Molecular Dynamics Study on the Photothermal Actuation of a Glassy

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Molecular dynamics study on the photo-thermal actuation of glassy photoresponsive polymer reinforced with gold nanoparticles with size effect Joonmyung Choi, Hayoung Chung, Jung-Hoon Yun, and Maenghyo Cho ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b04818 • Publication Date (Web): 23 Aug 2016 Downloaded from http://pubs.acs.org on August 24, 2016

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ACS Applied Materials & Interfaces

Molecular Dynamics Study on the Photo-Thermal Actuation of Glassy PhotoResponsive Polymer Reinforced with Gold Nanoparticles with Size Effect Joonmyung Choia, Hayoung Chunga, Jung-Hoon Yuna, Maenghyo Choa,*

a

Division of Multiscale Mechanical Design,

School of Mechanical and Aerospace Engineering, Seoul National University, San 56-1, Shillim-Dong, Kwanak-Ku, Seoul151-744, Korea

Abstract We investigated the optical and thermal actuation behavior of densely crosslinked photoresponsive polymer (PRP) and polymer nanocomposites containing gold nanoparticles (PRP/Au) using all-atom molecular dynamics (MD) simulations. The modeled molecular structures contain a large number of photoreactive mesogens with linear orientation. Flexible side chains are interconnected through covalent bonds under periodic boundary conditions. A switchable dihedral potential was applied on a diazene moiety to describe the photochemical trans-to-cis isomerization. To quantify the photo-induced molecular reorientation and its effect on the macroscopic actuation of the neat PRP and PRP/Au materials, we characterized the photo-strain and other material properties including elastic stiffness and thermal stability according to the photo-isomerization ratio of the reactive groups. We particularly examined the effect of nanoparticle size on the photo-thermal actuation by varying the diameter of the nanofiller (10 to 20 Å) under the same volume fraction of 1.62%. The results indicated that the insertion of the gold nanoparticles enlarges the photo-strain of the material while enhancing its mechanical stiffness and thermal stability. When the diameter of the *

Corresponding author: Tel.: +82-2-880-1693, Fax: +82-2-886-1645. E-mail address: [email protected] 1

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nanoparticle reaches a size similar to or smaller than the length of the mesogen, the interfacial energy between the nanofiller and the surrounding polymer matrix does not significantly affect the alignment of the mesogens, but rather the adsorption energy at the interface generates a stable interphase layer. Hence, these improvements were more effective as the size of the gold nanoparticle decreased. The present findings suggest a wider analysis of the nanofiller-reinforced PRP composites and could be a guide for the mechanical design of the PRP actuator system.

Keywords: Photo-thermal actuation, Photo-responsive polymer (PRP), Nanocomposites, Gold nanoparticle, Molecular dynamics simulation, Size effect

1. Introduction Shape memory polymer (SMP) is a promising polymer material which changes its conformation of polymer molecules and their inter- and intra-molecular interactions by multiple external stimuli1,2. During the past decade, SMPs have received increasing attention not only in polymer science, but also in the mechanical engineering field due to their considerable potential for multifunctional structures3. The deformation path and state of the responsive region of the SMP are determined by both of its functional groups in the polymer and by the entanglements of the polymer networks and physical interlocking among them. Hence, the multiple deformation behavior of the material can be designed by applying two or more types of stimuli, by utilizing the chemical reaction of the functional sites and the phase transition of the polymer networks. Some mechanical tuning techniques, such as the prestretching and quenching processes4,5 or the multi-layering process6, are also applicable for the modulation of the deformation field. Because the material can be precisely operated with 2


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the user’s own environment and preference, it is particularly useful as a mechanical device for the bending actuator7, wireless and implantable drug delivery system8, three-dimensional (3-D) flexible microchannel9, and biomimetic artificial muscle10, etc. The characteristics of the SMP implicitly depend on the type of energy source used as a trigger signal. Diverse types of SMPs with different functional groups of copolymer and polymer architecture have been developed to reach the desired deformation of the object3. Among these ‘smart’ materials, a photo-responsive polymer (PRP) which consists of a liquid crystalline polymer in the nematic state11 and photoactive agents such as azobenzene12-17, azotolane18, and diarylethene19 shows notable features and provides a new potential for the utilization of SMPs20. The PRP has advantages in that the deformation event occurs not only because of the thermal transition of liquid crystalline phases, but also because of the disruption of the molecular orientation pattern caused by ultraviolet (UV) or visible light irradiation. The origin of such photo-responsibility of the material is attributed to the conformational isomerization of the photoactive agents of the polymer matrix. When the light is irradiated, the molecular geometry and the associated bonding characteristics are changed, allowing a nematic to isotropic (and vice versa) transition in the liquid crystalline polymer12. Such photo-sensitive behavior is indeed useful for the design of SMP devices because the light source can be remotely and momentarily delivered to the target locations on the object. Also, the light irradiation can be modulated specifically with high precision by changing the focus position or by blocking out the rays. The attachment of any additional components (e.g. electric circuit or battery) on the material would not be required for the operation. These characteristics of the PRP material enable the development of optically and thermally responsive structures and hence widen the application fields of SMP21.

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The most important aspect of the PRP is that the atomic scale dislocation and reorientation dynamics induced by the photo-isomerization directly affect the bending and/or stretching behavior of the material and the deformation is large enough to be detected with the naked eye. Accordingly, in recent studies, various photo-mechanical devices using the multifunctionality of PRP material have been suggested. Iamsaard et al.22 developed photoresponsive ribbons which show large but reversible deformation in a variety of shapes. The deformation types between stretching and curvature could be easily selected from the direction in which the layered PRP film was cut. Particularly, they proposed a robust design method for a coiled spring structure in terms of an angular offset between the molecular orientation and cutting direction, and realized mixed-helicity springs by experiment. Yamada et al.23 developed photo-driven motors by utilizing the photo-induced rolling motion of a continuous ring of laminated film composed of a PRP layer (surface) and a liquid crystalline elastomer (bulk). Because the system can be operated under non-contact and battery-free conditions, the researchers claimed that the minimum operation size of the device could be significantly reduced and hence adaptable to microscale and nanoscale applications. Liu et al.24 designed a microscale-patterned PRP film with the use of indium tin oxide electrodes and controlled the surface topology of the film using UV light and heat. Such a ‘smart surface’ is especially suitable for the development of the photo-responsive microfluidic channel, which could be spatially controlled by optical elements from the environment. One important issue in the development of PRP materials and structures is that the sufficient level of mechanical strength and thermal stability must be maintained for their useful mechanical design. Accordingly, two approaches have been mainly considered for the fabrication of stable and multi-components’ reactive PRP material. One approach involves the formation of densely crosslinked, glassy photo-responsive networks having a preferred 4


