How Competitive Interactions Affect the Self-Assembly of Confined

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How Competitive Interactions Affects the SelfAssembly of Confined Janus Dumbbells José Rafael Bordin, and Leandro Batirolla Krott J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 04 Apr 2017 Downloaded from http://pubs.acs.org on April 5, 2017

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The Journal of Physical Chemistry

How Competitive Interactions Affects the Self-Assembly of Confined Janus Dumbbells José Rafael Bordin∗,† and Leandro B. Krott∗,‡ Campus Ca¸capava do Sul, Universidade Federal do Pampa, Av. Pedro Anuncia¸cão, 111, CEP 96570-000, Ca¸capava do Sul, RS, Brazil, and Centro Araranguá, Universidade Federal de Santa Catarina, Rua Pedro João Pereira, 150, CEP 88905-120, Araranguá, SC, Brazil. E-mail: [email protected]; [email protected]

∗

To whom correspondence should be addressed Campus Ca¸capava do Sul, Universidade Federal do Pampa, Av. Pedro Anuncia¸cão, 111, CEP 96570-000, Ca¸capava do Sul, RS, Brazil ‡ Centro Ararangu´ a, Universidade Federal de Santa Catarina, Rua Pedro João Pereira, 150, CEP 88905120, Ararangu´ a, SC, Brazil. †

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Abstract We explore the self-assembled morphologies of Janus nanoparticles under cylindrical confinement. Langevin Dynamics simulations are employed to study the behavior of two types of dimers inside cylinders with distinct radius. The first type of nanoparticle was modeled using one monomer that interacts by a standard Lennard Jones potential and another monomer that is modeled using a purely repulsive two length scale shoulder potential. The second type is composed by a Lennard Jones monomer and a repulsive monomer which interacts by the purely repulsive Weeks-Chandler-Andersen potential, which have only one length scale. The two length scale potential used in the first type of nanoparticle models a monomer with competitive interaction. Our results show that the aggregated structures are completely distinct for each type of nanoparticle. As well, our simulations indicate that the cylinder radius can be used to control the type of selfassembled cluster. Small clusters, tubular and donut-like micelles with central holes, with potential application to molecules encapsulation were observed regarding on the nanoparticles specificities and the cylinder radii. As well, bilayer lamellae structures where obtained depending on the type of nanoparticle and the cylinder size.

Introduction Spontaneous self-assembly of chemical building blocks as amphiphilic molecules, block copolymers, colloids and nanoparticles have attracted the attention in condensed matter physics in recent years. 1–3 Among the several macromolecules with self-assembly properties, Janus colloids arise as a promising building block for aggregates with controlled shape and morphologies. Janus nanoparticles are characterized by the presence of two distinct surfaces, with different chemical or physical properties, and can have various shapes, including rods, ellipsoids, spheres and dumbbells. Particularly, the dumbbell shape consists of two linked spherical monomers with the same or distinct diameters, separated by a distance that can go from an almost total overlap to two times the monomer diameter. Each monomer have dis2


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tinct properties, which gives the Janus characteristic to the colloid. There is a large range of applications for dimeric Janus dumbbells in medicine, self-driven molecules, catalysis, photonic crystals, stable emulsions, biomolecules and self-healing materials. 4–12 Self-assembly lamellae and micellae phases were observed on these systems due the competition between attractive and repulsive forces. 13–16 In order to control the shape of the self-assembled morphologies, distinct approaches were proposed, including confinement. 17 Previous studies have shown that confinement can tune the self-assembly of polyhedral nanoparticles, 18 patchy spherical colloids, 19 asymmetric and symmetric dumbbells 20,21 surfactants and polymers 22–24 and soft hydrogels nanoparticles. 25 New lamellae structures were observed for Janus dumbbells confined between parallel plates. 26,27 Particularly, the confinement using nanotubes has been employed to study the morphologies of self-assembled clusters of lipid and cholesterol, 28 surfactants, 29,30 diblock copolymers, 31 triblock 32 and spherical Janus nanoparticles. 33–35 Square-well or Lennard-Jones potentials are used in the standard models employed in most of the molecular simulations of colloidal systems. 36 These potentials are characterized by having only one characteristic scale of distance between the particles, usually the particle diameter. On the other hand, the interaction between core-softened colloids can show competitive scales. For example the hard core-soft shell nanoparticles, characterized by a solid core with size σ grafted by polymers or hydrogels. 25,37–39 Experimental studies 40–42 also have shown that suspensions of spherical colloids can have competitive interactions, with two characteristic length scales. As well, this same characteristic can be observed in globular proteins. 43,44 To model systems with competitive interactions a set of core-softened potentials have been proposed. 43,45–47 These potentials have two characteristic distances, or two length scales (TLS), and have been extensively used to understand the anomalous behavior of water 48,49 and others materials, as silicon 50 and silica. 51 As examples of these anomalous behavior, we can cite the density anomaly, characterized by the increase of density as the pressure

