Molecular Dynamics Study of Morphology of ... - ACS Publications

Subscriber access provided by HACETTEPE UNIVERSITESI KUTUPHANESI

Article

Molecular Dynamics Study of Morphology of Doped PEDOT: From Solution to Dry Phase Juan Felipe Franco-Gonzalez, and Igor V. Zozoulenko J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b01510 • Publication Date (Web): 05 Apr 2017 Downloaded from http://pubs.acs.org on April 8, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Molecular Dynamics Study of Morphology of Doped PEDOT: From Solution to Dry Phase Juan Felipe Franco-Gonzalez and Igor V. Zozoulenko* Laboratory of Organic Electronics, ITN, Linköping University, 60174 Norrköping, Sweden

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT.

Morphology

of

the

conducting

polymer

Page 2 of 38

PEDOT:TOS

(Poly(3,4-

ethylenedioxythiophene) doped with molecular tosylate) and its crystallization in aqueous solution were studied using atomistic molecular dynamics simulations. It was found that (a) PEDOT comprises crystallite aggregates consisting of 3-6 π-π stacked chains. The crystallites are linked by interpenetrating π-π stacked chains such that percolative paths in the structure are formed. (b) The size of the crystallites depends on the water content but the π-π stacking distance is practically independent of the chain length, charge concentration and water content. (c) TOS counterions are located either on the top of the chains or on the side of the crystallites and their distribution depends on the charge concentration but is practically independent of the water content; (d) PEDOT chains and crystallites exhibit bending that depends on their length and water content.


2

Page 3 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. Introduction

Poly(3,4-ethylenedioxythiophene) (PEDOT)1–3 is one of the most studied conducting polymers with the number of research articles addressing this material exceeding 1000 per year and growing with an increasing pace4. The interest to PEDOT is due to its excellent thermal and air stability, well-developed and relatively simple synthesis methods that allow a large-scale manufacturing, and custom-designed pattern coating and printing technologies. PEDOT is highly transparent in the visible range; a pristine (i.e. as synthesized) PEDOT is highly doped and subsequent post-treatment by solvents can bring it in a highly conductive state, which can be tuned by electrical or electrochemical means. A combination of all these properties makes PEDOT the material of choice for many electronic, optoelectronic and bioelectronics applications such as electrochemical transistors5, sensors6, electrochromic displays7, organic electronic ion pumps8, electrodes interfacing with neuronal systems9 and implantable drug delivery devices10. PEDOT has been used as the electrode in ion-based energy storage devices, such as supercapacitors11; in addition to being extensively utilized as the interlayer and electrode in various solid-state devices, such as in organic light emitting diodes12, field effect transistors13 and photovoltaics14. (For reviews see e.g.4,15–18). During recent years massive attention has been devoted to understanding the mechanisms of conductivity in PEDOT and related conducting polymers4,15–32. This represents an extremely challenging task, as it requires understanding of electronic and material properties on different scales. This includes an Ångström’s scale defining the nature of charged states (bipolaron vs polaron or polaron pairs)33–37 a nanometer scale defining the character of conductivity (hopping transport vs band transport)38–42, and a nanometer/submicrometer scale representing a complex


3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 38

morphology of these systems24,43–46. It is generally recognized that the morphology of these materials constitutes one of the major factors affecting their performance, and hence massive efforts have been recently devoted to the investigation of their morphology1,17–20,23,24,27–32. Powerful tools for structural characterization of these materials are the grazing incidence wide angle X-ray scattering (GIWAXS)47,48 combined with the high-resolution transmission electron microscopy, scanning electron microscopy or atomic force microscopy. The results emerging from morphology studies show that PEDOT films contain highly crystalline domains consisting of 3-10 stacked chains surrounded by amorphous matrix16,28,30. Unfortunately, these studies are not in the position to reveal a microscopic picture of the morphology such as a local structure at the sub-nanometer scale, a structure of the interface between the crystallites and amorphous regions, positions of counterions, etc. As a result, a number of conjectures concerning the material’s morphology are based on indirect evidence obtained from e.g. transport and optical measurements, which, in turn, can lead to morphology models that are not always consistent with each other16–19,21,22,26–28,31. It is remarkable that despite the tremendous interest in the morphology of PEDOT, there have been very few theoretical studies that experimentalists can rely upon37,41,49–53. Most of the available theoretical work on PEDOT and related conducting polymers have been limited to largely oversimplified models such as perfect periodic crystals41,49,50 or single oligomers37,51. Neither of these models are able to adequately describe the morphology of realistic PEDOT thin films that exhibit a limited crystal-like order with a dominate amorphous character. Hence, the computational studies of morphology and structure of realistic PEDOT thin films are in critical demand and the lack of the theoretical understanding of practically all aspects of the morphology represents the major obstacle for further improvement of the performance of PEDOT-based


4

Page 5 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


devices. It is noteworthy that computational modelling has already become a vital tool in the majority of other fields of material research, e.g. batteries54, biomolecular systems55 and organic electronics, just to name a few, where it provides the essential insight into fundamental processes that are not otherwise accessible. In the present paper, we report molecular dynamics studies of the conducting polymer PEDOT doped with molecular counterions, and address the basic and the most fundamental questions concerning its morphology, such as crystallization, degree of crystallinity, distribution of counterions and many others. Particular attention is paid to the role of water and to a comparison of morphology of wet and dry films. Note that a polymeric counterion polystyrene sulfonate (PSS) represents the most studied counterion for PEDOT to date. However, during recent years various molecular counterions, in particular, tosylate (TOS), emerge as the more efficient alternative to the polymeric one56. This is because PEDOT with molecular counterions consistently outperforms PEDOT:PSS showing conductivities exceeding 3000 S/cm-1. Moreover, utilization of molecular counterions results in semimetallic56 or metallic behavior57 of PEDOT. (Note that the room-temperature conductivity of pristine PEDOT:PSS is typically below ~ 1 S/cm-1;17,56,57 the posttreatment with different solvents or adding ionic liquids or other compounds can however increase conductivity of

PEDOT:PSS by several orders of

magnitude4). Because of these important advances in our work we focus on the case of molecular counterion TOS and report molecular dynamics studies of PEDOT:TOS (“PEDOT:TOS” stands for conducting polymer PEDOT with molecular counterions TOS; see Figure 1a). Our simulations correspond to the most common fabrication techniques where PEDOT thin films are produced by drop-casting, spin-coating, vapor phase polymerization or related methods where polymerization, oxidation and crystallization takes place in a bulk in the presence of


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 38

solvent/water1. Our study does not concern the special case of ultrathin PEDOT films grown on a steel surface where the structural organization of PEDOT film is completely different as it is primarily determined by the steel surface structure and the adhesion of polymeric chains to the surface52. We envision that the obtained computational results herein will aid in understanding and guide the material and device design for enhanced performance, in addition to providing motivation for further computational studies of this material.

