David Bourgogne

Sandrine Therias

Jean-Luc Gardette
email: luc.gardette@uca.fr

Wavelength effect on polymer photooxidation under LED weathering conditions

Keywords: Photooxidation, UV LED 365, polychromatic irradiation, poly(N-vinylcarbazole, polyethylene

This paper is devoted to the investigation of the photooxidation of poly(N-vinylcarbazole (PVK) and polyethylene (LDPE) by exposure to λ ≥ 300 nm polychromatic light (SEPAP 12.24) or UV light produced by a new setup equipped with LEDs emitting at 365 nm (LED 365), both at a temperature of 60 °C. Photooxidation was studied by infrared and UV-visible spectroscopies and emission spectroscopy in the case of PVK. The mechanisms by which the oxidation products were formed in both polymers were recalled. Depending on the conditions of ageing, i.e., polychromatic light or exposure to LED 365, the same oxidation products were obtained but with different rates and different relative amounts. This result reflected the influence of the wavelengths on the mechanisms.

In the case of PVK, the formation of oxidation photoproducts and yellowing were not impacted, but the kinetics of the decrease in excimer fluorescence, which is linked to the crosslinking of the polymer, were dramatically modified. In the case of LDPE, wavelength effects on the photolysis of ketones by Norrish reactions were observed. As a consequence, irradiations with the LED 365 setup could not be claimed to be representative of polychromatic irradiations because the shortest wavelengths ((300 nm < < 350 nm)) were missing and could not reproduce natural outdoor conditions of weathering.

Introduction

Accelerated weathering testing of polymeric materials is expected to speed time to market and reduce the indirect costs associated with long-term outdoor exposures. Laboratory devices for artificial accelerated weathering of polymers have been the object of considerable interest in the last fifty years, and many commercial testing equipment have become available to study and predict the weathering performance of polymeric materials. Over the years, numerous technical improvements have been made in the design, construction and control of these devices.

However, testing conditions can seriously bias experimental results if performed in weathering conditions that are not relevant to weathering in "use" (generally outdoors) conditions. The UV weathering of polymeric materials depends on many factors, and it is currently admitted that several conditions must be respected to produce relevant results. Scientists working in the field of polymer photodegradation agree on some very basic rules. Among these rules, short wavelengths below 300 nm must be excluded since they produce nonrelevant phenomena [START_REF] Gardette | Photothermal oxidation of thermoplastic polyurethane elastomers. 3-Influence of the excitation wavelengths in the oxidation evolution of polyurethane in the solid state[END_REF] , high intensities should be avoided since they are likely to provoke heterogeneous oxidation due to diffusion limited oxidation [START_REF] Celina | Review of polymer oxidation and its relationship with materials performance and lifetime prediction[END_REF] and a correct balance between photo-and thermo-ageing must be respected. Too high intensities (laser sources), which could provoke biphotonic excitation, should be also avoided.

One can currently observe a growing interest in the use of light emitting diode (LED) technology, and in particular, the lighting market for LEDs is rapidly expanding. White light output in LEDs can be generated using different methods, where the most widely used approach is based on the application of a blue light chip with yellow phosphor [START_REF] Mueller-Mach | Phosphor materials and combinations for illumination graded white pcLED Third Int[END_REF] . LED lighting systems consist of several components, which makes them relatively complex systems. The degradation of different optical materials in LED-based products, in particular that of the polymeric components of typical LED systems, has received attention and has been reviewed [START_REF] Mehr | Degradation of optical materials in solid-state lighting systems[END_REF] . The mechanism of optical degradation for light emitting diode (LED) packages in light bars under high-temperature ageing conditions [START_REF] Tsai | Investigation on some parameters affecting optical degradation of LED packages during high temperature aging[END_REF] has also been investigated. Commercial testing equipment has recently become available to expose polymer samples to high-intensity blue light LEDs in the 400-500 nm domain and used to study the yellowing of polycarbonate [START_REF] Gandhi | Acceleration parameters for polycarbonate under blue LED photo-thermal aging conditions[END_REF] . A newly developed test setup to age optical plastics by visible radiation (450 nm) has been recently described and applied to the photodegradation of polycarbonate [START_REF] Hemmerich | Advanced Test Setup for Accelerated Aging of Plastics by Visible LED Radiation[END_REF] . Ageing experiments were performed over a period of 5000 h to evaluate the stability of PLA under the influence of extreme levels of optical LED radiation (λ max = 450 nm) [START_REF] Hemmerich | Photostability of polylactide with respect to blue LED radiation at very high irradiance and ambient temperature[END_REF] .

