Supporting Information for

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1 Supporting Information for Sequence-Regulated Supracolloidal Copolymers via Copolymerization-Like Coassembly of Binary Mixtures of Patchy Nanoparticles Xiaodong Ma, Mengxin Gu, Liangshun Zhang, * Jiaping Lin * and Xiaohui Tian Shanghai Key Laboratory of Advanced Polymeric Materials, State Key Laboratory of Bioreactor Engineering, Key Laboratory for Ultrafine Materials of Ministry of Education, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai , China * zhangls@ecust.edu.cn (Zhang L.); jlin@ecust.edu.cn (Lin J.) Contents Part A: Details of simulation method Part B: Self-assembly behaviors of divalent patchy nanoparticles Part C: Coassembly kinetics of binary mixtures Part D: Prepolymerization strategy of binary mixtures Part E: Self-assembly behaviors of monovalent patchy nanoparticles Part F: Coassembly kinetics of monovalent and divalent nanoparticles S1

2 Part A. Details of simulation method Dissipative Particle Dynamics In the model, the beads of dissipative particle dynamics (DPD) simulations represent a group of atoms or a volume of fluids and interact through short-ranged potentials. S1 The beads labeled by index i = 1, 2,, N occupy continuous positions r i and velocities v i. The temporal evolution of i-th bead is described by the Newton's motion equations dr i dt = vi and m i dv i dt = fi, where m i is bead mass. The total force f i on the i-th bead is sum of conservative force F C ij, dissipative force F D ij and random force F R ij, i.e., f i = j i (F C ij +F D ij + F R ij). The conservative force for non-bonded beads is expressed as F C ij = { a ij(1 r ij r c )r ij (r ij < r c ) 0 (r ij r c ) (S1) where the interaction parameter a ij determines maximum repulsion and r c represents cutoff radius of interaction. The dissipative and random forces are respectively given by F D ij = γ ω D (r ij )(r ij v ij )r ij and F R ij = σω R (r ij )ξ ij r ij / δt, where r ij r i -r j and v ij v i -v j. r ij is relative displacement between the i-th and j-th beads and r ij = r ij r ij is the corresponding unit vector. The friction coefficient γ and the noise amplitude σ govern magnitude of dissipative forces and intensity of random forces, respectively. The weight functions ω D (r ij ) and ω R (r ij ) respectively determine range of dissipative and random forces and vanish for. The r ij r c term ξ ij is a random variable with zero mean and unit variance. δt is time step of simulations. In addition, constraints between the connected beads within polymer chains are described by simple harmonic force, where C S and r eq respectively denote spring F S ij = C S (r ij r eq )r ij constant and equilibrium bond length. The interaction parameters a IJ (subscripts I and J respectively represent the types of i- S2

3 and j-th beads) in Eq. (S1) depend on the underlying atomistic interactions according to the linear relationship a IJ = a II χ IJ at number density ρ = 3, where χ IJ is the Flory-Huggins parameters. a II = 25.0 denotes the DPD interaction parameters between the beads of same type. The value of a IJ > 25.0 corresponds to χ IJ > 0, implying that the I- and J-type beads are incompatible. Simulation details The coarse-grained mapping of realistic systems including solvent molecules and polymers is utilized to construct our model systems of copolymer-like superstructures via the hierarchical self-assembly. The polymers correspond to the polystyrene-block-polybutadiene-block-poly(methylmethacrylate)(ps-b-pb-b-pmma) used in the Müller's group. S2,S3 Polymeric PS, PB and PMMA monomers are denoted by A, B (or D) and C beads, respectively. The N,N-dimethylacetamide and mixed acetone/isopropanol solvents are represented by S and S beads, respectively. In addition, the interaction parameters a IJ in Eq. (S1) are deduced from the Flory-Huggins interaction parameters, which are obtained via the atomistic molecular dynamics simulations of pure and binary systems. All the interaction parameter settings are shown in Table S1. More details about the coarse-grained mapping and the atomistic molecular dynamics simulations can be found in our previous work. S4 Below, the hierarchical self-assembly of A x B 15 C 17-x and A y D 15 C 17-y triblock terpolymers (subscripts x and y denote the tunable lengths of A blocks) is chosen as a representative example to illustrate the procedures of DPD simulations, which are schematically illustrated in Figure S1. In the first step of our simulations, the B- and D-type patchy nanoparticles of triblock terpolymers are achieved via the stepwise assembly strategy. Specifically, the S3

