Nanorods with Different Surface Properties in Directing the

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Nanorods with Different Surface Properties in Directing the Compatibilization Behavior and the Morphological Transition of Immiscible Polymer Blends in Both Shear and Shear-Free Conditions Yongxiang Zhou,†,‡ Manxia Huang,†,‡ Teng Lu,†,‡ and Hongxia Guo*,†,‡ †

Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China ‡ University of Chinese Academy of Sciences, Beijing 100049, China S Supporting Information *

ABSTRACT: To explore the mechanism of how the nanorod surface properties regulate the compatibilization behavior and the morphology transition in demixing polymer blends, we perform dissipative particle dynamics simulations and study the impact of three typical nanorods on the phase separation kinetics and structure as well as their location and arrangement under both shear-free and shear conditions with the variation of nanorod−polymer affinity parameters. Depending on the dispersion and location of nanorods, blends in the quiescent case either undergo full phase separation and generate bulky two-phase morphology, or experience microphase separation and form BμE-like structure, or proceed viscoelastic phase separation and take the kinetically trapped cocontinuous network morphology, whereas shear flow can either accelerate domain coarsening or strongly impact the phase behavior through shear-induced bulk phase separation or shear-induced ordering transition. Particularly, the shear-induced lamellar phase in Janus nanorod-filled blends chooses parallel orientation and displays the lateral ordering within layers.

1. INTRODUCTION Blending polymers is a practical and simple means as to design new materials with beneficial properties of the individual components. However, the miscibility between chemically different polymers is very low; thus, there is a constant search for efficient compatibilizing agents.1 Adding copolymers is not only to improve miscibility2−6 but also can produce a wide range of thermodynamically stable microphase-separated morphologies such as the bicontinuous microemulsion (BμE) and the lamellar phase, which have many technological applications.7,8 Besides copolymers, adding nanoparticles9−12 is an alternative approach to stabilize the immiscible polymer blends.13−16 Among various shapes, rod-type nanoparticles (nanorods, NR) have attracted great interest due to their significant potential in achieving both orientational and positional ordering,17,18 which are desirable for the fabrication of functional materials.19,20 Typically, depending on the surface chemical makeup, nanorods can be classified into three main types: the homogeneous nanorod with a preferential attraction toward one of the two homopolymers (C1), the homogeneous nanorod with a nearly equal affinity for the two homopolymers (C2), and the Janus nanorod (CJ) with a surface divided into two regions of different chemical composition and thereby of opposite affinity toward the two homopolymers. Although previous studies have shed more light onto the close relation © XXXX American Chemical Society

between surface chemistry of nanorods and their compatibilizing capability in polymer blends,21−25 our knowledge of the effect of the surface property on coarsening suppression ability and phase morphology is limited. Particularly, there are still unsolved issues or conflicting results, i.e., the affinity degree of nanorods to the polymers in controlling the spatial location of the nanorods in polymer blends and in stabilizing the systems against coalescence and under what condition C1s can produce the “stable” or long-lived metastable cocontinuous phase morphologies and their underlying mechanisms.26,27 Clearly, a systematic investigation of three typical nanorods such as C1, C2, and CJ in directing the compatibilization behavior and the morphological transition of immiscible polymer blends by tuning the interactions between nanorods and polymers is crucial for uncovering the precise mechanism and factors optimizing the role of nanorods and relevant information is important for tailoring particle surface properties for practical applications. Additionally, in many polymer-processing operations, shear flow is usually involved; therefore, the investigation of polymer blends under shear is of huge importance not only for the technical applications but also for nonequilibrium thermodyReceived: December 10, 2017 Revised: April 3, 2018

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DOI: 10.1021/acs.macromol.7b02624 Macromolecules XXXX, XXX, XXX−XXX

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property on the compatibilization behavior and morphological transition in homopolymer blends; a DPD simulation with simplified or generic coarse-grained models is expected to be sufficient to provide useful information. In this work, we will consider simple ternary blend systems with the homopolymers A and B (denoted as polyAs and polyBs, respectively) having equal lengths and compositions blended with one type of nanorods. Following ref 34, the polyAs and polyBs are modeled as bead−spring chains containing 10 beads per chain (that is, NA = NB = 10) and interacting via a harmonic spring force of

namics. Recent experimental studies on polymeric bicontinuous microemulsion by Bates et al.28,29 indicate that the moderate shear rates induce anisotropy in the nanometer-scale BμE structure while higher rates induce macroscopic phase separation. Nevertheless, to our best knowledge investigations on the effect of shear flow on the behavior of phase-separating homopolymers containing nanorods are rather scarce. On the one hand, a recent experimental study30 demonstrated that Janus nanoparticles can be located at the blend interface under high-shear conditions, while a significant fraction of the block copolymer stabilizers are lost from the interface during the high-shear extrusion process. On the other hand, molecular simulation31 found the shear-induced copolymer contraction along the blend interface normal, which could ultimately lead to the macroscopic phase separation. Whereas shear flow can only induce nanorods to orient, their sizes remain fixed. Meanwhile, the rigid difference between copolymer chains and nanorods may result in a contrast in the elastic properties between the copolymer-laden interface and the nanorod-laden interface, which determines the fluctuation effects and the stability of a BμE. Along this line, introducing nanorods into an immiscible polymer blend could make the whole sample to undergo qualitatively different morphological transformations under flow. The resulting phase behavior may become more complex as nanorods can be selectively located in the homopolymer phases or at the interface depending on their surface property. Therefore, the ternary blends containing nanorods with different surface property are highly interesting systems to study. With the rapid development in computational power and algorithms, the dissipative particle dynamics (DPD) simulation method has become a promising tool to investigate various aspects of polymer blends including phase behavior, dynamics, and morphology evolution.9,10 Considering its instinct strength such as the used soft interaction potential and coarse-grained model which allows us to access the mesoscopic scale at a reasonable computational cost,5,12,16 as well as the fact that in DPD simulations one can nearly continuously change the affinity degree between NRs and polymers, we adopt the DPD simulation technique and systematically study the impact of three typical nanorods of C1, C2, and CJ on the phase separation kinetics and morphology of the immiscible polymer matrix as well as their location and arrangement under both shear-free and shear flow conditions with the variation of nanorod−polymer interaction parameters.

S

2 aijrc ⎛ rij ⎞ ⎜1 − ⎟ 2 ⎝ rc ⎠

if rij ≤ rc

rc

ij

between the adjacent beads in a chain, where

the spring constant and the equilibrium bond length are set to k = 100kBT/rc and r0 = 0.7rc, respectively. Note that the spring force is also part of conservative force. To provide systematic evaluations of the influences from nanorod surface properties, we consider three types of nanorods such as C1, C2, and CJ. As schematically illustrated in Figure 1, each nanorod used in our simulations is

Figure 1. Schematic of the model of nanorods studied in this work; from left to right, the type of the nanorods corresponds to C1, C2, and CJ, respectively.

constructed by assembling many DPD beads with large number density for avoiding the undesirable penetration.35 C1 interacts favorably with polyAs while C2 interacts favorably with both polyAs and polyBs. C2s prefer to lie at the interface between demixing homopolymers with their long axis oriented parallel to the plane of the interface, to maximize the interfacial coverage per nanorod and minimize the system free energy. For CJ, to achieve a fair comparison of these nanorods, we consider lying CJ with its dividing surface parallel to its long axis, which also prefers to segregate at the interfaces with its long axis along the interface. As shown in Figure 1, CJ consists of two equally sized compartments (denoted by p and q) with different chemical makeups, each of which has a preferential affinity with one of the two homopolymers. In this work we will concentrate on the nanorods with aspect ratio of v = 10, wherein all three types of nanorods have the same height of L = 10rc and the same bottom face radii of R = 0.5rc. The volume fraction of nanorods is chosen to be 0.15, that is, ϕrod = 15% and ϕA = ϕB = 42.5%, and the resulting Onsager’s dimensionless parameter ϕrodv is small enough so that all types of nanorods remain in the isotropic state in the shear-free case.