One issue that is not fully considered is the representativeness of the experiments performed with blue LEDs emitting in the visible range in comparison to conventional devices in the area of degradation and stabilization of polymers. The literature shows that, generally, the ageing experiments are conducted on polymers that do not absorb the incident light emitted by blue LEDs, and one can question the mechanisms involved. In the present article, we approach the issue of material degradation from the photochemistry viewpoint and focus on the impact of UV radiation, which is present in the solar spectrum. The present article describes the use of LEDs emitting at 365 nm to produce the photodegradation of polymers. The goal is to see whether such exposure conditions can reproduce the photodegradation provoked by exposure in a "conventional" device equipped with polychromatic light sources. To reach this goal, we selected two polymers whose photodegradation mechanisms are well characterized and which could discriminate the impact of different wavelengths in the emission spectra of the light sources. On the one hand, we focused on poly(N-vinylcarbazole (PVK), which contains intrinsic chromophores; on the other hand, we focused on polyethylene (LDPE), where photooxidation is initiated by chromophoric defects.

Experimental part

Materials

Free-standing thin (25 µm) films of PVK (Mw = 1 100 000, T g = 501 K Aldrich, Germany) were prepared by evaporating polymer solutions in 1-4 Dioxane solution on glass plates at room temperature. Then, the films were dried in vacuum at room temperature. The solvent evaporation was carefully controlled by IR analysis. The mean thickness of the samples was 25 microns.

The polyethylene (PE) in this work was a grade Repsol Alcudia PE033 (low density polyethylene grade) and irradiated in the form of free-standing films with a thickness of approximately 150 microns.

Irradiation

Irradiation was performed under artificial ageing conditions under either polychromatic light (ƛ above 300 nm) (SEPAP 12/24) or light emitted by LEDs centred at 365 nm (LED 365). The SEPAP test devices were developed based on numerous studies on the photoaging processes that affected polymer materials. The SEPAP 12/24 unit 9 from Atlas is equipped with four medium pressure mercury lamps (Novalamp RVC 400 W) in a vertical position at each corner of the chamber.

Wavelengths below 295 nm were filtered by the glass envelope of the sources. The temperature at the surface of the samples was fixed at 60 °C. The irradiance at 300-420 nm was measured as 90 W m -2 (see spectrum in Fig. 1).

Irradiation under LED light was performed in a homemade LED 365 unit (see Scheme S1 of the supporting information). This chamber was equipped with four LEDs (365 nm LED Gen 2 Emitter from LED ENGIN) with an emission centred at 365 nm and a full width at half maximum (FWHM) of 10 nm (see spectrum in Fig. 1). The distance between the LEDs was 60 mm, and the distance from the LEDs to the polymer samples was 110 mm. The temperature inside the chamber was regulated using a silicone heater mat. The samples to be irradiated were placed on the mat, and the temperature during exposure was 60 °C. The irradiance in the LED 365 device was measured as 82 W m -2 . The irradiances in the SEPAP and in the LED 365 setup were measured using a radiometer ILT 800

CureRight (International Light Technologies) and a calibrated spectroradiometer QE6500 (Ocean Optics inc.)

Analysis

The chemical changes caused by oxidation reactions were followed by infrared spectrometry. The IR Wavelength (nm) spectra were recorded in transmission mode using a Thermo Scientific Nicolet 6700 FTIR spectrophotometer (nominal resolution of 4 cm -1 , 32 scans summation). Deconvolutions of the infrared spectra were performed using OMNIC software. The UV-visible spectra were recorded using a Shimadzu UV-2600 spectrophotometer with an integrating sphere. The fluorescence spectrum of PVK was measured under an excitation wavelength of 300 nm. It consisted of a band with a maximum at approximately 420 nm that was assigned to the low-energy excimer 10 . The fluorescence spectra were obtained using a Varian Cary Eclipse spectrofluorimeter. The spectra were not corrected for grating efficiency and photomultiplier response. The excitation and emission slits were 2.5 and 5 nm, respectively.

