Photocontrollable Self-Assembly of Azobenzene-Decorated

Article pubs.acs.org/Macromolecules

Photocontrollable Self-Assembly of Azobenzene-Decorated Nanoparticles in Bulk: Computer Simulation Study Jaroslav M. Ilnytskyi,*,†,‡,§ Arsen Slyusarchuk,‡ and Marina Saphiannikova§ †

Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv, Ukraine National University Lviv Politechnic, Lviv, Ukraine § Leibniz Institute of Polymer Research, Dresden, Germany ‡

ABSTRACT: Decoration of nanoparticles by specific functional groups provides means of controlling their aggregation and self-assembly into ordered morphologies. We study the photocontrollable self-assembly of the azobenzene-functionalized nanoparticles using coarse-grained molecular dynamics simulations. With no illumination applied, a monodomain smectic morphology is formed only via cooling the isotropic system at a sufficiently slow rate. Quenching the system below the smectic−isotropic transition results in formation of a polydomain glass-like state with restricted dynamics of nanoparticles. Upon irradiation with appropriate wavelength and intensity, the azobenzenes undergo trans−cis−trans photoisomerization cycles which unlock the interdomain links and induce uniaxial orientation of domains with their local director perpendicular to the polarization axis of irradiation. As demonstrated by the simulations, this transition can speed up essentially the self-assembly of decorated nanoparticles from the isotropic to the monodomain smectic phase, both via gradual cooling down and via quenching in a broad temperature interval below the smectic−isotropic transition.

1. INTRODUCTION Functionalized nanoparticles (FNPs) have gained tremendous importance due to their unique optical, electronic, magnetic, and chemical properties.1 Potential applications include medical diagnostics, drug delivery, cancer therapy, nanoelectronics and information storage, imaging and super resolution microscopy, sensors, solar energy conversion, (photo)catalysis, or surface coatings.2 Depending on the particular application, one is focused on achieving either good dispersion of FNPs or the opposite effects such as micellization, sedimentation, or selfassembly into certain ordered phase. One of the examples are the FNPs decorated by the liquid crystalline (LC) groups, as far as these “involve almost all kinds of supramolecular interactions such as van der Waals interaction, dipolar and quadrupolar interactions, charge transfer and π−π interaction, metal coordination and hydrogen bonding etc.”3−6 One of the most important factors that affect the FNPs self-assembly is their decorating (grafting) density. Namely, upon its increase the symmetry of the ordered morphology changes from the lamellar smectic to the columnar and then to the cubic one. The FNPs shape changes respectively from the rod-like to the disc-like and then to the spherulitic shape reflecting strong shape-phase relation similarly to the case of the LC-functionalized dendrimers.4,7,8 This effect is also observed in computer simulations.9−11 Besides the decorating density, the FNPs self-assembly can be controlled by external stimuli such as mechanical force, heat, and electric and magnetic fields. © XXXX American Chemical Society

One of the most recent and fascinating ways to control the aggregation of FNPs is by light (see e.g. ref 12). To this end the chromophoric (e.g., azobenzene, cinnamoyl, diarylethene dithiophenols, etc.) functional groups are incorporated into FNP. Examples of applications include photocontrolled micellization,13,14 optically switchable devices,15,16 networks of FNPs with optically switchable conductance,17 etc. These effects share some similarities with photoinduced structural changes observed in azobenzene-containing side-chain polymers, studied intensively during the past two decades due to numerous applications.18−21 Photocontrollable self-assembly is found to depend on a number of conditions, such as availability of a free volume around each chromophore, separation between the gold nanoparticle electronic system and that of a chromophore, and the difference in properties of two isomers. The details are discussed in section 2. Let us consider now a particular case of the azobenzene chromophore which exists in two forms: trans- and cisisomer.18−21 One of the differences between these two isomers is the magnitude of their dipole moment. In particular, in the case of 4-alkoxyazobenzene the dipole moment of trans-isomer is about 1D, whereas it is about 5D for the cis-isomer.22 For the FNPs decorated by these chromophores, one observes the dispersion of particles in a hydrophobic solvent such as Received: August 28, 2016 Revised: November 7, 2016

A

DOI: 10.1021/acs.macromol.6b01871 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

information on the system behavior on the scales smaller than that for coarse-grained beads. The model FNP consists of a large core bead decorated by Nch chains each terminated by a chromophore (see Figure 1).

