Dissipative particle dynamics simulation on the self-assembly of linear ABC triblock copolymers under rigid spherical confinements

3.1 Block sequence

Generally, the effect of block sequence on morphologies for multiblock copolymers is vital. Therefore, the morphology for linear ABC terpolymers with three difference sequences (A-B-C, B-A-C, and B-C-A) is examined under the following stationary conditions. Two sets of parameters for the selectivity of confined wall are fixed as α_AW=50, α_BW=25, α_CW=120, and α_AW=α_BW=α_CW=120, respectively. The interaction parameters between different blocks are listed in Table 1. The radius of spherical cavity is R=60. First Figure 2 gives a series of morphologies from symmetrical A₂B₂C₂, B₂A₂C₂, and B₂C₂A₂ triblock copolymers at two sets of interaction parameters (α_iW). As for α_BW(25)<α_AW(50)<α_CW(120) (Figure 2a), the sequence of B-A-C, that is, B₂A₂C₂, can result in the formation of a normal onion-like corona-shell-core (CSC) structure. In detail, blocks B, A, and C aggregate into the corona, shell, and core, respectively. After exchanging the position of blocks A and C, B₂C₂A₂ still aggregates into the normal CSC structure. The only difference is that the porous shell is from block C and the salient core is from block A. When block B is placed in the middle, that is, A₂B₂C₂, the CSC structure disappears which replaced by coupling striped patterns from blocks A and C. It is interesting that block B forms the small core away from the confined wall, although the wall is partial to block B. Then the parameters of α_BW=α_AW=α_CW=120 (Figure 2b) are used to weaken the effect of wall selectivity, in this way, blocks A, B, and C have the equal chance to form the inner core, in order to avoid the contact with the wall. The diagonal of Figure 2b clearly shows the different morphologies of block A, that is, the irregular core for A₂B₂C₂, the helical structure for B₂A₂C₂, and the lamella for B₂C₂A₂. Under the condition of α_BW=α_AW=α_CW=120, the effect of wall selectivity is eliminated; therefore, it thoroughly shows the effect of block sequences. Outwardly, the block sequence of block B in one end (B-A-C and B-C-A) can result in the similar morphologies, as compared with the other sequence of B in the middle (A-B-C). It is worth to note that the interaction parameters between different blocks (α_AB=45, α_BC=75, and α_AC=90) also enter for the characteristic of morphologies.

Figure 2:

Simulation morphologies for symmetrical A₂B₂C₂, B₂A₂C₂, and B₂C₂A₂ triblock copolymers under two sets of interaction parameters of α_iW as a function of block sequences. Pink, green, and blue represent A-, B-, and C-rich domains, respectively.

For several asymmetric triblock copolymers, we also compared the variation of morphologies caused by block sequences, and the results are depicted in Figure 3. Similarly, the discussion still begins with the first parameters of α_BW(25)<α_AW(50)<α_CW(120). In Figure 3a, A₈B₈C₂ and B₈A₈C₂, with the position exchange of blocks A and B, show an interesting phenomenon, that is, the morphology of the exchanged blocks A and B has hardly any variation, and that of block C changes from several inlaid small dots to a whole core. The similar phenomenon is also found for A₂B₈C₈ and A₂C₈B₈ with the position exchange of B and C. B₂A₈C₈ and B₂C₈A₈ exhibit a slightly difference after switching the place of A and C. Block B actually becomes a core (B₂C₈A₈) from a corona (B₂A₈C₈). However, blocks A and C still occur a visible change, that is, a cage of block A around a polyhedral core of block C in B₂A₈C₈ and the coupled blocks A and C. So we can know that the hydrophilic B can bring complex variations if it is short and at the end.

Figure 3:

Simulation morphologies for asymmetrical A₈B₈C₂ and B₈A₈C₂, A₂B₈C₈ and A₂C₈B₈, B₂A₈C₈ and B₂C₈A₈ triblock copolymers under two sets of α_iW as a function of block sequences. Pink, green, and blue represent A-, B-, and C-rich domains, respectively.