Results and discussion

Poly(N-vinylcarbazole) (PVK)

Poly(N-vinylcarbazole) (PVK) (Scheme 1) has been studied in recent years, and its photodegradation mechanism has been proposed [START_REF] Rivaton | Investigation of the Photophysical Processes and Photochemical Reactions Involved in PVK Films Irradiated at λ > 300 nm[END_REF][START_REF] Bussière | Photocrosslinking of poly(Nvinylcarbazole): Implementing a complementary set of techniques to characterize the three-dimensional network formation[END_REF] .

Scheme 1. Structure of poly(N-vinylcarbazole) (PVK)
Infrared spectroscopy is a useful and frequently used analytical technique to monitor the oxidation process of polymers [START_REF] Gardette | Handbook of polymer degradation[END_REF] . The modifications of the infrared spectra resulting from exposure in the SEPAP and LED 365 units were recorded and are represented in Figures 2 and3, respectively. The shapes of the spectra are similar for both irradiation units, but the irradiation times required to reach a similar absorbance are different.

The products resulting from the photooxidation of PVK were identified 11 by physical treatments, involving photolysis and thermolysis, which showed evidence of the formation of quinonic structures, ketones, N-cetylcarbazole, hydroperoxides, and various chemical derivatizations based on SF 4 and NH 3 reactions to characterize the formation of acids, esters, and anhydrides. In the region of 1500-1900 cm -1 , the formation of a CO band with a maximum centred at 1720-1730 cm -1 was attributed to anhydrides, acid groups and ketones, which were quantitatively identified as the main photoproducts. These products accumulate in the polymer during photooxidation. In the region between 2700-3700 cm -1 , which is not shown here, the formation of a broad band at 3100-3600 cm -1 was observed and indicated the formation of OH, NH and COOH end groups. The formation of these photoproducts was accompanied by a decrease in the CH bands and a loss of C-N bonds. The increase in absorbance at 1730 cm -1 can be used to follow the extent of photooxidation.

In parallel, we monitored the changes in the UV-visible absorption spectra of the irradiated samples. The main routes of photooxidation that account for the formation of oxidation products detected by infrared analysis and those responsible for the crosslinking of PVK are represented in scheme 2.

Scheme 2. Simplified photooxidation mechanism of poly(N-vinylcarbazole) (PVK)

The oxidative degradation of PVK involves many routes. The proposed photoageing mechanism [START_REF] Rivaton | Investigation of the Photophysical Processes and Photochemical Reactions Involved in PVK Films Irradiated at λ > 300 nm[END_REF] indicates that light absorption provokes the homolysis of C-N bonds on the macromolecular chains, which forms carbazolyl radicals and macroradicals on the polymeric chain. The macroradicals may recombine, which leads to cross-linking that may or may not include oxygen atoms. The carbazolyl radicals are likely to initiate chain oxidation by hydrogen abstraction on the macromolecular chains.

The abstraction of a hydrogen atom preferentially occurs at the tertiary carbon of the structure and leads to polycarbazolyl radicals. The polycarbazolyl radicals can also react with oxygen to give hydroperoxides, which decompose to give alkoxy radicals. Then, several reactions likely occur; the main reaction is identified as the β-scission of the alkoxy radicals, which gives N-acetylcarbazole groups. This last reaction is accompanied by the formation of alkyl radicals that can be oxidized into hn , O 2

Loss of fluorescence

carboxylic acids or isomerize to more stable tertiary radicals. These last radicals continue the oxidation process and lead to chain-scissions.

