Letter Cite This: ACS Macro Lett. 2019, 8, 304−309
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Connecting 1D and 2D Confined Polymer Dynamics to Its Bulk Behavior via Density Scaling Karolina Adrjanowicz,*,†,‡ Roksana Winkler,†,‡ Andrzej Dzienia,‡,& Marian Paluch,†,‡ and Simone Napolitano§ †
Institute of Physics, University of Silesia, 75 Pulku Piechoty 1, 41-500 Chorzow, Poland Silesian Center for Education and Interdisciplinary Research (SMCEBI), 75 Pulku Piechoty 1a, 41-500 Chorzow, Poland & Institute of Chemistry, University of Silesia, Szkolna 9 1, 40-007 Katowice, Poland § Laboratory of Polymer and Soft Matter Dynamics, Faculté des Sciences, Université libre de Bruxelles (ULB), CP 223, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
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‡
S Supporting Information *
ABSTRACT: Under confinement, the properties of polymers can be much different from the bulk. Because of the potential applications in technology and hope to reveal fundamental problems related to the glass-transition, it is important to realize whether the nanoscale and macroscopic behavior of polymer glass-formers are related to each other in any simple way. In this work, we have addressed this issue by studying the segmental dynamics of poly(4-chlorostyrene) (P4ClS) in the bulk and upon geometrical confinement at the nanoscale level, in either one- (thin films on Al substrate) or two- (within alumina nanopores) dimensions. The results demonstrate that the segmental relaxation time, irrespective of the confinement size or its dimensionality, can be scaled onto a single curve when plotted versus ργ/T with the same single scaling exponent, γ = 3.1, obtained via measurements at high pressures in bulk. The implication is that the macro- and nanoscale confined polymer dynamics are intrinsically connected and governed by the same underlying rules.
P
the latter one results in either in an increase, decrease, or no effect on Tg, as compared to the bulk. The importance of both factors in determining the properties of spatially constrained glass-formers is indisputable. However, a closer look at the glass-transition behavior of polymer films of nanometer thickness has also revealed a critical role of the preparation/processing conditions.22−25 Polymers spin-coated on nonrepulsive substrates are not able to immediately pack themselves in a similar manner as that characteristic for a bulk material, especially in the close proximity of the confining surface. Such local density fluctuations at the polymer substrate interface might alter the global segmental dynamics of the thin films.26−30 In line with this finding, in 2D geometries it has been demonstrated that the frustration in the packing density, as due to vitrification of the interfacial layer, results in enhanced mobility of the molecular liquids and polymers constrained within the nanopore walls.31−35 Faster dynamics in nanoscale confinement has also been associated with the excess of free volume as a result of the interactions with the confining substrate/pore
olymers confined to nanometer dimensions reveal numerous peculiar changes in their structure and dynamics, sometimes hardly or even completely impossible to attain/observe at the macroscale.1−7 For that reason, the interest in nanoconfined polymer materials covers a broad range of technological applications including organic electronics, smart coatings, photovoltaics, biosensors, and so on.8−11 Understanding how the properties of polymers change at the nanometer length scale is critical for the rational design of novel materials or functional devices, while at the same time shed new light on the most topical problems of the soft matter physics, like the glass-transition.12−15 Geometrical confinement can be realized under different conditions depending on the dimensionality (1D refers to thin films, 2D to nanopores/nanochannels, while 3D to nanospheres) or the characteristics of the host material with respect to that being confined (soft vs hard boundaries). Over the past years, numerous experimental studies utilizing diverse confinement configurations have led to a general conclusion that the behavior of spatially constrained glass-formers depends on the interplay between finite size effect and surface interactions.16−21 The former one is usually responsible for a downward shift of the glass-transition temperature, Tg, while © XXXX American Chemical Society
Received: December 26, 2018 Accepted: February 25, 2019
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DOI: 10.1021/acsmacrolett.8b01006 ACS Macro Lett. 2019, 8, 304−309
