Yulin Zhang

Christelle Urtado
email: christelle.urtado@site-eerie.ema.fr

Sylvain Vauttier
email: sylvain.vauttier@site-eerie.ema.fr

Connector-driven gradual and dynamic software assembly evolution

Complex and long-lived software need to be upgraded at runtime. Replacing a software component with a newer version is the basic evolution operation that has to be supported. It is error-prone as it is difficult to guarantee the preservation of functionalities and quality. Few existing work on ADLs fully support a component replacement process from its description to its test and validation. The main idea of this work is to have software architecture evolution dynamically driven by connectors (the software glue between components). It proposes a connector model which autonomically handle the reconfiguration of connections in architectures in order to support the versioning of components in a gradual, transparent and testable manner. Hence, the system has the choice to commit the evolution after a successful test phase of the software or rollback to the previous state.

Introduction

The role of software architectures in software engineering becomes increasingly important and widespread [START_REF] Garlan | Software architecture: a roadmap[END_REF]. Software architectures model the structure and behavior of systems. Architecture description languages (ADLs) [START_REF] Medvidovic | Moving architectural description from under the technology lamppost[END_REF] are not solely used during the design steps of the development process anymore, but also at runtime after deployment, to manage the evolution of application architectures. However, most ADLs do not fully support the evolution process of software systems. Software evolution is the process to change a software system from some version to a newer version. It consists in adding, deleting and replacing software components or connectors. Replacing a software component with one of its newer versions is the basic evolution operation that has to be supported. It is also the simplest and the more frequently used to improve software functionality, performance or reliability. However, component upgrading is an error-prone operation as it is difficult to guarantee (at least) the preservation of the functionality and quality. Some validation process should secure com-ponent upgrading to avoid errors or regressions to be introduced by the new component version new version. Evolution mechanisms are provided in the main representative ADLs [START_REF] Medvidovic | A language and environment for architecture-based software development and evolution[END_REF][START_REF] Rakic | Increasing the confidence in off-the-shelf components: A software connector-based approach[END_REF][START_REF] Roshandel | Mae-a system model and environment for managing architectural evolution[END_REF] to deal with component replacement in software architectures. However, existing works only propose limited support for evolution control that increases the chances for successful dynamic evolution. This paper considers applying an autonomic approach to manage and control evolution at runtime. A connector model is proposed which embeds the intelligence necessary to monitor and drive architecture modifications: we talk about connectordriven architecture evolution. Connectors are internally designed as expendable and reconfigurable component assemblies, able to manage various evolution concerns, depending on the requirements. A first application of these connectors is presented here: gradual evolution of assemblies in which new component versions are transparently tested before they effectively replace older ones. The remaining of this paper is organized as follows. Section 2 defines the context of this research and spans existing related work. Section 3 specifies our objectives and describes the illustrative example we use throughout the paper. Section 4 describes our intelligent connector model and shows how it is component version evolution. Section 5 details our connector-driven gradual evolution process. Section 6 briefly describes the implementation of our model as an extension of the Julia implementation of the Fractal component model while Sect. 7 concludes with future work directions.

Context and related works

To develop a connector-driven gradual and dynamic evolution process requires an understanding of existing ADLs that support dynamic evolution and connector modelings.

Software evolution: definitions

Lehman [START_REF] Lehman | Towards a theory of software evolution -and its practical impact[END_REF] defines software evolution as the collection of all programming activities intended to generate a new version of some software from an older operational version. If these activities can be performed at runtime without the need for system recompilation or restart, evolution is called dynamic software evolution. An explicit architectural view can enhance flexibility of software evolution. The software architecture of a program or computing system defines the structure of the system, which comprise software component types and connector types, the externally visible properties of those component types and connector types and the relationships among them [START_REF] Bass | Software Architecture in Practice[END_REF]. Architectural configurations are connected graphs of concrete components (instanciated component types) and concrete connectors (instanciated connector types) that conform to the architectural structure [START_REF] Medvidovic | A classification and comparison framework for software architecture description languages[END_REF]. Figure 1 provides an example of both an architecture and a conforming configuration using the syntax of the C2 ADL [START_REF] Medvidovic | Formal modeling of software architectures at multiple levels of abstraction[END_REF]. Existing work propose various typologies for evolution [START_REF] Buckley | Towards a taxonomy of software change: Research articles[END_REF][START_REF] Lientz | Software Maintenance Management[END_REF], some of which we are going to use to precise which evolution is supportedin this paper . Dynamic software evolution may affect component or connector types at the architecture level or component or connector instances at the configuration level [START_REF] Medvidovic | A classification and comparison framework for software architecture description languages[END_REF]. More precisely, component instance evolution potentially affects four elements of components: their name, interface, behavior protocols or implementation (as described by Palsberg and Schwartzbach [START_REF] Palsberg | Three discussions on object-oriented typing[END_REF]). Sometimes several of these elements can be simultaneously affected during evolution. Thus, rules that constrain valid evolution transitions migth concern several elements. For example, behavioral conformance allows any class to be a subtype of another if it preserves the interface and behavior protocol of all methods defined in the supertype. Lientz and Swanson [START_REF] Lientz | Software Maintenance Management[END_REF] provide an orthogonal classification of evolution based on the reason that motivates the evolution. They identify three purpose-oriented evolution categories:

• corrective evolution, where the new version corrects errors / bugs identified in the old one,

• perfective evolution where the code of a component is evolved to improve non-functional attributes of the software (such as time performance),

• adaptive evolution where components are adapted (or extended) to meet changes in their environment or in requirements on the software.

Dynamic evolution in existing ADLs

Few ADLs focus on supporting dynamic software evolution. Three representative approaches specify dynamic evolution in an ADL by providing a dedicated mechanism: decomposition and composition in ArchWare [START_REF] Morrison | Support for evolving software architectures in the archware adl[END_REF], an Architecture Modification Language (AML) in C2 [START_REF] Oreizy | Architecturebased runtime software evolution[END_REF] or the use of multi-version connectors in MAE [START_REF] Rakic | Increasing the confidence in off-the-shelf components: A software connector-based approach[END_REF]. ArchWare uses hyper code to examine the coherence of new configuration and implements evolution by decomposing the targeted configuration and then composing the new configuration. However, it focuses on configuration evolution and do not provide support for component substitution. In C2, an AML is proposed to manage configuration evolutions and to check their consistence. Component substitutions are controlled thanks to a subtype relationship [START_REF] Palsberg | Three discussions on object-oriented typing[END_REF] based on component specifications. However, it lacks to test the actual implementation of the new component. Cook and Dage [START_REF] Cook | Highly reliable upgrading of components[END_REF] propose arbiters to run conjointly multiple versions of components that are transparently perceived by the rest of the system as single components. This approach is also proposed by MAE but uses connectors instead of arbiters. However, these two latter approaches aims at keeping old versions along with newer ones in the system for downward compatibility. The system thus grows in complexity and size. This is not suitable for a long-term, scalable solution, in which newer versions aim at replacing older ones after an interim test period. The above representative ADLs contain useful insights for evolution, but they fail to account for several pertinent issues. There is: (1) no gradual process to ensure safe dynamic evolution, (2) no test of the actual implementation of the new component (functions might not be able to execute properly), (3) no mechanism to deal with system recovery when evolution fails. Connectors bind components together and act as media-

Goals and illustrative example

The example of a bike rental system illustrates the concepts of our evolution process throughout the paper (cf. Fig. 2). In this example, the Vendor component manages the user interface. It cooperates with the Basket component which handles user commands. The Basket component cooperates with the User, BikeTrip and Account components respectively to identify the user, check the balance of its account, assign an available bike and finally calculate the price of the trip when the bike is returned. Component BikeTrip manages the courses for each bike and each user and is designed to retrieve the location and calculate the distance between departure and arrival point. The evolution objective is to replace the version 1 of the Basket component by its version 2. It implies changing the architecture from the original architecture represented on Fig. 2(a) to the target architecture represented on Fig. 2(c). Evolution concerns the return provided interface and its purpose is corrective. Contrary to most evolution approaches, we propose to deploy a transition architecture (cf. Fig. 2(b)) to smoothly switch from an architecture to another through a test period.

Intelligent connector model

In this section, our definition of the conceptual models of component architectures and connectors are presented. In our models, a software configuration is defined as a col-lection of components and connectors which are contained in and managed by a container. These architectural entities are composed of core and extension elements. Core elements consist of classes which describe the basic, invariable part of the different kinds of architectural entities, i.e. their functional concerns. Extension elements are added to architectural entities in order to support the non-functional concerns which apply specifically, depending on the management policies defined by ADL descriptors, regarding for instance the dynamic evolution of components. Extension elements consist of meta-objects, Controllers and Control interfaces, that are added to the definition of components to modify and control their behavior. Figure 3 shows the class model of architectural elements.

Figure 3. Class model of intelligent connector

A container is a core architectural element that encapsulates a set of connectors and components which describe a system as an assembly. It is extended by an evolution manager which manages the evolution of the its inner components and evaluates the feedback from its inner connectors. A Component has a name, a set of interface elements, an associated behavior protocol and an implementation as its minimal core requirements. Components should not communicate directly by referencing each other. Instead, they should use connectors. This minimizes coupling between components and enables binding decisions to change without requiring component modification. Components are extended by StateTrace controllers. A StateTrace controller keeps track of the component states each time the component is modified. Its purpose is to recover from a failure and put back the component into a sound state to prevent system breakdown. Connectors govern communication between components. Its core is composed by interfaces, glues and properties. Interfaces can be of two types: required or provided. Glues define the protocols of connection and interaction between connectors and components. Properties are non-functional attributes of connectors: they record version and type information. Connectors are extended in order to manage and control the evolution of each connected component, control the dataflow between components and collect test samples of component inputs and outputs. The extension of connectors consists of three controllers: the connector controller, the dataflow controller and the time controller. The connector controller controls evolution procedures for the connected components. The dataflow controller controls the dataflow that traverses the connector and records messages from each connected component to compare them in case evolution is declared to be corrective. The time controller records input and output time of each message that traverses the connector to compare them in case evolution is declared to be perfective. These controllers are structured into three levels. Evolution manager is a top-level controller that controls the entire configuration evolution process by managing connectors and components. Connector controllers and stateTrace controllers separately control local evolution actions of respectively on connectors and components. Dataflow and time controllers are third level controllers that are used by Connector controllers to control and collect data on connectors.

