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Thermal Evolution of One-dimensional Iodine Chains Dingdi Wang, Haijing Zhang, William W. Yu, and Zikang Tang J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 16 May 2017 Downloaded from http://pubs.acs.org on May 21, 2017

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The Journal of Physical Chemistry Letters

Thermal Evolution of One-dimensional Iodine Chains Dingdi Wang*,†,‡, Haijing Zhang†, William W. Yu‡,|| and Zikang Tang*,§

†

Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay,

Kowloon, Hong Kong ‡

State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin

University, Changchun 130012, China §

The Institute of Applied Physics and Materials Engineering, University of Macau, Avenida da

Universidade, Taipa, Macau ||

Department of Chemistry and Physics, Louisiana State University, Shreveport, LA 71115, United States

AUTHOR INFORMATION Corresponding Author E-mail: [email protected] (D. W.); [email protected] (Z. T.)

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Abstract: In one-dimensional (1D) systems, the definition of three common states of matter (solid, liquid and gas) becomes obscure, because it has been theoretically predicted that a 1D system has no phase transition. Due to technical difficulty in tracking 1D thermal evolution, hardly any experimental evidence has demonstrated whether there exist these three states. Here we report Raman experimental observation that 1D iodine molecular chains formed inside the nano-sized channel undergo continuous transformation from chain structure to single molecules with increasing temperature, without having a sudden change as commonly observed in phase transition. At low temperatures, short-range order exists and manifests itself as long chains in structure, which gradually break into shorter chains with raising temperature. The 1D system progressively gets more and more disordered, which is in agreement with the theoretical derivations. Our work may benefit the emerging molecular scale electronics.

TOC GRAPHICS

KEYWORDS: Phase transitions, One-dimensional iodine molecular chains, Raman spectroscopy, Density-functional calculations, Zeolites


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The three states of matter (solid, liquid and gas) are very common in our daily life. Upon increasing temperature, a substance will change its phase from solid to liquid at melting point, and liquid to gas at boiling point. For a one-dimensional (1D) system, at least two “phases” can be identified: the linear chain as “solid” and single molecule as “gas”, although the definition of liquid phase is vague. The question is whether there exist melting point and boiling point in 1D system, since it has been theoretically predicted that a 1D system with short-range interaction has no phase transition.1-5 The phase transition behavior of sufficiently small three-dimensional (3D) clusters may give us some hints. For example, the melting point of sodium cluster shows irregularly large variations (±40 K) with cluster size varying from 50 to 360 atoms,6-8 and the step-like phase transition has broadened into a gradual transition over a finite temperature range (about 20 K),6-7, 9 because the singular point (melting point) of Gibbs free energy G is smoothed out for a finite number of atoms.10-13 The solid and liquid clusters can coexist over a temperature range, instead of a melting point. But for 1D chains, theoretically, no phase transition can occur since G is an analytical function of temperature with no singularity.1-5 Only one phase exists, and 1D system is in a disordered state at T > 0 K. Unfortunately, almost no experimental work is devoted to elucidating detailed structural progression of 1D matter as a function of temperature. In this paper, we utilized the nano-sized channels of zeolite AlPO4-11(AEL) single crystal to confine the linear iodine molecular chains inside, which would keep their 1D nature even though they are broken up, in order to make the dynamic study possible. By consistently binding together Landau’s “domain wall” theory and experimental Raman spectroscopy, assisted by density functional theory (DFT) calculations of 1D iodine molecular system, the absence of 1D phase transition is clearly substantiated. An iodine crystal is of a layered structure,14-15 which is similar to that of graphite, topological insulator or black phosphorus. Each layer is a two-dimensional (2D) zigzag I2 network, as illustrated in Figure 1a (based on the iodine crystal structure data in Ref. 14). A small portion of valence electron density is transferred from intramolecular I-I bond to intermolecular coupling, thus the I-I bond elongates to 2.715 Å (from 2.666 Å of I2 in gaseous state),16 whereas intermolecular distance shortens to 3.496 Å (from 3.96 Å of van der Waals contact distance).17 Consequently, iodine crystal becomes a 2D semiconductor ACS Paragon Plus Environment

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(Section S5 in Supporting Information).18 As will be discussed later, the coupling energy between I2 is relatively small, hence the self-assembly and break-up of 1D (I2)n chain is straightforward and will reveal the stability limit of 1D system which is adapted from a 2D semiconductor.

