Out of Equilibrium Self-Assembly of Janus Nanoparticles: Steering It

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Out of equilibrium self-assembly of Janus nanoparticles: steering it from disordered amorphous to 2D patterned aggregates. Andrea Tagliabue, Lorella Izzo, and Massimo Mella Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b02715 • Publication Date (Web): 03 Nov 2016 Downloaded from http://pubs.acs.org on November 8, 2016

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Out of equilibrium self-assembly of Janus nanoparticles: steering it from disordered amorphous to 2D patterned aggregates.

†

Andrea Tagliabue,‡ Lorella Izzo,¶ and Massimo Mella∗,‡ Dipartimento di Scienza ed Alta Tecnologia, Universit` a degli Studi dell’Insubria, via Valleggio 11, 22100 Como (I), and Dipartimento di Chimica e Biologia, Universit` a degli Studi di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (I) E-mail: [email protected] Phone: +39 0312386625. Fax: +39 0312386630

Abstract Solvent evaporation driven self–assembly of Janus nanoparticles (J–NPs) has been simulated employing lattice–gas models to investigate the possible emergence of new superlattices. Depending on the chemical nature of NP faces (hence solvophilicity and relative interaction strength), zebra–like or check –like patterns, and micellar agglomerates can be obtained. Vesicle–like aggregates can be produced by micelle–based corrals during heterogeneous evaporation. Patterns formed during aggregation appear to be robust against changes in evaporation modality (i.e. spinodal or heterogeneous) or interaction strengths, and they are due to a strictly nanoscopic orientation of single † AT carried out the Monte Carlo simulations analyzing the results and contributed to the writing of the manuscript; MM ideated the study, analyzed the results, and contributed to the writing of the manuscript; LI ideated the study and contributed to the writing of the manuscript. ∗ To whom correspondence should be addressed ‡ uninsubria ¶ unisa

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J–NPs in all cases. Due to the latter feature, the aggregate size growth law N (t) ∝ ta has its exponent a markedly depending on the chemical nature of the J–NPs involved in spite of the unvaried growth mechanism. We interpret such finding as connected to the increasingly stricter orientation pre–requirements for successful (binding) NP landing upon going from isotropic (a ≃ 0.50), to “zebra” (a ≃ 0.38), to “check ” (a ≃ 0.23), and finally to “micelle” (a = 0.15–0.17) pattern forming NPs.

Introduction Self–assembly of nanoparticles (NPs), whether directed via templates and fields or exploiting only NP characteristics, has developed to be a prominent technique for generating materials whose advanced properties may be easily tuneable modifying the parameters that control the processes involved 1–10 . Applications of such idea are now leading to the production of “metamaterials” (aggregates of nano–sized materials already presenting useful properties) 4,9,11–17 , occasionally including two or more different type of NPs. Multiple NP types are used in order to expand our ability in tuning properties for the specify task at hand. As for controlling spatial dispositions in the latter cases, relative size seem to matter most 18 . This notwithstanding, many–body forces are also known to play a role in defining aggregation modes 19 . An additional degree of freedom in designing NPs and NP aggregates to fulfil task–specific requirements appears if one moves away from NPs with an uniform interaction modality or strength across their surface 20 . Among the variety of choices available to widen up the “Lego box” 4 at our disposal, Janus NPs (J–NPs, i.e. NPs presenting two geometrically separated surface patches with different composition, properties and interactions) have been attracting attention over the last few years 21–27 . Despite the processes involved in preparing J–NPs not being straightforward, faces with different properties can be obtained using inorganic materials, perhaps starting from a mono component core, to be subsequently: a) “stained” with different species 28,29 ; b) modified by attaching ligands with different lyophilic2