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deformation axis created by the local director orientation of a liquid crystalline network25, and the other approach involves the use of multifunctional nano-sized particles26. The former approach has been adopted to achieve complex macroscopic shapes such as spiral ribbons and helicoids by controlling the chiral arrangement of the liquid crystal mesogens. This concept is certainly beneficial in the design of complex mechanical systems, as the synthesized material shows various states of deformation with merely the alignment of the internal microstructures. However, managing only the homogeneous phase of the material is insufficient to overcome the intrinsic weaknesses of the PRP material (high brittleness, low thermal stability, and a slow response time); thus, an investigation regarding the PRP nanocomposite system must be conducted. The insertion of nanoparticles induces multi-functionality in a material while also enhancing its structural properties. For more than 20 years, polymer nanocomposites containing functional nanoparticles in the host polymer have received a considerable amount of attention as promising materials due to their outstanding thermomechanical properties relative to those of microcomposites with identical volume fractions27,28. When the diameter of the particle decreases to the nanoscale, the interfacial area between the nanoparticle surface and the surrounding polymer segments is significantly enlarged due to the enormous surface-to-volume ratio of the nanoparticles. In particular, if the size of the nanoparticles approaches the radius of gyration of the polymers, the polymer chains near the surface of the nanoparticle are critically immobilized and become strongly adsorbed onto the surface of the nanoparticle. This ‘interphase’ region possesses properties which are distinct from those of the neat polymer and affects the structural properties of the overall nanocomposites29,30. To systematically design the mechanical behavior of the above-mentioned methods with mechanical rigor, analyses are needed for opto-mechanical and thermo-mechanical properties 5



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of the PRP material. Hence, these analyses must be preceded by sub-continuum scale level analyses because the origin of the opto-thermal actuation of the PRP material is strongly related to the photo-isomerization of the photoactive molecules and the thermal phase transition of the liquid crystalline microstructures. Furthermore, to predict the effective material properties of PRP composites structure reinforced by nanoparticles, the interfacial effects and their role in nanocomposites need to be verified.However, while numerous experimental studies have been devoted to the measurement of net deformation of the specimen, until recently, little attempt has been made to comprehend the intrinsic molecular structure both in the bulk and interfaces of the stimulus field. Against the above background, in this study, we carried out a computational study on the effects of photo isomerization and thermal phase transition on the mechanical behavior of glassy PRP and PRP nanocomposites using all-atom molecular dynamics (MD) simulations. Oriented liquid crystalline molecules with many photoactive functional groups were formed in silico and polycondensated to generate a glassy network. By selectively applying photoactive energy on random isomerization sites within the unit cell, a change of microstructure during dislocation was observed and the effect on the bulk thermo-mechanical properties was predicted. Moreover, we characterized the nanoparticle size effect on the structure and properties of the material because it is the most important point for the design of multifunctional polymer nanocomposites27,28,31. In the present computational work, the role of the interfaces between the nanofiller and the liquid crystalline matrix on the opto-thermal behavior of the PRP nanocomposites and their microstructure was discussed. Another goal of the model is to support the data for a multiscale design guideline of the PRP nanocomposites structures and devices by integrating with the continuum mechanics32,33.

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2. Computational approach 2.1. Crosslinked PRP and PRP nanocomposites model preparation Highly crosslinked PRP and PRP nanocomposites reinforced with gold (PRP/Au) were modeled by MD simulations. The configurations of polymer molecules and spherical gold nanoclusters used in this study are shown in Figure 1. To

address

the

nematic phase of a liquid crystalline polymer as well as the nanoparticle size effect simultaneously with an all-atom model, we carefully considered the composition and its associated model size of the nanocomposites. We selected a liquid crystalline molecule 6[4-(4-ethoxyphenylazo)phenoxy]hexyl acrylate and a crosslinking agent 4,4’-di(6(acryloxy)hexyloxy)azobenzene for the modeling of the polymer structure that was typically used in previously reported experimental surveys16,34. Both molecules contain azobenzene chromophore, in which photo-isomerizes from trans-to-cis form on UV light irradiation and cis-to-trans form on visible light irradiation (or heat). The present PRP model has an advantage due to the many photoactive sites in nanoscale; the entire polymer network structure can be fully described by all-atom MD without the aid of mesoscopic modeling or coarse-graining of the molecular system. This sort of modeling would be essential if 1) the material under consideration has a greater degree of ordering than the nematic phase, or 2) the material contains only a small amount of azobenzene molecules13,14,35. In this study, we modeled an azobenzene-rich material in the nematic phase as a matrix to ensure the greatest number of azobenzene moieties possible. The modeling of polymer chain molecules and polymer nanocomposite structures with a full atomic representation was carried out with the commercial MD package, Materials Studio 6.0 (Accelrys Inc.). The opto-thermal actuation of the models was 7



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observed and the characterization of their microstructural and mechanical properties described below was carried out by using the open-source MD code, LAMMPS (Sandia Lab.).

Figure 1. Molecular structure of the components contained in photo-responsive polymer and its nanocomposites (a) liquid crystal monomer compound, (b) diacrylate crosslinking agent, and (c) gold nanoparticles. The neat PRP model was adopted from our previous work36. Initially, the liquid crystalline molecules and crosslinking agents were randomly included in the periodicallybounded amorphous unit cell box in a 7:1 molar ratio while preserving the orientation of the azobenzene groups along the x direction. The geometry relaxation was performed using the conjugated gradient method with a convergence cutoff of 0.1 kcal/mol Å, followed by isothermal (NVT) ensemble at 300K for 5ns and isothermal-isobaric (NPT) ensemble at 300K and 0.1MPa for 5ns. The equations of motion were integrated using the Verlet velocity algorithm with a timestep of 1fs. During the model equilibration, all the bonded and non-bonded interactions between the atoms were calculated by the polymer consistent force field (PCFF)37. To generate a crosslinked polymer network structure, all the distances between the two end sites of the methyl side chains were measured and artificial covalent bonds were generated where the distance is shorter than the cutoff distance.The simulation procedure 8


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for the crosslinking among the polymer molecules and the corresponding change of the internal substructure of the molecular unit cell are illustrated in Figure 2(a). This method is conventional in modeling the fully cured polymer network via MD simulation36,38,39 and it provides a thermodynamically consistent behavior for the macromolecular structure with periodic boundary conditions. The model studied in the present paper includes a polymerization reaction of a liquid crystalline monomer unit as well as a crosslinking reaction of the agent. In this work, we separated the procedure for the formation of chemical bonds into two steps, as depicted in Figure 2(b), to generate a properly networked polymer system in the unit cell model. It is important to note that each crosslinking agent should bridge two adjacent liquid crystalline monomers with a sufficient crosslinking ratio; this is important for the modeling step because there are fewer inserted crosslinking agent molecules than liquid crystalline monomer molecules, and the agents are essential components of this network system. If we change the crosslinking/polymerization sequence or carry out all of the reactions simultaneously, the crosslink agent occasionally fails to serve as a bridging point between the monomers, and the desired polymer network structure cannot be constructed. In the first step, therefore, the crosslinking agents were linked to the surrounding liquid crystalline monomers in order to build the side branch of the polymer network. The distance cutoff started from 1.0 Å and increased to 5.4 Å with the step increment of 0.2 Å. The energy minimization with conjugated gradient method (convergence cutoff was 10 kcal/mol Å) and NVT ensemble at 400 K for 50 ps were executed for every possible cutoff point to enable all the intramolecular structures of the connected units to relax effectively. Eighty percent of all the reactive sites of the crosslinking agents were crosslinked during the first step. The second step involved the polymerization of the liquid crystalline monomers. Because the 9