Figure 1. The schematic diagram of iodine molecular chains formed inside the nano-channels of AEL crystal. (a) The ball and stick as well as van der Waals (translucent) representations of a 2D network plane inside iodine crystal. (b) The sketch of I2-loaded AEL crystal with an array of nano-channels. (c, d) The top view (c) and lateral view (d) of (I2)n chain inside the nano-channel. The molecular surface of the nano-channel is plotted in translucent blue color. The intermolecular couplings which are present in iodine crystal would facilitate the formation of 1D molecular chains in the nano-channel by linking “lying” I2 end to end. Owing to the special structure of the nanochannel, some “standing” I2 may be trapped by the wide part of the channel, away from the linear chains.

The 1D iodine chain inside carbon nanotube has been observed directly via high-resolution transmission electron microscopy.19 The existence of iodine chain-like structures in the nano-sized channels of zeolites has been substantiated by Raman spectroscopy.20-21 In this letter, we will investigate the thermal variation of 1D (I2)n chains to test whether there is any phase transition. The linear (I2)n chains are confined inside the 1D nano-channel of zeolite AEL crystal, which can accommodate the thinnest 0.3 nm carbon nanotube or small guest molecules,21-28 and the optical transparency of crystal facilitates the Raman exploration of the confined molecules.28-32 Moreover, the confined chains would keep their 1D nature even if they are ACS Paragon Plus Environment

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broken up, so their dynamics can be tracked within the whole temperature range. In our previous study,28 we had already demonstrated that isolated I2 molecules could only be oriented along (lying) or perpendicularly (standing) to the nano-channel axis by means of polarized Raman spectroscopy and DFT calculation. Therefore, it can be imagined 1D (I2)n chain in the nano-channel may be easily assembled by linking “lying” I2 end to end, as shown in Figure 1d. The “standing” I2 is in disfavor because of its higher energy and incommensurate periodicity with chains, so they will stay out of the 1D chains.

Figure 2. The dissimilar transition behavior of 3D iodine crystal and 1D iodine chain under atmospheric pressure. (a) The Raman spectra of crystalline, liquid and gaseous iodine at different temperatures. The phase transitions at the melting point of 386.75 K and boiling point of 457.67 K result in distinct characteristics. (b) The Raman spectra of (I2)n chains in AEL crystal at several selected temperatures. The transition from the chain mode of 195.3 cm-1 to the monomer mode of 209.2 cm-1 is smooth and continuous, no phase transition can be identified. The small peak at 214.7 cm-1 is owing to the “standing” I2. The chains undergo a progressive breaking process. The average chain length at each temperature is marked on the corresponding spectrum based on Landau’s theory.


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Figure 2a shows the archetypal Raman spectra of iodine in solid, liquid and gaseous phases. The phase transitions at the melting point of 386.75 K and boiling point of 457.67 K lead to the distinct vibrational features.16 The in-phase (180.2 cm-1) and out-of-phase (189.6 cm-1) vibrational modes of iodine crystal, which are ascribed to the two different I2 molecules in primitive cell (Figure 1a), only broaden slightly with raising temperature. When iodine crystal melts, the two modes shift to the right and are transformed into two broad peaks, which will be further converted into a single peak (213.0 cm-1) of gaseous I2. For the Raman spectra of 1D (I2)n chains in AEL crystal, as shown in Figure 2b, the mode of 195.3 cm-1 at 77 K is attributed to long chains, whereas the mode of 209.2 cm-1 is already identified as the vibrational frequency of single “lying” I2 in low-density AEL samples.28 The transition from chain structure to monomer is progressive (the complete data set is provided in Figure S1a, Supporting Information) and reversible (Figure S1b, Supporting Information), no phase transition can be identified. This behavior can be reproduced in different samples, and it is even not relevant to the loading density (as long as the filling ratio is not extremely low), which demonstrates an intrinsic characteristic of 1D iodine chains. With increasing temperature, long chains would gradually break into shorter chains, thus the equilibrium I-I bond length becomes shorter due to a weaker intermolecular coupling, which leads to the blue shift of vibrational mode. The average chain length at each temperature can be estimated according to Landau’s theory, which will be discussed later. The small peak centered at 214.7 cm-1 is related to the “standing” I2, whose vibrational frequency does not change with the increase of temperature (Figure S1c, Supporting Information). The equilibrium structures of (I2)n chains can be established by DFT calculations (Section S4 and S6 in Supporting Information). For the infinite (I2)∞ chain, the coupling length (Figure 3a) is 3.36948 Å while I-I bond length is 2.70172 Å, which are comparable to that in iodine crystal (Figure 1a). For the finite (I2)n chain, apart from the end I2, the states of interior I2 approach that of infinite chain rapidly with the increase of chain length (Figure 3c, d). The asymptotic behavior of average coupling energy Ec (Figure 3e) further demonstrates the progressive transformation of iodine monomer into infinite chain. The calculated principal vibrational frequency (pink pentagons in Figure 3b), which possesses the maximum Raman ACS Paragon Plus Environment