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ities and capable of self–segregating 24,26,27,30 , or by growing polymeric chains with different monomers exploiting surface–induced desymmetrization 31 . Alternatively, one may exploit divergent polymer structures (e.g. star–like polymers 32,33 ) or multi–block linear polymer chains 7,10,23,34,35 . J–NPs have been shown to be useful, di per se, in tasks such as stabilizing immiscible polymer blends 35–37 . More attention, however, has been paid to study the formation of J–NPs aggregates with the goal of producing materials with size–controlled properties. For instance, nearly spherical amphiphilic J–NPs can assemble to produce micelles 7,38 and super–micelles 31 , Janus cylinders can form fibrils 17 , and Janus disks produce aggregates whose shape is modulable by changing peculiarities of the solvent and disks themselves 39 . Such agglomerates are usually produced in bulk solvents, with properties carefully controlled to modify the free energy surface 40–49 that guides agglomeration, size increase, or monolayer ordering 50–53 . In this context, theoretical and simulation tools have been frequently used to help rationalizing experimental aggregation results because they allow one a rapid investigation on the impact of changing parameters such as the relative lyophilicity of Janus faces 54,55 , ionic strength 56 , J–NP size or shape 39,57–59 , the mobility of surface adsorbed species 30 or relative interaction strength (hence miscibility) between polymer chains “grafted from” a rigid particle core 27 . Despite the vast amount of work so far presented, our perusal of the literature has evidenced that only a few articles discuss the effect of coupling Janus self–assembly with processes or fields (e.g. evaporation 35 , flows 14 , etc) compared to near–thermodynamics studies; this contrasts sharply with the attention paid toward the self–assembling under various solvent evaporation conditions of mono or poly–dispersed NPs with homogeneous interactions 60–84 . Noticeably, the latter studies have shown how a wide set of final aggregation patterns can be induced upon varying specific details such as the evaporation regime or ratio between diffusion and evaporation rates. Thus, coverage patterns such as disks 60 , worm– like aggregates 60,84 , networks 60,76,79–81,85 , rings 63,78,81,83 and hexagons 75,83 , fingers 80–82,85,86 ,

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linear or bridged wires 66 , stalagmites 62,87 and check 61 or stripe 61,88 patterned aggregates have been shown and interpreted with the help of simulation approaches. In view of the vast zoology of evaporation–induced self–assembled (EISA) materials that can be obtained using homogeneous NPs, it thus seems surprising that no attention has been paid, so far, to the dewetting–driven self–assembly of J–NPs, especially with respect to the formation of 2D aggregates or thin polymer plaques of J–NPs (perhaps with both lyophilic faces). As a consequence, we set as main aim of our work to explore possible aggregation modalities of a few different kind of J–NPs (vide infra) and how these may be modified by changing NP or evaporation characteristics. Specifically, we tackle such task via theoretical calculations based on mesoscopic lattice–gas simulations as originally done for the case of homogeneously interacting NPs 60 , with the goal of presenting a sufficiently general picture capable of guiding synthesis and aggregation modalities. To bridge the gap with published experimental work, we mention here that Janus species with lyophilic faces are of relevance for recently proposed bactericidal non–quaternized tree– like A(BC)n polymers (A =mPEG, BC = P(MMA–ran–DMAEMA) copolymer; MMA= methylmethacrilate, DMAEMA= 2–di(methylammino)ethyl methacrylate ) 89,90 , which can be easily casted from evaporating chloroform solution into robust structural materials. The surface morphology (hence the bactericidal capability) and mechanical properties of the latter, however, seem to depend on both the relative composition and number of BC arms, alkyl amino groups, and casting temperature as these may induce a different exposure to water or relative surface distribution of the tertiary amines. It is, in fact, the protonation of the latter, which can be enhanced by the proximity of two basic pendants via the formation of ammonium–amino dimers 91,92 even under spatial confinement 93 , that generates a positive surface charge sufficiently high to induce bacterial death. As PMMA and mPEG seem to form distinct micro–domains in the solid phase 94,95 , and they have an opposite relative departure direction from the branching point in A(BC)2 and A(BC)4 , a basic model that may be able to represent the anisotropic nature of the latter species is a J–NP–type species 96 .

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The organisation of the manuscript is as follow. In the Methods and Models section we present the details of the models and simulation approaches employed to investigate the time–dependent aggregation, emphasising the relationship between our model J–NPs with synthesised or synthesizable species. In the following section, simulation results are presented and discussed separating findings for lyophilic species from the ones obtained with amphiphilic NPs. To emphasise the effects due to simultaneous evaporation/self–assembly, comparisons are made with results obtained with constant solvent coverage. Worth citing at this stage, it is the formation of striped domains seen for lyophilic NPs with preferentially self–interacting faces and that can be used as templates. Micelles of tubular form and, occasionally, vesicle–like aggregates are instead formed in case of amphiphilic species moving from homogeneous to heterogeneous evaporation. Finally, we conclude with additional comments and discussions on possible applications of our results, also touching upon possible avenues of future work.