The photophysics of PVK has been extensively studied, and most of the studies are devoted to excimer fluorescence. The published studies report the presence of two distinct excimer sites with typical photophysical properties, which is considered unique among vinyl aromatic polymers. A lower-energy excimer is formed when two carbazolyl groups have achieved an eclipsed fully overlapping "sandwich-like" conformation [START_REF] Johnson | Emission properties of vinylcarbazole polymers[END_REF] . The emission spectrum of PVK under an excitation wavelength at 300 nm consists of a band with a maximum at approximately 420 nm assigned to the low-energy excimer [START_REF] Itaya | Emission Spectra of the Vinyl Polymers with Pendant Carbazolyl Groups[END_REF] (Fig. 5). A decrease in the emission intensity band is observed under irradiation in the SEPAP unit or LED 365 device. Obviously, the rate at which the intensity of the fluorescence decreases depends on the photooxidation conditions. After only 5 hours in the SEPAP, no more emission can be detected, whereas it necessitates 60 hours in the LED 365 device.

The disappearance of the excimer fluorescence at 420 nm of PVK resulted from a decrease in local mobility provoked by the crosslinking of the polymer film upon light irradiation in the presence of oxygen [START_REF] Rivaton | Investigation of the Photophysical Processes and Photochemical Reactions Involved in PVK Films Irradiated at λ > 300 nm[END_REF] . The cross-linking of the polymer and decrease in the fluorescence simultaneously occur and at a low conversion degree of irradiated films.

These experiments indicate that the changes monitored by infrared, UV, and fluorescence spectroscopies are similar when irradiation is performed under both weathering conditions, e.g., SEPAP 12.24 and LED 365 units. However, our results demonstrate dramatic differences that concern the kinetic aspects. Figure 6 compares the increase in absorbance in the carbonyl region as a function of the dose for irradiation performed in the SEPAP (0-20 h) and LED 365 (0-60 h) units. ).

The rate of photooxidation was higher in the case of SEPAP exposure. An absorbance of 0.1 is reached after 47 h (13875 kJ m -2 ) of exposure in the LED 365 device, whereas only 14 h (4536 kJ m -2 ) is required to reach the same absorbance in the SEPAP unit. Following a methodology reported in the literature by Gillen and Clough [START_REF] Gillen | Time-temperature-dose rate superposition: a methodology for extrapolating accelerated radiation aging data to low dose rate conditions[END_REF] , the rate enhancement can be determined by plotting the data on the same graph, which allows determining a shift factor, which is the relative rate. A shift factor of 3.5 was determined. The data obtained for LED irradiations were then superposed to SEPAP data using a shift factor of 3.5. This is illustrated in Fig. 7. Fig. 7 shows that the shaped of the curves are similar and that the data superpose well. The kinetic curves of yellowing provoked by exposure in both devices (Fig. 4) were also measured. This is shown in Figure 8, which represents the variations in absorbance at 400 nm. ) and in the LED 365 setup (irradiance 82 W m -2 ).

Interestingly, the kinetic curves have a similar shape to those in Figure 6. The data shown in this figure were superposed using the shift factor 3.5 determined from the data given in Fig. 6. This is shown in Fig. 9. As observed in Fig. 7, one notes a good superposition, which suggests that the mechanism proposed to explain the formation of the oxidation products and the yellowing is the same. This result was not unexpected since the proposed mechanisms to explain the photooxidation of PVK show that the formation of the photoproducts detected by infrared or by UV-visible analysis involve identical mechanisms [START_REF] Rivaton | Investigation of the Photophysical Processes and Photochemical Reactions Involved in PVK Films Irradiated at λ > 300 nm[END_REF] , which can be verified by plotting the variations of absorbance at 400 nm vs. the increase of the absorbance at 1730 cm -1 in the SEPAP and LED 365 units, as presented in Figure 10. The results in Fig. 10 indicate that the correlation "yellowing" vs. "carbonyls" is identical in both irradiation units. This supports the conclusion obtained from the superposition method that the mechanism proposed to explain the formation of the oxidation products and the yellowing is the same.

From the fluorescence spectra in Figure 5, one can plot the kinetics of the fluorescence intensity (Fig. 11). ) and in the LED 365 setup (irradiance 82 W m -2 ).