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intensity and represents the in-phase vibration of all I2 in the chain, also shows the asymptotic trend. This frequency corresponds to the infinite diatomic chain’s optical phonon at the Brillouin zone center, which is the simplest Raman-active phonon discussed in the textbooks.33 To the best of our knowledge, the progression of Raman spectrum in Figure 2b is the first experiment to clearly exhibit the evolution of 1D optical phonon with the increase of chain length.

Figure 3. The structural information of iodine molecular chains obtained from DFT calculations. (a) The ball and stick representation of iodine chains from I2 to (I2)6 as well as the infinite (I2)∞ chain. (b-e) The variations of the calculated principal vibrational frequency (b), the intermolecular coupling length (c), the intramolecular I-I bond length (d), and the coupling energy per I2 (e) with the increase of chain size. The transformation of iodine monomer into infinite chain is obviously progressive, which is in accord with the experimental observation. The states of inner I2 (marked with orange bond length) in a longer chain are very similar to that of I2 in the infinite chain.


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The average chain length at each temperature can be derived by modifying Landau’s “domain wall” theory (Section S3 in Supporting Information).4 In this work, the “domain wall” formed between two sections of different phases in Landau’s theory is replaced by the broken connection between iodine chains. If m connections of a 1D N-molecule chain break, the free energy is increased to G = H − TS = H 0 + mEc − k BT ln

{( N − 1)!

}

 m !( N − 1 − m ) ! , where H0 is the initial enthalpy and

kB is Boltzmann constant. The derivative is ∂G ∂m = Ec − k BT ln ( N − 1) m − 1 . If m ≪ (N – 1), then

∂G ∂m < 0 . With increasing m, the chain continues to break up, thus G will be gradually reduced to the

0 . At equilibrium minimum that ∂G ∂m = Ec

N − 1 k BT n = = e + 1. m

(1)

As long as N ≫ 1 and m ≫ 1, N/(m + 1) ≈ (N – 1)/m, andn can be defined as the average chain length.

Given Ec ≈ 0.03 eV (Figure 3e),n is calculated and marked on Figure 2b accordingly. Equation (1) is reminiscent of Boltzmann distribution. In fact, the breaking process can be regarded as the probability

(

= p 1 e distribution among a two-level system, with the probability

Ec k BT

)

+ 1 of the upper energy level

Ec. An immediate consequence of Equation (1) is that if (N – 1) ≪n, the chain will not decompose, since

in this case m ≪ 1. Meanwhile,n should be large enough (Ec ≫ kBT), which reduces the breaking probability p to ensure the cracking would instantaneously recover in a tiny interval and be undetectable. So the value ofn serves as a stability criterion in designing the molecular circuits.