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ACS Macro Letters walls.36 Therefore, what makes the behavior of 1D and 2Dconfined systems to be very much alike is that they both alter the average density/or the average free volume of the system. However, it is still not clear yet if this eventually gives a consistent picture of the glass-transition dynamics. When it comes to recognizing the density variation/free volume effect on the glass-transition dynamics, a great contribution to the field comes from the high-pressure studies of bulk liquids and polymers.37−39 In the past decades, it has been demonstrated that both thermal energy and density fluctuations play an important role in controlling dynamics of glass-forming liquids. Along with that, from the high-pressure experiments, we get a brilliant idea of the density scaling, i.e., the ability to describe the evolution of the α-relaxation time or the viscosity measured under different temperature and pressure conditions through a simple scaling relation, ργ/T, where γ is a material-specific constant.40−42 The underlying theoretical grounds of this remarkable experimental finding suggest an intimate link between dynamics, thermodynamics, and intermolecular potential of the glass-forming systems.43−45 The central idea behind the present work is related to a fundamental question of whether the highly nontrivial dynamics of glass-forming systems in nanoscale confinement, where entirely different phenomena come to the fore, can be described/connected to its bulk behavior. To facilitate such an investigation, we take advantage of the universal character of the density scaling relation which predicts that the evolution of the α-relaxation dynamics via scaling variable ργ/T holds not only in the experimentally accessible T−p range but also, more fundamentally relevant, in the T−V space. The first experimental evidence that confined and bulk dynamics can be linked using ργ/T scaling relation were given recently for van der Waals bonded liquids embedded within nanopores of different sizes.33 In this Letter, we verify that the ργ/T scaling is valid in the case of confined polymers irrespective of confinement dimensionality or its size. Our results are a strong evidence that the macro- and nanoscale dynamics are intrinsically connected and governed by the same underlying rules. In this manner, from a more practical point of view, we verify that the density scaling can describe and predict how spatial restriction affects the dynamics of various glass-formers. To validate our claims, we have examined the segmental (α-) relaxation dynamics of a model polymer glass-former under various (T, p) conditions and upon confinement at the nanoscale level in either 1- or 2-dimensions. Carrying out such tests is a great experimental challenge that starts with a careful choice of the studied polymer system as well as the confining environment. Here, the focus is on soft matter bounded at the nanoscale level by hard interacting walls. 1D confinement was realized by capping thin polymer films between Al layers, whereas 2D confinement was achieved by infiltrating the polymer in nanoporous alumina membranes composed of cylindrical and non-cross-linking channels. This procedure, essentially, allowed us to work at constant interactions between the confined polymer and the confining surface. Because not all the materials are suitable to be confined within different types of geometries, we have selected a high-molecular-weight polymer glass-former, poly(4-chlorostyrene) of MW∼ 75k and PDI 1.48. This material, with a calorimetric glass-transition temperature Tg = 400 K, can be easily prepared in the form of thin films of nanometric thickness via spin-coating and infiltrated in porous channels by the capillary forces (via
solvent aided softening method). Owing to the large value of its dipole moment (μ = 2.09 D for P4ClS unit),46 the segmental mobility of the studied material can be easily monitored by using dielectric spectroscopy, both at varying thermodynamic conditions (T, p) as well as in the presence of hard nanoscale confinement. More details on materials and methods can be found in the Supporting Information. To test the validity of the density scaling for the dynamics of nanoconfined polymers, we have performed a series of different measurements. At first, we have determined the value of the exponent γ via measurements of bulk samples at different temperature and pressures. Then, we have verified that the same γ value can be used to rescale the dynamics under 2D confinement, where (quasi)isochoric (= constant volume) conditions are reached. Finally, we have validated the scaling in the case of thin films, where the perturbations in volume upon 1D confinement require a more careful treatment. Figure 1a displays dielectric loss spectra collected upon compression of P4ClS at a constant temperature, T = 439.5 K.
Figure 1. (a) Dielectric loss spectra recorded for bulk P4ClS at T = 439.5 K while increasing pressure. (b) Pressure dependence of αrelaxation time as measured along isotherms 419.5 K, 427.5 K, 439.5 K. The inset shows variation of the glass transition temperature as a function of pressure obtained from the high-pressure dielectric studies and parametrized with the use of the Andersson−Andersson relation.55 Glass-transition was defined as either T or p at which τα = 10 s. (c) Isothermal and isobaric dependences of α-relaxation time plotted as a function of specific volume. Solid lines are fits to the data with the use of the modified version of Avramov’s equation.56,57 Volumetric data V(T, p) were taken from the literature,58 parametrized with the use of Tait EOS, and then used to convert from T− p to T−V dependences.59,60 (d) Density scaling of the segmental dynamics with γ = 3.1 for P4ClS. Scaling plot includes isobaric and isothermal data measured for the bulk sample.