Methods and Models Model definition The mathematical model that we propose is derived from a previous work by Rabani et al. 60 Thus, we use the lattice–gas model represented in Figure 1 to investigate the self–assembly process of antisymmetric J–NPs during solvent evaporation. As usual, the linear dimension of solvent/vapor cells is similar to the solvent correlation length, so that events in neighbor cells can be considered uncorrelated. As shown in Figure 1, each NP covers an area of 4 × 4 solvent cells and it is divided in two halves, P and N , each of which consists of a 2 × 4 rectangle. Each cell of the lattice is described by three binary variables, l, n and p, and four possible different cells states are allowed: cells filled with vapor (l = 0, n = 0, p = 0), with liquid (l = 1, n = 0, p = 0) or with one of the two different halves of a NP (N sections are identified by the state l = 0, 5


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The latter depends on the starting position of each element on the lattice, positions that are chosen at random at the beginning of each simulation. The latter choice is consistent with results from simulations with ǫll ≃ ǫlp ≃ ǫln ≃ ǫpn showing no instance of agglomeration in absence of evaporation (for instance, see all movies in the Supporting Information tagged as “noevap”). To conclude to the description of our model, we point out that the latter is intended to represent anti–σv –symmetric spherical NPs, in the same exact spirit as the original approach implemented by Rabani et al. 60 described spherical isotropic NPs. Such choice has obvious limitations when it comes to compare with dumbbell–like, prolate or oblate species. Apart from the dissimilarity in shape, which may be somewhat corrected by using NPs with different aspect ratios (vide infra for further discussion), our model may not be able to describe possible effects due to the curvature of NP surfaces (e.g. solvent trapping between aggregate NPs) that may be instead captured by more elaborate shapes 64 . In view of the previously demonstrated successes obtained in modelling complicate evaporation scenarios for isotropic NPs, the simple square NP model seems to provide an adequate first attempt also for J–NPs in spite of such limitations.

Model dynamics The dynamics followed by the model is stochastic with respect to fluctuations in solvent density and NPs diffusion; it is thus performed using a Monte Carlo algorithm 60 . At variance with previous works 60–63,72,86,87 , which described the dynamics of evaporation/recondensation of the solvent and the translational NPs diffusion, we simulate also the rotational diffusion of NPs due to the J–NPs anisotropy. Hence, the algorithm stochastically runs three different process during the evolution of the system: 1. random attempts of evaporation (or recondensation) of a liquid (or vapor) cell with a probability PSV ;

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2. random attempts to translate NPs up/down or left/right by one liquid cell with probability PT ; 3. random attempts to rotate NPs by 90 degrees with probability PR . As a consequence, we define a Monte Carlo step as consisting of NSV + (DT + DR )NN P random moves, where DT and DR are parameters that establish the number of attempts to move and rotate each NP every time an attempt of changing the state of all liquid and vapor cells is made. In other words, DT and DR regulate the two diffusivities of the NPs. The probabilities are then defined as follows:

PSV =

PT = PR =

NSV

NSV + (DT + DR )NN P

NSV

NN P DT + (DT + DR )NN P

NSV

NN P DR + (DT + DR )NN P

(2)

Due to the close relationship between translational and rotational diffusion rates (i.e. DR ∝ DT /(L2 ) for regular solids such as sphere of radius L or cylinders of length L 97 ), we simplify the dynamics imposing DT = DR ≡ D in all the simulations. A few cases with DT 6= DR were nevertheless studied to verify that such choice had only a limited impact; qualitatively similar results were in fact found. Albeit we opted for simulating square NPs as first approach toward the self–assembly of materials with anisotropic interaction, it seems nevertheless worth noticing that making such choice rather than using rectangles or even more complicate nano rod–like species 64 may have an impact on the morphology of the emerging aggregates. In this respect, one should expect that the formation of the clusters may be somewhat more hindered (i.e. slower) the more the NP aspect ratio differs from unity. This may be of particular relevance for the eventual formation of patterns (i.e. relative disposition of N /P sides) induced by a specific choice of potential parameters, which may present a higher number of holes or rougher borders. We 8


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expect this to become more likely upon decreasing DT /DR ratio, as the capability of NPs to reorient in order to decrease the system energy may be expected to decrease more if the fluctuation in nanorod local density due to spatial motion are less likely. Beside, the NP aspect ratio also appears to impact on both the dynamic and the size of the formed domains, especially in the case of homogeneous evaporation conditions. Heterogeneous evaporation may, instead, induce nanorod alignment parallel to the growing vapour cavities, and an increase in fractal nature upon increasing the aspect ratio 64 . As usual, attempted moves are accepted with the Metropolis acceptance criterium pacc

pacc = min 1, exp

−∆H kB T

,

(3)

where T is the temperature, kB is the Boltzmann’s constant and ∆H is the resulting change in energy due to the attempted state change. Notice that we impose ∆H = ∞ for a move that implies a NP translation into a vapor–filled cell. In other words, NPs can diffuse only if the four cells that shall be occupied by the NP are filled with liquid (subsequently positioned in the wake of the NP movement) to model the observation that NPs show a very low mobility on a dry surface; for the same reason, a NP is not allowed to rotate if totally surrounded by vapor.