4 A x B 15 C 17-x and A y D 15 C 17-y triblock terpolymers are respectively dispersed in S solvents. The interaction parameters between beads of terpolymers and solvents are set as a AS = 27.9, a BS = 82.4, a DS = 82.4 and a CS = Under these conditions, spherical micelles with dense B or D core are formed. Subsequently, the S solvents for the formation of spherical micelles are replaced by the S beads. The environmental change for the spherical micelles is mainly manifested through the change of interaction parameter from a AS = 27.9 to a AS = 4. As a result, the collapse of A blocks occurs and induces formation of patchy nanoparticles, in which two solvophobic A patches reside on the opposing sides of dense B or D cores and are partially covered by the solvophilic C blocks. In the second step of our simulations, mixtures of B- and D-type patchy nanoparticles in the selective S solution are used to probe into their coassembly behaviors. The number of triblock terpolymer chains per patchy nanoparticle has a value of 60, corresponding to the peak position of probability distribution of chain number in the spherical micelles. To obtain the initial configurations of random mixtures of B- and D-type nanoparticles, we first carry out the DPD simulations with extra 10 5 time steps, where the interaction parameters a IJ between all components are set as a IJ = 25.0 and each patchy nanoparticle is fixed as a rigid body. S5 Then, the rigid restrictions of nanoparticles are cancelled and the interaction parameters are reset as the values listed in Table S1. The DPD simulations with more than time steps are carried out to obtain the superstructures of patchy nanoparticles. To ensure that the observed superstructures are not accidental, the DPD simulations for given parameter settings are repeated 10 times using different initial configurations. The other parameter settings of DPD simulations are presented as follows: All the S4

5 simulations are performed in cubic boxes with edge size L = 9r c under the periodic boundary conditions at constant number density ρ = 3. The noise amplitude σ is set as 3.0. The spring constant C S is fixed at 4.0. Note that all the units in DPD simulations are scaled by bead mass m, cutoff radius r c and thermal energy k B T. The volume V bead of coarse-grained beads is chosen as 520 Å 3 in this work, and the cutoff radius r c has a value of r c (ρv bead ) 1/3 = 25.0 Å. The time unit τ is estimated by expression τ~14.1n 5/3 w = 75.0 ns, where N w is a renormalization factor corresponding to the volume ratio of DPD beads to water molecules with a value of 30 Å 3. S6 Table S1. Interaction parameters a IJ between I- and J-type beads. a IJ S S A B D C S a S b A B c 41.1 D C 25.0 a. S represents the N,N-dimethylacetamide solvent, which is used to construct the spherical micelles in the first step of simulations. b. S represents the mixed acetone/isopropanol (volume fraction 60%/40%) solvent. c. Interaction parameter between the B and D beads is set as a BD = 8 to prevent the fusions between the B- and D-rich domains. S5

6 1 st step A x B 15 C 17-x A y D 15 C 17-y Triblock terpolymers S S Spherical micelles S S Polymeric self-assembly 2 nd step B-type D-type Patchy nanoparticles Supracolloidal copolymers Nanoparticle coassembly Figure S1. Schematic representation of hierarchical self-assembly of A x B 15 C 17-x and A y D 15 C 17-y triblock terpolymers. In the 1 st step of DPD simulations: Triblock terpolymers dispersed in selective S solvents first self-assemble into spherical micelles, which then transit into patchy nanoparticles with two solvophobic A patches through modulation of solvent quality. In the 2 nd step of DPD simulations:binary mixture of B- and D-type patchy nanoparticles coassembles into supracolloidal copolymers. S6