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increases, and the diffusion anomaly, where the self-diffusion constant D increases as the pressure increases. Recently the production of Janus dumbbells where one monomer have competitive characteristic were reported, as silver-silicon (Ag-Si) 52 and silica-polystyrene (SiO2 -PS) 53 dimers. In these cases, one monomer is made of a material with anomalous properties, silicon or silica, and, therefore, can be modeled with a TLS potential. As well, soft colloidal, 54,55 metallic/polymer 56,57 and liquid-crystal/polymer 58 Janus dumbbells have a engineered colloidal monomer whose competitive interaction can be described by a TLS potential. 43 Also, coarse-grained models for short alcohols have been proposed using Janus dimers where one monomer is modeled by a TLS potential. 59–61 In our previous studies we have reported the behavior of Janus dimers with competitive interactions in bulk 62,63 and in thin films confined between parallel plates. 26,27 However, a detailed comparison with the morphologies observed in Janus dumbbells without competitive interactions have not been done in the literature. Therefore, our goal is to investigate and analyze the different aggregates observed for dimers with competitive interactions and compare with the micelles formed by dumbbells without competitive characteristics. This comparison is done in the framework of confined nanoparticles, analyzing the effects of the cylindrical geometry with distinct pore radii to tune the self-assembled morphologies. The paper is organized as follows: first we introduce the model and describe the methods and simulation details; next the results and discussion are given; and then we present our conclusions.

The Model and the Simulation details In this work all physical quantities are computed in the standard Lennard Jones (LJ) units, 36

r∗ ≡

r , σ

ρ∗ ≡ ρσ 3 ,

and t∗ ≡ t

4

ǫ 1/2 , mσ 2


(1)

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for distance, density of particles and time, respectively, and

p∗ ≡

pσ 3 ǫ

and T ∗ ≡

kB T ǫ

(2)

for the pressure and temperature, respectively, where σ, ǫ and m are the distance, energy and mass parameters, respectively. For simplicity, the

∗

will be omitted, since all physical

quantities are defined in reduced LJ units. Our system consists of N dumbbells nanoparticles confined inside a cylinder of radius a and length Lz . Two species of nanoparticles were simulated separately, namely AB and AC dimers. AB dimers are formed by monomers of type A and B, and are linked rigidly at a center to center distance of λ = 0.8. This specific distance was chosen since is the same used in our previous works. 26,27,62 AC dimers are also linked rigidly at the same distance λ, but are composed of monomers of type A and C. Each species of monomer have distinct properties. The specie A of monomers was modeled as standard LJ particles, interacting by the cut and shifted LJ potential

U A (rij ) =

   ULJ (rij ) − ULJ (rc ) ,

rij ≤ rc ,

  0,

(3)

rij > rc ,

where rij = |~ri − ~rj | is the distance between two A particles i and j and rc = 3.0. Here, U LJ (rij ) is the standard LJ 12-6 potential, 36

U LJ (rij ) = 4ǫ

"

σ rij

12

−

σ rij

6 #

.