Simulation experiments Via a set of preliminary simulations, we identified three archetypal sets of parameters defining types of J–NPs with different nucleation outcomes (also, vide infra for the impact of changing ǫ values). These are: (1) ǫln = 1.50ǫll , ǫlp = 1.50ǫll , ǫnn = 2.00ǫll , ǫpp = 2.00ǫll , ǫnp = 0.50ǫll for J–NPs (J– NP1) with halves having the same solvophilicity and preferably interacting via similar faces (i.e., N –P interactions are less stabilizing than N –N and P–P interactions, as expected in the case of polystyrene–poly(methyl methacrylate)); 9


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(2) ǫln = 1.50ǫll , ǫlp = 1.50ǫll , ǫnn = 0.50ǫll , ǫpp = 0.50ǫll , ǫnp = 2.00ǫll for J–NPs (J–NP2) having halves with the same solvophilicity and interacting between them preferably via opposite faces. For instance, the two faces can expose alternatively weak acid and – basic groups, oppositely charged ionic groups (e.g. –N(CH3 )+ 4 ...SO3 –), or the whole

NP may be carrying a magnetic dipole; (3) ǫln = 1.50ǫll , ǫlp = 0.50ǫll , ǫnn = 2.00ǫll , ǫpp = 2.00ǫll , ǫnp = 1.75ǫll for J–NPs (J–NP3) having one half with low solvophilicity and with a slight preference toward N –N and P–P interactions, such as J–NPs with a hydrophobic polystyrene side and a hydrophilic side composed of mPEG, poly–methacrylic acid (PMAA) or PDMAEMA . All the ǫ parameters presented above are expressed in unit of ǫll . The drying–mediated self–assembly process of the nanoparticles has been studied in different conditions, i.e. varying the coverage fraction ρ, the rate of translational and rotational diffusion and the limits of two dynamical evaporation modes observed by Rabani et al. 60 . These are the homogeneous (or spinodal) and heterogeneous evaporations. Transition between these evaporation modes can be actuated by tuning the temperature T , the chemical potential µ and/or ǫll 60 . Specifically, we used kB T = 0.50, ǫll = 1.00, and µ = −2.25ǫll = −2.25 for homogeneous evaporation, kB T = 0.50, ǫll = 2.00, and µ = −2.25ǫll = −4.50 for heterogeneous evaporation. Simulations were performed in a 500 × 500 square closed domain with wet boundaries, i.e. the edges of the lattice are always in contact with the solvent. Notice that this condition allows to simulate the self–assembly process that takes place in a thin solution of NPs evaporating in a flat container (e.g. a Petri dish), where walls remain constantly wet due to the liquid–dish adhesion forces. For these reasons, all the quantitative analysis presented (e.g. cluster size and shape) in the following had been performed only considering those clusters that are not directly in contact with the edges of the simulation box, as the latter present distorted morphologies.

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Results and discussion Solvent evaporation dynamics Details on the solvent evaporation dynamics are presented in the Supporting Information (Figures S1–S4) in order to provide one with the necessary background information on the timescales involved in NP nucleation and the degree of spatial homogeneity during the process. Obviously, the presence of the NPs perturbs somewhat the dynamics due to the fact that ǫll 6= ǫln , ǫlp ; even so, we stress that evaporation behaviour at low NP density appears quite similar to the ρ = 0 case thanks to the overwhelming number of solvent cells. Despite the higher ρ (i.e. 0.33 or 0.5), strong similarities with pure solvent evaporation remain even for our most concentrated systems (e.g. see Figures S5 and S6).