2. Methods

Molecular Dynamics Simulations: Molecular Dynamics Simulations were performed using General AMBER Force Field (GAFF)58 employing the moltemplate code59 in LAMMPS software suite60. Water molecules were described by a model of SPC/E 61. PEDOT chains, TOS and water molecules were randomly placed in a computational box 12×12×12 nm3, which typically contained ≈100,000 atoms. The chosen computational box is big enough such that no further averaging over different initial realizations is required, see Figure S1 in the Supporting Information. At the same time the size of the computational domain is smaller than a typical width of PEDOT thin films (which is 200-300 nm). That is, our calculations correspond to volume calculations of the polymeric thin film. The system was then minimized and equilibrated by 20 ns run of canonical nVT (at 293.15 K) ensemble using the Nose-Hoover thermostat62–64 and the time integration method of Verlet 65. Then, water was consecutively removed in 5 steps, such as the water concentration was reduced from 82% w.t. (initial solution) to 70% w.t., 60% w.t., 43% w.t., 13% w.t. and finally 0% w.t. (i.e. a dry phase). The system was equilibrated in each step by a npT (at 1 atm and 293.15 K) ensemble for 10 ns run with both barostat and


6

Page 7 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


thermostat as Nose-Hoover62–64. Note that we also performed calculations with another atomistic force field for PEDOT chains and TOS molecules, Optimized Potentials for Liquid Simulations, OPLS-AA66, (the same SPC/E model61 was used for water), and obtained similar results, see the Supporting Information more details, Figure S2). The radial distribution function g(r) (also defined as a pair correlation function gA-B(r)) was calculated as implemented in GROMACS package67 and is defined in the following way: ∑ ∑ 〉

= 〈

(1)

Where NA and NB are the number of particles A and B respectively; 〈ρB〉 is the particle density of B averaged over all spheres around particles A with radius r; rij is the distance between particles i and j; and δ(rij-r) is the Dirac's delta function (δ=1 for rij=r and δ=0 for rij ≠ r). The range of r is considered from 0 to the dimension of the simulation box. The distance between PEDOT chains was estimated by calculating the radial distribution function gP-P(r) for the carbon atoms in the backbone belonging to different PEDOT chains. Hence, particles of type A correspond to the carbon atoms of one chain and particles of type B belong to the carbon atoms of the remaining chains. Then, the gP-P(r) is evaluated for all PEDOT chains. In a similar way, the distance between SO3 from TOS and Sulfur atoms from PEDOT was estimated by calculating the radial distribution function gS-S(r). Particles of type A correspond to the S atoms in the PEDOT chains and particles of type B are the S atoms from SO3 belonging to TOS. Ab initio Calculations: Doped PEDOT belongs to p-type material where charge carriers correspond to positive holes. In conducting polymers including PEDOT the strong electronlattice interaction leads to charge localization turning holes into quasiparticles such as polarons


7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 38

and bipolarons that are localized over several monomer units33,34,37,68. Note that polarons and bipolarons also remain localized in π-π stacked chains (crystallites) because the inter-chain hopping is an order of magnitude weaker than the intra-chain one42. In order to account for localized nature of charge carriers in PEDOT, we calculated the partial charges on each atom of PEDOT chain and TOS molecules using first-principles density-functional theory (DFT) with the functional WB97XD69 and the 6-31+g(d) basis set70 as implemented in Gaussian package71. The partial charge per atom were taken from the fitting to electrostatic potential (ESP)72 population analysis as implemented in Gaussian suite71. A charge distribution for representative charge concentration ch = 33% and ch = 18% is shown in Figure S3.

3. Results and Discussion

We start with a diluted water solution of PEDOT chains and TOS counterions (Figure 1a) and gradually evaporate water in order to reach a dry phase in a similar way as it has been done in an experimental study of Polymbiny et al27. We consider PEDOT chains with a relative concentration of holes per monomer of up to ch = 33%, i.e. up to one charge per three monomers (note that ch = 33% corresponds to pristine PEDOT:TOS). The distribution of charges in the PEDOT chains was calculated by the density-functional theory as described in Section 2. The chain length of PEDOT is not known exactly experimentally but is estimated to be in the range of N=10-20 monomer units depending on the synthesis method employed3,29. In our calculations we consider chains with a number of monomers N=3, 6, 12 and 18. (Note that in chemistry, molecular units consisting of a few monomer lengths are usually referred to as oligomers as opposed to polymers, which consist of many monomer units. However, in all papers PEDOT is


8

Page 9 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


referred to as a polymer, and because the boundary between “few” and “many” is rather diffuse, to be consistent with the literature we will also refer to the PEDOT in our system as a polymer, even for the case of N=3). PEDOT chains and TOS counterions were randomly located in a cubic computational box 12×12×12 nm3 solvated by water molecules (see Figure 1b) and then equilibrated to let the crystal nucleation take place in the solution. Figure 1c exhibits a representative snapshot of the system after the equilibration is achieved. It shows a structure that comprises crystallites (aggregates of several π-π stacked PEDOT chains). The PEDOT chains in crystallites are π-π stacked with a stacking distance rπ-π ≈ 3.45 Å. This means that the crystal nucleation occurs spontaneously in the aqueous solution, which is known for similar polymeric systems73,74 The crystallites are embedded in an amorphous matrix of PEDOT chains. (We define the amorphous matrix as a part of the polymeric structure that is not aggregated in crystallites). Proceeding with water evaporation and performing the equilibration on each evaporation step we arrive to a dry system as illustrated in Figure 1d. In the dry phase PEDOT chains and crystallites are apparently situated closer to each other as compared to the aqueous solution, but the crystallite structure is clearly preserved (Figure 1e). In addition, a formation of lamellar structures can be seen when crystallites are stacked parallel to each other with a typical stacking (lamella) distance of rlam ≈ 12.5 Å, see Figure 1f. TOS counterions are located either on the top of the chains or on the side of the crystallites with no apparent periodic arrangement.


