Strong Suppression of Thermal Conductivity in the Presence of Long Terminal Alkyl Chains in Low-Disorder Molecular Semiconductors

While the charge transport properties of organic semiconductors have been extensively studied over the recent years, the field of organics-based thermoelectrics is still limited by a lack of experimental data on thermal transport and of understanding of the associated structure-property relationships. To fill this gap, a comprehensive experimental and theoretical investigation of the lattice thermal conductivity in polycrystalline thin films of dinaphtho[2,3-b:2',3'-f]thieno[3,2-b]thiophene (Cn-DNTT-Cn with n = 0, 8) semiconductors is reported. Strikingly, thermal conductivity appears to be much more isotropic than charge transport, which is confined to the 2D molecular layers. A direct comparison between experimental measurements (3ω–Völklein method) and theoretical estimations (Approach-to-Equilibrium Molecular Dynamics – AEMD – method) indicates that the in-plane thermal conductivity is strongly reduced in the presence of the long terminal alkyl chains. This evolution can be rationalized by the strong localization of the intermolecular vibrational modes in C8-DNTT-C8 in comparison to unsubstituted DNTT cores, as evidenced by a vibrational mode analysis. Combined with the enhanced charge transport properties of alkylated DNTT systems, this opens the possibility to decouple electron and phonon transport in these materials, which provides great potential for enhancing the thermoelectric figure of merit ZT .