Nucleation of J–NP1 and J–NP2 The mesoscopic structures emerging during homogeneous solvent evaporation from solutions containing either J–NP1 or J–NP2 appear somewhat similar, and they are also comparable with the results obtained by Rabani et al. using isotropic NPs 60,61 (see also, Figures S5 and S6 in Supporting Information). This finding is due to the fact that all these NPs have the same solvophilicity; conversely, the finer–grain structure produced by J–NPs markedly depends on how the latter interact with each other. Figure 2 shows trajectory snapshots for J–NP1/2 taken at early (t = 1, in units of Monte Carlo step, MCS), intermediate (t = 64 MCS) and late (t = 32768 MCS) times. The simulations were performed with a fractional coverage ρ = 0.20. At t = 1 MCS (right panels), J–NPs randomly fill lattice cells, with the remaining cells being filled with liquid. Due to the value assigned to the chemical potential (µ = −2.25), the system evolves with the evaporation of the solvent. At t = 64 MCS (middle panels), the solvent is almost completely evaporated, and the J–NPs are aggregated into worm–like clusters. Owing to the stabilizing interactions (ǫlp , ǫln > ǫll ), a thermally stable layer of solvent is present at the 11


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Conversely, a check –like structures whithin the domains is observed when ǫnn = ǫpp < ǫnp . The latter substructure is similar to the one observed by Rabani et al. in their work on the “out of equilibrium” self–assembly of binary mixtures of NPs 61 , and this type of ordering occurs when a NP (or particle half in our case) results energetically stabilized by being surrounded by different NPs (halves). The zebra patterned aggregates, instead, somewhat resemble the lamellar–like structure obtained from Janus N –P dumbbells upon increasing the system pressure. The J–dumbbells had N sides interacting via a two-length scale potential, while the interaction between P sides and N –P pairs were modelled via a truncated–shifted Lennard–Jones potential with or without attraction minimum 98,99 . Aggregates resulting from J–NP1 and J–NP2 differ between them, as well as from isotropic NP (iso–NPs) ones, also with respect to their average size N (t) (i.e. the number of NPs composing a cluster at the chosen time t). As shown in Figure 3, our quantitative analysis indicates that domains formed by iso–NPs are, in average, composed of more NPs than those formed by J–NP1/2 (Niso (t) > NJ–NP1/2 (t)); moreover, NJ–NP1 (t) > NJ–NP2 (t). In spite of these differences, the evolution of the cluster sizes follow the same behavior in all three cases: after an initial transient during which N (t) remains nearly constant, it suddenly raises (MCS 10–100) due to the evaporation of the solvent. Subsequently, N (t) grows as ta . Linearly fitting the last 5 points of the plots (i.e. from t = 2048 to t = 32768 MCS) we obtained: aiso = 0.432 ± 0.008, aJ–NP1 = 0.379 ± 0.009, aJ–NP2 = 0.218 ± 0.007 when D = 100; aiso = 0.499 ± 0.031, aJ–NP1 = 0.379 ± 0.007, aJ–NP2 = 0.248 ± 0.007 when D = 1000 (please, see Ref. 100 ). The relative values of the a coefficients as a function of D suggest that a variation of the latter influences more aiso than aJ–NP1 or aJ–NP2 , which we take as an indication that the kinetic of the coarsening process for the J–NPs may be controlled, at least partially, also by other factors. In any case, changing D does not seem to induce any major modification in the check or zebra patterns emerging at the end of the simulations. Importantly, the values of a just presented, together with the visual representation provided by Figure 3, quantitatively support the observation that the coarsening rate (iso>J–NP1>J–NP2) de-

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pends markedly on the details of the interaction. In particular, we notice that the most complicate superlattice, i.e. the one formed by J–NP2, is also the slowest to form as it requires a more stringent pre–orientation of the NPs before a strongly binding contacts is formed upon landing 101 . Before discussing the interpretation of the obtained values for the a exponent, it seems useful to provide indication on the physical time scale involved in our simulations by attaching an approximate value to the lapsed wall-clock time per MCS. As suggested 60 , this task can be accomplished by measuring h[r(t) − r(0)]2 i = 4DM C NM CS with simulations on non– evaporating systems (see Figure S7 in the Supporting Information) to estimate DM C in units of MCS and lattice size, and computing DM C /Dexp for specific systems. For instance, exploiting the results provided in refs. 70 and 102 and setting DT = DR = 10, one estimates a MCS to be, respectively, equal to 7.5 and 230 s for NPs that are soluble in the evaporating solvent. Unfortunately, we have been unable to find information allowing us to assign a physical time step for amphiphilic J–NP3 despite being able to compute their h[r(t)−r(0)]2 i. Apart from governing the rate of agglomerate accretion, different values of the exponent a may also indicate a dependency of the coarsening mechanism on the intradomain structure 61,103–105 . In discussing of possible variations in accretion mode due to changes in the interaction models, it is important, however, to remember that NP mobility is permitted only in presence of liquid solvent in the NP proximity, so that a straight relationship between a value and coarsening mechanism may not be easily found as in the case of thin atomic film coarsening 61,104,105 . Looking at the formation of defective contacts (e.g. the presence of perpendicular zebra patterns in a specify agglomerate), we have in fact found evidences that once agglomeration nuclei are formed, they merge via direct collision generated by terrace diffusion without any evident dependency on the specific superlattice formed (specifically, see long time behavior in JNP1homo and JNP2homo movies in the Supporting Information). Subsequently, the newly–joined aggregates rearrange to generate homogeneous (i.e. uniformly oriented) patterns (see Figure 4). As for the latter two processes, it is useful to point