(4)

These monomers are responsible for the attractive part in the dumbbell, while monomers of type B and C are purely repulsive. Particles of type B interact by a two length scales (TLS) potential, potential B, defined as 46

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"

σ rij

1 u0 exp − 2 c0

U B (rij ) = 4ǫ "

12

−

rij − r0 σ

σ rij

6 #

2 #

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+

,

(5)

where rij = |~ri − ~rj | is the distance between two B particles i and j. The first term of the potential is the 12-6 LJ potential and the second one is a Gaussian shoulder centered at r0 , with depth u0 and width c0 . The parameters used in this work are the same that in the original work that proposed the potential 46 and in our previous works, 26,62? u0 = 5.0, c0 = 1.0 and r0 /σ = 0.7. This potential with this specific parameters have two characteristic distances, at σ and 2.2σ, and shows water-like anomalies. 46,64 Monomers of type C are modeled by the WCA potential, defined by the equation 3 with a cutoff rc = 21/6 . At this distance, the cut and shifted potential is purely repulsive, with one preferential distance at σ. Monomers of distinct types also interact by the WCA potential, and all monomers are repelled by the cylinder wall by the WCA potential. All potentials are shown in figure 1.

Figure 1: Interaction potential between particles of type A (dashed red line), between particle of type B (dot-dashed blue line) and between particles of type C (solid green line). Inset: Janus dumbbells formed by A-B and A-C monomers. Since colloidal suspensions are usually dissolved in a solvent, we employed Langevin 6


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Dynamics simulations using the ESPResSo package. 65,66 The number density is defined as ρ = 2N/V , where V = πa2 Lz is the volume inside the cylinder. ρ was varied from ρ = 0.05 up to ρ = 0.50, ρ = 0.65 or ρ = 0.75, accordingly with characteristics of each case study. Two sets of simulation were performed for each specie of nanoparticle. In the first one, the cylinder radius was a = 5.0, and in the second a = 3.0. Here, a stands for the effective radius available for the nanoparticles since the cylinder has a thickness σ. The real cylinder radius is a + σ. In all simulations, Lz was obtained from Lz = [2N/(ρπa2 )]. The simulation box is a parallelepiped of dimensions Lx × Ly × Lz , where Lx = Ly = a + 4.0σ, and standard periodic boundary conditions is applied in the z-direction, while in the x- and y-directions there is the cylindrical constraint. 65,66 The temperature was simulated in the interval between T = 0.05 and T = 0.50, with viscosity γ = 1.0. The equations of motion for the fluid particles were integrated using the velocity Verlet algorithm, with a time step δt = 0.01. We performed 1 × 106 steps to equilibrate the system. These steps are then followed by 5 × 106 steps for the results production stage. To ensure that the system was equilibrated, the pressure, kinetic and potential energy, number and size of aggregates were analyzed as function of time, as well several snapshots at distinct simulation times. For the smaller radius, a = 3.0, N = 500 dimers were used, and for the simulations with a = 5.0 we have used N = 1000 dimers. Once confined systems can be sensitive to the number of particles in the simulation, in some points we have carried out simulations with up to 2000 and 5000 dimers, and essentially the same results were observed. As well, we run some points with a production time of 1 × 108 to test if the system was well equilibrated, and the same results were obtained. For simplicity, these simulations with a large number of particles and larger simulation time were omitted. The system dynamics was analyzed using the mean square displacement (MSD) as function of time in the z-direction, given by

h[zcm (t) − zcm (t0 )]2 i = h∆zcm (t)2 i ,

(6)

where zcm (t0 ) and zcm (t) denote the z coordinate of the nanoparticle center of mass (cm) at 7



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a time t0 and at a later time t, respectively. The MSD is related to the diffusion coefficient, Dz , by the Einstein relation, h∆zcm (t)2 i . t→∞ 2t

Dz = lim

(7)

The pressure in the z-direction, pz , was obtained from the normal stress in this direction, pz = σzz . The radial density profile ρ(r) was also computed. It gives the density as function of the Euclidean distance from the z axis in cylindrical coordinate, r = (x2 + y 2 )1/2 . Once we compare the profile of distinct total densities, we normalize ρ(r) using

ρnormalized (r) = R

ρ(r) . ρ(r)dr

(8)

Here we have used the center of mass position of each nanoparticle to evaluate the density profile. The fluid and aggregated regions in the pz × T phase diagrams were defined analyzing the snapshots of the systems, the diffusion coefficient, Dz , the radial density profile and the axial density profile. As in previous studies, 26,27,63,67 we use a geometrical condition to define the nanoparticles in the same aggregate. If the distance between one monomer of one dimer and a monomer of a distinct dimer is smaller than rmin = 1.5σ then both dimers belong to the same cluster.