Protocols of evolution

The main idea exposed in this paper is to get the original configuration evolve to a target configuration through a transition step. The transition configuration aims to test new component versions and either validate the evolution or invalidate it to return to the original state. To achieve this, we propose a four step evolution process controlled by an evolution manager:

1. Preparation stage to collect evolution description and deploy new component versions (connecting new component versions).

Test stage to collect observations from original and new component versions and determine if the new ver-

sions meet the requirements induced by the declared purpose of evolution.

3. Observation stage to maintain original component versions as backup in case new versions cause failures.

4.

Abandonment stage to enact changes (disconnect the now useless original versions).

Each stage obeys two protocols: evolution and validation protocols. Evolution protocols define how connectors realize each evolution stage. Validation protocols are designed to examine the validation of activities in each stage.

Preparation Stage

Preparation is a vital aspect of the evolution process. Its objective is to change the original configuration into the transition configuration by collecting and deploying evolution descriptions. Evolution description must define what to evolve and how. What to evolve refers to (1) references of old and new component versions, (2) interfaces changed and their change purpose (corrective or perfective), and (3) change test condition for corrective evolution. How to evolve refers the number of collected samples that are to be used during tests. In the example of Fig. 2, the return interface of Basket is modified in the new version for corrective evolution purposes: if type of bike is tandem then price is twice the normal price. Secondly, the evolution manager deploys evolution descriptions according two connector groups: changed group and unchanged group. Changed group contains connectors which connect to changed interfaces like rent, return and selectBike. These connectors drive the evolution process. Unchanged group contains all other connectors like login, pay, etc. At the validation step, the evolution manager collects feedback from all connectors. If all connectors connect successfully with new component version, the evolution process passes to next stage.

Test Stage

The test stage aims at examining the behavior of component new versions according to their evolution purposes. Test stage thus involves collecting observations on component new versions in connectors and evaluating these observation in the evolution manager. Measurements are decomposed into to two sub-stages: offline and online test. Offline test is focused on the functioning of the new version, keeping it transparent to the rest of the system. Old version is dominant, which means that connectors just propagate old version's results to the rest of system, while new version is insulated from the system. Online test aims at adapting the system to new versions. As this entails risks of system failures, a state-trace mode is activated. All components' StateTrace controllers record the state modification of each component. When critical errors happen, the system rolls back to its previous safe state, as every component rolls back to its previous safe state.

Each test of a changed interface is controlled by the connector which connects with this interface. This includes dataflow control and data collection. Thus, according to the direction of interface (provided or required), test and evaluation behave differently. For instance (see Fig. 4), the rent (P1) interface illustrates provided interface evolution, and its returnBike (R1) interface illustrates required interface evolution. Provided interface evolution has either a corrective or per- To evaluate a new version, observations encompasses various data, ranging from dataflow (corrective evolution) to execution times (perfective evolution) as listed in Table 1.

The dataflow controller is in charge of collecting input and output data. The time controller is responsible for collecting time for each input and output. The evaluation of observations is handled by the evolution manager which collects all the observations from connectors. For corrective evolution, the new version must meets its predefined evolution condition. For perfective evolution, the new version must execute faster than the old version. Performance is calculated upon the net response times of components, T response = T go + T back (see Fig. 4). This means that the execution times of the functions called on other components is deducted from the observable response time of the component. After the new version passes the offline and online evaluation, the evolution process proceeds to the next stage.

Observation Stage

Observation stage is another feature used to further secure evolution. In this stage, the old version remains in the system, but only as a backup (it is not active anymore). The system is still in a state-trace mode. If a failure arises, the old version will be activated to replace the new version to roll back to the system to its previous sound state.

Abandonment Stage

Finally, the evolution manager either commits or abandons evolution. The unused version is disconnected and uninstalled.

Implementation in the Fractal component model

Our model is implemented as an extension of Julia, an open-source java implementation of the Fractal component model 1 . Fractal components are managed by controllers contained in the membrane of components. It thus was straightforward to adapt our model to this implementation. First, we added an element-type controller to specialize Fractal components into three sub-types -components, connectors and container. Then, we added specific controllers (as described in Sect. 4) to the adequate sub-type. The evolution manager implements controls evolution through two mains functions. The connect function automatically generates a suitable connector and uses it to connect given components. The cmpEvol function triggers component version evolution: its parameters define the old and new component versions, the set of interfaces that are impacted by the change and the purpose of the evolution. Figure 5 shows a code sample that uses these functions.

// connect aComp to cComp1 Fractal.getEvolutionManager(container). connect (aComp, "r", cComp1, "f");

// evolve component cComp1 to cComp2 // (corrective evolution) Fractal.getEvolutionManager(container). cmpEvol (cComp1, "f", cComp2, "corrective", "if(m.equal("bike")) rent(m)=1;");

Conclusion and Perspectives

This paper presents and illustrates our connector-driven gradual and dynamic software assembly evolution process. Few existing ADLs fully support component replacement evolution process from its description to its test and validation. These ADLs do not support either component substitution, or any test phase, or the complexity induced by multi-version components. The evolution process proposed in this paper is a gradual, testable, transparent, repairable and spans the whole evolution process. It relies on a connector model that embeds the necessary intelligence to monitor and drive architectural configuration modifications. Perspectives for this work are numerous. First, we plan to use the same evolution process to fully manage configuration evolution: component addition or suppression could benefit from an interim configuration as we propose. We also plan to tackle the "architecture drift" [START_REF] Perry | Foundations for the study of software architecture[END_REF] problem which is a crucial coherence problem after architectural configuration evolution.

Figure 1 .

 1 Figure 1. Sample architecture (left) and a conforming configuration (right) described using C2

Figure 2 .

 2 Figure 2. Example of basket evolution configuration comparison

Figure 4 .

 4 Figure 4. Net response time fective purpose. The return connector (cf. Fig. 4) collects test data and controls the evolution of the return interface of the Basket component. During offline test, component Basket1 is dominant. The dataflow controller of the return connector distributes incoming calls to two versions, while all connectors block outgoing calls from Basket2 to keep it transparent to system. During online test, the situation is reversed: Basket2 becomes dominant. The collected data elements are listed in Table 1. Required interface evolution has a corrective purpose. The returnBike connector in Fig. 4 collects test data and controls the evolution of thereturnBike interface of the Basket component. During offline test, the dataflow controller of the returnBike connector blocks Basket2 incomings and let pass Basket1 incomings. The outgoings of the BikeTrip component are sent to the two versions of Basket. During online test, the dataflow controller reverses the situation to make the new version (Basket2) become the dominant.To evaluate a new version, observations encompasses various data, ranging from dataflow (corrective evolution) to execution times (perfective evolution) as listed in Table1.

Figure 5 .

 5 Figure 5. Using the evolution manager

Table 1 . Offline and online data collected by controllers.

 1

	Controllers	Provided interface evolution	Required interface evolution
	Dataflow Controller (DC)	(method, input, outputOld, outputNew)	(method, inputOld, inputNew, output)
	Time Controller (TC)	(method, inputTimeOld, outputTimeOld, inputTimeNew, outputTimeNew)

http://www.objectweb.org


Justin T Foy

Quan Li

Antoine Goujon

Jean-Rémy Colard-Itté

Gad Fuks

Emilie Moulin

Olivier Schiffmann

Damien Dattler

Daniel P Funeriu

Nicolas Giuseppone
email: giuseppone@unistra.fr

Dual-light control of nanomachines that integrate motor and modulator subunits

A current challenge in the field of artificial molecular machines is the synthesis and implementation of systems that can produce useful work when fueled with a constant source of external energy. [START_REF] Abendroth | Controlling Motion at the Nanoscale: Rise of the Molecular Machines[END_REF][START_REF] Erbas-Cakmak | Artificial Molecular Machines[END_REF][START_REF] Coskun | Great expectations: can artificial molecular machines deliver on their promise?[END_REF][START_REF] Browne | Making molecular machines work[END_REF][START_REF] Kinbara | Toward Intelligent Molecular Machines: Directed Motions of Biological and Artificial Molecules and Assemblies[END_REF] The first experimental achievements of this kind have consisted of machines with continuous unidirectional rotations [START_REF] Kistemaker | Unidirectional rotary motion in achiral molecular motors[END_REF][START_REF] Greb | Synthetic Molecular Motors: Thermal N Inversion and Directional Photoinduced C=N Bond Rotation of Camphorquinone Imines[END_REF][START_REF] Guentner | Sunlight-powered kHz rotation of a hemithioindigobased molecular motor[END_REF][START_REF] Greb | Light-Driven Molecular Motors: Imines as Four-Step or Two-Step Unidirectional Rotors[END_REF][START_REF] Wang | Dynamic Control of Chiral Space in a Catalytic Asymmetric Reaction Using a Molecular Motor[END_REF][START_REF] Kudernac | Electrically driven directional motion of a four-wheeled molecule on a metal surface[END_REF][START_REF] Klok | MHz Unidirectional Rotation of Molecular Motors[END_REF][START_REF] Eelkema | Molecular machines: Nanomotor rotates microscale objects[END_REF][START_REF] Koumura | Light-driven monodirectional molecular rotor[END_REF] and translations [START_REF] Ragazzon | Light-powered autonomous and directional molecular motion of a dissipative selfassembling system[END_REF][START_REF] Cheng | An artificial molecular pump[END_REF][START_REF] Balzani | Autonomous artificial nanomotor powered by sunlight[END_REF] that make use of "Brownian ratchets" [START_REF] Cheng | Design and Synthesis of Nonequilibrium Systems[END_REF][START_REF] Astumian | Microscopic reversibility as the organizing principle of molecular machines[END_REF][START_REF] Serreli | A molecular information ratchet[END_REF][START_REF] Astumian | Design principles for Brownian molecular machines: how to swim in molasses and walk in a hurricane[END_REF][START_REF] Chatterjee | Beyond Switches: Ratcheting a Particle Energetically Uphill with a Compartmentalized Molecular Machine[END_REF][START_REF] Mahadevan | Motility Powered by Supramolecular Springs and Ratchets[END_REF][START_REF] Astumian | Thermodynamics and Kinetics of a Brownian Motor[END_REF][START_REF] Peskin | Cellular and thermal fluctuations: the Brownian ratchet[END_REF] in order to bias random motions. An intrinsic limitation of such designs is that an inversion of directionality requires heavy chemical modifications in the structure of the actuating motor part. [START_REF] Ruangsupapichat | Reversing the direction in a light-driven rotary molecular motor[END_REF][START_REF] Fletcher | Unidirectional Molecular Rotary Motor Driven by Chemical Energy[END_REF] Here we show that by connecting subunits made of both unidirectional light-driven rotary motors and modulators, which respectively braid and unbraid polymer chains in crosslinked networks, it becomes possible to reverse their integrated motion at all scales. The photostationary state of the system can be tuned by modulation of frequencies using two irradiation wavelengths. Under this out-ofequilibrium condition, the global work output (i.e. contraction or expansion of the material) is controlled by the net flux of clockwise and anticlockwise rotations between the motors and the modulators.

