Jacek Fal
email: jacekfal@prz.edu.pl

Jolanta Sobczak

Ryszard Stagraczyński

Patrice Estellé

Gawel Żyla

Gaweł Żyła

Electrical conductivity of titanium dioxide ethylene glycol-based nanofluids: Impact of nanoparticles phase and concentration

Keywords: nanofluid, titanium dioxide, anatase, rutile, electrical conductivity Conceptualization, Methodology, Investigation, Formal analysis, Writing -Original Draft, Visualization, Writing -Review Data Curation, Investigation Formal analysis, Visualization Investigation, Validation, Writing -

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The intensive growth in nanofluids research observed for over twenty years was initiated by Choi at al. [START_REF] Choi | Enhancing thermal conductivity of fluids with nanoparticles[END_REF]. Since this time, many papers concerning nanofluids have been published and their number increase from year to year. Carbon-based material as new type of nanomaterials including multiwalled carbon nanotubes [START_REF] Balaji | Enhanced heat transfer characteristics of water based hybrid nanofluids with graphene nanoplatelets and multi walled carbon nanotubes[END_REF][START_REF] Ghalandari | Applications of nanofluids containing carbon nanotubes in solar energy systems: A review[END_REF], nanofibers [START_REF] Said | Stability, thermophysical and electrical properties of synthesized carbon nanofiber and reduced-graphene oxide-based nanofluids and their hybrid along with fuzzy modeling approach[END_REF], graphene [START_REF] Balaji | Enhanced heat transfer characteristics of water based hybrid nanofluids with graphene nanoplatelets and multi walled carbon nanotubes[END_REF][START_REF] Ba | Review on the recent progress in the preparation and stability of graphene-based nanofluids[END_REF] or fullerenes [START_REF] Ahmadi | Experimental investigation of rheological behavior of fullerene/hydraulic oil nanofluid[END_REF][START_REF] Jin | Thermal conductivity of fullerene and TiO 2 nanofluids[END_REF][START_REF] Martin | Determination of thermal diffusion coefficient of nanofluid: Fullerene-toluene[END_REF] are largely considered. Also, more regular and traditional materials, such as metals [START_REF] Warrier | Effect of particle size on the thermal conductivity of nanofluids containing metallic nanoparticles[END_REF] or oxides [START_REF] Suganthi | Metal oxide nanofluids: Review of formulation, thermo-physical properties, mechanisms, and heat transfer performance[END_REF], are used in the preparation of nanofluids and show interesting thermophysical properties.

One of the most often used nanoparticles are oxides and among them is titanium dioxide (TiO 2 ) which is cheap and generally well characterized [START_REF] Siegel | Synthesis, characterization, and properties of nanophase TiO 2[END_REF][START_REF] Tang | Optical properties of anatase (TiO 2 )[END_REF][START_REF] Awin | Electrical and thermal conductivities of dilute nanofluids-experimental determination and parametric studies[END_REF]. TiO 2 nanoparticles are well known as semi-conductors for photocatalytic applications in a wide range of fields, including energy and environment [START_REF] Kaplan | Simple synthesis of anatase/rutile/brookite TiO 2 nanocomposite with superior mineralization potential for photocatalytic degradation of water pollutants[END_REF][START_REF] Hanaor | Morphology and photocatalytic activity of highly oriented mixed phase titanium dioxide thin films[END_REF]. They can be found under three crystalline forms, namely anatase, rutile and in a less extend brookite. Stable rutile comes from the transformation of metastable anatase (or brookite) at high temperature and can be obtained under various processes and methods as reviewed in [START_REF] Hanaor | Morphology and photocatalytic activity of highly oriented mixed phase titanium dioxide thin films[END_REF]. Anatase and rutile have a tetragonal structure sharing four and two edges, respectively. The reader is referred to the study by Hanaor and Sorrel [START_REF] Hanaor | Morphology and photocatalytic activity of highly oriented mixed phase titanium dioxide thin films[END_REF] for a comprehensive differentiation between anatase and rutile species, and their ratio following the synthesis conditions followed. Like dry TiO 2 nanoparticles, nanofluids containing this type of nanoparticles are also widely investigated. The percentage distribution of studied properties of titanium oxide based nanofluids, presented in Fig. 1, shows that the researchers mainly focused on the thermal conductivity and viscosity of those types of nanofluids. Rheological behavior of ethylene glycol-based nanofluids containing TiO 2 nanoparticles was examined by many reserchers [START_REF] Cabaleiro | Rheological and volumetric properties of TiO 2 -ethylene glycol nanofluids[END_REF][START_REF] Longo | Experimental measurements of thermophysical properties of 23 Al Oand TiO 2 -ethylene glycol nanofluids[END_REF][START_REF] Shu | Preparation and rheological behavior of ethylene glycol-based TiO 2 nanofluids[END_REF][START_REF] Hamid | Effect of temperature on heat transfer coefficient of titanium dioxide in ethylene glycol-based nanofluid[END_REF]. It was presented that nanofluids containing high fraction of particles exhibit non-Newtonian nature [START_REF] Cabaleiro | Rheological and volumetric properties of TiO 2 -ethylene glycol nanofluids[END_REF][START_REF] Shu | Preparation and rheological behavior of ethylene glycol-based TiO 2 nanofluids[END_REF], while a low fraction generally induces a Newtonian one [START_REF] Longo | Experimental measurements of thermophysical properties of 23 Al Oand TiO 2 -ethylene glycol nanofluids[END_REF]. Thermal conductivity of TiO 2 -EG nanofluids was also well studied, as shown in Refs. [START_REF] Longo | Experimental measurements of thermophysical properties of 23 Al Oand TiO 2 -ethylene glycol nanofluids[END_REF][START_REF] Hamid | Effect of temperature on heat transfer coefficient of titanium dioxide in ethylene glycol-based nanofluid[END_REF][START_REF] Alias | Thermal characteristic of nanofluids containing titanium dioxide nanoparticles in ethylene glycol[END_REF][START_REF] Lee | Characterization of ethylene glycol based TiO 2 nanofluid prepared by pulse wire evaporation (pwe) method[END_REF]. More information about the thermophysical properties of various nanofluids could be found in the state-of-the-art review paper by Qiu et al. [START_REF] Qiu | A review of recent advances in thermophysical properties at the nanoscale: From solid state to colloids[END_REF]. As illustrated by Figure 1, the Web of Science database evidence that only few papers considering nanofluids containing titanium dioxide nanoparticles in various base fluids and their electrical properties were published (data collected at 07-09-2021). A short summary of the main studies in this field is presented in Table 1. The most often used base fluid for titanium dioxide nanofluids is water (W).

Awin et al. [START_REF] Awin | Electrical and thermal conductivities of dilute nanofluids-experimental determination and parametric studies[END_REF] studied the electrical conductivity (EC) of nanofluids based on titanium dioxide dispersed in water with volume concentration of 0.0015 -0.005%. The electrical conductivity of nanofluids was obtained from two different methods. Firstly, the authors evaluated the electrical conductivity based on the refractive index and the absorbance. Next, both results

were compared and good agreement between them was confirmed.  for 1 and 3 vol% respectively. Moreover, the favourable effect of temperature on the electrical conductivity of titanium dioxide water-base nanofluids was also highlighted. Electrical conductivity of titanium dioxide water nanofluid was also studied by Sikdar et al. [START_REF] Sikdar | Investigation of electrical conductivity of titanium dioxide nanofluids[END_REF]. The nanoparticles used to prepare nanofluids with volume concentration range of 0.5% to 3.0% were a mixture of two TiO 2 phases, anatase 76% and rutile 24% respectively.

Investigations were conducted for four temperatures [START_REF] Chereches | Electrical conductivity of new nanoparticle enhanced fluids: An experimental study[END_REF][START_REF] Żyła | Experimental studies on viscosity, thermal and electrical conductivity of aluminum nitride-ethylene glycol (AlN-EG) nanofluids[END_REF][START_REF] Sarojini | Electrical conductivity of ceramic and metallic nanofluids[END_REF]45 C  ) and show 25-fold and 80-fold increase in electrical conductivity for 0.5 and 3.0 vol% respectively. For those date the simple correlation with two factor were also introduced. Kumara et al. [START_REF] Kumar | Effect of nanoparticle on rheological properties of surfactant-based nanofluid for effective carbon utilization: capturing and storage prospects[END_REF] studied the impact of titanium dioxide nanoparticles on electrical properties of pure ethylene glycol (EG) and their mixtures with two type of surfactants. Using two step method they prepared samples with mass concentration ranging from 0.05 to 1.0 %. The studies conducted at temperature range from 30 to 90 C  show that the electrical conductivity is enhanced by increase in load of TiO 2 nanoparticles. Also, addition of both surfactants causes slight increase in electrical conductivity, especially in lower tested temperatures; for higher temperatures this effect was weaker. The maximum value of electrical conductivity was obtained for the highest tested mass concentration (1.0 wt%) of TiO 2 nanoparticles supported by SDS surfactant.

The effect of TiO 2 nanoparticles on EC of oil (O) was studied by Cieśliński et al. [START_REF] Cieśliński | Measurement of temperature-dependent viscosity and thermal conductivity of alumina and titania thermal oil nanofluids[END_REF].

They presented results for nanofluids based on thermal oil with dispersed of TiO 2 nanoparticles 47 nm in average diameter and revealed a decrease in electrical conductivity with increasing temperature.

In the most of the published works, the authors highlighted the incompatibility of classical models of electrical conductivity and introduced their own empirical correlations to describe the dependency of electrical properties on the concentration of nanoparticles and temperature, which are mostly suitable only for one specific nanofluid. Therefore, it is important to ACCEPTED MANUSCRIPT -CLEAN COPY provide new experimental data to contribute to the development of better models describing the electrical properties of nanofluids. The availability of more experimental data on the electrical conductivity of various nanofluids can help in the work, both theoretical and numerical, on the preparation of a uniform model of the electric conductivity of nanofluids that could be used in numerical simulations and theoretical analysis as example. In this paper, the electrical conductivity of ethylene glycol based TiO 2 nanofluids, considering three different types of nanoparticles, with range of mass fraction (0.01-0.20) was presented. The dependence of electrical conductivity on mass fraction and temperature was investigated.