The second parameters of α_BW=α_AW=α_CW=120 (Figure 3b) are also chosen to remove the effect of wall selectivity. First by comparing Figure 3a and b, the variation of block sequences under this set of interaction parameters brings the entirely different morphological evolution. Taking A₈B₈C₂ and B₈A₈C₂ as an example, blocks A and B exchange the position and, meanwhile also switch their morphological structures. It is different with the above-mentioned situation that they retained the respective morphological characteristic after exchanging the position. If we neglect the small fluctuation of morphologies caused by the different block interactions (i.e. α_AB, α_BC, and α_CA), the similar conclusion can be obtained from A₂B₈C₈, A₂C₈B₈, B₂A₈C₈, and B₂C₈A₈.

3.2 Wall selectivity

Besides block sequences, the selectivity of confined wall also plays a significant role for the self-assembly under confined spaces. Combined with the fixed other parameters, we then tuned the parameter of α_iW to build the different wall selectivity, which includes α_AW=25, α_BW=α_CW=120 (means the wall prefers block A to other two blocks, defined as AW), α_BW=25 α_AW=α_CW=120 (liking block B, BW), and α_CW=25 α_AW=α_BW=120 (liking block C, CW), as shown in Figures 4–6. In fact, the different block lengths are also considered when building the phase diagrams for all linear ABC triblock copolymers. Therefore, the following discussion also includes the effect of block lengths.

Figure 4:

Morphologies for all l-ABC triblock copolymers at α_AW=25, α_BW=α_CW=120 (defined as AW), α_BW=25 α_AW=α_CW=120 (BW), and α_CW=25 α_AW=α_BW=120 (CW). Pink, green, and blue represent A-, B-, and C-rich domains, respectively.

Figure 5:

Morphologies for all l-BAC triblock copolymers at α_AW=25, α_BW=α_CW=120 (AW), α_BW=25 α_AW=α_CW=120 (BW), and α_CW=25 α_AW=α_BW=120 (CW). Pink, green, and blue represent A-, B-, and C-rich domains, respectively.

Figure 6:

Morphologies for all l-BCA triblock copolymers at α_AW=25, α_BW=α_CW=120 (AW), α_BW=25 α_AW=α_CW=120 (BW), and α_CW=25 α_AW=α_BW=120 (CW). Pink, green, and blue represent A-, B-, and C-rich domains, respectively.

Figure 4 first shows morphologies of all l-ABC terpolymers (2-2-2, 2-2-8, 2-8-2, 2-8-8, 8-2-2, 8-2-8, 8-8-2) in the rigid spherical cavity with R=60. On the whole, l-ABC terpolymers prefer to form the CSC structure, except for those at the second selectivity of BW. In other words, if the block liked by the confined wall locates in the middle of ABC terpolymers, they would generally possess the larruping rule of morphological variation. For instance, the morphologies of l-A₂B₂C₂, l-A₂B₈C₂, and l-A₈B₂C₈ at the first selectivity (AW) are similar to those at the third selectivity (CW), but very different to those at the second one (BW). In detail, for l-A₈B₂C₈ of AW parameters, block A forms the multiporous corona, block B forms the stripped shell, and block C aggregates the irregular core. For the same polymer, the wall selectivity of CW parameters can simply exchange the morphologies of blocks A and C and hardly alter the morphology of B. However, for BW parameters, the morphology, a patch of block C is sewn on block A by a string of block B, is far away from the normal CSC structure. In fact, block B with the good wall selectivity does not form the corona because it is too short compared with the other two blocks. For l-A₂B₈C₂ of BW parameters, the longer B block is easier to build the cagelike corona of imprisoning several small spheres such as “fish” formed by blocks A and C.

As for all l-B_yA_xC_z and l-B_yC_zA_x triblock copolymers, the influence of the different wall selectivity on the morphology is also investigated, as drawn in Figures 5 and 6, respectively. Theoretically, the law of the two types of terpolymers should be similar to that of l-A_xB_yC_z. In Figure 5, B₂A₂C₂ assembles the normal CSC structure at both BW and CW parameters and the coupled double-helix at AW parameters. l-B₈A₂C₈ aggregates two helical strips from the longer blocks B and C that are sewn by the shorter block A. This morphology is very different to the CSC structures with the distinctly corona and core, which corresponds to the different BW and CW parameters, respectively. In addition for l-B₂A₈C₂, the selectivity of AW parameters also brings an A-cage entangling several B- and C-“fishes”. Here, we can ensure that the law of wall selectivity shown by l-B_yA_xC_z is consistent with that by l-A_xB_yC_z. In Figure 6, for symmetric l-B₂C₂A₂, the selectivity of AW and BW parameters only can exchange the corona and core of CSC structures. The selectivity of CW parameters results in a rambling CSC aggregate, which is different with the helix formed by l-A₂B₂C₂ and l-B₂A₂C₂. The reason may be the asymmetrical block interactions, and block C has the large repulsive characteristic with blocks A and B. However, for the asymmetric l-B₂C₈A₂ and l-B₈C₂A₈, the effect of asymmetrical block interactions seems lost, and we still find the similar morphological evolution with other two types of terpolymers. Therefore, we do not describe the morphological details again.