Results and Discussion Since we have simulated two types of nanoparticles and two distinct radii, we have separated the results and discussion in two cases, namely case 1, for nanoparticles inside cylindrical nanopores with radius a = 5.0 and case 2, for dimers inside cylindrical nanopores with radius a = 3.0.

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Case 1: Nanoparticles inside cylindrical nanopores with radius a = 5.0

Figure 2: (A) Mean number of dimers in each cluster as function of the system density at temperature T = 0.10 for AB nanoparticles inside cylindrical nanopores of radius a = 5.0. The dashed vertical lines separate the clustering regions I, II, III, IV and V. (B) Energy per particle as function of the density for the same temperature and radius. Errors bars smaller than the data point are not shown. We start our discussion with the case of AB nanoparticles inside cylinders with radius equal to 5.0. As usual for these systems, the Janus nanoparticles assemble in distinct clusters as function of the system density and temperature. The dependence of the mean number of particles in each cluster, < nc >, and the dependence of the potential energy, U , with the density ρ is shown in the figure 2 for the temperature T = 0.10. As expected, < nc > increases with ρ, while the potential energy decreases since more particles are aggregated. Nevertheless, here the curve reaches a plateau with < nc >< N at high densities. These can look odd in a first moment, once in our previous study, for AB nanoparticles confined between parallel plates, 26 this plateau take place when < nc >= N . However, for the case of cylindrical constraint with a = 5.0 the plateau is reached at < nc >≈ 50. This indicates that for systems with competitive interaction the shape of the confinement will affect not only the aggregates morphologies, but also the maximum number of nanoparticle in each cluster. In order to understand this feature we split the aggregated state in different regions, 9



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Figure 3: Janus AB dumbbells morphologies inside cylinders with radius a = 5.0 for the regions I to V. Region I states for lower densities and temperatures, where the nanoparticles are aggregates in dimeric (nc = 2), trimeric (nc = 3), tetrahedral (nc = 4) and hexahedral clusters (nc = 6). In region II we observe the same type of clusters, but the colloids are arranged in two layers: one external layer near the wall and a central (inner) layer. Region III is dominated by small spherical or elongated aggregates ordered in two layers. In region IV we observe larger spherical and elongated aggregates in the external layer and small clusters in the central layer, and in region V the central layer is also composed of spherical and elongated aggregates, but the external layer is a series of donut-like structures. namely regions I, II, III, IV and V, to analyze each behavior separately. As we discuss below, each region is composed by a set of densities and temperatures where the same structural properties were observed. First, in the regions I and II, located at the lower values of density, the < nc > is between ≈ 2 and ≈ 6. This indicates that the aggregates here are dimeric, with nc = 2, trimeric, with nc = 3, tetrahedral, with nc = 4, or hexahedral, with nc = 6. These aggregates were 10