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 38

Figure 1. (a) Molecular structure of PEDOT and TOS. (b)-(e) Snapshots of the PEDOT:TOS structures. PEDOT is shown in blue, TOS in green and water in light blue; for clarity, water is not shown in (c)-(f). (b) Random initial position of PEDOT chains, TOS and water in 12×12×12 nm3 computational box; PEDOT chain length N = 12, ch = 33%.(c) Aqueous PEDOT:TOS solution after equilibration time of 20 ns; water content is 82% w/w (only thiophene rings and sulphur atoms from TOS are showed for clarity). (d) PEDOT:TOS in a dry phase after five steps of water evaporation (H and O atoms and methyl groups from TOS are not shown for clarity). (e) A zoom of a representative crystallite from (d) with the indicated distances rSO3-S (in Å) between sulphur atoms of PEDOT and TOS. α and β mark TOS molecules, which contribute to respective peaks in Figure 3e. (f) Previous crystal rotated 90° (left) and a neighboring crystallite (right). Molecular images were prepared using VMD75


10

Page 11 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Snapshots of the aqueous PEDOT:TOS solution for different chain length N=3, 6 and 18; water content is 82% w/w, ch = 33%. (Only thiophene rings in PEDOT chains and sulphur atoms from TOS are showed for clarity; water is not displayed). Representative percolative paths for charge carriers in PEDOT chains are indicated in green. (Percolative paths connect neighboring carbon atoms on the same PEDOT chain or on π-π stacked chains). Figure 2 shows the corresponding snapshots for different chain lengths N=3, 6 and 18, respectively. It is believed that the chain length N has a tremendous impact on the mobility76. However, our calculations indicate that this is not the case. Indeed, the crystallites are effectively connected via π-π stacked PEDOT chains such that percolative paths in the structure are formed for all chain lengths. Some representative percolative paths are shown by green lines in Figure 2. (We define percolative paths as those where charges can jump along the same PEDOT chain or between the neighboring π-π stacked chains). Even in the case of the shortest chains, N = 3, the percolative paths due to π-π stacked chains can effectively connect different regions of the PEDOT structure. In order to quantify these observations and characterize structural conformation and morphology changes along the evaporation process, X-ray diffraction, radial distribution functions and geometric conformation parameters describing bending and twisting were


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 38

calculated. X-ray diffraction patterns were simulated as described by Coleman et. al.77 and implemented in LAMMPS suite60. The Bragg reflection angle, 2θ, is related to the scattering vector Q by the relation Q=(4π /λ)sin(2θ) (with λ being the wavelength of CuKα1, λKα1 = 1.540593 Å typically used in GIWAXS studies16,28,30,46,47,78). The diffraction patterns were calculated for PEDOT:TOS structure for different water contents, PEDOT chain lengths and carrier concentrations, see Figure 3a-c. They all reveal a pronounced peak centered around Q=1.8 Å-1 corresponding to the distance d =2π/Q ≈ 3.5 Å. The peak, as expected, matches the ππ stacking distance rπ-π and hence corresponds to the formation of crystallites. The mean size of the crystallites, L, in the π-π stacking direction can be evaluated using the Scherrer’s equation79, =

∆ !"

,

(2)

where ∆2θ is the full width at the half maximum of the peak, and K ≈ 0.93 is the shape factor. Equation 2 gives values of L ≈ 14-16 Å corresponding to the PEDOT crystallites consisting of Nchains = 4-5 π-π stacking chains, which agrees well with the experimental data from GIWAXS measurements

16,28,30

. It is noteworthy that Equation 2 should be used with additional care when

applied to interpretation of the experimental data because there are a number of factors that can affect the value of the shape factor K and a measured value of ∆2θ. This includes accounting for the finite grain size, grain size to the film thickness, shape of grains (e.g. spherical vs cylindrical), and the effect of the final resolution in experimental measurements80. All these factors can contribute to an uncertainty in experimentally reported values of the size of crystallites. However, we stress that these limitations of the Scherrer’s equation concern an interpretation of the experimental data but not the calculated results. This is because the calculated size of crystallites as extracted from Equation (2) can be directly verified by the


12

Page 13 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


analysis of the calculated distribution functions, which are not accessible experimentally (see Figure 3d and corresponding discussion in the text below). While the broadening of the diffraction peak is inversely proportional to the size of the crystallites, the height of the peak is proportional to a relative volume occupied by crystallites. Figure 3a shows an evolution of the diffraction peak during water evaporation. As water evaporates the peaks becomes higher and wider, which means that the mean size of the crystallites decreases (from Nchains=5 to Nchains=4 chains), and the relative volume occupied by crystallites increases, c.f. Figures 1c and 1d. Since a number of chains in the crystallites do not change significantly as water evaporates, we conclude that the crystallites are already formed during the initial stage of the system evolution. Note that in a realistic system one can expect that crystallization occurs simultaneously with polymerization. A description of the polymerization is beyond the classical MD simulations used in the present study because it requires a description of the formation of chemical bonds. This description, in turn, would involve a utilization of computationally expensive first-principle approaches, which would greatly limit the size of computational domain making it difficult to address morphology of realistic polymers. Because within our MD approach it is not possible to study crystallization for the system when polymer chain length growths, to address the effect of polymerization we instead investigate the morphology of PEDOT chains for different chain lengths. Note that this question is also interesting because, as mentioned previously, the exact length of PEDOT chains is not known experimentally. Figures 3b shows the diffraction patterns calculated for PEDOT of different chain lengths N. All diffraction patterns are practically indistinguishable, which indicates that the morphology of PEDOT is independent of the chain length N. This finding strongly suggests that our simulations provide accurate results for the morphology even though we did not account for


13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 38

polymerization during crystallization. Note that we also calculated the solvent accessible surface area (SASA) for PEDOT chains (which gives an area probed by a rolled sphere representing a water molecule), and the distribution function gS-O(r) of distances between S from PEDOT chains and O from water molecules, see Supplementary information, Figure S5. Both SASA and gS-O(r) are also practically insensitive to the chain length N, which reflects the fact that water is equally effective as a solvent for polymers of different lengths N. As the water concentration is reduced below 45% w.t. an additional peak at Q=0.45 Å-1 becomes discernable. This peak corresponds to the formation of periodic lamellar structures with the stacking distance rlam ≈ 12.5 Å as illustrated in Figure 1f. Note that in experimental GIWAXS patterns this peak is much more pronounced. We attribute this to the effect of the substrate, which is instrumental in ordering of crystallites in the same direction. A radial distribution function gP-P(r) for the distance between PEDOT chains provides complementary information to the diffraction pattern, see Figure 3d. It exhibits sharp peaks at the integer values of 1 ≤ r/rπ-π ≤ 6, which describes a formation of crystallites consisting of up to 6 chains. This is consistent with the crystallite’s size calculated from the Scherrer’s equation (2). As water is evaporated a broad background for r/rπ-π > 1 develops, which reflects the fact that crystallites aggregate and move closer to each other.


