Gauthier Pellet

Carmen Stefanescu

Franck Carbonnel

Laurent Peyrin-Biroulet

Xavier Roblin

Christophe Allimant

Maria Nachury

Stephane Nancey

Jerome Filippi

Romain Altwegg

Hedia Brixi

Ginette Fotsing

Laure De Rosamel

Sarah Shili

Professor David Laharie
email: david.laharie@chu-bordeaux.fr

Efficacy and Safety of Induction Therapy With Calcineurin Inhibitors in Combination With Vedolizumab in Patients With Refractory Ulcerative Colitis

Keywords: ulcerative colitis ASUC: acute severe ulcerative colitis TNF: tumor necrosis factor UCEIS: ulcerative colitis endoscopic index ulcerative colitis, anti-TNF refractory, GETAID, vedolizumab, cyclosporine

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

Introduction

Ulcerative colitis (UC) is a chronic inflammatory bowel disease that always affects the rectum with a retrograde continuous extent into the colon. The two main criteria [START_REF] Satsangi | The Montreal classification of inflammatory bowel disease: controversies, consensus, and implications[END_REF] driving UC treatment are disease extent and severity. Indeed, treatment is mainly based on topical therapy when UC is limited to the rectum, while systemic treatments are needed in a more extensive disease [START_REF] Harbord | Third European Evidence-based Consensus on Diagnosis and Management of Ulcerative Colitis. Part 2: Current Management[END_REF] . Approximately 20% of UC patients will experience an acute severe flare during their life. In patients with uncomplicated acute severe UC (ASUC), a standardized rapid step-up medical approach is needed [START_REF] Harbord | Third European Evidence-based Consensus on Diagnosis and Management of Ulcerative Colitis. Part 2: Current Management[END_REF] . It is recommended to start with intravenous steroids and to give cyclosporine or infliximab as a second-line medical therapy in steroid-refractory patients [START_REF] Laharie | Ciclosporin versus infliximab in patients with severe ulcerative colitis refractory to intravenous steroids: a parallel, open-label randomised controlled trial[END_REF][START_REF] Williams | Infliximab versus ciclosporin for steroidresistant acute severe ulcerative colitis (CONSTRUCT): a mixed methods, open-label, pragmatic randomised trial[END_REF] .

Regarding cyclosporine and due to its long-term toxicity, it is given as a bridging therapy to thiopurine in patients without prior failure to these agents.

During the past decades, thiopurines, cyclosporine and infliximab have been increasingly prescribed in patients admitted in tertiary centers for an active UC [START_REF] Kaplan | Decreasing colectomy rates for ulcerative colitis: a population-based time trend study[END_REF] . Accordingly, there was a trend towards a decrease in colectomy rates [START_REF] Rungoe | Changes in medical treatment and surgery rates in inflammatory bowel disease: a nationwide cohort study 1979-2011[END_REF] . As a consequence, there an increasing number of ASUC patients loosing response especially to anti-TNF that are now admitted in the referral centers.

Vedolizumab has demonstrated its efficacy in UC, as an induction and maintenance therapy in patients who have been exposed or not to thiopurines and anti-TNF [START_REF] Feagan | Vedolizumab as Induction and Maintenance Therapy for Ulcerative Colitis[END_REF][START_REF] Colombel | The safety of vedolizumab for ulcerative colitis and Crohn's disease[END_REF] . However, it acts progressively and can takes 14 weeks to reach its full efficacy [START_REF] Amiot | Effectiveness and Safety of Vedolizumab Induction Therapy for Patients With Inflammatory Bowel Disease[END_REF] . Vedolizumab has never been evaluated in the setting of ASUC where a prompt efficacy is needed. Therefore, a strategy combining a calcineurin inhibitor (cyclosporine or tacrolimus) as an induction therapy with vedolizumab as maintenance could be an attractive approach for UC patients who have failed a treatment with thiopurines and anti-TNF or that have a contra-indication to these drugs. The aim of the present study was to assess the efficacy and safety of this combination in patients with steroid and anti-TNF-refractory UC.

Methods

Study design and patients

We performed a retrospective multicenter observational study in 12 French tertiary academic centers affiliated to the Groupe d'Etude Thérapeutique des Affections Inflammatoires du tube Digestif (GETAID).

From December 2014 to May 2017, patients with an active steroid-refractory UC were consecutively enrolled when they received a calcineurin inhibitor (cyclosporine or tacrolimus) as an induction therapy and vedolizumab as maintenance. Patients were eligible when they were admitted for a refractory UC, that could be an ASUC (defined according to the Truelove and Witts criteria 10 ) or not, and if they previously did not respond adequately to at least one anti-TNF agent or if it was contraindicated. Baseline corresponded to the date of the first vedolizumab infusion.

Cyclosporine was started by continuous intravenous infusion at an initial dose of 2 mg/kg/d or orally at 4 mg/kg/d. The dose was subsequently adjusted to obtain a cyclosporine concentration between 150 and 250 ng/mL. When response was achieved with intravenous cyclosporine, it was switched to oral drug (Neoral®), given twice a day at 4 mg/kg/d. Tacrolimus was started orally at 0.05-0.1 mg/kg/d secondary adjusted on plasmatic concentration targeting blood concentration of 10-15 ng/mL until week 2 and 5-10 ng/mL thereafter. Choice of calcineurin inhibitor molecule -cyclosporine or tacrolimus -depended on centres routine practice. Both calcineurin inhibitors were given as a bridge therapy to vedolizumab for approximately three months in responders. They were intentionally withdrawn at this time, or previously in case of intolerance or failure.

In France, vedolizumab is licensed only in patients who are in failure of a treatment with anti-TNF or in whom these drugs are contraindicated. Inclusion date was the first vedolizumab infusion.

All patients received treatment according to clinical need. Medications were those currently recommended in UC, according to their licensed or published doses. Patients were informed by written notice of their participation. The French Data Protection Agency (Comité Consultatif sur le Traitement de l'Information en matière de Recherche dans le domaine de la Santé, n° of approval 17-037) and investigational review board of each center approved the study. All authors had access to the study data and have reviewed and approved the final manuscript.

Data collection

At inclusion, the following characteristics were recorded for each patient: sex, age, disease duration, smoking status, UC characteristics according to Montreal Classification, extraintestinal manifestation, prior received treatments (steroids, thiopurine, methotrexate, infliximab, adalimumab and golimumab) and reasons for discontinuation (primary failure, loss of response or intolerance), disease activity according to the partial Mayo and the Lichtiger scores, endoscopic activity measured with the endoscopic Mayo subscore and UC endoscopic index of severity (UCEIS), severe endoscopic lesions, C-reactive protein (CRP), haemoglobin, and albumin levels.

Follow-up

Follow-up started from inclusion up to august 2017. Vedolizumab 300mg infusions were administered intravenously at weeks 0, 2 and 6, and then every 8 weeks. If needed, vedolizumab could be prescribed every 4 weeks from week 10.

Other UC treatments, including calcineurin inhibitors, corticosteroids or thiopurines were given according to clinical need as judged by the physician. Treatment duration of each drug was collected during the follow-up period.

UC clinical activity (according to the partial Mayo score), received treatments and CRP measurements were collected at each vedolizumab infusion -i.e. at least at weeks 2, 6 and 14 -until death, colectomy, vedolizumab discontinuation or end of follow-up. Reasons for vedolizumab withdrawal were collected and investigated. Due to its retrospective design, no standardized endoscopic assessment was performed during the study.

Each adverse event occurring during the follow-up period was collected and investigated.

Objectives

The primary objective was survival without colectomy. Secondary objectives were survival without colectomy according to disease severity, survival without vedolizumab discontinuation, clinical response at weeks 6 and 14, clinical remission at weeks 6 and 14, biochemical remission at weeks 6 and 14, predictive factors of colectomy and safety.

Clinical response was defined by decrease of the partial Mayo score of at least 3 points with decrease of at least 30% and reduction of at least 1 point on the bleeding subscore with subscore of 0 or 1, as compared to inclusion. Clinical remission was defined by partial Mayo score of less than 3, without any of the subscores having a value higher than 1. Biochemical remission was defined by normal CRP level, below 5 mg/L. Adverse effects were classified as severe when they lead to treatment interruption, hospitalization or death.

Statistical analysis

Continuous variables were reported as median and range. They were compared with the Student t-test or Mann-Whitney-Wilcoxon test for variables with abnormal distribution, and categorical variables with Pearson's chi-square or Fisher's exact tests where appropriate.

Regarding assessments at weeks 6 and 14, patients who underwent colectomy or vedolizumab discontinuation since inclusion were considered as failure.

For the survival analysis, a Kaplan-Meier curve and a log-rank test were used. Because there were no deaths in our study population, there was no need for considering competitive risk.

Cox proportional hazard models were used to identify predictors of surgery. Variables associated with colectomy with a p < 0.30 in univariate analysis were included in the multivariate model. ASUC is a well-known risk factor for colectomy and then was forced into the multivariate model, whatever the result of the univariate analysis. The final cox model was obtained by a backward stepwise selection of variables with a p value < 0.05. SAS Software 9.4 and R were used for statistical analysis.

Results

Patient characteristics

Thirty-nine UC patients were included in 12 centres during the study period. Their main characteristics are shown in Table 1. To summarize, 23 patients (59%) were women, with a median age of 32 (range: 17-73) years. None underwent prior liver transplantation. Median disease duration was 4.0 (0.2-23.9) years and 31 patients (79%) were admitted for an ASUC.

Thirty-three patients (85%) had been previously exposed to thiopurines, 1 (%) to methotrexate and 36 (92%) to at least one anti-TNF agent. Three (8%) other patients had a contraindication to anti-TNF agents due to multiple sclerosis (1), recent malignancy (1) or tuberculosis (1). Twenty-six (67%) patients received an anti-TNF agent in the three previous months, and 13 (33%) in the last month. Median interval between the last anti-TNF administration and first vedolizumab infusion was 43 days (7-3230 days). Thirty (77%) patients received corticosteroids at baseline. Regarding calcineurin inhibitor, 37 (95%) patients received cyclosporine and 2 (5%) tacrolimus. Vedolizumab was started after a median interval of 7 (0-180) days after the calcineurin inhibitor (one patient received cyclosporine for 180 days waiting for vedolizumab approval in France). Thirty-six (92%) patients started calcineurin inhibitors before vedolizumab. The remaining three patients started calcineurin inhibitor during the vedolizumab induction regimen, within a median interval of 30 days. Calcineurin inhibitor was continued for a median duration of 80 (5-384) days since inclusion.

