Enhancing Diagnosis Ability for Embedded Electronic Systems Using Co-Modeling

Keywords: hierarchical modeling, HW/SW co-modeling, real time simulation

This paper describes a new modeling and simulation approach in order to enhance the diagnosis ability of an electronic embedded system, including in the automotive field. Our modeling approach integrates the hardware specifications to the functional model in order to establish better system observation. It is based on hardware/software (HW/SW) comodeling with multilevel of granularity.

To reach this objective, we have set up a relationship between the desired diagnosis accuracy and the level of granularity of the HW/SW co-model, for every Electronic Computing Unit (ECU). Our contribution allows the attribution of the right co-simulation hierarchical level by attributing the right simulation accuracy, for each function under observation.

I. INTRODUCTION

The technological development encourages the car manufacturers to propose advanced driving assistance functions that involve more than one computing unit. In fact, a computing unit uses information issued from sensors or other computing units, yielding a "system with distributed functions". In a vehicle, the functions are sometimes distributed on several components or subsystems (computing units, wires, sensors, actuators…), communicating with several interconnection networks [START_REF] Paret | Multiplexed Networks for Embedded Systems: CAN, LIN, FlexRay, Safe-by-Wire[END_REF].

However, one of the disadvantages of this distribution is the difficulty of the real time supervision to detect and localize a fault, especially electronic hardware faults. To bring out the advantages of a highly distributed architecture, we propose a modeling methodology that benefits from the existing link between the software and the hardware platforms.

Our contribution in this paper is to enrich the functional models with hardware characteristics, at the very first phase of establishing the diagnosis models (system observation), in order to reproduce the appropriate behavior of the system in a set of comprehensible models showing at the same time the hardware and the software behaviors.

To present our contributions, this paper is structured as follows:

First, we present the need of HW/SW co-modeling for embedded electronic systems supervision. Then, we present the related works done in the field of the HW/SW co-design [START_REF] Micheli | Readings in hardware/software codesign[END_REF].

In section IV, we show a relationship between the required accuracy for fault detection and the level of granularity in the HW/SW co-model, in order to find an appropriate compromise between fault detection accuracy and simulation speed. In section V, we use SystemC as a working environment for the hierarchical HW/SW co-modeling of our embedded electronic architecture. We present the results in sections VI and VII.

Finally, in the last section we conclude this paper and present our future works.

II. HARDWARE/SOFTWARE CO-MODELING FOR EMBEDDED ELECTRONIC SYSTEMS

Car manufacturers usually employ software models expressing the embedded functions to make fault detection and diagnosis. However, when the hardware architecture reaches a complex level of functional distribution, it becomes difficult to a diagnosis designer to maintain the HW/SW link for each function or sub-function of the system in the diagnosis model.

We believe that every sub-function has a link with at least one hardware sub-component, and a hardware fault appears in the system as a functional fault. Therefore, if we detect the functional fault we can localize the hardware fault if we know exactly the existing link between the sub-function and the hardware sub-component.

The electronic distributed architecture that we study is embedded on board of a truck. It is composed of a set of ECUs connected by the interconnection bus CAN (Controller Area Network) [START_REF] Paret | Le bus CAN description : de la théorie à la pratique[END_REF]. Every ECU is composed of a processor, a memory, a CAN interface and eventually Inputs/Outputs interfaces.

Manel KHLIF, Mohamed SHAWKY Heudiasyc -UMR 6599 Université de Technologie de Compiègne Centre de Recherches de Royallieu BP 20529

Functional models

Hardware description models

Hardware-software co-models

Co-simulation

System observation for diagnosis Fig. 1. Hardware and software models for system observation for diagnosis.

Some existing techniques of fault detection and diagnosis, especially of electronic systems, are based on functional simulation of the real controlled system, running on a prototyping platform, in parallel with the real time operation of the system [START_REF] Hamscher | Readings in model-based diagnosis[END_REF]. These techniques do not describe hardware components (i.e. architecture and behavior description) and need to be more accurate by expressing simultaneously both hardware and software behaviors, in order to lead to more accurate results of fault detection (Fig. 1).

We aim at modeling the functional distribution on the hardware architecture, in a coherent way, offering the ability to be connected to other models that may be proposed by different manufacturers of such heterogeneous electronic system. Our approach should allow the supervision system designer to integrate different models to simulate and test the system.

In the next section we present research works close to our objectives, and that use mix hardware and software information for simulation.

III. HW/SW CO-DESIGN

Hardware/software co-design is a set of methodologies and techniques specifically created to support the concurrent design of both systems, effectively reducing multiple iterations and major redesigns [START_REF] Micheli | Readings in hardware/software codesign[END_REF].

Within the context of co-design methodologies, concurrent hardware and software techniques have been proposed in the literature employing for example SpecC to add more details at the specification level [START_REF] Gajski | SpecC: Specification Language and Methodlogy[END_REF]. The adoption of various formal languages for co-simulation, like SDL and C [START_REF] Gioulekas | Heterogeneous system level co-simulation for the design of telecommunication systems[END_REF] is mainly used for the design of reactive systems, following the stimulus-response paradigm of behavior, like telecom systems such as wireless protocols employing different and standardized formalisms. On the other hand, functional models compatible with HDL (Hardware Description Language) models [START_REF] Wong | Hardware/software co-design language compatible with VHDL[END_REF] are needed to get accurate hardware specifications using for example RTL (Register Transfer Level) level of modeling. However when it concerns HW/SW co-design for providing observation and verification, system's behavior and properties are specified in a single formal language such as in [START_REF] Csertan | Modeling of Fault-Tolerant Computing Systems[END_REF] and [START_REF] Csertan | Dependability Analysis in HW/SW co-design[END_REF].

Even though Hardware/Software co-design is receiving a lot of attention in literature, most published works do not address model-based diagnosis for electronic systems. In this paper, we are not interested by dependability analysis (fault simulation, estimation of optimal diagnostic strategies, etc,), but we focus on co-modeling of the appropriate behavior of an electronic system for co-simulation oriented diagnosis.

IV. MULTILEVEL OF GRANULARITY CO-MODELING

Multilevel of granularity is a hierarchical view of a system, expressing in each level a degree of details and accuracy.

Our objective is also to develop a relationship between the accuracy of the expected on-line fault detection and the level of granularity of hardware/software co-modeling (Fig. 2).

Sub-system co-modeled with a "g" granularity level

Functional model

A fault

Hardware description model

The hardware source of fault Fig. 2. Relationship between a sub-system HW/SW co-model and hardware source of fault.

As a first step, we have to model the hardware architecture as a set of hardware sub-components. Then, we have to model the software platform as a set of sub-functions allocating them to the modeled hardware sub-systems.

As a second step, we define a scale of criticality levels for the sub-functions. Then we allocate a granularity level of modeling to every criticality level, and hence, each subfunction is co-modeled with a corresponding granularity level (Fig. 3).