We recently demonstrated the integration and out-of-equilibrium actuation of rotary molecular motors as mechanically active reticulation nodes in polymer networks (Fig. 1a). [START_REF] Li | Macroscopic contraction of a gel induced by the integrated motion of light-driven molecular motors[END_REF] UV irradiation of such molecular motor/polymer conjugates triggers and sustains the continuous rotation of the motors, producing a subsequent twisting of pairs of polymer chains (i.e. braiding) up to reaching a macroscopic contraction of the entire material. Because the braiding of the polymer chains cannot be reversed without chemical modification of the motor, the resulting twisted conformation is persistent and the process is limited to a unique contraction event. Access to controlled reversibility is an important issue to address when considering future developments in the field of molecular machines. Indeed, because the intrinsic functioning of individual molecular motors is founded on an asymmetric Brownian ratchet mechanism [START_REF] Cheng | Design and Synthesis of Nonequilibrium Systems[END_REF][START_REF] Astumian | Microscopic reversibility as the organizing principle of molecular machines[END_REF][START_REF] Serreli | A molecular information ratchet[END_REF][START_REF] Astumian | Design principles for Brownian molecular machines: how to swim in molasses and walk in a hurricane[END_REF][START_REF] Chatterjee | Beyond Switches: Ratcheting a Particle Energetically Uphill with a Compartmentalized Molecular Machine[END_REF][START_REF] Mahadevan | Motility Powered by Supramolecular Springs and Ratchets[END_REF][START_REF] Astumian | Thermodynamics and Kinetics of a Brownian Motor[END_REF][START_REF] Peskin | Cellular and thermal fluctuations: the Brownian ratchet[END_REF] in order to enforce unidirectionality in thermal noise, the reversibility aspect becomes pivotal for systems connecting out-of-equilibrium molecular motors to one another, or to other elements. We now propose a general systemic approach to overcome this limitation. It uses elementary modules made of a combination of two different mechanically active molecular units (Fig. 1b). In this particular network configuration, an elementary module is composed of one rotary motor and one rotary modulator linked by polymer chains. Chemically, the rotary motor is based on a tetra-substituted photoisomerizable crowded alkene [START_REF] Koumura | Light-driven monodirectional molecular rotor[END_REF] (Fig. 1c(i)), while the modulator is based on a tetra-substituted dithienylethene photoswitch [START_REF] Irie | Photochromism of Diarylethene Molecules and Crystals: Memories, Switches, and Actuators[END_REF] (Fig. 1c(ii)) (see Supplementary Information section 2 for the synthesis and characterization of all compounds). The role of the modulator is to act as an ondemand elastic releaser that operates at a wavelength different from the wavelength that actuates the motor. With UV light, the motor is continuously rotating, while the modulator is in its cyclized form, thus sustaining the torsion of the polymer chains generated by the motor. These combined effects lead to the global contraction of the material. Conversely, when irradiated with visible light, the motor ceases its rotation and the modulator is switched to its open form. The free rotations around C-C single bonds generated can then release the elastic energy accumulated in the braided polymer chains as kinetic energy of rotation until reaching thermodynamic equilibrium. During the process, some energy is also partially dissipated by friction between chains and other irretrievable motions in the gel. More complex out-of-equilibrium situations may also appear when both the motor and the modulator are concomitantly rotating, thus braiding and unbraiding the polymers with different frequencies.

We first explored a theoretical model of the reversibility at infinite time of such twisted conformation by considering all the possible connections within a large random network (as expected in the gel form). Our mathematical model of the system considers the chemical gel as a random graph embedded in a threedimensional space. Each vertice is either a motor or a modulator, while edges of the graph are the polymer chains linking them (Figure 2a). The appropriate mathematical model is that of constrained Erdos-Renyi random graphs, and it leads to the following conclusions (see Supplementary Information Section 3 for the full demonstration). (i) In the simplest situation, when the system contains an equal number of motors and modulators with each motor linked to a modulator (bipartite graph), the complete unbraiding capacity of the entire network depends only on the number and length of "favorable cycles" in the graph. A "favorable cycle" is defined as a loop containing a series of motors and modulators with at least one motor and one modulator involving "coupled edges" within this loop (see Figure 2a-c for the definition of "coupled edges"). The length l of a favorable cycle is the number of vertices or motors and modulators in the loop. When the total number N of vertices is high, as it is experimentally in the gel, we can precisely determine this number of favorable cycles for each given length and we show that it increases with the power of l. (ii) For more complex situations, we have incorporated in our equation the possibility to change the ratio of modulators in the network (let denote 𝜃 = modulator / (motor + modulator)), and to model the efficiency of the unbraiding process by adding two supplementary parameters (𝛾 and 𝛽): 𝛾 reflects how more efficient is a shorter cycle compared to a longer one in the unbraiding process, while 𝛽 measures how more efficient is a cycle containing many active modulators as compared to a cycle containing fewer modulators in the unbraiding process. By taking these parameters as full modeling descriptors of our system, we obtain the following formula:

𝜃 𝑐𝑟𝑖𝑡 = ( 𝜋 𝑒 3 𝛾 -1 -2 -𝑒 -𝛽 )(𝑒 𝛽 -𝑒 -𝛽 ) -1
In other words, at the asymptotic limit N → ∞, the polymer network is fully uncoiling if 𝜃 ≥ 𝜃 𝑐𝑟𝑖𝑡 . For instance, and for one of the less favorable situations (𝛾 = 0.06, 𝛽 = 2), a concentration of only 5% in open modulator is sufficient to fully unbraid the system once the motor is stopped (see plotted equation in Supplementary Information).

Further, a molecular study of the modulator subunit proved its kinetic efficiency of rotation and thus its potential as an elastic releaser. Dithienylethene tetra-benzylic alcohol 1 open was first synthesized in 8 steps from commercially available products, and its structure was confirmed by X-ray crystallography (Figure 3a,b) (see also Supplementary Information Sections 2 and4). 1 open exists as a mixture of two conformers (parallel and antiparallel) with a ratio of 77:23 in acetonitrile as determined by [START_REF] Abendroth | Controlling Motion at the Nanoscale: Rise of the Molecular Machines[END_REF] H NMR (see Supplementary Information Section 5).

Photocyclisation of 1 open into 1 closed is achieved by irradiation with UV light, while the reverse process is performed by irradiation with visible light. The ring closure is confirmed by the appearance of a characteristic purple color with a maximum absorption band at 530 nm during UV irradiation; and the ring opening is confirmed by the color disappearance when using visible light (Fig. 3c). At the photostationnary state with UV light, [START_REF] Abendroth | Controlling Motion at the Nanoscale: Rise of the Molecular Machines[END_REF] 3d and Supplementary Information section 7). We found two close transition states TS1 (63.2 kJ.mol -1 ) and TS2 (66.7 kJ.mol -1 ), confirming a full and easy rotation at room temperature with a frequency of 10.1

Hz. This higher rotation rate compared to 1 and 2 is explained by the absence of internal hydrogen bonds or bulky substituents in the molecular model, and confirms the possibility for the modulator to perform its role as a conformational disentangler by full rotation when connected in the chemical gel.

With these preliminary elements in hand, we chemically linked the motor and modulator subunits in different proportions within cross-linked gels (Fig. 4a). A first reference Gel 0 (containing 0 mol% of modulator) was obtained by reacting one equivalent of enantiopure motor tetra-alkyne 3 with one equivalent of motor tetra-azide 4 by a copper-catalyzed Huisgen[3+2] cycloaddition ('click reaction')

(see Supplementary Information Section 9 for the choice of working in enantiopure series). At the opposite, Gel 50 (containing 50 mol% of modulator) was obtained using the same reaction conditions but by mixing one equivalent of motor tetra-alkyne 3 with one equivalent of modulator tetra-azide 2. Gels of intermediate compositions (Gels 25, 12, 5) were also synthesized following the percentages of the chart shown in Fig. 4a. By performing the 'click' reaction directly in metallic molds of fixed volumes, transparent gels were obtained with thicknesses comprised between 476 m and 2 mm, and with a surface comprised between 2 and 4 cm 2 (Fig. 4a). We first investigated a set of contraction experiments on Gel 50 swollen in acetonitrile and noticed that the absorption of dithienylethene was important and that UV light cannot penetrate the entire volume of the sample for a thickness above 1 mm (see Supplementary Figure 5).

We thus studied the contraction of the series Gel 0-50 for a thickness of 476 m.

