Understanding the Formation of Pentagonal Cyclic Twinned Crystal

Sep 26, 2013 - Understanding the Formation of Pentagonal Cyclic Twinned Crystal from the Solvent Dependent Assembly of Au Nanocrystals into Their Coll...
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Understanding the Formation of Pentagonal Cyclic Twinned Crystal from the Solvent Dependent Assembly of Au Nanocrystals into Their Colloidal Crystals Shixiong Bao,† Jiawei Zhang,† Zhiyuan Jiang,*,† Xi Zhou,‡ and Zhaoxiong Xie*,† †

State Key Laboratory of Physical Chemistry of Solid Surfaces & Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, People’s Republic of China ‡ Research Center of Biomedical Engineering, Department of Biomaterials, College of Materials, The Key Laboratory of Biomedical Engineering of Fujian Province, Xiamen University, Xiamen, 361005, People’s Republic of China S Supporting Information *

ABSTRACT: Due to the presence of high-density twinned-defects and diffuse elastic strain, pentagonal cyclic twinning (PCT) structures may have more fascinating properties than the corresponding single crystalline structure. Although there are a lot of reports concerning the PCT nanocrystals of many monometals and bimetal alloys, the established growth mechanisms of PCT structures are still not straightforward and usually inconsistent with each other. In this Letter, using dodecanethiol-capped Au nanocrystals (NCs) as building blocks, taking self-assembly of Au NCs into their colloidal crystals as the crystallization model, we found the competition of crystal cohesive energy and surface free energy plays an important role in the formation of PCT colloidal crystal. By rationally selecting the solvent to tailor the crystal cohesive energy, the structure of the colloidal crystals can be tuned. PCT structures are more likely to form when the interaction between building blocks is weak, while the single crystal structure is formed when the interaction is strong. The results demonstrate that the thermodynamic factors are the origin of pentagonal cyclic twinning. SECTION: Physical Processes in Nanomaterials and Nanostructures

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increasing the overall reaction rate, were also thought to be crucial to achieve PCT structures.2,3,5 Moreover, there is not a reliable common view for controllable synthesis of PCT NCs yet. The difficulty to clarify the growth mechanism of PCT is due to the lack of experimental tools for directly observing, identifying, and monitoring the nucleation and growth process.9,10 For the conventional crystallization from atoms, ions, or molecules, the crystal building blocks are too small to be identified in real space, the nucleation and growth process is too fast to be observed and monitored in most cases. It is also hard to regulate and control thermodynamic quantities related to crystallization, such as interactions among the crystal building blocks.9−11 In one word, the lack of direct observation and investigation of conventional crystallization process has impeded understanding the formation of PCT. Although increasingly sophisticated theories have been formulated and refined to simulate and account for crystallization process, large discrepancies between the simulation results and those obtained from experiments still exist.12 Self-assembly of NCs into their colloidal crystal offers a great opportunity to study

entagonal cyclic twinning (PCT) is a general crystallographic phenomenon, which is often found in many nanocrystals (NCs) of face-center-cubic (fcc) structure.1 Due to the presence of high-density of twinned-defects and diffuse elastic strain in the PCT structures, some fascinating properties arise particularly from PCT structures in comparison with the corresponding single crystalline structure.2−4 For example, the Pt3Ni icosahedral NCs exhibit superior oxygen reduction reaction (ORR) activity relative to octahedral NCs, profiting from the diffuse elastic strain.2 Pt−Pd icosahedral NCs showed much higher activity to methanol oxidation than that of Pt−Pd nanotetrahedrons because of the effect of the multiply twinned defects.3 With the twinned boundaries acting as diffusing channels for atoms, PCT Ag NCs could form perfect single crystal Ag2Se, while the single-crystal Ag NCs transformed into a Ag2Se shell with a hollow core.4 Due to the peculiar properties of PCT structures, PCT NCs including decahedral and icosahedral NCs of many monometals5−7 (e.g., Au, Ag, Pt, Pd) and bimetal alloys2 (e.g., Pt- Co, Ni, Pd and Au) have been successfully synthesized. However, to date, the growth mechanisms established are still not straightforward and usually inconsistent to each other. For instance, PCT NCs are supposed to be thermodynamically favored at small sizes in consideration of the internal elastic strain and twin boundary energy,8 while the reaction kinetics, such as reducing or © 2013 American Chemical Society