2. METHODOLOGY DPD is a particle-based mesoscale simulation method which was first introduced by Hoogerbrugge and Koelman32 and improved by Espanol and Warren.33 In DPD simulations, an individual bead represents a cluster of atoms or molecules and interacts via soft conservative potentials Vijpot =

rij − r0

( )e

F⃗ ij = k

(1)

where the interaction range or cutoff distance rc defines the basic length scale of the system. The parameter aij represents the bead−bead repulsive strength and henceforth has the units of kBT/rc. Full details of the implementation of DPD method are given in the Supporting Information. Molecular Model. Our main objective is to obtain a fundamental understanding of the effects of nanorod surface B


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Macromolecules Simulation Parameters. The parameter space of our studied ternary polyAs/polyBs/nanorods blends with NA = NB = 10, L = 20R = 10rc, and ϕA = ϕB = (1 − ϕrod)/2 = 42.5% are rather large, as we have at least three types of beads (for example, A and B for polyAs and polyBs; another one or two for C1s, C2s, or CJs) and at least six repulsion interaction parameters. For simplification, the repulsive parameters for the like particle pairs in polyAs and polyBs are set at the usual value of aAA = aBB = 25kBT/rc, while for the unlike homopolymer beads, they are set as aAB = aBA = 80kBT/rc. Then, the resulting Flory−Huggins parameter χAB is 16.83 (more details of this mapping are presented in the Supporting Information), quite larger than the critical interaction parameter χc = 2/N with NA = NB = 10. Note that by choosing such a low compatibility between unlike homopolymer particles, it is possible to speed up the separation process, and the phase separation kinetics can be investigated in a reasonable simulation time. As for the homopolymer−CJ and CJ−CJ interactions wherein p and q represent the beads of two compartments of the Janus nanorod, to simplify our model, the interaction parameters between the unlike beads are set to be equal to aAB; that is, aAq = aBp = apq = aqp = 80kBT/rc. Furthermore, by assuming no preferential interaction between any two CJs, we choose app = aqq = 50kBT/rc. In this study, we attempt to optimize the affinity degree of nanorods to the polymers in controlling the spatial location of the nanorods in polymer blends as well as in stabilizing the systems against coalescence. We hence are only concerned with the affinities of two beads p and q with their favorite homopolymers and tailor such an affinity effect by tuning the values of aAp = aBq from 5kBT/rc to 25kBT/rc with an interval of 5kBT/rc. To fairly compare the effects of nanorod surface properties, repulsion interaction parameters for our studied ternary polyAs/polyBs/C1s systems and polyAs/polyBs/C2s systems are specified in the same way with the aAC1, aAC2, and aBC2 values varied in a range of 5kBT/rc to 25kBT/rc. The complete lists of repulsion interaction parameters for our studied ternary systems are reported in Tables S1−S3 of the Supporting Information. With all the other repulsion parameters fixed, we thus represent aAp, aBq, aAC1, aAC2, and aBC2 by aij in the ensuing simulations unless noted otherwise. Additionally, as aij increases from 5kBT/rc to 25kBT/rc, the corresponding conservative interaction potential energy is varied within several or a dozen kBT (more details of this mapping are presented in the Supporting Information). For example, it changes from 2.5kBT to 0kBT when rij increases from rij = 0 to rij ≥ rc at aij = 5kBT/rc and from 12.5kBT to 0kBT at aij = 25kBT/rc. Although our simulations are undertaken with a simplified generic model without the microscopic details of real systems, it is meaningful to estimate the correspondence between the affinity of polymeric species and functional groups on nanorods and the aij parameter values. Here, we take the C1 nanorod as an example. In experiments, due to modification with dimethyldichlorosilane, the surfaces of fumed silica nanoparticles become hydrophobic, and these hydrophobic nanosilica are dispersed almost exclusively in a polystyrene (PS) matrix with the formation of an adsorbed layer of polymer segments near the particle surface.36 Such preferential affinity between PS chains and dimethyldichlorosilane corresponds to aij ≈ 5− 15kBT/rc in our DPD simulations, since in this case we find the formation of wetting layers on the surface of C1s in the C1sfilled blends as will be given below. Besides, by functionalizing gold nanorods (Au NRs) with a short PS brush,37 these PS-

functionalized Au NRs aggregate instead of disperse in a longchain PS matrix, and the wettability between NRs and polymers is reduced. Such a weak NR−polymer affinity to PS roughly corresponds to aij ≈ 25kBT/rc in our DPD simulations, since in this case the reduced affinity of C1−polymer brings more close contact between C1s which enforces rod aggregates or the rod network and minimizes the wetting layer effect in the C1s-filled blends as will be given below. Simulation Details. In the present work, the cutoff distance, bead mass, and energy are set as the reduced units, that is, rc = m = kBT = 1. Therefore, in what follows, we refer aij without the unit of kBT/rc unless noted otherwise. Then the reduced time unit is defined as τ = mrc 2/kBT . In addition, both rc and τ can be scaled to the realistic units, i.e., rc = 1.06 nm and τ = 15.38 ps (the detailed mapping process is described in the Supporting Information). All simulations are performed in a NVT ensemble with a time step of Δt = 0.01τ and a fixed noise amplitude of σ = 3. Considering the calculation economy, simulations are implemented in a cubic box with a size of L = 40rc, covering 8160 polyAs, 8160 polyBs, and 1222 nanorods. Moreover, additional runs with larger simulation boxes of L = 60rc are carried out to demonstrate that our results are not an artifact of finite-size effect. To allow a meaningful assessment of the performance of these nanorods, most simulations are started from isotropic configurations with nanorods well dispersing in the mixing polymer blend. The equilibration is considered to be reached when the thermodynamic quantities (such as the total energy and bulk pressure) as well as the structural properties (such as radius of gyration of polymer chains, structure factors of the whole sample, and so on) do not change within the simulation time. Simple shear flow was induced by means of the Lees− Edwards boundary conditions (PBC)38 with the shear velocity in the x-direction and the shear gradient in the z-direction at a shear rate of γ̇. In shear simulations, we also start from randomly mixed configurations and exert shear and quenching simultaneously and then analyze the phase separation or phase behavior under shear. For each shear rate, simulations are carried out until the time dependencies of energy and other variables of interest appear to be constant. It must be noted that within our studied shear rate regime from 0.001τ−1 to 0.08τ−1, all nanorod-filled samples were observed to display shearthinning behavior through checking the steady shear viscosity as a function of shear rate, as typically illustrated in Figure S1. Meanwhile, all samples display linear shear velocity profiles, and the average temperature derived in terms of the instantaneous velocity relative to the drift velocity remains at its equilibrium value of 1.0. However, according to τ = 15.38 ps, the applied γ̇ in our work is in the range of 0.65 × 108−52 × 108 s−1. We note that experimental shear rates are limited to around 105 s−1, and thus our shear rates are relatively high but are still common for current DPD simulations (108−1011 s−1).39−41 On the one hand, the smallest shear rate used in computer simulations is often limited by the requirement to establish a steady-state shear velocity profile while the largest shear rate is limited by the stability (i.e., the average temperature at its equilibrium value). On the other hand, the time required to reach steady state increases as shear rate decreases. If simulating with the experimentally accessible shear rates, i.e., 105 s−1 (corresponding to γ̇ ≈ 1.5 × 10−6τ−1), one must perform simulation over times of the order of multiples of 10−5 s = 10 μs (corresponding to one strain) to establish the steady shear, which corresponds C


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Figure 2. Snapshots of morphology evolution for the typical nonsheared and sheared systems of γ̇ = 0.03τ−1 = 1.95 × 108 s−1 with aij = 5: (a) C2− 0.00−5; (b) C2−0.03−5; (c) CJ−0.00−5; (d) CJ−0.03−5; (e) C1−0.00−5; (f) C1−0.03−5. The green and blue spheres represent polyAs and polyBs, respectively, whereas the red ones correspond to C1s and the p part of CJs and yellow ones to C2s and the q part of CJs.

