constituting components. Apart from the melting point difference between the two components and mutual immiscibility, the relative composition of the constituting components plays a critical role in determining phase behavior, crystallization mechanism, and morphological development. Increasing composition heterogeneity (viz., one component is higher in proportion than the other) leads to changes in glass transition, melting, and crystallization temperature affecting crystal morphology. For example, in the blends of poly(ethylene suberate) (PESub) and PEO,25 where the melting and glass transition temperatures of the components are close to each other (PESub, Tm ∼ 62 °C, Tg ∼ −48 °C; PEO, Tm ∼ 64 °C, Tg ∼ −51 °C), the crystallization behavior is largely governed by the relative composition of the components. The major component crystallizes first, and the minor component is either expelled from the crystalline domain or included in the interlamellar spacethus, a fractional crystallization of the minor component is observed. A variety of phenomena have been observed in the crystallization of asymmetric binary polymer blends. For example, in the blends of poly(3-hydroxybutyrate) (PHB) and PEO,26 increasing % of PEO leads to an increase in melting and glass transition temperature of PHB, whereas the melting temperature of PEO decreases and a fractionated crystallization of PEO is observed.27 Isothermal crystallization reveals that the crystallization rate of PHB decreases in the presence of PEO.6 Blends of PHB and poly(L-lactic acid) (PLLA) show the composition dependent24 and PHB molecular weight (MW) dependent8 miscibility behavior. The melting point of PLLA increases in the presence of PHB;28 lamellar thickness increases in the presence of ataPHB,8 which is incorporated within the interlamellar region of PLLA spherulites. The crystallization mechanism also changes depending on the composition: for a symmetric blend, it follows a simultaneous crystallization, whereas, in an asymmetric blend, it follows a sequential crystallization pathway.24 Usually, the simultaneous crystallization behavior is shown by the blends where Tm’s of the components are closed enough.29 However, in the blend of PHB and PLLA, the 50:50 miscible blend follows a simultaneous crystallization mechanism, although the rate of crystallization of PLLA is faster than that of PHB, and the final crystallinity of PLLA is less due to the simultaneous crystallization.24 In the blend of polypropylene (PP) and PLA,5 the melting temperature of PP decreases by ∼5 °C on increasing PLA composition from 40−60%. On the other hand, in the blend of PLLA and poly(ethylene succinate) (PES),30 being an immiscible blend, Tg and Tm appear to be independent of composition. However, the rate of crystallization of PLLA is increased with increasing PES content, which is attributed to the fact that the interface acts as a nucleating agent for the crystallization of PLLA. In contrast, the rate of crystallization of PES is decreased with increasing PLLA content because the crystallization of PLLA happens under confinement created during the crystallization of PLLA. In the blend of poly(butylene succinate) (PBS) and PEO,31 with increasing % of PEO, crystallization of PBS is inhibited with a melting point depression. On the other hand, the crystallization rate of PHBV decreases with increasing PBS content.32 In the blend of PBS and PCL, the crystallization of PBS is almost unaffected by PCL.33 However, crystallization of PCL exhibits two opposite

trends with increasing PBSfirst an increase and then a decrease with increasing content of PBS. This unexpected trend in crystallization behavior is attributed to the fact that initially formed crystalline domains of PBS act as nucleating agents, enhancing the crystallization of PCL, but subsequently, due to the confinement effect, the crystallization of PCL is decreased. In the blend of PEO and PCL,23 which form an immiscible and biphasic melt, the crystallization rate of the PEO decreases with increasing % of PCL; however, crystallization of PCL remains almost unaffected due to a change in relative composition. In the blend of PEO and PES,22 PES is the HMC (Tm ∼ 101 °C) that crystallizes first, followed by the crystallization of PEO (LMC, Tm ∼ 59 °C). When PEO is added ≤20%, the crystallization kinetics of PES are enhanced, which is attributed to the dilution effect due to which the chain mobility increases. However, a reduction in the crystallization driving force is observed when PEO is added beyond 20%. Kinetic analysis reveals a path-dependent (viz., one-step and two-step cooling) crystallization behavior. In one-step cooling, usually the crystallization mechanism follows a simultaneous crystallization, where both components crystallize simultaneously but with a different rate of crystallization.24 However, if the rate of crystallization of one component (usually, HMC) is fast enough to fill the entire space before the other component (LMC) starts to crystallize, then the mechanism changes to sequential crystallization, typically observed in two-step cooling.9 Recently, we have demonstrated that the increase in the segregation strength leads to the formation of smaller and thinner crystals with less crystallinity in a symmetric binary polymer blend.34 In the present study, we report simulation results on the effect of blend composition on the crystallization and morphological development of a series of binary blends. We present our simulation results based on two different levels of segregations. At weak segregation, our results show a nonmonotonic trend in crystallinity and lamellar thickness with increasing composition of the B-component, which is attributed to the dilution effect exhibited by the B-component. Similar nonmonotonic crystallization behavior is also observed in isothermal experiments. We organize our paper as follows. In section 2, we present our model and simulation technique. Following this, we discuss our key results in section 3 and summarize our results in section 4.