cyclohexane in dark and under visible light, where most chromophores are found in the unpolar trans-form. Upon irradiation with the ultraviolet light, the chromophores photoisomerize into a polar cis-form and a rapid sedimentation of FNPs is observed.22 A similar effect was reported for FNPs dispersed in a toluene.23 An opposite effect of FNPs aggregation under visible light and their dispersion upon ultraviolet illumination is reported as well.24,25 However, there are more differences between the trans- and cis-isomers of azobenzene that can be exploited for the sake of photocontrollable self-assembly of the azobenzene-decorated FNPs, as is discussed in a recent experimental work.26 Indeed, as has been known for some time, the prolate trans-isomers are mesogenic (i.e., are able to form the LC phases), whereas the bent cis-isomers are not.21,27,28 Another difference is that the rate of the trans−cis photoisomerization is angle-selective, whereas that for the reverse cis−trans photoisomerization is not.29 Given the illumination conditions that the absorption bands for both transformations overlap, the continuous trans− cis−trans isomerization cycles take place and result in the reorientation of the trans-isomers predominantly perpendicular to the light polarization axis (“orientation hole-burning” or Weigert effect29). Both polarized and unpolarized light can be used to photoalign the trans-isomers. In the latter case, as pointed out by Ikeda,21 “only the propagation direction is in principle, perpendicular to the electric vector of the light. Thus, when unpolarized light is employed, it is expected that the azobenzene moieties become aligned only in the propagation direction of the actinic light”. The orientation hole-burning effect serves as a basis for numerous theoretical30,31 and simulation32,33 studies for the photoinduced deformations in azobenzene polymers and is justified recently using the combination of deterministic simulations and stochastic kinetic equations.34 All this indicates the possibility for a photocontrollable self-assembly of azobenzene-decorated FNPs into bulk phases. The aim of the current study is to perform coarse-grained molecular dynamics (MD) simulations of the photocontrollable self-assembly of the azobenzene-decorated FNPs. The same model for FNPs is used as in a number of previous works,9−11 and the deterministic-stochastic simulation technique suggested in ref 34 is employed. The outline is as follows. The details of a coarse-grained model and of a simulation approach are provided in section 2, structural changes undergone by a system at the smectic−isotropic transition are discussed in section 3, self-assembly in the case of no illumination is considered in section 4, and finally, a photocontrolled selfassembly is discussed in section 5 followed by Conclusions.

Figure 1. Generic coarse-grained model for the FNP. The central core is shown in pink, spacer beads in gray, and terminating chromophore units as blue spherocylinders.

All constituents mimic their respective chemical counterparts on a coarse-grained level. In particular, the core bead stands for a solid nanoparticle, and each soft bead of a chain represents a group of approximately 3 hydrocarbons, whereas the chromophore represent the features of the azobenzene.9,34,35 The diameter of a core bead sets the curvature of the decorating surface of the FNP which affects the amount of available free volume around each chromophore. As discussed in ref 12, the lack of such free volume may hinder the photoisomerization in the case of monolayers densely grafted on planar gold surface, but photoisomerization is unlocked in the case of 2 nm gold FNPs.39,40 Similar results are reported for the case of azobenzene-functionalized dendrimers,41 where for the generation n = 1−4 dendrimers in a solvent no dependence of the quantum yield on n was detected for the terminal azobenzenes, whereas the photoisomerization may be hindered within the densely packed flat smectic layers.41 These results correlate well with the estimate made for the average dimension of a dendritic core in the case of the generation 3 carbosilane dendrimer being in a range of 2 nm.35 The length of a spacer sets the level of decoupling between the core bead and the chromophores. It is important to minimize possible resonance energy transfer between their respective electron systems; otherwise, quenching of the excited states of the chromophore electrons will occur, and thus, photoisomerization will be suppressed. The effect was studied for the case of 2.5 nm gold FNP with the spacer length varying from l = 1 to 12 methylene groups.42 The suppression of the photoisomerization due to grafting, defined as the ratio between the quantum yield in solution and its counterpart on the FNP surface, is found to change substantially from 137 at l = 4 to 1.5 at l = 12. One can conclude that the spacer length of at least l ∼ 12 methylene units is needed to enable quantum yield for the azobenzenes photoisomerization comparable to that in solution. The conditions for the central core diameter ∼2 nm and the spacer length of ∼12 methylene units are met in the case of the model FNP used in the previous simulation studies;9−11 therefore, we used the same model here. In particular, the diameter of a core bead is σ1 = 2.137 nm. Each spacer consists of four smaller soft spherical beads, each representing a group of about three hydrocarbons. The diameter of the first bead of each spacer is σ2 = 0.623 nm, whereas for the following beads

2. MODELING DETAILS In this study we employ a coarse-grained modeling technique which makes use of the effective potentials. These potentials act between the groups of atoms represented as beads and are parametrized to mimic the volume of each group and the average forces acting between them35 (see also refs 36−38 for more details). The main reason for this choice of modeling is the need to cover the close to micrometer scale of the ordered morphologies and typically long relaxation times in concentrated solutions of FNPs. In short, one may say that in this way one considers the atom−atom interactions to some degree implicitly, at the level of their impact on a larger scale behavior of the system. The obvious drawback is, of course, lack of B


Article

Macromolecules σ3 = 0.459 nm. These dimensions are obtained initially from the estimates of solvent-accessible surface area for these fragments.35 The FNP is kept together by means of bonded interactions which include harmonic bond and harmonic angle bending terms Vb =

Nb

Na

i=1

i=1

∑ k b(li − l0)2 + ∑ ka(θi − θ0)2

VSR

(3)

The energy scale U is set the same as for VSS; d′(qij) = d(qij)/D is the reduced distance between the cores of two spherocylinders. As it was found in ref 46, the system of soft repulsive spherocylinders of the length-to-breadth ratio L/D = 3 interacting via potential (3) does not exhibit orientationally ordered phases and, thus, can be used to mimic the c-beads. The liquid crystallinity of such spherocylinders can be greatly enhanced by complementing eq 3 with an additional anisotropic attractive term.47 We will write down such potential, VSA, in a form suggested in ref 48:

(1)

where the following force field constants are used for the first term (harmonic bonds): kb = 5 × 10−17 J/nm2; bond lengths: l0 = 1.49 nm (core bead-to-first spacer bead), 0.36 nm (first-tosecond spacer beads), 0.362 nm (following spacer beads), and 0.298 nm (between the centers of the last spacer bead and that of the nearest spherical cap of a chromophore). The second, pseudovalent angle bending, term in eq 1 is defined between each triplet of consecutive beads in a spacer and accounts for the spacer rigidity on a coarse-grained level. It is introduced due to the reason that the bond length between beads is about 0.36 nm, which is less than the Kuhn length for polyethylene 0.54 nm. li and θi are instant values for ith bond length and ith pseudovalent angle, respectively; Nb and Na are their total numbers within one molecule. The pseudovalent angle constant is θ0 = π, and the bending force constant is ka = 2 × 10−19 J/rad. The nonbonded interactions between spherical beads are of soft quadratic type typically found in the dissipative particle dynamics simulations.43 Let rij be the vector that connects the centers of ith and jth spherical beads and σi and σj their respective diameters. Then the sphere−sphere interaction potential, VSS, reads ⎧[1 − r′]2 , r′ ≤ 1 ⎪ ij ij VSS = U ⎨ ⎪ 0, rij′ > 1 ⎩

⎧[1 − d′(q )]2 , d′(q ) ≤ 1 ⎪ ij ij = U⎨ ⎪ 0, d′(q ij) > 1 ⎩

⎧U {[1 − d′(q )]2 − ϵ′(q )}, d′(q ) < 1 ij ij ij ⎪ ⎪ 2 ⎪U {[1 − d′(q ij)] − ϵ′(q ij) ⎪ VSA = ⎨ 1 [1 − d′(q ij)]4 }, d′(q ij) ∈ [1, dc′] ⎪− ϵ′ 4 ( q ) ⎪ ij ⎪ ⎪ 0, d′(q ij) > dc′ ⎩ (4)

Here the dimensionless configuration-dependent well depth ϵ′(qij) is obtained from the requirement that both the potential and its first derivative vanish at d′c; for details see ref 47. This potential is used in our study to describe the anisotropic interaction between two t-beads, which reflects the liquid crystallinity of trans-azobenzene. The remaining types of the pairwise interactions: t-bead with c-bead, t-bead with a sphere, and c-bead with a sphere are described all by the soft repulsive form (3). For the two latter cases, d(qij) is the shortest distance between the core of the spherocylinder and a center of a sphere and its reduced counterpart is d′(qij) = d(qij)/σ̅, where σ̅ = (σi + D)/2. Following the approach developed in ref 34, the simulation of the system under illumination comprises both deterministic and stochastic parts. The deterministic part is performed via molecular dynamics (MD) simulation in the NPxPyPzT ensemble,49,50 a variant of the more general Parrinello− Rahman approach.51 The benefit of using this ensemble is that the shape and dimensions of the simulation box are able to change in a course of a run resulting in self-adjusting of the simulation box to the characteristic dimensions of the spontaneously grown morphology. One should note that most of the pairwise nonbonded interactions in the system are described by repulsive potentials (2) and (3). Therefore, to achieve the normal conditions densities of the order of 1 g/cm3, the system is kept at the external pressure of 50 atm, in which case bulk ordered morphologies have been found.9−11 To reproduce a bulk system, the periodic boundary conditions are applied along all three axes of the simulation box. The time-step of the MD integrator is chosen equal to Δt = 20 fs, which is of the order of magnitude larger than for the case of atomistic simulations, due to softness of the interaction potentials (2)− (4). The system is thermostated by rescaling the velocities separately for each group of similar beads (core beads, spacer beads, and chromophores) after each 20 MD steps. The stochastic part of the simulations describes, on a coarsegrained level, the effects related to the photoisomerization of chromophores. The quantum mechanical nature of photo-

(2)

Here U = 7 × 10−19 J provides the energy scale of the potential, and r′ij = |rij|/σ̅ is reduced distance between the centers of two spheres, where σ̅ is found according to the combination rule σ̅ = (σi + σj)/2. We will switch now to the interaction between chromophores. These have two states, termed hereafter as the t-bead and the c-bead, and they mimic on a coarse-grained level the properties of the trans- and cis-isomers of azobenzene, respectively. With respect to the self-assembly of FNPs, the principal difference between the two is that the trans-isomers are mesogenic, whereas the cis-isomers are not,21,27,28 and this should be reflected in the properties of the t- and c-beads. To simplify simulations, we opted for the description of both t- and c-beads by the particles of the same spherocylinder shape with the breadth D = 0.374 nm, whereas the difference in their liquid crystallinity is accounted for by the form of the interaction potentials. The mutual arrangement of the pair of spherocylinder beads i, j is characterized by the set of variables denoted thereafter as qij = {êi, êj, rij}. Here rij is the vector connecting their centers, and êi and êj are their respective orientations in space. Then, according to Kihara,44,45 one evaluates the shortest distance d(qij) between their internal cores (the lines connecting the centers of two spherical caps within each spherocylinder). The generalization of eq 2 for the case of two spherocylinders reads C


Article

Macromolecules isomerization29,52−54 is taken into account implicitly, by applying the kinetic equations of a general form for the probabilities of the transitions between the t- and c-state of each ith bead: pi (t → c) = pt (eî · i )̂ 2 pi (c → t) = pc