The DFT calculated frequencies ranging from 196.1 cm-1 of (I2)∞ chain to 222.3 cm-1 of I2 molecule (pink pentagons in Figure 3b) only slightly deviate from the experimental values from 195.3 cm-1 to 209.2 cm-1 (Figure 2b). In order to quantitatively interpret the experimental observations, the calculated frequencies are scaled by a linear function to match the experimental range (blue balls in Figure 3b). The justification of scaling procedures is provided in Section S8 of Supporting Information. Following this operation, the calculated Raman spectra of the first six (I2)n chains are demonstrated in Figure 4a, which ACS Paragon Plus Environment

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are dominated by the scaled principal frequencies. The simulated Raman spectra (solid curves in Figure 4b), which are weighted sums of the calculated spectra of the first 10 chains (longer chains are omitted) at the corresponding temperature, are in good agreement with the experimental data (dotted curves in Figure 4b), except for the “standing” mode of 214.7 cm-1. Raman intensity of every kind of linear chain is supposed to be directly proportional to the amount of I2 it contains, so the relative intensities (Figure 4c) represent the I2 distribution among the first 10 chains and the corresponding chain length distribution with an average length ofn′ can be calculated, which reasonably matches the value ofn (Figure 2b or Figure 4b) deduced from Landau’s theory.

Figure 4. The theoretical modelling of thermal evolution of 1D iodine chains. (a) The DFT calculated Raman spectra of chains from I2 to (I2)6 at T = 273 K. (b) The simulated Raman spectra (solid curves), which are weighted sums of the calculated spectra of chains from I2 to (I2)10, fit the experimental data (dotted curves) quite well, aside from the “standing” mode of 214.7 cm-1. (c) The histogram is the relative intensity employed to simulate the Raman spectra in (b), and denotes the I2 distribution among the 10 chains. The average chain lengthn′ can be calculated accordingly, which is consistent with the value ofn marked on (b) deducing from Landau’s theory. The histogram generally obeys Poisson distribution with an average chain lengthn″. A clear physical picture of the dynamic transformation of 1D chains with increasing temperature is illustrated, which corroborates the absence of phase transition in 1D system.


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As shown in Figure 4c, the I2 distribution among chains can be well represented by Poisson distribution (dot lines are guides to the eyes), which takes the long chains’ influence into account and corrects the average chain length asn″ (Section S9 of Supporting Information). Based on the above discussions, the thermal evolution of 1D chains is well understood. At low temperatures, chain length has a relatively broad distribution centered at large values (Figure 4c). With raising temperature, the distribution progressively moves towards the smaller-value side. The gradual loss of short-range order confirms that the 1D system has no phase transition. It should be noted that it is difficult to differentiate between long chains (n > 10), since the states of their inner molecules are almost identical (Figure 3). This is totally different from 3D crystal, which would show dramatic structural transformation from bulk construction to shell structure if the crystal only contains hundreds of atoms.6, 8, 11, 34-35 The confined 1D (I2)n molecular chains offer us such an opportunity to explore the structural evolution of 1D system as a function of temperature, which directly confirms the absence of 1D phase transition. With the development of carbon nano-materials, 1D carbon chain (also called carbyne) has also been extensively

explored,36-38

and

other

1D

chains

are

investigated

as

well.39-40

They

possess a good application prospect in molecular scale electronics. However, the theory of non-existence of 1D phase seems to contradict the 1D chain results.37, 39 Our work has revealed that they are actually consistent with each other. The non-existence of 1D phase is valid in thermodynamic limit, but shortrange order still exists as clearly demonstrated by Raman spectroscopy and DFT calculations, and the

= n equilibrium length

e Ec kBT + 1 of short chains can be deduced from Landau’s theory, which sets an

upper limit on the 1D chain length. Consequently, the obtained 1D chains in literature can be regarded as short chains, and this work solves the conflict and serves as a bridge between theory and experiment. EXPERIMENTAL AND COMPUTATIONAL METHODS The Preparation of iodine-loaded AEL crystals: The AEL single crystals with a common size of 10×30×80 μm were synthesized hydrothermally.41 Iodine molecules were diffused into nano-channels by