2. MODEL AND SIMULATION TECHNIQUES In recent years, several Monte Carlo (MC) based simulation algorithms have been developed to simulate polymers. Some of the methods such as the pruned enriched Rosenbluth method (PERM),35 configurational biased Monte Carlo (CBMC),36 random end-switch-configuration biased Monte Carlo (RESCBMC),37 and wormhole algorithm38 are suitable for single chain simulation but not suitable for simulating a dense system, such as polymer melts. Dense polymer systems in the lattice model are successfully investigated by the cooperative motion algorithm (CMA) developed by Pakula and co-workers,39,40 and the single site bond fluctuation model41−43 by Hu.44−47 CMA is efficient to simulate a dense system with 100% occupancy. However, there is always an ambiguity in mapping the time evolution of the morphology with the Monte Carlo steps. In contrast, Hu et al.47 have applied the single site bond fluctuation model to investigate the effect of comonomer content and sequence distribution on the crystallization of 5854

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is the temperature in Kelvin; thus, Up ∼ 1/T. Now the change in energy per MC move is modified as follows:

statistical copolymers, and successfully reproduce the experimentally observed nontrivial phenomena. The single site bond fluctuation has also been successfully employed to investigate crystallization in the presence of sticky additives,48 crystallization of double crystalline diblock copolymer,49,50 and binary blend.34 Therefore, we use a dynamic Monte Carlo (DMC) method to address the composition dependent crystallization behavior of binary polymer blends. Below, we describe our simulation technique in detail. We use a coarse-grained lattice model of A- and B-polymers, each with 64 coarse-grained units. In a cubic lattice of size 32 × 32 × 32, we put a total of 480 chains consisting NCA number of A- and NCB number of B-polymers, along the lattice grids. Thus, the occupation density becomes 0.9375, representing a bulk polymer system. To implement a variation in composition in the blend, we vary the composition of B-polymer, with xB ranging from 0.125 to 0.875 with an interval of 0.125. Accordingly, numbers of A- and B-polymer chains are decided. For example, if xB = 0.25, then NCB = 480 × 0.25 = 120 and the remaining chains (viz., 480 × 0.75 = 360) are of A-polymer. In the crystallization process, crystallization is facilitated by the crystallization driving force, whereas the chemical dissimilarity between A- and B-units promotes immiscibility between them and leads to a phase separated state. We model the crystallization driving force as an attractive interaction between neighboring parallel bonds and collinear bonds within A- or Btype units, represented by Up and Uc, respectively. The interaction between A- and B-type units is modeled as a repulsive interaction represented by UAB. The change in energy per Monte Carlo move is then