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also observed for the bulk and plate confined systems. 26,27,62 Despite the similar number of nanoparticles in each cluster, the distribution inside the cylinder is distinct for each region. In the region I the cluster are uniformly spread over all the cylinder, while in the region II the cluster forms two layers: an inner layer, near the z-axis, and a shell or contact layer, located at the wall. This can be seen in the figure 3, where we show the frontal and side views for each region. From the frontal view the layering is clear for the region II, and it is reinforced by the analysis of the density distribution in the radial direction, shown in figure 4. For densities inside the region I, as ρ = 0.05, the density profile do not indicate any organization. However, for the density ρ = 0.15, inside the region II, the layered structure is evident. More than this, the two peaks near the wall (remember that the density profile is related to the center of mass of each dimer) and the frontal view from figure 3 show that in the external shell the B monomer is in contact with the cylinder wall or in the outside part of the micelles, while the A monomers are in the internal part. The distribution in two layers goes up to the higher simulated densities, as we shown for ρ = 0.45 in figure 4. The aggregates observed in the inner layer of the region II are also shown at the bottom of figure 3. As we can see, in the inner layer is also observed non aggregated (isolated) nanoparticles and clusters composed by only two dimers. This distinct conformations also reflects in the potential energy dependence with the density. Inside each region, I and II, we can draw a linear fit for the potential energy values. However, between the two lines there is a small gap, as can be seen in the figure 2(B). Increasing the density leads to clusters with more nanoparticles. In the region III the system is mainly aggregated in short spherical and elongated micelles in both inner and contact layers, while in region IV we observe the same kind of micelles in the inner layer, but the contact layer is formed exclusively by long elongated micelles, as shown in figure 3. Here, in the transition from region III to region IV, the dimer distribution inside the cylinder does not change. Also, since the micelles grows from spherical to long elongated, even the shape of the aggregates do not have a drastic change. This reflects in the potential energy behavior.

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Figure 4: Normalized radial density distribution for temperature T = 0.10 and densities ρ = 0.05 (solid black line), ρ = 0.15 (dashed red line), ρ = 0.40 (dot–dashed blue line) and ρ = 0.45 (solid blue line) for AB nanoparticles inside cylindrical nanopores of radius a = 5.0. As shown in the figure 2(B), the linear fit for regions III and IV have the same inclination. However, in the transition from region IV to region V there is a gap in the potential energy linear fit. As in the transition from region I to II, this gap is related to a drastic change in the Janus dumbbells conformation, as we discuss below. In region V the inner layer have the same characteristics observed in regions III and IV. Nevertheless, the interesting cluster is observed in the contact wall. Here, the nanoparticles aggregate in donut-like micelles along the cylinder, as we can see in figure 3. This kind of micelles is a consequence of competitive interactions from the two length scale potential. Once the temperature is low, the B particles can not reach the first length scale, at a distance rB1 ≈ σ. Therefore, they remain in the second length scale, rB2 ≈ 2σ. Notice that this distance is favored by the donut shape. Therefore, the competitive interaction characteristic of the TLS potential is essential to observe this micelles morphologies. As well, the confinement geometry favors the donut micelles. Another interesting feature observed for this case is the coexistence of distinct morphologies of clusters. In our previous works, for both bulk 63,67 or thin films, 26,27 we have not observed smaller clusters, as tetrahedral and hexahedral, in the same region where spherical or elongated micelles were assembled. Now, due the geometry of the confinement and the layering, it is possible to obtain distinct types of aggregates with 12


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the same values of temperature and density. This result is particularly interesting to control the shape of the aggregates and create different self-assembled morphologies at the same time.

Figure 5: (A) Mean number of dimers in each cluster as function of the system density at temperature T = 0.05 (black line, square points) and T = 0.20 (red line, diamond points) for AC nanoparticles inside nanotubes with radius a = 5.0. The dashed vertical lines separate the micellation regions I, II and III. (B) Potential energy per dimmer as function of the density for T = 0.05 (upper panel, black line, square points) and T = 0.20 (lower panel, red line, diamond points). Errors bars smaller than the data point are not shown.

Removing the competitive characteristic of the repulsive monomer leads to drastic modifications in the self-assembled morphologies. In figure 5 we plot the mean number of AC nanoparticles in each cluster and the potential energy per dimer dependence with the density. As we can see, for the temperatures T = 0.05 and T = 0.20 we have distinct behaviors. At lower temperatures < nc > increases from < nc >≈ 30 at ρ = 0.05 to < nc >≈ 175 at ρ = 0.25, and then all dumbbells assemble in only one cluster. On the other hand, for T = 0.20 all particles are in the same cluster when ρ = 0.15. This result is unexpected, once we should expect that at higher temperatures the aggregation in one single cluster will occur for higher densities. As in the previous case, the changes in the aggregates shapes leads to gaps in the potential energy, as we can see in the figure 5(B). In order to understand this behavior we analyze the shape of the observed clusters. At lower densities, below ρ = 0.15, and for all temperatures, the micelles are spherical or 13



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Figure 6: Micelles observed for AC nanoparticles inside cylindrical nanopores with radius a = 5.0 at temperature T = 0.20. In the region I the Janus dimers assemble in spherical and elongated micelles. In the region II a bilayer is observed, while in region III the nanoparticles are aggregated in a hollow cylindrical cluster.