Main Text:
Thermoelectric materials offer a simple solution for direct heat-to-electricity conversion from a variety of heat sources via the Seebeck effect.Worldwide, about 2/3 of primary energy is currently wasted as heat [1] .Therefore, there exist great opportunities for enhancing the energy efficiency of many power generation and industrial processes.Current thermoelectric materials operate far from theoretical efficiency limits.There are intense ongoing research efforts to improve efficiency and enable wider applications in waste heat harvesting [2][3][4] .One class of materials being explored for this purpose is that of organic semiconductors (OSCs).
The efficiency of a thermoelectric material is determined by the dimensionless figure of merit zT = S 2 σT/(κe+κph), where S [V K -1 ] denotes the Seebeck coefficient; σ [S m -1 ], the electrical conductivity; κe and κph [W m -1 K -1 ], the electronic and phononic components of the thermal conductivity, respectively; and T [K], the absolute value of the average temperature between the cold and hot sides.For a good thermoelectric material, it is also desirable to decouple electron and phonon transport; the notion of an electron crystalphonon glass originally proposed by Slack [5] , in which electron mean-free paths are long while phonon mean free paths are short, remains an important concept, whose implementation has been attempted in different classes of inorganic materials with skutterudites [6] and clathrates [7] being among the best known examples.
Herringbone-stacked alkylated thienoacene-based molecular materials have recently emerged as some of the best performing OSCs, a result of p-type charge carrier mobilities that can reach over 10 cm 2 V -1 s -1 [8][9][10] .Amongst this family, dinaphtho[2,3-b:2',3'-f]thieno [3,2-b]thiophene (DNTT) derivatives have been investigated in detail both experimentally and theoretically; the results point to a favorable two-dimensional character of charge transport (i.e., within the layers) [11][12][13][14][15][16][17][18] .Importantly, the origin of their high charge mobilities has recently been attributed to their reduced dynamic disorder, coupled to an isotropic electronic coupling pattern within the plane of charge transport.Indeed, alkylation has been demonstrated to: (i) shift in-plane phonon modes to higher frequencies, hence suppressing their impact on disorder; and (ii) reduce the amplitude of the out-of-plane long-axis sliding motions (the so-called killermode) [19][20][21] .Combined to good environmental stability and ease of processing through vapor and solution deposition techniques [22] , these materials thus constitute ideal candidates for thermoelectric applications.However, a detailed investigation of their ability to transport heat has not been performed yet.
To date, only few studies have been dedicated to the thermal transport properties of OSCs [23] .
The thermal conductivity in organic materials is usually assumed to be low due to lattice disorder.More specifically, the limited thermal conductivity in such systems is attributed to localization of lattice vibrations described via the Einstein model of isolated atomic oscillations [24] with heat being carried out through the lattice via random walk rather than through wavelike motions of collective oscillations [25] .The exact mechanism of phonon localization, however, is not well understood.The Einstein-like behavior was observed in small single crystals of alpha-monoclinic selenium [26] and, in spite of their microcrystallinity, in C60/C70 [27] .More recently, very low values of thermal conductivity were also found in layered WSe2 crystalswhich was speculated to be caused by phonon localization induced by random stacking of two-dimensional crystalline thin sheets [28] and in the fullerene derivatives PCBM and PCBNB [29,30] which was explained, similarly to C60/C70, by localization of vibrational modes of the rigid buckyball molecules.The in-plane and out-of-plane thermal conductivities of various systems (pentacene, Alq3, C60, rubrene, TIPS-pentacene, CuPc) [31][32][33][34][35][36] with sample ranging from polycrystals to single crystals, have been measured macroscopically using techniques such as ac-calorimetry, the 3ω method or time domain thermo-reflectance measurements and have been found to be in the range 0.1-0.8W m -1 K -1 .However, a detailed understanding of structure-property relationships remains elusive.
One reason for the lack of studies of the thermal transport properties is that thermal conductivity is a challenging transport coefficient to measure reliably.Thermal conductivity  is defined according to Fourier's heat conduction equation: , where  ̇ [W m -2 ] is the heat flux passing through the sample; Δl [m], the sample length; and ΔΤ [K], the temperature difference across the sample.Parasitic heat transfer through radiative (infrared) heat exchange with the surroundings and losses due to thermal resistance at interfaces present in virtually every experimental system create high uncertainty in the measured heat flux values [37,38] .
Another unexpectedly large uncertainty in thermal conductivity measurements comes from measurements of sample dimensions, as has been demonstrated by an international round-robin testing of bulk thermoelectric materials [39] .As a result, even for measurement setups designed in accordance with well-established measurement standards, the combined measurement uncertainty can reach up to 20% for bulk materials.Reduced sample dimensions in the case of thin films worsen the situation and the experiments require extra care at every step to keep the overall uncertainty within acceptable limits.
In this work, we report a comprehensive experimental and theoretical investigation of the lattice thermal conductivity in polycrystalline thin films of dinaphtho[2,3-b:2',3'-f]thieno [3,2b]thiophene (Cn-DNTT-Cn with n = 0, 8) semiconductors (the molecular structures are given in Figure 1 (a)).Considering the anisotropy of the material properties and the fact that DNTT molecules tend to have a preferential orientation with their long molecular axis nearly perpendicular to the substrate plane, it is important to distinguish between the in-and out-ofplane transport directions.Wang et al. [23] measured the thermal conductivity of DNTT thin films in the out-of-plane direction with the traditional 3ω-method [40] .However, in view of the potential thermoelectric applications, the thermal transport in the in-plane direction of thin films of small-molecule semiconductors is more relevant since it aligns with the direction of fast electrical transport in these materials.Here, we measured the in-plane thermal conductivity of undoped DNTT and its alkylated derivative C8-DNTT-C8 following our previously established protocol that reduces measurement uncertainty [41] .The experimental setup is schematically presented in Figure 1 (b).Thermal conductivity measurements were performed in the in-plane direction according to the 3ω-Völklein method [42,43] implemented in a commercial Linseis Thin Film Analyzer (TFA) [44] .