ΔE = [− (ΔNp + ΔNc)A − λm(ΔNp + ΔNc)B + λΔNAB]Up

We apply a set of micro relaxation moves to simulate polymer chains in the lattice. We employ the single site bond fluctuation algorithm along with periodic boundary conditions to move chain molecules along the lattice grids. The coordination number of our cubic lattice is 26 (6 along the lattice axis, 12 along the face diagonals, and 8 along the body diagonal). Thus, the bond length can be 1 (along the axis), √2 (along the face diagonal), or √3 (along the body diagonal) lattice units. We start our simulation by selecting a vacant site randomly from the available vacant sites and searching for a nearest site occupied by either A- or B-type units. Once an occupied site is found, an appropriate micro relaxation move is selected according to their position along the chainfor terminal units, end bond rotation and slithering diffusion is selected with equal probability; for nonterminal units, a single site bond fluctuation is implemented.34,48 During the movement, we have strictly implemented the excluded volume effectone lattice site is occupied by one unit (either A- or Btype), and no bond crosses each other. Once this self-avoiding criterion is satisfied, we calculate the change in energy associated with the movement. We employ the Metropolis sampling scheme to sample new conformations. The probability of an MC move is given by exp(−ΔE). We accept a new conformation if exp(−ΔE) ≥ r, where r is the random number in the range (0, 1), generated by using the random number generator MT19937.51 We simulate the crystallization of a binary blend by varying Up from 0 (viz., at infinite temperature, athermal state) to 0.6 with a step size of 0.02, to represent a step cooling from a high temperature melt. To equilibrate the system, we calculate the mean square radius of gyration, ⟨Rg2⟩, as a function of Monte Carlo steps (MCS). Variation of ⟨Rg2⟩ with MCS does not show appreciable change beyond 5000 MCS, and it is considered as the equilibration time. We calculate thermodynamics and structural parameters averaged over subsequent 5000 MCS. We define one MCS as 480 × 64 MC moves, viz., on average, one attempted MC move for each unit (A- and B-type) present in the simulation box. To monitor transition from a disordered melt to an ordered crystalline phase, we calculate specific heat (Cv) and fractional crystallinity, of A-polymer (XA), B-polymer (XB), and overall (X) as a function of Up. Specific heat is calculated as equilibrium specific heat from the total energy fluctuations (for all the Aand B-type units in the simulation box), similar to that of Dasmahapatra et al.34,48 We define crystallinity as the ratio of numbers of crystalline bonds to the total numbers of bonds present in the system. A bond is considered to be crystalline if it is surrounded by more than five nearest nonbonded parallel bonds.34,49,50 To locate the macrophase separation point, we calculate Cv for the A−B pair (Cv_AB) on the basis of the demixing energy between A- and B-polymer.34 To monitor the relative mobility of the chain molecules during crystallization, we calculate the mean square displacement of the center of mass (dcm2) at each Up, of each polymer, averaged over all of the chains present in the system. We also calculate the mean square radius of gyration, ⟨Rg2⟩, average crystallite size, ⟨S⟩, and lamellar thickness, ⟨l⟩, as a function of Up, for both polymers. A crystallite size S is defined as a microscopic aggregate having S number of crystalline bonds (A- or B-type) oriented in the same direction. We express lamellar thickness as the average

ΔE = −(ΔNpUp + ΔNcUc)A − (ΔNpUp + ΔNcUc)B + ΔNABUAB

where ΔNp and ΔNc represent the net change in the number of parallel and collinear bonds, respectively, for the A and B polymer and ΔNAB represents the change in the number of contacts between A and B units during each Monte Carlo move. We model A-polymer as the high melting component (HMC); thus, it will crystallize before B-polymer during crystallization from a high temperature homogeneous melt. Therefore, the crystallization driving force for B-polymer would be relatively less compared to A-polymer. To implement this, we take UpB = λmUpA and UcB = λmUcA for the parallel and collinear bond interaction energy, respectively, and we set λm = 0.75 ( 0.28, ⟨Rg2⟩ shows almost a constant value after a marginal increase, where B-polymer crystallizes in the confined space created during the crystallization of A-polymer.

one-step cooling

composition (xB)

Up = 0.28

Up = 0.6

Up = 0.6

0.125 0.25 0.375 0.5 0.625 0.75 0.875

0.085 0.097 0.103 0.107 0.111 0.112 0.112

0.684 0.673 0.683 0.685 0.683 0.694 0.718

0.632 0.640 0.640 0.641 0.648 0.663 0.690

However, at λ = 6, the value of ⟨Rg2⟩ remains almost constant for Up > 0.28, for all of the compositions. The insets of Figure 6 display the value of ⟨Rg2⟩ at Up = 0.28 (where A-polymer crystallizes) and Up = 0.6 (at the end of crystallization of both A- and B-polymer) as a function of xB. Two opposite scenarios on the composition dependency have been observed for λ = 1 and 6. At λ = 1, as the composition heterogeneity decreases (viz., xA ∼ xB), the value of ⟨Rg2⟩ shows a relatively lower value, whereas, when either xA > xB or xB > xA, the values are relatively large. This unexpected trend in ⟨Rg2⟩ is attributed to the dilution effect in the presence of a higher degree of composition heterogeneity. As discussed before, composition asymmetry retards macrophase separation (see Figure 4). As a result, the formation of individual domains of the minor component becomes less facile, which causes the enhancement of ⟨Rg2⟩. However, as xA ∼ xB, the formation of individual domains and macrophase separation becomes more probable. As a result, the value of ⟨Rg2⟩ decreases. On the other hand, at λ = 6, we see an opposite scenario. When xA ∼ xB, the value of ⟨Rg2⟩ shows a relatively higher value. This nonintuitive trend in