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distances between crosslink sites on the residual molecules became wider after the first crosslinking step, we applied a longer reaction distance cutoff (7.5 Å) with the increased step increment of 0.5 Å. The potential energy of the model was minimized again for each distance cutoff. It was found that the final crosslink density of the liquid crystalline molecules reaches to 45% and all the monomers are fully interconnected not only in the unit cell but also across the boundaries of the periodic cell box. The crosslinked macromolecular structure was equilibrated again by the NVT ensemble at 300 K for 5 ns and the NPT ensemble at 300 K and 0.1 MPa for 10 ns. To examine the effect of the nanofiller addition on the thermal and mechanical properties of the PRP, we also considered PRP nanocomposite structures with embedded spherical gold nanoparticles. It is well known that the incorporation of nanoparticles in a polymer matrix leads to the desired functions based on the properties inherent in the nanoparticles, as well as enhancing the mechanical properties. The gold nanoparticle used in this study is one of the promising nanoscale materials because the diameter can be controlled with nanometer precision40 and has multifunctional properties such as good conductivity41, non-toxicity42, and high mechanical stability43. The material is especially suitable as a reinforcement in PRP matrix composites because the nematic phase of liquid crystal molecules enables the spatial arrangement of nanoparticles44. Some experiments and theoretical analyses have thus been performed for the PRP/Au nanocomposites or nanofilm system and proved the potential applicability of the system45,46. The most important design variable for the multifunctional polymer nanocomposites is the size of the nanoparticle. The effective material properties of nanocomposites are dominated by the localized polymer-rich phase around the nanoparticle surface and its interfacial behavior. Nevertheless, the size effect of the nanoparticle on the whole PRP 10


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system has not been characterized until now due to the difficulty of quantifying the nanoscale architecture of the material. Accordingly, we prepared four different nanocomposite unit cells with different-sized gold nanoparticles (10 to 20 Å in diameter)under a constant volume fraction (1.62 vol.%) to systematically compute the bulk property of the system, and therefore to characterize the effect of nanoparticle size on the opto-thermal actuation of the PRP material. The detailed material composition for the neat PRP and PRP/Au nanocomposite models is given in Table 1. The model equilibration process for PRP/Au nanocomposite systems was the same as that of the neat PRP model described above, except that the spherical gold nanoparticle was positioned in the center of the unit cell. To avoid any unintended interference between the nanoparticle and uncrosslinked PRP compounds such as the ring catenanes of the cyclic group of atoms or penetrations of the polymer chains into the gold nanoparticle, the initial positioning of the molecules in the unit cell box was conducted under a very low density level (< 0.1 g/cc). The numbers of liquid crystalline monomers and crosslinker molecules were determined, in which the volume fraction of the gold nanoparticle becomes 1.62%. Note that the actual value of the nanoparticle volume fraction should change slightly during the NPT ensemble step owing to the conformation change of the polymer matrix. When the nanoparticle diameter condition is varied, the percentage of the depletion region as well as the overall density of the nanocomposite model change significantly. Hence, it is difficult to hold the volume fraction of the nanoparticle to a constant value in MD simulations, and we presumed that differences in the nanoparticle volume fractions (around 0.5 percent point) among the models were inevitable. To clarify this, we also list the actual volume fraction of each nanocomposite model in Table 1 as well as the targeted volume fraction. 11



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To meet the consistency of the polymer structure, in all cases the crosslink density of the liquid crystalline molecules was fixed as 45 percent by suitably varying the maximum distance cutoff for the crosslinking simulations. The simulation process, therefore, was carried out in the same manner described above and was then terminated when the crosslink density of the reaction sites reached a desired value. After the oriented PRP molecules and a gold nanoparticle were constituted, the unit cell box was hydrostatically compressed until the density reached that of the neat PRP material (1.07 g/cc). During the compression, the total internal energy of the system was minimized by the conjugated gradient method. Next, another NVT run at 300 K for 3 ns and NPT run at 300 K and 0.1 MPa for 5 ns were applied for equilibration. As shown in Table 1, the nanocomposite models were further compressed during the NPT run and had a much higher density than the neat PRP structure. Interestingly, the density of the nanocomposites increased further when the size of the filler was decreased, implying that a dense and richly structured polymer layer was spontaneously formed around the nanoparticle surface during the equilibration period. As the nanoparticle size decreased, the distance between nanoparticles was reduced while the non-bond interaction feature between the particle surface and the surrounding polymer layer remained unchanged. Accordingly, smaller nanoparticles widened the particle/matrix interacting region, and the overall density of the nanocomposite system therefore increased. The equilibrated PRP/Au nanocomposites unit cell model used in this study is shown in Figure 3. Due to the dense crosslinking simulation, all the polymer molecules are interconnected and represent a macromolecular network. The methyl side chain units are randomly dispersed in the simulation cell while the azobenzene moieties within the crosslinked polymer are aligned along the nematic director. To better understand the 12


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microstructural behavior of the matrix phase in the vicinity of the nanoparticle, the structural properties of the azobenzene liquid crystal and methyl side groups in the polymers will be further discussed in the result section.

Figure 2. (a) Snapshots before and after the crosslinking event of the azobenzene molecules and their polymer networks, and (b) workflow of the two-step crosslinking simulation used in this study.

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Figure 3. Configuration of the modeled PRP/Au nanocomposites’ periodic unit cell. (a) Front view of the original configuration, (b) highlighted view of crosslinked polymer chains in green, (c) highlighted view of photoactive mesogens as ellipsoidal inclusions, and (d) sideview of the configuration of (c).

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Table 1. Neat PRP and PRP/Au nanocomposite systems studied Actual Cubic Targeted nanoparticle nanoparticle Crosslink cell volume volume density length fraction (%) fraction (%) (Å)

System

Gold diameter (Å)

Neat PRP

-

PRP + 10Å Au

10

2.02

PRP + 13Å Au

13

1.68

PRP + 16Å Au

16

PRP + 20Å Au

20

-

No. of Total no. Density photoactive of atoms (g/cc) sites

37.91

85

5,113

1.07

29.56

34

2,103

1.58

40.91

102

6,349

1.43

1.61

51.07

204

12,755

1.38

1.58

64.20

408

25,001

1.36

0.45

1.62

2.2. Implementation of the photo-reactive dihedral potential to the PRP models The photo-responsibility of the PRP material originated from the isomerization reaction of the photoactive molecules in the system. As shown in Figure 4(a), the azobenzene moiety used in this study is representative of the photoactive functional group which changes its molecular conformation upon irradiation with UV light (~365 nm) and with visible light (~520 nm). Because the conventional force fields including PCFF potential do not provide the basis for simulating this type of stimulus, an additional interatomic potential which specifies the change of molecular geometry at the photoactive sites should be required for the computation in MD simulations. In the present study, therefore, we treated the dihedral potential parameters for the neat PRP and PRP/Au nanocomposites unit cell models in accordance with the method by Heinz et al47. From a molecular structural point of view, the photo-isomerization of azobenzene is reproduced by changing the equilibrium dihedral angle of the diazene group from 180˚to 0˚ or vice versa. The quartic form of the torsional energy (E) used in a 15