The formation of carbonyls and yellowing involve similar time scales (see Figures 6 and8), which are much higher than the required time to decrease the fluorescence emission (Figure 11). Based on the results in Figures 6, 8 and 11, one can plot the emission intensity at 420 nm as a function of the absorbance at 1730 cm -1 or 400 nm in the SEPAP and LED 365 units, as shown in Figure 12. The superposition method was also applied to the disappearance of the excimer fluorescence, using the same shift factor of 3.5. This is shown in Fig. 13. Here, one observes no superposition, which indicates that the mechanism is changed. nm, which in turn leads to the fluorescence loss. In the case of the LED 365 setup, the emission band centered at 365 nm is relatively broad (see Fig. 1) and part of this band (350-360 nm) is in the range of PVK absorption. This is the absorption of these photons that is responsible for the fluorescence loss, which was experimentally observed (Fig. 5 -right).

On one side, more photons are absorbed in the case of exposures performed in the SEPAP, and on the other side, different excited states with higher energies can be populated. The result is a much faster loss of fluorescence (Fig. 5). However, it is difficult to discriminate both these contributions, more absorption vs. population of excited states of higher energy responsible for the loss of the fluorescence.

Polyethylene

Figure 14 illustrates the modification of PE spectra during exposure in the SEPAP 12.24 (the spectra are presented as subtracted spectra with the spectrum before irradiation as a reference). In the range of carbonyl absorption, the modification of the spectrum indicates that ketones (1720 cm -1 ) are formed in the initial steps, and carboxylic acids (1713 cm -1 ), esters (1735 cm -1 ) and lactones (1780 cm -1 ) form in secondary processes. One can also notice the formation of double bonds (1640 cm -1 ). The absorbance at 1713 cm -1 after 400 hours is approximately 1.3.

In the absorption range of unsaturations, one notices an increase in intensity of the bands at 909 and 991 cm -1 , which indicates the formation of vinyl unsaturations, and at 965 cm -1 , which is characteristic of t-vinylene groups. No modification is observed in the intensity of the vinylidene group at 888 cm -1 .

In the range of hydroxyl frequencies (not shown here), a broadband band with a maximum at 3420 cm -1 and a sharp absorption band at 3550 cm -1 appear in the spectrum. These bands are known to come from the formation of monomeric hydroperoxides (3550 cm -1 ) and hydrogen-bonded alcohols and hydroperoxides (3420 cm -1 ). The intensities of both bands remain very low, where a stationary concentration of hydroperoxides reaches a plateau at approximately 5.10 -2 mol/L [START_REF] Gardette | Photo-and thermaloxidation of polyethylene: Comparison of mechanisms and influence of unsaturation content[END_REF] .

Figure 15 illustrates the modification of PE spectra during exposure in the LED 365 device. In the range of 1500-1900 cm -1 , absorption bands form at similar frequencies to those reported for photooxidation in the SEPAP device (1720 cm -1 , 1713 cm -1 , 1735 cm -1 , 1780 cm -1 ), which indicates that the same products are formed. However, the shape of the complex carbonyl band strongly differs, which reflects dissimilar relative concentrations of the photoproducts. The main absorption maximum is observed at 1720 cm -1 , which is characteristic of ketones, whereas it appears at 1713 cm -1 in the case of photooxidation in the SEPAP unit. Then, ketones are the main products formed by exposure in the Led 365 device. No absorption band at 1640 cm - 1 can be observed, which would have reflected the formation of double bonds. This is confirmed by the spectra in the range of 1000-800 cm -1 , which do not indicate the formation of absorption bands that could be attributed to unsaturation. The absorbance at 1720 cm -1 after 1280 hours is approximately 1.8. In the range of hydroxyl frequencies (not shown here), the modifications of the spectra provoked by irradiation in the SEPAP unit or in the LED 365 setup were similar, showing a very weak increase of the absorbance with a broad band at 3420 cm -1 .

We have checked that the oxidation of PE exposed in the LED 365 device did not come from a thermal effect, by exposing a PE film to 60 °C without light (dark control). No modification of the infrared spectrum could be detected after more than 1500 hours.