(5)

where i ̂ is the unit vector collinear with the light polarization axis, and pt and pc are the respective transition rates. The latter depend on the chemical details of the chromophore group, as well as the intensity and the wavelength of the illumination; particular choices are discussed in section 5. The switch of the state is attempted for each chromophore at each MD step, and the state dictates which form of the potential, (3) or (4), is to be used when evaluating its interaction with other chromophores. Selective absorption of the light by the azobenzene chromophores29,52 is mimicked here by the angular dependence of the transition probability pi(t → c) for their model counterparts. Another factor to consider is the unknown change in the orientation of the azobenzene chromphore after the photoisomerization.53 We take it into account by performing stochastic reorientation of a model chromophore after its change of state:34 bi = eî + æs,̂

êinew =

bi |bi |

Figure 2. Snapshots for the monodomain SmA phase at T = 400 K (on the left) and for the I phase at T = 520 K (on the right).

section we will concentrate on the changes in the system structure that take place during this transition. These changes are studied on a level of FNPs by examining their shape, positions, and orientations. To this end, for each FNP, the gyration tensor G is evaluated with its components given by55 Gαβ =

1 N

N

∑ (ri ,α − R α)(ri ,β − Rβ) i=1

(7)

Here N is the number of point masses per one FNP, α and β denote Cartesian axes, and ri,α is the coordinate of ith point mass. Here and thereafter we use the coordinates of the core bead, R = {Rα}, in place of the coordinates of the center of mass of a FNP. Each spherical bead of a FNP is considered as a unit point mass and to account for the elongated shape of chromophores each of them is replaced by four unit point masses arranged regularly along a mesogen core.9 The components of the gyration tensor G characterize mass distribution within a FNP with respect to a laboratory frame. The eigenvalues λ1 > λ2 > λ3 and the respective eigenvectors L̂1, L̂ 2, and L̂ 3 define the equivalent ellipsoid with the squared semiaxes equal to λα with their respective orientations in space given by L̂ α. The equivalent ellipsoid describes the general shape of a FNP and its orientation in space, Ê , is set equal to L̂1. The average asphericity (alternatively termed as a “relative shape anisotropy”) of FNPs in a system is defined as

(6)

Here ênew is the new orientation for ith bead, æ is the i “orientation memory” weight, and ŝ is the random unit vector with its orientation distributed evenly on a sphere. The coarse-grained model used in this study is rather generic and incorporates the principal features of the FNPs such as realistic dimensions of its constituents, flexibility of the decorating chains, and ability of the chromophores to photoisomerize and change their interaction in accordance with the experimental knowledge. The quantum nature of the photoisomerization is taken into account implicitly by introducing stochastic changes into the state of chromophores. It is assumed that the transition rates applied in simulations can be achieved experimentally by the use of appropriately substituted azobenzene chromophores at particular intensity and the wavelength of the illumination. However, appropriate parametrization of the interaction potentials and the transition rates should, in principle, allow for tuning this generic model toward particular chemical realization of interest.

A = ⟨a⟩,

a=

2 2 2 3 λ1 + λ 2 + λ3 1 − 2 (λ1 + λ 2 + λ3)2 2

(8)

where a is the asphericity of an individual FNP characterized by a set of λα and averaging is performed over all FNPs. The global orientational order in a system of FNPs is defined via the nematic order parameter S2

3. STRUCTURAL CHANGES AT THE SMECTIC−ISOTROPIC TRANSITION We consider a system of Nmol = 200 FNPs (with the molecular architecture shown in Figure 1) in a bulk. As was shown previously,10 such a system can be assembled into a monodomain smectic A (SmA) or columnar morpology depending on a number of attached chains, Nch. The assembly can be performed with the aid of an external orientational field which acts on pending mesogens and induces the arrangement of FNPs into a regular structure. Here we consider the case of Nch = 12; the FNPs with such molecular architecture can be assembled ino the SmA morphology only.10 At T* ≈ 510 K, the SmA morphology (shown in the left frame of Figure 2) transforms into the isotropic (I) phase (see the right frame of Figure 2, where this phase is shown at T = 520 K). In this

S2 = ⟨P2(Ê ·N̂ )⟩

(9)

evaluated for a system of FNPs with the orientations Ê . The nematic director N̂ is evaluated in way usual for liquid crystals via diagonalization of the nematic tensor (see e.g. ref 56). Global smectic order in a system is linked to the level of “lamellarity” in the arrangement of FNPs. It is quantified via the amplitude of the density wave for the coordinates R for FNPs core beads along the layer normal. For the case of the SmA phase the latter is assumed to be collinear with the nematic director N̂ . The smectic order parameter for FNPs is evaluated by founding the maximum of the expression D


Article

Macromolecules ̂

S(p) = max ⟨ei2π(R·N)/ p⟩

(10)

as a function of p (here i = −1 ). The maximum position p∥ provides the pitch of the SmA phase, whereas the smectic order parameter is Ss = S(p∥). Local smectic order can be characterized by the number and the size distribution of SmA domains (clusters). The clusters are identified using the Hoshen−Kopelmann algorithm57 where we assume that mth and nth FNPs belong to the same cluster if either (i) they are highly collinear and adjacent in a side-to-side way within the same layer Ê n || Ê m,

Ê n⊥R̂ mn,

R mn = p⊥ ± Δp⊥

Figure 4. Temperature dependence of the molecular asphericity A, the order parameters S2 and Ss (left frame) and of the cluster density Nc and the maximum cluster size Mc (right frame). Separate run at each temperature is performed starting from the monodomain SmA morphology and allowing system to equilibrate at specified T.