7 Part B. Self-assembly behaviors of divalent patchy nanoparticles In this part, B-type nanoparticles are chosen as typical examples to illustrate self-assembly behaviors of divalent patchy nanoparticles. The DPD simulations start from a random dispersion of 120 B-type nanoparticles in the S solvent (i.e., the initial concentration of B-type active ends has a value of C B 0 = n B 0/(N mol L -1 A L 3 ) =, where n B 0 = 240 is initial number of B-type active ends, L is edge size of simulation box and N A is the Avogadro constant). Figure S2a shows the morphological evolution of self-assembled superstructures of B-type nanoparticles obtained from the A x B 15 C 17-x triblock terpolymers with A block length x = 10. In the divalent nanoparticles, solvophobic A patches generate attractions due to unfavorable contacts of A blocks with S solvent, but solvophilic C blocks produce repulsions to avoid non-directional aggregations (t = μs). To minimize interfacial energy of system, the divalent nanoparticles self-assemble into supracolloidal polymers via attachment of solvophobic A patches (t = μs). As demonstrated in our previous work, S4 such self-assembly process of patchy nanoparticles obeys the model of diffusion-controlled step-growth homopolymerization kinetics, which is similar to the homopolymerization kinetics of molecular systems. The extended Flory s model in the field of polymer science is utilized to describe the growth of supracolloidal polymers from the divalent nanoparticles. The B-type nanoparticles with two patches behave as free monomers with two active ends. Initial concentration of active ends is denoted as. In the self-assembly of nanoparticles, consumption of active ends obeys the C B 0 following rate equation dc B dt = 2 k BB C 2 B (S2) S7

8 where C B is concentration of B-type active ends at time t. It is assumed that the rate coefficient k BB is inversely proportional to the number-average degree X n of polymerization defined in the main text (i.e., k BB = k BB 0 /X n, where k BB 0 is the rate constant of self-assembly of B-type patchy nanoparticles and ). Integration of Eq. (S2) yields relationship X n = C B 0 C B between X n and t = 4k BB 0 C B 0t + 1 (S3) Figure S2b displays the relationship between the number-average degree X n of polymerization and the assembly time t under various lengths x of A blocks. The solid lines in Figure S2b represent the fitted curves based on Eq. (S3). The theoretical model well describes linear increase of with t, further suggesting that the growth of supracolloidal polymers follows the diffusion-controlled step-growth homopolymerization kinetics. Importantly, self-assembly rate constant of patchy nanoparticles is evaluated by k BB 0 = (d/dt)/(4c B 0) From the slopes of fitted lines in Figure S2b, the self-assembly rate constants k BB 0 (S4) in the cases of x = 6, 8 and 10 are estimated as L mol -1 s -1, L mol -1 s -1 and L mol -1 s -1, respectively. With an increase in the length x of A blocks, a larger value of k BB 0 is achieved, originating from an increase in the exposed area S A of A patches (Figures 1b and 1c of main text). It should be mentioned that the value of k DD 0 for homopolymerization-like process of D-type nanoparticles is identical to the case of. k BB 0 S8

9 (a) μs μs (b) 4 x = 6 x = 8 3 x = x x x10 3 Figure S2. (a) Morphological evolution of self-assembled superstructures of B-type patchy nanoparticles obtained from A x B 15 C 17-x triblock terpolymers with A block length x = 10. (b) Square of the number-average degree of polymerization as a function of the assembly time t under different lengths x of A blocks. The solid lines represent the fitted curves on the basis of Eq. (S3). S9

10 Part C. Coassembly kinetics of binary mixtures Coassembly kinetics Random mixtures of B- and D-type divalent nanoparticles in selective S solution serve as initial configurations of DPD simulations to probe into the coassembly behaviors of binary mixtures. The total number of B- and D-type nanoparticles in the binary mixtures is fixed at 120, that is initial concentration C = C B 0 + CD 0 = mol L -1, where C B 0 and C D 0 are respectively initial concentrations of active ends of B- and D-type nanoparticles. The number of triblock terpolymers in both B- and D-type nanoparticles is chosen as 60. Herein, coassembly kinetics of binary mixtures of B- and D-type divalent nanoparticles into supracolloidal copolymers is examined by tracking the number-average degree X n of polymerization. The generalized definition of X n is given by X n, where and are respectively numbers of B- n i [X B i (ω B 1) + X D i (ω D 1)]/ n i X B i X D i and D-type nanoparticles in a single chain and n i is number of chains containing X B i + X D i patchy nanoparticles. ω B and ω D are respectively number of active ends in each B- and D-type patchy nanoparticles, e.g., ω B = ω D = 2 for divalent nanoparticles. Figure S3a shows the square of number-average degree of polymerization as a function of the assembly time t for the binary mixtures of divalent nanoparticles with different relative activities r. The initial ingredient of binary mixtures is set as f = 0.5. The value of increases with the assembly time t. With an increase in the relative activity r of binary mixtures, the growth rate of supracolloidal copolymers increases. Figure S3b shows the square of number-average degree of polymerization as a function of the assembly time t for the binary mixtures with different initial ingredient f. The relative activity between B- and D-type nanoparticles is set as r = As the initial ingredient of binary mixtures S10