Materials and Methods

Materials

In this study, three different types of TiO 2 nanoparticles were used. All of them are commercially available on the market and were purchased from PlasmaChem GmbH. According to the manufacturer data, one of them should be in anatase phase (labelled as TiO 2 A), the second in rutile phase (labelled as TiO 2 M1) and the third is a mixture of both anatase and rutile phases (labelled as TiO 2 M2) with average diameter 4-8 nm, 2 nm and 21 nm respectively. To confirm properties declared by the manufacturer, a series of measurements were performed including X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDS) and Brunauer, Emmett and Teller (BET) characterizations as explained in section 3.1. Ethylene glycol (EG) manufactured by Fisher Chemical (Loughborough, UK, purity over 99%) was used as the base fluid.

Nanofluid preparation

For the purpose of this study three types of titanium (IV) oxide (TiO 2 ) nanoparticles were used to produce nanofluids with various mass concentration from 1 to 5% with 1% step. In addition, higher concentrations 10, 15, 20% were also considered. (1)

Experimental Methods

The X-ray diffraction patterns of nanoparticles were measured in the 20-90 2 range with a step size of about 0.015  and collection time of 250 s/step using a monochromatized (Cu K  1,  =1.5406 Å ) Bruker D8 Advance diffractometer equipped with a fast LynxEye detector.

The powder X-ray diffraction patterns were refined by the Rietveld method [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF] using the FullProf software [START_REF] Rodríguez-Carvajal | Juan rodríguez-carvajal[END_REF], enabling the quantification of the phases in presence. The fitting of the peak broadening using a Thompson-Cox-Hasting function enables the deconvolution of the instrumental (determined from a corundum standard sample) and sample contributions to the broadening [START_REF] Rodríquez-Carvajal | Line broadening analysis using fullprof*: determination of microstructural properties[END_REF].

A Micromeritics Gemini VII 2390t instrument using a mixture of N2/He (30%/70%) was used to experimentally evaluate from nitrogen physisorption the (BET) specific surface area of TiO 2 nanoparticles. Before BET measurement, all the tested samples were previously outgassed under vacuum at 100 C  in order to avoid the nanoparticle surface hydration.

Scanning electron microscopy (SEM) characterization of the different types of TiO 2 nanoparticles was carried out with JEOL-JSM-7100F (JEOL USA Inc., Peabody, USA) equipment operating at 10 kV coupled with energy dissipative X-ray spectrometer (EDS) for ACCEPTED MANUSCRIPT -CLEAN COPY chemical composition evaluation of powder. Powder samples were deposited on a carbon adhesive tape substrate then submitted to carbon metallization under vacuum before to be tested.

To evaluate the electrical conductivity of nanofluids, a conductivity meter MultiLine 3630 (WTW GmbH, Weilheim, German) coupled with conductivity probe TetraCon 925 (for high conductive samples) and LR925/01 (for low conductive samples) (WTW GmbH, Weilheim, German) were used. The accuracy of the used conductivity probe was evaluated elsewhere, and it is 1% and 2% for TetraCon 925 [START_REF] Żyła | Experimental studies on viscosity, thermal and electrical conductivity of aluminum nitride-ethylene glycol (AlN-EG) nanofluids[END_REF] and LR925/01 [START_REF] Traciak | Experimental study on the density, surface tension and electrical properties of ZrO 2 -EG nanofluids[END_REF] respectively. For temperature control and stabilization self-made system was made. The detailed description of whole measuring station can be found elsewhere in [START_REF] Fal | Electrical conductivity and dielectric properties of ethylene glycol-based nanofluids containing silicon oxide-lignin hybrid particles[END_REF]. All measurements were conducted without undue delay directly after sample preparation in a temperature range from 10 to 45 C  (283.15-318.15 K) with 5 C  step and the accuracy of temperature stabilization was 0.2. The measurements for each temperature were conducted at least during 10 minutes and the average value was taken as an electrical conductivity for specific temperature.

Results and discussion

TiO 2 nanoparticles

The refined powder X-ray diffraction pattern of the different types of TiO 2 nanoparticles are presented in the Fig. 2. XRD experiments and data of Table 2 revealed that TiO 2 A nanoparticles are well made of anatase phase, and that average crystallite size is close to the average size of nanoparticles while the nanoparticles appears mainly aggregated in SEM characterization. Contrary to manufacturer specification, the Table 2 shows that TiO 2 M1 is mainly composed of nanoparticles with anatase phase while pure rutile was expected. In addition, TiO 2 M2 nanoparticles are dominated by rutile phase. Average crystallite sizes of TiO 2 M2 nanoparticles agree with average size of nanoparticles reported by the manufacturer. With TiO 2 M1, the average crystallite sizes of nanoparticles is 10 times higher than average nanoparticle size given by the manufacturer but agree with SEM characterization. (down) the anatase phase (I4 1 /amd space-group). TiO M2 nanoparticles are separate, near spherical and with similar average diameter of about 100 nm.

EDS spectroscopy of the TiO 2 nanoparticles is depicted in Figure 3. It shows that TiO 2 samples are mainly composed of Ti and O as expected but they also contain some other species.

The presence of Al is noticed with TiO 2 A and TiO 2 M2 samples. Many different other species appear in TiO 2 M1 sample that makes this sample not strictly pure. It should be finally denoted that several EDS spectra have been taken in different locations for all the samples, and similar spectra were obtained.

Electrical properties of TiO 2 -EG nanofluids

Effect of TiO 2 nanoparticles characterized by various phase (anatase and mixture of anastase and rutile) and temperature on electrical conductivity of ethylene glycol was investigated and results are presented in Figure 4, as well summarized in Table A.6. The graphs clearly show that addition of titanium dioxide nanoparticles, even in small amount and irrespective of their ACCEPTED MANUSCRIPT -CLEAN COPY phase, contributes to increase the electrical conductivity of base fluid, what was also reported elsewhere [START_REF] Awin | Electrical and thermal conductivities of dilute nanofluids-experimental determination and parametric studies[END_REF][START_REF] Angayarkanni | Effect of nanoparticles aggregation on thermal and electrical conductivities of nanofluids[END_REF][START_REF] Chereches | Electrical conductivity of new nanoparticle enhanced fluids: An experimental study[END_REF][START_REF] Islam | Electrical and thermal conductivities of 50/50 water-ethylene glycol based TiO 2 nanofluids to be used as coolants in pem fuel cells[END_REF][START_REF] Islam | Experimental investigation of using ZnO nanofluids as coolants in a pem fuel cell[END_REF][START_REF] Islam | Prediction of electrical conductivity of TiO 2 water and ethylene glycol-based nanofluids for cooling application in low temperature pem fuel cells[END_REF][START_REF] Kumar | Effect of nanoparticle on rheological properties of surfactant-based nanofluid for effective carbon utilization: capturing and storage prospects[END_REF]. The scale of observed changes in electrical conductivity of various titanium dioxide-ethylene glycol nanofluids are different and depends on the average size of nanoparticles or phase of used TiO 2 nanoparticles and their ratios.

In this study, the most significant increase in electrical conductivity was observed for nanofluids with TiO 2 particles in anatase phase (TiO 2 A) with declared average particle size of 4-8 nm (Fig. According to the best author knowledge, such an increase is the highest measured for nanofluids containing titanium dioxide nanoparticles and one of the highest for ethylene glycol based nanofluids. Other two types of nanofluids also present enhancement in electrical conductivity with increasing content of nanoparticles, but in their case observed increase is much lower than that case of TiO 2 anastase nanoparticles. This difference can be caused by the nature of the anatase phase of TiO 2 , which researchers [START_REF] Mazzolini | Tuning of electrical and optical properties of highly conducting and transparent ta-doped TiO 2 polycrystalline films[END_REF] show has better electrical properties than that rutile phase. For the nanofluids containing TiO 2 M1 nanoparticles where 93% is in anatase phase also occurs significant increase in electrical conductivity with increasing mass fraction of nanoparticels. The highest enhancement, again was observed for the lowest tested temperatures at highest mass fraction and it was 154242%. The highest increase for TiO 2 M2-EG nanofluid was observed at the same conditions and the enhancement was 8616%. The main differences between used nanoparticles is in the anatase phase. Obtained results allow to conclude that the higher content of anatase phase the higher electrical conductivity on nanofluid can be achieved.

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As it was reported earlier, an increase in electrical conductivity of nanofluids can be caused mainly by two factors, namely (a) variation of electrical double layer (EDL) [START_REF] Awin | Electrical and thermal conductivities of dilute nanofluids-experimental determination and parametric studies[END_REF][START_REF] Angayarkanni | Effect of nanoparticles aggregation on thermal and electrical conductivities of nanofluids[END_REF] and (b)

creating conduction paths at higher concentrations of nanoparticles [START_REF] Sobczak | Thermophysical profile of ethylene glycol based nanofluids containing two types of carbon black nanoparticles with different specific surface areas[END_REF] or their combination. The size of EDL is strictly related with Debye length and nanoparticles size, and the greater size of EDL the greater bulk electrical conductivity. In case of titanium dioxide ethylene glycol nanofluids it seems to that also the phase of used TiO 2 particles has an impact and in this context the anatase phase is favourable.

Data presented in this paper have also been compared to some theoretical models and numerical constellations proposed by other researchers. There were many attempts to develop theoretical models of electrical conductivity or improve the existing. The Maxwell model ( 2) is largely used in the literature, in most cases, it underestimates the experimental data:

3( 1) = 1 , ( 2
) ( 1) v nf bf v              (2)
where =/ p bf    . This is because the Maxwell model concerns only volume fraction, electrical conductivity of base fluid and particles [START_REF] Chereches | Electrical conductivity of new nanoparticle enhanced fluids: An experimental study[END_REF][START_REF] Islam | Electrical and thermal conductivities of 50/50 water-ethylene glycol based TiO 2 nanofluids to be used as coolants in pem fuel cells[END_REF]. Additionally, it assume that particles are spherical, randomly arranged and distance between them is considerably larger than their diameter so it is applicable only for low concentrations [START_REF] Cruz | Electrical conductivity and stability of concentrated aqueous alumina suspensions[END_REF]. It does not take into account factors such as (a)

Brownian motion, (b) EDL, (c) nanoparticles size, and (d) specific surface area, which can affect on electrical properties of nanofluids. According the best authors knowledge there is only one case where Maxwell model does not differ much from experimental data and it was presented by Sarojini et al. [START_REF] Sarojini | Electrical conductivity of ceramic and metallic nanofluids[END_REF] for copper-water and copper-ethylene glycol nanofluids.