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class II force field is described as 3

E = ∑Vn 1− cos ( nϕ − ϕn0 ) 

(1)

n=1

where Vn is the dihedral coefficient and

ϕn0

is the equilibrium dihedral angle. The

parameters of photoactive potential energy and the calculated molecular geometry of the azobenzene unit used in this study are shown in Table 2.The isomerization reaction was simulated in twosteps. The first involved the excited trans-state (second row potential in Table 2) and the second was relaxation to the ground trans- (first row) or cis- (third row) state through a modification of the equilibrium dihedral angle. It should be noted that the actual photo-isomerization dynamics and the corresponding pathway of azobenzene are much more complex, as the reaction can take place not only by rotation but also by in-plane inversion and again, these isomerization routes depend highly on the excitation state of the azobenzene. These issues have been studied intensively by other researchers using experiments and/or density functional theory calculations48,49. However, the coverage of the present MD study is confined to quasistatic properties, and the underlying reaction mechanism of azobenzene is therefore simplified. Moreover, the nature of an isomerization reaction in a condensed system is not deterministic but probabilistic. Hence, it is difficult with PRP nanocomposites explicitly to characterize the structural-property relationships induced by photo-isomerization reactions in an experiment. Accordingly, we believe the simulation method used in this study is quite simple but nonetheless sufficient to observe the influence of the conformational changes of the molecules and how they affect the thermal and mechanical properties of bulk PRP nanocomposites and the associated interphase regions. In any case, the geometrical properties of trans- and cis-isomers calculated from the present MD 16


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simulation were in fairly good agreement with the density functional results obtained by Cembran et al.50 and those in our previous study36. For each reactive point, the photoreactive potential energy was added to the C-N=N-C dihedral component to overcome the thermal conversion barrier (~24 kcal/mol) while the equilibrium angle was reversed. During the MD run, the modified potential field significantly changed the bulk properties of the system as well as the geometry of the microstructure. This modified potential formalism has been extended in various ways such as the photoresponsive self-assembly of monolayer phase45, the light-driven DNA51, RNA52, and peptide53 structures, and the mechanical modeling and analysis of the photoresponsive solid actuator33,36.

Figure 4. Trans-cis photo-isomerization of azobenzene: (a) schematic of the conformation change of diazene group and (b) dihedral potential energy functions for the reproduction of trans-cis transition of the azobenzene used in MD simulations

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Table 2. Dihedral force field parameters for the diazene group and the corresponding molecular geometry of azobenzene molecule State

Dihedral energy coefficients47 0 0 V2 V3 1 2

V1

ϕ

ϕ

(kcal/mol)

(deg)

(kcal/mol)

(deg)

5.2

180

12

0

Molecular geometry of azobenzene

ϕ

NN

NC

NNC

NCC

CNNC

(kcal/mol)

(deg)

(Å)

(Å)

(deg)

(deg)

(deg)

0

0 1.270

1.460

129.0

118.4

0.0

1.283

1.394

123.7

121.2

180.0

0 3

Thermal equilibrium trans-AZ

34

180

0

0

0

0

cis-AZ

34

0

5.2

180

0

0

We modulated the photo-isomerization ratio by selectively adapting the modified dihedral potential described above to the diazene groups of the unit cell. Beginning from all the trans-state, the azobenzene moieties in the equilibrated models were randomly selected and converted to cis-state with the conversion ratios of 0%, 25%, 50%, 75%, and 100%, as shown in Figure 5.It is well known that the wavelength of light in the environment is directly related to the cis-fractions of the materials; the fraction of cis-isomer of the microstructure is very high for UV and quite low for visible light54. The conformational change of azobenzene molecules is dominated by the wavelength condition of the environment, indicating that we can intuitively interpret the snapshots shown in Figure 5 as a gradual shift of onset light exposure from visible (for low ratios of cis-isomers) to UV (for high ratios of cisisomers).Another interesting point regarding the present model is that the light intensity and irradiation time are closely related to the photo-isomerization reaction ratio of azobenzene inside the PRP structure on the macroscopic scale. Because light can only be irradiated onto the surface of a specimen in an actual environment, the intensity varies significantly beneath the surface of a material. Our research group examined this issue and developed a model which predicts the trans-cis population ratio of a single azobenzene monomer by combining 18


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stimulated Raman passage calculations with experiments55. The literature cited here indicates that the effective isomerization ratio according to the depth is not a step function but decreases continuously. Accordingly, the effective cis-isomer ratio at a certain material depth ranges from 0 to 1. In other words, when the light is irradiated on the PRP surface, the photoisomerization of PRP is partially driven depending on the transparency of the material and the light intensity of the environment. From this viewpoint, the present work can serve as a touchstone for those undertaking macroscopic mechanical designs of PRP nanocomposites and their applications, especially regarding the photo-bending or photo-twisting motion of a material, which mainly depend on the light penetration depth and the associated isomerization ratio of the azobenzenes in the system. The unit cells were equilibrated for another 3 ns in the NPT ensemble at 300 K and 0.1 MPa. Here, to estimate the effective strain of the models during the photo-isomerization simulation, the x, y, and z dimensions of the unit cell box were independently controlled. The effective photostrain ( ε

ph

) of the modeled system can be simply defined by the change in

the length of the unit cell ( l ) along the x direction described as36,

ε ph =

where the bracket

lcis − ltrans ltrans

(2) x

refers to the ensemble average of the last 500 ps of simulation. To

reduce the uncertainty caused by the sampling of the reactive constituent, the photostrain calculation was repeated 9 times with randomly chosen sets of isomerization reaction locations and the results were averaged.

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Figure 5. Trans-to-cis photo-isomerization simulation for the modeled PRP unit cell. As the isomerization reaction was progressed, both the disorder of the alignment of polymer molecules and the shrinkage of the system along the x direction were observed.

2.3.

Characterization

of

the

effective

material

properties

of

the

PRP/Au

nanocomposites During the photo-isomerization reaction, not only the mesogen alignment but also the density distribution of the crosslinked side chains was varied due to the polymer relaxation. In particular, the polymer conformation of the PRP/Au nanocomposites also significantly changes with the interfacial features between the reinforcements and the matrices, i.e. generating interphase layers distinguished with the neat PRP on the nanoparticle surfaces44,56-58. Therefore, to comprehend the effect of the photo-reaction on material properties and the associated microstructures, we derived the structural, mechanical, and thermal properties of the prepared PRP and PRP/Au nanocomposites models as follows. Scalar orientational order of the mesogen (S): To estimate the directionality of the PRP matrices during the MD simulations, artificial line segments joining both ends of the azobenzene phenyl rings were considered. By measuring the angle ( θ) between the defined line segment and the x-axis (desired 20


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molecular orientation), the alignment of the mesogen could be computed. The scalar orientational order of the PRP material was therefore derived as, S=

3 cos 2 θ − 1 2

(3)

is the ensemble average over all molecules in the system.

where the bracket symbol

When the photo-isomerization or thermal phase transition occurs, the uniaxial nematic phase of the modeled structure converts to the isotropic phase and the value of S is close to zero. Thus, eq. (3) is able to estimate how the polymer molecules react to the external stimuli.