All the five gels significantly contracted as shown by the variations of volume as a function of time (Fig. 4b). As the percentage of modulator was decreased, we observed a higher speed of contraction at initial time and a higher maximal percentage of contraction at steady state. Moreover, for high amounts of modulator (Gel 50) an observable activation period is taking place at the early irradiation times. This is likely the signature of a cooperative effect: as the motor is pulling on the polymer chains, the antiparallel / parallel ratio of the modulator is increasing, leading to a different photostationary state more biased in favor of the closed form. This amplification of the bias is much less pronounced for lower percentage of modulator (Gel 25) and, for Gel 5, the initial rate of the contraction (V0 = 63 vol%.h -1 ; corresponding to an apparent frequency of the motor 𝐹 𝑎𝑝𝑝 𝑐𝑜𝑛𝑡 = 31.7 10 -3 Hz) is close to the one observed for reference Gel 0 (V0 = 84 vol%.h -1 ;

𝐹 𝑎𝑝𝑝 𝑐𝑜𝑛𝑡 = 42.2 10 -3 Hz) (see Supplementary Information Section 8 for the determination of the apparent frequencies in the gel state). As expected, when switching off the UV lamp and exposing the sample to white light, all gels went back close to their initial volume within tens of hours at room temperature, except non-reversible Gel 0 which maintained its full contraction (Fig. 4c). The expansion of the gels is the result of two parameters: the elasticity of the braided polymer These experiments indicate that small ratios of modulators/motors can be used, as suggested by our mathematical model. This decrease of modulator concentration allows for an improved work output of the system, namely a faster kinetic response and a higher maximal contraction at steady state.

Finally, in order to regulate the contraction of a 1 mm thick Gel 50, we performed a dual light control experiment involving constant UV irradiation (continuous rotation of the motor), while varying at the same time the quantity of open modulator with a white light emitting diode (LED, 30 lm) placed at variable distances from the sample (Fig. 4d). By finding an appropriate regime between the intensities of the UV lamp and the LED, we confirmed that one can finely tune at steady state the contraction of the gel depending on the intensity delivered by the LED (being here regulated by the distance between the source and the sample).

This key observation shows that the work produced by the system at the photostationary state is the result of a net flux of rotations at nanoscale between the motors and the modulators turning in opposite directions.

The results reported here show the fully out-of-equilibrium control of artificial molecular machine-based materials. The basic concept rests on connecting a nanomotor to a releasing elementary unit (that functions as a clutch) within modules that are functionally robust against thermal noise. This systemic approach provides a general solution to overcome the unidirectionality limitation associated with the necessary use of Brownian ratchets when working out-ofequilibrium at nanoscale. Because the individual units of the module can be actuated at two different wavelengths, the work output at steady state can be finely tuned by modulation of frequencies. In order to produce a useful work with such systems, the only constraint is that the apparent frequency of the motor has to be set higher than the apparent frequency of the modulator (see Supplementary Information Section 9). This new kind of artificial materials stimulates the necessary transition engaged by chemists from the control over individual molecular motors towards the design of more complex nanomachines integrating different operating units that work in concert. Here the reversibility process relies on the elasticity of the polymer system and on osmotic pressure, as for example it is the case in biology with cytoskeleton and titin proteins resetting the sarcomere units in muscles. [START_REF] Maughan | A quantitative analysis of elastic, entropic, electrostatic, and osmotic forces within relaxed skinned muscle fibers[END_REF] Further, by using these general out-of-equilibrium principles that are reminiscent of life-like materials, [START_REF] Boekhoven | Transient assembly of active materials fueled by a chemical reaction[END_REF][START_REF] Grzybowski | The nanotechnology of life-inspired systems[END_REF] one can imagine a plethora of artificial systems in order to convert energies and to modulate functions at all scales. The highest G ≠ value corresponds to the interaction between the left methyl and the right aromatic ring of the dithienylethene (TS2).

1 and of 1 . 5 Hz for 2 .

 1152 photostationnary state with UV light,[START_REF] Abendroth | Controlling Motion at the Nanoscale: Rise of the Molecular Machines[END_REF] H NMR reveals a ratio 1 open :1 closed of 60:40

  network and the osmotic pressure generated by the solvation of the polymer chains. The solvent, after expulsion during the contraction (syneresis), participates to the reversibility of the process by swelling the gel. Indeed, a visible irradiation of the contracted gel in the dry state did not show expansion. In another control experiment under proper swelling conditions, the UV light was turned off after full contraction of Gel 50. We measured a complete but slower expansion in the dark (𝐹 𝑎𝑝𝑝 𝑒𝑥𝑝 = 1.7 10 -4 Hz) compared to the expansion under visible light (𝐹 𝑎𝑝𝑝 𝑒𝑥𝑝 = 4.8 10 -4 Hz), indicating that the percentage of efficient open modulators is indeed lower without specific activation of the photochemical switch. The decrease of modulator percentage in the gel also moderately affects its rate of expansion, with apparent frequencies comprised within 4.8 10 -3 Hz for Gel 50 and 1.3 10 -3 Hz for Gel 12.

Figure 2 |

 2 Figure 2 | Schematic representations of the mechanical topology acting in the gel. a, In this simplest example, a random bipartite graph is used to model the polymer-motor-modulator system: it is composed of 50% motors and 50% modulators as vertices, and of polymer chains as edges. "Coupled edges" are defined by two polymer chains attached to the same side of agiven motor/modulator. A coupled edge corresponds to the two chains that will be braided by a single motor; or to the two chains in a braid that will be unwound by a modulator. Note that in a bipartite graph, each motor is linked to a modulator. b, Schematic representation of a (8,1,2) cycle of length 8 (8 vertices), and containing 1 motor and 2 modulators with coupled edges within this cycle (see circled connections). The chemical topology of this particular cycle is favorable for both braiding (due to the coupled edges motor) and unbraiding (due to the two coupled edges modulators). c, Mathematical graph encoding the cycle represented in (b).

Figure 3 | 1 : 2 :

 312 Figure 3 | Rotational dynamics in individual modulator subunits. a, Dithienylethenes are engaged in coupled equilibria when submitted to a UV irradiation. The first one occurs between a parallel and an anti-parallel open form by rotation of two C-C single bonds. This rotation is associated to the activation energy (G ≠ ) that determines the frequency of rotation at a given temperature (and which also depends on the bulkiness of the R substituents). The experimental values of G ≠ for 1 and 2 were determined by variable temperature 1 H NMR experiments. The

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013) / ERC Starting Grant agreement n°257099 (N.G.). We thank ANR (project INTEGRATIONS) for financial support. We also wish to thank the Centre National de la Recherche Scientifique (CNRS), the COST action (CM 1304), the international center for Frontier Research in Chemistry (icFRC), the Laboratory of Excellence for Complex System Chemistry (LabEx CSC), the University of Strasbourg (UdS), and the Institut Universitaire de France (IUF). Q.L. thanks the China Scholarship Council (CSC) for a doctoral fellowship. We are grateful to Gérard Strub for manufacturing the molds to shape the gels, Julie Lemoine for HPLC purifications, and J.-M. Strub for HRMS. The authors also thank Dr. Vincent Le Houerou for discussions.

(red and blue cylinders) with the subsequent braiding of the polymer chains, leading to a macroscopic contraction of the entire network. A braid is defined as a twisted pair of polymer chains. b, Schematic representation of a polymer-motor-modulator gel which proceeds as in (a) when exposed to UV light, but which unbraids the polymer chains when exposed to Vis light by activating the modulator part (green and purple cylinders). Visible light-activation of the modulator allows its rotation in the opposite direction of the elastic torque initially produced by the motor, thus leading to a full re-expansion of the network at thermodynamic equilibrium. c, Chemical structures composing the polymer-motor-modulator system studied herein, involving enantiopure crowded alkenes as motors (i) and photoswitchable dithienylethenes as modulators (ii). Under UV irradiation, the motor is continuously rotating in one direction while the modulator is locked in its closed form. Conversely, under Vis light irradiation, the motor is stopped and the modulator is switched to its open form that liberates two freely rotating single bonds that can unbraid the adjacent polymer chains.

Additional Information

Supplementary information is available in the online version of the paper. Reprints and permission information is available online at http://npg.nature.com/reprints.

Correspondence and requests for materials should be addressed to N.G.

Competing Financial Interests

The authors declare no competing financial interests.


Quan Li

Gad Fuks

Emilie Moulin

Mounir Maaloum

Michel Rawiso

Igor Kulic

Justin T Foy

Nicolas Giuseppone
email: giuseppone@unistra.fr

Macroscopic contraction of a

come

Making molecular machines that can be useful in the macroscopic world is a challenging long-term goal of nanoscience. [START_REF] Feynman | There's plenty of room at the bottom[END_REF] Inspired by the protein machinery found in biological systems, [START_REF] Schliwa | Molecular motors[END_REF][START_REF] Vale | The way things move : looking under the hood of molecular motor proteins[END_REF] and based on the theoretical understanding of the physics of motion at the nanoscale, 4 , 5 organic chemists have developed a number of molecules that can produce work by contraction or rotation when triggered by various external chemical or physical stimuli. 6 , 7 , 8 , 9 In particular, basic molecular switches that commute between at least two thermodynamic minima, and more advanced molecular motors that behave as dissipative units working far from equilibrium when fuelled with external energy [START_REF] Reinmann | Brownian motors: noisy transport far from equilibrium[END_REF][START_REF] Li | Relative unidirectional translation in an artificial molecular assembly fueled by light[END_REF][START_REF] Balzani | Autonomous artificial nanomotor powered by sunlight[END_REF][START_REF] Koumura | Light-driven monodirectional molecular motor[END_REF] have been reported. However, despite recent progresses, 14 , 15 , 16 , 17 the ultimate challenge to coordinate individual molecular motors in a continuous mechanical process that can have a measurable effect at the macroscale has remained elusive. [START_REF] Browne | Making molecular machines work[END_REF][START_REF] Feringa | Macromolecules flex their muscles[END_REF] Here we show that by integrating light-driven unidirectional molecular rotors as reticulating units in a polymer gel, it is possible to amplify their individual motions to achieve macroscopic contraction of the material. Our system uses the incoming light to operate under far-from-equilibrium conditions and the work produced by the motor in the photostationary state is used to twist the entangled polymer chains up to the collapse of the gel. Our design could be a starting point to integrate nanomotors in metastable materials to store energy and eventually to convert it.