Based on the pioneering work by Carlsson and Wiles 18 , one can deconvolute the complex spectrum in the carbonyl domain to highlight the main bands that contribute to the broad absorption of carbonyls. Curve fitting analysis of the IR carbonyl band can be achieved by direct mathematical treatment of the spectra, considering the absorption maxima identified by chemical and physical treatments of the oxidized samples [START_REF] Wilhelm | Infrared identification of carboxylic acids formed in polymer photooxidation[END_REF] . The carbonyl envelop into the component peaks was resolved following a procedure previously reported [START_REF] Gardette | Photooxidation of polyphasic ethylene-propylene polymers[END_REF] . The selected absorption maxima to perform deconvolution are shown in Table 1. The deconvoluted spectra in the carbonyl domain after 400 h of exposure in the SEPAP unit and 1115 h of exposure in the LED 365 unit are presented in Figure 16. Nice fits were obtained between the recorded "experimental" spectra and the spectra rebuilt after deconvolution. The deconvolution of the infrared spectra confirms the above interpretations:

dissimilarity between relative concentrations of the photoproducts. The concentration of saturated ketones is proportionally higher in the case of irradiation in the LED 365 setup than in the case of irradiation in the SEPAP unit. Ketones are indeed photochemically unstable and should degrade when exposed to light. Ketones do not absorb light in the LED 365 unit and subsequently accumulate, which is not the case for irradiation in the SEPAP device. To verify this issue, a PE was first irradiated in the LED 365 device for 2270 h and subsequently irradiated in the SEPAP unit for relatively short durations (1-20 h). The modification of the spectra is presented in Figure 17. The spectra in Figure 17 indicate that the absorbance at 1720 cm -1 (ketones) decreases upon exposure in the SEPAP unit, whereas the absorbances at 1785 and 1735 cm -1 increase. The absorption bands at 1640 cm -1 and 909 cm -1 (unsaturations) appear. These results clearly demonstrate the reactivity of ketones. As recalled above, photooxidation of polyethylene produced by exposure to both SEPAP and LED 365 produces almost identical oxidation products, but their relative concentrations are different. The Norrish reactions that occur in photooxidation are responsible for these differences. The same carbonyl products are formed in both cases but not in the same quantities: ketones and conjugated ketones accumulate during exposure in the LED 365 device because they do not absorb the 365-nm light, whereas they disappear to yield new unsaturations upon exposure in the SEPAP unit due to the absorption of light in the range of 300-330 nm. Vinyl and vinylene unsaturations can appear through Norrish reactions [START_REF] Kirkbride | The photochemical properties of the carbonyl group[END_REF] .

Scheme 3. Photolysis of ketones involving Norrish type-I and type-II reactions

The reactivity of ketones may be further confirmed when recording the UV-visible spectra of the PE films exposed in both irradiation units. No modification of the UV-visible absorption characteristics was observed during exposure in the SEPAP unit, but some notable changes appeared in the spectra as a result of exposure in the LED 365 device (Figure 18). Our results confirm that ketones are a key intermediate photoproduct in the photooxidation of polyethylene. Irradiation at "long" wavelengths that are not absorbed by ketones allows these photoproducts to accumulate in the polymer, which changes the photooxidation mechanism reported for irradiation under polychromatic light. Photooxidation at "long" wavelengths is more similar to thermooxidation than photooxidation.

Conclusion

The results in this article unambiguously show that irradiations in a wavelength domain that covers only a narrow part of the solar light and omits the shortest wavelengths (300 nm < < 350 nm) Similar conclusions can be given in the case of polyethylene, even if the reasons are different. In the case of PE irradiated under polychromatic light, the reported photooxidation mechanism in the literature involves the photoreactivity of ketones as intermediates. In the case of irradiation with LEDs with a peak wavelength of 365 nm, the photooxidation mechanism is different, since the ketones do not absorb and are subsequently relatively stable. Then, the photooxidation mechanism is more similar to a thermooxidation mechanism.

To make this type of irradiation acceptable to weather polymers in relevant conditions to natural weathering, it is necessary to add a source of light with shorter wavelengths, e.g., supplementary

LEDs with a peak wavelength of 305 nm, to our setup. The results will be the object of a forthcoming paper that also considers the case of polycarbonate and polyethylene terephthalate as examples to prove the relevance of this new setup.