Elastic stiffness ( Cij ): After the photo-isomerization process was completed, we calculated the elastic mechanical properties in all modeled cases by applying a longitudinal uniaxial tensile strain of up to 0.3% with engineering strain rates of 106/s. Based on the virial theorem, the atomic stress tensor ( σ) during the mechanical loading can be computed as59, σ=

 1 N 1 N N T  − ∑ mi ( v i v i ) + ∑ ∑ rij Fij  V  i 2 i j≠i 

(4)

where V is the volume of the unit cell, N is the number of atoms in the unit cell,

vi

are the mass and the thermal velocity of the i-th atom, respectively, and

mi

and

rij and Fij are

the interatomic distance and the force between the i-th and j-th atoms, respectively. Because the virial stress excluding the effect of the velocity of atoms is equivalent to the mechanical Cauchy stress39,60, we deliberately excluded the kinetic energy of the atoms in the unit cell when calculating the mechanical stiffness tensor during the tensile loading of 21



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the models; i.e., the tensile simulations were carried out using the NVT ensemble at 0.1K. With sufficient time integration, the nanocomposite structure in the unit cell would show quasi-static behavior and the stiffness components can be determined using only the interatomic potential over all constituent atoms. Although the strain rate is very high compared to the experimental conditions, the value represented what was thought to be necessary to obtain an acceptable static loading solution. Note that the strain-rate dependence on the mechanical properties of polymers and polymer nanocomposites is as important as the viscoelasticity and thermo-elasticity, but the properties are mainly attributed to temperature-dependent changes rather than phenomena which arise in zerotemperature cases. The remaining potential part of σ is therefore expressed as a summation of the interatomic pair, bond, angle, torsional angle, and out-of-plane angle as,

σ ij = −

1 V

1 1  ∑ ( r1i F1 j + r2i F2 j ) + ∑ ( r1i F1 j + r2i F2 j ) + 2 bond  2 pair 1 1 r1i F1 j + r2i F2 j + r3i F3 j ) + ∑ ( r1i F1 j + r2i F2 j + r3i F3 j + r4 i F4 j ) + (5) ( ∑ 3 angle 4 torsion  1 r1i F1 j + r2 i F2 j + r3i F3 j + r4 i F4 j )  ( ∑ 4 oop 

.

For transversely isotropic material (both for the neat PRP and PRP/Au nanocomposites considered in this study), the axial stress components which are normal to the nematic director (yz-plane) are averaged, as shown in Eqs. (6) and (7).  σ xx  σ =  σ yx  σ zx 

σ xy σ xz   σˆ11 σˆ12 σˆ12   σ yy σ yz  ≅  σˆ12 σˆ 22 σˆ 23  σ zy σ zz   σˆ12 σˆ 23 σˆ 22 

where

22


(6)

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1 (σ xy + σ xz + σ yx + σ zx ) , 4 1 1 σˆ 22 = (σ yy + σ zz ) , σˆ 23 = (σ yz + σ zy ) . 2 2

σˆ12 =

(7)

The elastic stiffness tensor written in Voigt’s notation can be simply derived under Hooke’s law:

σi = Cijε j (i, j =1,...,6)

(8)

The obtained mechanical stresses include uncertainties depending on the relaxed conformation of the partially or fully photo-isomerized polymer networks. Therefore, in order to guarantee computational accuracy, the tensile loading simulations were carried out 15 times (5 times for each loading direction) for each condition and the elastic constants were averaged.

Thermal phase transition and corresponding thermal stretching ratio ( ∆λT ): To estimate the thermal stability of the PRP/Au nanocomposites, the heating-up simulations from 250 K to order clearing temperature ( Tiso ) at a rate of 5K/ns were carried out in all cases under the isobaric conditions at 0.1 MPa. The order clearing temperature was defined in which the alignments of the mesogen were fully disordered (S < 0.05)36 and had no preferential orientation. During the heating-up simulations, the change of length of the unit cells along the x axis and the associated orientational order parameter of the mesogen were recorded simultaneously. The ratio of unit cell length ( lT) at a given temperature to the corresponding value at a clearing temperature ( lTiso ) describes the thermal stretching ratio of the material, as

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∆λT =

By monitoring the correlation between

∆λT

lT lTiso

.

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(9)

x

and S during the heating-up simulation, we

examined whether the phase transition of the liquid-crystalline structure is sufficient to address the macroscopic deformation of the solid nanocomposites. The characterization of the material properties of PRP nanocomposites is particularly important for the design and analysis of the smart material in mechanical terms because the intrinsic multifunctionality that arises from the polymer architecture and the interfaces determines the photo-thermal actuation performance of the material. For convenience, the overall workflow of the simulation procedures described above are summarized and presented in Figure 6.

24


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Figure 6. Overall workflow of the current study. 3. Results and discussion 3.1. Structural characteristics of the PRP molecules during the photo-isomerization reactions The length distribution of the azobenzene molecules in the equilibrated system after the photo-reactive dihedral potential applied to the model is shown in Figure 7.The length of azobenzene was measured according to the length of a straight line joining both ends of the phenyl rings, as in our previous study36. When trans-azobenzene is converted to cis-azobenzene, the effective length of the molecules reduces by 25%. In all cases, the conversion ratio of the azobenzene molecules in the unit cell reached the desired photo25



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isomerization ratio; it is thus verified that the provided photo-reactive potential energy for the diazene moiety is sufficient to overcome the energy barrier required for the kink motion in the crystalline glassy polymer phase. One aspect of the result is that the deviation of the length distribution of cis-azobenzene is significantly larger than the corresponding length distribution of trans-azobenzene. This deviation indicates that the molecules converted to the cis-form lose their rod-like rigidity and bridging ability and thus the width of the angular amplitude of oscillation of the kinked moieties increases. The effect of the molecular structural mechanics of azobenzene groups on the structural properties and stabilities of the bulk PRP and PRP nanocomposites materials will be further discussed in the following section.