The active chemical structures used in this study involve modifications of rotary motor 1 (Fig. 1). This functional core unit takes inspiration from the seminal work of Feringa and collaborators and, in particular, from their development of a second generation of light-driven motors which can rotate with high frequencies (up to 3 MHz). [START_REF] Klok | MHz unidirectional rotation of molecular rotary motors[END_REF][START_REF] London | Light-driven altitudinal molecular motors on surfaces[END_REF][START_REF] Pollard | Light-driven rotary molecular motors on gold nanoparticles[END_REF] For further incorporation in responsive macroscopic materials, we have first developed an original asymmetric synthetic pathway which allows for the gram-scale synthesis of enantiopure functional motors (see Supplementary Information for the synthesis and characterization of the molecules). By introducing two chiral auxiliaries of (R) configuration, the stereochemistry of (R,R,S)-1 can be fully assigned thanks to single-crystal X-ray diffraction. Such chiral motors produce unidirectional rotation when pushed far from equilibrium by continuously repeating a sequence of light-activated cis-trans isomerization of the central double-bond combined with a thermal helix inversion. [START_REF] Koumura | Light-driven monodirectional molecular motor[END_REF] In addition, 1 was modified with two orthogonal sets of two protected reactive groups in its upper and bottom parts (ethyl esters and tertbutyldimethylsilyl ethers, respectively) in order to connect it further with polymer chains and to enforce entanglement upon rotation. Following a series of chemical transformations, compounds 2 and 3 were obtained as key polymermotor conjugates. Even though both of them incorporate two chains of tri(ethylene glycol) with a terminal alkyne in their bottom part, they differ from the molecular weight of the azide-terminated poly(ethylene glycol) attached to their upper part (M = 5 000 g.mol -1 for 2, and M = 10 000 g.mol -1 for 3). In this orthogonal configuration, and at high dilution, the two bottom alkyne groups of a single polymer-motor conjugate can selectively react with its two upper azides by a copper-catalysed Huisgen[3+2] cycloaddition ("click reaction"), which leads to the formation of two triazole units. This double intramolecular cyclisation is very efficient to produce with good yields 8-shaped polymers 4 and 5 containing the rotary motor in their centers. By using the same click reaction, but at higher concentration, the subsequent intermolecular formation of triazoles leads to cross-linked chemical gels 6 and 7 which incorporate the rotary motors as reticulation units.

The 8-shaped configuration is considered complementary to the gel for probing the effect of light-induced rotation in a discrete self-entangled macromolecule (Fig. 2). In particular, we have performed small angle X-ray scattering (SAXS) on both compounds 4 and 5 in dilute toluene solutions. By using a Kratky representation of the scattered intensity, we can observe the presence of a characteristic bump for a figure-of-eight polymer, [START_REF] Shimamura | Scattering functions of knotted ring polymers[END_REF] with a radius of gyration (Rg) associated to the position of the peak in the reciprocal space (Rg(4) = 2.58 nm; Rg(5) = 3.48 nm). These values are in agreement with theory for 8-shaped polymers made of polyethylene glycol and having such molecular weights (see Supplementary Information for details). Interestingly, when compound 4 is irradiated in toluene with a UV lamp of 6W (0.96 mW.cm -2 at 366 nm), the shifts of the scattering peaks in the Kratky plot indicate an evolution towards smaller radius of gyration values (from 2.58 nm to 2.24 nm). In addition, the 50% increase of the scattered intensity reveals much higher internal densities of the polymer. This global behavior is expected for a mechanically enforced coiling of the selfentangled polymer chains upon rotation of the motor. These results, obtained on an average population of 8-shaped polymers in the reciprocal space, are confirmed by imaging individual macromolecules 5 in the real space thanks to atomic force microscopy (AFM) using the peak force tapping mode. In its initial state, the 8-shape is clearly evidenced when unfolded on a mica surface. The diameter of each ring is in the range of 15 nm, which is in good agreement with the expected theoretical value for a cyclic 10 000 PEG chain (Supplemntary Information). After UV light irradiation for 15 min, no more 8-shaped configurations are detected by AFM, but only collapsed (spherical or more elongated) coils with smaller dimensions. This type of conformation is expected regarding the winded topology of the contracted 8 upon rotation of the motor.

For chemically cross-linked polymer-motor conjugates in the form of gel 6 at 10% w/w in toluene, fluorescence and macroscopic contractions are satisfyingly observed at room temperature thanks to a simple irradiation with UV light (Fig. 3 and Supplementary Movie 1). We concomitantly performed a control experiment for which a similar gel was synthesized, but having the rotating double bond blocked by an episulfide function (see compound 28 in Scheme S7). In this case, the gel did not show any fluorescence and/or contraction after 240 min of irradiation in the same conditions, correlating the macroscopic contraction to the molecular rotation (Supplementary Movie 2). The macroscopic shape of the active gel 6 is not significantly modified during the contraction, indicating an isotropic process. By measuring the surface reduction of the gel after 120 min and assuming an isotropic effect on the volume, we approximate a maximum contraction of about 80%. After longer times of irradiation, we notice a rupture of this gel which recovers its initial volume and shape. This event is concomitant with the loss of fluorescence in the broken regions (see differences between z1 (not yet broken) and z2 (broken) in Fig. 3c, t = 170 min), indicating a probable disruption by oxidation of the motor double bond and a loss of conjugation, while keeping a single bond and thus a reticulated topology when unwinded up to its initial swollen equilibrium state. The oxidative degradation of the double bond to a single one was supported by experiments on individual motors which can be damaged with long time UV irradiation and in the presence of air. This reactivity of the double bond is greatly enhanced when the gel becomes tensed, but it can be delayed for several hours by working under argon or by stopping the irradiation.

In some experiments, the free energy contained in the tensed gel is so high and the dissipative rupture so sudden that it leads to a jump of the entire piece of gel in the vial (Supplementary Movie 3). The maximum of energy stored in the gel corresponds to the transfer in twisted entanglements of the free energy of the motor G° (32 kJ.mol -1 ; 12.8 kBT per motor) and which characterizes the difference between its unstable thermal state and its stable thermal state during the helix inversion (Fig. 3d, red curve). Considering that the maximum of mechanical work stored in the gel requires 120 min of irradiation, and knowing the absorption of the gel at 366 nm over this period, one can estimate an energy conversion of 0.15% for the contraction (see Supplementary Information). To understand the correlations existing at all scales, we started by plotting the contraction of active gel 6 as a function of time (Fig. 3e). One can see that after an activation period comprised between 0 and 30 min, and corresponding to the time necessary to tense the polymer chains with the first twists, the contraction then enters an apparent linear regime for 60 min. This non-equilibrium steady state part of the contraction indicates that a single process of twisting is involved (and that is not followed by a supercoiling of the polymer chains which would produce a second regime of contraction). Then, the contraction slows down at higher tension and all the double bond breaks simultaneously at the maximum of twisted torsion, representing an interesting type of chemical activation upon mechanical constraints. One can estimate the maximum number of turn (n < 105) in the twisted configuration during this time of contraction, as being the ratio between the contour length (Lc) of the PEG 5 000 polymer (that is 40 nm) and its persistence length (Lp, that is 0.38 nm). It results that the maximum frequency for the motor in the gel is Fgel6 = 3.16 10 -2 Hz (t1/2gel6 = 22 seconds) at 25°C, corresponding to an activation energy G ≄ gel6 = 81.5 kJ.mol -1 (as the rate limiting step of the process is the thermal helix inversion). [START_REF] Klok | New mechanistic insight in the thermal helix inversion of second generation molecular motors[END_REF][START_REF] Cnossen | Structural dynamics of overcrowded alkene-based molecular motors during thermal isomerization[END_REF] This can be compared with the activation energy for the polymer free motor determined by DFT calculations (G ≄ free = 31.9 kJ.mol -1 ; Ffree = 8.05 MHz; t1/2free = 4.3 10 -8 s at 25°C), and which is in good agreement with similar structures in the literature. [START_REF] Cnossen | Structural dynamics of overcrowded alkene-based molecular motors during thermal isomerization[END_REF][START_REF] Klok | Motors for in molecular nanotechnology[END_REF] This extra 50 kJ.mol -1 for gel 6 represents the penalty to twist the reticulated polymer chains, also meaning that the slope of the contraction as a function of time should be dependent on the size [START_REF] Chen | Molecular stirrers in action[END_REF] of the polymers linking the dissipative units of the gel. As an example, by contracting gel 7 (with PEG chains having a double molecular weight of 10 000 g.mol -1 ), we could not visualize significant contraction at room temperature after 8 hours. However, by raising the temperature to 50°C, a maximum contraction was evidenced after 18 hours, illustrating a slower rotation frequency of Fgel7 = 3.28 10 -3 Hz (t1/2gel7 = 105 s) at 50°C, giving G ≄ gel7 = 87.0 kJ.mol -1 , and which after extrapolation at 25°C (1.74 10 -3 Hz; t1/2 = 200 s) gives a speed one order of magnitude slower than 6. Interestingly, gel 7 also leads to a maximum contraction of 75-80% (Supplementary Movie 4). By looking closer at the topological process, one can determine that in principle the maximum contraction is reached for any polymer when each twist reaches the most tensed circular curvature with a minimum radius related to Lp. As Lc is invariant, the size of such a twisted chain compared to its untwisted form was determined to be 66% (25% in volume). This simple model also indicates that (i) nmax should be dependent on Lp for each given polymer, and that (ii) for sufficiently soft twisted polymer chains and without supercoiling, the contraction should be always close to a ratio of (2/)  for the maximum number of turn (nmax) at the end of the process, as observed experimentally (see Supplementary Information). This very strong macroscopic contraction was also probed at the microscopic scale by AFM (Fig. 4). Images of the gel surface show an important change in the average size of the pore diameters when comparing the initial state (8 nm) and the contracted state (20 nm). This confirms that the macroscopic contraction is the result of the microscopic twisting of entangled polymer chains in the tensed gel, leaving more empty spaces (i.e. larger pores) between denser winded regions.