More information about the method and its advantages and can be found in the Supporting Information.
The samples were prepared through thermal evaporation of a DNTT layer on top of the membrane of the measurement chips using a masking shutter that allows the deposition of four different thicknesses within the same conditions.Adequate masking insured specific deposition over the active area.Grazing-Incidence Wide-Angle X-ray Scattering (GIWAXS) and Atomic Force Microscopy (AFM) investigations allowed us to analyze the film microstructures and surface morphologies as well as to determine their respective thicknesses.
The maximum thickness of the DNTT films was ~ 240 nm and all films showed a polycrystalline structure with a preferred orientation where the long molecular axis is nearly perpendicular to the substrate plane.In the case of C8-DNTT-C8 films, the growth rate was enhanced and the maximum thickness was ~ 530 nm (for similar deposition conditions, see Methods).The thinnest C8-DNTT-C8 film showed a preferred orientation while thicker C8-DNTT-C8 films showed powder-like distribution of crystallites (causing rings in the GIWAXS data) and only a slightly preferred orientation of the crystallites (peaks on rings), pointing to an edge-on orientation as in the case of DNTT (Figure S3).The AFM topography for the C8-DNTT-C8 films also revealed larger features and a higher surface roughness (Figure S4).In spite of these differences, the average crystallite size was found to be the same for all samples in the study, in the range of ~ 7-10 nm (Table S1).
As pointed out previously, parasitic heat losses at interfaces with thermal contact resistances are among the major sources of uncertainties in thermal conductivity measurements.One of the interfaces where thermal contact effects are likely to arise in the present setup is that between the sample film and the membrane (marked in red in Figure 1 (b) (inset)).The contribution from this interface can be estimated by plotting the apparent thermal resistance, , with respect to the sample thickness and approximating the intercept of the curve with the y-axis [41] .For all samples under investigation, the total thermal resistance (sample + membrane) was clearly separable from that of the empty membrane, indicating a clear contribution of the sample to the thermal response (Figure S5).
The evolutions of  ℎ versus sample thickness are presented in Figure 1 (c-d).Note that since the direction of heat transport is in the plane of the sample film, the sample thickness defines the cross-sectional area of heat transfer, not the sample length.The effective thermal resistance is thus plotted versus inverse sample thickness.Linear extrapolation of the intercepts with the y-axis including the uncertainty of the linear regression resulted in small, yet not negligible values.However, the clear linear trends for both DNTT and C8-DNTT-C8, consistent with the scaling sample cross-section, indicated that the apparent thermal resistance is dominated by the material property and that the offset is likely caused by the uncertainties associated with repeatability of thermal conductivity measurements and film thickness determination.
The temperature evolutions of the thermal conductivities of DNTT and its alkylated derivative, C8-DNTT-C8, are presented in Figure 2. Due to high thermal resistance of the films under investigation, we were able to obtain reliable data only from the effective sample area on top of the smaller membrane; as a result, it was not possible to correct for the radiative losses in these experiments.Thus, the reported data present an apparent thermal conductivity that includes thermal conduction through the material and conduction through infrared radiation; hence, the values are overestimated.The thermal conductivity decreases with temperature, which is consistent with the trend found in crystalline materials [45] .The decrease may appear statistically insignificant in case of C8-DNTT-C8; however, the trend is more evident when the error bars do not include the standard deviation associated with the thickness determination (Figure S6).Since the film thickness is not expected to change significantly as a function of temperature (substantial thermal expansion and material degradation typically occur at higher temperatures (above 100 °C [46,47] )), this standard deviation would cause an offset in the mean thermal conductivity value without changing the overall trend.We note that in the case of C8-DNTT-C8 samples, this trend was not found in the thicker films presenting only a slightly preferred orientation of crystallites, compared to the thinnest film for which the preferential alignment was clearly demonstrated (Figure S6).The most striking result, however, is the extremely low thermal conductivity of the alkylated derivative C8-DNTT-C8 compared to its non-alkylated counterpart.Since the C8-DNTT-C8 film with preferred orientation of crystallites had similarly low thermal conductivity, the thermal conductivity reduction cannot be correlated solely with the decrease in preferential alignment of crystallites.We also note that the despite the complications due to orientational changes with increasing thickness measurements of the thermal resistance as a function of inverse thickness exhibit a clear linear behaviour across the entire thickness range (Figure 1 (c-d)) for both molecules.This also suggests that orientational effects are not the dominant factor when comparing the thermal conductivity extracted for the two molecules.The room temperature value of ~ 0.05 W m -1 K -1 is comparable to the ultralow thermal conductivities observed in a few systems, such as C60/C70 [27] , layered WSe2 [28] crystals, and the fullerene derivatives PCBM and PCBNB [29,30] .