(11)

or (ii) they are highly collinear and are adjacent in a end-to-end way belonging to two adjacent layers Ê n || Ê m,

Ê n || R̂ mn,

R mn = p∥ ± Δp∥

490 K; therefore, a rather modest run duration of 20−50 ns was used in this case. The same run duration was used at T > 520 K but for a different reason: here a rapid order−disorder transition takes place followed by fast relaxation of the system in the I state. However, in the temperature range of T = 490− 520 K much longer runs of 120−160 ns are performed due to the known effect of critical slowing down. As one can see in Figure 4, all the characteristics displayed there undergo sharp changes at T* ≈ 510 K. Namely, both order parameters S2 and Ss sharply drop to zero at this temperature, indicating a presence of the order−disorder transition. The synchronicity in the behavior of the asphericity A and both order parameters S2 and Ss indicates (i) the absence of the purely nematic phase characterized by S2 > 0 and Ss = 0 and (ii) a strong relation between the molecular shape and the symmetry of the ordered morphology, being pointed out earlier.7,9,58 Therefore, the transition that occurs at T* is the SmA−I transition. The nematic order parameter S2, defined via eq 9, approaches values close to 1 in the SmA phase, much higher than when evaluated in the smectic phase of low molecular weight liquid crystals (typically, S2 ≈ 0.659). Such high values of S2 in the simulations are explained by two factors: strengthening of the orientational order of FNPs by a microphase seggregation between the polymer and mesogenic subsystems of FNPs and elimination of the orientational fluctuations of individual mesogens in each FNP, as far as the orientations Ê i of the whole FNPs are considered only. The behavior of the cluster density Nc and the maximum cluster size Mc reveals three types of a cluster structure. In the SmA phase (T = 400−500 K) one has Nc → 0 and Mc → 1, i.e., a single cluster containing all 200 FNPs. The system is found in the monodomain SmA phase. On the opposite side, in the I phase (T > 520 K), Nc → 1 and Mc → 0, indicating no SmA clusters (200 disjoint FNPs). The transition region, T = 500− 520 K, is characterized by a sharp decrease of the maximum cluster size and sharp increase of the number of clusters. As we will see in the following sections, the behavior of the system in this region is important from the point of view of the spontaneous self-assembly of the monodomain SmA phase.

(12)

In eqs 11 and 12 we introduced intermolecular vector Rmn = Rm − Rn with the magnitude Rmn = |Rmn| and related to it unit vector R̂ mn = Rmn/Rmn. The value of p∥ is introduced above, whereas p⊥ is the average distance between the FNPs cores within the same layer. Both criteria are depicted in Figure 3.

Figure 3. Illustration of the criteria for two FNPs to belong to the same cluster (see eqs 11 and 12). The FNPs are represented via their equivalent ellipsoids.

More specifically, for the model used in this study, we use the following values: p∥ ≈ 6.3 nm and p⊥ ≈ 1.8 nm estimated from the respective core−core pair distribution functions, in the SmA phase; see ref 9 for details. Their respective tolerances are Δp∥ = 1 nm and Δp⊥ = 0.6 nm, whereas the collinearity/ perpendicularity is allowed up to the tolerance of 15°. After the identification of the clusters we evaluate two properties, such as the cluster density per molecule, Nc = [no. of clusters]/ Nmol, and reduced maximum cluster size, Mc = [max cluster size]/Nmol. In terminology of the network theory, the latter can be termed as the giant component weight. The changes in the system structure, when undergoing the SmA−I transition, are reflected in the temperature dependencies of the set of properties S2, Ss, A, Nc, and Mc shown in Figure 4. At each temperature T, we started from the monodomain SmA phase obtained with aid of an external orienting field10 and equilibrated the system at this temperature by means of a separate NPxPyPzT MD simulation run. The length of each run is chosen depending on the temperature. In particular, no structural changes are observed at 400 K < T
470 K, liquid crystallinity of a system is weakened due to thermal fluctuations, and its dilution by c-beads affects the order inside smectic domains, preventing formation of a monodomain smectic phase. The plot for fc in Figure 10 indicates the threshold value of about 0.05, and if fc is higher than this value, then the self-assembly fails. The results for a set of properties A, S2, Ss, Nc, and Mc obtained in respective stationary states in a course of quenching runs under illumination are collected in Figure 11. These

Figure 11. Same as in Figure 5 but for the stationary states of quenching runs at various temperatures under illumination.

should be compared with their counterparts in Figure 4. One finds the curves of similar respective shapes, but these are shifted to the lower temperatures in Figure 11. Therefore, computer simulation studies indicate the possibility to selfassemble the monodomain SmA phase by quenching the system in a broad temperature interval under illumination, which was found impossible for the unilluminated system. Finally, we will provide some considerations on the comparison between the time scale of the simulations with I