Figure 13. Change in crystallization half-time with composition, xB, for A- and B-polymer at (a) λ = 1 and (b) λ = 6. The lines joining the points are meant only as a guide to the eye. 5860

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Figure 14. Snapshots of semicrystalline structures for λ = 1, xB = 0.25 (a) at Up = 0.6 (one-step isothermal cooling), (b) at Up = 0.28 (during twostep isothermal cooling), and (c) at Up = 0.6 (during two-step isothermal cooling). Blue and magenta lines represent crystalline bonds of A- and Bpolymer, respectively; yellow lines represent noncrystalline bonds of both polymers.

(pure A-homopolymer), and finally reaches saturation crystallinity at xB ∼ 0.5. However, the abruptness in the value of crystallinity decreases with increasing xB. The change in crystallinity of A-polymer (XA) and B-polymer (XB) with Up at λ = 1 and 6 is presented in Figure S5, Supporting Information. The saturation crystallinity (Xsat) of A-polymer, Bpolymer, and overall is presented in Figure 7b as a function of xB. With increasing xB, the overall saturation crystallinity (Xsat) lies within a narrow range, ∼0.73−0.77. The saturation crystallinity of pure A-polymer (viz., xB = 0) is ∼0.79 (Figure 7a). The degree of cooling is primarily responsible for the initial development of crystals. As the simulation is carried out with the same degree of cooling, the crystallization of A-polymer is largely governed by the thermodynamic driving force rather than the composition. Moreover, at higher values of xB, Apolymer yields higher crystalline structures, which is attributed to the dilution effect shown by B-polymer (see section 3.1.1). Therefore, the development of crystallinity of A-polymer appears to be almost independent of xB. A marginal increase in crystallinity of the B-polymer is attributed to the higher composition. However, at low xB, crystallinity of the B-polymer is comparatively less compared to A-polymer, because Bpolymer crystallizes in the confined space created during macrophase separation and subsequent crystallization of A-

⟨Rg2⟩ is attributed to the strong repulsive interaction between the components. As the composition of both components is relatively large, formation of large size domains (A- or B-type) is less facile under the influence of strong segregation strength. Large numbers of interconnected (viz., a chain is a part of several domains) smaller size domains are formed. As a result, the chains are relatively stretched and exhibit a higher value of ⟨Rg2⟩. The trend at Up = 0.28 is retained at Up = 0.6, which signifies that the morphology set during the macrophase separation and subsequent A-polymer crystallization is retained (viz., unperturbed) during the subsequent crystallization of Bpolymer. Crystallization of B-polymer happens in the confined space created during the crystallization of A-polymer (see Figure S4, Supporting Information, for the snapshots at Up = 0.28, where A-polymer is almost crystallized and B-polymer is still in a molten state). 3.1.3. Development of Crystallinity. We study the development of crystallinity during nonisothermal crystallization by calculating the crystallinity of A-polymer (XA), B-polymer (XB), and overall (X) as a function of Up, for a series of xB. Overall crystallinity (X) is calculated as a weighted average of summation of A- and B-components: X = XAxA + XBxB. Figure 7a shows a gradual increase in X (λ = 1) with Up and an abrupt increase at Up ∼ 0.28 for all of the values of xB, including xB = 0 5861

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Figure 15. Snapshots of semicrystalline structures for λ = 1, xB = 0.75 (a) at Up = 0.6 (one-step isothermal cooling), (b) at Up = 0.28 (during twostep isothermal cooling), and (c) at Up = 0.6 (during two-step isothermal cooling). Blue and magenta lines represent crystalline bonds of A- and Bpolymer, respectively; yellow lines represent noncrystalline bonds of both polymers.