11 increases, the growth rate of supracolloidal copolymers decreases. Theoretical model The copolymerization model of molecular comonomers is extended to quantitatively describe the coassembly kinetics of binary mixtures of divalent nanoparticles. S7 Our systems consist of B- and D-type patchy nanoparticles with the binding capabilities on their two active ends. Initial concentrations of B- and D-type active ends in the binary mixtures are denoted by C B 0 and C D 0, respectively. Initial ingredient of binary mixtures is expressed as f = CB 0 ( C B 0 + C D 0). By assuming that the rate constants of self-assembly are independent upon the penultimate nanoparticles in the copolymer-like superstructures, S8,S9 consumptions of B- and D-type active ends are expressed by the following rate equations dc B dt = 2kBB C 2 B 2k BD C B C D dc D dt = 2kDD C 2 D 2k BD C B C D (S5) (S6) Herein, C B and C D denote concentrations of residual active ends of B- and D-type nanoparticles at time t, respectively. The rate coefficient k IJ (I, J = B and D) of self-assembly is inversely proportional to the number-average degree of polymerization, that is k IJ = k IJ 0/X n, where k IJ 0 is the rate constant. S4,S10,S11 In the coassembly of divalent B- and D-type nanoparticles, the number-average degree of polymerization is expressed as X n = n i[x B i (ω B 1) + X D i (ω D 1)] n i = CB 0 + C D 0 C B + C D (S7) and the time derivation of is expressed as d dt = dt( CB 0 + C D 0 C B + C D) 2 (S8) We introduce deviation of the ingredient of residual active ends at time t from the initial value f, defined as ε = C D f - (1-f)C B, and relative deviation of ingredient is given by ε/c, S11

12 where C = C B +C D is total concentration of residual active ends at time t. S12 The time derivation of is expressed in terms of an effective rate constant k eff of coassembly and a correction term o(ε/c) d dt = 4k effc 0 +o(ε C) (S9) where the effective rate constant is given by k eff = k BB 0 f 2 +2k BD 0 f(1 f) + k DD 0 (1 f) 2, and the correction term is expressed as o(ε C) = 8n 0 (fk BB 0 + fk DD 0 2fk BD 0 + k BD 0 k DD 0 )(ε C) +4C 0 (k BB 0 + k DD 0 2k BD 0 )(ε C) 2. When the ingredient of residual active ends in the course of coassembly is kept close to the initial value f, that is ε/c 0, the correction term o(ε/c) in Eq. (S9) can be ignored. Under this condition, the integration of Eq. (S9) yields 4k eff (C B 0 + C D 0)t + 1 (S10) will linearly increase with the assembly time t, which is utilized to deduce the value of k eff as illustrated in Figure S3. Meanwhile, the rate constant k co of coassembly is well-approximated by the effective rate constant k eff, that is k co k eff = k BB 0 f 2 +2k BD 0 f(1 f) + k DD 0 (1 f) 2 (S11) However, as the deviation of ingredient of residual active ends becomes large, the correction term o(ε/c) cannot be ignored. In this case, ~t will deviate from the linear relation. The dashed lines in Figure S3a represent the fitted curves based on Eq. (S10) in the early stage of coassembly, and the inset shows the corresponding values of ε/c as a function of the assembly time t. For the coassembly of binary mixtures at r = 1.00, the relative deviation of ingredient is kept at ε/c 0. As a result, the simulation data are well fitted by Eq. (S10). For the coassembly of binary mixture with r < 1.00, the value of ε/c gradually increases with the S12