The initial size of the pores is recovered after oxidation of the motor double bond to a single one for longer times of irradiation, which is also in agreement with an uncoiling of the gel while keeping its overall network topology. Complementary SAXS experiments show that the Lorentzian analytical form prevailing for a semidilute polymer solution [START_REF] De Gennes | Scaling concepts in polymer physics[END_REF] cannot really describe the scattered intensity from gel 6 at swelling equilibrium. That presumably results from the existence of heterogeneities as well as from the form factor of the chemical junctions in the gel.

Nevertheless, we measure a very strong increase of the scattered intensity upon irradiation, indicating a densification of the polymer chains by aggregation and shrinkage at maximum contraction, in agreement with macroscopic and AFM observations as well as with the proposed simplified model of twisting.

The unidirectional rotations of molecular motors fuelled by light and working out of equilibrium are thus able to produce powerful macroscopic contraction by operating together in a fully integrated metastable system when coupled to properly entangled polymer chains. This actuation results from the work performed by the motor that twists the polymer chains (instead of being fully dissipated thermally), and transforms a nanorotation into a contraction event at higher scales. In such a topology, the maximum number of turns nmax is dependant on Lp and Lc, but the contraction ratio is invariant when reaching nmax. The rate of rotation in the gel is strongly dependent on the size of the polymer but, with a suitable chemical design, it can reach sufficient frequencies at room temperature to be of practical interest. Such system represents a new and general way to connect molecular motors at all scales and up to the macroscopic one. By essence, it profoundly differs from any material based on machines that switch stepwise by a dual activation between two thermodynamic minima and which can work only when pre-oriented in the solid state [START_REF] Yamada | Photomobile polymer materials: towards light-driven plastic motors[END_REF][START_REF] Ube | Photomobile polymer materials with crosslinked liquidcrystalline structures: molecular design, fabrication, and function[END_REF] or at surfaces. [START_REF] Bernà | Macroscopic transport by synthetic molecular machines[END_REF][START_REF] Huang | A nanomechanical device based on linear molecular motors[END_REF] Indeed, our system can function: (i) continuously out of equilibrium, (ii) using a single stimulus, (iii) in an isotropic medium submitted to Brownian motion, [START_REF] Coskun | Great expectations: can artificial molecular machines deliver on their promise?[END_REF] and (iv) by increasing its global free energy over time. In particular, this means that such materials can store energy from light in entangled polymer chains by mainly decreasing their entropy in twisted topologies. Further uses of this energy in other processes different from mechanical motions, such as in catalysis, represent some of the next possible challenges.

Figure 1 |R 1 :Figure 2 |Figure 3 |e

 1123 Figure 1 | General chemical design to access enantiopure polymer-motor conjugates.Key molecular motor intermediates 2 or 3 can be engaged either (i) in a double intramolecular "click" cyclisation catalysed by Cu(I) yielding 8-shaped compounds 4 and 5 which incorporate the rotary unit in their core; or (ii) in a intermolecular "click" cross-linkage catalysed by Cu(I) to yield chemical gels 6 and 7 which incorporate rotary units as mechanically active reticulating nodes. The blue color highlights the rotor part of the motor, while the red part shows the stator part, both linked by the axial photoisomerizable double bond.

Figure 4 |

 4 Figure 4 | Micro-and nanoscopic characterizations of mechanically active gels based on chemically cross-linked polymer-motor conjugates. a, AFM images of gel 6 submitted to different irradiation times of UV light (0.96 mW.cm -2 ): before contraction (t = 0), after contraction (t = 135 min), and after rupture (t = 195 min). b, Detailed AFM images before and after contraction of gel 6 upon UV light irradiation, showing an increase of the average pore sizes from 8 nm to 20 nm. c, SAXS data obtained before and after irradiation of gel 6.

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013) / ERC Starting Grant agreement n°257099 (N.G.). We thank ANR (project INTEGRATIONS) for financial support. We also wish to thank the Centre National de la Recherche Scientifique (CNRS), the COST action (CM 1304), the international center for Frontier Research in Chemistry (icFRC), the Laboratory of Excellence for Complex System Chemistry (LabEx CSC), the University of Strasbourg (UdS), and the Institut Universitaire de France (IUF). Q.L. thanks the China Scholarship Council (CSC) for a doctoral fellowship. We thank Albert Johner for fruitful discussions. We also thank Mélodie Archimbaud for HPLC purifications, Guillaume Fleith for SAXS experiments, as well as Ran Liu and Tom Ellis for technical helps at various stages.

Additional Information

Supplementary

Competing Financial Interests

The authors declare no competing financial interests.


Vina Faramarzi

Frédéric Niess

Emilie Moulin

Mounir Maaloum

Jean-François Dayen

Jean-Baptiste Beaufrand

Silvia Zanettini

Bernard Doudin
email: bdoudin@unistra.fr

Nicolas Giuseppone
email: giuseppone@unistra.fr

Jean- François Dayen

Light triggered self-construction of supramolecular organic nanowires as metallic interconnects

The construction of soft and processable organic material that would display metallic conduction propertiesi.e. with a large density of freely moving chargesrepresents a major challenge for electronics. Films of doped conjugated polymers are widely used as semiconductor devices, but a metallic-type transport in the bulk of such materials remains extremely scarce. Alternatively, single wall carbon nanotubes can exhibit remarkably low contact resistances with related large currents, but are intrinsically very difficult to isolate and process. Here, we report the assembly of supramolecular organic nanowires between two metallic electrodes, from a solution of triarylamine derivative, under the simultaneous action of light and electric field triggers. They display a combination of large conductivity values (>5.10 3 S.m -1 ) and a low interface resistance (<2.10 -4 Ω.m). Moreover, the resistance of the nanowires in series with metal interfaces systematically decreases when the temperature decreases to 1.5 K, revealing an intrinsic metallic behaviour.

For more than three decades [START_REF] Shirakawa | Synthesis of electrically conducting organic polymers: Halogen Derivatives of Polyacetylene, (CH)x[END_REF][START_REF] Heeger | Nobel lecture: Semiconducting and metallic polymers: The fourth generation of polymeric materials[END_REF] , the performances of conjugated organic polymers as active semiconducting components have been remarkably improved [START_REF] Burroughes | Light-emitting diodes based on conjugated polymers[END_REF][START_REF] Forrest | The path to ubiquitous and low-cost organic electronic appliances on plastic[END_REF][START_REF] Miller | Introduction: Materials for Electronics[END_REF] . For instance, the intrinsic charge transport along polymer chains has been enhanced by controlled chemical or electrochemical doping [START_REF] Bredas | Handbook of conducting polymers[END_REF] , while crystal engineering [START_REF] Stutzmann | Self-aligned, vertical-channel, polymer field-effect transistors[END_REF][START_REF] Mcculloch | Liquid-crystalline semiconducting polymers with high chargecarrier mobility[END_REF] has reduced the incoherent inter-chain hopping regime, yielding much higher mobilities of charge carriers. Still, soft interconnects with even better conductivities and limited interface resistance values with metals are needed for low-power plastic electronics, in particular when considering the miniaturization of devices at nanoscale. In a recent and unique example, the landmark of metallic resistivityi.e. a monotonic decrease in resistance with temperature [START_REF] Kohlman | Limits for metallic conductivity in conducting polymers[END_REF] has been reached in bulk films of doped polyaniline prepared by selfstabilized dispersion polymerisation [START_REF] Lee | Metallic transport in polyaniline[END_REF] . Non mouldable metallic organic conductors have also been reported in bulk crystals made of charge-transfer salts [START_REF] Jerome | Organic conductors and superconductors[END_REF] , although interface resistance can possibly hinder metallic properties [START_REF] Alves | Metallic conduction at organic charge-transfer interfaces[END_REF] . Indeed, the charge injection/extraction of the organic layer at the metal electrodes persists as a limiting factor owing to the contact resistance limiting devices downscaling [START_REF] Crispin | Characterization of the interface dipole at organic/metal interface[END_REF][START_REF] Ishii | Energy level alignment and interfacial electronic structures at organic/metal and organic/organic interfaces[END_REF][START_REF] Bürgi | Close look at charge carrier injection in polymer field-effect transistors[END_REF][START_REF] Meijer | Scaling behaviour and parasitic series resistance in disordered organic field-effect transistors[END_REF] . Moreover, the band-type conduction regime being reduced at the metal/organic interface, the related resistance can increase exponentially as the temperature decreases, precluding a metallike behaviour for a two-terminal device [START_REF] Hamadani | Temperature-dependant contact resistances in highquality polymer field-effect transistors[END_REF] . A different class of materials with metallic resistance behaviour involves a particular type of so-called metallic carbon nanotubes, which are allotropes of carbon with high aspect ratio cylindrical nanostructures (1-3 nm diameter) and a well-defined symmetry of their honeycomb crystal lattice. Optimized choice of metallic conducting electrodes material, which are quite challenging to achieve, can result in two-terminal carbon nanotubes circuits with metallic behaviour [START_REF] Mann | Ballistic transport in metallic nanotubes with reliable Pd ohmic contacts[END_REF] . However, metallic carbon nanotubes remain intrinsically very difficult to isolate, to sort, and to position [START_REF] Harutyunyan | Preferential growth of single-walled carbon nanotubes with metallic conductivity[END_REF][START_REF] Green | Processing and properties of highly enriched doublewall carbon nanotubes[END_REF] .