to several times of 6.5 × 107 steps (corresponding to one strain) in our DPD simulations. As time scales of this size 10 μs and higher are rather difficult to access for current computer simulations, it is infeasible for computer simulations to use experimentally accessible shear rates. Thus, the shear rates studied by DPD are often of order 0.001−0.1τ−1. Moreover, the Weissenberg number42 (Wi, the product of γ̇ and the end-toend relaxation time of the polymer chain) is a measure of nonlinearities due to the flow-induced polymer deformation. The onset of flow-induced effects is expected to occur for Wi ≈ 1. If we use experimentally accessible shear rates (∼105 s−1 or γ̇ = 1.5 × 10−6τ−1), then the resulting Wi number is much smaller than 1, i.e., about Wi ≅ 9 × 10−5 for polyAs, which suggests actually shear has little effects on the polymer conformation. Thus, for investigating the sheared polymer systems with obvious flow-induced effects, we must use large high shear rates for making Wi > 1. Although the extremely high shear rates are adopted in our DPD simulations, the corresponding Wi of polyAs varies from 0.06 to 4.97, suggesting that the two homopolymer components of A10 and B10 in our model systems are in a crossover from a Newtonian plateau with shear viscosity independent of shear rate at Wi < 1 to the nonNewtonian shear-thinning behavior with a shear-rate dependent viscosity at Wi > 1. Specifically, with such high shear rates all the nanorod-filled blends exhibit shear thinning behavior as mentioned before, and the resulting sheared structure is different from the equilibrium structure as will be given afterward. Thus, we expect experimental researchers to compare their results with our simulation results at the same Wi, rather than at the same shear rate (γ̇ = 0.001τ−1−0.08τ−1 or γ̇ = 0.65 × 108−52 × 108 s−1). In this case, by using high molecular weight molecules, the relaxation time becomes large enough that the shear-thinning regime in our simulations, that is Wi > 1, can be achieved in experiments by using low shear rates accessible to experiment. For example, the relaxation time of C1024H208243 is about 10−4 s, so that experimental researchers just use a shear rate of 104 s−1 to reach Wi ≈ 1.

Besides, to learn the effect of nanorods on the rheological properties of homopolymers, we measured the steady shear viscosity and/or zero-shear viscosity for the pure polymer melt (A10), the binary immiscible blend of A10 and B10 (A10 + B10), and the mixture of A10 and C1s (A10 + C1), and the relevant results are shown in Figure S2. As expected from the Wi, shear viscosity of A10 melts in a steady shear flow presents a crossover roughly at 6.5 × 108 s−1, below which we see a Newtonian plateau and above which we see shear thinning. This crossover can be understood by considering the competition between chain relaxation dynamics and imposed shear flow. Similar results are obtained in the binary A10 + B10 blend except that its viscosity is some larger than that of A10. Particularly, we found that adding C1s to A10 dramatically increases the viscosity of the bulk phase, leading to a large viscosity contrast between A10 and A10 + C1, and the A10 + C1 sample yields a distinctive non-Newtonian shear thinning behavior. Since our studied ternary mixtures containing nanorods exhibit similar response within 0.001τ−1 to 0.08τ−1, whence we focused only results at an applied shear rate of 0.03τ−1 (1.95 × 108 s−1) in the present work. In what follows, we refer to studied systems as x−n−m for conciseness. Here, the symbol x represents the type of nanorods, x = C1, C2, and CJ, respectively. n represents the applied shear rate, while m denotes the aij value for the nanorod−polymer affinity. For example, C1−0.03−5 means a ternary system containing two immiscible homopolymers and C1 nanorods at aAC1 = 5 under a shear flow of γ̇ = 0.03τ−1. In addition, for a further simplification, we use the symbol x−n to represent a series of ternary blends containing one type of nanorods of x with the aij value varying in a range of 5−25 with an interval of 5 at a shear rate of γ̇ = 0.03τ−1. For example, C2−0.03 means a group of ternary systems containing two immiscible homopolymers and C2 nanorods at aAC2 = aBC2 = 5−25 under a shear flow of γ̇ = 0.03τ−1. Observables. Besides a direct view of the morphology evolution of our studied ternary blends in both quiescent and D


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Macromolecules shearing conditions, we monitor some quantitative observables such as structure factor, the time-dependent average domain size R(t), 2D radial distribution function for the mass center of nanorods g⊥(r⊥), the flow-alignment angle φ, and the orientational order parameter as a function of the rod−polymer affinity for three types of nanorods. As the definitions of these observables have been presented extensively elsewhere,34,44−47 only a brief description is provided in the Supporting Information.

3. RESULTS AND DISCUSSION In order to more comprehensively understand the correlation of nanorod surface chemistry to the compatibilization behavior and morphological transition of polymer blends under both shear-free and shear fields, we performed extensive DPD simulations on three typical blending systems, i.e., polyAs/ polyBs/CJs, polyAs/polyBs/C1s, and polyAs/polyBs/C2s with the variation of nanorod−polymer affinity parameters aij. Interestingly, aij greatly affects the nanorod positional distribution, particularly for C2s. For example, for a strong enthalpic interaction between nanorod unit and its preferred polymer units, that is, aij ≤ 15kBT/rc, most of C2s stay inside the polyAs and polyBs domains; thus, C2s have a high solubility in the polymer components,which leads to a poor compatibilization efficiency. Whereas, for a weak NR−polymer affinity, that is,15kBT/rc < aij ≤ 25kBT/rc, most of C2s adsorb at the interface of polyAs and polyBs, which leads to a good compatibilization efficiency. Therefore, in the following, to elucidate the mechanism of how the nanorod surface property regulates its coarsening suppression ability as well as the structure and dynamics of demixing polymer blends, we present our results in two parts according to the magnitude of aij. 3.1. Phase Separation Kinetics and Morphology at aij ≤ 15. PolyAs/PolyBs/C2s. Although C2s are often referred to as surface-active homogeneous nanorods to inhibit the domain growth and stabilize the immiscible polymer blend,48,49 at a strong NR-polymer affinity of aij ≤ 15 the ternary blends filled with C2s undergo a full phase separation with C2s spreading everywhere as typically illustrated in Figure 2a for the sample at aij = 5. Furthermore, on the basis of direct visual observations, we found that in these C2s-filled blends highly interconnected structure of tiny domains of like polymer beads with C2s inside first appear and gradually increase in size, then coalesce, and grow until the macrophase-separated state with a bulky twophase morphology that spans the whole sample is formed. Hence, the polyAs/polyBs/C2s systems with aij ≤ 15 behave just like a symmetric pure binary polymer blend. However, compared to the neat polymer blend the domain coarsening is slowed down, as typically indicated by comparing the timedependent average domain size curves for the polyAs/polyBs blend and the C2−0.00−5 sample in Figure 3. This is not surprising as the preferential affinity between homopolymer chains and C2s nanorods not just increases the viscosity of polymer phases but also restrains the dynamics of polymer chains. We note that if C2s reside at the polyAs/polyBs interface, the number of unfavorable A/B pairs reduces, and consequently the system enthalpy will decrease; meanwhile, the translational entropy of C2s associated with localizing them at the domain interface will decrease. As a result, whether C2s are adsorbed at the interface or not is determined by a complex interplay between entropy and enthalpy within the system. For the C2sfilled blend with a strong NR−polymer affinity of aij ≤ 15 visual

Figure 3. Time evolution of the average domain size for the four typical systems: pure binary polyAs/polyBs blend, the C1s-filled blend with aij = 5, the C2s-filled blend with aij = 5, and the CJs-filled blend with aij = 5 under shear-free (pure−0.00, C1−0.00−5, C2−0.00−5, CJ−0.00−5) and shear flow of γ̇ = 0.03τ−1 = 1.95 × 108 s−1 (pure− 0.03, C1−0.03−5, C2−0.03−5, CJ−0.03−5).

inspection of our simulation results suggests that most C2s are held inside the polymer domains, which is substantiated by tracking the amount of C2s at the interface. For example, we check and compare the number of C2s at the interfaces between A and B homopolymer regions under various aij conditions after the average domain size of our studied systems approaches saturation or at the last minute of phase separation. As illustrated by the black dotted curve in Figure 4, for the macrophase separating sample with aij = 5 at 10000τ, only 410 C2s are localized at the interfaces, i.e., corresponding to 2/3 C2s randomly dispersed in the homopolymer-rich domains. As aij increases to 10 and 15, the number of C2s adsorbed at the

Figure 4. Number of nanorods at the interface for the C2s-filled systems and the CJs-filled systems with different aij values under both shear-free and shear conditions of γ̇ = 0.03τ−1 = 1.95 × 108 s−1 after the average domain size of our studied systems approaches saturation or at the last minute of phase separation of 10000τ. The whole number of nanorods is fixed at 1222 in the blend. E