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out that they are facilitated by the solvophilicity of both N and P sides (ǫln = ǫlp = 1.5ǫll ), which, fostering vapor condensation on NPs, guarantees the possibility of NP detachment from the cluster perimeter and NP migration along its solvent–covered periphery. Notice that the latter process can also happen with NP sliding onto an aggregate while maintaining favourable contacts. Also noteworthy, it is the fact that the layers of condensed solvent always provide a form of “cushioning” during collisions between clusters, somewhat reducing the chance of unfavourable contacts in case of J–NP1/2 aggregates (see Figure S8). Indeed, the presence of a solvent bilayer allows inter–cluster NP exchange via translational diffusion and, possibly, reorientation of the transferring NPs; once again, it does so with no regard for the internal structure of joining clusters. In conclusion, it seems that the variation in a induced by moving from isotropic, to J–NP1, and eventually to J–NP2 species ought to be connected more with details of the NPs dynamics at the periphery of aggregates or in regions surrounding them rather than to sound mechanistic differences. Another property useful to characterize aggregation modalities is the time–dependent shape s(t) of a NP aggregate; the latter is defined as the ratio between the two eigenvalues, λmin /λmax , of the cluster inertia tensor T , 

 T = P

P

(x − JCM )

2

(x − JCM )(y − ICM )

P



(x − JCM )(y − ICM ) . P 2 (y − ICM )

Here, the summations are taken on each cell with coordinates x, y belonging to the cluster, and ICM , JCM are the coordinates of the center of mass of the latter. It follows that s ∈ (0, 1], with s = 1 describing a perfect square, while s ǫll . Once formed, the vapour–filled cavity should nevertheless be capable of nucleating on itself the evaporation of the liquid 107 . Demonstration that expecting the formation of aggregates with different shapes than the ones in Figures 2 and 5 may indeed be correct is clearly provided by Figures 6 and S14. In fact, they show that heterogeneous evaporation induces large square–like holes, occasionally separated by relatively thin isthmuses, reminiscent of bubble formation. This deviation notwithstanding, patterns inside domains are well maintained despite the change in evaporation modality, a finding suggesting that a variation of the amount of thermal energy stored into the liquid may not be sufficient to modify the relative orientation preference for J– NP1 and J–NP2 species. Obviously, the structural differences discussed above can be easily rationalised assuming that NPs are sufficiently mobile (as they seem to be when D > 100) to effectively track the front of growing vapor nuclei during heterogeneous evaporation, as

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the final aggregates ought to be expected to show the structural history of evaporation. At a closer glance, also the process of J–NP2 coarsening seems to proceed somewhat differently in the two evaporation limits; in fact, the domains shown in Figs. 6 and S14 feature more solvent–filled cavities compared to those formed under spinodal condition. De facto, we have found, respectively, 700±30 and 284±8 cavities after 32768 MCS of evaporation. Also, the relaxation of these defects apparently occurs on a much longer time scale (or not at all, vide infra). A similar comment can also be expressed with respect to the rougher domain perimeters formed under J–NP2 heterogeneous evaporation especially for the high coverage and relatively low D case in Figure S14. As a higher degree of fractal nature has an obvious associated energetic cost due to the longer perimeter, this observation can be rationalised only invoking either a kinetically trapped state or a reduced restructuring capability. Indications that the latter aspect could provide the most important contribution to such characteristic can be found comparing with domains obtained via the self–assembly of isotropic NPs under completely similar conditions and solvent–NP interaction parameters, which produces even smoother, more compact and less defective domains than J–NP1 species (see Figure S6). In other words, it seems that the stricter orientational requirements imposed by the J–NP2 potential model for the formation of non–defective check pattern, and for which we argued of a likely impact on both the absolute growth rate and exponent a (vide supra), may also be able to induce more fractal perimeters in heterogeneously assembled aggregates.