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sealing the AEL and iodine crystals (Acros Organics, ≥ 99.5 %) together in a vacuum Pyrex tube and heating that at 573 K. The initial filling ratio of I2 in the nano-channel relative to infinite molecular chain is estimated at around 50%, which can be controlled by the solid I2/AEL weight ratio. The Raman experiment: Polarized Raman measurement was performed by Jobin-Yvon T64000 microRaman spectrometer in a backscattering configuration. The output 514.531-nm beam of Innova 70CSpectrum laser was employed as the excitation light, which could be polarized either along or perpendicularly to the crystal axis to detect the Raman signal of 1D (I2)n chains or “standing” I2 molecules. The detailed configuration was described in Ref. 28. The Raman spectra were recorded at several selected temperatures, which were controlled by putting the iodine-loaded AEL crystal (or a flat cuvette which contains iodine crystals) into the Linkam THMS600 Heating and Freezing stage system. The sample chamber was continuously purged by nitrogen gas with a flow rate of 30 cc/min, which was discharged into the atmosphere directly through an outlet. Therefore, the pressure inside the chamber was maintained at atmospheric pressure. For I2-loaded AEL crystal, firstly the crystal temperature was increased from room temperature to 473 K and was maintained 30 min for annealing, then the temperature was unceasingly decreased to 77 K. The first Raman spectrum was measured at 77 K, then recorded every 50 K from 123 K to 573 K, and afterwards from 573 K back to 77 K (Figure S1, Supporting Information). The heating or cooling rate was 20 K/min. The temperature homogeneity was guaranteed by taking the spectrum with a 5-min delay. The laser was focused on the sample surface by a long-working-distance 50× microscope objective. The laser power on the sample was about 0.05 mW, which only raised the local temperature by around 10 K (Figure S2, Supporting Information). The spectral resolution was about 0.1 cm-1 by utilizing the sub-pixel acquisition function of T64000 spectrometer. The DFT calculation: The plane-wave CASTEP module in Materials Studio 7.0 was utilized to carry out first principles DFT calculation. The gradient corrected PBEsol functional served as the exchangecorrelation potential.42 London dispersion correction is represented by the Tkatchenko-Scheffler (TS) scheme.43 Norm-conserving pseudopotential of iodine atoms was adopted, which was generated from the


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state-of-the-art and open-source software Opium 3.7. Further details are described in the Supporting Information. ASSOCIATED CONTENT Supporting Information The details of Raman experiment including the reversible behavior of continuous transition, and DFT calculation (PDF) ACKNOWLEDGMENT We thank the National Supercomputing Center in Shenzhen (China) for providing the supercomputing service and Materials Studio 7.0 software. This research was supported by National Natural Science Foundation of China (Grant No. 11504124, 61225018) and Research Grants Council of Hong Kong (Grant No. 604210). REFERENCES 1. Van Hove, L. Sur l'intégrale de configuration pour les systèmes de particules à une dimension. Physica 1950, 16 (2), 137-143. 2. Ruelle, D. Statistical mechanics of a one-dimensional lattice gas. Commun. Math. Phys. 1968, 9 (4), 267-278. 3. Ruelle, D. The Problem of Phase Transitions. In Statistical Mechanics: Rigorous Results, World Scientific Publishing: 1999; pp 108-144. 4. Landau, L. D.; Lifshitz, E. M. The impossibility of the existence of phases in one-dimensional systems In Statistical Physics, Third ed.; Pergamon Press Ltd 1980; p 537. 5. Lieb, E. H.; Mattis, D. C. Chapter 1 - Classical Statistical Mechanics. In Mathematical Physics in One Dimension, Academic Press: 1966; pp 3-24. 6. Schmidt, M.; Kusche, R.; von Issendorff, B.; Haberland, H. Irregular variations in the melting point of size-selected atomic clusters. Nature 1998, 393 (6682), 238-240. 7. Schmidt, M.; Donges, J.; Hippler, T.; Haberland, H. Influence of energy and entropy on the melting of sodium clusters. Phys. Rev. Lett. 2003, 90 (10), 103401. 8. Haberland, H.; Hippler, T.; Donges, J.; Kostko, O.; Schmidt, M.; von Issendorff, B. Melting of sodium clusters: where do the magic numbers come from? Phys. Rev. Lett. 2005, 94 (3), 035701. 9. Schmidt, M.; Kusche, R.; Kronmüller, W.; von Issendorff, B.; Haberland, H. Experimental determination of the melting point and heat capacity for a free cluster of 139 sodium atoms. Phys. Rev. Lett. 1997, 79 (1), 99-102. 10. Berry, R. S. Thermodynamics: size is everything. Nature 1998, 393 (6682), 212-213. 11. Berry, R. S.; Smirnov, B. M. Where macro meets micro. Phys. Chem. Chem. Phys. 2014, 16 (21), 9747-9759. ACS Paragon Plus Environment

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Thermal Evolution of One-Dimensional Iodine ... - ACS Publications

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