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that the growing domains are elongated along the flow direction, resulting in an anisotropic morphology. As typically illustrated in Figure 2b for the C2−0.03−5 system at 1000τ (corresponding to a shear strain of 30), the polysA-rich and polysB-rich channels are sufficiently elongated with nanorods macroscopically aligning in the shear flow direction, while for the nonsheared counterpart both domain shape and nanorod arrangement are isotropic at 1000τ in Figure 2a. Further quantitative characterization in Figures S3 and S4 shows that in the presence of shear field these C2s rods in the two polymer phases orient well along the flow direction with the steady flow alignment angle at 5.54° and exhibit a long-range orientational ordering with the resulting orientational order parameter value higher than 0.9. Therefore, the shear flow drives the anisotropic C2s rod into the nematic phase despite the small Onsager’s parameter. Furthermore, this shear-driven alignment is relatively fast. For example, as indicated by the black curve in Figure S4, for the typical sample of C2−0.03−5, at around time of 1000τ S approaches the limit of near-perfect orientational order, whereas the domain still grows definitely with time as shown by the blue solid line in Figure 3. Apparently, these aligned rods can also help to stretch effectively the phaseseparating cocontinuous morphology into elongated domains. The elongation promotes the collision and the coalescence of C2s-dispersed polymer domains along the flow direction and enhances the domain coarsening in this direction, in agreement with the effects of shear flow on the kinetics of domain growth in binary mixtures.50 Thus, on the basis of both the time evolution of phase-separating morphologies (i.e., Figure 2) and the corresponding time-dependent domain size (i.e., Figure 3), we see the shear flow accelerate the domain growth. For instance, the sample of C2−0.03−5 at 5000τ already attains the bulky two-phase morphology that spans the whole sample, and the corresponding domain size entraps into a finite length roughly corresponding to half a box, while for its counterpart system C2−0.00−5 at 5000τ domains still coarsen with a size obviously smaller than the former. For the C2s with aij ≤ 15, accompanied by the shear-induced C2s orientation along the shear direction, shear flow disturbs the interfacial adsorption of C2s, which results in the number of C2s localized at the interface smaller than that without shear flow, as illustrated by the black solid and dotted lines in Figure 4. This implies that C2s are more preferred to stay in two homopolymer phases when subjected to the shear flow. As only a smaller fraction of the C2s can be absorbed at the A/B interfaces, the resulting more incomplete coverage of the interface leads to a higher interfacial tension, which should also account for the faster domain growth under shear in comparison to the nonsheared samples. Nevertheless, like the nonsheared samples, with the increase of aij the adsorption tendency of C2s in the shearing blends to the polymer interface increases, and thus the domain growth rate and the final domain size in these systems become smaller, as separately illustrated in Figures 4 and 5. All these results indicate that the interplay between the increasing interface tension due to the unfavorable adsorption of C2s at interfaces and the deformation due to shear gives rise faster kinetics of phase separation in C2s-filled polymer blend with a strong polymer− NR affinity of aij ≤ 15. PolyAs/PolyBs/CJs. Unlike the above surface-active homogeneous nanorods C2s that undergo a full phase separation, the CJs-filled systems at aij ≤ 15 go through a microphase separation and form a bicontinuous microemulsion-like

interface increases; i.e., at the same time of 10000τ the number is 556 and 675, respectively, but still nearly half C2s rods remain in matrix domains. These imply that for the C2s with a more favorable affinity of aij ≤ 15 to demixing polymers, the decrease in translational entropy upon nanorods residing at the A/B interface is some dominant over the enthalpy reduction, and thus C2s prefer to stay in the homopolymer-rich domains. However, with the increase of aij, the preferential affinity of C2s to polymers becomes weaker; the ability of C2s to segregate at the interface and reduce the unfavorable A/B pairs gradually increases, which can eventually overcome the entropy loss. Therefore, we see in Figure 4 as aij increases, the tendency of C2s to adsorb at the interfaces is increased. Accordingly, we can expect that as aij is further increased to aij > 15, the preference of C2s to localize in polymer domains will be balanced by the segregation of C2s to the interface, leading to most C2s to reside at the interface. Therefore, the dispersion and location of these homogeneous surface-active nanorods in polymer blends are governed by their affinity to homopolymers, and the adsorption capacity of C2s at the interface of immiscible polymers becomes better with aij increasing. On the other hand, the enhanced interfacial adsorption improves the reduction in interfacial tension, which is the driving force toward macrophase separation. Thus, with aij increasing the domain growth rate in these systems becomes slower, and the resulting final domain size is smaller as indicated by the black dotted line in Figure 5. Moreover, as

Figure 5. Extracted domain sizes as a function of aij for the sheared (γ̇ = 0.03τ−1 = 1.95 × 108 s−1) and nonsheared C2s-filled, CJs-filled, and C1s-filled systems after the average domain size of our studied systems approaches saturation or at the last minute of phase separation of 10000τ.

expected, due to the small Onsager’s parameter of ϕrodv C2s nanorods dispersed within polymer phases under nonsheared conditions stay in an isotropic state without any collective alignment. In the case of phase separating system undergoing shear, the shear flow competes with the phase separation process through its coupling to concentration fluctuations, which could influence the morphology and domain growth kinetics or even lead to shear-induced phase transitions. For the above C2s-filled blends subjected to shear, the visual inspections show F


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Macromolecules disordered phase with the structure factor well fitted with the T−S model. As typically illustrated in Figure 2c for the CJ− 0.00−5 blend, accompanied by like polymer beads aggregating into small network-like domains, these lying Janus nanorods are quickly adsorbed at the interface instead of being mainly confined to polymer domains. This not only drastically slows down domain coarsening in comparison to the neat binary polymer blends as well as the C2s-filled polymer blends but also inhibits the full phase separation with the domain growth exponent n decaying to near zero with the average domain size saturating to a finite and small value, as typically indicated by Figure 3. Because of the unique amphiphilic structure of each individual CJ, the reduction in enthalpy when it resides at the A/B interface with each compartment protruding into its favorite homopolymer domain can overcome the entropic loss. Therefore, in contrast to C2s, CJs strongly segregate to the interface with almost all rods localizing at the interfaces between A and B homopolymer regions. For example, as illustrated in Figure 4, for the CJ−0.00−5 sample at 10000τ, all CJs in the sample are found at the interfaces. In this way, CJs can more greatly reduce the interfacial tension or the driving force for phase separation.34,35 As a result of a very small interfacial tension, the domain growth curves for the CJs-filled systems at aij ≤ 15 (Figure 3) display a slow asymptotic saturated growth dynamics, an indication of microphase separation. The data in Figure 4 for the series of CJ−0.00 systems with aij ≤ 15 show that the number of CJs adsorbed at the interface slightly decreases with the increase of aij. This can be rationalized by considering the role of thermal energy in disrupting the “equatorial” adsorption of Janus nanorods at the interface (that is, the dividing surface or the plane of maximum sectional area, sitting at the interface) and in actuating their wobble or rotation at the interface, which would give rise to a desorption of the CJs. With aij increasing, the preferential affinity of CJs to the polymer matrix becomes weaker, the driving force responsible for the interfacial segregation of CJs will be reduced, and accordingly the effect of thermal fluctuation will turn to be stronger. Therefore, for the CJs with aij ≤ 15, despite the fact that the vast majority of CJs are localized at the A/B interfaces, there is still a slightly reduced adsorption capacity of CJs with aij, which is totally different from the C2s-filled counterpart systems. As indicated by morphology evolutions in the CJs-filled blend, the domain growth kinetics at early times is determined by the interplay between the spinodal decomposition process driven by the minimization of the interfacial free energy and the adsorption of CJs at the interfaces. The slightly reduced adsorption of CJs may lead to a little higher interfacial tension at larger aij, resulting in a faster coarsening in the initial stage of domain formation. Accordingly, the average domain size at late times when the domain growth appears halted, as illustrated in Figure 5, is increased with aij. As for the phase separating CJs-filled blend under shear, it is very interesting to observe the shear-induced ordering transition from isotropic to lamellar. As typically illustrated in Figure 2d, upon the onset of shear, the initial randomly mixed configuration evolves into a connected network, which is distorted along the flow direction at time of 100τ. As the shear strain is increased, the domains are highly elongated with their long axes rotated to the direction of shear flow, but the domain size perpendicular to the flow direction is slightly increased. Meanwhile, due to the shear-induced coalescence, the finer