Figure 7: Normalized radial density profile for temperature T = 0.20 and densities ρ = 0.10 (solid black line), ρ = 0.20 (dashed red line), ρ = 0.40 (dot–dashed green line) and ρ = 0.50 (solid blue line) for AC nanoparticles inside cylindrical nanopores of radius a = 5.0. elongated, as we show in the upper snapshot of figure 6, and are mainly in the central axis of the nanotube, as the radial density profile in the figure 7 shows for T = 0.20 and ρ = 0.10 (solid black line). This region with spherical and elongated micelles will be named as region I. Increasing the density at lower temperatures the size of the micelles grows, as the figure 5(A) indicates and the second snapshot in figure 6 shows. However, the repulsion between the C 14


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monomers in the external surface of the cluster prevent the larger micelles to aggregate in only one micelles. To overcome this repulsion, the system needs energy. Therefore, when the temperature is T ≥ 0.20 all the elongated micelles combine in one single bilayer structure, as we show in the first snapshot for the region II in figure 6. Increasing the density the single micelles splits in two bilayer structures. Increasing even more the density, and for temperatures up to T = 0.30, the AC nanoparticles aggregate in a hollow cylindrical cluster, assuming the confinement shape. As the density profile for ρ = 0.50 shows in figure 7, the nanoparticles move from the central axis to the walls. As we can see, the morphologies are completely distinct from the observed for nanoparticles with competitive interactions. The bilayer and hollow tubular micelles were only observed for AC dimers, while the donut shaped micelles was obtained by the self-assembly of AB dumbbells. Also, here only one morphology was obtained in each region, different from the observed for AB nanoparticles.

(A)

(B)7 diffusion extrema TMD

V

10

6 5

pz

IV

pz

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5

III

4 3

III

I

2

II

II

1 I 0

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

0.3

0.4

0.5

T

T

Figure 8: (A) pz ×T phase diagram for AB nanoparticles confined inside cylindrical nanopores with radius a = 5.0. The five micellation regions are indicated and separated by solid black lines. The isochores in the fluid region are the dashed gray lines, and goes from ρ = 0.05 to ρ = 0.65. The diffusion anomaly extrema is indicated by the dot-dashed blue line, and the TMD by the dashed red line. (B) pz × T phase diagram for AC nanoparticles confined inside cylindrical nanopores with radius a = 5.0. The three micellation regions are indicated and separated by solid black lines. The isochores in the fluid region are the dashed gray lines and goes from ρ = 0.05 to ρ = 0.50. The results for AC and AB nanoparticles confined inside cylinders with a = 5.0 are

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summarized in the pz × T phase diagrams show in figure 8. We should address that this phase diagram is purely qualitative, once others techniques are required to predict the exact point of phase transition. For the competitive case, the five regions for the different shapes of clusters and layering are indicated figure 8(A), and the dashed gray lines are the isochores. As well, in the fluid region this system shows density and diffusion anomalies. In order to check if the Janus system shows density anomaly we evaluate the temperature of maximum density (TMD). Using thermodynamical relations, the TMD can be characterized by the minimum of the pressure versus temperature along isochores,

∂pz ∂T

=0,

(9)

ρ

while the diffusion anomaly is characterized by a increase in Dz with the increase of ρ. In figure 8 the TMD is indicated by dashed red line and the maximum and minimum in Dz by dot-dashed blue line. The anomalous regions in the pz × T phase diagram are smaller and the aggregate region is shifted to higher temperatures when compared with the system confined between parallel plates. 26 This behavior was already observed for confined anomalous fluids, 68 where the nature of the confinement can lead to shifts in the anomalous regions. The three different self-assembly clusters region observed for the system without competitive interactions are shown in figure 8(B): region I for spherical and elongated micelles, region II for bilayers and region III for hollow cylinders. As usual for LJ systems, the diffusion and density anomalies were not observed for AC dimers.