Soft supramolecular organic self-assemblies represent another class of emerging materials which are promising for the design of organic conductors in the 5-100 nm size range, bridging the gap between single molecules and standard thin-film organic electronics. In particular, supramolecular self-assemblies of -conjugated systems [START_REF] Hoeben | About supramolecular assemblies of -conjugated systems[END_REF] can result in high mobility semiconductors (i.e. in which charge carriers are only scattered by a few structural defects, impurities, and phonons). Their properties are commonly tunable by the surface deposition parameters, usually through control of the solvent evaporation process [START_REF] Schenning | Supramolecular electronics; nanowires from self-assembled -conjugated systems[END_REF] . These self-assemblies are structured by amphiphilic interactions, hydrogen bonds, or - stacking, and present a wide variety of shapes such as rod-like helical dendrimers [START_REF] Percec | Self-organization of supramolecular helical dendrimers into complex electronic materials[END_REF] , nanoribbons [START_REF] Welte | Highly conductive self-assembled nanoribbons of coordination polymers[END_REF] , or columnar liquid crystals [START_REF] Samori | Self-assembly of electron donor-acceptor dyads into ordered architectures in two and three dimensions: surface patterning and columnar "double cables[END_REF] . For instance, the electrical conduction of -stacked self-assembled graphitic nanotubes [START_REF] Hill | Self-assembled hexa-peri-hexabenzocoronene graphitic nanotube[END_REF] were measured by their random deposition on Pt electrodes separated by a gap of 180 nm in length, showing a semiconductor behavior with a resistance comparable to inorganic gallium nitride (≈10 M). In another example, efficient n/p-heterojunctions (in which holes and electrons can migrate in opposite directions towards electrodes) were constructed on large gold surfaces, by taking advantage of highly modified naphtalenediimides capable of ordering through supramolecular -stacks [START_REF] Bhosale | Topologically matching supramolecular n/p-heterojunction architectures[END_REF] . Good mobilities were determined in these selfassemblies with short-circuit current density up to 78.10 -6 A.cm -2 . However, reaching a metallic conductivity together with controlled positioning of these soft organic selfassemblies between electrodes remains an enormous challenge.

Results and discussion

Very recently [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] , we described a new kind of self-assembly that is produced by the non-covalent polymerisation of catalytic amounts of triarylammonium radicals, which stack with their neutral counterparts. The process results in the formation of highly structured supramolecular triarylamine nanowires (STANWs), which aggregate into larger fibres (typically 10-50 nm in width and 50-1000 nm in length). Interestingly, in a synergistic process, STANWs permanently stabilize the charges of the initial radicals by an extended electronic delocalization within the fibres. We determine a minimal ratio of 1 charge per 160 triarylamines (but which can be higher), corresponding to an estimated perfect delocalization length of 80±3 nm [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] . Another aspect of this process is the possibility to trigger the self-assembly by using visible light irradiation that results in the formation of a few cationic radicals and thus primes the self-assembly.

We now show how to take advantage of this triggering capability in order to probe the conductivity properties of the supramolecular assemblies by trapping them between pre-patterned metallic electrodes (Fig. 1). For that, we used a lateral device geometry with inter-electrode distance matching the observed delocalization length of STANWs in solution, i.e. in the 50-100 nm range. Large aspect ratio 'nanotrenches' of high reliability were made for this purpose, using simple optical lithography techniques (Supplementary Fig. 1) [START_REF] Dayen | Nanotrench for nano and microparticle electrical interconnects[END_REF]30 . We fabricated trenches of typically 80±20 nm length and 100 m width, made of Au and Ni, with leakage current below 1 pA (Supplementary Fig. 2a). We immersed this circuit in a solution of molecule 1 in 1,1,2,2-tetrachloroethane (C2H2Cl4) (Fig. 1b), and observed current in the hundred of pA range, with related conductance well below the S range, typically not exceeding a few nS, under a voltage difference of a few hundreds of mV (Fig. 2a,b). Subsequent sample irradiation using white light resulted in a rise of six orders of magnitude of the current, attaining values in the mA range, with the corresponding conductance values reaching several tens of mS (Fig. 2a). These twoterminal devices, with channel and interface contacts in series, exhibit a ohmic resistive nature related to high conductivity values as shown by I(V) measurements (Fig. 2c,d). We estimate a channel conductivity exceeding 5.10 3 S.m -1 , which is a minimum value supposing that the resistance originates from the bulk STANWs only. Alternatively, we estimate that interface resistance per unit length is below 2.10 -4 .m, which is a maximum limit under the hypothesis that the samples' resistance originates from interfaces only.

Only single wall metallic carbon nanotubes with ballistic charge transport (i.e. exempt of charge scattering) can exhibit better values, being bound by the quantum interface resistance resulting from relaxation in the metallic terminal [START_REF] Mann | Ballistic transport in metallic nanotubes with reliable Pd ohmic contacts[END_REF] . However it should be noted that ensembles of parallel metallic carbon nanotubes arrays exhibit optimized conductivity of 10 4 to 10 5 S.m -1 , which is only one order of magnitude higher than our findings on STANWs [START_REF] Tawfick | Flexible high-conductivity carbon-nanotube interconnectsmade by rolling and printing[END_REF] .

After extensive rinsing of the sample with solvents, AFM imaging of the gap revealed the presence of wires similar to those observed in solution [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] , with a length and positioning matching exactly the electrode gap (Fig. 1c-d), oriented along the electric field direction applied during the assembly, and with homogeneous diameters of 12±2 nm (Supplementary Fig. 3). The combination of both light-triggering and voltage-casting processes therefore results in an organic conductor geometry that fills the void between metallic contacts. We also found that applying an initial voltage threshold through the gapconcomitantly to the light irradiationwas a necessary condition for an efficient and stable formation of STANWs (Supplementary Fig. 2b). This suggests that the optimal formation scenario leading to a localised assembly starts at one electrode attracting a positively charged radical, which shares its electronic wave function with the metallic substrate, and then primes the next molecules stacking over it. The elongation process is polarized along the electric field and is self-limiting: when the other electrode is reached, its electron reservoir provides the neutralization path for stopping STANWs' growth. This scenario is also supported by the fact that a shorter exposure time to white light is able to prime the interconnect construction, with a resistance closure occurring afterwards in the dark. This process illustrates the concept of in situ self-construction which results from a light-triggered supramolecular polymerization as described in solution [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] , together with an additional and precise spatial positioning. This latter and crucial aspect is brought by the perfect electric-field-casting that enforces the orientation in the device for an electrode separation around 100 nm, which corresponds to the estimated delocalization length of the self-assembly [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] . This is supported by the facts that currents measured using more distant electrodes (500 nm) increase by only 1-2 orders of magnitude compared to the immersed empty gap, and fibres fully disassemble with extensive solvent washing. We also observe a reversibility of the process when heating the connected STANWs in C2H2Cl4 at 60 °C overnight, after which the non-covalent structure collapses and the wires dissolve, just as happens in solution [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] . Because the radical remains stable only within the self-assembly, when breaking this later by heating above its thermal stability, the radical is subsequently reduced [START_REF] Fitzgerald | The photochemical oxidation of some aromatic amines in chloroform[END_REF] and the system cannot self-assemble without a new light excitation / radical generation. We found no significant differences when repeating (up to six times) the self-assembly process between the electrodes, indicating that the metallic interconnects are not significantly harmed during the self-assembly and heating processes. Furthermore, after solvent drying, the structures become stable and provide reproducible results after overnight heating at 100 °C. Sample performance is not noticeably sensitive to moisture and oxygen, which constitutes a strong asset for organic electronic devices. No inert atmosphere conditions were used during the self-assembly, and samples left on the bench for one month (after AFM measurements for instance) showed reproducible transport properties.

Temperature-dependent studies revealed resistivity values systematically and reliably diminishing with decreasing temperatures, down to 1.5 K (Fig. 3a), confirming the high conductivity of our samples. We can therefore infer that the sum of ohmic contact resistance and intrinsic conductivity of STANWs has a metallic character. This also explains the contact resistance value six orders of magnitude smaller than that measured for the best conducting polymers [START_REF] Crispin | Characterization of the interface dipole at organic/metal interface[END_REF][START_REF] Ishii | Energy level alignment and interfacial electronic structures at organic/metal and organic/organic interfaces[END_REF] , and four orders of magnitude lower than those of the best contacts on organic semiconductor single crystals [START_REF] Hulea | Reproducible low contact resistance in rubrene single-crystal field-effect transistors with nickel electrodes[END_REF] . To date, only ballistic carbon nanotubes with highly transparent resistance contacts had shown such a characteristic [START_REF] Mann | Ballistic transport in metallic nanotubes with reliable Pd ohmic contacts[END_REF] .

In addition, a similar k range of resistance per fiber is estimated by counting their number through AFM imaging. We observe that perfect ohmic behavior persists up to high currents values (at atmospheric pressure (Fig. 2d), and under vacuum (Fig. 3c)).

When large current stress was applied, small deviations from perfectly linear I/V curves can be attributed to sample heating (Fig. 3b). We nevertheless measure currents up to 25 mA for the lowest resistance samples submitted to a 1 V bias under vacuum conditions.

The limited environmental thermalization of our suspended samples can possibly explain the measured current self-heating. This is supported by the fact that the sample slowly recovers its initial zero bias conductance value, as expected when thermal equilibrium is retrieved in the cryostat at 4K (Supplementary Fig. 4a). In addition, another sample measured at 200K, shows similar parabolic dI/dV without hysteresis, which is attributed to the better thermal equilibrium at higher temperature environment and to the smaller voltage (current) stress value (Supplementary Fig. 4b). The corresponding current density is thus estimated in the order of 2.10 6 A.cm -2 , which is remarkably large for organic films and corresponds to the onset current density value for electromigration in metallic circuits. The technologically relevant value is the Blech length [START_REF] Blech | Electromigration in thin films on titanium nitride[END_REF] , the product of the current density by the channel's length. In our case, the estimate of 20 A.cm -1 is only 75 to 250 times below the so-called 'immortal interconnect' conditions [START_REF]International technology roadmap for semiconductors[END_REF] (i.e. with expected long term stability needed for industrial reliability).

From a mechanistic point of view, we found that the temperature-dependence data can be satisfactorily fitted using predictive models established for quasi-1D polymer metallic conduction [START_REF] Kilveson | Intrinsic conductivity of conducting polymers[END_REF] (Fig. 3a), and one may correlate these fits with the unidirectional supramolecular shape of the wires that we initially described (see previous studies) [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] .