Figure 7. Length distribution of the azobenzene moieties in the neat PRP unit cell according to the photo-isomerization ratio. Regarding the PRP/Au nanocomposite models, the radial density distribution profile of the polymer matrix surrounding the nanoparticle is obtained and shown in Figure 8(a). Note that the density calculated in Figure 8 is only for the crosslinked side chains of the polymer networks, subtracting the contribution by azobenzene groups in the molecules. 26


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The crosslinked polymer networks in the vicinity of the nanoparticle surface strongly interacted with the gold atoms and the local density in that region would be higher than that of the pure polymer. As the result indicated, the radial density of the PRP phase is not uniform but depends on the distance from the nanoparticle surface; the peak density point is observed at the nearest surface of the particle, and the value gradually converges to the density of the bulk system as the radial distance increases. Such morphological change of polymer chains caused by the non-bonded interaction with the nanoparticle is well known in the polymer nanocomposites field27,28,31,39,61. The tightly coated polymer chains at the interface, the so-called interphase, renders the matrix phase more stable and enhances the mechanical properties of the material. One can anticipate that the local density and stability of the interphase depend strongly on the thickness of the interfacial region because there is a depletion region in front of the radially adsorbed polymer chains. Regarding this, our group has intensively undertaken the characterization of the effective interphase thickness and studied the properties of polymer nanocomposites from a mechanical viewpoint. We concluded that the thickness of the interphase region exceeds the first peak density point of the adsorbed polymer matrix (the value is ~1nm, but it depends on the material composition)39,62. When we assume that the interphases of PRP nanocomposites also have identical structures (hollow sphere shells ~1 nm thick with the inner surface of the shell on the nanoparticle surface), it can easily be predicted that the density of the shell will be greater than that of the neat PRP despite the fact that the region incorporates a depletion region. The result shown in Figure 8(a) also indicates that the interfacial characteristics play an important role in the microstructure and the relevant physical properties of highly crosslinked nematic networks. When the components were mixed before crosslinking, the 27



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interaction energy between the flexible fragments of the polymer chains and the nanoparticle generated the interphase layer, and the melt was then solidified during thermal curing. One interesting aspect is that the morphological stability of PRP around the nanoparticle was sustained even after the trans-azobenzene was fully transformed to cisazobenzene, as shown in Figure 8(b). When the isomerization occurs due to the light irradiation, the rod-like features of the azobenzene molecules disappeared and the direct mesogen-mesogen interactions did not hold the alignment of the polymer chains. On the other hand, the adsorption characteristics of the flexible methyl side chains are not associated with the structural change of the azobenzene and thus the interphase around the filler particles clearly remain. Instead, because there is less mesogen-mesogen ordering under cis configuration, the structural interference during the photoisomerization of the azobenzene becomes weaker and the interfacial energy of the polymer chains with the nanoparticle dominates the relaxation kinetics of the atoms. Accordingly, the first peak of the radial density is slightly shifted toward the nanoparticle surface with higher local density in all the considered cases.

Figure 8. Radial density distribution of the polymer backbone constituents according to the size of the nanoparticle: (a) non-isomerized PRP/Au models and (b) fully isomerized PRP/Au 28


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models.

The issue whereby the alignment feature of the liquid crystalline polymer networks are also substantially affected by the shape and size of the filler might appear to be a concern. However, the change of the local orientation of the nematic azobenzene polymers surrounding the nanoparticle is not significant in this study because the size of the filler is in the order of only a few nanometers. As described in Figure 9, the local orientation of the azobenzene does not show a distinct change even for the largest nanocomposites model (PRP/20Å Au). This result is strongly consistent with the reported results57, demonstrating that the influence of the nanoparticle on the orientation of the liquid crystalline director is short ranged. As the size of the filler reaches nanometer scale and becomes comparable to the length of the mesogen, the planar anchoring effect of the particle appears only at the near-interface layer. Meanwhile, because the polymer matrix considered in this study was fully crosslinked in nematic states, the alignment change of mesogens caused by the insertion of nanoparticles was rather restricted in the present model. While the nano-architecture of the macromolecular polymer system did not induce a significant change in the orientation of the matrix, the photo-isomerization of the azobenzene exerted a significant effect for that trait. As the photo-isomerization occurred, the orientational order of the matrix was drastically decreased, regardless of the radial distance from the nanoparticle surface, even under the low isomerization ratio. Because the isomerization sites were randomly selected and sparsely dispersed at a low isomerization ratio, the result depicted in Figure 9 shows that the trans to cis isomerization ratio of the isomers mainly determines the structural features and properties

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of the material. Therefore, the photo-isomerization ratio is an important design variable for understanding the photo-mechanical behavior of the PRP nanocomposites. One unusual feature observed in our study is that the orientational order of the azobenzene mesogens in the nematic phase was not completely destroyed during the isomerization reaction at room temperature. The result depicted in Figure 9 (b) indicates that the isomers in the unit cell retain their initial orientation even after all of azobenzenes are isomerized to the cis-form and lose their long-range ordering. We presume this residual order parameter of cis-isomers to be related to the spatial confinement effect of the crosslinked polymer network of the matrix. Because the polymer chains are crosslinked in the nematic phase, there should be strict confinement if the polymers are in a glassy state and maintain little segmental mobility during the isomerization reaction. Accordingly, the azobenzene groups also tend to preserve the initial direction despite the findings that the conformation of the molecules changes drastically and the molecules lose their local integrity.

Figure 9. Radial distribution of the scalar orientational order parameter of the PRP/20Å Au nanocomposites according to the photo-isomerization ratio of the azobenzene. (a) Local orientation of the azobenzene was measured from the arbitrarily defined spherical shell around the nanoparticle with given thickness (tint). (b) Obtained distributions of the orientational order parameter of azobenzene molecules along the nematic director. 30


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3.2. Nanoparticle size effect on photostrain and mechanical properties of the PRP/Au nanocomposites To further investigate the effect of nanoparticle size on the vicinity of the interface during the photo-isomerization, we characterized the photostrain and the mechanical properties of the considered nanocomposites models as well as of the neat PRP model. Using Eq. (2), we derived the photostrain of the modeled unit cells according to the photo-isomerization ratio of the azobenzene molecules and depicted the result in Figure

10. In all cases, the uniaxial strain along the nematic director steadily increases as the trans-to-cis isomerization ratio reaches 1. Note that the maximum deformation of the PRP obtained by experiments (the material was composed only of azobenzene moieties, so the composition is almost identical to the neat PRP model) is about 13%63, which is very close to the photostrain value of the completely isomerized model in the present study. In comparison, the estimated photostrains in the PRP/Au nanocomposites models are remarkably higher (a rate of increase of the value is from 31% to 47%) than those of the neat PRP model, regardless of the photo-isomerization ratio and the size of the nanoparticle. The reason for the higher photostrain of the PRP/Au nanocomposites than the neat PRP is the dense interphase formed by the flexible methyl groups in the polymer. As mentioned in Figure 8and Figure 9, the polymer chains were wrapped on the nanoparticle surface while keeping the alignment of the azobenzene groups. They inhibit the spontaneous rotation of the molecules in a random direction while assisting the compressive deformation of the microstructure along the pre-aligned direction. Another important feature in Figure 10 is that the photostrain of the nanocomposites material continuously increases as the inserted nanoparticle size decreases when the 31



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trans-to-cis conversion ratio of the unit cell does not exceed 75%. The main cause of the nanoparticle size dependence on the photostrain is the finite depletion zone between the nanoparticle and the polymer matrix. While the photo-isomerized molecules and their surrounding matrix environment were covalently crosslinked, the isomers around the nanoparticle surface were connected with the particle only by non-bonded contacts. Therefore, the isomers in the interphase had sufficient spatial freedom for shrinkage of the structure along the nematic director during the isomerization. Because such effect mainly occurs in the interphase region, a more distinct photo-shrinkage activity of the material can be observed as the size of the nanoparticle decreases and the associated interface has a larger surface-to-volume ratio. Especially, this size effect is clearly observed under low photo-isomerization ratio and then fades out as the photoisomerization ratio reaches over 50%. The result indicates that, under the high photoisomerization ratio condition, the converted azobenzene groups gain sufficient energy to transform the entire matrix region, and thus the measured photostrain is saturated.