The more accurate the level of granularity, the longer the simulation time is. Thus, it is possible to switch between two or more levels of granularity according to the criticality level of eventual faults and to the diagnosis system needs (e.g.: functions priorities). This is the main advantage of our approach of modeling at various levels of granularity. "g" <->"p" "p" <->"a"

Accuracy "a" of supervision Fig. 3. Granularity-accuracy relationship.

V. WORKING ENVIRONMENT

A. SystemC One of the most promising SystemC advantages is HW/SW co-modeling to develop virtual platforms, because it supports a unified language of HW/SW modeling [START_REF] Grötker | System Design with SystemC[END_REF].

We have selected SystemC as a working environment because it has many advantages:

• SystemC allows hierarchical modeling to express the multilevel of granularity modeling • It allows HW/SW modeling with the same language • The models could be easily connected to any other hardware models [START_REF] Bombana | SystemC-VHDL co-simulation and synthesis in the HW domain[END_REF], or functional models (e.g. in Simulink) [START_REF] Warwick | SystemC calls MATLAB[END_REF][13] [START_REF] Boland | Using Matlab and Simulink in a SystemC verification Environment[END_REF] • SystemC environment includes also a simulator: it consists of C++ library and an event-based motor for simulation • Any C or C++ library can be included in a HW/SW comodel Hence, we can describe the appropriate behavior of the electronic embedded system with different levels of hierarchy. Thus, every sub-system that should be under supervision can be hierarchically co-modeled.

B. Cycle Accurate modeling

SystemC Transaction-level modeling (TLM) is a high-level approach to model digital systems where details of communication among modules are separated from the details of the implementation of functional units or of the communication architecture [START_REF] Cai | Transaction level modeling: An overview[END_REF].

A Cycle Accurate (CA) model is a TLM model that represents the stage of communication refinement, in which communication is modeled accurately down to the level of bus cycles, and even clock cycles. CA modeling allows hardware verification, evaluating the state of every component in every cycle and running software device drivers. CA simulation speed varies between 10 and 100 KHz. A CA model consists of a set of processes that run once per cycle. This fits with the use of SC_METHOD processes and non-blocking calls. Fig. 4 shows that TLM projects do not require a lot of effort and time to be correctly modeled compared to RTL projects. In fact, a Cycle Accurate project may need approximately half of the time compared to an RTL project for its realization.

For these advantages, we have used the CA level to comodel our HW/SW platform as shown in the next section.

VI. MULTILEVEL CO-MODELS

A. Multilevel of granularity using TLM modeling

We co-modeled with TLM, hierarchically, each HW/SW sub-system beginning with the highest level of granularity. Thus, on each level of granularity, we find a set of models representing at the same time the functional behavior and the hardware architecture.

In the next sub-sections we show an example of TLM model representing the embedded electronic architecture.

B. ECUs and CAN bus modeling

The whole architecture consists of n ECUs communicating through the CAN network [START_REF] Paret | Le bus CAN description : de la théorie à la pratique[END_REF]. In this part of the work, we have modeled the CAN protocol real-time behavior to realize communications between ECUs models. We have simplified the details to ease the modeling; by implementing a virtual arbiter in the bus. With the Transaction modeling, the communication between components is described as function calls.

Each ECU is master and slave at the same time and has one bidirectional port in each module. It is used to send orders to the bus (Requests) and getting data and information from the bus (Responses) (see Fig. 5). Each ECU that wants to send a message sends a request to the bus. If at least 2 ECUs request a bus transmission at the same time (i.e. in a time shorter than a bus cycle), the bus arbiter selects the most important message by comparing arbitration fields in the two messages.

Only one clock is used for all processors when the level of granularity is high and the accuracy of the model for simulation is set to the ECU clock cycle.

It is important to note that full CAN protocol is used only in models with high level of granularity, expressing transactions between ECUs. With a more accurate level of granularity, the processor and the memory models of every ECU are wrapped into SystemC modules in order to communicate with other devices such as CAN controllers. Anyway, the transactions are kept cycle accurate.

C. HW/SW models interfacing

The communication between hardware modules and software modules should be done through message exchange. Messages should be exchanged through a shared interface between the two sides, implementing the needed methods for message exchange and eventually using blocking calls (Fig. 6).

We have co-modeled in SystemC a sub-function of Lane Keeping [START_REF] Claeys | Chauffeur Assistant Functions. Report restricted to RENAULT TRUCKS[END_REF]; a given function from a truck manufacturer. The Lane Keeping should keep a truck centered in the current lane of a highway, detected by an embedded camera. Fig. 6 shows also the example of the embedded camera software that sends the acquired videos to an ECU (the hardware module), which is responsible of filtering all extra images from the video sequence, to get only the video sequence of the highway.

D. Interfacing SystemC co-models

A systemC co-model may be the result of a higher level system level modeling, such as SySML [START_REF]Systems Modeling Language (SysML) Specification. Version 1.0 alpha[END_REF] or AADL (Architecture Analysis and Design Language) [19]. A SystemC co-model can also integrate other functional models in Simulink [START_REF] Warwick | SystemC calls MATLAB[END_REF] for SW description and VHDL [START_REF] Cote | Automated SystemC to VHDL translation in hardware/software co-design[END_REF] for HW description models. We show also that co-simulation is possible by using interfaces between the heterogeneous simulators (Fig. 7). For example, [START_REF] Bombana | SystemC-VHDL co-simulation and synthesis in the HW domain[END_REF] presents some results of design practice of HW modules; co-simulation and synthesis are combined to achieve higher abstraction levels in the design. The SystemC-VHDL co-simulator tool is also based on a SystemC/C++ front-end developed to support the cosimulation between VHDL and SystemC. Another example of co-simulation tool is shown in [START_REF] Czerner | Modeling Cycle-Accurate Hardware with Matlab/Simulink using SystemC[END_REF] using Simulink with SystemC in a cycle-accurate context.

VII. CO-SIMULATION FOR DIAGNOSIS

The supervisory system can simulate the co-models beginning with the highest level of the hierarchy in order to observe the electronic system. In case of incoherence detection in a given level of the hierarchy, our approach brings the advantage of co-simulating the system with a more accurate level in order to increase the accuracy of incoherence localization (Fig. 8). It is important to add that this approach of modeling for diagnosis is simple to implement when the embedded functions are cyclic, as progressive and repetitive simulations may be done with real input values. For this reason, we have tested our approach with the Lane Keeping (LK) system described earlier (Fig. 9). This system supplies a wheel angle set point sent to the ECUs, and does not require any driver intervention. At any time, the driver can deactivate the LK function. The LK system recognizes the lane markings using an embedded camera. In case of fault detection with a high level of granularity cosimulation, the diagnosis system should make sure that the electronic embedded system may suffers from a fault by cosimulating and testing the same sub-function (e.g. Highway videos capturing) with a more accurate level of granularity until reaching the sub-system eventual source of fault.