3.3 Spherical radius

In the previous sections, we examined the effect of block sequence and wall selectivity. Here, the effect of radius of confined spherical cavity on self-assembled morphologies is considered. Two kinds of radii are used, that is, R=60 and 80. The corresponding morphologies for R=60 have been seen in Figures 2 and 3, and those for R=80 are shown in Figures 7 and 8 for comparisons.

Figure 7:

Morphologies of three symmetrical A₂B₂C₂, B₂A₂C₂, and B₂C₂A₂ terpolymers at R=80. Pink, green, and blue represent A-, B-, and C-rich domains, respectively.

Figure 8:

Morphologies of six asymmetrical A₈B₈C₂, B₈A₈C₂, A₂B₈C₈, A₂C₈B₈, B₂A₈C₈, and B₂C₈A₈ terpolymers at R=80. Pink, green, and blue represent A-, B-, and C-rich domains, respectively.

We first compared the morphological diversity of symmetric terpolymers in Figures 2 and 7, respectively. In R=60 (Figure 2a), l-B₂A₂C₂ forms the normal CSC structure when α_AW=50, α_BW=25, and α_CW=120. However, when spherical radius increases from 60 to 80, its morphology shows a slight difference, as shown in Figure 7a. The routine corona becomes more scattered, and extra core also becomes the bigger than that in R=60. Besides, the A-shell and C-core also grow many porous. The previous phenomenon is also found for l-B₂C₂A₂. l-A₂B₂C₂ for R=80 (Figure 7a) has the thinner coupled strips than that for R=60 (Figure 2a). In Figure 7b (α_AW=α_BW=α_CW=120), all three symmetric terpolymers form the coupled and independent helix that look like lamella from the whole morphology. Although Figure 2b shows a real lamella for l-B₂A₂C₂, and the thick strips with a little link for l-A₂B₂C₂, from the angle of the whole morphology, we can still think that when α_AW=α_BW=α_CW=120, the radius of spherical confinement does not obviously change the morphology of symmetrical ABC triblock copolymers.

Second we also analyze the morphological difference of asymmetric ABC triblock copolymers, as shown in Figures 3 and 8. When the wall selectivity is fixed at α_AW=50, α_BW=25, and α_CW=120, for example, we can clearly find that the morphology of l-B₈A₈C₂ in R=80 (Figure 8a) shows an obvious change by comparing that in R=60 (Figure 3a). In detail, l-B₈A₈C₂ in R=60 forms the normal CSC structure with the B-corona, A-shell, and C-core. However, when the radius increases from 60 to 80, block B becomes the corona to the irregular core (like a four-way connection), and blocks A and C become the cage shape that corresponds to the corona and the shell, respectively. The terpolymers of l-A₈B₈C₂, l-A₂B₈C₈, and l-A₂C₈B₈ also have the similar phenomena, as shown in Figure 8a. In addition, the morphology of l-B₂C₈A₈ also shows the distinct variation only for blocks A and C, that is, in R=60 blocks A and C form the two occlusive strips; however, in R=80, block A becomes an irregular core with several hump and block C develops into a cage. Only l-B₂A₈C₈ does not show the marked morphological variation. If the wall selectivity is fixed at α_AW=α_BW=α_CW=120, l-A₂B₈C₈, l-A₂C₈B₈, and l-B₂A₈C₈ express the similar laws with the previously mentioned findings from l-A₈B₈C₂, l-B₈A₈C₂, and l-A₂B₈C₈. In detail, in R=80 (Figure 8b) middle blocks aggregate the cagelike structure that are different with those in R=60 (Figure 3b). Other three terpolymers (l-A₈B₈C₂, l-B₈A₈C₂, and l-B₂C₈A₈) do not show the marked morphological variation under this repulsive wall selectivity and spherical radius. Again, we repeat our findings on the effect of spherical radius. The increase of radius of spherical confinement can significantly change the morphology of linear ABC triblock copolymers, especially for asymmetric block compositions and α_AW=50, α_BW=25, and α_CW=120. Symmetrical block compositions are not easily influenced by the spherical radius, especially for the wall selectivity of α_AW=α_BW=α_CW=120.