Figure 10. Calculated photostrain of the neat PRP and the PRP/Au nanocomposites models according to the photo-isomerization ratio. Because the trans-to-cis isomerization simulation induced the shrinkage of the unit cell, we plotted the compressive strain as positive. Error 32


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bars for the nanocomposites models represent one standard deviation around the mean value. Note that the increase of the photostrain of the material under partially photoisomerized condition is particularly important in the mechanical design of the PRP device. Generally, the entire thickness of the PRP specimen in the experiment reported in the literature is a few micrometers16,34 and thus, only the surface of the material would be completely exposed to the light stimuli, while the intensity gradually decreases below the surface. Again, the finite penetration depth of the light characterizes a certain profile for the effective photo-isomerization ratio according to the thickness of the material55. Because the present MD study systematically identifies the deformation range of the PRP nanocomposites structure according to the effective isomerization ratio inside the microstructure, the results are able to be adapted to the nano-continuum bridged multiscale mechanical model suggested in a previous study33. In order to better discuss the implications of the morphological change of the polymer, we derived the overall mechanical properties of the modeled structure from the tensile loading simulations. Figure 11 shows the obtained anisotropic elastic stiffness of the neat PRP and PRP/Au nanocomposites along the nematic axis ( C11 ) and normal plane ( C22 ).In all the considered cases the PRP/Au nanocomposites models show higher normal and transverse stiffness components than the corresponding components of the neat PRP model, regardless of the particle size or photo-isomerization ratio of the azobenzene. The PRP nanocomposite material exhibits mechanical anisotropy, with the C11 component having the highest value because the PRP chains of the nanocomposite model are well aligned and crosslinked with each other in the nematic direction. These results are in line with the non-reinforced PRP model, except for the increased value of the elastic stiffness. Due to the high anisotropy of the matrix, the influence of the reinforcement on the elastic 33



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constants depends on the desired mesogen direction along the loading axis. Both the absolute value of C22 and how rapidly it increased are less than the corresponding results for C11 . However, the reinforcement effect of filler nanoparticles on the transverse stiffness is observable, especially for the condition with a low photo-isomerization ratio.Also, the nanoparticle size effect on the mechanical properties is observed: the elastic stiffness of the PRP/Au nanocomposites becomes increased as the embedded nanoparticle size is decreased because the fraction of the occupied volume of the interphase in the matrix is increased. Such enhancement features are sustained after the azobenzene groups in the matrix are changed from trans- to cis-state, as mentioned in detail above.

Figure 11. Elastic stiffness components of the PRP/Au nanocomposites according to the photo-isomerization of the azobenzene molecules inside of the structure. (a) Normal (x-axis) and (b) transverse (y- and z-axes) stiffness along the nematic axis of the azobenzene.

3.3. Linear correlation between micro-macro deformation phenomena explained with photo-thermal phase transition The nematic-isotropic phase transition of conventional liquid crystal also occurs when the thermal energy is sufficient to overcome the orientational forces of the molecular 34


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field. Both the photo-isomerization and the thermal isomerization induce the macroscopic mechanical motion of the stimuli-responsive polymer material as well as the change in its microstructure. Even though the outward appearances of the deformation are similar, the intrinsic mechanism evolved by the microstructure significantly differs. In the case of the thermal isomerization, the liquid crystalline molecules lose their alignment due to the large kinetic energy while maintaining their rod-like shape. In comparison, the photoisomerization directly changes the molecular conformation of the azobenzene so the isomers affect the arrangement of the surrounding molecules, independent of the thermal effects. To thoroughly examine the multi-stimuli responsive effect, we therefore carried out heating-up simulations in MD for the PRP nanocomposites models in all photoisomerization ratio conditions and plotted the orientational order profiles in Figure 12. The modeled PRP nanocomposites showed thermal-phase transition behavior and associated changes of the structural properties. This also indicates that the constructed unit cell satisfactorily represents the desired thermo-mechanical behavior of the bulk material. More specifically, if the size of the unit cell was too small and the number of incorporated azobenzene molecules was insufficient, the orientational order profile of azobenzene moieties during the ‘heating-up’ phase would be largely scattered, preventing a determination of the ordering state. However, in this study the opto-thermal actuation characteristics of the PRP nanocomposites could be elucidated clearly, even for the smallest unit cell. When the photo-isomerization progresses prior to the heating-up, the initial orientational order of the azobenzene molecules is reduced by more than 50% and the results concur with the structural and mechanical characteristics of the matrix phase in the nanocomposites mentioned above. The remaining orientation gradually collapses and the 35



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material becomes isotropic (S< 0.05) when the given temperature reaches the order clearing point of the unit cell. As the temperature of the material increases and as the mobility of the associated polymer chains improves, it is not difficult to predict that the residual order parameter would quickly be removed. In other words, the crosslinked structure and hindered mobility of the glassy chains would strongly affect the alignment of the cis-azobenzene during the isomerization reaction only at a low temperature. One noticeable difference of the photo-thermal behavior of PRP/Au nanocomposites compared to the corresponding behavior of the neat PRP is that the collapse of the orientation is considerably retarded and hence the clearing temperature of the material is increased. It is important to note that there are many experimental reports on the relationship between nanoparticle reinforcements and the thermal stability of polymers, with this work continuing, as the issue remains unresolved. Recent studies have led to a consensus that the incorporation of nanoparticles has both positive64and negative64,65 effects on the apparent thermal stability levels of polymer nanocomposites. Specifically, the thermal stability of nanocomposites depends strongly on the performance of the interface between the gold nanoparticle and the polymer matrix. If the particle phase is dilute, the particles become trapped in the polymer matrix, with the restriction of the mobility of the polymer chains increasing the thermal properties of the material. On the other hand, the polymer chains around the interface are destabilized if the nanoparticles become aggregated, and the improvement is degraded or the rate of thermal decomposition is accelerated64,65. In the present MD simulations, we positioned a single gold nanoparticle in the unit cell with low volume fraction of 1.62 % with periodic boundary conditions. Thus, aggregation between the nanoparticles was completely excluded. Therefore, the polymer 36