parallel layers with the elongated polyAs and polyBs domains separated by CJ monolayers are formed. As indicated by the snapshot at 1000τ, this structure resembles the lamellar morphology of microphase-separated diblock copolymers. Particularly, the pattern does not appear to coarsen further with time, and the layer width remains almost unchanged (Figure 3). Furthermore, some handles or conduits in-between layers along the gradient direction are pinched off, leading to the development of a fully aligned lamellar phase with longrange order. To our knowledge, this is the first simulation study to show that shear can induce a phase transition to the lamellar phase in an immiscible polymer blend containing Janus nanorods, while its quiescent structure is BμE. This finding is not entirely surprising as the primary role of shear is to suppress concentration fluctuations. A similar shear-induced ordering phenomenon has been reported in block copolymer melts51,52 and surfactant solutions.53 Moreover, the interfacial adsorption of rigid rods can stiffen the polymer interface and increase its persistence length,3 which in turn enhances the correlation of these parallel layers along the shear gradient direction and improves the tendency to order into the longrang lamellar phase. Note that the shear-induced lamellar phase chooses parallel orientation with the layer normal along the shear gradient direction (∇v), as typically shown for CJ−0.03−5 in Figure 2d. Such parallel alignment seems to occur at all accessible shear rate of 0.001τ−1 to 0.08τ−1 and apparently related to the suppression of concentration fluctuations in the gradient direction. In addition, we find that the rod alignment is also responsible for the development of the so-called parallel orientation. Like C2 rods, although confined to the interface, these lying-type Janus rods still prefer to rotate their long axis toward the shear flow direction with the flow-alignment angle approaching to about 2.64° at aij = 5 and the resulting orientational order parameter close to 0.8 for aij ≤ 15, as indicated in Figures S3 and S5. Such preferential parallel arrangement of CJs may facilitate the homopolymer domains to transform into the parallel alignment state, which allows the lamellar structure to develop in the parallel orientation rather than the perpendicular orientation seen during the shear alignment of lamellar diblock copolymers.51,52 Particularly, the above shear-induced ordering transition occurs independent of the initial states of the CJs-filled system either randomly mixed configurations or microphase-separated BμE-like systems. For the quiescent BμE structure undergoing shear flow, we observed that the shear flow drives the system to self-assemble into a parallel lamellar structure within our studied shear rates from 0.001τ−1 to 0.08τ−1; the typical result is illustrated for CJ−0.03−5 in Figure S6. The above shearinduced ordering transition indicates again that the primary role of shear in the CJs-filled polymer blend is to suppress concentration fluctuations and stabilize the ordered phase. We note that the role of shear in inducing structural transitions in these structured, but fluid phases is of interest from both theoretical and practical points of view. Experimental studies on the related ternary polymer blend containing diblock copolymers as compatibilizing agents have indicated that applied shear can bring the polymeric BμE into a bulk phase separation28,29 instead of the above orientationally distinct selfassembled states. Such difference in shear responses of the diblock copolymer-filled blends and the CJs-filled blends provides a convincing proof of the superior performance of CJs for compatibilizing polymer blends under shear. Actually, G


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More interestingly, for the CJs-filled blend at aij ≤ 15, this shear-induced microphase ordering can go along with the lateral ordering of CJs within the layers in the lamellar phase as illustrated by Figure S7. As this in-layer ordering or packing behavior induces some additional order within the lamellar layers, thus the hierarchical control of the spatial location of Janus nanorods is accessible by applying shear flow, which provides a new route for the fabrication of nanostructured functional materials. PolyAs/PolyBs/C1s. In contrast to the above surface-active C2s or amphiphilic CJs that are either dispersed in the two polymer phases or segregated at their interface, C1 rods under the same condition of aij ≤ 15 are exclusively located in its preferred polyAs-rich domains, as typically illustrated in Figure 2e for the sample at aij = 5. We have noted that in the C2s-filled blend the preferential affinity between homopolymers and nanorods slows down the phase separation as the incorporation of nanorods not only increases the viscosity of polymer phases but also restrains the dynamics of polymer chains. Similarly, for the blends with C1s loadings of 15%, the selective dispersion of C1s in the polyAs-rich phase greatly increases its viscosity, as shown by Figure S2. For example, the zero-shear viscosity is 2.1 × 10−4 Pa·s (T = 298.15 K) for the pure polyAs melt while it is 6.61 Pa·s (T = 298.15 K) with the addition of 26 vol % C1s to polyAs at aij = 5. Meanwhile, the strong preferential interaction of C1s with polyAs at aij ≤ 15 drives the formation of wetting layers on the surface of C1s, as typically indicated by the distribution function g(r) of A beads around the lateral surface of individual C1 rod at aij = 5 in Figure S9. The wetting layers confines or retards the motion of polyAs chains in the vicinity of the rod surface. Hence, the domains in the C1s-filled blend coarsen more slowly, as indicated by comparing the timedependent average domain size curves for the binary blend and the C1−0.00−5 sample in Figure 3. More than the above-mentioned effects which just slow down the kinetics of phase separation, the selective inclusion of C1s into the polyAs-rich phase results in the viscoelastic contrast between polyAs-rich and polyBs-rich phases; i.e., the zero-shear viscosity ratio between the C1s-dispered polyAs-rich phase and the polyBs-rich phase is as high as 32093.3. So the C1s-filled blend may proceed viscoelastic phase separation, which has been known to induce the long-lived percolating network of the more viscoelastic phase even when this phase is in the minority.55−58 In addition, the preferential location of C1s in the polyAs-rich phase could increase its effective volume; i.e., the apparent volume fraction increases from 42.5% to 57.5%, which will be beneficial to the stability of viscoelastic network in polyAs/polyBs/C1s blends. However, this effect should be minor, since the resulted composition asymmetry between the two phases is not significant (i.e., 57.5:42.5), and its role in determining the blend morphology is negligible. Accordingly, we can still take the two dynamically asymmetric homoploymer phases to be in a near-critical composition. Thus, the phase separation behavior of C1s-filled blends is expected to be controlled by the interplay between thermodynamics and viscoelasticity. When our initial randomly mixed configurations deeply quenched, the immiscible polymers first phase separate as usual spinodal demixing and highly interconnected structure is developed. During this early coarsening stage, C1 rods gradually enrich within the polyAs-rich phase. As a result, the role of dynamic asymmetry becomes prominent, and viscoelastic phase separation controls the subsequent coarsening and morphology transition. Indeed, visual inspection and

due to the unique combination of amphiphilicity with the particle character, CJs are strongly adsorbed at the interface even in the shear field, as indicated in Figure 4. For example, at aij ≤ 15, CJs are localized almost exclusively at the interface of homopolymer-rich domains. Whereas for the diblock copolymer-stabilized BμE, it was suggested that the shear flow reduces the energetic gain from the interfacial localization of diblock copolymers, and thus most of the diblock copolymer stabilizers do not adsorb at the interface but become solubilized in the homopolymer-rich phases under high shear flow.31,54 Hence, the diblock copolymer-filled sample behaves just like a typical binary polymer blend. At the same time, by comparing the two solid curves at aij ≤ 15 in Figure 4, we note that the strong interfacial adsorption of CJs can persist during high shear blending in comparison to the C2s, implying that CJs can be used as a more effective stabilizing agent than homogeneous nanorods for immiscible polymer blends undergoing the shear process. As mentioned before, the rigid nanorod-laden interface the weak thermal fluctuation effects. The increased interface persistence length3 enhances the orientation correlation of neighboring interfaces and drives the phase-separating or phase-separated CJs-filled polymer mixtures into to a distinct parallel-oriented lamellar phase. Like in the quiescent state, for the sheared CJs-filled blends with a strong CJ−polymer affinity of aij ≤ 15, as illustrated in Figure 4, the CJ adsorption amount still slightly decreases with the increase of aij. Similarly, accompanied by the gradually weakened driving force toward the interfacial segregation for the CJs, the relatively enhanced thermal fluctuation effect is responsible for such reduced adsorption behavior. Hence, not only in the nonsheared condition but also in the shearing state the tendency of interfacial adsorption capability of surfaceactive Janus CJs with the NR−polymer affinity is very different from that of surface-active homogeneous C2s. Besides, accompanied by the shear-induced CJs aligning toward the shear flow direction, the interfacial adsorption of CJs is still disturbed a bit by shear flow, especially for these nonequatorially adsorbed Janus nanorods that arises from the fluctuation effects. This eventually leads to the fact that the adsorbed number of CJs at the interface becomes a little smaller than that without shear flow, as illustrated by the red solid and dotted lines in Figure 4. However, it is interesting to find that the time-dependent average domain size of the CJs-filled blend with shear flow is smaller than that without shear flow as typically shown in Figure 3. For the phase-separating CJs-filled blend, the shear flow at small strain does not significantly affect the domain growth kinetics; thus, at early times there is no notable quantitative difference in the time-dependent average domain size curves under shear and nonshear conditions. With the elapse of time, the shear strain increases; by suppressing the concentration fluctuations the shear slows down the domain coarsening. As a result, the time-dependent domain size curve under shear turns to stabilize at a smaller value than that in the nonsheared conditions. Obviously, such shear-suppressed coarsening in CJs-filled blends is very different from the case in C2s-filled blends, as typically illustrated by the blue and pink solid lines in Figure 3. Moreover, similar to the nonsheared counterpart, with aij increasing the domain size of the sheared CJs-filled blend slightly increases as indicated in Figure 5; thus, interlamellar spacing also increases. This finding can be rationalized from the reduced interfacial adsorption capability of surface-active Janus CJs with the NR−polymer affinity. H