Our experimental results thus suggest that the in-plane thermal conductivity is significantly reduced by adding alkyl chains on the terminal aromatic rings.Indeed, such observations are convincingly strengthened by the following theoretical estimations.Herein, we focused exclusively on the lattice thermal conductivity since the electronic contribution to the thermal transport is expected to be weak in neutral or slightly doped OSCs [48] , see the discussion in the Supporting Information; all our experimental data were collected on undoped samples.Owing to the air stability of DNTT-based materials [22] , we do not expect significant unintentional doping by environmental contaminants (O2 and H2O).This is supported by our experience with FET devices made with the two molecules which generally exhibit very low OFF currents [21] .
We estimated the lattice thermal conductivity in single crystals made of DNTT cores and their alkylated derivatives C8-DNTT-C8 via the Approach-to-Equilibrium Molecular Dynamics (AEMD) method [49] .In essence, AEMD computes the lattice thermal conductivity of a material based on the rapid decay time of a thermal gradient initially created along a specific crystal orientation.More precisely, this property is deduced from the exponential fit of the timedecreasing temperature difference between the hot and cold region of the simulation box with an appropriate solution of the one-dimensional heat equation [49] : Therefore, the lattice thermal conductivity, κ [W m -1 K -1 ], can be straightforwardly derived from the thermal diffusivity,  = /  [m 2 s -1 ], provided that the mass density,  [kg m -3 ], and heat capacity,   [J kg -1 K -1 ], of the system are well defined.Here, we relied on the Dulong-Petit model [50] , which considers the specific heat capacity   to be strictly equal to 3R.Further description of the method, its advantages as well as an example of a typical AEMD simulation can be found in the Supporting Information.99.860° for C8-DNTT-C8; respectively [21] ) and a herringbone packing motif, which is essentially maintained by CH -π interactions in the ab plane, with the c-axis lying perpendicular with respect to the substrate plane.A linear regression through the data gives lattice thermal conductivity values of 0.79, 0.73, and 1.40 W m -1 K -1 along directions a, b, and c for DNTT and 0.35, 0.31, and 1.14 W m -1 K -1 along the same directions for C8-DNTT-C8.
In the latter case, our results are consistent with those of the theoretical work of Shi.et al., [51] who have reported very similar thermal conductivity values in the ab plane by using the NEMD method for the study of dioctyl [1]benzothieno [3,2-b][1]-benzothiophene (C8-BTBT-C8).The thermal conductivity ratios a/b, c/a, and c/b are 1.08, 1.77, and 1.92 for DNTT and 1.13, 3.26, and 3.68 for its alkylated derivative.Of notable interest is that the phonon mean free paths (MFPs), lbulk [Å], can be extracted from the analytical equations associated with the extrapolation curves.Without dwelling on theoretical concepts that have already been discussed in detail elsewhere [52][53][54] , we simply mention that such a deduction is made possible by combining the kinetic formulation of the thermal conductivity (namely,  = between molecules lying in adjacent layers [11][12][13]55,56] , the computed thermal conductivity appears to be much more isotropic, with the most efficient direction for heat transport actually corresponding to the interlayer axis. Since he 3ω-Völklein method used experimentally on the polycrystalline samples provides an isotropically averaged value through the ab plane, we have defined in turn an average thermal conductivity as κin = (κa +κb)/2 for ease of comparison with the experimental data.On that basis, the calculations indicate that the thermal conductivity is reduced within the layers upon alkylation of the DNTT core, which is fully consistent with the experimental results.In addition, this structure-property relationship is consistent with a recent joint experimental and theoretical investigation of thermal transport properties of non-alkylated and alkylated BTBT derivatives probed by Thermal Scanning Microscopy along the out-ofplane (interlayer) direction [57] .From a quantitative perspective, the effects of alkylation of DNTT lead to a decrease in the calculated in-plane thermal conductivity by a factor of ~ 2.3, with this drop being experimentally even more pronounced (a factor of ~ 4).As mentioned earlier, our experimental data on the thermal conductivity of C8-DNTT-C8 are very similar to those observed in the state-of-the-art fullerene derivatives PCBM and PCBNB; such a low thermal conductivity could be of great interest for the development of efficient thermoelectric applications.We also draw attention to the fact that the calculated in-plane thermal conductivities κin are 3.8 and 6.6 times higher for DNTT and C8-DNTT-C8 when compared to the corresponding experimental measurements.The origin of these overestimations could be threefold: (i) the predominance of the harmonic approximation in the expression of the potential energy (i.e., for bonds and angles) while anharmonic terms would yet better account for phonon-phonon interactions; (ii) the occurrence of scattering processes at grain boundaries due to the polycrystalline nature of the organic thin films, as confirmed by the GIWAXS experiments; and/or (iii) the presence of impurities that can strongly affect thermal transport by acting as phonon scattering centers.Another source of overestimation could arise from the absence of quantum corrections in our calculations; nevertheless, the Dulong-Petit model [50] can be considered as valid since the MD simulations are conducted at room temperature while the Debye temperature θD of many OSCs rarely exceeds 100 K [58,59] .It is worth noting that Wang et al. [23] reported an out-of-plane thermal conductivity κout = 0.45±0.06W m -1 K -1 for a DNTT thin film with a thickness of 50 nm, as measured at room temperature by means of the differential 3ω method.By combining this value with the current experimental data, we obtain The origin of such a strong suppression of thermal transport in the alkylated derivatives can be explained via the estimation of the participation ratio (PR) of the lattice vibrational modes [60] .
As described in the Methods Section, this parameter is derived from the diagonalization of the into the one-dimensional heat equation [49] .Note that   and   are coefficients depending on the size of the supercell, the integer  and the initially imposed temperature gradient.