Cruz et al. [START_REF] Cruz | Electrical conductivity and stability of concentrated aqueous alumina suspensions[END_REF] proposed to simplify the Maxwell model for three cases: (a) when conductivity of particles is much lower than base fluid:

3 = 1 , 2 nf v bf        (3)
(b) when conductivity of particles is comparable to conductivity of base fluid:

=, nf bf  (4)
(c) when conductivity of particles is much higher than base fluid:

  = 1 3 . nf v bf     (5)
The behaviour of electrical conductivity for nanofluid with dispersed TiO 2 nanoparticles ACCEPTED MANUSCRIPT -CLEAN COPY

nf v v T       (8)
An equation for electrical conductivity of titanium dioxide water ethylene glycol nanofluids were also introduced by Islam et al. [START_REF] Islam | Prediction of electrical conductivity of TiO 2 water and ethylene glycol-based nanofluids for cooling application in low temperature pem fuel cells[END_REF]:

  = 11.214 2.626 ln 0.2371ln . nf v bf T     (9)
The comparison of previous equations and numerical fittings to obtained results are presented in Fig. 5. For this purpose, the experimental data of the three types of titanium dioxide nanofluids at 25 C  (298.15 K) were presented as electrical conductivity as a function of volume concentration ACCEPTED MANUSCRIPT -CLEAN COPY The experimental data presented in this paper have also been numerically analysed and the evolution of electrical conductivity of titanium dioxide ethylene glycol nanofluids can be described with good accuracy by the following power function:

  = 1 . A nf m bf B     (10)
Consequently, the enhancement in EC can be expressed by following equation:

= 1 , nf A m bf B     (11)
where A and B are numerical factors. The fitting was performed with OriginPro software with R 2 better than 0.997 for TiO 2 A-EG, TiO 2 M1-EG and 0.928 for TiO 2 M2-EG nanofluids. The results of the fitting can be seen in Figure 6 where experimental data and obtained functions were presented. The conductivity data analysis was based on power function introduced in relation [START_REF] Siegel | Synthesis, characterization, and properties of nanophase TiO 2[END_REF].

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Prescribed normalization reduces the complexity of problem as all thermal dependent factors purely related to the base fluid are included in the corresponding denominator. Further all values on the right hand side of equation [START_REF] Siegel | Synthesis, characterization, and properties of nanophase TiO 2[END_REF] were shifted. This procedure was realized by introducing a normalized conductivity N  defined by a simple substitution:

= 1. nf N bf     (12)
Finally the power law of equation [START_REF] Siegel | Synthesis, characterization, and properties of nanophase TiO 2[END_REF] was rewritten in a form:

=. A Nv B  (13)
Further simplification was possible since the equation ( 13) is linearizable:

log( ) = log( ) log( ), Nv AB   (14)
where the coefficients A and B and the corresponding uncertainties () uA and () uB was calculated using the linear regression model. The normalized conductances N  plotted in Fig. 8 are in good correspondence with relation [START_REF] Kaplan | Simple synthesis of anatase/rutile/brookite TiO 2 nanocomposite with superior mineralization potential for photocatalytic degradation of water pollutants[END_REF] and creates relationship close to linear . To confirm this statement all the fitting details for each sample was presented in Tables 345, where it can be seen that A coefficients for each type of sample take similar values. The calculated coefficient of determination for the samples for the remaining one is not less than 0.96 . This observation suggests that it may be sufficient to assume that the power of concentration is temperature independent. However this statement needs further investigations of experimental data.

Conclusions

The electrical conductivity of three various type of titanium dioxide ethylene glycol nanofluid were investigated. The samples were prepared by two-step method with mass fraction range from 0.01 to 0.20. The obtained results show increase in electrical conductivity with the content of TiO 2 nanoparticles in ethylene glycol, and it power is dependent on phase composition of TiO 2 nanoparticles. The most significant enhancement was noted for nanofluids containing titanium dioxide with pure anatase phase and it was over 4586400% at 10 and 20 wt.%. Also 2 TiO M1-EG nanofluids are characterized by quite high increase in electrical conductivity at the same conditions. On the other hand, the lowest TiO 2 nanoparticles effect was observed for samples where the prevailing phase was rutile. It allows to conclude that anatase phase is favourable for electrical conductivity enhancement. The experimental results were also compared with available models and theoretical correlations. It was concluded that there is no consistent with those models and new one was proposed for the investigated nanofluids. [START_REF] Cieśliński | Measurement of temperature-dependent viscosity and thermal conductivity of alumina and titania thermal oil nanofluids[END_REF] *data read from graph, † authors gives only enhancement of electrical conductivity.

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Figure 1 :

 1 Figure 1: Percentage distribution of studied properties of titanium oxide based nanofluids, based on Web of Science, 2021-09-07.

  Nanofluid samples were obtained by the two-step method. Firstly, the right amount of nanopowder has been weighed using an analytic balance (Pioneer Semi-Micro PX225DM, OHAUS Corporation, Parsippany, NJ, USA, an accuracy of 0.01 mg ). Next step was adding the ACCEPTED MANUSCRIPT -CLEAN COPY base fluid and mechanical stirring for 30 min using Genius 3 Vortex (IKA, Staufen, Germany).Later in order to break potentially remaining agglomerates in nanofluids the ultrasonic bath (Emmi 60 HC EMAG, Moerfelden-Walldorf, Germany) was employed for 200 minutes. The last stage included a high-energy ultrasounds procedure with a probe (Sonics Vibracell VCX130, Sonics & Materials Inc., Newtown, USA) for 5 min in order to ensure a good homogeneity of the sample. No surfactant were used during the preparation and the samples were immediately investigated after preparation. Based on the visual observation nanofluids were stable at least 6 hours after preparation, which was enough to perform all measurements. After this time the sedimentation occurs. The relation between the volume and the mass fraction of mentioned nanofluids can be represented by the following equation:

Figure 2 :

 2 Figure 2: Rietveld refined powder X-ray diffraction pattern of TiO 2 a) anatase, b) rutile, c) mixture and their scanning electron microscopy images . The experimental data are plotted as red

Figure 3 :

 3 Figure 3: Energy dispersive X-ray spectroscopy (EDS) spectra of a) TiO 2 A, b) TiO 2 M1, c) TiO 2 M2.

Figure 4 :

 4 Figure 4: The electrical conductivity of various type of titanium dioxide nanofluids (a)

Fig. 5 (

 5 Fig. 5 (a) and volume fraction Fig. 5 (b). Results are presented in both volume fraction and concentration due to some of previous models/correlations were introduced for volume fraction and volume concentration. A comparative analysis of experimental data and theoretical and numerical models published previously show significant discrepancy. The classical model such as Maxwell and it simplification proposed by Cruz show very high underestimations, as well as the correlation proposed by Islam et al.[START_REF] Islam | Electrical and thermal conductivities of 50/50 water-ethylene glycol based TiO 2 nanofluids to be used as coolants in pem fuel cells[END_REF]. Also, functions proposed by Chereches and Minea are not suitable for predicting the electrical conductivity of any of the titanium dioxide nanofluid presented in this study. For TiO 2 A-EG show large underestimates, while for the other two they strongly overestimate. The observed discrepancy between experimental data and models is caused by previously mentioned imperfections of assumptions of the used models and correlations , such as taking into account only the load of nanoparticles and their electrical conductivity.

Figure 5 :

 5 Figure 5: The comparison of theoretical model and numerical fittings to experimental data at 25 C  for data and models presented in (a) volume fraction , and (b) volume concentration . Points are for experimental data and solid lines are fitting functions or theoretical models.

Figure 6 :

 6 Figure 6: The electrical conductivity of various type of titanium dioxide nanofluids (a) TiO 2 A-EG, (c) TiO 2 M1-EG (e) TiO 2 M2-EG and their enhancement (b) TiO 2 A-EG, (d) TiO 2 M1-EG (f) TiO 2 M2-EG. Dots represents experimental data and solid lines are fitting functions, lines colour correspond to temperature presented by dots with the same colour.

Figure 7 :

 7 Figure 7: The ability of the proposed power-law function to describe experimental results obtained by Sikdar et al.[START_REF] Sikdar | Investigation of electrical conductivity of titanium dioxide nanofluids[END_REF]

  The results confirm increase in electrical conductivity with increasing of TiO 2 nanoparticles in base fluid. For the lowest

	(0.0015%) and the highest (0.005%) tested volume concentration the electrical conductivity was
	approximately 2.3 approximately 800 and 1500 / S cm 	and 2.75 / S cm		/ S cm	at 25 C		/ S cm	for pure water to

 respectively. Titanium dioxide-water nanofluids were also studied by Angayarkanni et al.

[START_REF] Angayarkanni | Effect of nanoparticles aggregation on thermal and electrical conductivities of nanofluids[END_REF]

, but data concerning electrical conductivity are presented in a limited way. Only one concentration (4% in vol.) and temperature (25 C  ) were tested, but a large enhancement in EC of about 8876% was reported. Chereches and Minea

[START_REF] Chereches | Electrical conductivity of new nanoparticle enhanced fluids: An experimental study[END_REF]

also studied titanium dioxide water-based nanofluids in volume concentration range 1-3 %. They reported an increase in electrical conductivity from 25.77

Table 1 :

 1 Summary of electrical properties of TiO 2 nanofluids with various base fluids. glycol (W/EG). As a part of preliminary studies, dispersion of TiO 2 nanoparticles in a mixture of water and ethylene glycol was investigated by Islam et al.[START_REF] Islam | Experimental investigation of using ZnO nanofluids as coolants in a pem fuel cell[END_REF] in the context of applications in Proton Exchange Membrane Fuel Cell (PEMFC).