13 assembly time t. As a consequence, Eq. (S10) well describes the simulation data in the early stage of coassembly, but gradually overestimates the data due to larger contribution of correction term o(ε/c) in Eq. (S9). Figure S3b and its inset show the fitted curves of and the values of ε/c as a function of the assembly time t at different initial ingredients f. It is further confirmed that temporal change of follows linear relation as the contribution of correction term o(ε/c) is small, but deviates from linear relation as the value of ε/c becomes large. Estimation of rate constant k BD 0 As shown in Eq. (S11), the coassembly rate constant k co or k eff has a tight relationship with the rate constants ( and ) for k BB 0 k DD 0 homopolymerization-like process of B- and D-type nanoparticles as well as the rate constant ( k BD 0 ) for heteropolymerization-like process between the B- and D-type nanoparticles in the early stage of coassembly. To estimate the rate constant k BD 0, we perform a series of simulations for the binary mixtures with various initial ingredients f. Figure S4 shows the coassembly rate constant k co as a function of the initial ingredient f for the binary mixtures at relative activity r = Herein, the values of k co are obtained from the slopes of fitted curves of ~t in the time range of t μs when the value of ε/c is small. The solid line in Figure S4 represents the fitted curve of k co with respect to the initial ingredient f on the basis of Eq. (S11), which yields the value of 0 = L mol -1 s -1. The rate k BD constant k BD 0 for heteropolymerization-like process is intermediate between the homopolymerization rate constants and. To validate the value of obtained k BB 0 k DD 0 k BD 0 from the linear fitting in the early stage, we perform the numerical integrations for Eqs. (S5-S7). As shown by the solid lines in Figures S3a and S3b, the numerical values match well S13

14 with the simulation data. Table S2 lists the heteropolymerization rate constant k BD 0 for the binary mixtures of nanoparticles with different relative activities r deduced by Eq. (S11). In addition, Table S2 presents the values of k BD 0 evaluated by the mixing rules of k BD 0 = (k BB 0 k DD 0 ) 1/2 and k BD 0 = (k BB 0 + k DD 0 )/2. The value of k BD 0 can be approximately estimated from the homopolymerization rate constants via the mixing rule of k BD 0 = (k BB 0 k DD 0 ) 1/2 instead of k BD 0 = (k BB 0 + k DD 0 )/2. For example, the homopolymerization rate constants for the binary mixtures at r = 4 have values of k BB 0 = L mol -1 s -1, k DD 0 = L mol -1 s -1, and the heteropolymerization rate constant is k BD 0 = L mol -1 s -1, which is close to the estimated value of L mol -1 s -1 from the mixing rule of k BD 0 = (k BB 0 k DD 0 ) 1/2. (a) 9 6 r=4 r=0.27 r=1.00 ε / C x x10 3 (b) 9 6 f=0 f=0.30 f=0.60 f=1.00 ε / C x x x x x x x x10 3 Figure S3. (a) Square of number-average degree of polymerization as a function of the assembly time t for the coassembly of binary mixtures of B- and D-type divalent nanoparticles with different relative activities r. The initial ingredient of binary mixtures is set as f = 0.5. (b) Square of number-average degree of polymerization as a function of the assembly time t at different initial ingredients f. The relative activity of B- and D-type nanoparticles is chosen as r = The dashed and solid curves represent the fitted lines S14

15 based on Eq. (S10) and the values of numerical integration of Eqs. (S5-S7), respectively. Insets show value of ε/c as a function of the assembly time t. Error bars indicate the standard deviations. 5.0 k co (10 7 L mol -1 s -1 ) f Figure S4. Dependence of rate constant of coassembly upon the initial ingredient f of binary mixtures. The solid line represents the fitted curve of k co with respect to the initial ingredient f based on Eq. (S11). Table S2. Rate constants ( k BB 0, k DD 0 and k BD 0 ) a for homopolymerization-like and heteropolymerization-like processes at different relative activities r. k BB 0 k DD 0 r (k BB 0 k DD 0 ) 1/2 (k BB k BD 0 a. All the rate constants are in units of 10 7 L mol -1 s k DD 0 )/2 S15

16 Part D. Prepolymerization strategy of binary mixtures Prepolymerization strategy The prepolymerization strategy used in synthesis of molecular block copolymers is extended to enable the growth of sophisticated supracolloidal copolymers with elaborately designed sequence. S9,S13 Herein, 60 D-type patchy nanoparticles first assemble into supracolloidal homopolymers with prepolymerization degree X 0 n = 3.0, and then are mixed with 60 B-type free nanoparticles. The coarse-grained simulations for the systems of D-type prepolymers and B-type nanoparticles are preformed until the number-average degree of polymerization reaches X n 5.0. Figure S5a depicts the temporal variation in fractions of supracolloidal polymers with different sequences of nanoparticles during the coassembly of D-type prepolymer/b-type nanoparticle mixtures at relative activity r = The superstructures grow by the attachment of B-type nanoparticles or oligomers to the ends of D-type prepolymers. Consequently, the fraction of homopolymers decreases, whereas the fraction of diblock and triblock copolymers increases. Unlike the aforementioned random copolymers obtained from simple copolymerization-like strategy, the block copolymer-like superstructures with regular arrangement of nanoparticles are achieved at X n 5.0. Figure S5b shows the concentrations of bead-stick pairs as a function of the assembly time t. Since the D-D pairs have already been formed in the prepolymerization process, the concentration of D-D pairs is invariable. However, the concentrations of B-D and B-B pairs increase with X n in the subsequent stages of coassembly. The summation of concentrations of B-B and D-D pairs is larger than the concentration of B-D pairs, which is different from the case of copolymerization strategy shown in Figure 2b of main text. This phenomenon results in the formation of a large fraction S16