Efficacy

The median duration of follow-up was 10.8 (0.4-30.2) months. No deaths occurred and no patient was lost to follow-up. Eleven (28%) patients underwent colectomy after a median duration of 112 (11 -344) days.

Six of them underwent early surgery, before week 14. The survival rate without colectomy was 68% at one year (95% confidence interval -95%CI: 53-84%) (Figure 1A).

At one year, rates of survival without colectomy were 64% (IC95%: 46-83%) in patients with ASUC and 87% (IC95%: 65-100%) in those without ASUC (p=0.32) (Figure 1B). Nineteen (49%) patients stopped vedolizumab during the study period: 18 due to lack of efficacy and one due to intolerance (depression). After one year of follow-up 44% (IC95%: 27-61%) of patients were still treated with vedolizumab (Figure 2). Vedolizumab was intensified every 4 weeks in 26 (67%) patients (in 19 patients at week 10 and 7 after week 14). Among the 19 optimised patients at week 10, 9 (47%) were in clinical remission at week 14. Regarding the 18 patients who did not respond to vedolizumab, 11 underwent colectomy and 7 were treated with another medical treatment (combotherapy with infliximab and thiopurines for two patients, inclusion in a clinical trial for three -tofacitinib (2) and fecal microbiota transplantation (1) -, allopurinol plus thiopurine for one and oral tacrolimus for one).

Median partial Mayo score were 7 at baseline, 2 at week 6 and 3 at week 14, respectively.

Clinical response and clinical remission, were achieved in 25/39 (64%) and 18/39 (46%) patients at week 6 and, in 22/39 (56%) and 15/39 (38%) at week 14, respectively (Figure 3). Among the 30 patients receiving corticosteroids at baseline, steroid free remission was achieved in and 7/30 (23%) at week 6, and 12/30 (40%) at week 14. Proportions of patients still receiving the calcineurin inhibitor were 25/39 (64%) at week 6, and 8/39 (21%) at week 14.

There were 9/32 (28%) patients in biochemical remission (CRP <5mg/L) at week 6 and 8/34 (24%) patients at week 14. Median CRP was 6 mg/L at week 6, and 7.8 mg/L at week 14.

In multivariate analysis, four baseline factors were associated with colectomy during the follow-up period: female gender (HR: 10.5; 95%CI: 2.05-54.33; p=0.004), age more than 31 years (HR: 13.16; 95%CI: 2.27-76.26), concomitant immunosuppressant (HR: 9.59; 95%CI:

1.13-81.60) and haemoglobin more than 11.2 g/dL (HR: 1.93; 95%CI: 0.59-6.32).

Safety

Eleven (28%) patients experienced at least one adverse event during the study. They are summarized in the table 2. Four of them were severe: three patients developed mild and transient renal failure, leading to cyclosporine withdrawal in one case and, one patient developed a Campylobacter jejuni colitis while treated with vedolizumab and tacrolimus that completely recovered with antibiotics. No opportunistic infection or malignancy was observed. One patient in clinical remission decided to stop vedolizumab due to a depression that was thought to be due to the drug.

Discussion

In the present multicentre cohort of patients admitted for a steroid-refractory UC with prior anti-TNF failure, a combination between a calcineurin inhibitor with vedolizumab could avoid colectomy in approximately two out of three patients within one year, whatever disease severity, with a good safety profile. As far as we know, this study is the largest to investigate this association in a cohort of highly selected patients with refractoriness to all current licensed drugs in UC [START_REF] Szántó | New promising combo therapy in inflammatory bowel diseases refractory to anti-TNF agents: cyclosporine plus vedolizumab[END_REF][START_REF] Christensen | Safety and efficacy of combination treatment with calcineurin inhibitors and vedolizumab in patients with refractory inflammatory bowel disease[END_REF] .

The number of UC anti-TNF refractory patients is de facto increasing in parallel with the growing use of these drugs. Currently, these patients are candidates to either vedolizumab or colectomy. Until now, vedolizumab has not been evaluated in patients with ASUC who were excluded from the pivotal trials. In addition, physicians are reluctant to use vedolizumab in this setting, because of its delayed efficacy [START_REF] Feagan | Vedolizumab as Induction and Maintenance Therapy for Ulcerative Colitis[END_REF][START_REF] Amiot | Effectiveness and Safety of Vedolizumab Induction Therapy for Patients With Inflammatory Bowel Disease[END_REF] . However, and as a parallel with the bridging strategy combining cyclosporine and thiopurine in the management of patients with steroidrefractory UC before the anti-TNF era [START_REF] Cohen | Intravenous cyclosporin in ulcerative colitis: a fiveyear experience[END_REF] , it could be attractive to combine a calcineurin inhibitor as induction therapy with vedolizumab as maintenance in these patients.

Although patients recruited in the present cohort were more severe, the efficacy of vedolizumab was similar with that reported in the literature in UC. Published clinical response and remission rates at week 14 were 43-57% and 23-39% respectively, as compared to 56% and 38% in our cohort. In addition, reported vedolizumab failure rates within the first year of treatment were of 35-48% in previous series [START_REF] Eriksson | Long-term effectiveness of vedolizumab in inflammatory bowel disease: a national study based on the Swedish National Quality Registry for Inflammatory Bowel Disease (SWIBREG)[END_REF][START_REF] Stallmach | Vedolizumab provides clinical benefit over 1 year in patients with active inflammatory bowel disease -a prospective multicenter observational study[END_REF][START_REF] Amiot | One-year effectiveness and safety of vedolizumab therapy for inflammatory bowel disease: a prospective multicentre cohort study[END_REF] , and 49% in our cohort. However, as vedolizumab was given as a last-chance drug before surgery in the present cohort, the absence of colectomy during the follow-up does not necessarily mean that the drug was efficient. Indeed, half of patients discontinued vedolizumab within one year, while approximately one third were operated on. Moreover, some patients continued the drug despite partial efficacy. This illustrates the impact of a limited therapeutic choice on drug persistence.

In ASUC patients from the present cohort, the 36% one-year colectomy rate was similar to those reported with cyclosporine (29%) or infliximab (31%) when combined with azathioprine after intravenous steroid failure [START_REF] Laharie | Long-term outcome of patients with steroidrefractory acute severe UC treated with ciclosporin or infliximab[END_REF] .

As observed in controlled trials and observational studies, vedolizumab appears to have a good safety profile [START_REF] Colombel | The safety of vedolizumab for ulcerative colitis and Crohn's disease[END_REF] . Yet, concomitant use of calcineurin inhibitor was not allowed in the GEMINI trial and the experience of combining an anti-integrin with a calcineurin inhibitor is very limited in UC as well as in multiple sclerosis. A prior study conducted in 9 patients with Crohn's disease and 11 with UC did not observed additional safety event than those related to calcineurin inhibitors alone. Adverse events observed in the present cohort were mostly related to calcineurin inhibitors except one case of Campylobacter jejuni colitis associated with vedolizumab. No other case of opportunistic infection or malignancy was observed.

This study has several limitations inherent to its retrospective design. Treatments were not standardized as well as outcome measures, especially endoscopic assessments. Patients were selected in few referral centres and most of them were primary responders to calcineurin inhibitors who received vedolizumab only when they responded adequately to the induction therapy. The follow-up was limited to 11 months.

Overall, a strategy combining a calcineurin inhibitor with vedolizumab in patients with steroid-refractory UC and prior anti-TNF failure or contra-indication can avoid colectomy in approximately two third of the patients within one year and seems safe. It can be considered in patients with ASUC or non-severe UC when they are refractory to all conventional therapies, including anti-TNF agents. The safety profile of this combination will require further investigation.

Figure legends : Figure 1 :

 :1 Figure legends:

Figure 2 :

 2 Figure 2: Survival without vedolizumab discontinuation among 39 patients with refractory

Figure 3 :

 3 Figure 3: Clinical response, clinical remission and steroid-free remission at weeks 6 and 14

Table 1 :

 1 Main patients' characteristics at baseline

	N=39 (%)


Changzhao Pan
email: changzhao.pan@lecnam.com

Jue Wang

Kaiqi Luo

Liubiao Chen

Hai Jin

Wei Cui

Junjie Wang

Yuan Zhou
email: zhouyuan@mail.ipc.ac.cn

Jue Wang

Junjie Wang

Numerical and experimental study of VM type pulse tube cryocooler with multi-bypass operating below 4 K

Keywords: VM, thermal-compressor, pulse tube, multi-bypass, 4K cooling chain

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

Introduction

With recent developments in quantum physics and cryoelectronics, the need for cryocooler operating below 4K is increasing. Even though traditional commercial 4K cryocoolers (GM or GM type pulse tube cryocooler) can meet most requirements, the use of advanced detectors, such as superconducting nanowire single-photon detectors (SNSPD) [START_REF] Marsili | Detecting single infrared photons with 93% system efficiency[END_REF] , superconducting transition-edge sensor (TES) [START_REF] Miller | High resolution x-ray transition-edge sensor cooled by tunnel junction refrigerators[END_REF] , low-TC SQUIDs [START_REF] Schmidt | A SQUID system for geophysical measurements cooled by a pulse tube cryocooler[END_REF] and et al., has given rise to some new challenges for its cooling system. Especially in space applications, the cryocooler must have smaller size, lower power consumption, higher efficiency and lower temperature. Therefore, it is important to develop the next generation cryocooler to meet those challenges.