Received: August 7, 2013 Accepted: September 26, 2013 Published: September 26, 2013 3440

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Figure 1. Representative SEM images of morphologies of the colloidal crystals self-assembled from Au NCs dispersed in (a,b) cyclohexane and (c,d) hexane, respectively. High-resolution SEM image shows an fcc (ABCABC...) packing in the single crystal colloidal crystal from step surface (b).

crystallization.13−15 For example, our previous study of selfassembly of MnO octahedral NCs to their colloidal crystals reveals that the self-assembly approaches size selection and orientation adjustment, which is analogous with the normal crystallization process.16 In addition, typical characteristics like dislocations and twinning also occur in the colloidal crystal, which illustrate the similarities between colloidal crystal consisting of NCs and the conventional crystals consisting of atoms or molecules.15,17 Importantly, when taking self-assembly of NCs into their colloidal crystal as the model system to study the crystal growth process, we are able to regulate some thermodynamic quantities like interactions among the crystal building blocks, which is impossible to tune in a conventional crystal growth system.18 In this Letter, taking self-assembly of Au NCs into their colloidal crystals as the crystallization model, we studied the formation mechanism of the PCT, the unique crystallization phenomenon. We found that the competition of crystal lattice energy and surface free energy greatly affects the formation of PCT nanoparticles, which indicates thermodynamic factors are the origin of pentagonal cyclic twinning. Self-assembly of Au NCs capped with alkane-thiol into their colloidal crystals is a convenient model system for crystallization because these Au NCs are stable under ambient conditions, and it is easy to achieve narrow size distributions during the synthesis.19,20 More importantly, the colloidal crystal nucleation and growth process of Au NCs capped with alkanethiol is mainly driven by solvent-mediated interactions (such as solvophobic interactions) rather than the van der Waals attraction between nanocrystal cores;21,22 therefore the crystal cohesive energy between Au NCs can be regulated by means of selecting the appropriate solvent. The Au NCs as building blocks to assemble colloidal crystals were about 5.8 nm in size and capped with dodecanethiol surface ligands, which were synthesized according to the reported method.20 The Au NCs were monodispersed and of

nearly round shape (typical transmission electron microscopy (TEM) image is shown as Figure S1 in the Supporting Information). To assemble the Au NCs into their colloidal crystals, a two-layer phase diffusion method was employed (see also experimental section for the details in the Supporting Information, Figure S2).23 First, ethanol, a poor solvent for dodecanethiol-capped Au NCs, was added into a glass bottle. Then, the colloidal solution of Au NCs using hexane or cyclohexane as a good solvent was carefully added into an ethanol solvent to form a separate layer. Driven by the diffusion of the poor solvent ethanol into a colloidal solution, Au NCs assemble into colloidal crystals. After a few hours, the interface between ethanol and the colloidal solution disappeared, and some precipitates were obtained on the bottom of the vessel. The precipitates were taken out carefully and dropped on a Si wafer for scanning electron microscopy (SEM) characterization. Figure 1a shows the morphology of Au NCs colloidal crystals crystallized from a solution of cyclohexane and ethanol. It can be found that Au NCs assembled into well-shaped colloidal crystals with a size of several hundred nanometers to a few micrometers, and almost all of them were single-domain triangular or hexagonal shape. High-resolution SEM image shows that the flat surface consisted of close-packed nanocrystals. A close look at some step edges (Figure 1b) revealed that the colloidal crystals were assembled by Au NCs in the manner of ABCABC stacking (i.e., an fcc packing), as indicated by the arrows on the image.24 Small-angle X-ray diffraction patterns of these colloidal crystals (Supporting Information, Figure S3) also indicated that the colloidal crystals are of fcc structure with lattice parameter a = 10.6 nm, matching well with the colloidal crystal model of dodecanethiol-capped 5.8 nm Au nanocrystals.20 Surprisingly, when the hexane was used instead of cyclohexane, many of the precipitates were PCT colloidal crystals with decahedral/icosahedral (Figure 1c, Figure 3441