	They showed 890%

Another group of titanium dioxide nanofluids are those based on the mixture of water and ACCEPTED MANUSCRIPT -CLEAN COPY ethylene

Table 2 :

 2 Main parameters obtained from the Rietveld refinements of the different TiO 2 samples The (BET) specific surface area of TiO 2 nanoparticles was determined to 3.51  0.08 2 m /g, 38.3  0.2 m 2 /g and 51.9  0.2 m 2 /g for TiO 2 A, TiO 2 M1 and TiO 2 M2 powder sample respectively. SEM pictures of TiO 2 nanoparticles are reported in Fig. 2. This figure shows that anatase particle (TiO 2 A) are mainly in form of dense aggregates of several  m, while TiO 2 M1 and 2

  4, Table A.6). The highest value of electrical conductivity was noted for the highest tested content of TiO 2 A nanoparticles (20 wt.%) in ethylene glycol at 318.15 K and it was 10728

		/ S cm	. On the other hand, the highest enhancement in comparison to base fluid in the same
	temperature was observed for 20 wt.% at 283.15 K. In this case a 4586458% enhancement was
	observed, for comparison at highest tested temperatures (318.15 K) it reaches 3461838%.

  was described by Awin et al.[START_REF] Awin | Electrical and thermal conductivities of dilute nanofluids-experimental determination and parametric studies[END_REF]. They proposed the following equation which takes account volume fraction and temperature in range from 0.0015 to 0.005% and 25 to 45 C

					 respectively:
		0.968 0.24 v  = 0.459 nf T	.	(6)
	Also Chereches and Minea [24] proposed a formula for electrical conductivity of titanium dioxide
	nanofluid, which was obtained by numerical fitting with coefficient R 2 = 0.94 at ambient
	temperature and volume fraction between 1 and 3%:
		= 388.11  	337.29,	(7)
		nf	v
	where	 is the nanoparticle volume concentration expressed in %. They also present regression
		v
	equation for titanium dioxide water nanofluid in volume concentration range of 1-3% and
	temperature between 20-60 C  :
		= 491.56 104.67		71.37	2	4.19 .

Table 3 :

 3 Fitting parameters with corresponding coefficients of determination for the TiO 2 A-EG nanofluids

Table 4 :

 4 Fitting parameters with corresponding coefficients of determination for TiO 2 M1-EG nanofluids

Table 5 :

 5 Fitting parameters with corresponding coefficients of determination for TiO 2 M2-EG

nanofluids

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Table 1 :

 1 Summary of electrical properties of TiO 2 nanofluids with various base fluids.

					Electrical
	Base	Nanoparticles size	Nanoparticles	conductivity	Temperaturę	Preparation	Ref.
	fluid	(nm)		load	range (µS/cm)	rangę (°C)	method
							2-step, various
	W	10-20	0.0015	0.005 vol%	2.3 -5*	25-45	sonication	[13]
							time (30-180 min)
	W	13.5	0.25* -4 vol%	8876% †	25	-	[23]
	W	-	1 -3vol%	26 -1500*	20-60	dilutions	[24]
	W	20-30	0.5 -3.0 vol%	3 -2 75	24-45	2-step	[25
	W/EG	40	0.05 -0.5 vol%	5 -65*	50	2-step, 1h	[26]
							sonication
	W/EG	-	0.05 -0.5 vol%	20 -77*	20 -70	2-step	[27]
	W/EG	40	0.05 -0.5 vol%	5-77*	20-70	2-step	[28]
	EG	20	0.05 -1.0 wt%	2 -7 5*	30-90	2-step, 1h	[29]
							sonication
	O	47	0.1wt.%	0.5*	2 0 -45	2-step, 1h
							sonication

Table 2 :

 2 Main parameters obtained from the Rietveld refinements of the different TiO2 samples

	Sample Name	Phase in presence	Cell parameters	Phase proportion	Average crystallite size
	[-]	[-]	[Å]	[wt.%]	[Å]
	TiO 2 (A)	anatase	a = 3.796(2) c = 9.508(4)	100	31
	TiO 2 (M1)	anatase rutile	a = 3.7867(1) c = 9.5105(3) a = 4.5948(3) c = 2.9580(4)	93 7	203 250
	TiO 2 (M2)	anatase	a = 3.7869(1) c = 9.5111(3)	10	185
		rutile	a = 4.5954(3)	90
			c = 2.9608(3)

Table 3 :

 3 Fitting parameters with corresponding coefficients of determination for the TiO2A-EG nanofluids

	T	A	u(A)	B	u(B)	R 2
	10 0.83862 0.01274 5.61289 0.02371 0.99867
	15 0.83946 0.01243 5.56246 0.02314 0.99869
	20 0.84218 0.01197 5.57273 0.02228 0.99879
	25 0.84172 0.01067 5.55205 0.01987 0.99904
	30 0.84532 0.01164 5.54980 0.02167 0.99886
	35 0.85255 0.01294 5.55678 0.02408 0.99862
	40 0.84401 0.01027 5.52911 0.01911 0.99911
	45 0.84119 0.00966 5.49884 0.01799 0.99921

Table A .

 A 6: The electrical conductivity of the different TiO 2 -EG nanofluids Sample Name φ m electrical conductivity, µS/cm 283.15 K 288.15 K 293.15 K 298.15 K 303.15 K 308.15 K 313.15 K 318.15 K

		0.000	0.08	0.11	0.13	0.16	0.19	0.22	0.26	0.31
		0.010	257.08	313.67	374.62	441.61	514.92	592.84	678.00	765.06
		0.020	466.02	562.77	668.91	783.38	901.94	970.29	1175.36	1316.95
		0.030	619.54	753.51	900.00	1054.87	1221.83	1412.15	1602.17	1814.12
		0.040	801.47	976.12	1178.53	1384.08	1613.43	1853.38	2110.72	2391.87
	TiO 2 (A)	0.050	931.02	1139.92	1379.28	1627.05	1890.90	2180.31	2512.96	2818.39
		0.100	1778.47	2155.67	2568.49	3047.14	3549.35	4086.71	4672.46	5250.95
		0.150	2702.32	3283.02	3958.32	4672.57	5436.00	6273.17	7110.17	8014.18
		0.200	3669.17	4490.34	5402.31	6283.77	7409.00	8491.03	9650.83 10727.98
		0.010	8.44	10.50	12.91	15.55	18.71	22.11	25.95	30.46
		0.020	14.60	18.10	22.06	26.95	32.50	38.46	45.61	52.54
		0.030	22.29	27.49	33.62	40.75	48.74	57.65	67.59	78.52
	TiO 2 (M1)	0.040 0.050	29.51 36.22	36.60 44.63	44.82 54.44	54.14 66.12	64.77 78.97	76.50 93.59	89.57 109.25	104.48 126.89
		0.100	65.60	81.50	99.65	121.65	145.48	172.29	203.39	236.84
		0.150	92.91	116.83	143.79	174.54	210.03	249.58	293.05	342.61
		0.200	123.39	151.65	188.57	227.48	272.90	326.39	384.02	451.21
		0.010	0.92	1.16	1.91	1.80	2.19	2.67	3.18	3.85
		0.020	1.37	1.78	2.30	2.92	3.53	4.26	5.19	6.20
		0.030	1.70	2.21	2.83	3.76	4.41	5.32	6.47	7.77
		0.040	1.86	2.37	3.58	3.75	4.63	5.77	7.09	8.98
	TiO 2 (M2)	0.050	2.25	2.94	3.71	4.65	5.74	7.11	8.61	10.52
		0.100	3.09	3.92	4.92	6.02	7.43	9.15	11.41	13.99
		0.150	4.19	5.30	6.60	8.02	9.84	12.01	14.63	17.82
		0.200	6.89	8.67	10.11	12.38	15.22	17.83	21.66	25.85

Acknowledgments

PE wishes to acknowledge M. Pasturel & M. Dallon from ISCR, Université Rennes1 for their assistance with XRD experiments, as well as L. Jarny from CMEBA, Université Rennes1 for SEM characterizations.

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Appendix A. The electrical conductivity of the different TiO 2 -EG nanofluids

Appendix B. Numerical analysis of experimental data

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Highlights

The electrical conductivity of titanium dioxide ethylene glycol was investigated. A significant increase in the electrical conductivity of nanofluids was observed. Crystalline phase effect on electrical conductivity of TiO2-EG nanofluids was shown. The new correlation of electrical conductivity of TiO2-nanofluids was introduced.


Florent Moutier

Dr Jana Schiller

Dr Constance A Lecourt

Ali Moustafa Khalil

Vincent Delmas

Guillaume Calvez
email: guillaume.calvez@insa-rennes.fr

Karine Costuas
email: karine.costuas@univ-rennes1.fr

Christophe Lescop
email: christophe.lescop@insa-rennes.fr

Dr Mr F Moutier

Dr V Khalil

Dr G Delmas

Dr K Calvez

Dr C Costuas

Lescop

Impact of intermolecular non-covalent interactions in a CuI8PdII1 discrete assembly: conformers' geometries and stimuli-sensitive luminescence properties