Results and discussion: J–NP3 To explore the effects due to increasing solvophobicity of one side of J–NPs, we developed the parameters for J–NP3. These allow the N face (green) to maintain the same high solvophilicity of the J–NP1/2 (i.e. ǫln = 1.50ǫll ), while the same property is much reduced for the P face (red), ǫlp = 0.50ǫll . To limit structural biases, we also avoided imposing any strong preference for the interaction between similar faces (compare ǫnn = ǫpp = 2.00ǫll with

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Figure 6: Final snapshots for a total coverage of 20% (top, D = 500) and 30% (bottom, D = 150) under heterogeneous evaporation conditions. The left and right panels correspond to J–NP1 and J–NP2, respectively. Total evolution time t = 16384 MCS.

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ǫnp = 1.75ǫll ) as it is commonly done to model solvophobic forces. Under homogeneous evaporation, the coarsening of J–NP3 leads to the formation of structures that are very reminiscent of tubular micelles showing the less solvophilic faces interacting with each other, and the other halves being exposed to the solvent. Examples of these results are shown in Figure 7 for ρ = 0.10 and D = 1000. The same behaviour is also found in different conditions; for instance, Figure S15 shows the typical evolution of a simulation with J–NP3 during spinodal evaporation, ρ = 0.20 and D = 100 (see also JNP3homo movie in the Supporting Information). From both Figures, one notices that only a very few MC steps are sufficient for the low solubility of the P half to drive the formation of micellar oligomers; the latter increase in size forming micelles larger and larger as time elapses. Importantly, notice that the structures just discussed are due to the juxtaposition of both solvent evaporation and low solvophilicity of P. In fact, neither the former or the latter would have been capable of inducing an identical organization as N –P contacts can be created or destroyed with a limited energetic cost given the similar miscibility of the two sides. Thus, micelles formed in absence of evaporation (obtained increasing µ so that solvent–covered surfaces becomes thermodynamically stable) appear (see Figure S16 and JNP3noevap movie in the Supporting Information) longer, more kinked, partially capped by J–NPs exposing the solvophilic N side, and with less N –P contacts than seen in Figures 7 and S15 (e.g. notice the capping provided by a micelle to another in the inset of Figure 7). Cylindrical micelles with no defects equilibrated also simulating low density Janus N –P dumbbell fluids 98,99 , hence supporting the idea that non–spherical species may be obtained also changing physical conditions rather than only the critical packing parameter 108 . Finally, Figure 8 presents the last configuration obtained for the homogeneous evaporation– driven self–assembly of J–NP3 when ρ = 0.50. From this, it is immediately evident that increasing the fractional coverage leads to the formation of a complex network of worm–like micelles, which are longer than the one formed when ρ = 0.20 (see Figure S15). Also, the network appears occasionally interrupted by solvent–filled cells flanked by N sides; these

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Figure 8: Last simulation configuration (t = 32768 MCS) for the nucleation and coarsening of J–NP3 with ρ = 0.50 under homogeneous evaporation conditions, and a diffusion rate D = 100.

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of the pores originally seen when using ǫlp = 0.50ǫll (see Figure 9). Noteworthy, not all J–NPs inside a micelle are oriented so to have only P–P or N –N contacts; this feature is fostered by the limited energetic difference of the latter with P–N interfaces, and it may be substantially rectified even by a small decrease in ǫnp as seen in the previously discussed case of simple micelles.

Conclusion In this work, the evaporation–induced self–assembly of model J–NPs has been studied computationally to investigate the impact that modifying material properties, coverage density and evaporation modality has on the structure of the formed “metamaterials”. As J–NPs provide a material scientist with “two handles” to independently vary the properties of NPs, it is possible to produce both materials that are perfectly soluble in the evaporating solvent, or markedly amphiphilic. While the latter should be expected to produce micelles (indeed, they do even in absence of dewetting), we have attempted to exploited the freedom provided by J–NPs to find whether or not it would be possible to generate super–lattice features inside mesoscopic or microscopic domains formed during aggregation by appropriately tuning model interaction and experimental conditions. Indeed, it has been possible to find ranges of interaction parameters able to guarantee the formation of zebra and check patterns. Such ranges are wide enough to give hope for a successful experimental search in such direction. Importantly, our computational experiments sharply highlight the impact that dewetting has on the final structure of the obtained materials, as the latter are somewhat under kinetic control. Thus, wider zebra and check domains (as well as cavities) are formed under heterogeneous evaporation compared with spinodal condition at the same coverage fraction. Moreover, long–range bridging between domains “pushed away” by bubble expansion seem to be possible already when ρ ≃ 0.3, especially if NP diffusion is not so fast to quickly rearrange following the dewetting front (see also Figure 4a and 4b in the work by Rabani et al. 60 );