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Very interestingly, like both C2 and CJ nanorods, the effect of C1s on the compatibility of polymer blends and phase separation kinetics can be adjusted by NR−polymer affinity of aij. With the increase of aij, the preferential interaction of polyAs chains with the surface of C1 rods becomes weaker, and thus the tendency of polyAs chains to be adsorbed on the surface of C1s reduces, as indicated by the distribution function g(r) of A beads around the C1 lateral surface in Figure S9. Therefore, the coarsening suppression ability of wetting layer is expected to decrease. On the contrary, raising aij reduces rod-to-rod distance, as illustrated by the radius distribution function g(r) of C1 mass centers in Figure S10, which may enforce the rod network and its ability to kinetically arrest coarsening is expected to be enhanced. Because of the interplay of the above two effects, the resulted level of kinetics arresting in the C1sfilled blend will be a nonmonotonic function of aij, although the persisted network structures induced by viscoelastic phase separation are well persevered in these systems. As expected, with the increase of aij, the domain growth rate at aij ≤ 15 is dominated by the former effect, and the resulting final domain size grows as indicated in Figure 5. While, for the C1s-filled blends with 15 < aij ≤ 25, as we will show in the next section, the domain coarsening rate is dominated by the latter effect, leading to the slower phase separation kinetics. Additionally, like C2s- or CJs-filled polymer blends, shear flow can strongly affect the phase-separation behavior and morphological transition in the C1s-filled blends. In the quiescent state, the cocontinuous network morphology is kinetically trapped due to the complex interplay between viscoelastic phase separation, restrained dynamics of polymer chains within the wetting layers, and impeding effect of the percolated particle network on the phase interface movement and the domain coarsening. In the start-up of shear flow, the behavior of phase-separating C1s-filled blends will be very complex and involves complex combinations of kinetics, thermodynamics, hydrodynamics, and viscoelasticity. However, to the best of our knowledge, there is no study on the kinetics of phase separation and the structural evolution in an immiscible polymer blend containing C1 type of rods under shear. Our direct visual observations show that when the C1sfilled blend is deeply quenched and simultaneously undergoes shear, it first proceeds as in the quiescent state, involving the formation of continuous network morphology and selective dispersion of C1 rods into its preferred polyAs phase. Further, as typically illustrated in Figure 2f for the sample C1−0.03−5, with the increase of shear strain, not only these C1 rods rotate their long axis toward the shear flow direction, i.e., the steady flow-alignment angle close to 2.56° as indicated by Figure S3, but also the growing domains are elongated along the flow direction, in analogy with the C2 or CJs nanorods. Particularly, the viscoelastic contrast between polyAs-rich and polyBs-rich phases would make the continuous network structure more prone to shear-induced elongation and alignment. Therefore, in contrast to the nonsheared counterpart, the shear flow drives the anisotropic C1 rods within the polyAs-rich phase into the nematic phase with the resulting orientational order parameter higher than 0.9, as indicated in Figure S8, although the Onsager’s dimensionless parameter ϕrodv remains small with the effective local C1 volume fraction attaining to 0.15/(0.425 + 0.15) = 26%. Such parallel oriented rods would also promote the phase-separating cocontinuous network into elongated domains. As the elongation facilitates the domain collision and coalescence, the shear flow accelerates the coarsening of phase

cluster analysis of our simulation results on the C1s-filled blend with a strong NR−polymer affinity indicate the interconnected network structure in the early stage can sustain for a longer period of time. For example, as illustrated in Figure 2a,e, for the C1−0.00−5 sample the continuous network morphology remains for 10000τ, while for the dynamically symmetric C2s-filled counterpart a bulky two-phase morphology that spans the whole sample is already formed at 10000τ. Further prolonging simulation to 40000τ, the C1−0.00−5 sample is keeping the viscoelastic network, again showing the extreme slow pattern coarsening. On the one hand, preserving the continuity of more viscoelastic phase is a characteristic of viscoelastic phase separation. On the other hand, the inclusion of 15% rigid rods with aspect ratio of 10 and rod length of 10rc in a 42.5% homopolymer network with polymer chain size, i.e., the root-mean-squared radius of gyration equal to 1.05rc, could promote the networking of C1s within the polyAs-rich phase. This is confirmed by direct visual observations (Figure 2e), wherein the well-distributed and random-oriented red rods form a network structure that percolates throughout the continuous polyAs-rich domain. Such percolated particle network could restrain the dynamics of polyAs-rich phase and hinder the movement of phase interface. Therefore, in addition to the wetting layer that retards the domain growth by restricting the motion of polymer chains near particle surface,36,59 the C1 network also contributes to slowing down the phase separation process. In this case, it is not surprising to see that the coarsening is more sluggish in polyAs/polyBs/C1s samples than in polyAs/polyBs/C2s ones, as typically indicated in Figure 3, even if there are still 1/3 C2s localized at the interfaces in the C2s-filled systems, which has the effect of slowing down phase-separating process. Hence, for both types of systems that experience macrophase separation the derived domain size in the C1s-filled blend at the last minute of phase separation of 10000τ is smaller than in the C2s-filled blend, as indicated in Figure 5. Therefore, in the quiescent state, at a strong rod−polymer affinity the domain coarsening in C1sfilled blends is more sluggish than in C2s-filled ones. Similar percolated particle networks within one phase have been reported recently,30,60−62 although their formation mechanism and coarsening suppression ability vary depending on the studied samples. For instance, simulations show that when the C1 type of rods at relatively low content are immersed in a binary, phase-separating blend, they can self-assemble into needle-like percolated networks within their preferential minority phase due to the complex dynamic coupling of phase separation between the fluids, preferential adsorption of the minority component onto the mobile rods, and the rod− rod repulsion.60,62 Very recent experimental work demonstrates that due to attractive interactions between particles, the aggregation of rods at modest volume fractions into a percolated network or the aggregation-induced particle gelation can kinetically arrest a cocontinuous blend morphology.26 Our work further demonstrates that C1s with the repulsive interaction between nanorods can also induce the immiscible polymer blend to form a long-lived network at modest rod content. Nevertheless, compared with CJs segregated at the interface between two polymer phases, the percolated C1s network within one of the two phases of blends is still less effective to suppress the coarsening process, as indicated by time-dependent average domain size curves for the C1−0.00−5 and the CJ−0.00−5 samples in Figure 3 as well as the derived domain sizes in Figure 5. I


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Figure 6. Snapshots of morphology evolution for the typical nonsheared and sheared systems of γ̇ = 0.03τ−1 = 1.95 × 108 s−1 with aij = 25: (a) C2− 0.00−25; (b) C2−0.03−25; (c) CJ−0.00−25; (d) CJ−0.03−25; (e) C1−0.00−25; (f) C1−0.03−25. The green and blue spheres represent polyAs and polyBs, respectively, whereas the red ones correspond to C1s and the p part of CJs and yellow ones to C2s and the q part of CJs.