However, the hierarchical supramolecular structure of STANWs, which are made of bundles of stacked triarylamine-based fibrils, can exhibit a number of topographic defects [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] , and the maximum current densities observed are still not reaching those found with ballistic carbon nanotubes (4.10 9 A.cm -2 ) [START_REF] Hong | A flexible approach to mobility[END_REF] . The simple picture of perfect ballistic transport is therefore unlikely. If we suppose that carrier density corresponds to the density of cation radicals stabilized within supramolecular stacks, estimates based on the EPR experiments performed in solution range between 0.6% and 10% [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] . From the observed and calculated stacking geometry (see supporting information in ref. 28), the radicals density n lies in the 10 19 -10 20 cm -3 range, which typically corresponds to values encountered in semimetals, like graphite [START_REF] Kinchin | The Electrical Properties of Graphite[END_REF] . This very large density of hole carriersfor semiconductor standardscan explain the metallic character of STANWs, but this low densityfor metal standardscan also explain the absence of Peierls instabilities [START_REF] Grüner | The dynamics of charge-density waves[END_REF] and Luttinger condensation [START_REF] Egger | Luttinger liquid behaviour in metallic carbon nanotubes, interacting electrons in nanostructures[END_REF] in the experimental temperature range presented here. Better insight into structural properties of these organic interconnects are needed to unambiguously assess the dimensionality and transport mechanism in STANWs.

Owing to the spectacular nature of our findings, we took great care for discarding possible parasitic processes that might occur in our device, and we probed the hypothesis of electrode metallic residues creating shorts. We accordingly devoted a peculiar scrutiny to key control experiments, which are detailed in the supplementary information of this paper and summarized hereafter. i) We discarded the hypothesis of electromigration by establishing that the empty nanotrenches can withstand voltage bias much larger than those used in the self-assembly process, with or without illumination (Supplementary Fig. 5). ii) To probe the further involvement of an electro-migration process initiated by radical intermediate 1 •+ , we synthesized a series of analogues with electrochemical properties similar to those of STANWs building blocks, but without their propensity to self-assemble (Supplementary Table 1). In a blind test configuration, the closing of the gaps was only observed with molecules able to self-assemble, thus confirming that the conducting properties belong to STANWs themselves. iii) Systematic imaging of the gaps, including those which experienced several self-assembly processes, did not reveal any presence of metallic bridging structures [START_REF] Lau | Direct observation of nanoscale switching centers in metal/molecule/metal structures[END_REF][START_REF] Borghetti | Electrical transport and thermometry of electroformed titanium dioxide memristive switches[END_REF] , or extensive degradation of the metal (Supplementary Fig. 6).

Conclusions

We have discovered a fascinating soft supramolecular self-assembly which takes advantage of a self-organization process for creating metallic interconnects properties in two-point geometry. We have demonstrated that, in contrast to previous triarylamine derivatives, the self-assembly process leading to STANWs produces in turn exceptional conductivity properties. Although a theoretical understanding of such a conductivity level in STANWs remains to be explored, one may suggest that the estimated large density of hole carriers, the delocalization of the radicals throughout the triarylamine stacks [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF][START_REF] Pal | Resonating valence-bond ground state in a phenalenyl-based neutral radical conductor[END_REF][START_REF] Haddon | Localization of spin and charge in phenalenyl-based neutral radical conductors[END_REF] , and the share of their electronic wave functions with the metallic substrate 30 might be the reason explaining such a low resistance, both in the bulk and at the metal interface. The ease of solution processing, the light-triggered self-assembly, and the intrinsic selflimiting supramolecular process are shown to enable the insertion of organic interconnects in pre-determined positions by a bottom-up approach, making possible addressed control of nanoscale organic circuits. This illustrates how supramolecular selfassembly, when structured by advanced functions, will certainly represent an extraordinary tool for the next generation of smart materials. Finally, the versatile chemical structure of STANWs offers in principle numerous opportunities for tuning their electrical properties by straightforward variations using classical organic synthesis. This chemical asset might also contribute to their expected implementations towards various organic electronic devices.

Methods

Syntheses of triarylamine derivatives 1-6 (see structures in Supplementary Table 1) were performed as already described in the literature [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] . Electrodes were fabricated using edge mediated shadow mask lithography and angle deposition technique, according to a previously reported technology [START_REF] Dayen | Nanotrench for nano and microparticle electrical interconnects[END_REF] . A Ti(5nm)/Ni(35nm)/Au(20nm) trilayer was first deposited using electron beam evaporation followed by a standard lift-off process. The second step involves a 65° angle deposition, creating a Ti(5nm)/Ni(25nm)/Au(10nm) trilayer, flowed by lift-off. The first electrode has a composition related to the superposition of the two steps, and the thinner second electrode has a composition corresponding to the second deposited trilayer, explaining the height difference observed by AFM. Nanotrenches were fabricated with a fixed inter-electrode gap of 80 nm and lengths of 100 micrometers (Supplementary Fig. 1). After checking for absence of leakage current, a solution of 1 (1mg/mL in C2H2Cl4) was deposited by drop casting over the electrodes. A DC bias larger than 0.3 V and up to 0.8 V was immediately applied between the electrodes, and the evolution of current as a function of time was recorded using a Keitley 6517B Electrometer/High Resistance Meter. The sample was irradiated during a few seconds under a microscope condenser illumination (numerical aperture 0.55) with a 100 W halogen light source. Infrared filtering was used to limit sample heating to a few degrees, resulting in irradiation of a broadband power density of 10 W.cm -2 . The typical 10 s irradiation time corresponds to the total number of photons used in about 30 minutes for a self-assembly made in solution using a power density of ≈ 0.07 W.cm -2 , which is more than enough to trigger the self-assembly [START_REF] Moulin | The hierarchical self-assembly of charge nanocarriers: a highly cooperative process promoted by visible light[END_REF] . We also determined that a transition metal component in the electrode material was a necessary condition for successful interconnects self-assembly. No reliable and stable self-assembly occurred between electrodes made of Au or Pt only (with Ti adhesion layer). Self-assemblies with better than 90% success rate were obtained between Ni and Fe electrodes. We also found that covering the electrodes with Au provided better long-term sample stability, overcoming the problem of transition metals surface oxidation. In addition, performing the experiment with Au electrodes in the presence of a Ni wire dipped in the solution of 1 did not produce any conductivity/self-assembly, thus excluding a scenario where the radical would dissolve Ni(0) and generate co-self assemblies of STANWs trapping Ni salts or even Ni wires in their core. From this series of observations, we deduce that a priming effect is provided by the transition metal substrate, likely improving the chemisorptions of triarylamine radicals by oxidation of the surface metal atoms and thus creating an optimum interface resistance. After STANWs formation, the sample was washed with chloroform, followed by extensive acetone, then ethanol washing, and finally dried with a stream of nitrogen. Low temperatures electrical measurements were carried out inside a vacuum-pumped cryostat (P < 10 -6 mbar) with 3.5 K base temperature, or in a He flow system going down to 1.5 K. Measurements of electrical properties were performed using an Agilent E5270B semiconductor parameter analyzer (DC properties), and a SRS 830 lock-in amplifier (AC properties) using a 4mV peak-to peak voltage excitation.

Graphical Abstract

Under white light irradiation and in the presence of a voltage, solution of triarylamine derivatives have been self-assembled into organic nanowires between two electrodes.

These fibers possess a very high electric conductivity as well as a metallic behaviour down to a temperature of 1.5 K.

nm

High electric conductivity

Ni SiO 2 Au

Figure 1 │ 1 +

 11 Figure 1 │ Triggered self-construction process of STANWs within a nanotrench geometry together with corresponding AFM imaging. a, A solution of triarylamine 1 (1 mg.mL -1 in C2H2Cl4) is drop-casted, in the dark, on nano-patterned Au/Ni electrodes schematically represented in b (trench width = 100 m; length = 0.08 m; V = 0.3 -0.8 V). The device is then submitted to a white light irradiation (Power density ≈ 10 W.cm -2 during 10 s), which enables the production of a catalytic quantity of radicals 1 •+ . The triarylammonium 1 •+ induces a supramolecular polymerisation with neutral 1 that results in the self-assembly of STANWs aligned

Figure 2 │character up to 1 Figure 3 │

 213 Figure 2 │ Electrical properties of nanotrench devices when self-assembling STANWS. a, Conductance measured for the nanotrench device immersed in a solution of 1, as a function of time in the dark and then (after 180 s) submitted to a white light irradiation (Power density ≈ 10 W.cm -2 during 10 s). The negligible initial conductance of the triarylamine derivative solution in the dark, in the 10 -9 -10 -7 S range, strongly increases after illumination with visible light, reaching values in the 10 -2 -10 -1 S range. This increase by more than 6 orders of magnitude indicates the construction of low-resistance interconnects. b, I/(V) of the reference nanotrench (width = 100 m; length = 0.08 m) covered with a solution of triarylamine 1 (1 mg.mL -1 in C2H2Cl4), and before light irradiation. The negligible residual current is attributed to ionic impurities in solution. c, I/(V) measurements of the nanotrench (width = 100 m; length = 0.08 m) after self-assembly of 1 (1 mg.mL -1 in C2H2Cl4), upon light irradiation (P=10 W.cm -2 during 10 s) and an initially applied voltage of 0.3 V. The two-point measurement set-up includes track resistance of typically 600-800  resulting in a sample potential drop smaller than the indicated voltage scale. d, Current vs voltage curve after self-assembly, rinsing, and drying of the device. The pseudo 4 points measurement, performed at 4 K and under atmospheric pressure, shows a perfectly linear

Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013) / ERC Starting Grant agreement n°257099 (N.G.). We wish to thank the CNRS, the icFRC, and the University of Strasbourg for financial support. The support from cleanroom facilities (STnano) is gratefully acknowledged, as well as the expertise of the technical staff of the DMONS Department. This work was also partly funded by the NanoSciERA program (project INTERNET) (B.D.) and by the Agence Nationale de la Recherche: projects MOSE and SUD (B.D.), and projects Multiself and STANWs (B.D., E.M., M.M., and N.G). This work was supported by doctoral fellowships of the French Ministry of Research (V.F., F.N., S.Z., and J.-B.B.).

Additional Information

Supplementary information including figures and control experiments accompany this paper at www.nature.com/naturechemistry. Reprints and permission information is