For the traditional 4K cryocooler, some researchers have made efforts on the low-power consumption GM type cryocooler, but the large bulk and high power (~ 1kW [START_REF] Hiratsuka | Performance estimation of an oil-free linear compressor unit for a new compact 2K Gifford-McMahon cryocooler[END_REF] [START_REF] Schmidt | A small two-stage pulse tube cryocooler operating at liquid Helium temperatures with an input power of 1 kW[END_REF] ) is still the main obstacle for its application in space applications. The Joule-Thomson (J-T) cryocooler is the traditional 4 K cryocooler, which has been used in the ASTRO-H [START_REF] Kanao | Cryogen free cooling of ASTRO-H SXS Helium Dewar from 300 K to 4 K[END_REF] and SNSPD missions. This type of cryocooler needs to be precooled by another 20K cryocooler. So this hybrid 4K cooling system has the disadvantage of complexity and some technical risks of internal wear, outgassing, etc.

Even worse, some impurities in helium may block the J-T valve and result in cooling system failure [START_REF] Sato | Outgas analysis of mechanical cryocoolers for long lifetime[END_REF] . Therefore, it is advantageous to develop alternative cooling methods.

The Multi-stage High frequency Stirling type pulse tube cryocooler (HSPTC) is one relatively new cryocooler capable of reach 4K [START_REF] Nast | Development of a 4.5 K pulse tube cryocooler for superconducting electronics[END_REF] [START_REF] Zhi | A three-stage Stirling pulse tube cryocooler reached 4.26 K with He-4 working fluid[END_REF][10] [START_REF] Liubiao | Numerical and experimental study on the characteristics of 4 K gas-coupled Stirling-type pulse tube cryocooler J[END_REF] . Because there are no moving components in its cold finger, the HSPTC has the advantages of compactness, long life, and low vibration. And based on the Stirling cycle, this type cryocooler should have more potential to obtain a higher efficiency. But until now, HSPTC is very difficult to obtain the temperature below 4K, even by using helium-3 [START_REF] Dotsenko | Integration of a 4-Stage 4 K pulse tube cryocooler prototype with a superconducting integrated circuit[END_REF] [START_REF] De Waele | Cryocoolers near their low-temperature limit[END_REF] . That is because HSPTC is normally working at the frequency above 20Hz driven by a linear compressor. The high-frequency oscillating flow generates high pressure drop loss in regenerator, which makes it difficult to achieve high efficiency at 4 K. So a feasible way to increase its efficiency is to develop the Low frequency Stirling type pulse tube cryocooler (LSPTC).

A VM type pulse tube cryocooler (VPTC) is driven by a thermal-compressor, and is a new type of LSPTC. Dai et al. introduced the concept of VPTC and built a cryocooler, which obtained the lowest temperature of 3.5 K by using 77 K and 20 K pre-coolers [START_REF] Dai | Experimental results on VM type pulse tube refrigerator[END_REF] . This work demonstrated its capacity to operate at liquid helium temperatures. More recently, Wang et al. [15][16] developed a 15 K single-stage VPTC by using an 80 K Stirling type PTC as pre-cooler, and then a lowest temperature of 7.58K has been obtained after optimizing. In our laboratory, VM type cryocooler has been in development for many years. The "first generation" VPTC in our laboratory obtained a no-load temperature of 2.5K [START_REF] Pan | A novel coupled VM-PT cryocooler operating at liquid helium temperature[END_REF][18] [START_REF] Wang | A novel method to hit the limit temperature of Stirling-type cryocooler[END_REF] . In our "second generation" VPTC, we removed its displacer in the first stage and developed a single-stage structure for practical application. We successfully obtained a no-load temperature of 4.9K in the second generation VPTC [START_REF] Pan | Progress on a novel VM-type pulse tube cryocooler for 4 K[J][END_REF] . These results showed great potential to be the next-generation pulse tube cryocooler.

This paper presents the recent advance on the second generation VPTC. First, the evolution of our VPTC will be presented and its advantages will be discussed. Then, the mechanism of multi-bypass is numerically studied and clarified. After optimizing its performance, the phase relationship distributions and exergy-loss distributions will be presented. The interaction of multi-bypass and double-inlet was studied comprehensively and optimized by experiment. The influence of orifice, operating frequency and average pressure on the multi-bypass was also experimentally studied.

Finally, the optimal performance of this VPTC is presented. And based on this VPTC, an alternative sub-kelvin cooling chain is proposed.

Evolution of cryogen-free VM type pulse tube cryocooler

Figure 1 shows the evolution from the first generation VPTC to the second generation VPTC and the next-generation VPTC. There are mainly three changes at present work from the first generation:

(1) Cryogen-free. A dry 77K mechanical cryocooler, GM cryocooler (only the first-stage being used), was used to replace the liquid nitrogen as pre-cooler. The facilitated measuring the power consumption of the thermal-compressor. Because the pre-cooling power is used more efficiency, the new structure also increase the efficiency of our second generation VPTC (the exergy efficiency is about 0.6% in our previous paper [18][19] , and the exergy efficiency increases to about 0.9% as shown in the next section).

(2) Removed the displacer and reduced the stroke of the thermal-compressor. A pulse tube was used to replace the displacer in the former VPTC. So the vibration would be lower and the heat losses caused by movement were eliminated, such as the shuttle loss, leakage loss, abrasion loss, etc. In addition, the stroke of thermal-compressor was reduced from 32mm to 20mm, so the input power of our second generation VPTC was much smaller than before. Reducing the stroke was also expected to reduce vibration.

(3) Single-stage structure. A multi-bypass was used to simplify the former gas-coupled structure (two-stage). It makes the system more compact and easier to integrate with applications. The smaller mass is also very important for space applications.

In the next-generation VPTC, a high-efficiency 77K pulse tube cryocooler, currently being designed, will replace the present GM cryocooler. This is a critical step for demonstrating, a hybrid 4K cooling chain that can be used in space.

Numerical simulation and discussion

Ssimulation model

The numerical simulation was conducted by using SAGE10.0 software [START_REF] Gedeon | Sage user's guide[END_REF] , a 1D simulation program based on Navier-Stokes equations. The LTcooler module was used to build the simulation model of the VPTC. As shown in Figure 2, the whole model was composed by each submodule, and the parameters of each part are shown in table 1. In the simulation, the operating frequency was kept at 2Hz, and the average pressure at 1.0MPa. In order to analyze the mechanism of multi-bypass and its difference from a double-inlet, the resistance of orifice (capillary tube) was set a constant value.

Simulation results and discussions

The mechanism of multi-bypass

Multi-bypass, invented by Zhou and Han, enables the PTC to reach a lower temperature [START_REF] Zhou | Pulse tube refrigerator research[END_REF] . By using a multi-bypass, a single-stage SPTC has obtained a no-load temperature of 13.9K, which was better than some two-stage SPTC [23][24] . In our previous work, the multi-bypass was used in the VPTC and obtained a lowest temperature of 4.9K [START_REF] Pan | Progress on a novel VM-type pulse tube cryocooler for 4 K[J][END_REF] . To further clarify its mechanism, its function was numerically compared with double-inlet, because double-inlet has been studied widely.

Figure 3 (a-d) shows the simulation results. Figure 3-a and 3-b are the results of double-inlet and figure 3-c and 3-d are the results of multi-bypass. Similar to the double-inlet, there exists an optimal value for the opening of the multi-bypass that yields the lowest no-load temperature. Different from the double-inlet, the temperature of multi-bypass stage would decrease with the opening of multi-bypass because some amount of working gas would flow through multi-bypass and generate cooling effect. But for the double-inlet, the temperature of multi-bypass stage (the same position) would increase. It is because the double-inlet would decrease the input acoustic power of cryocooler.

Similar to the double-inlet, the multi-bypass can improve the phase relationship between mass flow rate and pressure in the cold end, shown in the figure 3-d. But the phase adjusting capability of multi-bypass is weaker than double-inlet. On the other hand, the optimal opening of multi-bypass for the lowest temperature does not correspond to the best phase relationship. It is different from double-inlet in which the optimal opening was the same for the lowest temperature and phase relationship. It can be explained from the viewpoint of input acoustic power. With the opening of multi-bypass or double-inlet, the input acoustic power of regenerator-2 would decrease correspondingly. But the input acoustic power of regenerator-2 decreased more obvious with increasing of multi-bypass. So before its phase relationship reaching to the optimal value, the input acoustic power has decreased too small to generate enough cooling power to overcome heat losses, which makes it higher temperature at the optimal phase relationship.

The interaction between double-inlet and multi-bypass

Figure 4 shows the interaction between a double-inlet and multi-bypass. The opening of the multi-bypass has values of 0.3mm, 0.4mm and 0.5mm, but the opening of double-inlet varied from 0.3-0.9mm. When a multi-bypass is used, the double-inlet has two effects. First, the temperature of the multi-bypass stage decreases with the increasing opening of double-inlet, which is different from the trend in Figure 3-a.

This further showed that multi-bypass has a cooling effect similar to another stage.

Second, the optimal opening of the double-inlet depends on the opening of the multi-bypass. The optimal value first decreases and then increase, and after the best coupling with multi-bypass, its optimal value would decrease slightly. Based on this optimization process, a lowest temperature of 3.69K was obtained with the optimal opening of multi-bypass 0.4mm and double-inlet 0.8mm. With these parameters, the temperature of multi-bypass stage was about 34.8K.

The distribution of phase relationship

The distributions of phase relationship in the VPTC are presented in Figure 5.

Here, the phase angles were expressed by the leading angle of mass flow rate to pressure. Because the phase of pressure almost didn't change in the VPTC, the positive real axis was used to present all the phases of pressure. In figure 5, if the mass flow rate is in quadrant Ⅰ or Ⅱ, it meant the mass flow rate leaded the pressure.

But if the mass flow rate is in quadrant Ⅲ or Ⅳ, it meant the mass flow rate lagged pressure. Here, the subscript "tc" means thermal-compressor, the subscript "r" means regenerator, the subscript "p" means pulse tube, the subscript "i" means inlet, and the subscript "o" means outlet. The subscript "1" and "2" can be found in figure 1.