VIII. CONCLUSIONS AND PERSPECTIVES

This paper has presented a co-modeling technique with multilevel of granularity under SystemC for electronic systems. Cycle accurate models of the CAN bus, CAN interfaces and ECUs including memories and processors has been co-modeled with different levels of granularity.

The impact of a multi-granularity HW/SW model for the hardware real-time fault detection has been shown. This result shows that such modeling method is suitable to simulate distributed real time HW/SW architecture, especially electronic architectures and allows the supervision designer to re-use the co-models in embedded simulations for real time supervision or to simulate and test the system off-line.

As future work, we aim to extend the multilevel granularity modeling to other computing platforms, like SoC (System On Chip) for example; a technology which is gaining interest for car manufacturers. The TLM is very suitable to model the architecture of a SoC, in order to enable development of the embedded software in advance of the hardware, and to carry out analyses earlier in the design cycle.

Fig. 4 .

 4 Fig. 4. Time and effort spent for RTL and TLM use cases [16].

Fig. 5 .

 5 Fig. 5. CAN bus TLM model.

/Fig. 6 .

 6 Fig. 6. HW/SW modules interfacing.The advantage of the proposed multilevel granularity comodeling is the possibility of establishing a link between a HW/SW co-model and another type of models in any level of detail and having several possibilities of co-simulation speed for fault detection.

Fig. 7 .

 7 Fig. 7. SystemC co-models communication with different simulation tools.

F1Fig. 8 .

 8 Fig. 8. Multilevel of granularity co-simulation.

Fig. 9 .

 9 Fig.9. Lane Keeping function[START_REF] Boland | Using Matlab and Simulink in a SystemC verification Environment[END_REF]

ACKNOWLEDGMENT

We would like to thank Amanie Ghannoum and Janine Alhassan for their contribution to this work.


domain: spi chim

text:
Ch Chilev

I Pentchev

B Weinberger

F Darkrim Lamari

A COMPARISON BETWEEN THE DIFFERENT METHODS FOR THE MEASUREMENT OF AN EXCESS ADSORPTION OF PURE GASES ON POROUS ADSORBENTS AT HIGH PRESSURE

Keywords: measurement of excess adsorption, porous adsorbent, pure gases, high pressure

The topic of this work is to compare several experimental methods such as volumetric and volumetric-gravimetric methods for measuring the equilibrium states of pure gases being adsorbed on the surface of solid materials. The investigation of different type methods and their advantages end disadvantages are discussed. The installations used for measuring the adsorption equilibrium by these methods are discussed in details. The installation for measuring the helium density of materials, i.e. volumetric density of solid adsorbents is also presented.

INTRODUCTION

The physical adsorption of high-pressure fluids onto micro-porous solids is very important both in science and engineering. The interest on this phenomena has reflected in a growing number of chemical, petrochemical and biochemical processes including adsorption based separation processes, purification of gases [START_REF] Hester | Center for Hydrate Research[END_REF], solid-phase extraction, adsorbent regeneration using supercritical fluids [START_REF] Strubinger | Surface Excess (Gibbs) Adsorption Isotherms of Supercritical Carbon Dioxide on Octadecylbonded Silica Stationary Phases[END_REF], etc. There are also important industrial applications in storage of fuel gases [START_REF] Weinberger | Molecular Modeling of oh H 2 Purification on Na-LSX Zeolite and Experimental Validation[END_REF], in catalysis and chromatography [START_REF] Barto | Fundamental of Adsorption[END_REF]. Most of these processes today are still driven by the respective adsorption equilibrium. As the gas adsorption equilibrium data up to now can not be calculated accurately by theoretical or analytical simulation based models, it is necessary to measure them, i.e. to determine them by reliable and accurately performed experiments. Gas adsorption equilibrium can be measured by several basically different methods. In all cases the procedure must be adapted to the range of measure (temperatures and pressures) and the state of the gas adsorbed at these conditions. Also differences the temperature and the pressure, the properties of the solid adsorbent (chemical reactivity, state of aggregation, etc.) are very important for the measurements.

The standard method for the measure of pure gas adsorption equilibria is the volumetric or mano-metric method [START_REF] Dollimore | The design and operation of a simple volumetric adsorption Fig. 8. Comparison of nitrogen measurements obtained by gravimetric-volumetric device (LIMHP) and volumetric device (AL) on the zeolite 13X. apparatus[END_REF]. Basically it is the mass balance of a certain amount of gas partly adsorbed on the sorbent material.

More accurate and reliable measurements can be performed by weighing the sorbent mass exerted to the gas atmosphere using a very sensitive microbalance. This is the gravimetric method [START_REF] Benham | Experimental Determination of Absorption-Desorption Isotherms by Computer-Controlled Gravimetric Analysis[END_REF][START_REF] De | Automated determination of high-temperature and high-pressure gas adsorption isotherms using a magnetic suspension balance[END_REF][START_REF] Dreisbach | Gravimetric Measurement of Adsorption Equilibria of Gas Mixture CO/H 2 with a Magnetic Suspension Balance[END_REF][START_REF] Staudt | A Note on Gravimetric Measurement of Gas-Adsorption Equilibria[END_REF].

Volumetric/manometric measurements and gravimetric measurements can be performed simultaneously on the same gas adsorption system in a single instrument [START_REF] Weinberger | Molecular Modeling of oh H 2 Purification on Na-LSX Zeolite and Experimental Validation[END_REF][START_REF] Dreisbach | Messmethoden für Gasphasen-Adsorptionsgleichgewichte[END_REF][START_REF] Keller | Volume-Gravimetric Measurements of Binary Gas Adsorption Equilibria[END_REF][START_REF] Vidal | Measurement of physical adsorption of gases at high pressure[END_REF]. This technique of measurement is known as a volumetric-gravimetric method.

The aim of this study is to compare several techniques for measuring of the adsorption equilibrium.