Estimation of the participation ratio
We studied the vibrational properties of both DNTT and C8-DNTT-C8 by setting up and diagonalizing the dynamical matrix of one snapshot of the samples, given by: In this formula, Greek letters indicate the (x,y,z) Cartesian components while Latin indices are used for labelling atoms.Here mi is the mass of the ith atom.Fiα is the force on the ith atom along direction α and rj an infinitesimal displacement of atom j along direction β.
The calculation of the first derivative in the above equation has been performed by finite difference with an atomic displacement of 5 x 10 -4 .The dynamical matrix has then been diagonalized by means of the SLEPc library [66] by obtaining the eigenvectors es and eigenvalues ω 2 s where s = 1, . . .,3N counts eigenmodes.
The participation ratio (PR) is finally estimated as [67] :

Atomic Force Microscopy (AFM)
The measurements were performed with an MFP-3D AFM System (Asylum/Oxford Instruments) in AC (non-contact) mode.The samples thickness was obtained by calculating an average step height in the topography scans taken at the sample edges in the proximity of the four corners.

Grazing-Incidence Wide-Angle X-ray Scattering (GIWAXS)
GIWAXS measurements were performed using a Xeuss 2.0 SAXS/WAXS system (Xenocs) with a Dectris Pilatus3R 300 K detector using a wavelength of 1.5406 Å and an angle of incidence of 0.2°.For the measurements, the sample was placed in a vacuum chamber to reduce air scattering.

Figure 1 .
Figure 1.Molecular structures of the investigated materials and experimental details of the

Figure 3 .
Figure 3. Inverse of the lattice thermal conductivity as a function of the inverse of the box length

1 3𝜌𝐶 𝑝 𝜏 𝑏𝑢𝑙𝑘 2 𝑙
; where τbulk [fs] is the bulk phonon relaxation time) with the decomposition of τbulk into separate terms due to the independence of the various scattering events arising in the system, as predicted by the Matthiessen's rule.Hence, the average phonon MFPs along directions a, b, and c are 129.0, 293.0, and 129.0 Å for DNTT and 15.0, 43.6, and 44.0 Å for C8-DNTT-C8, respectively.Unexpectedly, in contrast to the generally two-dimensional character of charge transport in molecular semiconductors with very weak electronic coupling

Figure 4 .
Figure 4. (a) Estimated Participation Ratio (PR) as a function of frequency for DNTT (red) and

4 (
figure of merit ZT.The combination of molecular design and accurate investigations of charge estimation of the subgroup of atoms involved in the s-th vibrational mode.The spatial extension of such a subgroup is linked to the localized or extended nature of that mode: for extended modes PR ∼ 1, while localized modes have a smaller ratio, down to the limit PR = 1/N for a mode completely localized on a single atom.It is worth noticing that, according to its very definition, a PR exactly equal to unity is obtained solely for vibrational modes in ideal crystalline systems, in which the atomic displacements are perfectly periodic within the sample.In turn, its value rapidly decreases if tiny inhomogeneities are present in the atomistic coordinates or as a consequence of a possible numerical uncertainty in the atomic displacements.In both cases, the extended character of the vibrational modes is preserved.Calculated values of PR for extended modes in non-crystalline systems lie in the range [0.4-0.6].

TOCA
comprehensive experimental and theoretical investigation emphasizes a significant drop in in-plane thermal conductivity upon end alkylation of the aromatic rings of dinaphtho[2,3b:2',3'-f]thieno[3,2-b]thiophene, which is understood from a detailed vibrational-mode analysis.Combined with their enhanced charge transport, the results suggest the possibility to decouple electron and phonon transport in alkylated DNTT systems, which opens pathways for improved thermoelectric applications.