In figure 5, the red arrows located at the Ⅲ quadrant are the phase relationships in the thermal-compressor. This means the propagation direction of acoustic power was negative. Therefore, in the VPTC, the acoustic power is generated in the cold cavity of thermal-compressor and propagated into the pulse tube cryocooler and the hot end of thermal-compressor. Figure 5-a shows the distributions of phase relationship without double-inlet and multi-bypass. It is the typical phase relationship in the orifice type pulse tube cryocooler [START_REF] Radebaugh | Inertance tube optimization for pulse tube refrigerators[END_REF] . Figure 5-b shows the distributions of phase relationship at the optimal condition. Even though the phase of mass flow rate was still leading the pressure in the regenerator, the phase difference has been reduced, as seen in the phase of m , . This result was also shown in figure 3. The main reason was the phase in the pulse tube had been changed by the double-inlet and multi-bypass. As shown in figure 5-b, because of the effect of multi-bypass, the phase of mass flow rate was almost same as the pressure at the outlet of pulse tube 2. This relationship is the same as for an orifice pulse tube cryocooler. So from the view of phase relationship, the multi-bypass has functions like an orifice, yielding behavior similar to a two-stage cryocooler. And for the double-inlet, figure 5-b shows that it would make the phase of mass flow rate lag to the pressure at the outlet of pulse tube 1. So it would realize the same-phase for the mass flow rate and pressure in the midpoint of pulse tube 1. This also reduces the phase difference at the cold end.

In sum, the simulation showed the multi-bypass has two functions. First, multi-bypass has the similar function as double-inlet (located at lower temperature), which can improve the phase relationship in the cold end and reduce acoustic power transferring to the cold end. Second, multi-bypass has the similar function as orifice, which makes it work like as another stage, generating a lower temperature at the position of the multi-bypass.

The distribution of exergy loss

Finally, figure 6 shows the distribution of exergy loss in VPTC. Here, we refer the reader to our previous work [START_REF] Zhang | Numerical investigation and experimental development on VM-PT cryocooler operating below 4 K[END_REF] for the detailed definition of exergy loss. As mentioned previously, the acoustic generated in the cold cavity of thermal-compressor.

The acoustic power, as exergy flow, flows into thermal-compressor and cryocooler. In the optimal case, a total of 23.25W acoustic power is generated in the cold cavity of the thermal-compressor. About 8.5W of acoustic power flowed into the thermal-compressor, and about 14.75W of acoustic power flowed into the cryocooler.

Figure 6 also gives the amount and the percentage of exergy loss in each part. The results shows that the main exergy loss in the thermal-compressor was the loss in the heat exchanger, and the main exergy loss in the cryocooler was the loss in the regenerator. There is additional exergy loss in the thermal-compressor, the shuttle loss caused by movement of the displacer. Its value was about 20W, so it is the largest loss in the VPTC. For this case, a total of about 43.25W cooling-power is needed to precool the VPTC at 77K.

Experiment and discussions

Experimental system

Figure 7 shows the picture of the experimental system. It was the same as our previous system [START_REF] Pan | Progress on a novel VM-type pulse tube cryocooler for 4 K[J][END_REF] , and was precooled by Sumitomo RDK-415D cryocooler. As shown in the figure 7, the displacer of thermal-compressor was driven by a crankshaft.

Its stroke was about 20mm, and operated at the range 0~3Hz. The pulse tube cryocooler was coaxial in structure and a picture of each part can be found in figure 7.

The detailed parameters of thermal-compressor and pulse tube cryocooler can be found in table 1. In the experiment, the pressure in the hot cavity was measured by a capacitive differential pressure sensor. The temperature was measured by Rh-Fe resistance thermometer calibrated by TIPC (with accuracy of 0.1 K).

2Experimental results and discussions

2.1 Interaction between double-inlet and multi-bypass

In order to find the optimal interaction between double-inlet and multi-bypass, three multi-bypasses with different opening of double-inlet were studied: 0.38mm, 0.5mm and 0.55mm. The case of 0.45mm multi-bypass has been studied in our previous work [START_REF] Pan | Progress on a novel VM-type pulse tube cryocooler for 4 K[J][END_REF] , but the influence of double-inlet was not studied in that case, so it was not used to compare with the other results. Figure 8 shows the influence of double-inlet on the different openings of the multi-bypass. The optimal double-inlet for the multi-bypass of 0.38mm was about 0.75mm. For the multi-bypass of 0.5mm, its optimal value decreased to about 0.6mm, and then increases to about 0.75mm for the multi-bypass of 0.55mm. Its changing trend was partly consistent with the simulation results in the figure 4. In the simulation, the optimal opening of double-inlet would decrease again after the best coupling value, but the optimal value in the experiment did not follow that trend. This discrepancy has been found in other reference by using Sage software [18] [26] . This is mainly because that Sage is a 1-D software, which cannot simulate the flow and heat transfer in the cryocooler accurately, especially in such low temperature.

In the present experimental results, the optimal opening of multi-bypass was about 0.5mm and the corresponding opening of double-inlet was about 0.65mm. With this optimal opening, this VPTC has obtained a lowest no-load temperature of 3.7K, and it can supply about 14mW cooling power at 4.2K. It is the first time for single-stage VPTC to obtain the temperature below 4K. Its performance has reached or even exceeded some two-stage VPTC [START_REF] Dai | Experimental results on VM type pulse tube refrigerator[END_REF] .

Influence of orifice

The orifice, as the traditional phase shifting method, has an important effect on the operating parameters of a VPTC. As shown in our previous work, a capillary tube was used as the orifice. In present work, a length of 50mm capillary tube was added on the former capillary tube (∅1mm × 3m), called capillary tube-1. The influence of its inner diameter was studied in the present experiment.

Figure 9 shows the influence of capillary tube-1 on the temperature of cold end and multi-bypass stage. With an increase of the inner diameter of capillary tube-1, the temperature of cold end would decrease. But for the temperature of multi-bypass stage, its temperature would increase first and then decrease. It is to say that a higher or lower resistance of orifice all can obtain a lower temperature for the multi-bypass.

The reason is related to its optimal operating frequency, as shown in the figure 10.

Figure 10 shows that the optimal operating frequency was in positive correlation with the diameter of capillary tube. A higher operating frequency would consume more pre-cooling power in the thermal-compressor and result in a higher inlet temperature of hot end. That is because a lower resistance of orifice means more working gas flowing into pulse tube and gas reservoir. Also, a higher phase shifting capacity is needed to satisfy the phase relationship in the PTC. So its optimal operating frequency would increase to improve its phase adjusting capability. On the other hand, the temperature of multi-bypass stage is affected by both the amount of working gas and the inlet temperature of hot end. A lower orifice resistance can also lead more working gas flowing through the multi-bypass and generate a more significantly cooling effect, which can make a lower temperature of multi-bypass stage. On the contrary, it would lead a higher inlet temperature of hot end, which can make a higher temperature of multi-bypass stage. Therefore, the lower inlet temperature of hot end makes a lower temperature of multi-bypass stage for capillary tube of 0.5mm, and a more amount of working gas flowing through the multi-bypass also makes a lower temperature of multi-bypass stage for capillary tube of 0.7mm and 1mm.

Influence of operating parameters

Figure 11 shows the influence of operating frequency on the temperature of multi-bypass stage and cold end. There is an optimal operating frequency (about 1.57Hz) for the cold end. But for the multi-bypass, its temperature would increase with an increase of operating frequency. This is mainly because a higher operating frequency generates a larger flowing resistance, which results in a smaller amount of working gas flowing through multi-bypass stage. Besides, the inlet temperature of hot end would increase with the increasing of operating frequency. Those all result in a higher temperature of the multi-bypass stage.

Figure 12 shows the influence of average pressure on the temperature of multi-bypass stage and cold end. Similar to the influence of operating frequency, there is an optimal average pressure (about 1.2MPa) for the temperature of cold end. But for the multi-bypass, its temperature would increase with the increase of average pressure. The main reason is that a higher average pressure increases the loading of the regenerator and the inlet temperature of hot end. Those all make the temperature of multi-bypass stage higher.

Thermal performance

After optimizing all above parameters, a lowest no-load temperature of 3.7K has been obtained in present VPTC, and a corresponding temperature of multi-bypass stage of about 33.2K. Figure 13 and figure 14 show the cooling power of the cold end and multi-bypass. The cold end can supply about 14mW cooling power at the temperature of 4.2 K, and its multi-bypass can supply above 100mW cooling power at the temperature of 35K. In this condition, the pre-cooling temperature of the GM cryocooler was about 45K and the temperature of hot end (VPTC) was about 80K. When 100mW heating was added at the multi-bypass stage, the temperature of cold end increased just 0.08K. So this VPTC can supply cooling power at cold end and multi-bypass stage simultaneously. Because this VPTC needs only about 35W precooling power at 80K, its total input electrical power of this cryocooler should be below 400W when a high-efficiency 77 K PTC is used as pre-cooler. So the relative Carnot efficiency of present VPTC could reach higher than 0.25%.

Prospect of its application in cooling system of HUBS

HUBS (Hot Universe Baryon Surveyor) is being conceptualized in China as a major X-ray mission for the next decade. It is designed to be highly focused scientifically, with the primary driver being to look for "missing baryons". The superconducting transition-edge sensor (TES) is the key technology in HUBS, which requires cooling to below 100mK.

Based on this VPTC, a new cooling chain from 300K to 100mK can be designed, as shown in figure 15. This cooling chain can supply cooling to three radiation shields at 80K, 35K and 3.7K respectively. Considering the areas of each radiation shield (0.9 m 2 , 0.5 m 2 and 0.2 m 2 ), the theoretical radiation load for each is about 7.5W@80K, 15mW@35K and 0.25mW@4K respectively. Adding the heat consumption for the thermal-compressor, this cooling chain needs no more than 45W cooling power at 77K. By using two 25W@77K high-efficiency PTC as pre-cooler on the both sides of thermal-compressor, the total input electrical power could be below 600W. So it is theoretically possible that this new cooling chain has the capability of pre-cooling the ADR and isolating radiation heat leakage for ADR. In the future works, the VPTC with two multi-bypasses or two-stage VPTC may be designed and built to obtain the temperature around 2.2K. In that case, a single-stage ADR could obtain the temperature below 100mK.