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chains around the nanoparticle surface are suitably densified, and it is clear that the thermal phase-transition temperature of the material is improved by the addition of gold nanoparticles in this condition. Moreover, because of the non-bond interaction energy between the nanoparticle and the surrounding matrix, the local liquid crystalline polymer chains near the nanoparticle sustain their alignment until the bulk matrix region outside the interphase has undergone thermal isomerization. The improvement of the thermal stability of the liquid crystal alignment according to the nanoparticle additive shows good agreement with the previous theoretical and experimental results56,66,67. Another interesting feature seen in Figure 12 is that the change of the microstructure of the PRP/Au nanocomposites during the heating-up simulation is not abrupt but occurs gradually over a wide range of temperature, whereas the pure, non-isomerized PRP shows a sudden drop at the transition temperature36. In the case of neat PRP material with nonisomerized azobenzene, the polymer chains were closely packed and all the microstructures showed uniform distribution. Accordingly, all the mesogen molecules in the unit cell sustain their alignment directly before the temperature reaches order clearing point and the transition then occurs immediately over the entire domain. On the other hand, free space surrounds the matrix containing the nanoparticle or cis-isomers. The associated PRP participant around the free space has local material characteristics regarding the structure and kinetics of the crosslinked polymer; thus, the alignment parameter of the molecules has a continuous variation. To examine the correlation between the disordering of the polymer microstructure and the macroscopic deformation of the material, we plotted the compressive normal strain along the x-axis of the unit cell in Figure 13 with respect to the orientational order parameter during the heating-up simulations. While the deformation quantity of the non-isomerized PRP model without 37



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nano-reinforcements is severely scattered and shows low correlation with the orientation of the microstructure, the photo-isomerized and other PRP/Au nanocomposites models show a clearly linear trend with the orientation of the microstructure. Therefore, the result in Figure 13 implies that the insertion of the gold nanoparticle has a positive role in widening the transitional state of the polymer, while the photo-thermal actuation features of the material are guaranteed in accordance with the conditions of temperature and light. If the relationship between the light irradiation condition and the corresponding population of the cis-isomers in the PRP microstructures can be identified in future experiments, more realistic and accurate simulations will be possible with the present method. Lastly, to provide evidence that the material is in a glassy state at room temperature, we determined the glass transition behavior of the modeled neat PRP and PRP/Au nanocomposites. The glass transition temperature was obtained from the densitytemperature relationship during the heating-up simulation under an isobaric condition68,69. The point of intersection between the two least-square fits of the density-temperature relationship below (from 300K to 340K) and above (from 450K to 480K) the candidate glass-transition region was derived. As shown in Figure 14, the density-temperature profile has a concave shape and the transition temperature can be approximated from the point of the intersection between the two regression lines. We found that the glass transition temperature of the material is much lower than the order-clearing temperature, but the value is located far above room temperature; i.e., the modeled PRP and PRP/Au nanocomposites behave as glassy materials. It is also important to note that the nanoparticles increase the glass transition temperature of neat PRP by around 15K,

38


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similar to the thermoset polymer nanocomposites69, indicating that the localized polymer chains are bound by the surface of the nanoparticle and shift the transition temperature29.

Figure 12. Thermal phase transition profile of the PRP/Au nanocomposites according to the photo-isomerization ratio of the azobenzene:(a) PRP/10Å gold, (b) PRP/13Å gold, (c) PRP/16Å gold, and (d) PRP/20Å gold. We defined the order clearing point of the material where the averaged orientational order of the microstructure is lower than 0.05.

39



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Figure 13. Linear correlation between the macroscopic deformation of the modeled unit cell and the microscopic orientational order of the internal molecules according to the diameter of gold nanoparticle in the unit cell:(a) PRP/10Å gold, (b) PRP/13Å gold, (c) PRP/16Å gold, (d) PRP/20Å gold, and (e) Neat PRP. The final graph in (e) was obtained fromearlier simulation data34. We defined the compressive strain as positive.

40


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Figure 14. Density-temperature relationships between the neat PRP and the PRP/13Å Au nanocomposites at a wide range of temperatures.

4. Conclusions In this work, MD simulations were carried out to investigate the photo-thermal actuation behavior of the neat PRP and the PRP/Au nanocomposites. The photoisomerization reaction of azobenzene caused by light exposure was represented by applying the photo-reactive potential energy absorbed by the azobenzene moiety to the dihedral potential for diazene groups in the unit cell. According to the photoisomerization ratio of the azobenzene isomers and the size of the embedded gold nanoparticle under constant volume fraction, we obtained the bulk properties including the photostrain, stiffness constants, and thermal phase transition of the considered material. During the simulation, the internal microstructure of the polymer phase as well as the interfacial region between the particle and the matrix were also examined to clarify the origin of the photo-induced characteristics. 41



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The results indicated that the nano-sized reinforcement not only increases the thermomechanical properties of the liquid crystalline polymer, but also increases the photostrain of the microstructure. The strong non-bond interactions between the particle and the matrix generate the densely packed local structure at the interfacial region and enhances the overall properties of the material.Particularly, as the nanoparticle size decreases under a constant volume fraction, the elastic stiffness of the overall nanocomposite structure also increases, in line with previous observations of polymer nanocomposites made by our group27,39,62. Nevertheless, the degradation of the preferred orientation caused by the reinforcement is observed only at sites close to the surface of the nanoparticle. Also, the depletion region at the interface allows a conformational mobility of the crosslinked polymer along the alignment direction during the photo-isomerization reaction. Accordingly, this improvement of the multi-functionality becomes more significant as the nanoparticle size decreases owing to the increase of the effective area occupied by the interphase. Based on the current numerical results, we reached two crucial conclusions regarding a way to improve the mechanical stability of the PRP material by using the reinforcements while maintaining the material’s photo-deformation behavior. First, provided the size of the nanofiller is comparable or smaller than the length of the mesogen molecules, the nanofiller only slightly changes the alignment of the nematic phase and the multifunctional behavior of the PRP material would be preserved. Secondly, if an attractive interaction develops between the filler and the matrix, the polymer matrices around the nanoparticles form the interphase which strengthens the overall composite structures and assists the prompt deformation response to the light stimuli. The results obtained thus far provide important insight into the mechanical design of the stiff 42


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but resiliently deformable PRP nanocomposite materials and enables quantitative analysis of their mechanical properties at a given temperature and light exposure conditions. The present MD data can provide a new perspective on the mechanical design of PRP nanocomposite materials. To assess the photo-thermal actuation properties of the bulk material (under a stress-free condition) as well as the inherent load transfer mechanism at the interface between the nanoparticle and the matrix (under mechanical loading) via continuum mechanics, one can establish a multiscale model which provides a design guide for PRP nanocomposites in a multi-physical environment. The orientational order parameter of the liquid crystal phase of the material obtained from MD simulations can be described as a function of the shape parameter, which enables the design of macroscopic photo-bending for a PRP nanocomposite specimen and related applications in terms of the mechanics of the materials31. Furthermore, the effective stiffness and spatial range of the interphase layer can be numerically identified using a multi-inclusion finite element model with homogenization39,62. The roles of interfacial interactions between the nanoparticles and the polymer matrix under mechanical loading can be explicitly characterized, along with the inherent nanoparticle size and effects of the photoisomerization reaction on the material. Lastly, to enhance the accuracy and realism of the present simulation method further, concurrent multiscale modeling which consists of first-principles calculation, molecular dynamics and a coarse-graining technique35 should also be adopted in the near future.

Acknowledgements This work was supported by a grant from the National Research Foundation of Korea (NRF) funded by the Korea government (MSIP) (No. 2012R1A3A2048841). 43



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Graphical Abstract 1918x1436mm (96 x 96 DPI)


Molecular Dynamics Study on the Photothermal Actuation of a Glassy

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