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The recent development in science and technology targeting photofunctional molecular materials have highlighted for such derivatives appealing perspectives in manifold fields including organic light emitting diodes, [1] solar cells, [2] luminescent sensors, [3] or anti-counterfeiting, [4] just to name a few. Among these materials, an ever-growing number of stimuli-responsive luminescent sensors has been reported, comprising rich thermo-, mechano-, vapo-or solvato-chromic luminescence properties. Regarding more specifically mechanochromic derivatives, [5] the color of the light emitted by the luminescent material is altered upon application of a mechanic stress. The mechanisms at the origin of such properties changes are generally ascribed to stimuli-induced transformations of structural arrangements and/or packing modes (molecular conformations and/or intermolecular interactions) in the solid-state, that concomitantly impact the electronic structures and solid-state photophysical properties. In this context, the rationalization of the way intermolecular or intramolecular non-convalent interactions between emissive centers can be modified in the solid-state carries a paramount importance in order to design, understand, optimize and control the mechanochromic response of luminescent molecular materials. So far, in the field of mechanochromic materials, the majority of systems that have been reported are organic dyes [5a,6] and gold [7a-k] and platinum [7l-r] metal-based compounds [5b] which show a rich variety of mechanochromic properties. In this field, the development of mechanochromic luminescent Cu I coordination complexes offers particularly appealing perspectives for upcoming developments not only because of the low cost and relatively high abundance of copper but also due to the fascinating and various photophysical properties these complexes can exhibit. [5b,8,9,10] The emission behaviors of Cu I complexes are indeed characterized by the large diversity of the radiative relaxation processes involved with a rising attention being paid to derivatives exhibiting Thermally Activated Delayed Fluorescence (TADF). [8f,g, 9] In such complexes, spatially wellseparated HOMO and LUMO orbitals induce small lowest energy singlet-triplet energy gap. This can allow thermal population of the lowest energy excited singlet state (S1) from the lowest energy triplet excited state (T1), via a reverse intersystem crossing (RISC) inducing efficient radiative relaxation to the ground state and exalted solid-state luminescence properties that occurs ideally at temperatures close to room temperature (RT). Importantly, this phenomenon is not only observed for mononuclear Cu(I) complexes but several polynuclear Cu I complexes have been also reported with enhanced solid-state luminescent properties. [5b, 9n-x, 10d-j] In such derivatives non-covalent short intermetallic cuprophilic interactions (d(Cu-Cu) bellow ca. 2.9 Å) [11] can be found in the ground state and/or in the excited states relaxed geometries. [9t,u] Such interactions induce a significant enhancement of the spinorbit coupling (SOC) constants compared to the one induced by the presence of non-interacting Cu I ions for which intrinsic individual SOC is generaly moderate. Consequently, radiative rates constants for the T1 states are increased, promoting efficient RISC to the S1 states but also fast and efficient phosphorescent relaxation process to the ground states (S0). While luminescent Cu I derivatives focused so far a great attention for the preparation and study of innovative emitters in OLEDs, [8f,9] these systems also deserve interest as new sources of stimuli responsive multifunctional luminescent materials. [10] Indeed, the Cu I ion presents a coordination sphere characterized by a high degree of flexibility and lability which renders the gross conformation of Cu I species very sensitive to external stimuli, and concomitantly impacts their photophysical properties. In this context, Perruchas et al. have extensively studied in the recent years the mechanochromic responses of a series of copper iodide clusters mostly based on Cu4I4 cubane units stabilized by various phosphine ligands. [5b,12] Using a variety of solid-state characterization techniques including Powder X-Ray Diffraction (PXRD), solid state 63 Cu and 31 P NMR, solid-state IR and Raman spectroscopies, these studies have allowed to assign the origin of the mechanochromic properties to modifications of the intermetallic cuprophilic interactions as a result of the application of a mechanical stress. It was revealed that such stress induces a transition from crystalline to a partially amorphous state in which intermolecular contacts in the crystal packing are likely to be altered. As a result, the molecular geometries can relax to an energetically more favored conformation than the one stabilized in the single crystals. Indeed, in such mechanically induced phases, individual molecules are released from some of the stabilizing intermolecular packing non-covalent interactions whose accumulation can impose specific molecular conformations. Similarly, Chen et al. and Jin et al. recently reported luminescent Cu I derivatives whose mechanochromic properties are assigned to - interactions or hydrogen bonds alteration upon grinding from the pristine crystalline phases to the grinded amorphous phases, supporting the crucial importance of intermolecular interactions in the solid-state to control stimuli-responsive luminescence properties. [13] Artem'ev et al. also recently described the first Cu I trimers reported to date to be stabilized by triply bridging phosphine ligand in which the mechanochromic behaviors observed are assigned by the authors to the crystalline to amorphous phase transition and concomitant local molecular geometry reorganizations. [14] Herein, we report firstly the polymorphic behavior of a luminescent [Cu8Pd1(CN)8dppm8](PF6)2, thereafter named Cu I 8Pd II 1, discrete polymetallic assembly (dppm = 1,1bis(diphenylphosphino)methane). While the 'open-form' Bo was initially reported as being the only phase obtained upon crystallization, we have observed recently the formation upon the same crystallization conditions of traces of a 'closed-form', Bc (scheme 1). X-ray crystal structure resolution reveals that Bc is a conformational isomer of Bo in which intermetallic Cu We have previously reported that the pre-assembled solid-state blue luminophore tetrametallic metallacycle A [9t] (Scheme 1), based on the connection of two [Cu2(2-dppm)2] dicationic units with two bridging cyanide ligands, can behave as a very versatile precursor. By reacting it with various pseudo-halide ions (cyanido CN -, dicyanamide N(CN)2 -or azido N3 -ions), a variety of polymetallic Cu I derivatives has been prepared

Figure 1. a) Molecular X-ray structure, simplified 'top' and side views of the species Bo [15] and accordingly to an adapted coordination-driven supramolecular synthetic strategy. [15,16] These derivatives present a variety of molecular structure and luminescence properties due to the versatile photophysical processes and the remarkable conformational flexibility (variation of the intermetallic Cu(I)-Cu(I) distances and of the bite angle of the dppm ligands) lying in the [Cu2(2-dppm)2] building blocks. In particular, we have characterized that the straightforward reaction of two equivalents of A with one equivalent of the [Pd(CN)4] 2-metallo-ligand affords (Scheme 1) in the solid-state the Cu I 8Pd II 1 assembly in good yield as the room temperature (RT) weakly luminescent Bo phase. [15] For the sake of the analysis and comparison of the results described herein, structural and photophysical parameters of this previously published [15] polymetallic discrete assembly will be shortly first detailed. Derivative Bo, that can be isolated in a good yield (ca. 70 %) accordingly to the previously published synthetic procedure, [15] crystallizes in the P21/n space group of the monoclinic system. This derivative can be described as resulting of the connection of four [Cu2(2dppm)2] 2+ fragments with four 2-ditopic 'external' cyanido ligands forming a ''Cu8(CN)4'' metallacycle sub-unit having a slightly twisted rectangular shape (Figure 1a). [START_REF]Equal relative occupancies for C and N atoms have been modelled at the atomic position determined for the cyano ligands connecting two Cu(I) metal centers. For the Pd(CN)4 fragments, C atoms have been assigned to the atoms connected to the Pd(II) metal centres[END_REF] The backbone of the derivative Bo results of the connection of this Cu8 metallacyclic unit to a square planar 'Pd(CN)4' internal fragment. Importantly, within the Cu8 metallacycle sub-unit, the four 'internal' cyanido ligands present a slightly bended 2 coordination mode (N≡C-Cu = ca. 168 °). This coordination mode induces an asymmetry of the [Cu2(2-dppm)2] 2+ fragments with one Cu I metal center presenting a P2N1(C/N)1 distorted tetrahedral coordination sphere while the other Cu I metal center has a P2(C/N)1 distorted trigonal planar coordination sphere. [START_REF]Equal relative occupancies for C and N atoms have been modelled at the atomic position determined for the cyano ligands connecting two Cu(I) metal centers. For the Pd(CN)4 fragments, C atoms have been assigned to the atoms connected to the Pd(II) metal centres[END_REF] The intermetallic Cu I -Cu I distances in the [Cu2(2-dppm)2] 2+ subunits (ca. 3.40 Å) in Bo are too large for metallophilic interactions. In the solid state, polycrystalline sample of the derivative Bo displays upon excitation at 350 nm a weak RT greenish luminescence characterized by a broad and featureless band with emission maximum em centered at 500 nm. The emissive lifetime  is 12 s at 298 K and the emission quantum yield (EQY) is 2 % (Table 1). Upon stepwise cooling in the solid state the emission spectra (ex = 350 nm) of derivative Bo present gradual red-shifts associated with emergence of an intense solid state yellow-green luminescence at low temperature (em = 515 nm at 80 K (em(298K/80K) = 0.108 eV / 870 cm 1 )). Concomitantly, the thermal dependence of the emission decay lifetime  of Bo in the solid state presents a sigmoidal profile with a value of ca. 3 s at 400 K and a low temperature (80 K)  value of 222 s. While the large majority of the crystallization experiments (conducted at RT upon pentane vapor diffusions within CH2Cl2 solutions) exclusively afforded in high yield colorless and weakly RT luminescent needle-shaped crystals of the Bo phase, we observed sporadically a very few amount of tiny colorless prismshaped crystals of the new phase Bc that display at RT an intense eye-perceived yellow luminescence (seen under UV-vis lamp light excitation, ex = 365 nm). By repeating in a large number these crystallization experiments, it was possible to collect manually first a single crystal suitable for X-ray crystal structure determination [START_REF]Temperature-dependent X-ray crystal structure analyses were performed on the same single crystals of Bc at 250 K, 200 K, 150 K, and 100 K[END_REF] and in a second step sufficiently enough solid-state polycrystalline material [START_REF]For experimental details, spectroscopic, X-ray diffraction data and computational studies[END_REF] to allow the photophysical studies of Bc. The phase Bc crystallizes in the I422 space group of the tetragonal system. The unit cell of single crystals of Bc is composed of a quarter of a dicationic Cu8Pd1(CN)8dppm8 polymetallic assembly, one half of a PF6 - counter-anion and one included CH2Cl2 solvent molecule. The comparison between the X-ray crystal structure resolutions reveals that the dicationic Cu8Pd1(CN)8dppm8 species in Bc is a conformational isomer of the one observed in Bo (Figure 1b). Indeed, Cu I 8Pd II 1 in Bc similarly than Cu I 8Pd II 1 in Bo can be described as resulting of the insertion of a square planar 'Pd(CN)4' internal fragment within a ''Cu8(CN)4'' metallacycle sub-unit (Figure 1b) resulting of the connection of four [Cu2(2dppm)2] 2+ fragments with four 2-ditopic 'external' cyanido ligands. Note that the ''Cu8'' metallacycle sub-unit is strictly planar in the Bc scaffold (Figure 1b) which is not the case in the Bo scaffold. The main structural difference between the solidstate structures of Bc and Bo lies in the coordination modes adopted by the four 'internal' cyanido ligands: these cyanide ligands connect in Bc the central Pd II metal center to all the eight peripheral Cu I metal centers resulting in a symmetrical 3 coordination mode (versus a slightly bended 2 coordination mode in Bo). Therefore, the overall molecular structure of the phase Bc (Figure 1b) is more symmetrical than Bo (Figure 1a) with all the Cu I metal centers having a similar P2N1(C/N)1 distorted tetrahedral sphere. [START_REF]Equal relative occupancies for C and N atoms have been modelled at the atomic position determined for the cyano ligands connecting two Cu(I) metal centers. For the Pd(CN)4 fragments, C atoms have been assigned to the atoms connected to the Pd(II) metal centres[END_REF] In addition, and importantly, in the species Bc, the intermetallic distances within the bimetallic ; insert: plot of the emission decay lifetime against temperature (80 K to 300 K, the wavelength monitored was the wavelength for which the maximum of signal intensity was observed at a given temperature in the solid-state emission spectra), the red line represents the fit according to the TADF Boltzmann-type equation S1.