Conclusion

In this paper, the recent advance on the 4K VPTC in our laboratory is presented.

The most important element of the VPTC, the multi-bypass, was numerically studied.

From the view of phase relationship and acoustic power of cold end, the function of the multi-bypass is similar to a double-inlet, and from the view of the distribution of phase difference, its function is similar to an orifice. Those two aspects make it work effectively as a two-stage cryocooler.

The factors that impact the performance of VPTC were experimentally studied.

The results showed that the best coupling of multi-bypass and double-inlet for this VPTC is 0.5mm opening of multi-bypass and 0.65mm opening of double-inlet. For the orifice, it can change the optimal operating frequency of VPTC, and then affect the lowest temperature of cold end. For the operating parameters, the results showed that a higher operating frequency and a higher average pressure can result a higher temperature on the multi-bypass stage. But for the temperature of cold end, there existed an optimal value for each factor, which were 1.57Hz for frequency and 1.2MPa for average pressure. Finally, after optimization, a no-load temperature of 3.7K has been obtained in this VPTC, and it can supply about 14mW cooling power and about 100mW cooling power at 35K simultaneously, Based on this VPTC, a new cooling chain from 300K to 100mK is proposed.

After further development, the GM precooler in present system will be replaced by another 77K HSPTC, a key step in demonstrating a spaceworty cooling system for the HUBS satellite.

Figure Captions: Table 1 System configuration parameters

Figure.8

The interaction between double-inlet and multi-bypass.

Figure.9

The influence of orifice on the temperature of cold end and multi-bypass.

Figure.10

The influence of orifice on the optimal operating frequency and inlet temperature of hot end.

Figure.11

The influence of operating frequency on the temperature of cold end and multi-bypass.

Figure. 12 The influence of average pressure on the temperature of cold end and multi-bypass.

Figure. 13 The cooling power of cold end.

Figure. 14 The cooling power of multi-bypass.

Figure. 15 The design of new mK cooling chain for HUBS.

Figure 1

 1 Figure 1The evolution from hybrid two-stage gas-coupled VPTC to the single-stage

Figure 2

 2 Figure 2The simulation model in the Sage software.

Figure 3 Figure 4 Figure 5

 345 Figure 3Simulation results of the interaction between double-inlet and multi-bypass.

Figure 6

 6 Figure 6The picture of experimental system.

Figure. 7

 7 Figure.7 The simulation results of double-inlet and multi-bypass (a. the temperatures

Acknowledges

This work was supported by the Postdoctoral Innovation Talent Support Program of China (Foundation No. BX201600173). Strategic Pilot Projects in Space Science of China (Foundation No. XDA15010400).


H Nesser

J Grisolia
email: jeremie.grisolia@insa-toulouse.fr

A Mlayah

T Alnasser

D Lagarde

B Viallet

L Ressier

Plasmonic photo-capacitance of self-assembled gold colloidal nanoparticle monolayers

Keywords: sample fabrication process, equivalent electrical circuit, capacitance versus temperature, DDA simulations, numerical simulations of photo-capacitance photo-induced charge transport, surface plasmons, resistance, capacitance, gold nanoparticles, strain

We report on the plasmo-electronic properties of self-assembled monolayers of gold colloidal nanoparticles (NPs) formed on a polyimide flexible substrate. The work is focused on the understanding of both resistance and capacitance of these NP assemblies. Their dependence on temperature, bias voltage, optical excitation and strain is investigated both experimentally and theoretically. Resistance and capacitance appear to bring complementary information on the charge transport properties of the NP assemblies as they exhibit opposite behaviors. Based on a nano-circuit junction model combined with numerical simulations, we were able to account for both the resistance and capacitance and their photo-induced modifications. The dependence of the capacitance on laser irradiation intensity and wavelength was measured and the role of the surface plasmon resonance was pointed out. We show that the plasmonic induced photocapacitance can reach 43% for a moderate irradiation intensity of 3.5W/cm 2 . Moreover, the NP assemblies, deposited on flexible substrate, were submitted to a uniaxial strain which allows for controlling the inter-particle distances and hence for probing the plasmo-electro-mechanical properties of the assembly. We found that the photo-capacitance gauge factor is enhanced by a factor 3, by the plasmonic pumping of charges, compared to the one measured under dark conditions, in agreement with the calculations. The presented work thus paves the way to the emergence of a new class of plasmonic enhanced capacitance strain sensors.

Introduction:

The light-to-current transduction, via surface plasmon excitations and their decay into electrons and holes is the driving force of the emerging "plasmo-electronics" field which could provide a new class of opto-electronic devices [1]-[3]. It has been discovered that plasmonic excitations can influence macroscopic flows of charges and, conversely, that charging of metal

2 nanoparticles (NPs) can impact their plasmonic response [1]. For instance, hot electrons generated by surface plasmons, may easily tunnel through interparticle distances larger than expected for thermalized electrons. Moreover, the strong plasmonic electromagnetic near-field localized in the gap regions between metal nanoparticles [4] may facilitate the electron tunneling, thus enhancing the current across NP assemblies. Interestingly, both positive and negative photoconductivities have been evidenced on a new class of nanoparticle-based materials [1].

However, the study of the plasmonic photo-conductivity is still in its infancy and efforts must be undertaken in order to unravel the complex physics of these nano-hybrid systems. Indeed, the conversion of light into current occurs through a chain process involving electronplasmon, electron-phonon and phonon-phonon interactions. These relaxation mechanisms still need a fundamental understanding in connection with size, shape and surface properties at the nanoscale. Energy relaxation through emission of phonons also leads to heat generation and to hyperthermia phenomenon which in turn give rise to thermo-induced currents. Moreover, charge transport through the composite medium formed by the metal nanoparticles and the surrounding molecules has different origins: quantum tunneling, variable range hopping, phonon assisted, excitation transfer assisted, carrier trapping/detrapping... Up to now, most of the published works, devoted to the charge transport in NP assemblies, have focused on the characterization and modeling of the total electrical resistance R [5]- [8]. Very few studies were devoted to the total capacitance C [9]- [10]. There is a major interest in combining both R and C measurements as both electrical characteristics contain complementary information on the nature of the charge transport mechanisms and on the plasmonic pumping of the photo-current.

In this work, we investigate the plasmonic induced charge transport in gold NP monolayered assemblies formed on a polyimide flexible substrate. We combine resistance and capacitance measurements under resonant excitation of the surface plasmons and applied mechanical strain in order to identify and characterize the photo-induced charge excitation and transport mechanisms. The effects of temperature, bias voltage, applied strain and optical excitation wavelength and intensity are investigated systematically. We found a clear correlation between the resistance and capacitance characteristics which we interpret using a strain-sensitive and photo-responsive circuit model which describes the electrical interconnection between the nanoparticles. To scale up to the macroscopic level we have performed numerical simulations of the charge transport throughout the whole NP assemblies. The numerical results and the experimental data are compared for both resistance and capacitance which allows gaining a deeper understanding of the photo-induced charge transport phenomenon in NP assemblies.

-Materials and methods: 1.-Sample preparation and characterization:

Briefly, we first synthesized a colloidal dispersion of 14 nm spherical gold nanoparticles in toluene at a concentration of 2.10 15 NPs/ml following the protocol of H. Hiramatsu et al. [START_REF] Hiramatsu | A simple large-scale synthesis of nearly monodisperse gold and silver nanoparticles with adjustable sizes and with exchangeable surfactants[END_REF]. Second, 50 nm thick interdigitated gold electrodes were fabricated by laser photo-lithography (Dilase 650) on 125 µm polyimide (Upilex) films using the lift-off method and the ion beam sputtering (IBS-E) technique. This results in a 1 mm 2 area composed of 50 pairs of 5 µm wide interdigitated electrodes (Figure 1a). Then, a layer of self-assembled gold NPs was formed on the whole area by the convective assembly technique described in [START_REF] Gauvin | Plasmonic photo-current in freestanding monolayered gold nanoparticle membranes[END_REF] (Figure 1b). This method generates close-packed NP assembly with a long range as shown in Figure 1b andc. Resistance and capacitance measurements were carried out using an impedance analyzer (Keysight E4990A) operating in the femto-Farads (fF) capacitance range and in the 25 to 10 MHz frequency range. A nanoparticle-free reference sample, with the same geometry, was fabricated and used for calibration, before each measurement, in order to get rid of the capacitance of the inter-digited electrodes and of the parasitic capacitances.

The optical excitation of the NP assembly was achieved using a CW laser operating either at λ inc = 405, 532 or 640 nm. The laser is coupled to an optical fiber and the output power is few tens of mW (near 40mW) depending on the excitation wavelength. The optical fiber is mounted in a Janis probe station which allows focusing the laser down to a spot size of 1 mm 2 in order to illuminate the entire active area. The laser intensity was monitored using a diode driver. The maximum illumination intensity used in the experiments is 3.5W/cm 2 .

It is worthwhile to mention that the laser irradiation intensities used in this study are much weaker than the typical intensity (10kW/cm 2 ) for photo-thermal induced heating in self-assembled Au nanoparticles. The photo-thermal effect may lead to melting of the nanoparticles and collapse of the assembly for laser irradiation above 40kW/cm 2 [START_REF] Gauvin | Plasmonic photo-current in freestanding monolayered gold nanoparticle membranes[END_REF].

Electro-mechanical experiments of the NP assemblies were conducted by applying a uniaxial stress to the flexible polyimide substrate using a traction machine (Deben Tensile Stage 200N). The applied force was increased from 0 to 70 N (by steps of 0.1%).