domains in the dynamically asymmetric C1s-filled blend, in agreement with the effects of shear flow on the phase separation kinetics in the dynamically symmetric C2s-filled blends. Thus, according to the pattern evolution in Figure 2e,f as well as the corresponding domain size curves in Figure 3, we see the typical sample of C1−0.03−5 at 10000τ already loses its cocontinuous network nature and attains a full phase-separation state with two bulky domains, while for its quiescent counterpart sample the interconnected network structure is kinetically trapped. In addition to the shear-induced orientation or stretching of C1 rods and the phase domains that enhances the domain coarsening in the sheared C1s-filled blend, the external flow leads to the kinetics of phase separation in dynamically asymmetric C1s-filled systems faster than dynamically symmetric C2s-filled systems. As indicated by the morphological transition in Figure 2d,f as well as the corresponding timedependent domain size curves in Figure 3, the domain growth rate and final domain size in the C1−0.03−5 system are relatively large when compared to the dynamically symmetric C2−0.03−5 sample, while in the shear-free condition the counterpart C1−0.00−5 sample displays slower coarsening of the domain structure than the C2−0.00−5. The switch from a relatively slow coarsening to a relatively fast one upon the application of an external shear deformation is due to the viscoelastic contrast between polyAs-rich and polyBs-rich phases. Since the elastic stress induced in the higher viscoelastic phase makes phase domains easier to deform under shear flow, the interconnected structure becomes more anisotropic, and the shear-induced coalescence would be more significant. Furthermore, compared with the Janus rods in sheared blends, due to their excellent capacity of interface adsorption and lowering thermodynamic force for domain growth, CJS-filled blends undergo microscopic phase separation in the start-up of shear flow while C1s-filled blends undergo macroscopic phase separation with faster phase separation kinetics.

As for the effect of NR−polymer affinity on the kinetics of domain growth in sheared C1s-filled blend, with the increase of aij the domain growth rate reduces; hence, the final domain size in these systems become smaller, as illustrated in Figure 5. Note that the slow coarsening with aij in C2s-filled systems is due to the thermodynamic force of lowering the interface free energy, since the adsorption tendency of C2s in the shearing blends to the polymer interface increases with the increase of aij. In the C1s-filled system, raising aij reduces the rod-to-rod distance and enforces rod−rod interactions; thus, the C1s-reinforced polyAsrich domain will display greater strength than the soft polyBsrich domain. Although the viscoelastic contrast makes the domains more prone to shear-induced elongation and alignment, the higher elastic stress induced in the higher viscoelastic phase would slow down the domain coalescence. This is especially so for the soft polyBs-rich domain, as the coagulation of the neighboring soft domains would require the higher viscoelastic domain to drain away. Meanwhile, the enhanced rod aggregates within C1 nematic phase at larger aij could greatly hinder the motion of interfaces; the resulting slower interface relaxation also contributes to the observed sluggish domain coarsening for the shearing C1s-filled blends with the increase of aij. 3.2. Phase Separation Kinetics and Morphology at 15 < aij ≤ 25. PolyAs/PolyBs/C2s. As expected, when aij is increased to aij > 15, the preference of C2s to localize in polymer domains is overwhelmed by the segregation of C2s to the interface, leading to more than half of C2s absorbed at the interface, as illustrated in Figure 4. In this case, the C2s-filled systems undergo microphase separation and form a BμE-like structure, in contrast to the samples with aij ≤ 15 wherein the macrophase-separated state with a bulky two-phase morphology is observed. In addition, our direct visual observations suggest that the polyAs/polyBs/C2s systems with 15 < aij ≤ 25 behave like the polyAs/polyBs/CJs systems. Take the typical sample of C2−0.00−25 as an example (see Figure 6a); upon J


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localized at the interface decreases in Figure 4. The resulting weakened interfacial adsorption leads to a higher interfacial tension or driving force toward macrophase separation and accelerates the domain growth, as reflected in Figure 7. Particularly, the above shear-induced bulk phase separation phenomenon in C2s-filled systems with 15 < aij ≤ 25 is independent of initial states either the randomly mixed configuration or the quiescent microphase-separated BμE. We note again that the similar shear-induced bulk phase separation was reported in the three-component polymeric bicontinuous microemulsion containing diblock copolymers as compatibilizing agents.28,29 Such similarity also implies that like diblock copolymers,31,54 the strong interfacial adsorption of C2s with 15 < aij ≤ 25 cannot persist under shear flow. Thus, the surfaceactive homogeneous C2 nanorods are not effective stabilizing agents for immiscible polymer blends undergoing the shear process. In addition, like the nonsheared samples, with aij increasing, the interface adsorption capability of C2s in the shearing blends increases, and thus the domain growth rate reduces and the resulting final domain size becomes smaller, as illustrated by black solid lines in Figure 5. PolyAs/PolyBs/CJs. Similar to the structural evolution process and mechanism in the above CJs-filled systems at aij ≤ 15, when 15 < aij ≤ 25 the blends filled with CJs also undergo a microphase separation and form a BμE-like phase with most Janus rods localizing at the interfaces, as typically illustrated in Figure 6c. It is worthy to stress again that although both CJs and C2s can inhibit the immiscible polymers from full phase separation at a weak NR−polymer affinity, the phase separation dynamics of ternary systems containing CJs is slower and the average domain size at late times of phase separation process is smaller than the ones containing C2s. Thus, the compatibilization efficiency of Janus nanorods is better than the surface-active homogeneous nanorods. Furthermore, with aij increasing, the number of CJs adsorbed at the interface is decreased and the average domain size at late times is increased as in the aij ≤ 15 systems, which are also different from the C2sfilled counterpart systems. For the above phase-separating CJs-filled blends subjected to shear, the shear ordering phenomena seen in the aij ≤ 15 systems are also present, as typically illustrated in Figure 6d. Visual inspection of simulation results and data analysis of the domain growth kinetics (see Figure 7) and rod orientation (see Figures S3 and S5) suggest that the pathway and the origin of the shear-induced isotropic to lamellar phase transition with the lateral ordering of CJs are consistent with the findings in the aij ≤ 15 systems. In addition, the observed discrepancies in the shear-induced structure transitions between CJs- and C2s-filled blends at 15 < aij ≤ 25 can be attributed to their different interfacial adsorption capabilities. Furthermore, as the behavior of these sheared CJs-filled systems is controlled by the same physical mechanisms, tuning aij produces the exact same qualitative trends on the CJ adsorption and the domain size in the 15 < aij ≤ 25 samples as in the before-mentioned aij ≤ 15 systems. PolyAs/PolyBs/C1s. Unlike the above C2s- or CJs-filled blends that undergo a microphase separation and form a BμElike phase at 15 < aij ≤ 25, the C1s-filled blends under the same condition proceed via viscoelastic phase separation, and the cocontinuous network morphology is kinetically arrested, which are very similar to that observed in the aij ≤ 15 samples. However, compared to those interfacial particles, i.e., C2s or CJs at 15 < aij ≤ 25, this kinetic arrest is still less effective to

the initial randomly mixed configuration deeply quenched, the immiscible polymers first phase separate as usual spinodal demixing; then with the adsorption of more and more C2 nanorods at the interface, they evolve very slowly and proceed toward microphase separation. Further, as indicated in Figure 7,

Figure 7. Time evolution of the average domain size for the fourtypical systems: pure binary polyAs/polyBs blend, the C1s-filled blend with aij = 25, the C2s-filled blend with aij = 25, and the CJs-filled blend with aij = 25 under shear-free (pure−0.00, C1−0.00−25, C2−0.00− 25, CJ−0.00−25) and shear flow of γ̇ = 0.03τ−1 = 1.95 × 108 s−1 (pure−0.03, C1−0.03−25, C2−0.03−25, CJ−0.03−25).