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ρ, instead, needs to be raised up to ρ ∼ 0.5 under homogeneous evaporation to generate a percolating network. Also, micelles formed by J–NP3 under non–evaporating solvent condition appear longer and protect better the less solvophilic half by capping. In these respects, what still remains missing is the long term evolution of the patterns emerging from our simulations, perhaps even under the effect of alternating solvent condensation–evaporation cycles that may foster longer range pattern uniformity. As for the possible application of the results presented in this work, one may speculate about exploiting the nearly achieved percolation of tubular J–NP micelles (see Figure 8) to produce conducting networks with well defined lateral width in the nanoscale regime. Nano– patterning of linear (from J–NP1) or point–like (from J–NP2) regularly spaced molecular or metal aggregates may also be achieved in the proper conditions. This may be key, e.g., in the tissue engineering field, where the interaction of mammalian cells with topographically nano– patterned surfaces such as nanogratings, nanoposts, and nanopits seems to be important not only for controlling cell adhesion and proliferation, but also because it could potentially be employed as a signaling modality for directing differentiation 109 .

Acknowledgement The authors thanks Mario Vincenzo La Rocca for a careful read of the Manuscript, the Università degli Studi dell’Insubria for funding granted via the “Fondo dell’Ateneo per la Ricerca” (FAR 2015), and the Università degli Studi di Salerno for funding granted via the “Fondo dell’Ateneo per la Ricerca di Base” (FARB 13 and 14).

Supporting Information Available The file contains additional pictures describing the characteristics of our systems, including the time evolution of properties and links to movies of the solvent evaporation, NP dynamics under evaporating and non–evaporating conditions. This material is available free of charge via the Internet at http://pubs.acs.org/. 28


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(94) Li, Y.; Ma, Q.; Huang, C.; Liu, G. Crystallization of poly (ethylene glycol) in poly (methyl methacrylate) networks. Medziagotyra 2013, 19, 147–151. (95) Uhlherr, P. H. T., Ed. Proceedings of the Tenth International Congress on Rheology; 1988; p 278. (96) Given the topology of the A(BC)n polymers, one might expect a “mushroom”–like conformation in solution. The structural differences induced by deviations from the square–like NPs employed in this work will be the focus of further study. (97) Tirado, M. M.; Martnez, C. L.; de la Torre, J. G. Comparison of theories for the translational and rotational diffusion coefficients of rodlike macromolecules. Application to short DNA fragments. The J. Chem. Phys. 1984, 81, 2047–2052. (98) Bordin, J. R.; Krott, L. B.; Barbosa, M. C. Self–Assembly and Water–like Anomalies in Janus Nanoparticles. Langmuir 2015, 31, 8577–8582. (99) Bordin, J. R. Waterlike features, liquidcrystal phase and self-assembly in Janus dumbbells. Phys. A 2016, 459, 1 – 8. (100) The results obtained for aiso are seen to agree nicely with what shown by Rabani et al. 60 if one bears in mind that their definition for linear size R(t) is related to our size via N (t) ∝ R(t)2 ∼ (tα )2 , so that aiso ≃ 2α should be expected. (101) Movies provided as Supporting Information neatly show that incorrectly oriented (e.g. forming P–P contacts for J–NP2) ad–NPs desorb rather quickly thanks to the solvent layer that persists on the periphery of aggregates, while ad–NPs forming stabilizing contacts with a cluster surface present a much longer lifetime as ad–species. The difference in lifetimes due to different NP orientation provides, in reality, only a deficient estimate of the impact on the grow mechanisms imposed imposed by the strict orientation requirements as our movies do not provide evidence for all the adsorption attemps rejected during the Monte Carlo runs. 39


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Out of Equilibrium Self-Assembly of Janus Nanoparticles: Steering It

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