of smaller size domains are formed. These domains are interconnected, and some of the chains are significantly stretched, which is evident from the increased value of ⟨Rg2⟩ (Figure 6b). The composition dependent crystallinity development has been observed in several blends such as in the blend of PLA and poly(oxymethylene) (POM),16 with closely spaced melting points, the easily crystallizable POM crystallizes first and restricts the crystallization of PLA when POM is more than 50% . Similarly, in the blend of PBS and PEO,9,31 PBS crystallized first and the crystallization of PEO was restricted by the presence of already crystallized PBS. Figure 9 displays the snapshots of the crystalline structure at Up = 0.6 for xB = 0.25 and 0.75, λ = 1 and 6, respectively. Snapshots of the rest of the compositions are available in Figure S6, Supporting Information. 3.1.4. Structural Analysis. To get an insight into the structural evolution during crystallization, we estimate the average crystallite size, ⟨S⟩, and lamellar thickness, ⟨l⟩, as a function of Up at λ = 1 and 6, for both components and for all of the compositions. Crystallite size shows a wider distribution compared to that of lamellar thickness, and the magnitude of lamellar thickness is much smaller in comparison with crystallite sizeit indicates the formation of two-dimensional crystals during crystallization. The variation of ⟨S⟩ with Up for

polymer. At weak segregation, we observed a relatively higher chain mobility of B-polymer (see Figure 3) when A-polymer crystallizes at Up ∼ 0.28 (B-polymer is still in a molten state), across all of the compositions. As a result, crystallization of Apolymer is not hindered too much in the weakly segregated system. Therefore, the saturation crystallinity of both polymers lies within a narrow range with respect to the change in composition. However, in the strongly segregated system (viz., λ = 6), we see a significant change in crystallinity with increasing xB (Figure 8). Saturation values of XA, XB, and X show a nonmonotonic behavior as a function of xB and the values of saturation crystallinities of A- and B-polymer are significantly less compared to those at λ = 1. This decrease in crystallinity is attributed to the effect of the segregation strength. At strong segregation strength, the interface becomes rigid with the formation of large numbers of smaller size domains, producing less crystalline material compared to λ = 1. We also observed that, at strong segregation strength, the chain mobility of both polymers is significantly reduced (see Figure 3), suppressing the development of crystalline domains. With sat increasing xB, both Xsat A and XB first decrease and then increase. As the composition of each component is approaching being equal to each other (viz., xA ∼ xB), both polymers compete for the formation of individual domains. As a result, large numbers 5862

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Thus, it would be appropriate to infer from the above analysis that the dilution effect dominates in the presence of a higher degree of compositional asymmetry (viz., either xA > xB or xA < xB) but gradually fades away when xA ∼ xB. 3.2. Isothermal Crystallization. To understand the effect of thermal history (and cooling pathway) on crystallization and morphological development, we have carried out isothermal crystallization. We first equilibrate the sample system at Up = 0. Following this, we quench the sample system to Up = 0.6, and allow the system to anneal for 105 Monte Carlo steps (MCS), and measure the crystallinity of A-polymer (XA), B-polymer (XB), and overall (X) as a function of MCS. The overall crystallinity is calculated by the summation of the weighted average crystallinity of A- and B-polymer. The trend in overall crystallinity as a function of MCS reveals that the kinetic pathway for crystallization of two crystallizable components is a strong function of the relative composition (see Figure S9, Supporting Information). Figure 12 presents the change in overall saturation crystallinity (Xsat) with xB, at λ = 1 and 6. The overall saturated crystallinity shows a nonmonotonic trend with xB, at both segregation levels, establishing the dependence of transition kinetics on composition. When either of the components is large enough, the overall crystallinity is dominated by that component compared to the other, giving rise to higher crystallinity. When xA ∼ xB, both components compete with each other (since the thermal driving force is adequate for crystallization of both components), leading to the coincident crystallization with less crystallinity. This nonmonotonic trend in crystallinity is equally observed in both weak and strong segregations, although the level of crystallinity is drastically less with a wider variation across the composition in case of strong segregation, which is attributed to the strong repulsive interaction between A- and B-polymer making the interface more rigid and suppressing the crystal development.6 To get an estimate of the effect of composition on the rate of crystallization, we calculate the half-time (in terms of number of MCS) of crystallization for all of the compositions at λ = 1 and 6, and plotted in Figure 13a and b, respectively. The higher the value of t1/2, the slower is the rate of crystallization (viz., rate of crystallization ∼ t1/2−1). The results at λ = 1 (Figure 13a) show a nonmonotonic trend of crystallization half-time with composition, xB, establishing the composition dependency of crystallization. At high enough composition of xB, the rate of crystallization of B-polymer is faster than that of A-polymer, due to the presence of a large number of B-units. As discussed before, due to competitive crystallization at xA ∼ xB, the rate of crystallization slows down with the formation of less crystalline materials (Figure 12). On the other hand, at λ = 6, the rate of crystallization is extremely slow due to the presence of a strong repulsive interaction between the components. As the mechanism of crystallization is coincident, the rate of crystallization of A-polymer slows down at high enough xB. However, the saturation crystallinities of both components are extremely small due to the strong segregation strength, and follow a nonmonotonic trend (see Table S1, Supporting Information). Polymer crystallization is not truly an equilibrium phenomenon. The development of crystalline structure largely depends on crystallization temperature as well as on cooling pathway. In our present study of binary polymer melts, we model A- and Bpolymer with different crystallizability, and we expect that the quench depth may influence crystallization and morphological development. We carried out an isothermal experiment in two