-Theory and numerical simulations:

Calculations of the charge transport were performed assuming a monolayer of gold NPs arranged in a regular hexagonal lattice (Figure ESI 6) which mimics the actual arrangement of the NPs shown in Figure 1c. The NP diameter is 14 nm (i.e. the average size of the synthetized NPs) and the surface-to-surface distance is set to 1.2 nm (corresponding to the length of the C 12 molecules). Each nanoparticle, labeled i, is located at the node (x i , y i ) of the 2D network and defines, with the first neighbored particle j, an elementary parallel nano-circuit depicted in Figure 1e. The admittance χ ij of this nano-circuit is given by:

(1) χ ij = 1/R ij (ε, V ij , T)+ g photo (λ, I laser ) + jC ij ω.
where ω is the angular frequency and C ij the inter-particle local capacitance.

The inter-particle resistance R ij is given by [7]:

(2) = .

, where l ij ( ) is the surface-to-surface interparticle distance which depends on the NP positions and hence on their change with applied strain ε. k R is a proportionality constant and the parameter accounts for the electron tunneling between nanoparticles [7]:

(3) = - , , with , , = ! " # + % & " # '
where the tunneling decay constant β~3 nm -1 has been estimated in previous works [START_REF] Decorde | Small Angle X-ray Scattering Coupled With in-situ Electromechanical Probing of Nanoparticle-Based Resistive Strain Gauges[END_REF]. also depends on the Coulomb charging energy E C , temperature T and voltage drop V ij between adjacent nanoparticles.

According to [START_REF] Quinn | Manipulating the charging energy of nanocrystal arrays[END_REF] and [9], the inter-particle capacitance C ij is given by

(4) () = *ε + ε , -. + - ε ⁄
where d is the nanoparticle diameter, ε 0 is the vacuum permittivity, and ε r is the relative permittivity of the surrounding medium, i.e. of the organic ligand molecules in our case.

In order to introduce the inter-particle interaction in the admittance matrix, we assumed that all first neighbor nanoparticles located within a ring centered on the considered nanoparticle experience mutual capacitive influence.

In Equ. (1), g photo (λ, I laser ) accounts for the contribution of the optical excitation to the interparticle conductance, and depends only on the laser wavelength λ (resonance effects) and intensity I laser . The current flow, throughout the NPs assembly is computed by solving the matrix equation numerically [START_REF]Scilab: Free and Open Source software for numerical computation[END_REF]: ; the latter is the total admittance connected to node I [START_REF] Lagonotte | Réseaux électrocinétiques et algèbre linéaire (notions fondamentales)[END_REF]. The admittance is obtained according to Y 0 =V 0 /I 0 where V 0 is the last element of the voltage vector and I 0 is the injected current.

Under dark conditions, the macroscopic resistance R and capacitance C of the whole NP assembly are determined using R = 1/Re(Y 0 ), and C = Im(Y 0 )/ω [START_REF] Lagonotte | Réseaux électrocinétiques et algèbre linéaire (notions fondamentales)[END_REF].

The numerical approach allows to take into account disorder effects due to fluctuations of the nanoparticle size and position, and to introduce a deformation (eventually non-uniform) of the NP network. For a perfectly ordered and strain-free NP network, it is possible to derive analytical expressions for the macroscopic total resistance R and capacitance C [7], [START_REF] Moreira | Electron transport in gold colloïdal nanoparticle based strain gauges[END_REF]: (6) 7 = 8 7 . 7 9: and ; = 8 < . ; 56 where N R and N C are the numbers of series and parallel inter-particle junctions. The macroscopic resistance R depends on temperature and bias voltage through the inter-particle resistance R ij .

The voltage drop between nanoparticles V ij can then be approximated by V ij =V b /N j where V b is the applied bias voltage and N j is the number of junctions between electrodes in order to scale up the model from nano to macro circuit.

In the calculations, the optical excitation is treated at the macroscopic level: once the total resistance R and capacitance C are determined numerically, G photo is plugged into the parallel circuit as shown in Figure 1d. We adopt this approach for two main reasons. First, there have been very few theoretical works on the inter-particle photo-induced conductance and on the role of optical resonances [START_REF] Yajadda | Partial rectification of the plasmoninduced electrical tunnel current in discontinuous thin gold film at optical frequency[END_REF]; the predicted properties still need to be compared to experiments. On the other hand, the available measurements of the photo-conductance were performed at the macroscopic level (i.e. on large NP assemblies), only. The photo-induced modification of the charge transport between two isolated nanoparticles requires further experimental efforts.

Mangold et al. [2], [15] and Gauvin et al. [START_REF] Gauvin | Plasmonic photo-current in freestanding monolayered gold nanoparticle membranes[END_REF] showed that, for low laser irradiation (below 7kW/cm 2 ), the photo-conductance increases linearly with increasing laser intensity due to the photothermal induced heating of the NP assemblies:

(7) = >?@A@ >B ≈ >?@A@ D * 2 FGH , I J K
where the constant L MNOPO Q accounts for the optical resonances and for the transduction of the electromagnetic energy into electric current. For dodecanethiol coated Au NPs, a L MNOPO ~ 35.5 pS.cm 2 /kW at plasmon resonance (λ inc ~638nm) was found for optical excitation tuned to their plasmonic resonance [START_REF] Gauvin | Plasmonic photo-current in freestanding monolayered gold nanoparticle membranes[END_REF].

3-Results and Discussion:

3.1 -Resistance and Capacitance dependence on temperature and bias voltage:

Correlations between total resistance and total capacitance:

We first investigate the charge transport through the NP assembly without any applied optical excitation or mechanical stress. Our aim is to point out the correlation between resistance and capacitance characteristics. show the results of the measurements. The dashed lines are calculated curves using equations (2), (3), (6) and ( 8) and adjusted to the experimental data.

The total resistance R is in the order of few hundreds of MΩ and exhibits a non-metallic behavior, i.e. it decreases with increasing temperature which suggests that the surrounding molecules act as efficient inter-particle barriers against electron tunneling, as already reported in previous works [7], [18]. On the contrary, the capacitance increases with increasing temperature (see also Figure ESI 4) and reaches 350 fF at room temperature (Figure 2a). It was suggested that the thermal expansion of the polyimide substrate could be responsible for the temperature variation of electrical properties (Yajadda et al. [19]). However, calculations showed that the substrate effect is negligible given the rather weak thermal expansion coefficient of polyimide 30-60x10 -6 K -1 [20].

Figure 2b displays the variations, at room-temperature, of the relative resistance ∆R/R and relative capacitance ∆C/C as a function of bias voltage. ∆R/R is symmetric with respect to the sign of the bias voltage and decreases from 0 to c.a. -30% at +/-40V. ∆C/C is also symmetric with respect to the bias voltage and increases from 0 to c.a. +45% at +/-40V. As for the temperature dependence (Figure 2a), the change of ∆R/R and ∆C/C with bias voltage are opposite (Figure 2b). While the resistance properties of NP assemblies are fairly well understood [6], [START_REF] Moreira | Electron transport in gold colloïdal nanoparticle based strain gauges[END_REF]- [26], to the best of our knowledge, so far, there has been no interpretation of the relationship between resistance and capacitance observed experimentally.

Correlation between resistance and capacitance:

The electrical properties of the NP assembly were analyzed using numerical simulations of the charge transport (presented in section 2) which allow deriving the macroscopic resistance R and capacitance C of the NP assemblies from the nano-circuit model (Figure 1e). The parallel circuit, formed by the macroscopic resistance R and capacitance C (Figure 1d) can be transformed into an equivalent circuit, and it can be shown the relation between the macroscopic capacitance and resistance is then given by [START_REF] Goswami | Dielectric and optical properties of ZnS films[END_REF], [START_REF] Sakr | Effect of illumination and frequency on the capacitance spectroscopy and the relaxation process of p-ZnTe/n-CdMnTe/GaAs magnetic diode for photocapacitance applications[END_REF]:

(8) , R = ∞ + S K , R K ∞
where ω is the angular frequency and C ∞ is the high frequency total capacitance. The electrode resistance r s , which is very small with respect to the total resistance of the NP assembly (few Ω compared to few MΩ), can be included in the total resistance (see ESI Section II).

Equ. (8) shows that R and C are inversely proportional and hence should vary in opposite directions as a function of temperature and bias voltage, in agreement with the experimental observations Figure 2. More precisely, Figure 2 presents a comparison between calculated and measured resistance and capacitance. The calculated curves (using Equ. ( 2), (3) combined to Equ. ( 6)

and ( 8)) were adjusted to the measured ones using three fitting parameters: the number of junction N j between two electrodes, the charging energy E c and the total capacitance C ∞ . According to the geometrical characteristics of the NP assembly (5µm length, 14nm thick, 14nm NP size, and 1.2nm ligand length), the number of junctions is estimated to be c.a. N j ~ 300. In the numerical simulations, this value is taken as an initial input parameter and can vary between 100 and 500 (junctions). After convergence, we obtain N j = 305 junctions, E c = 20 meV and C ∞ = 10 fF [9]. It is worth mentioning that the fitting procedure was performed simultaneously using all experimental data, i.e. using the variations of both R and C as a function of temperature and bias voltage. As can be seen, the evolutions of resistance and capacitance as a function of temperature and bias voltage are well accounted for. In particular, the model describes rather well the increase of resistance and the correlated decrease of capacitance as a function of temperature. Also, the opposite variations of ∆R/R and ∆C/C with bias voltage are rather well described including their non-linear behavior.

The value obtained for the charging energy E c = 20 meV is in good agreement with the one determined previously [START_REF] Moreira | Electron transport in gold colloïdal nanoparticle based strain gauges[END_REF] for similar ligand molecules. It is comparable to the thermal activation energy (25 meV), at room-temperature, which indicates an intermediate Coulomb blockade regime. The fitted value of the total capacitance C ∞ = 10 fF is one order of magnitude smaller than the 100 fF obtained (at 10 MHz) with the same deposition technique, ligand molecules and gold NP diameter [9]. Such a difference can be ascribed to parasitic capacitances not completely eliminated during the calibration phase.