THEORY

According to the classical definition of adsorption [START_REF] Duong | Adsorption Analysis: Equilibria end Kinetics[END_REF], the all molecules which are within the field the atoms or molecules forces on the surface of a solid sorbent represented the absolute quantity adsorbed. By integration of the density r(x) at any position x with respect to the whole volume (V) of the adsorption space of a given system the distribution of density in the system can be obtained:

∫ = V a dV x m ) ( ρ (1)
In order to estimate the amount adsorbed the fundamental difficulty is the choice of the volume V used in the integration of Eq.( 1). The volume

) ( y V V = - , where ) ( y V
is the volume filled by the set (y) of all molecules of the adsorbate, i.e. all molecules of the sorptive fluid influenced by or exerted to the surface forces of the sorbent material. This is an energetic criterion determining whether a molecule from the fluid is adsorbed on the surface of the solid material or not. If the energy of the molecules (E) is:

s p f P kin E E E E + + = (2)
where E kin is the kinetic energy of the translation,

E E >>

it is considered that the molecules are adsorbed even not in direct contact with the solid surface. Otherwise the molecule is considered to be not adsorbed. Consequently, molecules from the fluid phase may change their status of being adsorbed or desorbed between two molecular collisions and the boundary between adsorbed and not adsorbed molecules from the fluid phase naturally will become fuzzy. The adsorption density distribution ( )

x ρ exhibits a gradual change from the solid surface to the bulk, and its approach to the bulk density at a distance away from the surface is usually in the form of an exponential decay:

) ( lim x x f ρ ρ ∞ → = (3)
For small pores, where the potential fields of the two opposite walls overlap, the density distribution everywhere will be greater than the bulk density. In such case one can choose the volume of the adsorbed phase as the pore volume and to calculate the absolute amount:

∫ = pore V a dV x m ) ( ρ (4)
Here pore V is the pores volume. Thus the adsorbed phase volume is pore-specific. So, the Gibbs excess mass can be define as:

( ) ∫ ∫ - = - = V V f f GE dV x V dV x m ρ ρ ρ ρ ) ( ) ( (5)
This surface mass excess represents the difference between the absolute amount adsorbed in a volume V and the amount of volume that could be occupied by molecules with the same density as that of the bulk. Thus the surface mass excess is positive if the adsorption density in the volume V is greater than the bulk density (see Fig. 1).

It is negative when the adsorption density is less than the bulk density everywhere throughout the volume V. According to [START_REF] Do | Adsorption of supercritical fluids in non-porous and porous carbon: analysis of adsorbed pfase volume and density[END_REF] for the absolute amount adsorbed:

ADS bulk GE a V m m ρ + = (6)
were ADS V is the volume of the adsorbed phase.

It is the volume whose boundary is such that the density at the boundary * ρ is equal to the bulk den- sity.

All sorbent materials may change their adsorption properties over the years due to internal physicochemical processes, but also due to uptake of gases and vapours (humidity) from the ambient air. Especially for carbon based sorbent materials this should be taken into account. The very important aspect of the equilibrium investigation is the activation or the preparation procedure of the sorbent material prior to adsorption of gases on it, i.e. degasification procedure, vacuum treatment, heating procedure. In this work the follow procedure for regeneration and secondary degasification of adsorbent are used:

• The adsorbent is put in a vessel, to be treated at a vacuum and to be heating up to 350 0 C during 24 h. The procedure is finished when the pressure is stabilized at 10 -6 Pa. Thus the adsorbent is regenerated completely.

• The adsorbent is refrigerated at room temperature. Then the vessel is filled with helium at one atmosphere. The helium penetrates into micropores of the solid adsorbent and blocks them for other molecules.

• The adsorbent is transferred from the vessel to the cell of adsorption. It has to be done helium quickly because the air from the surrounding will be adsorbed on the adsorbent.

• The cell is heated at temperature up to 350 0 C and treated with vacuum. The process is finished when the pressure is stabilized at 10 -6 Pa. The helium is adsorbed slightly, thus the secondary degasification is easy.

VOLUMETRIC MEASUREMENT TO THE VOLUMETRIC MASS OF MATERIAL

A very important aspect for the investigation of the adsorption equilibrium is to knowledge of the type and the structure of the solid adsorbents. There are many approaches to determine them [START_REF] Malbrunot | Adsorbent Helium Density Measurement and Its Effect on Adsorption Isotherms at High Pressure[END_REF]. In this work is used the volumetric helium measurement for the determination of the volumetric mass of the solid adsorbents. This information is very important to calculate the amount adsorbed. On Fig. 2 is shown the installation used for the volumetric measurement of helium density of material and on Fig. 3 the cell of adsorption. The adsorption of helium on the sorbent at temperature 400 0 C is very slow and it can be neglected it. Thus the volumetric mass of materials can be determined by mass balance of the system when the volume of the reservoir, the volume of the adsorption cell and the absolute mass of the adsorbent are preliminary known.

The adsorbent is regenerated following the procedure described above. The temperature and the pressure measured both in the thermostatic cage and in the reservoir. The procedure can be divided to the following steps.

1. The cage and the reservoir is calibrated with xenon (99.9996 %); 2. The adsorbent is regenerated at high temperature; 3. The system of heating of the adsorption cell is switched on and the process of heating is regulated at rate of increasing 2 0 C/min up to 100 0 C; 4. During the secondary degasification the temperature increases to 400 0 C; 5. The adsorption cell is cooling at ambient temperature;

6. The valve is closed and the pump is stopped; 7. The mass of the activated material is determined; 8. The system is connected to the reservoir; 9. Points 3-4 are repeated; 10. Helium is injected to the reservoir;

The volumetric mass of the material is determined by the following equation:

( ) ( ) ( ) ( ) ( ) ( ) , , , , C R Ads T p V T V T T p T p V T p ρ ρ ρ ρ - -     = 2 2 2 2 1 0 2 1 1 1 2 2 2 2 (7)
where 0 ρ is the density of helium in the reservoir be- fore the connection to the cell of adsorption, 1 ρ is the density of helium in the reservoir after the connection to the cell of adsorption, 2 ρ is the density of helium in the cell of adsorption, R V is the volume of reservoir, C V is the volume of the cell of adsorption, 1 T is the reservoir and 2

T is the temperature of the adsorption cell.

VOLUMETRIC MEASUREMENT OF PURE GAS ADSORPTION EQUILIBRIUM

The standard method for the measurement of the pure gas adsorption equilibrium is the volumetric or manometric method [START_REF] Dollimore | The design and operation of a simple volumetric adsorption Fig. 8. Comparison of nitrogen measurements obtained by gravimetric-volumetric device (LIMHP) and volumetric device (AL) on the zeolite 13X. apparatus[END_REF]. Basically it is the mass balance of a certain amount of gas partly adsorbed on the sorbent material. Complemented by a gas analyzer (chromatograph, mass spectrometer) this method also can be used for the measurement multicomponent adsorption equilibrium. The volumetric gas adsorption experiments consist in: a given amount of sorptive gas is expanded into a vessel which includes a sorbent sample and which initially has been evacuated. Upon expansion the sorptive gas is partly adsorbed on the (external and internal) surface of the sorbent material, partly remaining as gas phase around the sorbent. By a mass balance, the amount of gas being adsorbed can be calculated if the void volume of the sorbent, i. e. the volume which can not be penetrated by the sorptive gas molecules is known at least approximately. On Fig. 4 the installation for measurement of adsorption equilibrium by volumetric method is represented.