17 of supracolloidal diblock and triblock copolymers with regular arrangement of nanoparticles. It should be noted that similar sceneries are observed in the prepolymerization strategy for mixtures of D-type prepolymers and B-type nanoparticles at relative activity r = 4, which are shown in Figures S5c and S5d. Figures S6a and S6b show the effects of assembly strategies on the heterogeneity coefficient Ψ at r = 1.00 and 4, respectively. The heterogeneity coefficient of copolymer-like superstructures obtained from the prepolymerization strategy is lower than that of copolymerization strategy, indicating that the supracolloidal copolymers with higher ordering degree are yielded by the prepolymerization strategy. Effect of prepolymerization degree The prepolymerization degree X 0 n of D-type supracolloidal homopolymers plays a significant role in determining the ordering degree of supracolloidal copolymers. To verify this assumption, we perform the simulations for the mixtures of D-type homopolymers with prepolymerization degree X 0 n = 4.0 and free B-type nanoparticles at r = Figure S7a shows the fractions of copolymer-like superstructures with different sequences of nanoparticles at X n 5.0. When the prepolymerization degree is increased to 4.0, the fraction of supracolloidal diblock and triblock copolymers increases. Correspondingly, the heterogeneity coefficient of supracolloidal copolymers is further reduced to 0.30 (Figure S7b), indicating that the architectures of supracolloidal copolymers become more regular. S17

18 Fraction (a) Homopolymers Di- and triblock copolymers Multiblock copolymers C(10-6 mol L -1 ) (b) 12.0 B-D pairs B-B pairs D-D pairs Fraction (c) Homopolymers Di- and triblock copolymers Multiblock copolymers X n C(10-6 mol L -1 ) (d) B-D pairs B-B pairs D-D pairs X n X n X n Figure S5. (a and c) Fractions of supracolloidal homopolymers, diblock and triblock copolymers as well as multiblock copolymers as a function of the number-average degree X n of polymerization during the coassembly of D-type prepolymers and B-type nanoparticles. (b and d) Concentrations of bead-stick pairs as a function of X n. The solid lines denote the numerical integrated values of Eqs. (2-4) in main text. Relative activities: (a and b) r = 1.00 and (c and d) r = 4. The prepolymerization degree of D-type polymers is set as X 0 n = 3.0. S18

19 (a) 1.5 Copolymerization Prepolymerization (b) 1.5 Copolymerization Prepolymerization X n X n Figure S6. Heterogeneity coefficient Ψ as a function of the number-average degree X n of polymerization at relative activities (a) r = 1.00 and (b) 4. The solid lines denote the numerical integrated values of Eqs. (1-4) in main text. (a) 0.8 X 0 = 3.0 n Fraction X = 4.0 n (b) X 0 n = 3.0 X 0 n = 4.0 Homopolymers Di- and triblock copolymers Multiblock copolymers X n Figure S7. (a) Distribution of supracolloidal homopolymers, diblock and triblock copolymers as well as multiblock copolymers at X n 5.0 for different prepolymerization degrees. (b) X 0 n Heterogeneity coefficient Ψ as a function of polymerization degree X n for different prepolymerization degrees (1-4) in main text.. The solid lines denote the numerical integrated values of Eqs. X 0 n S19