-Zero strain plasmonic photo-capacitance:

Electrical measurements under optical irradiation were performed in order to investigate the coupling between the surface plasmons of the metal nanoparticles and their charge transport properties. We thus focus on the plasmo-electronic response of the NP monolayer, particularly on the capacitance variation induced by the optical excitation. inter-particle distances as extracted from the transmission electron microscopy (TEM) images (insert in Figure 3a and Figure ESI 5a). We found a good agreement between the measured and simulated DDA spectra, hence corroborating the plasmonic origin of the observed resonance. It is worthwhile to mention that the interaction between the NPs plays an important role as the plasmonic peak wavelength depends on the inter-particle distance. As a matter of fact, we found that inter-particle distances slightly larger (+10%) than those measured by TEM, account rather well for the plasmonic peak wavelength and line width (see Figure ESI 5b). This can be due to the variation of the steric interaction between the ligand molecules under ambient conditions compared to the high vacuum TEM environment.

As a matter of fact, according to the plasmonic absorption cross section calculated using the DDA simulations (Figure 3a) and to the nanoparticle density within the self-assembled layer, we estimate that the optical power absorbed by the nanoparticles within the 1 mm 2 active array to be around 70 mW. Moreover, assuming that the NP array consists mainly in gold and neglecting the contribution of the surrounding molecules to the thermal conductivity, we estimate the temperature increase due to the photo-thermal heating to be around 2K. The latter value indicate that, here, the contribution of the photothermal effect to the photoconductance is very weak change compared to previously reported studies where much larger laser intensities (few tens of kW/cm 2 ) were used.

Figure 3b and c display the variations of the relative resistance ∆R/R and capacitance ∆C/C as a function of laser intensity and for excitation wavelengths close to the plasmonic resonance. ∆R/R decreases with increasing laser intensity for all excitation wavelengths. This photo-induced effect has already been reported in previous works [START_REF] Gauvin | Plasmonic photo-current in freestanding monolayered gold nanoparticle membranes[END_REF] and was interpreted as due to the photo-thermal enhanced charge tunneling between nanoparticles, combined with charge trapping of the photogenerated carriers which leads to the non-linear variations observed in Figure 3b. On the contrary, ∆C/C increases with increasing laser intensity. Although smaller than ∆R/R, ∆C/C reaches 43% at I laser = 3.2 W/cm 2 . As for the temperature and bias voltage (Figure 2), the evolutions of the resistance and the capacitance as a function of laser intensity are opposite. Moreover, these variations depend on the excitation wavelength (Figure 3b,c). The ∆C/C measured with the 405, 532 and 640 nm excitation wavelengths (at 2.2W/cm 2 ) laser intensity are plotted in Figure 3a. A clear correlation between ∆C/C and the plasmonic resonance of the NP assembly is observed. Indeed, the maximum of ∆C/C is obtained for λ inc = 532 nm, nearly matching the plasmonic resonance which confirm the plasmonic enhancement of the capacitance Figure 3c. To the best of our knowledge, such effect is reported here for the first time.

The plasmonic effect, on both the resistance and the capacitance of the NP assembly, can be analyzed using the macroscopic circuit model (Figure 1d) in which the change of the conductance due to the optical excitation is included through the photo-conductance G photo term in Equ. (7). As for the effects of temperature and bias voltage, the photo-induced capacitance is deduced from the photoinduced resistance of the NP assembly using Equ. (8). One issue in estimating G photo is to determine the wavelength dependence of the k photo term in Equ. (7). To overcome this difficulty, we first assume that k photo is proportional to the wavelength-dependent optical absorption of the NP assembly and we use the absorption coefficient measured at 405 nm wavelength as a reference. We thus obtain k photo (532nm) = 3.1 x k photo (405nm) and k photo (532nm) = 2.8 x k photo (405nm). In order to determine k photo (405nm), we compare the measured and calculated variations of ∆R/R and ∆C/C as a function of laser intensity at 405 nm excitation wavelength and use k photo (405nm) as the only fitting parameter; all other parameters (N j , E C and C ∞ ) are fixed to their previously determined values (Figure 2). This fitting procedure is performed for ∆R/R and ∆C/C, simultaneously and the correlation between resistance and capacitance is still given by Equ. (8). We thus obtain k photo (405nm) ~ 5 pS.cm 2 /kW. Close to the plasmonic resonance (i.e. 532 nm) k photo|532nm ~16 pS.cm 2 /kW. The latter value is smaller than the one 35.5 pS.cm 2 /kW reported in Gauvin et al. [START_REF] Gauvin | Plasmonic photo-current in freestanding monolayered gold nanoparticle membranes[END_REF]. Such a difference may arise from, the fact that the NP assembly is here supported by the polyimide substrate and not suspended as in [START_REF] Gauvin | Plasmonic photo-current in freestanding monolayered gold nanoparticle membranes[END_REF] which may impact the overall absorption of the nanoparticle array and hence the k photo parameter. Figure 3b and Figure 3c show that the calculations account rather well for the experimental variations of both ∆R/R and ∆C/C

with the laser intensity. The deviations, between calculated and measured ∆R/R and ∆C/C at low laser irradiation, arise from the linear approximation of G photo used in Eq.7. It is worth to underline that the photo-induced electric response of the NP assembly is here introduced through the parameter G photo (Equ. (7)) which contains the physics of the plasmonic-to-electric energy conversion. This allows to account for the effect of the plasmonic pumping of electrons and holes on the inter-particle admittance (Equ. ( 1)) and finally on the overall resistance R of the nanoparticle assembly (Equ.( 6)).

Strain induced plasmonic photo-capacitance:

The NP assembly is formed on a stretchable substrate offering a unique mean of monitoring the inter-particle distances and hence their electronic and plasmo-electronic properties. Figure 4a shows capacitance measurements performed under laser illumination at 0.85W/cm 2 , for 405, 532 and 640 nm excitation wavelengths, as a function of applied extensive strain ranging from 0 to 1.5% (elastic domain of polyimide). As can be noticed, the variation of ∆C/C with strain is linear, whatever the optical conditions. Under dark conditions (no illumination), the measured gauge factor

TU < = ∆< < ⁄ W is around -1.2.
Remarkably, it is enhanced by nearly a factor 3 under laser illumination and for the excitation wavelengths nearly matching the plasmonic resonance (i.e. 532 and 640 nm). For the nonmatching wavelength (405 nm), the enhancement is only a factor 2.

Measurements of the gauge factor in dark conditions were performed before and after illumination at 0.85W/cm 2 following the sequence: dark, red laser, dark, green laser, dark, blue laser (Figure 4a). All the curves recorded under dark conditions systematically overlap, which indicates that there is no degradation of the NP assembly upon laser irradiation or mechanical deformation.

Irradiations with much larger laser intensities produce the melting and the coalescence of the nanoparticles [START_REF] Gauvin | Plasmonic photo-current in freestanding monolayered gold nanoparticle membranes[END_REF]. To gain a fundamental understanding of the plasmo-electro-mechanical properties of the NP assembly, we have performed numerical simulations based on the model introduced in section 2. As discussed previously, the inter-particle local resistance R ij (Equ. ( 2)) and capacitance C ij (Equ. ( 4))

both depend on strain through the inter-particle spacing. The uniaxial (x axis) applied strain ε is introduced in the numerical simulations by shifting the NP coordinates according to:

(9) x i , y i → x i .(1+ s.ε), y i .(1-υ poisson .s.ε)
where υ poisson = 0.37 is the Poisson's coefficient of the polyimide substrate, and s is the substrate-tolayer strain transmission factor (stick/slip) which is, in a first step, assumed to be 1 since the NP assembly is here formed by a single monolayer.

The inter-particle resistance R ij and capacitance C ij are calculated according to the strained NP network. The total resistance R and capacitance C are then computed using the numerical 1)-( 5) as discussed above. The simulations were performed for strain ranging from 0 to 1.5% with and without optical excitation at 0.85W/cm 2 . The results are presented in Figure 4b.

Under dark conditions, the relative capacitance ∆C/C decreases linearly with increasing strain as observed experimentally (Figure 4a) and in agreement with Equ.(4) which indicates that the interparticle capacitance decreases linearly with increasing inter-particle distance [9]. Under illumination, the gauge factor increases due to the photo-induced inter-particle conductance (G photo term in Equ. (7)) which impacts the overall resistance and thus the overall capacitance (Equ. ( 8)) of the NP assembly.

Using the values of k photo determined previously (section 3.3), the calculated GF c is increased by a factor 3 (compared to the dark conditions) for the 532 and 640 nm wavelengths, i.e., close to the plasmonic resonance, and by a factor 2 for the 405 nm wavelength, in agreement with the measurements (Figure 4a). However, the calculations overestimate the absolute values of ∆C/C by a nearly a factor 5. This can be explained by three main reasons. First, the strain within the NP assembly could be overestimated. Indeed, in Equ.( 9) the substrate-to-layer transmission coefficient is assumed to be 1, which could not be the case due to the weak adhesion of the layer on the substrate, as already observed for resistive strain gauges [START_REF] Decorde1 | Small Angle X-ray Scattering Coupled With in-situ Electromechanical Probing of Nanoparticle-Based Resistive Strain Gauges[END_REF]. Second, a rearrangement of the ligand molecules within the strained NP network may change the dielectric constant surrounding the metal NPs and hence the inter-particle capacitance (Equ. ( 4)). In order to investigate these two effects, we have performed numerical simulations of ∆C/C for various strain transmission coefficients (s = 1 to 0.7, Equ.( 9)) and dielectric constants (ranging from 2.3 to 2.32, Equ. ( 4)). As expected, both effects are responsible for a decrease of the sensitivity of ∆C/C to the applied strain (see Figure ESI 7). Finally, the applied stress may also be partially accommodated by disorder effects due to size and inter-particle distance fluctuations, as well as to defects in the NP arrangement within the network, thus limiting the strain of the NP assembly.