An instrument for volumetric measurements of pure gas adsorption basically consists of a gas storage vessel (volume V SV ) and an adsorption chamber (V AC ) being connected by a tube bearing a valve. Both vessels should be placed completely within a thermostat and provided with tubes for gas supply and evacuation as well as with thermometers and manometers for measurement of the temperature (T) and pressure (p) inside the vessels. The adsorption chamber includes a sample of sorbent material with mass (m s ) which prior to measurement have been activated at higher temperature under vacuum for 24 hours to reduce the amount of pre-adsorbed molecules. Standard procedures for activation have been described above. To measure adsorp- tion a certain amount of gas with mass (m*) is prepared in the storage vessel and the adsorption chamber is evacuated. When opening the expansion valve, the gas expands to the adsorption chamber where it is partly adsorbed on the (external and internal) surface of the sorbent material. After thermodynamic equilibrium, (constancy of pressure (p) and temperature (T) inside the vessels), has been realized, these data can be taken as a basis to calculate the mass of the gas adsorbed on the sorbent (m s ). From the mass balance of the sorptive gas we have:

( ) ( ) [ ]( ) ( ) 1 1 1 1 0 0 0 , , , T p V V T p T p V m Bulk Ads AC Bulk SV GE ρ ρ ρ - - - = ( 8
)
were 0 ρ is the density of gas prepared in the storage vessel, Bulk ρ is the density of the sorptive gas in the adsorption equilibrium state considered.

In the case of microporous adsorbents according to [START_REF] Do | Adsorption of supercritical fluids in non-porous and porous carbon: analysis of adsorbed pfase volume and density[END_REF], we can consider that pore Ads V V =

. Thus pore V can be obtained by experimental measurements of helium density of the adsorbent.

VOLUMETRIC -GRAVIMETRIC MEASUREMENT OF PURE GASADSORPTION EQUILIBRIUM

Volumetric/manometric measurements and gravimetric measurements can be performed simultaneously on the same gas adsorption system in a single instrument. The experimental measurements are based on the gravimetric-volumetric method [START_REF] Weinberger | Molecular Modeling of oh H 2 Purification on Na-LSX Zeolite and Experimental Validation[END_REF][START_REF] Dreisbach | Messmethoden für Gasphasen-Adsorptionsgleichgewichte[END_REF][START_REF] Keller | Volume-Gravimetric Measurements of Binary Gas Adsorption Equilibria[END_REF][START_REF] Vidal | Measurement of physical adsorption of gases at high pressure[END_REF]. In Fig. 5 the schematic setup used is shown.

The mass of the gas present in the system is dynamically measured. Moreover, after each state of equilibrium, the gas is re-injected to the system. As illustrated in Fig. 5, the system is weighed directly and the gas is injected by a capillary tube. To avoid the systematic errors due to the gas mass, the pressure vessel must be symmetrical and the axis should remain vertical. The vertical alignment of the system is obtained with a counterweight. This one compensates both due to the weight of the capillary tube. A precision adjustment is possible starting from the micrometric table (Fig. 6). At the left end of the capillary, the balance is connected and on the right-the micrometric table. The axial deviation (y) of the balance is slightly influenced by elasticity (E) of the capillary tube. We used a capillary tube (stainless 316L, 200 GPa) with a length of 1520 mm, where a load of 0.1 mg at the free end induces a deviation of the capillary tube equal to 0.02 mm. If the length of the tube is 1, the axial deviation is given by: ( ) Where e D is the external diameter and i d -the internal diameter of the capillary tube.

64 3 4 4 3 i e G d D E I F y - = π (10)
The procedure of measurement of the capacity of adsorption can be subdivided in several stages:

• The mass of the adsorption cell is obtained with an internal vacuum ;

• The volume of the cell is filled with the adsorbent (35 cm3) then it is sealed;

• The climatic chamber is set at 273.15 K to prevent the heating of the high pressure

• valve;

• The system is connected gradually to the pumping installation (see Fig. 3) ;

• The heating system of the cell is regulated with 2 K/min until 373.15 K;

• There is a stage at 373.15 K to eliminate water in the adsorbent cell;

• When secondary vacuum is reached, the heating process (2 K/min) continues until the final temperature is reached (573 to 723 K depending on the decomposition temperature of the adsorbent);

• The heating process is finished at high temperature and secondary vacuum;

• The adsorption cell is cooled down to ambient temperature;

• The high pressure valve is closed and the vacuum pump is stopped;

• The procedure is repeated (3-8) after having determined the mass of activated material;

• The acquisition of the measurements starts;

• The pressure is preset via the mano-pressure reducer;

• The gas is injected by opening the micro-valve;

• At equilibrium, the procedure 12 starts again until the end of the measurement.

The adsorbed gas mass m a is expressed in mole per gram. In this study the following equation was applied to the adsorption of pure gases. The adsorbed mass of these gases obtained by volumetric-gravimetric measurement is: The bulk density of the gas is evaluated by the equation of state of Peng-Robintson. In order to determine precisely the volumes, the thermal dilation of all materials is taken into account.

( ) ( ) ( ) [ ] ( )

RESULTS END DISCUSSION

On Fig. 7 the results (LIMHP) for adsorption of hydrogen on a zeolithe 13X obtained by volumetric-gravimetric method at three different temperatures and results of AIR LIQUIDE Co. for adsorption of hydrogen on the same adsorbent at same conditions obtained by volumetric method are compared. The maximum deviations are up to 2.5 % at 20°C, 3 % at 40°C and 3.5 % at 60°C. Thus there is very good correlation between the data. The isotherms of hydrogen in this range of pressure have a linear character. The deviations of the results obtained by the two methods increase with the increasing of temperature. It is due to the mode of calculation of adsorption results by volumetric method, i.e. the choice of equation of state for estimation of gas density.

Results of the equilibrium for nitrogen adsorption on a zeolithe 13X at three different temperatures are shown in the figure 8. There is the difference of 1.3 % at 20°C, 2.1 % at 40 0 C and 60°C in this case. The figure shows also that the isotherms are first type iso- therms. These data also show that the difference between the two methods increase with the increasing of the temperature.

CONCLUSIONS

The installations for volumetric and gravimetric-volumetric measurements as well as the installation of volumetric helium measurement for determination of the volumetric mass of solid adsorbents are described in details. The comparison between the results of adsorption equilibrium using volumetric-gravimetric technique and result obtained by AIR LIQUIDE Co. using volumetric method is made.

The volumetric measurements of gas adsorption equilibrium are reduced, if the mass of the sorbent sample used is preliminary known, to the measurements only of pressures and temperatures in gas phases.On the other hand prior to adsorption experiments the sorbent sample should be activated by heating the adsorption chamber, degassing etc. During this procedure the mass of sorbent is changed by 1 % or more. This change normally can not be included in volumetric experiments but must be taken into account afterwards, at least approximately. Gas adsorption processes may last for seconds, hours or sometimes even days. Therefore we can never be sure whether thermodynamic equilibrium in a volumetric experiment has been realized. Hence the time which should elapse between opening the expansion valve and reading of instruments, especially thermometer and manometer has to be chosen according to the experience. Finally upon expansion from the storage vessel the sorptive gas may not only be adsorbed on the surface of the sorbent material but also on the walls of the adsorption vessel and the tube connecting both vessels. This may cause additional uncertainties in measurement.