Article

Macromolecules

(8) Saez, I. M.; Goodby, J. W. Supermolecular liquid crystals. J. Mater. Chem. 2005, 15, 26. (9) Ilnytskyi, J.; Lintuvuori, J.; Wilson, M. R. Simulation of bulk phases formed by polyphilic liquid crystal dendrimers. Condens. Matter Phys. 2010, 13, 33001. (10) Ilnytskyi, J. Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study. Condens. Matter Phys. 2013, 16, 43004. (11) Slyusarchuk, A.; Ilnytskyi, J. Novel morphologies for laterally decorated metaparticles: molecular dynamics simulation. Condens. Matter Phys. 2014, 17, 44001. (12) Klajn, R.; Stoddart, J. F.; Grzybowski, B. A. Nanoparticles functionalised with reversible molecular and supramolecular switches. Chem. Soc. Rev. 2010, 39, 2203. (13) Bisby, R. H.; Mead, C.; Morgan, C. G. Active Uptake of Drugs into Photosensitive Liposomes and Rapid Release on UV Photolysis. Photochem. Photobiol. 2000, 72, 57−61. (14) Liu, X.; Jiang, M. Optical Switching of Self-Assembly: Micellization and Micelle−Hollow-Sphere Transition of HydrogenBonded Polymers. Angew. Chem., Int. Ed. 2006, 45, 3846−3850. (15) Raimondo, C.; Crivillers, N.; Reinders, F.; Sander, F.; Mayor, M.; Samori, P. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 12375−12380. (16) Faramarzi, V.; Raimondo, C.; Reinders, F.; Mayor, M.; Samori, P.; Doudin, B. Optically switchable molecular device using microsphere based junctions. Appl. Phys. Lett. 2011, 99, 233104. (17) Ikeda, M.; Tanifuji, N.; Yamaguchi, H.; Irie, M.; Matsuda, K. Photoswitching of conductance of diarylethene-Au nanoparticle network. Chem. Commun. 2007, 1355. (18) Viswanathan, N. K.; Kim, D. Y.; Bian, S.; Williams, J.; Liu, W.; Li, L.; Samuelson, L.; Kumar, J.; Tripathy, S. K. Surface relief structures on azo polymer films. J. Mater. Chem. 1999, 9, 1941−1955. (19) Rutloh, M.; Stumpe, J.; Stachanov, L.; Kostromin, S.; Shibaev, V. Influence of Liquid Crystallinity and Aggregation on Photoorientation. Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 2000, 352, 149−157. (20) Oliveira, O. N.; Kumar, L. L.; Tripathy, S. K. In Photoreactive Organic Thin Films; Sekkat, Z., Knoll, W., Eds.; Academic Press: 2002; pp 429−483. (21) Ikeda, T. Photomodulation of liquid crystal orientations for photonic applications. J. Mater. Chem. 2003, 13, 2037. (22) Akiyama, H.; Tamada, K.; Nagasawa, J.; Abe, K.; Tamaki, T. Photoreactivity in Self-Assembled Monolayers Formed from Asymmetric Disulfides Having para-Substituted Azobenzenes. J. Phys. Chem. B 2003, 107, 130−135. (23) Manna, A.; Chen, P.-L.; Akiyama, H.; Wei, T.-X.; Tamada, K.; Knoll, W. Optimized Photoisomerization on Gold Nanoparticles Capped by Unsymmetrical Azobenzene Disulfides. Chem. Mater. 2003, 15, 20−28. (24) Kawai, T.; Nakamura, S.; Sumi, A.; Kondo, T. Control of dispersion-coagulation behavior of Au nanoparticles capped with azobenzene-derivatized alkanethiol in a mixed chloroform-ethanol solvent. Thin Solid Films 2008, 516, 8926−8931. (25) Raimondo, C.; Reinders, F.; Soydaner, U.; Mayor, M.; Samorì, P. Light-responsive reversible solvation and precipitation of gold nanoparticles. Chem. Commun. 2010, 46, 1147−1149. (26) Zep, A.; Wójcik, M.; Lewandowski, W.; Sitkowska, K.; Prominski, A.; Mieczkowski, J.; Pociecha, D.; Górecka, E. Phototunable Liquid-Crystalline Phases Made of Nanoparticles. Angew. Chem., Int. Ed. 2014, 53, 13725−13728. (27) Ikeda, T.; Horiuchi, S.; Karanjit, D. B.; Kurihara, S.; Tazuke, S. Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors. Macromolecules 1990, 23, 42−48. (28) Barrett, C. J.; Mamiya, J.; Yager, K. G.; Ikeda, T. Photomechanical effects in azobenzene-containing soft materials. Soft Matter 2007, 3, 1249.

FNPs into a monodomain SmA phase. The latter is aided further by the reorientation of chromophores and, as the consequence, the reorientation of smectic domains due to the effect B. As indicated by this simulation study, photoaided selfassembly is based on selective weakening of the chromophore− chromophore interaction. The effect is small inside the domains that are already reoriented, as far as the chromophores are oriented mostly perpendicular to the polarization vector there and are rarely photoisomerized. On the contrary, frequent photoisomerizations occur for isotropically oriented chromophore−chromophore interdomain links. Such selectivity leads to intelligent steering of the system toward the monodomain phase. We see several practical outcomes of the photocontrollable self-assembly, as indicated by the computer simulations. The first is the possibility to apply up to 2−5 times higher cooling rates, when self-assembly is performed starting from the hightemperature isotropic state. The second is the possibility to form a monodomain ordered phase at low temperature, starting directly from the glass-like state. Here we found that the time scale of the self-assembly is practically independent of the temperature. With these simulational predictions we would like to inspire the experimental work toward practical realization of photocontrollable self-assembly in a bulk state.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.M.I.). ORCID

Jaroslav M. Ilnytskyi: 0000-0002-1868-5648 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We acknowledge financial support from the DFG Grant GR 3725/2-2. J.I. acknowledges fruitful discussions with A. Blumen and M. Dolgushev during the second International Workshop on Dendrimers and Hyperbranched Polymers held by Freiburg University, Germany during Nov 23−24, 2015 and the financial support toward participation in it by FP7 EU IRSES Project No. 295302 “Statistical Physics in Diverse Realizations”.