A- and B-polymer is available in Figure S7, Supporting Information. Figure 10 displays the variation of ⟨S⟩ with composition, xB, at Up = 0.6 for A- and B-polymer at λ = 1 and 6. In both segregation strengths, the crystallite size of A- and Bpolymers shows a nonmonotonic trend. At λ = 1, the variation of ⟨S⟩ with xB is relatively small compared to that at λ = 6, for both polymers. During crystallization of A-polymer, B-polymer is still in a molten state, offering less resistance toward the formation of larger size domains. At higher composition, due to the dilution effect of B-polymer, the formation of large size domains of A-polymer is facilitated. On the other hand, crystallization of B-polymer happens in the confined space created during the crystallization of A-polymer, and is almost unaffected by A-polymer. As a result, the crystallite size of Bpolymer also shows the almost composition independent behavior. At λ = 6, we observe a significantly larger variation in ⟨S⟩ compared to λ = 1. At λ = 6, with increasing composition asymmetry, the value of ⟨S⟩ for both components increases, which is consistent with the trend in chain mobility (see Figure 3) and the dilution effect (see section 3.1). At λ = 6, due to strong repulsive interaction between the components, the interface becomes more rigid compared to λ = 1. The formation of larger size crystallites is more probable at λ = 1 compared to that at λ = 6. As a result, the average domain size at λ = 6 is much smaller compared to that at λ = 1, resulting in less crystallinity (Figure 8b). We also examine the average lamellar thickness as a function of composition to get a better understanding on the morphological development during crystallization. The overall trend of ⟨l⟩ with Up looks similar to that of crystallinity (Figure S8, Supporting Information). As expected, the saturation value of ⟨l⟩ is higher for λ = 1 compared to that of λ = 6 for a given composition. Figure 11 represents the variation of the saturation value of ⟨l⟩ (viz., value at Up = 0.6) as a function of xB for λ = 1 and 6, respectively. At λ = 1, the saturation value of ⟨l⟩ for B-polymer, ⟨lB⟩, exhibits an overall decreasing trend with increasing xB, whereas ⟨lA⟩ increases at higher values of xB. This nonintuitive trend in lamellar thickness is attributed to the dilution effect shown by B-polymer. The crystallization mechanism follows different pathways as the relative composition of the blend changes. When xB is low, the crystallization of A-polymer follows a typical “melt crystallization” mechanism, where it is influenced by intra- and interchain entanglement. However, at higher values of xB, during the crystallization of A-polymer, B-polymer is still in the molten state. A-polymer crystallizes in a molten matrix of Bpolymer, which acts like a “solvent” for A-polymer, reduces the hindrance, and facilitates the formation of extended chain crystals. In the melt crystallization mechanism, folded chain crystals are preferred. Due to the formation of extended crystals, crystal thickening takes place with the formation of thicker crystals. When xB ≪ xA, ⟨lB⟩ > ⟨lA⟩, which can be explained as follows: when B-polymer starts crystallizing, Apolymer is already crystallized; therefore, B-polymer is not experiencing any hindrance from A-polymer, facilitating crystal thickening of B-polymer. As xB increases, due to the entanglement effect, the segmental mobility is reduced, and as a result, relatively thinner crystals formed. At very high xB, due to the presence of large composition, thicker crystals are formed with higher crystallinity. A similar nonmonotonic trend has also been observed in the case of strong segregation strength (λ = 6). The increased values of ⟨S⟩ and ⟨l⟩ are well consistent with the magnitude of crystallinity at higher xB. 5863