Basically, volumetric-gravimetric measurements (VGMs) combine all the advantages and the disadvantages which occur in either volumetric or gravimetric measurement procedures. Commercially available instruments for VGMs usually need several grams of sorbent material to perform reasonably accurate measurements. Operations technical of measurements are fairly simple end the procedure easily can be automated. Activation Procedure of the Sorbent Material is recommended to provide an electric heating system for the adsorption chamber of any instrument of VGMs. This will allow the activation of the sorbent material on site and thus avoid any pre-adsorption of for example ambient airs components, especially humidity, if the sample is activated outside the instrument and then built in the adsorption chamber.

E

  is the potential energy of interaction of the mol- ecules with other molecules from the fluid phase (f), end s p E is the potential energy of interaction of the molecules with the molecules of the solid.

Fig. 2 O

 2 Fig. 2 O, Oven; TC, Thermostatic cage; V R , Reservoir; HR, Oven regulation; CR, Cage regulation; H, Heating; R, Refrigeration; GP, Group of pumps; V 1 , V 2 end V 3 , Valves.

Fig. 1 .

 1 Fig. 1. Bulk end surface density.

3 .

 3 Cell of adsorption for measure to the mass volumetric of material.

Fig. 4 .

 4 Fig. 4. p, Manometer; T, Thermometer; R, Reservoir; H, Heating; C, Cage; A, Adsorbent; R, Refrigeration; P, Pump; BG Gas bottle.

Fig. 5 .Fig. 6 .

 56 Fig. 5. MC, Mass Comparator (Mettler Toledo, PR2004); E, Climatic Chamber (S.P.A.M.E.); C, Unichiller (Huber, 7006A-H); SC, Heating System; Pt 100, Platinum temperature sensor; R, Pressure Vessel; SCR, Heating system of the pressure vessel; F, Micro filters; v, Valves (Autoclave); RE, Climatic regulation (Eurotherm 2404), RCC; Regulation of the SCR (Watlow Série 93) ; TM, Micrometric table (Micro Controle); CP, Pressure gauge of reference (DH Budenberg DPM1); S, Security valve (Air Liquide) ; VM, Micrometric valve (Autoclave); BG Gas bottle; TC, Turbo pump (Pfeiffer Vacuum TSH 071); CW, counterweight.

  Gas m is the total mass of gas, Gas ρ -bulk the density of the gas, Int T -the temperature inside the cli- matic chamber, P -the gas pressure, c V -volume of the pressure vessel, Ads V -volume of the adsorbent, Ext T -the external temperature, Cap V -the volume of capillary tubes, Ads m -masse of the adsorbent and Gas M -is the molar mass of gas.

Fig. 7 .

 7 Fig. 7. Comparison of hydrogen measurements obtained by gravimetric-volumetric device (LIMHP) and volumetric device (AL) on the zeolite 13X.

Acknowledgements

The authors thank AIR LIQUIDE Co. for a financial grant and Dr. S. Moreau for the appropriation of the results obtained on their volumetric device. Also, we thank M. Bono and M. Beauverger for their permanent technical support.


Liquid Crystal Science from 1888 to 1922: Building a Revolution

Keywords: liquid crystals, discovery, history of science, Otto Lehmann

by the scientific community required more than two decades. This paper comes back to the early years of liquid crystal research, at the pivotal period between the nineteenth and twentieth centuries. Amazement, doubt, controversy, struggle, and finally acceptation were the successive steps of liquid crystal history from 1888 to 1907.

Introduction

A nematic liquid crystal (LC), which is used in flat-panel displays, looks like a school of fish. Rod-like molecules are on average parallel but have no particular position. From this orientational order comes the birefringence property, which is a property of a crystal. These same molecules constantly readjust their position, and this positional disorder gives the fluid state. This view is very far from the traditional view of the states of matter that scientists held during the pivotal period between the nineteenth and twentieth centuries, when, with much heterodoxy, the German physicist Otto Lehmann coined the term "liquid crystals" to describe these materials.

Carrot is ancestor of flat screen

We were in 1888, at the Institute of Plant Physiology at the German University of Prague. Friedrich Reinitzer (1857Reinitzer ( -1927; Figure 1) was a botanist-or biochemist in modern terms. He was working on crystals of cholesterol derivatives extracted from a carrot's root [START_REF] Reinitzer | [END_REF] and wanted to elucidate their structure. Amazingly, the cholesteryl benzoate had "two melting points." This was exactly the expression Reinitzer used in a letter dated March 14, 1888-sixteen pages long and written in Gothic letters. This letter was addressed to the crystallographer Otto Lehmann (1855Lehmann ( -1922; Figure 2), a physicist from the Polytechnical School of Aachen who specialized in growth phenomena and phase transitions in crystalline materials. Reinitzer explained to his colleague that the small crystals lost their rigidity at 145.5 °C-this "first" melting point was the temperature at which the solid turned into a milky fluid. At 178.5° C-the "second" melting point, later named the clearing point-the drop of material became perfectly transparent. Upon cooling, the material exhibited violet and blue colors, which then disappeared, leaving the substance cloudy but still liquid. This was surprising in view of current knowledge of crystalline matter at these times: a crystal must lose color and solidity at a single and unique temperature. However, a few decades earlier, in 1854, Rudolf Virchow [2] described similar unusual behavior for myelin-the sheath that surrounds nerve fibers-and Carl von Mettenheimer [3] showed that myelin was birefringent. Without realizing the meaning of their observations, these scientists had described the first example of a LC known in the scientific literature. Between 1861 and 1887, chemists had also reported strange color effects in cholesterol esters [4], but the complexity of their observations and the difficulty of duplicating them did not encourage them to pursue their investigations. For this reason, science historians consider that LCs were discovered in 1888 by Reinitzer: he was the first to give a detailed description of his observations and the first to recognize that the strange behavior of these "crystals" was a significant and new phenomenon-not an artifact.