14

Page 15 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. (a)-(c) X-Ray Diffraction Patterns of PEDOT:TOS for (a) different water content, (b) different chain length N, (c) different carrier concentration ch. In (a) ch = 33.3%, N = 12; in (b) dry sample, ch = 33.3%; in (c) dry sample, N = 12; (d) radial distribution function gP-P(r) for the distance between PEDOT chains; ch = 33.3%, N = 12; (e)-(f) radial distribution function gS-S(r) for the distance between SO3 from TOS and Sulfur from PEDOT for the case of (e) different carrier concentrations for water content 13% w/w and (f) different carrier distribution over chains; N = 12, dry sample. Counterions corresponding to peaks α and β are marked in Figure 1e. Details of carrier distributions in f) are outlined in Table S1. Spatial distribution of counterions around PEDOT chains have been determined by calculating the distribution function gS-S(r) for the distance between SO3 from TOS and S from PEDOT, Figures 3e-f. Figure 3e shows gS-S(r) for PEDOT:TOS for one representative water content. For lower charge concentration, ch = 8.3%, function gS-S(r) shows a peak at r ≈ 9 Å (marked “β” in Figure 3e), which corresponds to TOS counterions that are mostly located on the side of the


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 38

crystallites. As the charge concentration increases, more counterions move closer to the top of crystallites to screen positive charges there. As a result, a new peak at r ≈ 4 Å develops, (marked “α” in Figure 3e). TOS counterions contributing to the peaks α and β are shown in Figure 1e for a representative PEDOT:TOS structure. Note that relative intensities of both peaks “α” and “β” are the same for different water content, which means that the counterion distribution is primarily affected by the charge density and is rather insensitive to the water content (see Figure S4 in the Supporting Information). In our calculation we used a fixed charge distribution as described in Sec. 2 (Ab initio calculations). When electron transport takes place the charge distribution can change as a result of electronic transition between different states. A typical hopping time τel between electronic states in PEDOT is 0.01-1 ps40,81, which is several orders of magnitude faster than the typical time τconf associated with a conformational motion of polymer backbones seen in the MD simulations (10 ps-1ns). This means that many electron transitions take place during time τconf. Because τconf >> τel the polymer chain is not able to change its conformation (and thus the charge distribution) after each electronic transition. This justifies the utilization of the fixed charge distribution in MD simulations. Most importantly, a single electronic transition has very little effect on the total charge distribution because the latter is determined by the contribution of all electrons in all atoms in the PEDOT chain (not only π-electrons residing on carbon backbone and responsible for electronic transitions). This is illustrated in Figure S3 which shows that a relative charge distribution for different concentrations exhibits very similar patterns. To further investigate the effect of the charge distribution we calculate the diffraction pattern of PEDOT for the cases of different charge concentration, ch, see Figure 3c. All curves are practically identical and are peaked at the same Q, which means that the π-π stacking distance


16

Page 17 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and the crystallite sizes are not sensitive to the hole concentration ch. Finally, we note that for a given total average concentration ch, the distribution function gS-S(r) is the same regardless whether charges are distributed homogeneously over chains or not, see Figure 3f. This behavior of gS-S(r) provides a direct justification of the utilization of the fixed charge distribution. To reveal the geometrical conformation of PEDOT chains we calculate the angles between the first and last rings in the chain (θ) and dihedral angles between neighboring units along the backbone (Φ), see Figure 4a. The angle θ describes the bending of the chains as a whole, whereas the dihedral angle Φ quantifies the local twisting and bending between the neighboring monomers. Figures 4e-g show the probability functions P(Φ) and P(θ) for PEDOT:TOS for different chain lengths and water content. As expected, P(Φ) is not sensitive to the chain length N, because Φ is primarily affected by the local environment. In contrast, the distribution P(θ) is broader for longer chains because the local bending adds up for the whole chain. For example, in the dry phase, PEDOT chains with N=18 are bent in a broad interval 20° < θ < 140°, as compared to the case N=12 where 10° < θ < 90°. Also, as the water evaporates the distribution P(θ) broadens because the crystallites get closer and stronger affect each other. In order to visualize the bending of the polymer chains we plot all the chains in the system with their first ring aligned, see Figure 4b-d. This representation provides a graphical interpretation of the distribution function P(θ), outlining the fact that P(θ) becomes broader for longer polymer chains. A bending of polymeric chains is often characterized by the persistence length, lP., giving the length scale over which the correlation of the angles between different chain segments is lost. It is calculated using the equation82,


17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

.

〈cos ' ,( 〉 = exp ,− 0 ./

Page 18 of 38

(3)

where γ1,j is the angle between the 1st and jth rings (see Figure 4a), lj is the length of the polymer segment between 1st and jth rings measured along the chain, and stands for averaging. For entangled spaghetti-like polymers the distribution plotted in a logarithmic scale is expected to show a linear dependence with the slope defined by (lP)-1. Figure 4 i-k shows a calculated ln() for different chain length and for different water content for PEDOT:TOS. The calculated dependencies show strong deviations from the linear behavior and exhibit saturation for polymer segments of the length 1( ≳ 10. This means that for the system at hand the angle correlation between the different chains does not decay exponentially. We attribute this behavior to formation of crystallites that introduce stiffness to the chains and prevent their entangled behavior. Figure 4 h shows a persistence length of polymers of different lengths for the different solvent content obtained by fitting of Eq. (3) in the region 1( ≲ 10 (i. e. where shows the exponential decay). As expected, the lP decreases as the chain length and water content increase because the polymers become more flexible (which is also reflected in the angular distribution function P(θ), Figure 4e-g). Even for the longest considered chains, N=18, the persistent length remains comparable to the chain length. (Note however that there is an ambiguity in extraction of lP from Eq. (1) because of the saturation and non-exponential decay of the angle correlation; note also that alternative definitions of the persistent length were discussed in Ref.83).