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The Journal of Physical Chemistry B steps as follows: in the first step, we equilibrate the sample system at Up = 0 and quench to Up = 0.28, annealed for 105 MCS; and in the second step, we quench to Up = 0.6 from Up = 0.28, and annealed for 105 MCS. During the first step of quenching at Up = 0.28 (temperature below the melting point of A-polymer but above the melting point of the B-polymer), A-polymer crystallizes, while B-polymers are still in a molten state. Therefore, the crystallization of A-polymer is not hindered by B-polymer. During the second step of quenching at Up = 0.6 (temperature below the melting points of both polymers), B-polymer starts to crystallize within the confined domains created during macrophase separation followed by Apolymer crystallization. The presence of crystalline domains of A-polymer does not hinder the crystallization of B-polymer. Therefore, the mode of crystallization in two-step isothermal cooling is sequential crystallization, as evident by experimental work on blends of PHB/PLLA,24 where PLLA crystallizes at 120 °C followed by PHB at 90 °C. Similarly, in the PBS/PEO9 blend, crystallization of PBS (at 95 °C) is followed by the crystallization of PEO at 50 °C; also in PLLA/PEO63 blend, wherein PLLA crystallizes at 125 °C followed by PEO at 95 °C. The crystallinity of A-polymer is significantly enhanced during two-step crystallization, compared to one-step crystallization (Table 2). As discussed before, in one-step (viz., coincident) isothermal crystallization, when the sample is quenched at Up = 0.6, the crystallization temperature is well below the melting points of both A- and B-polymer, and hence the driving force is adequate for the polymers to crystallize. In our model, the crystallization driving force for A-polymer is higher than that for B-polymer; as a result, A-polymer possesses a higher crystallinity than B-polymer as the crystallization progresses with MCS. This observation is in close agreement with the experimental work on PHB/PLLA24 blend, when the blend is crystallized at 110 °C. It has been observed that, although PLLA and PHB crystallize simultaneously, the rate of crystallization of PLLA is significantly faster than that of PHB. However, in the blend of PBS and PEO,9 during one-step cooling at 50 °C, the exceptionally fast rate of crystallization of PBS filled the entire space before the crystallization of PEO started. Therefore, the mechanism of crystallization becomes sequential. In one-step isothermal crystallization (viz., quenching to Up = 0.6), interchain entanglement restricts the development of the crystallinity of A-polymer. However, the magnitudes of saturation crystallinity of the B-polymer in both experiments are close to each other (Table 2). Thus, two-step crystallization yields a better crystalline structure for A-polymer over B-polymer. Analysis based on lamellar thickness reveals that the lamellar thickness of A-polymer at Up = 0.6 (one-step quenching) is less than that of Up = 0.28, during the two-step cooling (Table S2, Supporting Information), which is in accord with the Hoffman−Weeks formulation64 and recent experimental observation on the blends of PBS/PEO.9 However, the lamellar thickness of the B-polymer, ⟨lB⟩, at Up = 0.6 in onestep cooling appears to be almost identical to that at Up = 0.6 in two-step cooling, for all of the compositions investigated (Table S3, Supporting Information). This nonintuitive trend in lamellar thickness may be interpreted as follows. Lamellar thickness is largely governed by the degree of undercooling (ΔT = Tαm − T). The effective ΔT for B-polymer remains the same in both one- and two-step isothermal processes, when quenched at Up = 0.6. Therefore, the development of crystal thickness remains identical in both cases. The lamellar thickness of A-polymer at high enough xB shows an increased

value, which is attributed to the dilution effect shown by Bpolymer. Higher crystallinity results due to the crystal growth along the lateral direction. Tables 1 and 2 also show the variation in crystallinity with composition in one- and two-step cooling, at λ = 1. Comparisons of saturation crystallinity of Aand B-polymer at λ = 6 are available in Table S4 and Table S5 of the Supporting Information, respectively. At Up = 0.28, in two-step cooling, as xB increases, the crystallinity of A-polymer remains almost constant except at very high xB (0.875), where it significantly decreases (Table 2). A similar decreasing trend is also observed at Up = 0.6, in two-step cooling. This is attributed to the lesser proportion of A-polymer compared to B-polymer. On the other hand, the crystallinity of B-polymer increases at a higher value of xB (Up = 0.6, xB = 0.875), due to the presence of a large proportion of the B-units. However, in every composition, two-step cooling yields a higher crystallinity than one-step cooling. Figures 14 and 15 display the snapshots of one- and two-step isothermal crystallization at λ = 1, xB = 0.25 and 0.75, respectively.