20 Part E. Self-assembly behaviors of monovalent patchy nanoparticles In this part, we examine the self-assembly behaviors of monovalent B-type nanoparticles, which are constructed from A 9 B 6 C z triblock terpolymers. All the simulations start from random dispersion of M B 0 = 200 monodisperse monovalent nanoparticles in the S solvent. The initial concentration of active ends of nanoparticles is denoted by C B 0 = n B 0/(N A L 3 ), where n B 0 = M B 0 is the initial number of active ends. The number of triblock terpolymers in each nanoparticle is fixed at 30. Figures S8a and S8b show the self-assembled superstructures of monovalent nanoparticles at the C block length z = 20. In the monovalent patchy nanoparticle, solvophobic A patch decorates one side of dense B core, and solvophilic C blocks emanating from the opposite side imperfectly cover the A patch (Figure S8a). To reduce unfavorable contacts between the A patches and the S solvents, dimerization of nanoparticles occurs and induces formation of clusters with termination of solvophilic C blocks (Figure S8b). We examine the self-assembly kinetics of monovalent nanoparticles by tracking the concentration C ct of clusters. Figure S8c shows the values of C ct as a function of the assembly time t for various initial concentrations C B 0 of active ends of B-type nanoparticles. The concentration of clusters rapidly increases in the early stage, but gradually approaches plateaus in the later stages. When the initial concentration of active ends increases, more clusters are formed. Similar to the case of divalent patchy nanoparticles in Part B, a theoretical model is proposed to capture the self-assembly kinetics of monovalent nanoparticles. Variation in concentration C B of B-type active ends follows the rate equation S20

21 dc B dt = 2kBB C 2 B where rate coefficient k BB equals self-assembly rate constant k BB 0 (S12) owing to the monovalent feature of nanoparticles. Since each cluster contains two B-type nanoparticles, the concentration of clusters is expressed as C ct = (C B 0 C B )/2 (S13) By integrating Eq. (S12), the analytic expression of C ct is given as C ct = C B 0Kt (1 + 2Kt) (S14) where K = C B 0k BB 0 is formation rate of clusters. Inset of Figure S8c shows formation rate K of clusters as a function of the initial concentration C B 0 of active ends of B-type nanoparticles at different C block lengths z. The formation rate K increases with. The solid lines in inset of Figure S8c represent the fitted C B 0 curves according to the relationship K = C B 0k BB 0, which deduces the self-assembly rate constants k BB 0 = L mol -1 s -1, L mol -1 s -1 and L mol -1 s -1 for the cases of C block length z = 8, 12 and 20, respectively (Figure S8d). S21

22 (a) (b) μs μs C ct (10-5 mol L -1 ) (c) K(10-3 μs -1 ) 30 z = 8 15 z = 12 z = C B 0 (10-5 mol L -1 ) C B 0 = mol L -1 C B 0 = mol L -1 C B 0 = mol L x x x10 3 k BB (10 7 L mol -1 s -1 ) 0 (d) z r Figure S8. (a and b) Self-assembled superstructures of monovalent B-type nanoparticles obtained from the triblock terpolymers with C block length z = 20 at the assembly time (a) t = μs and (b) μs. Insets show typical configurations of self-assembled superstructures. (c) Concentration C ct of clusters as a function of the assembly time t for various initial concentrations C B 0 of active ends of B-type nanoparticles. The solid lines denote the fitted curves on the basis of Eq. (S14). Inset shows dependence of formation rate K of clusters upon the initial concentration C B 0 of active ends of nanoparticles at different C block lengths z. (d) Effect of C block length z on the self-assembly rate constant of B-type nanoparticles and the relative activity r= /. k BB 0 k DD 0 S22

23 Part F. Coassembly kinetics of monovalent and divalent nanoparticles Random mixtures of monovalent B-type and divalent D-type nanoparticles in selective S solution serve as initial configurations of coarse-grained simulations to probe into the coassembly behaviors of binary mixtures. Herein, the monovalent B-type and divalent D-type nanoparticles are respectively constructed from A 9 B 6 C z and A y D 15 C 17-y triblock terpolymers. The numbers of triblock terpolymers in each B- and D-type nanoparticle are respectively set as 30 and 60. The initial number of divalent D-type nanoparticles in the binary mixtures is fixed at 100 (i.e., the initial concentration of D-type active ends is C D 0 = mol L -1 ). The initial ingredient f = C B 0/(C B 0 + C D 0 ) is tuned by varying the number of monovalent B-type nanoparticles. The length of A blocks in the divalent D-type nanoparticles is fixed at y = 9, and the self-assembly rate constant of nanoparticles has a value of k DD 0 = L mol -1 s -1. As the length of C blocks in the monovalent B-type nanoparticles is tuned from z = 20 to 8, the self-assembly rate constant k BB 0 of nanoparticles is changed from L mol -1 s -1 to L mol -1 s -1, corresponding to the relative activity r = in the range of 0.25 r (Figure S8d). k BB 0 /k DD 0 Effect of relative activity The coassembly kinetics of binary mixtures of monovalent B-type and divalent D-type nanoparticles with various relative activities r is examined by tracking the number-average degree of polymerization defined as X n n i [X B i (ω B 1) + X D i (ω D 1)]/ n i, where ω B = 1 for monovalent nanoparticles and ω D = 2 for divalent nanoparticles. Figure S9 depicts the square of number-average degree of polymerization as well as the concentrations of D-D, B-D and B-B bead-stick pairs as a function of the assembly time at different relative activities r. The initial ingredient is set as f S23