18

Page 19 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. (a) Definition of angles θ, Φ, and γ1,j. (b)-(d) Bending of polymer chains is visualized by plotting them with their first ring aligned; chain lengths N = 6, 12, 18 respectively; water content is 13% w/w. (e)-(g) Probability distribution functions P(Φ) and P(θ) for the angles between the first and last rings in the chain, θ, and the dihedral angles between neighboring units, Φ. (i)-(k) Logarithm of averaged cosine of γ1,j measured at different solvent content and with different chain lengths. The straight lines show a liner fit according to Eq. (3). (h) The calculated persistence length lP for different chain length and water content.

ch=33% for all

plots.


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 38

4. Conclusions

In conclusion, morphology and crystallization of doped conducting polymer PEDOT:TOS was studied using atomistic molecular dynamics simulations. Special attention was given to the role of water and to changes in morphology under the transition from the aqueous solution to the dry phase. Our main findings are as follows. (a) PEDOT chains are aggregated in crystallites consisting of 3-6 π-π stacked chains. The crystallites are embedded in an amorphous matrix of PEDOT chains and are linked by interpenetrating π-π stacked chains such that percolative paths in the structure are formed. The percolative paths are effectively formed even for short chains, N = 3, which indicates that long chains are not needed to achieve the high mobility. (b) The size of crystallites depends on the water content but the π-π stacked distance is practically independent to the chain length, charge concentration and water content. (c) TOS counterions are located either on the top of the chains or on the side of the crystallites and their distribution depends on the charge concentration but is rather independent to the water content. (d) PEDOT chains and crystallites exhibit bending which depends on their length and water content.

ASSOCIATED CONTENT Supporting Information X-ray diffraction patterns of PEDOT:TOS calculated for two different sample realizations corresponding to different random initial positions of PEDOT chains, counterions and water. Radial distribution function gS-S(r) for the distance between SO3 from TOS and Sulfur from PEDOT at different charge carrier concentration and different water content. Comparison of


20

Page 21 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


different Force Fields used in the molecular dynamics simulations. Definition of Mixures 1 - 3 in Figure 3f containing different proportions of PEDOT chains with different charge concentration. Charge distribution in a PEDOT chain for two different hole concentrations. SASA (Solvent accessible surface area) analysis performed on PEDOT:TOS. The Supporting Information is available free of charge on the ACS Publications website as a PDF file.

AUTHOR INFORMATION Corresponding Author Igor Zozoulenko *E-mail: [email protected] tel.: +46 11 363319 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest ACKNOWLEDGMENT This work was supported by the Swedish Energy Agency (grant 38332-1), and Knut and Alice Wallenberg Foundation (Project “The Tail of the Sun”). The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at NSC


21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 38

We greatly appreciate discussions with Robert Brooke, Drew Evans, Sandeep Kumar Singh, Xavier Crispin, Magnus Berggren, Roger Gabrielsson and Mats Sandberg.

REFERENCES (1)

Martin, D. C.; Wu, J.; Shaw, C. M.; King, Z.; Spanninga, S. a.; Richardson-Burns, S.; Hendricks, J.; Yang, J. The Morphology of Poly(3,4-Ethylenedioxythiophene). Polym. Rev. 2010, 50, 340–384.

(2)

Groenendaal, L.; Zotti, G.; Aubert, P. H.; Waybright, S. M.; Reynolds, J. R. Electrochemistry of poly(3,4-Alkylenedioxythiophene) Derivatives. Adv. Mater. 2003, 15, 855–879.

(3)

Elschner, A. PEDOT : Principles and Applications of an Intrinsically Conductive Polymer; CRC Press, 2011.

(4)

Shi, H.; Liu, C.; Jiang, Q.; Xu, J. Effective Approaches to Improve the Electrical Conductivity of PEDOT:PSS: A Review. Adv. Electron. Mat. 2015, 1, 1500017.

(5)

Nilsson, B. D.; Chen, M.; Kugler, T.; Remonen, T.; Armgarth, M.; Berggren, M. Bi-Stable and Dynamic Current Modulation in Electrochemical Organic Transistors. Adv. Mater. 2002, 14, 51–54.

(6)

Zhu, Z.; Mabeck, J. T.; Zhu, C.; Cady, N. C.; Batt, A.; Malliaras, G. G. A Simple PEDOT:PSS Transistor for Glucose Sensing at Neutral pH. Chem. Commun. 2004, 1556– 1557.


22

Page 23 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(7)

Tehrani, P.; Hennerdal, L.; Dyer, A. L.; Reynolds, R.; Berggren, M. Improving the Contrast of All-Printed Electrochromic Polymer on Paper Displays. J. Mater. Chem. 2009, 19, 1799–1802.

(8)

Isaksson, J.; Nilsson, D.; Robinson, N. D.; All, P. K. J.; Berggren, M.; Richter-dahlfors, A. Electronic Control of Ca2+ Signalling in Neuronal Cells Using an Organic Electronic Ion Pump. Nat. Mater. 2007, 6, 673–679.

(9)

Guimard, N. K.; Gomez, N.; Schmidt, C. E. Conducting Polymers in Biomedical Engineering. Prog. Polym. Sci. 2007, 32, 876–921.

(10)

Jonsson, A.; Song, Z.; Nilsson, D.; Meyerson, B. A.; Simon, D. T.; Linderoth, B.; Berggren, M. Therapy Using Implanted Organic Bioelectronics. Sci. Adv. 2015, 1, 1–7.

(11)

Malti, A.; Edberg, J.; Granberg, H.; Khan, Z. U.; Andreasen, J. W.; Liu, X.; Zhao, D.; Zhang, H.; Yao, Y.; Brill, J. W.; et al. An Organic Mixed Ion – Electron Conductor for Power Electronics. Adv. Sci. 2016, 3, 1500305.

(12)

Cai, M.; Ye, Z.; Xiao, T.; Liu, R.; Chen, Y.; Mayer, R. W.; Biswas, R.; Ho, K.; Shinar, R.; Shinar, J. Extremely Efficient Indium – Tin-Oxide-Free Green Phosphorescent Organic Light-Emitting Diodes. Adv. Mater. 2012, 24, 4337–4342.