The liquid crystalline phases Reinitzer observed were chiral phases-later named the cholesteric phase and the blue phases. Research activities accelerated when Reinitzer contacted Lehmann, whom he held as a partner of choice not only because he was an experienced crystallographer but also because he had fabricated a whole arsenal of microscopes (Figure 3) that allowed him to make in situ observations of crystals as the temperature changed. It was quite rare to find such apparatus on the shelves of laboratories. Lehmann and Reinitzer exchanged numerous letters and samples in March and April of 1888, and Lehmann observed the substances by polarized-light microscopy (Figure 4) [5]. They knew that "two-step melting" of crystalline matter would excite the curiosity of their colleagues, but they did not anticipate that these observations, and the forthcoming decision to name the substances with the oxymoron "liquid crystals," would trigger polemics and passionate reactions [6][7][START_REF] Knoll | Otto Lehmann-Researcher of the Liquid Crystals[END_REF]. Reinitzer was out of the subject as soon as Lehmann took control of operations, but he reappeared in the history of LC science some twenty years later, when Lehmann sought to rewrite the genesis of events and claimed priority [START_REF] Lehmann | [END_REF]. Reinitzer defended his pioneering work [10]: "It is indisputably clear that the unambiguous concept of flowing crystals was recognized by Lehmann first of all by studying my derivatives. Furthermore, it is obvious that the perception is due to Lehmann, but I also contributed considerably in this matter…. One should admit that the credit of discovering the phenomenon ought to be attributed to me." (translation from Ref. [START_REF] Sluckin | Crystals That Flow-Classic Papers from the History of Liquid Crystals[END_REF]).

Scientific context

From 1890 to 1900, Lehmann embarked on an exhaustive program of observations and reproducibility of Reinitzer's experiments with a large number of substances. Lehmann was quickly convinced that the milky liquid had both the characteristics of a crystal and of a liquid and, in 1889, he used the term "crystal that flows." He published numerous papers between 1890 and 1900, and the names followed each other: flowing crystal, viscous liquid crystals, crystalline fluid, and liquid crystals forming drops. Lehmann compiled his scientific literature in a generous treatise published in Leipzig in 1904 and finally entitled "Liquid Crystals" [START_REF] Lehmann | Flüssige Kristalle sowie Plastizität von Kristallen im allgemeinen, molekulare Umlagerungen und Aggregatzustandsänderungen[END_REF]. Lehmann's excessive attachment to the concept of liquid crystals probably contributed to an underestimation of the importance of the discovery and led to errors that required several decades to correct.

We must remember the current vision of matter at the period between the nineteenth and twentieth centuries. Why did the observations and terms used by Lehmann proved to be such a thunderbolt in the scientific community? When Reinitzer discovered liquid crystals, theories on phase transitions and polymorphism were just appearing. Reinitzer and Lehmann had no idea of the molecular composition of cholesterol esters. The very idea of crystalline structure did not exist. The abbot-crystallographer René Just Haüy had introduced the idea of periodic structure for crystals, from which his student Gabriel Delafosse deduced the concept of unit cell in 1840. This model was widely accepted in the late nineteenth century but controversies-such as that between Ernst Mach and Ludwig Boltzmann [START_REF] Cercignani | Ludwig Boltzmann : The Man Who Trusted Atoms[END_REF]-about the atomic nature of matter were still active. Major contributions came later from Max von Laue, Nobel Prize in Physics in 1914 "for his discovery of the diffraction of X-rays by crystals," while William Henry Bragg and his son William Lawrence were awarded the Nobel Prize in 1915 "for their services in the analysis of crystal structure by means of X-ray." Therefore, when Lehmann spoke of "liquid crystals," crystallinity and fluidity were considered incompatible, and

Lehmann's conclusions about the nature of the strange matter generated much more than skepticism among his colleagues.

The colloidal hypothesis

Georg which is an emulsion of water and fat. Tammann made an analogy with a water-phenol mixture.

Phenol is only partially miscible with water because miscibility depends on the relative concentration and, below a critical temperature, the two liquids phase separate with the consequence that the mixture appears milky. It was essentially the turbid aspect of a "liquid crystal" drop that caused objections and gave rise to the hypotheses of suspension and emulsion. Nevertheless, they did not fit very well with the observations. It would be understood later than the turbidity was due to changes in the average orientation of the molecules from one point to another of the sample, which consisted of many contiguous areas bounded by lines exhibiting optical and structural discontinuity-a polydomain texture, in other (modern) words. Light cannot propagate through the material without being deviated or scattered, which alters the LC transparency.

In 1889, Ludwig Gattermann (1860-1920; Figure 6) and A. Ritschke made the first chemical synthesis of LC molecules: para-azoxyanisole (PAA) and para-azoxyphenetole (PAP). The purity of these compounds was an argument against the hypothesis of poorly controlled mixtures given by Lehmann's opponents. Gattermann and Ritschke published an article in 1890 [START_REF] Gattermann | [END_REF] in which we find for the first time the term "liquid crystal" (Flüssige Kristalle), for which Lehmann would become a passionate promoter. In addition to his use of heterodox terms, Lehmann's links with the ultra-Darwinist Ernst Haeckel (1834-1919) would also detract from his credibility. Haeckel was a zoologist whose view on the theory of evolution was more than controversial. He believed that matter, including inert matter, was endowed with a soul. He spoke literally about "crystal souls" [START_REF] Haeckl | in foreword of Crystal Souls-Studies of Inorganic Life[END_REF].

He was convinced that Lehmann's LCs were the link between the living and the dead; a link he was desperately seeking. After giving a talk at a conference, Lehmann was accosted by a colleague who cruelly questioned him: "What's this about your liquid crystals? Can they now eat?" [START_REF] Sluckin | Crystals That Flow-Classic Papers from the History of Liquid Crystals[END_REF]. Leaving aside the nonscientific claims of Lehmann and Haeckel, we may probably say that they were the first scientists to propound the idea that the LC state is responsible for many of the processes of life [START_REF] Needham | Order and Life[END_REF][START_REF] Bouligand | Liquid Crystalline Order in Biological Materials in Liquid Crystalline Order in Polymers[END_REF][START_REF] Neville | Biology of Fibrous Composites-Development Beyond the Cell Membrane[END_REF][START_REF]Structural Biological Materials-Design and Structure-Property Relationship[END_REF][START_REF] Bouligand | [END_REF][21].

Rising controversy

The controversy between Lehmman and Tammann, the most virulent of his opponents, continued to rage in the pages of Annalen der Physik between 1900 and 1906. Tammann sarcastically entitled one of his articles "On the so-called liquid crystals" to which Lehmann immediately reacted with an angry article: "Liquid crystals: a refutation of Mr. Tammann's comment."

In 1903, although it did not yet propagate beyond the German community, research on the origin of LC phases was very active. An article on the subject appeared from the group of Daniel Vorländer (1867-1941) in Halle and focused on the classification of compounds based on whether or not they give rise to a LC state [22]. Although Vorländer must have been a coauthor, the article was signed only by his students-Meyer and Dalhem-which in itself is very informative about the climate in the scientific community at the time. Vorländer did not particularly wish to promote the careers of his young collaborators by pushing forward their names. It was rather a precaution, since he was anxious to get away from any eventual new controversy. It is interesting that Vorländer would refer to this paper after 1908 as the paper by "Vorländer, Meyer and Dahlem" [START_REF] Sluckin | Crystals That Flow-Classic Papers from the History of Liquid Crystals[END_REF].

In 1904, electrophoresis experiments excluded the hypothesis of a colloidal fluid [23,24]: an electric field should separate the particles in suspension in a fluid; however, it had no influence.