the average domain size at intermediate and late times follows slow nonalgebraic growth dynamics, and the domain growth appears to be halted. Furthermore, with the increase of aij the enhanced interfacial adsorption inhibits the domain growth more pronouncedly, and the resulting final domain size becomes smaller as indicated in Figure 5. Therefore, C2s have a good performance on compatibilizing polymer blends at a weak C2s−polymer affinity. However, the coarsening suppression ability of C2s at such a weak C2s−polymer affinity is still inferior to CJs no matter how strong or weak the CJs− polymer affinity is as the former systems have relatively larger domain sizes (Figure 5). The origin of this difference can be traced back to the two factors. On the one hand, due to the homogeneous surface property, C2s have a higher probability of desorption from the interface to the bulk than CJ.35 On the other hand, there is no energetically difference for the interfacial segregated C2s to embed more deeply into one phase than the other phase, whereas CJs prefer to reside with their dividing surface, that is, the plane of maximum sectional area, at the interface. Therefore, C2s are less effective than CJs in reducing the interfacial tension or the driving force for domain growth. Upon the onset of shear flow, in contrast to the CJs-filled system the shear-induced ordering transition does not occur in the C2s-filled system. As typically illustrated in Figure 6b, the stretched domains in the sheared C2s-filled blend at 15 < aij ≤ 25 evolve into a large strip structure with most C2s distributed in the homopolymer-rich domains. This is not surprising, as shear flow disturbs the interfacial adsorption of C2s. Like in the strong C2s−polymer affinity condition, for the C2s-filled blend at 15 < aij ≤ 25 accompanied by the shear-induced C2s orientation along the shear direction, the number of C2s K


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capability to kinetically arrest coarsening. In this case, the C2sfilled systems undergo microphase separation and form a BμElike structure, whereas at a strong rod−polymer affinity they experience a full phase separation with a bulky two-phase morphology. The switch from macrophase separation to microphase separation as aij increases is related to the trend of C2s to either localize in polymer domains or adsorb at the interface. In the presence of shear field, shear flow disturbs the interfacial adsorption of C2s, accelerates the domain growth, and even induces bulk phase separation. Thus, C2 nanorods are not effective stabilizing agents for immiscible polymer blends undergoing the shear process. Nevertheless, aij can regulate the interfacial adsorption tendency and coarsening suppression ability of C2s. With the increase of aij, the interface adsorption capability of C2s in both nonsheared and sheared blends increases, the domain growth rate reduces, and the resulting final domain size becomes smaller. For the Janus nanorods, the CJs-filled systems go through a microphase separation and form a BμE-like structure. Because CJs are strongly adsorbed at the interface even in the shear field, the compatibilization efficiency of CJs is better than the C2s. To our knowledge, this is the first simulation study to show the shear-induced ordering in an immiscible polymer blend containing Janus nanorods. Related experimental studies on the three-component polymeric BμE have indicated a shearinduced bulk phase separation. Such different response offers a convincing proof of the superior performance of Janus nanorods for compatibilizing polymer blends under shear conditions. Furthermore, the shear-induced lamellar phase chooses parallel orientation and exhibits the lateral ordering within the layers. Hence, the hierarchical control of the spatial location of Janus nanorods can be accessible by applying shear flow, which provides a new route for the fabrication of nanostructured functional materials. Additionally, with aij increasing, the adsorption capacity of CJs is reduced slightly, and the average domain size at late times is increased, which are different from the C2s-filled counterpart systems. For the homogeneous nanorods with a preferential attraction toward one of the two homopolymers, due to the selective dispersion of these C1 nanorods into the preferred polyAs-rich phase, the cocontinuous network morphology is kinetically arrested via a complex interplay between the viscoelastic phase separation, restrained dynamics of polymer chains within the wetting layers, and impeding effect of the percolated particle network on the phase interface movement and the domain coarsening. Accordingly, the resulting level of kinetics arresting in the C1s-filled blend is a nonmonotonic function of aij, in contrast to the C2s and CJs cases. Therefore, in the quiescent state, only at a strong rod−polymer affinity the domain coarsening in C1s-filled blends becomes more sluggish than in C2s-filled ones, but this kinetic arrest is still less effective to suppress the coarsening process when compared to those interfacial particles, i.e., CJs or C2s at a weak rod−polymer affinity. Note that recent experiments indicate a key for arresting a cocontinuous blend morphology at modest rod volume fractions is to have attractive rod−rod interactions. Our work further demonstrates that C1s with the repulsive rod−rod interaction can also induce the immiscible polymer blend to form a long-lived network at modest content. In the start-up of shear flow, we find the shear flow accelerates the coarsening of phase domains, and the long-lived cocontinuous network morphology is unattainable. Particularly, the domain growth rate and its size as well as phase morphology in the shear field

suppress the coarsening process, as typically indicated in Figures 7 and 5. Unlike the aij ≤ 15 case, for the C1s-filled blends with 15 < aij ≤ 25, the wetting layer effect is minimized; i.e., at aij = 25 there is a “depletion” layer without any A beads in it before the first main peak appears at a larger distance of 1.09rc from each individual rod when compared to the aij = 5 case as indicated by A bead distribution function g(r) in Figure S9. Whereas, with the increase of aij the resulting smaller interparticle distance enforces the rod network; i.e., the first main peak of the C1 mass center RDF shifts to a smaller distance and move to a quite higher intensity at aij = 25 when compared to the aij = 5 case as illustrated in Figure S10, and hence the kinetics arresting level turns to increase for the C1sfilled blend with 15 < aij ≤ 25. This leads to a slower phase separation process, and the resulting aij-dependent final domain size curve switches from a rise tendency at aij ≤ 15 to a downward trend within 15 < aij ≤ 25 as indicated in Figure 5. Like the aij ≤ 15 systems, the quiescent isotropic cocontinuous network morphology in the C1s-filled blends with 15 < aij ≤ 25 is disrupted by shear flow. However, instead of a full phase-separation state with two bulky domains at aij ≤ 15, when the latter systems are subjected to the shear flow they evolve into an elongated network with the polyBs-rich columns along the direction of the shear flow, as typically indicated by the morphological transition in Figure 6f. The origin of such different pattern-evolution process can be ascribed to the slow coarsening at higher aij. As the resulting smaller interparticle distance enforces rod−rod interactions, the enhanced viscoelastic contrast between the C1s-reinforced polyAs-rich domain and the soft polyBs-rich domain slows down the coalescence of the adjacent shear-elongated domains, particularly for the soft polyBs-rich domains which require the higher viscoelastic C1sreinforced polyAs-rich domains to drain away. Therefore, the restrained coagulation of the soft domains59 in comparison to the more viscoelastic domains leads to the polyBs-rich columns persist instead of connecting into one bulky domain. Nonetheless, when compared to the shear-free counterpart, the shear-induced orientation or stretching of C1 rods and phase domains still promotes the domain coalescence along the flow direction and enhances the domain coarsening in the sheared C1s-filled blend. Lastly, despite the C2s-filled systems with 15 < aij ≤ 25 undergoing shear-induced bulk phase separation, due to the viscoelastic contrast in C1s-filled systems and the weak but not negligible adsorption of C2s at the domain interfaces, the domain growth in the shearing C1s-filled blend with 15 < aij ≤ 25 is relatively faster than the C2s counterpart, as reflected in Figures 7 and 5.

4. CONCLUSION In this work, we adopt the DPD simulation technique and systematically study the impact of three typical nanorods such as C1s, C2s, and CJs on the phase separation kinetics and structure of the immiscible polymer matrix as well as their location and arrangement under both shear-free and shear flow conditions with the variation of nanorod−polymer affinity parameter aij. We find that the surface properties of nanorods and particularly the rod−polymer affinity control the compatibilization behavior and the morphology transition of polymer blends via manipulating their positional distribution inside the polymer blends. For the currently so-called “surface-active” homogeneous nanorods, only at a weak rod−polymer affinity these C2 nanorods can act as interface active particles with an enhanced L


Article

Macromolecules

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are also closely related to the rod−polymer affinity as in the quiescent case. Clearly, our study clarifies some unsolved issues or conflicting results as we posed earlier, i.e., the affinity degree of nanorods to the polymers in controlling the spatial location of the nanorods in polymer blends and in stabilizing the systems against coalescence and under what condition C1 can produce the long-lived metastable cocontinuous phase morphologies and their underlying mechanisms. Relevant information is important for tailoring nanorod surface properties and optimizing the role of nanorods in the rational design and fabrication of advanced nanocomposites and ordered nanostructures.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b02624.

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Figures S1−S10 and Tables S1−S3 (PDF)

AUTHOR INFORMATION

Corresponding Author

*(H.G.) E-mail [email protected]; Tel +86 10 82618124; Fax +86 10 62559373. ORCID

Hongxia Guo: 0000-0003-3655-6441 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the support of the NSF China (21174154, 21790343, and 20874110).

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REFERENCES

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Nanorods with Different Surface Properties in Directing the

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