(13)

Stutzmann, N.; Friend, R. H.; Sirringhaus, H. Self-Aligned, Vertical-Channel, Polymer Field-Effect Transistors. Science. 2003, 299, 1881–1885.

(14)

Sun, K.; Zhang, S.; Li, P.; Xia, Y.; Zhang, X.; Du, D.; Isikgor, F. H.; Ouyang, J. Review on Application of PEDOTs and PEDOT:PSS in Energy Conversion and Storage Devices.


23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 38

J. Mater. Sci. Mater. Electron. 2015, 26, 4438–4462. (15)

Lang, U.; Muller, E.; Naujoks, N.; Dual, J. Microscopical Investigations of PEDOT:PSS Thin Films. Adv. Funct. Mater. 2009, 19, 1215–1220.

(16)

Takano, T.; Masunaga, H.; Fujiwara, A.; Okuzaki, H.; Sasaki, T. PEDOT Nanocrystal in Highly Conductive PEDOT:PSS Polymer Films. Macromolecules 2012, 45, 3859–3865.

(17)

Fabretto, M. V; Evans, D. R.; Mueller, M.; Zuber, K.; Short, R. D.; Wallace, G. G.; Murphy, P. J. Polymeric Material with Metal-like Conductivity for next Generation Organic Electronic Devices Polymeric Material with Metal-like Conductivity for next Generation Organic Electronic Devices. Chem. Mater. 2012, 24, 1–6.

(18)

Kim, N.; Lee, B. H.; Choi, D.; Kim, G.; Kim, H.; Kim, J. R.; Lee, J.; Kahng, Y. H.; Lee, K. Role of Interchain Coupling in the Metallic State of Conducting Polymers. Phys. Rev. Lett. 2012, 109, 3–4.

(19)

Ionescu-Zanetti, C.; Mechler, A.; Carter, S. a.; Lal, R. Semiconductive Polymer Blends: Correlating Structure with Transport Properties at the Nanoscale. Adv. Mater. 2004, 16, 385–389.

(20)

DeLongchamp, D. M.; Vogt, B. D.; Brooks, C. M.; Kano, K.; Obrzut, J.; Richter, C. A.; Kirillov, O. A.; Lin, E. K. Influence of a Water Rinse on the Structure and Properties of poly(3,4-Ethylene dioxythiophene):Poly(styrene Sulfonate) Films. Langmuir 2005, 21, 11480–11483.

(21)

Kline, R. J.; McGehee, M. D.; Kadnikova, E. N.; Liu, J.; Fréchet, J. M. J.; Toney, M. F.


24

Page 25 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Dependence of Regioregular poly(3-Hexylthiophene) Film Morphology and Field-Effect Mobility on Molecular Weight. Macromolecules 2005, 38, 3312–3319. (22)

Kline, R. J.; McGehee, M. D.; Toney, M. F. Highly Oriented Crystals at the Buried Interface in Polythiophene Thin-Film Transistors. Nat. Mater. 2006, 5, 222–228.

(23)

Crispin, X.; Jakobsson, F. L. E.; Crispin, a; Grim, P. C. M.; Andersson, P.; Volodin, a; van Haesendonck, C.; Van der Auweraer, M.; Salaneck, W. R.; Berggren, M. The Origin of the High Conductivity of poly(3,4-Ethylenedioxythiophene)-Poly(styrenesulfonate) (PEDOT- PSS) Plastic Electrodes. Chem. Mater. 2006, 18, 4354–4360.

(24)

Nardes, A. M.; Kemerink, M.; Janssen, R. A. J.; Bastiaansen, J. A. M.; Kiggen, N. M. M.; Langeveld, B. M. W.; Van Breemen, A. J. J. M.; De Kok, M. M. Microscopic Understanding of the Anisotropic Conductivity of PEDOT:PSS Thin Films. Adv. Mater. 2007, 19, 1196–1200.

(25)

Wei, Q.; Mukaida, M.; Naitoh, Y.; Ishida, T. Morphological Change and Mobility Enhancement in PEDOT:PSS by Adding Co-Solvents. Adv. Mater. 2013, 25, 2831–2836.

(26)

Van De Ruit, K.; Cohen, R. I.; Bollen, D.; Van Mol, T.; Yerushalmi-Rozen, R.; Janssen, R. A. J.; Kemerink, M. Quasi-One Dimensional in-Plane Conductivity in Filamentary Films of PEDOT:PSS. Adv. Funct. Mater. 2013, 23, 5778–5786.

(27)

Palumbiny, C. M.; Liu, F.; Russell, T. P.; Hexemer, A.; Wang, C.; Müller-Buschbaum, P. The Crystallization of PEDOT:PSS Polymeric Electrodes Probed in Situ during Printing. Adv. Mater. 2015, 27, 3391–3397.


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(28)

Page 26 of 38

Palumbiny, C. M.; Schlipf, J.; Hexemer, A.; Wang, C.; Müller-Buschbaum, P. The Morphological Power of Soap: How Surfactants Lower the Sheet Resistance of PEDOT:PSS by Strong Impact on Inner Film Structure and Molecular Interface Orientation. Adv. Electron. Mater. 2016, 2, 1500377.

(29)

Ugur, A.; Katmis, F.; Li, M.; Wu, L.; Zhu, Y.; Varanasi, K. K.; Gleason, K. K. LowDimensional Conduction Mechanisms in Highly Conductive and Transparent Conjugated Polymers. Adv. Mater. 2015, 27, 4604–4610.

(30)

Gueye, M. N.; Carella, A.; Massonnet, N.; Yvenou, E.; Brenet, S.; Okuno, H.; Benayad, A.; Demadrille, R.; Simonato, J. Structure and Dopant Engineering in PEDOT Thin Films: Practical Tools for a Dramatic Conductivity Enhancement. Chem. Mater. 2016, 28, 3462.

(31)

Petsagkourakis, I.; Pavlopoulou, E.; Portale, G.; Kuropatwa, B. A.; Dilhaire, S.; Fleury, G.; Hadziioannou, G. Structurally-Driven Enhancement of Thermoelectric Properties within Poly ( 3 , 4-Ethylenedioxythiophene ) Thin Films. Sci. Rep. 2016, 6, 305101.