[Cu2(2-dppm)2] 2+ sub-units (d(Cu I -Cu I ) = 3.046(2) Å) are significantly shorter than in Bo (ca. 3.40 Å). Polycrystalline batch of phase Bc display solid-state luminescence properties that are markedly different from those of the phase Bo. [15] Indeed, derivative Bc displays in the solid-state at 298 K an intense eyeperceived yellow luminescence under excitation at 365 nm characterized by a broad and featureless band in the emission spectrum with a maximum in intensity at 550 nm (Figure 2), an emissive lifetime  of 15 s and a EQY of 42 % (Table 1). Therefore, the species Bc present a significant red-shift of its emission band and a remarkable increase of its RT EQY (Bc : 42 %; Bo : 2 %) compared to its conformational isomer Bo. Upon cooling from 298 K to 80 K under excitation at 365 nm, emission spectra of derivatives Bc exhibit gradual red-shifts associated with intense solid state red-orange luminescence at low temperature (Figure 2). At 80 K, the emission spectrum presents a broad and featureless band having an intensity maximum at em = 605 nm (em(298K/80K) = 0.205 eV / 1653 cm 1 ), with a shoulder observed at ca. 520 nm, while the emissive lifetime  increases up to 189 s. The detailed study of the temperature dependence of the emission lifetime of Bc (Figure 2) reveals mono-exponential decay times all along the temperature range with a sigmoidal progression that resembles those typically reported for Cu(I) TADF derivatives. In order to account the photophysics observed for the species Bc, it is quite likely that a single radiative relaxation pathway such as a TADF process would be operant along the entire temperature window. Yet, considering the thermal dependence of the emission spectra, the shoulder observed at ca. 520 nm beside the main large emission band centered at ca. 605 nm could suggests that several radiative relaxation pathways operate at low temperature. While this assumption cannot be formally excluded, it is more likely that this shoulder at 520 nm reveals the presence of traces of the Bo phase or eventually of the Bg phase (vide supra) in the batch of Bc crystals manually collected that would have been generated during the process of recovering of the single-crystals of Bc. Therefore, regarding this set of experimental data, a precise and definitive assignment of the relaxation processes occurring after UV-vis excitation in derivative Bc cannot be provided. Yet, by making the approximation that a TADF process dominates the photophysical processes in the species Bc, a fit of the thermal variation of the  values of Bc (Figure 2) to the Boltzmann-type equation S1 in SI derived from the TADF model, [8h,g] was attempted, affording the values of E(S1-T1) = 767 cm 1 , (S1) = 76 ns and(T1) = 191 s. This set of values ranges among those determined for the other Cu I assemblies based on the [Cu2(2-dppm)2] 2+ fragment (including the precursor A) that were identified as TADF luminophores [9t, 15, 16] which supports the assumption that such relaxation process can be taken into consideration in order to explain the photophysics of the species Bc. Accordingly, the RT kr radiative rate constant value for Bc (2.8*10 4 s -1 , Table 1) is in agreement with a thermally delayed fluorescence regime. Interestingly, in the case of Bo, the RT kr radiative rate constant value (1.6*10 3 s -1 , Table 1) supports a 3 MLCT phosphorescence rather than a TADF process. [8h,g] This underlines the crucial impact that the structural differences observed between the two confomers Bo and Bc have on their photophysical properties, in particular in the radiative relaxation processes. Indeed, while the kr value for Bc is one order of magnitude larger than for Bo, the knr non-radiative rate constant values for both species (Table 1) are significantly similar. This allows assigning the enhancement of the luminescence efficiency of the phase Bc to more efficient radiative relaxation pathways rather than reduced vibrational non-radiative processes lying at RT in Bc's scaffold compared to Bo. Likely, the significant decrease of the intermetallic Cu I -Cu I distances in the [Cu2(2-dppm)2] sub-units of Bc is a parameter that plays a role, at least partially, for such differences. It can induce an increase of the SOC components in the different processes, which favors radiative relaxation processes in particular when compared with the conformer Cu I 8Pd II 1 in Bo. Regarding the remarkable differences recorded in the solid-state luminescence properties between the weakly luminescent conformer Bo and the bright luminescent conformer Bc, we have triggered quantum chemical DFT molecular calculations to give insights into the reasons why the less emissive species Bo is predominantly obtained in the crystallization experiments. [START_REF]For experimental details, spectroscopic, X-ray diffraction data and computational studies[END_REF] The energies of the Bo and Bc Cu I 8Pd II 1 molecular conformers were calculated by freezing the copper atomic positions in their crystallographic configurations. Full geometry optimization was also performed. It revealed firstly that the energy difference in vacuum between the Bo and Bc Cu I 8Pd II 1 conformers is small (E = 14.6 kJ mol -1 ). Quite unexpectedly at first sight regarding experimental results, the Cu I 8Pd II 1 in Bo is the less stable conformer (Figure 3a). Additionnaly, the most stable calculated conformer in vacuum (Bcalc) is notably different from the experimental isomers found in Bo and Bc (Figure 3a). Bcalc is based on an almost planar Cu8Pd1(CN)8 core bearing two internal 2-CN and two internal 3-CN ligands (Figure 3b). Interestingly, while the calculated species Bcalc is less symmetrical than the experimentally observed conformers Bo and Bc, it bears 'intermediate' geometrical features with two sets of different intermetallic Cu I -Cu I distances in the [Cu2(2-dppm)2] sub-units (Table 1), associated either with 3-CN internal ligands (2.920 Å) or 2-CN internal ligands (3.128 Å). Apart from these intermetallic distances and the bridging coordination mode of the internal cyanido ligands, all the gross geometrical parameters are essentially similar within the series of the Bcalc, Bo and Bc conformers. The calculated isomer Bcalc can be considered as a molecular scaffold, in vacuum, in which is optimized the balance of energetic stabilization and destabilization factors that are Considering the overall moderate energy differences between Bcalc, Bo and Bc, (Figure 3a), multiple and complex fast equilibria based on intramolecular exchanges requiring minimum reorganization (mostly translation/rotation of the CN groups) must occur in solution at RT, allowing easy interconversion between these conformers. This allows concluding that all the three conformers and other intermediate structures must be present in solution at RT, an almost barrierless geometry reorganizations connecting the different arrangements. It can be deduced that it is the crystal growth which induces the predominance of isomer Bo at the solid-state. Such a selection in the solid state of the less stable of the two experimentally determined conformers can be assigned to the fact that the Cu I 8Pd II 1 assemblies Bo stacks on the top of each other in the crystalline solid state along infinite columns (Figure 1a) in which multiple lateral stabilizing CH-non-covalent interactions are cumulated between most of the phenyl rings of the dppm ligands of neighboring assemblies. In a marked contrast, in the crystalline solid state, the Cu I 8Pd II 1 species in Bc appear much more isolated from each other (Figure 1b), bearing less peripheral non-covalent CH- interactions. This may explain why this conformer is only observed as traces along crystallization experiments. Finally, the lower symmetry observed in the molecular scaffold Bcalc probably does not promote the formation, in the crystalline solid-state, of a set of cumulated stabilizing non-covalent intermolecular interactions as large as those experimentally observed in the case of the conformers Bo and Bc, which likely preclude its formation as single crystal. Therefore, the accumulation of stabilizing CH- non-covalent interactions along the crystallization process allows an inversion in the hierarchy observed in vacuum considering the relative stabilities of the conformers Bcalc, Bo and Bc. This dictates the almost exclusive isolation in fine of the species Bo. This behavior definitively favored by the very labile, flexible and low-directional coordination sphere of the Cu I ions that can accept manifold changes in their coordination numbers, bond lengths and angles for the expense of a minimal energy cost. This situation carries also a great impact on the electronic structures of these species as witnessed by the remarkable differences observed in the solid-state concerning the photophysical behaviors of conformers Bo and Bc (Table 1). Regarding the molecular scaffold calculated for the more stable specie (in vacuum) Bcalc which carry a set of geometrical parameters significantly different than those observed experimentally in Bo, it can be anticipated that the photophysical processes lying in the Bcalc scaffold should be markedly different compared to those observed for Bo, affording putatively an attractive new luminescent phase. This has triggered us to study the mechanochromic response of solid-state polycrystalline samples of Bo, anticipating that a partial amorphization or alteration of the pristine crystalline state organization would occur upon grinding. This would impact the long range columnar stacks observed in single crystals of Bo (Figure 1a) allowing some Cu I 8Pd II 1 assemblies to relax to an energetically more favored conformer bearing a molecular structure related to the one calculated in Bcalc, and therefore alterating the photophysical characteristics of the bulk solid. Indeed, a manual grinding at RT of the polycrystalline powder of Bo, affords the Bg phase (Scheme 1). The very weak greenish emission typical of Bo [15] under UV-vis lamp light excitation (ex = 365 nm) is transferred to a much brighter eye-perceived yellow-green emission, revealing a naked-eye highly observable mechanochromic effect. [20] Concomitantly, no alteration of the white color initially presented under visible light by the solid-state sample of Bo is observed during the grinding process. The RT emission of the Bg phase correspond to a large band centered at 500 nm (Figure 4, ex = 375 nm), revealing no spectral shift compared to the RT emission of Bo. The emissive lifetime  is 39 s at 298 K. Importantly, a remarkable change in the intensity of the luminescence signal is observed with an increase of the EQY from 2 % for Bo to reach 27% for Bg (Table 1). The RT photoluminance (measured with a flux of 3.55 W/m² for an excitation at 365 nm) of the solid-state samples of Bg (16.56 Cd/m²) is also significantly higher than for Bo (0.832 Cd/m²). Upon cooling from 290 K to 80 K under excitation at 375 nm, emission spectrum of derivative Bg exhibits a gradual red-shift associated with intense solid state yellowish luminescence at low temperature (Figure 4). Thus, at 80 K, the profile of the emission spectrum presents a broad featureless band having an intensity maximum at em = 522 nm, revealing a slightly larger red-shift at low temperature for Bg than for Bo (em = 515 nm at 80 K). The average emissive lifetime  at 80 K increases up to 282 s which is larger, but kept in the same range of values, than for Bo (222 s) and for Bc (189 s). The temperature dependence of the emission lifetime of Bg (Figure 4) was analyzed considering mono-exponential decay times all along the temperature range. It revealed an irregular but reproducible profile progression [20] upon cooling with a constant increase of the decay time value of the exited state (Figure 4). It is quite common that multiple emissions are detected in samples obtained after grinding treatments arising from multiple species and site heterogeneity. [9p,12] Regarding the variety of possible conformers (not only limited to Bo, Bc and Bcalc, since the quantum chemical DFT calculations performed do not consider intermolecular non-covalent interactions that may have crucial importance in the selection in the solid-state of a specific conformer) ranged in a quite narrow distribution of relative energies, it is not surprising that a grinding process applied on a polycrystalline sample of Bo would indeed afford several different emissive species based on structurally related polymetallic scaffolds. Therefore, the irregular profile [20] of the thermal dependence of the average decay time of the excited state recorded for Bg samples may account for cumulated independent contributions assigned to different emissive centers whose ratios are not clearly determinated. This precludes performing a deeper analysis of the set of data obtained for the thermal dependence of the observed decay time based on a treatment of the experimental data considering multi-exponential decay times. Yet, the value of the RT observed kr radiative rate constant that can be extracted for these measurements (Table 1) suggests that phosphorescence processes dominate at RT. PXRD studies were conducted on Bg samples to get insights about the structural modifications potentially induced by the application of the mechanical stress on Bo. [START_REF]phases Bg and Bm always yielded single-crystals of Bo, supporting the hypothesis that multiple[END_REF] The diagram recorded for Bg reveals a set of peaks that compares well with those observed in the diagram obtained for polycrystalline samples of Bo (Figure 5). This suggests that neither a complete amorphization nor crystal phase transitions take place during the application of the manual grinding on solid-state samples Bo. A mechanically induced chemical transformation is also precluded since Bg phase dissolved in CD2Cl2 afforded similar multinuclear NMR spectra [START_REF]For experimental details, spectroscopic, X-ray diffraction data and computational studies[END_REF] than those recorded for Bo [15] and afforded single crystals of Bo when recrystallized from CH2Cl2 upon pentane vapors diffusion. Yet, the peaks observed in the diagram of Bg are significantly broader and less intense than for Bo which supports the assumption of a partial amorphization of the bulk sample. Likely, the grinding process induces local effects, allowing the formation of new emissive species in low amount. This phenomenon was previously reported by Perruchas et al. investigating the mechanochromic behavior of Cu4I4 cubane clusters stabilized by phosphane ligands. 12 It was assigned to an effect of the mechanical stress application on the crystallite sizes and/or generation of microstrains which induces local apparition in a bulk composite sample of a small amount of a new generated amorphous emissive domains in addition to the original pristine crystalline phase. SEM pictures (Figure 6) recorded for Bo and Bg support this assumption since significantly similar patterns were observed in both cases revealing polycrystalline particles having quite a large size distribution with smaller average dimensions for Bg samples likely as a result of the grinding process. Therefore, in accordance with previously reported related manual grinding processes applied on Cu4I4 cubane clusters, [12a] an incomplete transformation of the crystalline state observed in the Bo phase likely occurs upon application of a mechanical stress, affording a new Bg phase with altered bulk luminescence properties. Interestingly, the TGA-DSC analysis of Bo showed an endothermic peak around 230 °C associated with no loss of mass, while the thermal decomposition started to occur at ca. 300 °C. [START_REF]For experimental details, spectroscopic, X-ray diffraction data and computational studies[END_REF] The peak at 230 °C corresponds to a melting transition and no exothermic peak is observed upon cooling the sample back to RT before the decomposition temperature was reached, probing that a recrystallization process does not occur. Accordingly, the visible appearance of bulk samples of polycrystalline white powder of Bo after being heated at 240°C and cooled back to RT changed to colorless clear glass-like solids, affording the new phase Bm (Scheme 1). Under UV-vis lamp light excitation (ex = 365 nm) at RT, samples of Bm exhibited an eye-perceived yellowish emission, clearly different from the very weak greenish emission of Bo. [15] The PXRD diagram of Bm showed two broad peaks around 8° and 20°, revealing an amorphous phase that is markedly different from the Bo and Bg phase. [START_REF]phases Bg and Bm always yielded single-crystals of Bo, supporting the hypothesis that multiple[END_REF] Therefore, the melting process implies a considerably larger solid-state organization alteration than the manual mechanical grinding process. Supporting this observation, SEM pictures taken for Bm sample (Figure 6) revealed particles with larger average size than those observed for Bo and Bg, with a flat and homogeneous surface microstructure suggesting that the melting process yielded a vitreous phase, in agreement with the PXRD diagram of Bm. The RT solid-state emission spectrum of the Bm presents a large featureless band centered at 559 nm (Figure 7, ex = 375 nm), which is significantly red shifted compared to the RT emission of Bo and Bg (ca. 500 nm) but comparable with the emission spectrum of Bc (550 nm). The emissive lifetime  is 35 s at 298 K. The RT EQY is 7 % and the RT photoluminance reaches (4.24 Cd/m², measured with flux of 3.55 W/m² for an excitation at 365 nm) values that are both ranging between those measured for Bo and Bg. Temperature dependent solid-state measurements of the emission spectra and the decay time of the excited state of Bm were conducted. Upon cooling from 298 K to 80 K under excitation at 375 nm, emission spectra of derivative Bm exhibit gradual blue-shifts associated with a solid-state eye-perceived greenish luminescence at low temperature (Figure 7). The emission spectrum at 80 K presents a broad featureless band having an intensity maximum at em = 538 nm. Such a hypsochromic shift upon cooling does not follow the trend observed for the phases Bo, [15] Bc and Bg in which a gradual redshift upon cooling is observed (Figure 2 and4). This confirms the large impact on the photophysical properties of the Cu I 8Pd II 1