We have shown that the change of resistance R, in turn, translates into a photo-capacitance through Equ. (8). However, as mentioned above, the impact of the optical excitation on the local photoconductance gphoto is not introduced explicitly in equation 1. To do so, a description, at the microscopic level, of the conversion of surface plasmons into charge carriers and current in the selfassembled nanoparticle array is required. For instance, the effect of optical excitation of the interparticle capacitance could be introduced as an AC plasmonic voltage superimposed on the applied DC voltage [START_REF] Yajadda | Partial rectification of the plasmoninduced electrical tunnel current in discontinuous thin gold film at optical frequency[END_REF]. The local electric field and potential may be enhanced by the plasmonic resonance and by the near-field interaction between the nanoparticles. In that case, one may expect a direct plasmonic contribution to the local capacitance and hence to the overall photocapacitance of the nanoparticle array. Also, the interparticle resistance may include a contribution which accounts for the decay of the surface plasmons into electrons (and holes) and their transport through tunneling effect and charge transfer via electron state hybridization between the metal nanoparticle and the coating molecules.

Moreover, under laser irradiation, the ligand molecules pinned to the nanoparticle surface, undergo a quite complex adsorption/desorption dynamics [START_REF] Mezni | Photochemistry at the Surface of Gold Nanoprisms from Surface-Enhanced Raman Scattering Blinking[END_REF] which may impact the charge tunneling and transfer and hence the overall photo-resistance and photo-capacitance.

Conclusions:

In summary, we have investigated the dependence on temperature, bias voltage, optical excitation and strain of the electronic transport properties of self-assembled gold nanoparticle monolayers. A special attention has been paid to the correlation between resistance and capacitance as both characteristic bring complementary information on the charge transport phenomenon in these complex molecules/nanoparticle hybrid systems. The interpretation of the experimental results was achieved using a detailed modelling of the charge transport both at the nanoscale and at the macroscopic scale of the NP assembly. The charge tunnelling and hopping between nanoparticles were describded using a nano-circuit junction with temperature, bias voltage and strain dependent resistance and capacitance. The effect of the optical excitation and transduction of the surface plasmons into an electric current was introduced as an additional photo-induced term to the macroscopic impedance. To connect the nanoscale and the macroscopic scale, the overall resistance and capacitance of the NP assembly were determined using numerical simulations. Our main findings can be summarized as follows: (i) the correlation between resistance and conductance characteristics was pointed out experimentally and interpreted using a quantitative analysis of the measurements based on the relation between the macroscopic resistance and capacitance. In particular, we found that the relative change of the capacitance can be as large as 43% at the surface plasmon resonance, which paves the way to applications of self-assembled gold NP monolayers as highly sensitive photo-capacitance sensors. (ii) the modification of the charge transport through the NP assembly under optical excitation and simultaneous applied stress showed that the capacitance strain gauge factor is increased by a factor 3 at the surface plasmon resonance, in agreement with the calculations. This result may be exploited for optically enhanced capacitance strain-sensors. The conversion of surface plasmons into electron-hole pairs transported throughout a network of nanoparticles is a complex multi-scale phenomenon. It requires a deep fundamental understanding of the interaction mechanisms underlying the generation and decay of the involved excitations, but also a detailed description of the molecule/nanoparticle charge transfer (hybridization, tunnelling, hopping and trapping). Our work contributes to bridge the gap between fundamental investigations of the optoelectronic properties of NP assemblies and their practical use as highly sensitive photo-resistance and photo-capacitance sensors.

II -Equivalent electrical circuit

The overall transport properties of the NP assemblies can be derived by from an equivalent circuit made of a parallel R-C resistance and capacitance, and a bulk resistance r s in series due in particular to lead lengths. However, we can consider that the electrode resistance r s is negligible with respect to the total resistance of the NP assembly (few Ω compared to few MΩ). The impedance Z of the circuit (Figure ESI 2a) can be written:

(1) X = , H + % S = %, H . %S K K K %S K K K - S K %S K K K
In order to extract the resistive and capacitive macroscopic characteristics of the circuit, it is useful to look for the equivalent series circuit. This impedance can also be represented in a simpler equivalent series circuit (Figure ESI 2b):

(2) X = H -S H By matching the real and imaginary parts of the two previous equations, we find the relation between resistance R and capacitance C and Rs series resistance and Cs serie capacitance:

(3) H = %, H . %S K K K %S K K YZ[ H = %S K K K S K K
It is worth noting that when the condition 1 ] ⁄ 7 ^;<<; is satisfied, the series capacitance C s tends towards the parallel capacitance C value, which is fulfilled which is fulfilled in our study, since, we have _ `ab < = 8d10 _f U<<;=3x10 -12 F (by roughly taking f~1x10 6 Hz, R = 250 M, C~3x10 -12 F).

III -Capacitance versus

V -Discrete dipole approximation (DDA) simulations

The simulations of the optical extinction spectra and electric near-field were performed using the ddscat 7. calculations. The optical index of gold was taken from [5] and the optical index 1.46 of dodecanethiol was assumed for the surrounding medium. As shown in Figure ESI 5b, the plasmonic resonance occurs around 600 nm. In order to estimate the effect of the electro-magnetic near-field interactions, the separation between the nanoparticles was artificially increased while keeping the same sizes and arrangement. In that situation, the surface plasmon resonance is now blue shifted to 540 nm (Figure 5b) as expected for isolated spherical gold nanoparticle. To introduce the strain, the nanoparticles positions are shifted according to Equ. 8 and the stick/slip s can be varied. The relative permittivity ε r , which appears (Eq. 3) in the capacitance C ij of the inter-particle junction model can also be changed. The relative capacitance is very sensitive to the change in relative permittivity. Indeed, increasing ε r from 2.3 to 2.32, which is less than 1% variation, decreases the gauge factor G fc from -5.8

to -4.9%. Similarly, reducing the stick/slip coefficient from 1 to 0.7, decreases the gauge factor from -

Figure 1 :

 1 Figure 1 : (a) Scanning electron microscopy (SEM) the interdigited electrodes on top of which the NP assembly is formed, (b) and (c) high resolution SEM image of the active area showing the close-packed self-assembled monolayer of 14nm gold nanoparticles (d) macroscopic model involving the total resistance R, capacitance C and photo-conductance G photo (e) nano-circuit model of the electric inter-particle junction involving the tunnel resistance (R ij ), capacitance (C ij ) and local photo-conductance (g photo ). The red arrows indicate the parameters (strain (ε) and laser excitations) to which these quantities are sensitive.

( 5 )

 5 / 0 = /10 /20 where [V] and [I] are respectively the voltage and the injected current vectors, [Y] is the complex admittance matrix of which non-diagonal and diagonal terms are, respectively, Y ij = -3 ij (i ≠j) and Y ii =∑ 3 56 6

Figure

  Figure2ashows the temperature dependence of the total resistance R and total capacitance C:

Figure 2 :

 2 Figure 2 : (a) Resistance and capacitance of the NP assembly versus temperature. The AC bias voltage is set to 100mV and 500 kHz (b) Room temperature variations of the relative resistance ∆R/R and capacitance ∆C/C as a function of bias voltage. The dots and squares in (a) and (b)

Figure 3 :

 3 Figure 3 : (a) Optical reflectance spectrum of the NP assembly (black) compared to the DDA simulated spectrum (red) and to the relative variation ∆C/C of the capacitance (blue dots) measured as a function of excitation wavelength at 2.2W/cm 2 laser intensity. Measured (dots) and calculated (lines) variations of the relative resistance (b) and capacitance (c) of the NP assemblies with laser intensity I Laser increasing from 0 to 3.2W/cm 2 and for excitation wavelengths λ inc = 405, 532, 640nm.

Figure 3a presents the

  Figure3apresents the measured optical extinction spectrum of the NP assembly of Figure1. A clear plasmonic resonance centered around 600 nm is observed. Calculations based on the Discrete Dipole Approximation (DDA) were performed in order to ascertain the origin of the optical resonance and to point out the role of the interaction between the metal nanoparticles. To do so, we have performed DDA simulations assuming nearly 120 nanoparticles with the actual positions, sizes and

Figure 4 :

 4 Figure 4 : Measured (a) and simulated (b) Relative capacitance ∆C/C of the NP assembly as a function of applied strain under dark conditions and for the excitation wavelengths λ inc = 405, 532, 640 nm. The laser intensity is set at 0.85 W/cm 2 . The lines in (a) show the results of a least-square linear fit which allow to extract the experimental gauge factors: G fc (dark) = -1.2, G fc (405nm) =-2.03, G fc (532nm) = -2.96 and G fc (640nm) = -2.85.

Figure ESI 1 :

 1 Figure ESI 1 : Fabrication process of the NP self-assembled samples

Figure ESI 2 :

 2 Figure ESI 2 : (a) Equivalent electrical circuit elements (R, C, and r s ) (b) Equivalent series circuit (C S and R S ).

Temperature:Figure ESI 4 :

 4 Figure ESI 4 : Capacitance variation versus temperature of the NP self-assembled sample at f=500 kHz.

  3 software by Draine and Flatau[8]-[9]. The positions and sizes of each nanoparticle were extracted from the transmission electron microscope (TEM) image (FigureESI 5a) assuming spherical nanoparticles. Each nanoparticle was discretized by a cubic mesh of nearly 2000 point dipoles distributed with inter-dipole separation as small as 0.5 nm in order to ensure full convergence of the

Figure ESI 5 : 21 Figure ESI 6 :

 5216 Figure ESI 5 : (a) Transmission electron microscopy image of the NPs assembly (b), full line DDA calculated spectra of the NP assembly located within the square region shown in (a). The dashed line shows the spectrum calculated for the isolated nanoparticle assembly.

Figure ESI 7 :

 7 Figure ESI 7 : Simulated variation of the relative capacitance for stick/slip coefficient s = 1 (full substrateto-layer strain transmission) and s= 0.7. Simulations were also performed for permittivity ε r = 2.3 and 2.32 while keeping the stick/slip coefficient s = 1.

Acknowledgements

This work was supported by "Initiatives d'excellence IDEX UNITI" in the framework of its program "Actions Thématiques Stratégiques" AAP 2015 (Project "WE CAN"). This work received computational support from HPC center CALMIP at Toulouse university.

Data availabitity:

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. The raw data required to reproduce these findings will be available to download very quickly from [http://lpcno.insa-toulouse.fr/spip.php?article1588&lang=en]. The processed data required to reproduce these findings will be available to download very quickly from [http://lpcno.insa-toulouse.fr/spip.php?article1588&lang=en].

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