4. CONCLUSIONS In this paper, we present simulation results on the crystallization of binary polymer blends to elucidate the effect of composition heterogeneity on crystallization and morphological development. In our model, A- and B-polymers become immiscible as we cool the sample system from a high temperature melt. The chemical dissimilarity between A- and B-polymer leads to a repulsive interaction, manifested by segregation strength. As we start cooling the sample system, they phase separate via macrophase separation prior to crystallization. We model A-polymer as a high melting polymer, and as a result, crystallization of A-polymer precedes the crystallization of B-polymer. During macrophase separation, Aand B-polymers form their respective domains and subsequent crystallization happens within the domains created during macrophase separation. In weakly segregated systems (viz., λ = 1), with increasing compositional asymmetry in the blends (viz., one component is present in a higher proportion than the other is), we observe a nonmonotonic trend in transition temperature, crystallization temperature, mean square radius of gyration, and lamellar thickness. As the composition ∼1:1, the respective values tend to possess a lower one, which is attributed to the competition between two components in forming individual domains. A similar trend is also observed with strongly segregated systems (viz., λ = 6), except for the value of ⟨Rg2⟩ which shows an opposite trend. As the composition approaches ∼1:1, due to the competition between two components, a large number of interconnected smaller size domains are formed, which give rise to a higher value of ⟨Rg2⟩. As the composition becomes more asymmetric, the major component excludes the minor component from its domains, and as a result, the value of ⟨Rg2⟩ again decreases. At high enough values of xB (0.75 and 0.875), the lamellar thickness of A-polymer increases, which is attributed to the dilution effect shown by B-polymer. When the composition of B-polymer is very high in the system, it acts like a “solvent” and reduces the topological restriction favoring the formation of thicker crystals of A-polymer. At weak segregation strength, the dilution effect dominates to give a nonmonotonic trend in the crystallization behavior. However, at strong segregation strength, the repulsive strength between two polymers coupled with the dilution effect shows a dramatic change in the crystallization behavior. Isothermal crystallization clearly shows that the crystallization 5864

DOI: 10.1021/acs.jpcb.7b02597 J. Phys. Chem. B 2017, 121, 5853−5866

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The Journal of Physical Chemistry B

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behavior is strongly influenced by the relative composition of the blend for both segregation strengths (viz., λ = 1 and 6). The rate of crystallization measured in terms of the half-time of crystallization also shows a strong compositional dependency. We have also elucidated the path dependent crystallization behavior. Sequential crystallization in two-step cooling yields higher crystallinity with thicker crystals compared to coincident crystallization in one-step cooling, for all of the compositions investigated.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b02597. Snapshots of various block compositions (xB) for λ = 1 and 6 for melt, macrophase separated melt, and semicrystalline state; change in mean square displacement of center of mass (dcm2) of A- and B-polymer with Up for λ = 1 and 6; change in crystallinity of A-block (XA) and B-block (XB) with Up for λ = 1 and 6; change in average crystallite size of A-block (SA) and B-block (SB) with Up for λ = 1 and 6; change in average lamellar thickness of A-block (lA) and B-block (lB) with Up for λ = 1 and 6; change in overall crystallinity with MCS for λ = 1 and 6; crystallinity and lamellar thickness of A- and Bpolymer at λ = 1 and 6 for one- and two-step cooling for various compositions (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +91-361-2582273. Fax: +91-361-2582291. E-mail: [email protected]. ORCID

Ashok Kumar Dasmahapatra: 0000-0002-0082-4881 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS Computational facility supported by the SERB, Department of Science and Technology (DST), Government of India (sanction letter no. SR/S3/CE/0069/2010), is highly acknowledged.

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REFERENCES

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