■

REFERENCES

(1) Yokoyama, M., Hosokawa, K., Nogi, M., Naito, T., Eds.; Nanoparticle Technology Handbook; Elsevier: Amsterdam, 2008. (2) Hepel, M., Zhong, C.-J., Eds.; Functional Nanoparticles for Bioanalysis, Nanomedicine, and Bioelectronic Devices; American Chemical Society: 2012; Vol. 1. (3) Demus, D., Goodby, J., Gray, G. W., Spiess, H.-W., Vill, V., Eds.; Handbook of Liquid Crystals Set; Wiley-Blackwell: 1998. (4) Bisoyi, H. K.; Kumar, S. Liquid-crystal nanoscience: an emerging avenue of soft self-assembly. Chem. Soc. Rev. 2011, 40, 306−319. (5) Wójcik, M.; Lewandowski, W.; Matraszek, J.; Mieczkowski, J.; Borysiuk, J.; Pociecha, D.; Górecka, E. Liquid-Crystalline Phases Made of Gold Nanoparticles. Angew. Chem., Int. Ed. 2009, 48, 5167−5169. (6) Lewandowski, W.; Wójcik, M.; Górecka, E. Metal Nanoparticles with Liquid-Crystalline Ligands: Controlling Nanoparticle Superlattice Structure and Properties. ChemPhysChem 2014, 15, 1283−1295. (7) Draper, M.; Saez, I. M.; Cowling, S. J.; Gai, P.; Heinrich, B.; Donnio, B.; Guillon, D.; Goodby, J. W. Self-Assembly and Shape Morphology of Liquid Crystalline Gold Metamaterials. Adv. Funct. Mater. 2011, 21, 1260−1278. J


Article

Macromolecules (29) Todorov, T.; Nikolova, L.; Tomova, N. Polarization holography 1: A new high-efficiency organic material with reversible photoinduced birefringence. Appl. Opt. 1984, 23, 4309. (30) Saphiannikova, M.; Neher, D. Thermodynamic Theory of LightInduced Material Transport in Amorphous Azobenzene Polymer Films. J. Phys. Chem. B 2005, 109, 19428−19436. (31) Toshchevikov, V. P.; Saphiannikova, M.; Heinrich, G. Theory of light-induced deformation of azobenzene elastomers: Influence of network structure. J. Chem. Phys. 2012, 137, 024903. (32) Ilnytskyi, J.; Saphiannikova, M.; Neher, D. Photo-induced deformations in azobenzene-containing side-chain polymers: molecular dynamics study. Condens. Matter Phys. 2006, 9, 87. (33) Ilnytskyi, J. M.; Neher, D.; Saphiannikova, M. Opposite photoinduced deformations in azobenzene-containing polymers with different molecular architecture: Molecular dynamics study. J. Chem. Phys. 2011, 135, 044901. (34) Ilnytskyi, J. M.; Saphiannikova, M. Reorientation Dynamics of Chromophores in Photosensitive Polymers by Means of CoarseGrained Modeling. ChemPhysChem 2015, 16, 3180−3189. (35) Hughes, Z. E.; Wilson, M. R.; Stimson, L. M. Coarse-grained simulation studies of a liquid crystal dendrimer: towards computational predictions of nanoscale structure through microphase separation. Soft Matter 2005, 1, 436. (36) Leach, A. Molecular Modeling: Principles and Applications; Pearson: Harlow, 2001. (37) Hou, T., Liu, C., Liu, J., Eds.; Multi-Scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations; Series in Contemporary Applied Mathematics; World Scientific: Singapore, 2009. (38) Rühle, V.; Junghans, C.; Lukyanov, A.; Kremer, K.; Andrienko, D. Versatile Object-Oriented Toolkit for Coarse-Graining Applications. J. Chem. Theory Comput. 2009, 5, 3211−3223. (39) Shin, K.; Shin, E. J. Photoresponsive Azobenzene-modified Gold Nanoparticle. Bull. Korean Chem. Soc. 2008, 29, 1259−1262. (40) Raimondo, C.; Kenens, B.; Reinders, F.; Mayor, M.; Uji-i, H.; Samorì, P. Au nanoparticle scaffolds modulating intermolecular interactions among the conjugated azobenzenes chemisorbed on curved surfaces: tuning the kinetics of cis−trans isomerisation. Nanoscale 2015, 7, 13836−13839. (41) Shibaev, V.; Bobrovsky, A.; Boiko, N. Photoactive liquid crystalline polymer systems with light-controllable structure and optical properties. Prog. Polym. Sci. 2003, 28, 729−836. (42) Zhang, J.; Whitesell, J. K.; Fox, M. A. Photoreactivity of Selfassembled Monolayers of Azobenzene or Stilbene Derivatives Capped on Colloidal Gold Clusters. Chem. Mater. 2001, 13, 2323−2331. (43) Groot, R. D.; Warren, P. B. Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys. 1997, 107, 4423. (44) Kihara, T. The Second Virial Coefficient of Non-Spherical Molecules. J. Phys. Soc. Jpn. 1951, 6, 289−296. (45) Kihara, T. Advances in Chemical Physics; Wiley-Blackwell: 1963; pp 147−188. (46) Hughes, Z. E.; Stimson, L. M.; Slim, H.; Lintuvuori, J. S.; Ilnytskyi, J. M.; Wilson, M. R. An investigation of soft-core potentials for the simulation of mesogenic molecules and molecules composed of rigid and flexible segments. Comput. Phys. Commun. 2008, 178, 724− 731. (47) Lintuvuori, J. S.; Wilson, M. R. A new anisotropic soft-core model for the simulation of liquid crystal mesophases. J. Chem. Phys. 2008, 128, 044906. (48) Ilnytskyi, J. M.; Trokhymchuk, A.; Schoen, M. Topological defects around a spherical nanoparticle in nematic liquid crystal: Coarse-grained molecular dynamics simulations. J. Chem. Phys. 2014, 141, 114903. (49) Ilnytskyi, J. M.; Neher, D. Structure and internal dynamics of a side chain liquid crystalline polymer in various phases by molecular dynamics simulations: A step towards coarse graining. J. Chem. Phys. 2007, 126, 174905.