As pressure increases, the α-relaxation peak moves toward lower frequencies indicating a systematic slowing-down of the segmental dynamics. The frequency corresponding to the maximum of the loss peak is commonly used to determine its characteristic relaxation time, 1/(2πf max). Evolution of the αrelaxation time as a function of pressure measured along three different isotherms is shown in Figure 1b. The linear character of τα(p) dependences is typically parametrized with the use of the pressure version of the Arrhenius law.47 To quantify the effect of pressure on the segmental dynamics of P4ClS, we have calculated the pressure coefficient of the glass transition 305
DOI: 10.1021/acsmacrolett.8b01006 ACS Macro Lett. 2019, 8, 304−309
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ACS Macro Letters temperature dTg/dp determined as the first derivative of experimentally measured Tg(pg) dependence in the limit of ambient pressure. To avoid extrapolation of the data and be consistent with the literature results,28,48 we define the glass transition for either T or p at which τα = 10 s. For P4ClS, this gives 0.481 K/MPa, which is consistent with the value of 0.491 K/MPa reported by White and Lipson based on volumetric data.49 The dTg/dp coefficient describes the pressure sensitivity of the glass-transition, and the value obtained for P4ClS is one of the highest ones reported until now for glass-forming systems. Ultimately, this suggests that the segmental dynamics of P4ClS can be largely affected even by a very small frustration in volume. However, to make it clear, experimentally measured τα(T, p) dependences were converted to T−V representation, as shown in Figure 1c. Finally, in Figure 1d we demonstrate the validity of the density scaling, with γ = 3.1 for the bulk polymer. Note that when moving along an isotherm by applying pressure (thermal energy contribution under control), a small variation in volume is able to significantly affect the segmental mobility. Therefore, our expectation is that such pronounced sensitivity to volume should induce a significant deviation from the bulk-like behavior of P4ClS under nanoscale confinement. Our hypothesis is, however, much stronger than such a qualitative picture. We expect that the dynamics of the confined polymer can be described by the same scaling exponent. In Figure 2, we present τα(T) for P4ClS confined within AAO templates of pores diameter ranging from 200 to 20 nm.
polymer chains interacting with the pores walls at a characteristic pore-size dependent temperature labeled here as Tg_interface. Because of the kinetic freezing of the interfacial layer, quasi-isochoric conditions are imposed in the nanoporeconfined system.32,33 With this idea in mind, in Figure 2, we have verified that below Tg_interface, the dynamics of P4ClS confined in AAO nanopores can be described via isochoric dependences, and consequently these data can be scaled according to the density scaling law with γ = 3.1. Details on the procedure allowing the generation of isochores using pressuredependent bulk dynamics can be found in the Supporting Information. Having verified that the density scaling is capable to describe segmental dynamics under 2D confinement, we considered experiments performed in thin films. Treating dynamics under 1D confinement requires, however, considering an extra variable with respect to the former nanogeometry. Differently, then in the case of nanopores, isochoric conditions are more difficult to reach in thin films, and the lack of such a feature does not allow identifying the glass transition of the interfacial layer. Figure 3 shows the temperature dependence of the α-
Figure 3. Segmental relaxation time plotted versus temperature for P4ClS in the bulk state and when confined in thin films of different thickness (99, 27, and 8 nm). Data were measured on slow heating. The 8 nm thin film dependence was taken from the literature.28 Dashed lines are the predicted isochoric dependences with the assumption of ∼10 nm error for film thickness. Upper inset: evolution of the segmental relaxation time as a function for volume for bulk P4ClS and 8, 27, and 99 nm films estimated from the bulk data by taking into account δfree(= 0.327 nm for P4ClS)/h correction, as proposed by White and Lipson.49 We assume the film thickness is determined with +10 nm error. Lower inset: specific volume at 433 K as a function of the inverse film thickness, h, or either pore diameter, d. Thin film data include segmental relaxation times for P4ClS films of thickness from 200 to 12 nm recorded at the onset of prolonged annealing carried out at 433 K; see reference to literature for more details.28