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(Uc) and surface energy (Us) have contribution during the crystallization, while for PCT structure, elastic strain (Ue) and twinned boundary energy (Ut) should be further taken into consideration. For the twinning on the (111) plane of a cubic closed packing structure, the twinning boundary energy is very small and can be neglected, because it is 2 orders less than the specific surface energy of corresponding (111) surface.26,27 Therefore, the total free energy of the single crystal structure (USingle) and PCT structure (UPCT) can be expressed as eq 1 and 2, respectively.

S4) morphologies. High-resolution SEM image (Figure 1d) clearly shows the pentagonal cyclic twinning feature of the products. It should be noted that the PCT colloidal crystals were obtained by simply replacing the solvent cyclohexane with hexane. This phenomenon motivated us to seek deeper understanding of the formation of the PCT crystals. For crystals with an fcc structure, the PCT decahedral or icosahedral particle consists of 5 or 20 single-crystal tetrahedral crystallites with (111) faces, respectively, as shown in Figure 2a.

USingle = Uc + Us = VEc + Sγ

(1)

UPCT = Uc + Us + Ue = VEc + Sγ + VW

(2)

In the above equations, Uc, Us and Ue are the crystal cohesive energy, the surface energy, and the elastic strain energy, respectively; V and S are the volume and the total surface area, respectively; Ec, γ, and W are the crystal cohesive energy per unit volume, the specific surface energy, and the elastic strain energy density for PCT structures (icosahedron and decahedron), respectively. Considering the case that both single-crystal and PCT particles have the same volume, the difference of free energy between the formation of single-crystal and PCT particles is the following: USingle − UPCT = ΔSγ − VW

(3)

where ΔS is the difference between the surface areas of single crystals and PCT particles, which is a positive value as the total surface area of PCT particles is smaller than that of single crystal. From the study of Marks on the elastic strains of PCT structures, the elastic strain energy density W has positive correlation with the rigidity (i.e., shear modulus and Poisson’s ratio) of PCT structures.28 It is well-known that the rigidity is dependent on the strength of connection between the building blocks of the solids (i.e., the crystal cohesive energy Ec),29 and therefore the elastic strain energy density W has positive correlation with the crystal cohesive energy Ec. Considering the above eq 3, we may estimate that single crystal is thermodynamically preferred when crystal cohesive energy (Ec) is large (i.e., the value of VW is large) or the specific surface energy (γ) is small, while PCT particles are favored during crystallization when crystal cohesive energy (Ec) is small (i.e., the value of VW is small) or the specific surface energy (γ) is large. In the case of assembly of dodecanethiol-capped Au NCs into their colloidal crystals, the crystal cohesive energy could be regulated by varying the solvent. It was reported that, for Au NCs capped by alkane-thiol, the presence of a good solvent results in purely repulsive interactions due to the “like dissolves like” rule.22,30 The released energy when an Au NCs in the solution deposits on the colloidal crystal nucleus is therefore smaller in a good solvent than in a poor solvent. As a consequence, the crystal cohesive energy is smaller in the good solvent than in the poor solvent. As the solubility (dispersibility) of dodecanethiol-capped Au NCs in hexane is larger than that in cyclohexane, the crystal cohesive energy in hexane is smaller than that in cyclohexane, i.e., Ec(hexane) < Ec(cyclohexane). Although the self-assembly of Au NCs was reported to depend on the crystalline nature of the Au NCs,31−33 in our experimental system, the difference between the effects of the crystalline feature of the building blocks in

Figure 2. Schematic diagram of (a) decahedron and icosahedron with {111} twinned boundaries; (b) a cross-section view along the longitudinal axis (⟨110⟩, the 5-fold axis) for five perfect fcc crystallites to form a planar cyclic PCT structure; (c) triangular plate and octahedron models of fcc single crystals terminated by only {111} facets.