24 = In general, incorporation of monovalent B-type nanoparticles leads to suppression of growth rate of polymer-like superstructures at the later stages of coassembly, which strongly depends upon the relative activity r. In the range of 0.25 r 2.50, divalent D-type nanoparticles first self-assemble into polymer-like superstructures, and then monovalent B-type nanoparticles act as chain stoppers attaching to the ends of superstructures. As a result, an increase in relative activity r accelerates the attachment of monovalent B-type nanoparticles to the ends of D-type polymer-like superstructures, as reflected by an increase in concentration of B-D pairs (Figure S9c). Correspondingly, the concentration of D-D pairs is reduced (Figure S9b). Thus, change of the relative activity r from 0.25 to 2.50 lowers the growth rate of polymer-like superstructures and the value of at t = μs (Figure S9a). However, when the activity of monovalent B-type nanoparticles is much larger (e.g., r = 15.00), B-type nanoparticles tend to self-assemble into clusters (formation of B-B pairs) and act as chain stoppers (formation of B-D pairs) (Figures S9c and S9d). Such depletion of B-type nanoparticles leads to formation of D-D pairs in the later stage (Figure S9b). As a consequence, the mixtures of B- and D-type nanoparticles with higher relative activity r coassemble into polymer-like superstructures with a higher value of X n at t = μs (Figure S9a). Theoretical model The classic Flory s model is extended to describe the coassembly kinetics of binary mixtures of monovalent and divalent nanoparticles. The rate coefficient for the D-type active ends is inversely proportional to the polymerization degree X n (i.e., k DD = k DD 0 /X n ). Following the assumption of Leite and co-workers, S14 the rate coefficients S24

25 involving the B-type active ends are given by k BB = k BB 0 and k BD = k BD 0. Herein, the rate constant of heteroassembly is estimated by the rate constants of homoassembly, that is k BD 0 (k BB 0 k DD 0 ) 1/2. In the coassembly of monovalent and divalent nanoparticles, the number-average degree of polymerization is expressed as X n n i[x B i (ω B 1) + X D i (ω D 1)] n i = C D 0 C D 0 2C D D (S15) On the basis of rate constants, and, the concentrations of different k BB 0 k DD 0 k BD 0 bead-stick pairs can be predicted from the rate equations dc B B dt = k BB C B 2 dc D D dt = k DD C D 2 dc B D dt = 2k BD C B C D (S16) (S17) (S18) where C B = C B 0 2C B B C B D and C D = C D 0 2C D D C B D are respectivley the concentrations of residual B- and D-type active ends at time t. By substituting the rate constants and the initial concentrations of active ends, numerical solutions of Eqs. (S15-S18) give the number-average degree of polymerization and the concentrations of bead-stick pairs, which are respectively presented by the solid lines in Figures S9a and S9b-d. The simulation data are well described by the extended Flory s model. S25

26 (a) 11.0 r = r = r = 0.25 (c) 12.0 r = r = 2.50 r = 0.25 C B-D (10-6 mol L -1 ) x x x C D-D (10-6 mol L -1 ) 3.0x x x10 3 (d) 12.0 r = r = 2.50 r = C B-B (10-6 mol L -1 ) (b) 12.0 r = r = 2.50 r = x x x x x x10 3 Figure S9. (a) Square X n 2 of number-average degree of polymerization of supracolloidal polymers as a function of the assembly time t at different relative activities r. (b-d) Concentration of D-D, B-D and B-B bead-stick pairs as a function of the assembly time t. Insets illustrate the representations of bead-stick pairs. The initial ingredient of binary mixtures is f = The solid lines denote the fitted curves on the basis of Eqs. (S15-S18). S26

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