Figure 2. Segmental (α-) relaxation time plotted versus temperature for P4ClS in the bulk and confined to AAO nanopores of different pore diameters as measured on slow cooling from 463 K (∼0.2 K/ min). Evolution of the α-relaxation times measured in the temperature region when confined dynamics start to deviate from the bulk was described using isochoric dependences. Red symbols are the segmental relaxation times for 23 and 220 nm thin films of P4ClS recorded at the onset of the annealing process at 433 K. These data were taken from the literature.28
relaxation time for 8, 27, and 99 nm P4ClS films recorded on slow heating. In this manner, the 99 nm film shows no confinement effect, while the segmental mobility of the thinner films is enhanced when decreasing the film thickness, though not essentially following the predicted, using high-pressure results, isochoric dependences (see dashed lines). This suggest that the density of the 1D confined polymer is not fixed (so τα(T) are not isochores), but constantly evolves with T. In
By lowering the temperature, the segmental dynamics of the nanopore-confined polymer becomes faster as compared to that of the bulk. This effect becomes even more pronounced when the restriction in size is larger, i.e., the pores get smaller. Recent work recognized that such deviation from the bulk τα(T) dependence is due to vitrification of the molecules/ 306
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master curve validating in this way the applicability of the density scaling law for polymer dynamics under geometrical confinement, irrespective of its dimensionality or configuration. The implication of this finding is meaningful for many reasons. Foremost, it is a hallmark of universality that the αrelaxation time measured under different thermodynamic or confinement conditions scales as ργ/T. In turn, the same value of the scaling exponent γ indicates that the intermolecular forces related to the glass-transition dynamics are, surprisingly, not affected at all in the presence of hard nanoconfinement imposed in either 1D or 2D. With that, we end up with a remarkable conclusion that the bulk and nanoscale confined polymer dynamics must be intrinsically connected and comply with the same underlying rules. The density scaling, if satisfied, provides a straightforward information about the evolution of the α-relaxation times in the entire T−V space. From this very useful asset of the ργ/Τ scaling relation, we are then able to estimate the variation of the specific volume as a function of either pore diameter d or film thickness h. To do that, we have made use of the recent dielectric data on out-of-equilibrium dynamics of thin P4ClS films prepared on Al-supported substrate.28 Samples of film thickness ranging from 200 to 12 nm, prepared by following identical thermal protocol, were examined at 433 K for up to 48 h where the segmental relaxation time reported at the onset and after prolonged annealing were labeled, respectively, as τfilm 0 and τfilm 48h (see red and blue symbols in Figure 2 of ref 28 but also the density scaling plot in Figure 4, current work). The lower inset in Figure 3 demonstrates the specific volume of P4ClS films at the onset of annealing as a function of inverse film thickness (1/h), as determined from the density scaling law ργ/Τ, with γ = 3.1. The results show a clear linear trend and confirm an increase in film specific volume with lowering film thickness, as we expect. To make this picture complete, we also add AAO nanopore data which surprisingly turns out to fit perfectly into the linear dependence between Vsp and 1/h (1/ d). In agreement with that finding, we note that the timescale of the segmental mobility for 23 and 220 nm thin-films coincides with that obtained in AAO templates of the average pore sizes 20 and 200 nm, respectively (see red symbols in Figure 2). To summarize, for a very long time it has been believed that the bulk and nanoscale-confined glass-transition dynamics were distinctly different. Yet, more and more evidence shows that these two have very much in common. For example, Leporini and co-workers found by MD simulations that the thin supported molecular films exhibit the same scaling as the bulk between slow and fast dynamics and that the latter exhibits density scaling.62,63 In this work, we have demonstrated that (i) the polymer dynamics in the presence of hard confinement and regardless of its dimensionality can be modeled via the density scaling approach just like for the bulk material, and (ii) the same value of the scaling exponent superimposes segmental relaxation times measured under different thermodynamic or confinement conditions providing in this way a self-consistent picture of the glass-transition dynamics. The power of the density scaling idea is that it provides a very simple and straightforward connection between macro and nanoscale dynamics of glass-forming systems by capturing via a single parameter the individual contributions coming from the temperature and density fluctuations. Our finding provides new exciting opportunities for theoretical and experimental considerations aiming to understand better the