Case 2: Nanoparticles inside cylindrical nanopores with radius a = 3.0 Some new interesting features arise when we shrink the cylinder radius. As in the previous cases, we start analyzing the mean number of dumbbells in each cluster, < nc >, shown in figure 9. For the lowest values of densities the aggregates form trimeric and tetrahedral 16


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70 60 50

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40

I

II

III

IV

V

0.5

0.6

0.7

30 20 10 0

0.1

0.2

ρ

0.3

0.4

Figure 9: Mean number of dimers in each cluster as function of the system density at temperature T = 0.05 for AB nanoparticles inside nanotubes with radius a = 3.0. The dashed vertical lines separate the micellation regions I, II, III, IV and V. Errors bars smaller than the data point are not shown. clusters. However, these clusters can be arranged in a single file at the cylinder center or in a layer in contact with cylinder wall. The single file regime we will call region I, and the structure with contact layer will be the region II. We can see the structures in the figure 10, and in figure 11 we show the radial density profile for the temperature T = 0.05 and densities ρ = 0.05, where the single file was observed, and ρ = 0.10, where the density is already high enough to create the contact layer. This single layer and the transition to a contact layer was already observed in several cases of fluids confined inside nanotubes. 69–72 As in the case A for AB dimers, < nc > increases with the density until a threshold, according with our results shown in figure 9. Increasing < nc > leads to the region III, where the clusters are hexahedral, short spherical and short elongated micelles, and region IV, with long spherical and long elongated micelles, as we show in figure 10. The threshold happens in the region V, where < nc >= 62.5 for density ρ = 0.65 and above. Comparing with the a = 5.0 case, in region V the < nc > is higher for the tighter cylinder. However, inside cylinder with a = 3.0 there is only the contact layer – there is no space for the inner layer. Therefore, when a = 3.0 all nanoparticles are aggregated in the donut-like structure, which have higher < nc > than the clusters in the inner layer observed for a = 5.0, leading 17



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Figure 10: Aggregates obtained for AB nanoparticles confined inside cylindrical nanopores with radius a = 3.0. In the region I the Janus dimers assemble in trimeric and tetrahedral aggregates, and these aggregates are in a single file inside the cylinder. In the region II the same aggregates plus hexahedral micelles where observed, but the layer is near the wall. The cluster size increases in region III, where the nanoparticles are aggregated mainly in small spherical and elongated micelles, and in region IV, where we can see longer spherical and elongated micelles. For the higher densities, in region V, only bilayer donuts where formed.

Figure 11: Radial density profile for T = 0.05 and densities ρ = 0.05 and ρ = 0.10 showing the transition from single central file to a contact layer. to a bigger < nc > for the smallest cylinder. A consequence from the narrower cylinder confinement is that the densities for the region V is higher than in the wider cylinder. The competition between the confinement and the amphiphilic characteristic of the nanoparticle leads to this behavior. 68

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Figure 12: Micelles observed for AC nanoparticles inside cylindrical nanopores with radius a = 3.0. In the region I the Janus dimers assemble in spherical and elongated micelles. In the region II a bilayer is observed, while in region III the nanoparticles are aggregated in a cylindrical cluster. Finally, we show the aggregates obtained for AC dimers confined inside cylinders with a = 3.0. Essentially, the same structures observed for a = 5.0 where obtained. For lower densities, in the region I of the phase diagram, the Janus nanoparticles are assembled in spherical and elongated micelles, as we show in figure 12. Increasing the density, we observe the aggregation in a bilayer lamellae. Now, this bilayer region, named region II, goes up to lower temperatures, unlike the case with a = 5.0. At higher densities the bilayer structure can not be achieved due the confinement, and the nanoparticles assemble in a tubular micelles. However, this tubular structure does not have a central hole as for the case with wider cylinder, essentially because the tighter cylinder does not leave enough space to create the central hole. Examples of the observed structures are shown in the figure 12. The aggregate regions for both species of dimers are show in the pz × T phase diagram, figure 13(A) and (B). The dashed gray lines in the figures are the isochores. For the system with competitive interaction, figure 13 (A), the solid blue line in fluid phase is the TMD line. Comparing with the a = 5.0 case, the TMD line goes to higher temperatures and covers all isochores showed in the phase diagram, from ρ = 0.05 to ρ = 0.75. Fluids modeled by the equation 5, when confined between solvophilic plates 68 shows a similar behavior, where the TMD line increases as the confinement increases – therefore, decreasing a the TMD increases. The most curious phenomena in the fluid phase is that the diffusion anomaly vanishes when a = 3.0. Nevertheless, this can also be understood when we analyze the monomeric system, 19