To further investigate the effect of spherical radius on the morphologies, we amply draw the inner structure of several CSC aggregates with similar appearance under the different spherical confinements by cutting them. The results are given in Figure 9a. As shown by ball-and-stick models in Figure 9a, l-B₂A₂C₂ in R=80 forms the multilayer-onion structure with seven layers (that is BACABAC). However, the same terpolymer in R=60 forms one with five layers (that is BACAB). The l-B₂C₂A₂ has the similar results, that is, it forms seven layers (BCACBCA) in R=80 and five layers (BCACB) in R=60, respectively. Obviously, the reason is that the fully expanded length of linear ABC triblock copolymers is still far less than spherical radius. Therefore, they cannot fill in the cavity of R=80 by one chain, and need the relay of three chains (see Figure 9b). When the cavity decreases to R=60, they only need the relay of two chain to fill in it (see Figure 9c). They clearly show the influence of the block length/spherical radius on the morphology. It is easy to think that increasing the block length can decrease the layers of multilayer onion aggregates. Hence, we also check the morphology of l-B₂A₈C₈ with longer blocks A and C in R=60 and 80, respectively. The extended blocks A and C result in that the onion layers decrease from 7 to 5 in R=80 and 5 to 3 in R=60, respectively.

Figure 9:

(a) Inner structures of several CSC aggregates with similar outward for the different spherical radius (R=60 and 80) and α_AW=50, α_BW=25, and α_CW=120. To clearly expression, the left inner structures are shown by the ball-and-stick model; (b) and (c) sketch maps for the distribution of ABC blocks. Pink, green, and blue represent A-, B-, and C-rich domains, respectively.

3.4 Dynamic evolution

Up to now, we have known the effect of block sequence, wall selectivity, and spherical radius on the assembled structures of linear ABC terpolymers. Furthermore, we also found several typical morphologies, such as multilayer onion, lamella, helix, and so on. Then to seek the formation reason, we examine the dynamic formation pathways for these special aggregates.

For l-B₂A₂C₂ in R=80 and α_AW=50, α_BW=25, and α_CW=120, we have known its inner structure (Figure 9a). Here, we come to know the formation process. Figure 10 presents the separated dynamic evolution processes of A, B, and C domain, respectively. The microphase separation between blocks A, B, and C quickly appears at the primary stage of about t=1000 DPD steps and becomes more and more striking when the simulation time increases. Clearly, block C begins to form a core except for the corona. Both A and C form a shell with several porous and gradually close. Finally, block A becomes an imperforate shell and B becomes a multiparous shell. Other onion-like structures also have the similar evolution process. In addition, we also find that the formative process of onion-like structure is faster than others structures, and the time of self-assembly is generally less than t=10,000 DPD steps. For l-B₂C₂A₂ in R=60 and α_AW=α_BW=α_CW=120, the early phase separation results in the formation of several small and dispersed lumps. Then the lump from same blocks begin to fuse and become big continuous regions (t=4000 DPD steps). After t=20,000, three blocks have begun to form the alternate independent phase that is the embryonic form of lamella. For the same terpolymer, when the spherical radius increases to R=80, the formation pathway is very similar to the stacked lamellae structure, and the difference is that the last aggregate is helix, in detail, three coupled helixes. Under the condition of α_AW=α_BW=α_CW=120, all formed lamella-like morphologies in Figures 2b and 7b also have the similar dynamic evolution process. For l-A₂B₂C₂ in R=60 and α_AW=50, α_W =25, and α_CW=120, block B first aggregates several small balls, then go through the fusion, and finally arrive at the morphology of a core plus the corona. Almost from the outset, block A forms the last phase that is an irregular lump, and the corresponding shape evolution always accompany the changeover of block C, which change from a cage to a broken cage.

Figure 10:

Dynamic evolution of B₂A₂C₂, B₂C₂A₂, and A₂B₂C₂ in the different parameter spaces. t is DPD steps. Pink, green, and blue represent A-, B-, and C-rich domains, respectively.