assembly of the various large-scale organizations that can be encountered in the solid-state for this polymetallic assembly.

Thermally induced chemical reaction in the solid-state that would have altered the initial chemical structure of this metallacyclic assembly is precluded since dissolution in CD2Cl2 of the Bm phase afforded 31 P{ 1 H} and 1 H NMR spectra similar to those recorded for dissolved Bo and Bg phases. [START_REF]For experimental details, spectroscopic, X-ray diffraction data and computational studies[END_REF] In addition, recrystallization of the Bm phase from CH2Cl2 solution exposed to pentane vapors afforded single crystals of the Bo species in high yield. The thermal dependence of the emission decay time of the species Bm was treated successfully considering monoexponential decay times all along the temperature range, revealing a sigmoidal profile with a smooth and constant progression upon temperature cooling from 35 s at 298 K to 248 s at 80 K. Considering this set of data, it is possible to state that the temperature dependences of the photophysical properties in Bm are suggestive of the absence of a TADF mechanism. The hypsochromic shift upon cooling of emission maxima upon temperature variation is indeed not consistent with such a photophysical process. In addition, the value of the RT kr radiative rate constant (Table 1) supports a 3 MLCT phosphorescence process to account for the radiative processes observed at room temperature. The blue shift observed at low temperature for the emission maxima is in agreement with the rigidochromic effect that results from the increased rigidity at low temperature, leading to a smaller excited state distortion. In addition, a narrowing of the emission band width with decreasing temperature is also observed, in line with the lower accessibility of higher vibrational states at low temperature. The impact of the non-covalent intermolecular interactions in the various solidstate arrangements displayed by the different phases obtained for the Cu I 8Pd II 1 assembly is also essential at the excited state as it is highlighted by the difference of photoluminescence properties between the Bo and Bc phases. On the computational point of view, the optimization of the full solid-state structures at the excited states of these phases taking into account these non-covalent intermolecular interactions would be necessary to explain these differences, calculations which are not accessible to date. The observed partial or full amorphization of Bo and Bg phases is consistent with a release of the intermolecular interactions. In that case, full geometry optimizations based on the TD-DFT gradients of first singlet (S1) and triplet (T1) excited states of the Cu I 8Pd II 1 assembly could give substantial information to understand the photophysics observed. [START_REF]For experimental details, spectroscopic, X-ray diffraction data and computational studies[END_REF] This allows to access to the geometries of these excited states in vacuum or more generally in a non-constraining intermolecular environment. The resulting calculated geometries are sketched in Figure 8a. Interestingly, whereas Bcalc was the starting geometry (Figure 3) used to conduct these full geometry optimizations, the relaxation of the excited states S1-relax and T1-relax leads to arrangements having molecular organizations (Figure 8) being in the first glimpse similar to Bo (Figure 1) on the bonding point of view. Yet, the intermetallic Cu(I)-Cu(I) distances in the [Cu2(2-dppm)2] 2+ fragments present a larger distribution in these relaxed excited states' geometries (intermetallic distance distribution : Bo , 3.362 -3.459 Å ; S1-relax, 3.272-3.634 Å ; T1-relax , 3.362-3.546 Å) and larger D and d distances (Figures 3 and8) measured in the 'Pd1Cu8CN8' cyclic organic cores. Moreover as revealed by the comparison displayed in the figure 8b, the 'Pd1Cu8CN8' cyclic organic cores in the S1-relax and T1-relax are significantly more distorted from a strictly planar organization than in the case of the Bo scaffold (maximum deviation from the mean plane : Bo, 0.66 Å ; S1-relax, 0.85 Å ; T1-relax , 0.79 Å). Therefore, all in all, the geometries of the relaxed excited states S1-relax and T1-relax are less planar and more distorted than the scaffold observed in the Bo phase. In addition, as compared to the Bcalc arrangement (Figure 3 and Table 1), a significant elongation of the average intermetallic distances in the [Cu2(2-dppm)2] 2+ fragments is observed (+0.46 Å for S1-relax and +0.42 Å for T1-relax) but in each of the two relaxed excited state one of the four bimetallic subunits is significantly more affected than the three others with a Cu I -Cu I distance of 3.634 Å for S1-relax and 3.546 Å for T1-relax.