(32)

Rivnay, J.; Inal, S.; Collins, B. A.; Sessolo, M.; Stavrinidou, E.; Strakosas, X.; Tassone, C.; Delongchamp, D. M.; Malliaras, G. G. Structural Control of Mixed Ionic and Electronic Transport in Conducting Polymers. Nat. Commun. 2016, 7, 11287.

(33)

Van Haare, J. A. E. H.; Havinga, E. E.; Van Dongen, J. L. J.; Janssen, R. A. J.; Cornil, J.; Brédas, J. L. Redox States of Long Oligothiophenes: Two Polarons on a Single Chain. Chem. - A Eur. J. 1998, 4, 1509–1522.

(34)

Zamoshchik, N.; Bendikov, M. Doped Conductive Polymers: Modeling of Polythiophene with Explicitly Used Counterions. Adv. Funct. Mater. 2008, 18, 3377–3385.


26

Page 27 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(35)

Bubnova, O.; Khan, Z. U.; Wang, H.; Braun, S.; Evans, D. R.; Fabretto, M.; HojatiTalemi, P.; Dagnelund, D.; Arlin, J.; Geerts, Y. H.; et al. Semi-Metallic Polymers. Nat. Mater. 2014, 13, 190–194.

(36)

Tanaka, H.; Nishio, S.; Ito, H.; Kuroda, S. I. Microscopic Signature of Insulator-to-Metal Transition in Highly Doped Semicrystalline Conducting Polymers in Ionic-Liquid-Gated Transistors. Appl. Phys. Lett. 2015, 107, 243302.

(37)

Dkhissi, A.; Beljonne, D.; Lazzaroni, R.; Louwet, F.; Groenendaal, B. Modeling of the Solid-State Packing of Charged Chains (PEDOT) in the Presence of the Counterions (TSA) and the Solvent (DEG). Theor. Chem. Acc. 2008, 119, 305–312.

(38)

Van Der Holst, J. J. M.; Van Oost, F. W. A.; Coehoorn, R.; Bobbert, P. A. Monte Carlo Study of Charge Transport in Organic Sandwich-Type Single-Carrier Devices: Effects of Coulomb Interactions. Phys. Rev. B - Condens. Matter Mater. Phys. 2011, 83, 1–13.

(39)

Stallinga, P. Electronic Transport in Organic Materials: Comparison of Band Theory with Percolation/(variable Range) Hopping Theory. Adv. Mater. 2011, 23, 3356–3362.

(40)

Ihnatsenka, S.; Crispin, X.; Zozoulenko, I. V. Understanding Hopping Transport and Thermoelectric Properties of Conducting Polymers. Phys. Rev. B 2015, 92, 35201.

(41)

Shi, W.; Zhao, T.; Xi, J.; Wang, D.; Shuai, Z. Unravelling Doping Effects on PEDOT at the Molecular Level: From Geometry to Thermoelectric Transport Properties. J. Am. Chem. Soc. 2015, 137, 12929–12938.

(42)

Munoz, W. A.; Singh, S. K.; Linares, M.; Crispin, X.; Zozoulenko, I. V. Insulator to


27


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 38

Semimetallic Transition in Conducting Polymers. Phys. Rev. B 2016, 94, 205202. (43)

Nardes, A. M.; Janssen, R. A. J.; Kemerink, M. A Morphological Model for the SolventEnhanced Conductivity of PEDOT:PSS Thin Films. Adv. Funct. Mater. 2008, 18, 865– 871.

(44)

Noriega, R.; Rivnay, J.; Vandewal, K.; Koch, F. P. V; Stingelin, N.; Smith, P.; Toney, M. F.; Salleo, A. A General Relationship between Disorder, Aggregation and Charge Transport in Conjugated Polymers. Nat. Mater. 2013, 12, 1038–1044.

(45)

Zhang, X.; Bronstein, H.; Kronemeijer, A. J.; Smith, J.; Kim, Y.; Kline, R. J.; Richter, L. J.; Anthopoulos, T. D.; Sirringhaus, H.; Song, K.; et al. Molecular Origin of High FieldEffect Mobility in an Indacenodithiophene-Benzothiadiazole Copolymer. Nat. Commun. 2013, 4, 2238.

(46)

Wang, S.; Fabiano, S.; Himmelberger, S.; Puzinas, S.; Crispin, X.; Salleo, A.; Berggren, M. Experimental Evidence That Short-Range Intermolecular Aggregation Is Sufficient for Efficient Charge Transport in Conjugated Polymers. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 10599–10604.

(47)

Aasmundtveit, K. E.; Samuelsen, E. J.; Inganäs, O.; Pettersson, L. A. A.; Johansson, T.; Ferrer, S. Structural Aspects of Electrochemical Doping and Dedoping of poly(3,4Ethylenedioxythiophene). Synth. Met. 2000, 113, 93–97.

(48)

Hexemer, A.; Muller-Buschbaum, P. Advanced Grazing-Incidence Techniques for Modern Soft-Matter Materials Analysis. IUCrJ 2015, 2, 106–125.


28

Page 29 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(49)

Kim, E. G.; Brédas, J. L. Electronic Evolution of poly(3,4-Ethylenedioxythiophene) (PEDOT): From the Isolated Chain to the Pristine and Heavily Doped Crystals. J. Am. Chem. Soc. 2008, 130, 16880–16889.

(50)

Lenz, A.; Kariis, H.; Pohl, A.; Persson, P.; Ojamäe, L. The Electronic Structure and Reflectivity of PEDOT:PSS from Density Functional Theory. Chem. Phys. 2011, 384, 44– 51.

(51)

Poater, J.; Casanovas, J.; Solà, M.; Alemán, C. Examining the Planarity of poly(3,4Ethylenedioxythiophene): Consideration of Self-Rigidification, Electronic, and Geometric Effects. J. Phys. Chem. A 2010, 114, 1023–1028.

(52)

Zanuy, D.; Alemán, C. Resolving the Subnanometric Structure of Ultrathin Films of poly(3,4-Ethylenedioxythiophene) on Steel Surfaces: A Molecular Modeling Approach. Soft Matter 2013, 9, 11634.

(53)

Bhowmik, R.; Berry, R. J.; Varshney, V.; Durstock, M. F.; Leever, B. J. Molecular Modeling of Interfaces between Hole Transport and Active Layers in Flexible Organic Electronic Devices. J. Phys. Chem. C 2015, 119, 27909.