(B)

(A)12 V

5

TMD

4

9

IV

III

pz

3

pz

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III

6

2 II

II 3

0

1 I 0.1

0.2

0.3

0.4

0.5

0

I

0.1

T

0.2

0.3

Τ

0.4

0.5

Figure 13: (A) pz × T phase diagram for AB nanoparticles confined inside cylindrical nanopores with radius a = 3.0. The five micellation regions are indicated and separated by solid black lines. The isochores in the fluid region are the dashed gray lines and goes from ρ = 0.05 to ρ = 0.75. The TMD line is represented by the solid blue line. (B) pz × T phase diagram for AC nanoparticles confined inside cylindrical nanopores with radius a = 3.0. The three micellation regions are indicated and separated by solid black lines. The isochores in the fluid region are the dashed gray lines and goes from ρ = 0.05 to ρ = 0.50. where previous works 68 have shown that the diffusion anomaly shifts to higher densities and lower temperatures when the confinement increases. Once the micellation region have not changed the temperature range from the case with a = 5.0, figure 8(A), to the case with a = 3.0, figure 13(A), the diffusion anomalous region was wrapped by the micellation region, vanishing in the aggregated phase. The pz ×T phase diagram for AC nanoparticles confined inside cylindrical nanopores with radius a = 3.0 is shown in the figure 13(B). Comparing with the wider nanopore, figure 8(A), the more strict confinement increases the bilayer aggregation region II, observed in a large range of temperatures and densities. On the other hand, the region III is small and goes to higher densities. And as expected, anomalous behavior were not observed in the fluid region of AC nanoparticles.

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Conclusion We have used extensive Langevin Dynamics simulations to study two types of Janus dimers confined inside cylinders with two radius, a = 5.0 and a = 3.0. The first type of nanoparticle, namely AB, is formed by one LJ monomer and a monomer with competitive characteristics, while the AC nanoparticle is composed by a LJ monomer linked to a WCA monomer. Essentially, we have studied how the properties of the two length scale potential can lead to distinct self-assembly properties of the nanoparticles. AB nanoparticles inside cylinders assembles in trimeric, tetrahedral, hexahedral, spherical and elongated micelles, similar to the observed in bulk 62 and confined between parallel plates. 26,27 Inside the cylinder with a = 5.0 the aggregates are distributed in a contact layer, near the wall, and an inner layer. With this specific radius, we observe a coexistence of morphologies that were not observed in bulk or thin films. Shrinking the cylinder to a = 3.0 the inner layer vanishes due the strong confinement. For both values of radii, a new donut-like morphology arises as a combined effect of the two length scales potential and the cylindrical confinement. On the other hand, AC nanoparticles have distinct morphologies from AB nanoparticles and a small variety of cluster shape. For both size of cylinders, spherical and elongated micelles where observed, as well a bilayer lamellae phase. Inside wider cylinder, the nanoparticles at high densities are arranged in hollow tubular micelles, while for the cylinder with a = 3.0 the central hole in the tubular micelles was not observed. Our results show how dumbbells Janus nanoparticles with distinct properties can lead to distinct self-assembled structures. As well, we have shown that cylindrical confinement can be used to create donuts or tubular micelles with a central hole, which can be used to encapsulate molecules of interest.

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Acknowledgments JRB thanks the Brazilian agency CNPq for the financial support.

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How Competitive Interactions Affect the Self-Assembly of Confined

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