such case, the impact of confinement on the specific volume requires a bit different treatment and should, hence, be explicitly considered when describing the temperature evolution of the segmental relaxation. In agreement with experimental and computational studies reported for PS,49−51 we expect that the average density of spin-coated P4ClS films (i.e., 1/specific volume) is smaller than for the bulk polymer and decrease upon reduction of the thickness, h. Nevertheless, it should be also noted that, the density of thin films might be affect by numerous factors, and not essentially decrease as the films get thinner.52−54 Such densification of thin films seems to be in apparent contradiction to free-volume concepts commonly used to rationalize a drop of Tg with film thickness. Herein, to account for faster segmental dynamics of P4ClS films, the averaged free-volume/film density is assumed to increase/decrease, respectively. To explicitly account for the larger specific volume in 1D confinement, we have considered the framework recently introduced by White and Lipson and increase the volume bulk value at every given temperature by the term δfree/h, where δfree is an interface-related parameter which for P4ClS takes the value of 0.327 nm.49,61 The cooperative free volume (CFV) model describes thin-film dynamics through a simple weighted average contribution from the two regions, bulk and interfacial, where the latter one has enhanced the amount of free-volume as captured by the interface-related parameter, δfree. This is a T-independent parameter that characterizes the strength to which the interface alters the free volume (the larger δfree, the lower the interfacial density). As showed by Lipson and White, it can be determined even from very little thin film dynamics. Obtained using this approach, dependence of the segmental relaxation times as a function of volume for P4ClS films are shown in the upper inset of Figure 3. Knowing how the segmental relaxation time changes as a function of temperature and volume, we are finally ready to test the density scaling idea in 1D and 2D nanoconfinement. Figure 4 illustrates segmental relaxation time for P4ClS confined in alumina nanopores and thin films deposited on Al plotted versus the scaling variable ργ/T with γ = 3.1, as it was obtained for the bulk sample. Remarkably, we found that the high-pressure and confinement data fall onto a single
Figure 4. Segmental relaxation time plotted versus quantity 1000ργ/T with γ = 3.1 for P4ClS. Scaling plot includes dielectric results from the high-pressure studies as well as that obtained under different confinement conditions for both 1D and 2D nanoconfined systems. 307
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(7) Ediger, M. D.; Forrest, J. A. Dynamics near Free Surfaces and the Glass Transition in Thin Polymer Films: A View to the Future. Macromolecules 2014, 47, 471. (8) Ghosh, S.; Kouamé, N. A.; Ramos, L.; Remita, S.; Dazzi, A.; Deniset-Besseau, A.; Beaunier, P.; Goubard, F.; Aubert, P.-H.; Remita, H. Conducting Polymer Nanostructures for Photocatalysis under Visible Light. Nat. Mater. 2015, 14, 505−511. (9) Nyholm, L.; Nyström, G.; Mihranyan, A.; Strømme, M. Toward Flexible Polymer and Paper-Based Energy Storage Devices. Adv. Mater. 2011, 23, 3751−3769. (10) Sun, S.; Xu, H.; Han, J.; Zhu, Y.; Zuo, B.; Wang, X.; Zhang, W. The Architecture of the Adsorbed Layer at the Substrate Interface Determines the Glass Transition of Supported Ultrathin Polystyrene Films. Soft Matter 2016, 12, 8348. (11) Schwartz, G.; Tee, B. C.-K.; Mei, J.; Appleton, A. L.; Kim, D. H.; Wang, H.; Bao, Z. Flexible Polymer Transistors with High Pressure Sensitivity for Application in Electronic Skin and Health Monitoring. Nat. Commun. 