In 1905, the knockout blow was delivered to the LC opponents in a conference held in Karlsruhe by the physical chemist Rudolf Schenck (1870-1965; Figure 7), who was very attracted by LC research (fortunately, he did not follow the advice of his mentor Jacob Volhard: "Herr Schenck, leave this stupid stuff" [START_REF] Knoll | Otto Lehmann-Researcher of the Liquid Crystals[END_REF]). In his seminar he gave a solid demonstration of a discontinuity in the density and viscosity at the clearing point, which could not be the behavior of an emulsion. In addition, purification did not change the behavior. "Liquid crystals" did exist. It is said that the moderator of the session, Jacobus Henricus van't Hoff-the first winner of the Nobel Prize in chemistry four years prior, had to deploy treasures of diplomacy to avoid a physical confrontation between Tammann and Schenck. The controversy would gradually die down as from this moment, although an explanation of these famous LCs was still lacking. Van't Hoff proposed to form a committee to discuss the controversy, but the idea came to nothing because Lehmann refused to participate. Lehmann had developed pride and confidence in his own work that led him to take offence when it was challenged [START_REF] Dunmur | Soap, Science, & Flat-Screen TVs-A history of liquid crystals[END_REF]. Teamwork with him was impossible [START_REF] Knoll | Otto Lehmann-Researcher of the Liquid Crystals[END_REF]. He ruined much of his reputation by an imprudent dogmatism and permanent priggishness [START_REF] Knoll | Otto Lehmann-Researcher of the Liquid Crystals[END_REF]-behavior that would not help anyone who seeks to promote revolutionary ideas in science.

In 1907, Vorländer signed-alone this time-an article that would have a long-term influence in the field [START_REF] Vorländer | [END_REF]. It included an essential conclusion: most substances giving rise to LC phases are made with rod-like molecules. The same year, Emil Bose provided the first theory of the LC state, based on the work of Schenck and Vorländer. According to the French mineralogist Frédéric Wallerant, "Lehmann's discovery is definitely one of the most important of the last century. Its consequences are numerous and of the first order. They permit [us] in particular to sharpen our knowledge of crystalline matter." [27].

Amazement, doubt, controversy, struggle, and finally acceptance were thus the successive steps of LC research from 1888 to 1907.

Liquid crystals leave Germany

During the last period of his life (1908)(1909)(1910)(1911)(1912)(1913)(1914)(1915)(1916)(1917)(1918)(1919)(1920)(1921)(1922), Lehmann worked hard to disseminate the investigations into LCs beyond Germany. In 1909, he was invited to the Sorbonne in Paris to give a long seminar accompanied with experiments [28]. This visit was a great success and gave birth to the French school of LC science, with Charles Mauguin, Georges Friedel, and François Grandjean as pioneers. Until then, French scientists had not succeeded in obtaining a clear representation of Lehmann's descriptions, their efforts being polluted by all sorts of irrelevant considerations. How could one admit that, when sandwiched between two glass plates, a liquid film was able to move on these surfaces while always maintaining at every point, despite the thermal agitation, a constant (optical) axis of symmetry? It seemed simply impossible to them.

In 1922, Friedel published in Annales de Physique a seminal paper of more than two hundred pages [29] that gave the first classification scheme for naming the different phases of LCs: nematic, cholesteric, and smectic. The term cholesteric came from their discovery by Reinitzer in cholesterol esters. A sample of smectic LC (smectos means soap in Greek) behaves like stacked layers that can slide over one another in a manner similar to that of soapy film (which is in fact a LC). Much less known is the true origin of the term "nematic" [START_REF] Mitov | Sensitive Matter-Foams, Gels, Liquid Crystals and Other Miracles[END_REF]. One afternoon, when Friedel was relaxing with his daughters, he showed them photographs of LCs taken through a microscope. One daughter, Marie Friedel, who never graduated from high school but maintained her passion for ancient languages to her dying day, shouted with delight upon seeing the abundance of threadlike structures: The Greek word for thread is 'nêmatos'. You should call your liquid crystal 'nematic', Dad!

Friedel put an end to the confusion by introducing the correct definitions. He vehemently criticized the term "liquid crystal" and advocated for "mesomorphic states," which testified that the phases in question were full states of matter, intermediate (mesos in Greek) between crystalline and liquid phases.

Outlook

The heroic period of LC science ended in mid-1920s. Paradoxically, LC research started then to decline. LCs were considered by a few decision makers with disdain or irony; a "laboratory curiosity" (strictly speaking) that would never find practical applications. Researchers were encouraged to turn their attention to more fashionable subjects (e.g., quantum mechanics, nuclear physics) if they wished to obtain financial support. Although very valuable research activities into LCs continued, they remained rare and isolated. At this time, LCs were beginning their journey through the desert, which would last until the early 1960s, when people suddenly took out patents for thermography and display applications. "The so strange materials on which Lehmann had the great merit of drawing attention, but he made the mistake to name wrong"-to say it in Friedel's words-started again to focus the attention of the scientific community, but for other reasons now. The great revival occurred in the sixties spurned on by opportunities to use LCs in information-display technology [START_REF] Castellano | Liquid Gold-The Story of Liquid Crystal Displays and the Creation of an Industry[END_REF][START_REF] Geelhaar | [END_REF]. LCs would revolutionize this domain and give rise to nothing less than the creation of a new industry leading to low-power-consumption flat display screens.

Today it is evident that although LCs are famous for flat screen technology, this sector is only a very narrow niche in comparison with what LCs represent, as a compromise between order and disorder in matter. LCs: give rise to novel molecular designs and structures [33,34]; raise open questions on the relationship between molecular chirality and structure chirality, or on geometrical frustration in soft condensed matter; play a key role in nondisplay applications [START_REF] Mitov | Sensitive Matter-Foams, Gels, Liquid Crystals and Other Miracles[END_REF][START_REF]Liquid Crystals-Frontiers in Biomedical Applications[END_REF][START_REF] Mitov | [END_REF] such as

Figure 1 .

 1 Figure 1. Friedrich Reinitzer was the first scientist to give credit

Figure 2 .

 2 Figure 2. Otto Lehmann reproduced the phenomena seen by

Figure 3 .

 3 Figure 3. Picture of the "crystallization

Figure 4 .

 4 Figure 4. The first image of a cholesteric

  Quincke (1834-1924), Gustav Tammann (1861-1938; Figure 5), Georg Wulff (1863-1925), and Walther Nernst (1864-1941) were Lehmann's main opponents from 1890 to 1905.

Figure 5 .

 5 Figure 5. Gustav Tammann was the most vociferous opponent to

Figure 6 .

 6 Figure 6. Ludwig Gattermann: his group synthesized the first liquid-

Figure 7 .

 7 Figure 7. Rudolf Schenck unambiguously demonstrated that liquid crystals were not mixtures, but pure and single compounds.