(50) Ilnytskyi, J. M.; Saphiannikova, M.; Neher, D.; Allen, M. P. Modelling elasticity and memory effects in liquid crystalline elastomers by molecular dynamics simulations. Soft Matter 2012, 8, 11123. (51) Parrinello, M.; Rahman, A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 1981, 52, 7182. (52) Michl, J., Thulstrup, E. W., Eds.; Spectroscopy with Polarized Light: Solute Alignment by Photoselection, Liquid Crystal, Polymers, and Membranes Corrected Software ed.; VCH Publishers: 1995. (53) Dumont, M.; El Osman, A. On spontaneous and photoinduced orientational mobility of dye molecules in polymers. Chem. Phys. 1999, 245, 437−462. (54) Tiberio, G.; Muccioli, L.; Berardi, R.; Zannoni, C. How Does the Trans-Cis Photoisomerization of Azobenzene Take Place in Organic Solvents? ChemPhysChem 2010, 11, 1018−1028. (55) Šolc, K.; Stockmayer, W. H. Shape of a Random-Flight Chain. J. Chem. Phys. 1971, 55, 335. (56) Fabbri, U.; Zannoni, C. A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition. Mol. Phys. 1986, 58, 763−788. (57) Hoshen, J.; Kopelman, R. Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm. Phys. Rev. B 1976, 14, 3438−3445. (58) Ponomarenko, S. A.; Boiko, N. I.; Shibaev, V. P.; Richardson, R. M.; Whitehouse, I. J.; Rebrov, E. A.; Muzafarov, A. M. Carbosilane Liquid Crystalline Dendrimers: From Molecular Architecture to Supramolecular Nanostructures. Macromolecules 2000, 33, 5549−5558. (59) Kleman, M., Lavrentovich, O. D., Eds.; Soft Matter Physics: An Introduction; Springer: New York, 2004. (60) Allen, M.; Tildesley, D. Computer Simulation of Liquids; Oxford University Press: Oxford, 1986. (61) Gallani, J. L.; Hilliou, L.; Martinoty, P.; Keller, P. Abnormal viscoelastic behavior of side-chain liquid-crystal polymers. Phys. Rev. Lett. 1994, 72, 2109−2112. (62) Doi, M.; Edwards, S. The Theory of Polymer Dynamics; Clarendon Press: Oxford, 1994. (63) van der Spoel, D.; van Maaren, P. J.; Berendsen, H. J. C. A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field. J. Chem. Phys. 1998, 108, 10220. (64) Gotlib, Y. Y.; Torchinskii, I. A.; Toshchevikov, V. P.; Shevelev, V. A. Theory of the Relaxation spectra of polymer networks with included hard rodlike particles manifested in NMR. Appl. Magn. Reson. 2006, 30, 657−671. (65) Ahonen, P.; Laaksonen, T.; Nykänen, A.; Ruokolainen, J.; Kontturi, K. Formation of Stable Ag-Nanoparticle Aggregates Induced by Dithiol Cross-Linking. J. Phys. Chem. B 2006, 110, 12954−12958. (66) Mullin, J. Crystallization; Chemical Petrochemical & Process; Elsevier Science: 2001. (67) Petrova, T.; Toshchevikov, V.; Saphiannikova, M. Light-induced deformation of polymer networks containing azobenzene chromophores and liquid crystalline mesogens. Soft Matter 2015, 11, 3412− 3423. (68) Mechau, N.; Saphiannikova, M.; Neher, D. Dielectric and Mechanical Properties of Azobenzene Polymer Layers under Visible and Ultraviolet Irradiation. Macromolecules 2005, 38, 3894−3902. (69) Pastor, L.; Barberá, J.; McKenna, M.; Marcos, M.; MartínRapún, R.; Serrano, J. L.; Luckhurst, G. R.; Mainal, A. End-on and Side-on Nematic Liquid Crystal Dendrimers. Macromolecules 2004, 37, 9386−9394. (70) Martín-Rapún, R.; Marcos, M.; Omenat, A.; Serrano, J.-L.; Luckhurst, G. R.; Mainal, A. Poly(propyleneimine) Liquid Crystal Codendrimers Bearing Laterally and Terminally Attached Promesogenic Groups. Chem. Mater. 2004, 16, 4969−4979.

K


Photocontrollable Self-Assembly of Azobenzene-Decorated

Recommend Documents