(54)

Urban, A.; Seo, D.-H.; Ceder, G. Computational Understanding of Li-Ion Batteries. npj Comput. Mater. 2016, 2, 16002.

(55)

Zhou, H.-X. Theoretical Frameworks for Multiscale Modeling and Simulation. Curr. Opin. Struct. Biol. 2014, 25, 67–76.

(56)

Bubnova, O.; Khan, Z. U.; Malti, A.; Braun, S.; Fahlman, M.; Berggren, M.; Crispin, X.


29


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 38

Optimization of the Thermoelectric Figure of Merit in the Conducting Polymer Poly ( 3 , 4-Ethylenedioxythiophene ). Nat. Mater. 2011, 10, 429–433. (57)

Massonnet, N.; Carella, A.; de Geyer, A.; Faure-Vincent, J.; Simonato, J.-P. Metallic Behaviour of Acid Doped Highly Conductive Polymers. Chem. Sci. 2015, 6, 412–417.

(58)

Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and Testing of a General Amber Force Field. J. Comput. Chem. 2004, 25, 1157–1174.

(59)

Jewett, A. Moltemplate www.moltemplate.org (accessed Nov 18, 2015).

(60)

Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1–19.

(61)

Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. Interaction Models for Water in Relation to Protein Hydration. In Intermolecular Forces: Proceedings of the Fourteenth Jerusalem Symposium on Quantum Chemistry and Biochemistry Held in Jerusalem, Israel, April 13--16, 1981; Pullman, B., Ed.; Springer Netherlands: Dordrecht, 1981; pp 331–342.

(62)

Shinoda, W.; Shiga, M.; Mikami, M.; Carlo, M. Rapid Estimation of Elastic Constants by Molecular Dynamics Simulation under Constant Stress. Phys. Rev. B 2004, 69, 1–8.

(63)

Martyna, G. J.; Tobias, D. J.; Klein, M. L.; Martyna, G. J.; Tobias, D. J.; Klein, M. L. Constant Pressure Molecular Dynamics Algorithms. J. Chem. Phys. 1994, 101, 4177.

(64)

Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals : A New Molecular Dynamics Method. J. Appl. Phys. 1981, 52, 7182.


30

Page 31 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(65)

Tuckerman, M. E.; Alejandre, J.; Lopez-Rendon, R.; Jochim, A. L.; Martyna, G. Time A Liouville-Operator Derived Measure-Preserving Integrator for Molecular Dynamics Simulations in the. J. Phys. A. Math. Gen. 2006, 39, 5629–5651.

(66)

Jorgensen, W. L.; Tirado-rives, J.; Fields, F. Potential Energy Functions for Atomic-Level Simulations of Water and Organic and Biomolecular Systems. Proc. Natl. Acad. Sci. U.S.A 2005, 102, 6665–6670.

(67)

Hess, B.; Kutzner, C.; Van Der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435–447.

(68)

Salaneck, W. R.; Friend, R. H.; Brédas, J. L. Electronic Structure of Conjugated Polymers: Consequences of Electron–lattice Coupling. Phys. Rep. 1999, 319, 231–251.

(69)

Lin, Y. S.; Li, G. De; Mao, S. P.; Chai, J. Da. Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections. J. Chem. Theory Comput. 2013, 9, 263–272.

(70)

Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Self-Consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions. J. Chem. Phys. 1980, 72, 650– 654.

(71)

Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H. Z.; et al. Gaussian 09, Revision E.01. Gaussian, Inc. Wallingford(CT) 2009.


31


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(72)

Page 32 of 38

Singh, U. C.; Kollman, P. A. An Approach to Computing Electrostatic Charges for Molecules. J. Comput. Chem. 1984, 5, 129–145.

(73)

Harano, K.; Okada, S.; Furukawa, S.; Tanaka, H.; Nakamura, E. Formation of a Polycrystalline Film of Donor Material on PEDOT:PSS Buffer Induced by Crystal Nucleation. J. Polym. Sci. Part B Polym. Phys. 2014, 52, 833–841.

(74)

Liu, F.; Gu, Y.; Jung, J. W.; Jo, W. H.; Russell, T. P. On the Morphology of PolymerBased Photovoltaics. J. Polym. Sci. Part B Polym. Phys. 2012, 50, 1018–1044.

(75)

Humphrey, W.; Dalke, A.; Schulten, K. VMD--Visual Molecular Dynamics. J. Mol. Graph. 1996, 14, 33–38.

(76)

Bryan, A. M.; Santino, L. M.; Lu, Y.; Acharya, S.; Arcy, J. M. D. Conducting Polymers for Pseudocapacitive Energy Storage. Chem. Mater. 2016, 28, 5989.

(77)

Coleman, S. P.; Spearot, D. E.; Capolungo, L. Virtual Diffraction Analysis of Ni [0 1 0] Symmetric Tilt Grain Boundaries. Model. Simul. Mater. Sci. Eng. 2013, 21, 55020.

(78)

Seeck, O. H.; Murphy, B. M. X-Ray Diffraction : Modern Experimental Techniques; CRC Press: Taylor & Francis Group: Boca Raton, 2014.

(79)

Warren, B. E. X-Ray Diffraction; Dover Publications: New York, 1990.

(80)

Smilgies, D. M. Scherrer Grain-Size Analysis Adapted to Grazing-Incidence Scattering with Area Detectors. J. Appl. Crystallogr. 2009, 42, 1030–1034.

(81)

Kim, G.; Pipe, K. P. Thermoelectric Model to Characterize Carrier Transport in Organic Semiconductors. Phys. Rev. B - Condens. Matter Mater. Phys. 2012, 86, 1–5.


32

Page 33 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(82)

Ott, A.; Magnasco, M.; Libchaber, A. Measurement of the Persistence Lenght of Polymerized Actin Using Fluoresce Microscopy. Phys. Rev. E. 1993, 48, R1642.

(83)

Hsu, H.; Paul, W.; Binder, K. Standard Definitions of Persistence Length Do Not Describe the Local “ Intrinsic ” Stiffness of Real Polymer Chains. Macromolecules 2010, 43, 3094– 3102.


33


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 38

TOC Graphic


34

Page 35 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 1 160x119mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 2 119x40mm (300 x 300 DPI)


Page 36 of 38

Page 37 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 3 170x90mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 4 170x134mm (300 x 300 DPI)


Page 38 of 38

Molecular Dynamics Study of Morphology of ... - ACS Publications

Recommend Documents