2013, 4, 1859. (12) Seife, C. So Much More to Know. Science (Washington, DC, U. S.) 2005, 309 (5731), 78−102. (13) Chang, K. The Nature of Glass Remains Anything but Clear Anything but Clear. New York Times. July 29, 2008. (14) Berthier, L.; Biroli, G. Theoretical Perspective on the Glass Transition and Amorphous Materials. Rev. Mod. Phys. 2011, 83, 587. (15) Hanakata, P. Z.; Douglas, J. F.; Starr, F. W. Interfacial Mobility Scale Determines the Scale of Collective Motion and Relaxation Rate in Polymer Films. Nat. Commun. 2014, 5, 4163. (16) Alcoutlabi, M.; McKenna, G. B. Effects of Confinement on Material Behaviour at the Nanometre Size Scale. J. Phys.: Condens. Matter 2005, 17, R461. (17) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Size-Dependent Depression of the Glass Transition Temperature in Polymer Films. Nat. Commun. 1994, 27 (1), 59−64. (18) Richert, R. Dynamics of Nanoconfined Supercooled Liquids. Annu. Rev. Phys. Chem. 2011, 62 (1), 65−84. (19) Morineau, D.; Xia, Y.; Alba-Simionesco, C. Finite-Size and Surface Effects on the Glass Transition of Liquid Toluene Confined in Cylindrical Mesopores. J. Chem. Phys. 2002, 117, 8966−8972. (20) Fryer, D. S.; Peters, R. D.; Kim, E. J.; Tomaszewski, J. E.; De Pablo, J. J.; Nealey, P. F.; White, C. C.; Wu, W. L. Dependence of the Glass Transition Temperature of Polymer Films on Interfacial Energy and Thickness. Macromolecules 2001, 34 (16), 5627−5634. (21) Dynamics in Geometrical Confinement; Kremer, F., Ed.; Springer International Publishing: Cham, Switzerland, 2014. (22) Forrest, J. A.; Dalnoki-Veress, K. The Glass Transition in Thin Polymer Films. Adv. Colloid Interface Sci. 2001, 94, 167−196. (23) Reiter, G. Dewetting as a Probe of Polymer Mobility in Thin Films. Macromolecules 1994, 27, 3046−3052. (24) Non-Equilibrium Phenomena in Confined Soft Matter; Napolitano, S., Ed.; Springer International Publishing: Cham, Switzerland, 2015. (25) Mundra, M. K.; Ellison, C. J.; Behling, R. E.; Torkelson, J. M. Confinement, Composition, and Spin-Coating Effects on the Glass Transi-Tion and Stress Relaxation of Thin Films of Polystyrene and Styrene-Containing Random Copolymers: Sensing by Intrinsic Fluores-Cence. Polymer 2006, 47, 7747. (26) Napolitano, S.; Wü bbenhorst, M. The Lifetime of the Deviations from Bulk Behaviour in Polymers Confined at the Nanoscale. Nat. Commun. 2011, 2, 260. (27) Perez-de-Eulate, N. G.; Sferrazza, M.; Cangialosi, D.; Napolitano, S. Irreversible Adsorption Erases the Free Sur-Face Effect on the Tg of Supported Films of Poly(4-Tert-Butylstyrene). ACS Macro Lett. 2017, 6, 354. (28) Panagopoulou, A.; Napolitano, S. Irreversible Adsorption Governs the Equilibration of Thin Polymer Films. Phys. Rev. Lett. 2017, 119 (9), 097801. (29) Napolitano, S.; Capponi, S.; Vanroy, B. Glassy Dynamics of Soft Matter Under 1D Confinement: How Irreversible Adsorption Affects Molecular Packing, Mobility Gradients and Orientational
behavior of soft matter at the nanoscale level. With density scaling law successfully tested in hard confinement, an open question is whether the same applies for sof t confining boundaries. Future work should also address the impact of the polymer/solid interface interactions to test whether the density scaling is able to comprise the dynamics features of polymer glass-formers when changing the character of the polymer interactions with the hard confining walls. Such information is not only of fundamental relevance in science but also, from a much broader perspective, could be potentially very useful when developing nanoscale-confined polymeric materials for numerous applications.
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ASSOCIATED CONTENT
S Supporting Information *
includes . The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acsmacrolett.8b01006.
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Details on materials and methods, data treatment, additional results, and information on how to determine isochoric dependences of the α-relaxation time in confinement (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Karolina Adrjanowicz: 0000-0003-0212-5010 Andrzej Dzienia: 0000-0002-9628-0224 Simone Napolitano: 0000-0001-7662-9858 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS K.A. and R.W. acknowledge financial assistance from National Science Centre (Poland) within the Project OPUS 14 nr. UMO-2017/27/B/ST3/00402. S.N. acknowledges the Fonds de la Recherche Scientifique FNRS under Grant T.0147.16 “TIACIC”.
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REFERENCES
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DOI: 10.1021/acsmacrolett.8b01006 ACS Macro Lett. 2019, 8, 304−309
Letter
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DOI: 10.1021/acsmacrolett.8b01006 ACS Macro Lett. 2019, 8, 304−309