The nature of the excited state T1-relax radiative relaxation is better described as a metal-ligand to ligand excitation as revealed by the difference density map shown in Figure 8c. The associated emission wavelength arising from this excited state is calculated at 535 nm which is in line with the experimental observation at low temperature for the fully amorphous phase Bm (538 nm, Table 1) which a priori correspond to the phase where the long range organization due to extended network of intermolecular interactions has been very likely mostly vanished.

The difference in energy between the relaxed S1-relax and T1-relax arrangements is of 2090 cm -1 , a value hardly compatible with TADF process and supports the assignment of the experimental photophysical measurements to a 3 MLCT phosphorescence process for the fully amorphous phase Bm. It is yet important to stress that these relaxed excited states in vacuum correspond to isolated molecules and cannot strictly reproduce the situation encountered experimentally in the different Cu I 8Pd II 1 assemblies' phases in their solid-state environment in which weak intermolecular interactions should occur locally between the discrete molecules. Therefore, in spite of the good agreement between the calculated values and the experimental photophysics measured for Bm in particular, these results are mostly indicative and do not allow unambiguous assignation of the photophysics observed in the non-crystalline phase Bm. As previously discussed, the selection of the Bo geometry is very likely favored by the formation in the crystalline solid-state of one dimensional infinite columnar stacks that propagate perpendicular to the mean planes of the Cu I 8Pd II 1 assemblies. Due to such organisation in the Bo phase, distortion of the molecular scaffolds in the excited states in this phase as observed in S1-relax and T1-relax geometries is very probably energetically disfavored since it should induce a long-range reorganisation of the intermolecular interactions between the Cu I 8Pd II 1 assemblies. This might explain the differences in the photophysical properties observed experimentally in the Bo and Bm phases and those anticipated from the calculated relaxed excited states in vacuum, in spite of the gross geometrical similarities of the Cu I 8Pd II 1 assemblies in Bo, S1-relax and T1-relax. Finally, it is interesting to note that the Pd(CN)4 moieties within the calculated arrangements are almost unchanged upon excitation and are also similar to the Bo and Bc experimental molecular structures. While these square planar fragments do play an important role as structuring group, they do not contribute directly to the photophysical properties' differences between the different phases, allowing to assign the stimuli sensitive properties observed to the specificities of the coordination chemistry and electronic configurations of the Cu(I)based sub-units.

Conclusion

With the characterization of the minor crystalline phase Bc in addition to the previously observed Bo species, the variety of the molecular geometries that can be observed in the Cu I 8Pd II 1 multimetallic assembly is highlighted, as well as the major impact of these geometries on the photophysical properties of solid-state samples of the Cu I 8Pd II 1 derivative. DFT calculations highlight that a third conformer Bcalc presents the optimized geometry in vacuum, which allows concluding that the selection of the Bo species in the solid-state is due to cumulated intermolecular non-covalent -CH interactions within columnar stacks. Importantly, the diversity of the molecular scaffold that can be encountered in the solid-state for the Cu I 8Pd II 1 assembly is associated with overall moderate energy differences between all possible conformers. Easy interconversions between these conformers explain the large predominance of the Bo species as the Cu I 8Pd II 1 assembly derivative is recrystallized from the solution. The labile, flexible and low-directional coordination sphere of the Cu I ions that can accept manifold geometry changes at the expense of a minimal energy cost definitively favors such behaviors. More importantly, these interconversions between possible conformers can be also manipulated in the solid-state by applying mechanical and thermal stress to pristine solid-state samples of Bo, affording respectively new luminescent species Bg and Bm. The analysis of the various photophysical properties of this set of phases obtained for Cu I 8Pd II 1

assembly suggests that such stress-induced conformers conversions govern a subtle balance between different 3 MLCT phosphorescence (Bo, Bg and Bm phases) and TADF (Bc phase) relaxation processes. Therefore, playing with the non-covalent intermolecular interactions between individual molecular species allows tailoring the conformer scaffold present in the solid-state, giving an access to markedly different solidstate emitters generated from the same chemical structure. It is here important to stress that, while the Bo phase almost exclusively collected in the solid-state after the synthetic work-up is conducted is a weak RT luminophore, it allows to obtain the much more RT emissive material Bg after grinding. Indeed the EQY and photoluminance values are approximatively fifteen times larger for Bg than for Bo. This result highlights that the solid-state studies of the photophysics of Cu(I) based derivatives should not been restricted to the crystalline samples from which new highly luminescent phases can be obtained from thermal or mechanical treatments. Such stimuli-responsive behavior, that is likely to be promoted with luminescent coordination-driven Cu(I) polymetallic assemblies, offers therefore promising perspectives for this class of derivatives in the field of the design and study of stimuli-sensitive photoactive materials, but also for the preparation of new innovative emittors for lighting applications. and complex fast equilibria based on intramolecular exchanges occur in solution at RT, allowing easy interconversion between the conformers.

  Scheme 1. a) Preparation of the species Bo, Bc, Bg and Bm; b) Photographs of each sample under visible light (top) and UV-vis light (ex = 365 nm, bottom); Photographs of Bc sample have been taken with a magnification roughly tenfold larger than those that chosen for the views of Bo, Bg and Bm samples.

  Figure1. a) Molecular X-ray structure, simplified 'top' and side views of the species Bo[15] and view of the columnar solid-state stacking of the derivative Bo, b) Molecular X-ray structure, simplified 'top' and side views of the species Bc and view of the solid-state stacking mode of the derivative Bc (counteranions, H atoms and solvent molecules have been omitted for clarity, location of the C and N atoms of the cyano ligands has been chosen arbitrarily in the X-ray structure views excepted for the M(CN)4 fragments; green coloured ellipses represent the intermolecular -CH non-covalent interactions areas between neighbouring molecules in the crystal packings; black dots represent the central points of the Cu-Cu segments of each [Cu2(2-dppm)2] fragments).

Figure 2 .

 2 Figure2. Normalized solid-state temperature dependant emission spectra of Bc (ex = 365 nm); insert: plot of the emission decay lifetime against temperature (80 K to 300 K, the wavelength monitored was the wavelength for which the maximum of signal intensity was observed at a given temperature in the solid-state emission spectra), the red line represents the fit according to the TADF Boltzmann-type equation S1.

a

  the [Cu2(2-dppm)2] fragments at 150 K, photophysical data for species Bo (ex = 350 nm), Bc (ex = 365 nm), Bg (ex = 375 nm) and Bm (ex = 375 nm) at 298 K in the solid-state and calculated data for Bcal. Data recorded at 80 K are given in parentheses; b kr = Φem/τobs; c knr = (1-Φem)/τobs; d Calculated molecular structure and calculated phosphorescence wavelength at 0 K given in brackets. mainly the steric constraints (intramolecular repulsion between the phenyl rings of the dppm ligand belonging to different [Cu2(2-dppm)2] fragments) and stabilizing interactions (metallophilic interactions in the Cu I dimers resulting of short Cu I -Cu I distances, coordination modes of the cyanido ligands…).

Figure 3 .

 3 Figure 3. a) Relative energies in vacuum of the species Bo, Bc and Bcalc (phenyl rings and protons have been removed for the sake of clarity); b) View of the calculated molecular structure of Bcalc (protons have been removed for clarity), simplified 'top' and side views of the species Bcalc.

Figure 4 .

 4 Figure 4. Normalized solid-state temperature dependant emission spectra of Bg (ex = 375 nm); insert: plot of the emission decay lifetime against temperature (80 K to 300 K, the wavelength monitored was the wavelength for which the maximum of signal intensity was observed at a given temperature in the solid-state emission spectra).

Figure 5 .

 5 Figure 5. PXRD patterns of a) Bo, b) Bg and c) Bm angles.

Figure 6 .

 6 Figure 6. SEM images of Bo, Bg and Bm samples taken for a) 500 magnification and b) 2000 magnification.

Figure 7 .

 7 Figure7. Normalized solid-state temperature dependant emission spectra of Bm (ex = 375 nm); insert: plot of the emission decay lifetime against temperature (80 K to 300 K, the wavelength monitored was the wavelength for which the maximum of signal intensity was observed at a given temperature in the solid-state emission spectra).

Figure 8 .

 8 Figure 8. a) General geometries, simplified 'top' and 'side' views of the optimized geometries of S1-relax (top) and T1-relax (bottom), (H atoms omitted), b) comparative side simplified 'side' views of the experimental molecular structure of Bo and of the of the optimized geometries of S1-relax and T1-relax, c) Iso-surface representations of the electronic charge-density difference between the T1 excited state and the density of the closed shell singlet at this geometry (S0 # ): green = density depletion; purple = density increase; the isosurface is ±1.10 -4 e/bohr 3 .

Acknowledgements

This work was supported by the CNRS, the ANR (ANR PRC SMAC and ANR PRCI SUPRALUM), the French 'Ministère de l'Enseignement supérieur, de la Recherche et de l'Innovation' and the French 'Ministère des Affaires Etrangères'. C.L. thanks the Alexander von Humboldt Foundation for a fellowship for experienced researcher. K.C. and V.D. acknowledges support by the "Grand équipement national de calcul intensif (GENCI)" through HPC resources of CINES, TGCC and IDRIS (grants 2020/2021-A0080800649/A0100800649). Keywords: polymetallic Cu(I) ion complexes • conformers • luminescence • mechanochromism • TD DFT calculations

Entry for the Table of Contents

A combined experimental and computational study highlights the crucial role played by intermolecular non-covalent weak-interactions in the conformer selection, the solid-state organization and the photophysical properties observed in a series of phases of a Cu I 8Pd II 2 multimetallic assembly. Rationalization of the structure/properties relationships allows understanding their mechanical and thermal stimuli-sensitive responses.

Institute and/or researcher Twitter usernames: @chimie_ISCR