In these PCT particles, five tetrahedral units share a common [110] edge as the 5-fold symmetry axis, and every unit is twinned with its two neighbors by (111) lattice planes. It can be calculated that there will be a gap of 7.35° as the theoretical dihedral angle between two (111) planes of a tetrahedron is 70.53°, resulting in an angle difference of 1.47° between every two perfect fcc tetrahedral units of PCT crystal. Figure 2b shows the angular mismatch for five perfect fcc crystallites to form a PCT structure, projected along the 5-fold symmetry axis. To form a gapless structure, these gaps must be filled by expanding the lattice laterally. Such an expansion of lattice will cause internal lattice strain and reduce the lattice energy. As a consequence, the PCT crystals have lower lattice energy than their corresponding single crystals because of the existence of microelastic strain energy. However, from a thermodynamic point of view, besides lattice energy, the surface energy also contributes to the total free energy of the crystallite during the crystal growth. It is generally accepted that PCT crystals like icosahedral particles have smaller surface area than well-shaped single crystals like octahedral particles (the case of exposed (111) facets of lowest surface energy, as shown in Figure 2c.). Therefore, the balance between the lattice energy and the surface energy may decide the final shape of crystals. To get deep insight into the formation mechanism of PCT and single crystal structures, take the method of qualitative analysis for traditional crystals,25 a thermodynamic model based on the lattice energy and surface energy is then considered.18,25,26 For a single crystal, only crystal cohesive energy 3442

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Notes

different solvents should be very little and thus was not considered in the above discussion, as the building blocks for crystallization of different colloidal crystals are the same. Based on the above experiment results and discussion, the formation mechanism of PCT and single crystal in the present case can be proposed, as shown in Figure 3. When the Au NCs

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Basic Research Program of China (Grant Nos. 2011CBA00508, 2013CB933901) and the National Natural Science Foundation of China (Grant Nos. 21131005, 21021061, 21333008, and 21171141).

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Figure 3. Schematic illustration of solvent-dependent crystallinity tuning of colloidal crystal.

were dispersed in cyclohexane and then self-assembled into colloidal crystals, the cohesive energy (Ec) is large. In this circumstance, single crystal structure is preferred, as the elastic strain energy (Ue) would be huge if forming a PCT structure. By contrast, when the Au NCs were dispersed in hexane, the cohesive energy was small, and then PCT structures are likely to form. Although more systematic experiments and theoretical analysis should be carried out for fully understanding the formation of different types of colloidal crystals, the above experiments have demonstrated unambiguously that the competition between crystal cohesive energy and surface free energy plays a key role in the formation of PCT structures. In summary, taking self-assembly of Au NCs into the colloidal crystals as the crystallization model by regarding dodecanethiol-capped Au NCs as building blocks, we found that the structure of the colloidal crystal mainly depends on the competition of crystal cohesive energy and surface free energy. By rationally selecting the solvent, the cohesive energy can be adjusted, and the structure of the colloidal crystal can be tuned. When the interaction between building blocks is weak, the crystal cohesive energy is low, and PCT structures can be formed. It is also demonstrated that the thermodynamic factors are the origin for pentagonal cyclic twinning. Assisted by systematic experiments and sophisticated analysis, self-assembly of nanocrystals to their colloidal crystal should offer a great opportunity to study and understand complex crystallization.

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ASSOCIATED CONTENT

S Supporting Information *

TEM image of Au NCs, synthetic methods of Au NCs, schematic outline illustrating the concept of the two-layer phase diffusion procedure and SAXRD patterns of the colloidal crystals. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. 3443

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