Fig. 1 .

 1 Fig. 1. Emission spectrum of the mercury lamps in the SEPAP (left) and LED 365 (right)

Fig. 2 .Fig. 3 .

 23 Fig. 2. Infrared spectra of a PVK film during photooxidation (SEPAP 12.24) in the range of carbonyl absorption: direct spectra (left), subtracted spectra (right) (thickness 25 microns)

Figure 4

 4 Figure 4 represents the UV-visible absorption spectra of a PVK film exposed under polychromatic (SEPAP 12.24) or LED light (LED 365).

Fig. 4 .

 4 Fig. 4. UV-visible spectrum of a pristine PVK sample (thickness 25 microns) irradiated in the SEPAP unit (Left) and LED 365 device (right).

Figure 4

 4 Figure 4 indicates that with increasing irradiation time, the development of an unstructured absorption above 370 nm is observed by UV-visible spectroscopy. This absorption reflects the formation of various conjugated structures and is responsible for the yellowing of the photooxidized film. The shapes of the UV absorption spectra are similar for both irradiation units. However, the rates at which the absorbance increases are different, and the yellowing is much more rapid when irradiations are performed in the SEPAP unit.

Fig. 5 .

 5 Fig. 5. Emission spectrum of PVK after exposure in the SEPAP device (left) or in the LED 365 unit (right)

Fig. 6 . 2 )

 62 Fig. 6. Absorbance at 1730 cm -1 as a function of exposure in the SEPAP (irradiance 90 W m -2 ) and in the LED 365 setup (irradiance 82 W m -2

Fig. 7 .

 7 Fig. 7. Data for photooxidation (carbonyl formation) in the LED 365 setup superposed onto SEPAP data using a shift factor 3.5

Fig. 8 .

 8 Fig. 8. Absorbance at 400 nm as a function of exposure in the SEPAP (irradiance 90 W m -2

Fig. 9 .

 9 Fig. 9. Data for photooxidation ("yellowing") in the LED 365 setup SEPAP superposed onto SEPAP data using a shift factor 3.5

Fig. 10 .

 10 Fig. 10. Increase in absorbance at 400 nm vs. increase in absorbance at 1730 cm -1

Fig. 11 .

 11 Fig. 11. Emission intensity at 420 nm as a function of exposure in the SEPAP (irradiance 90 W m -2

Fig. 12 .

 12 Fig. 12. Decrease of the emission intensity at 420 nm as a function of the increase in absorbance at 1730 cm -1 (left) and at 400 nm (right) in the SEPAP and LED 365 units

Fig. 13 .

 13 Fig. 13. Data for photooxidation ("Emission intensity at 420 nm") in the LED 365 setup SEPAP superposed onto SEPAP data using a shift factor 3.5 The results represented in Figs. 12 and 13 unambiguously shows that the correlation between the disappearance of the excimer fluorescence of PVK at 420 nm and the oxidation of the polymer measured either by the carbonyl increase or by the yellowing depends on the wavelengths of irradiation. The disappearance of the fluorescence emission is closely related to the direct absorption of light by PVK, whereas the formation of oxidation products and subsequent yellowing result from direct photochemical reactions and induced photooxidation 11 . Both routes can be discriminated by varying the irradiation conditions. The superposition of the emission spectra of the SEPAP and the LED 365 to the absorption spectrum of PVK (spectrum obtained from ref. 10c) clearly shows that in the case of the SEPAP, the narrow line at 365 is almost not absorbed by PVK, but the lines at 334, 313, and 305 nm are in the range of absorption of PVK and are fully absorbed. The exposure in the SEPAP provokes the formation of excited states by absorption of these photons at 334, 313 and 305

Fig. 14 .

 14 Fig. 14. Subtracted infrared spectra of a PE film during photooxidation (SEPAP 12.24) in the absorption range of carbonyl absorption (left) and in the absorption range of unsaturations (right) (thickness 150 microns).

Fig. 15 .

 15 Fig. 15. Infrared subtracted spectra of a PE film during photooxidation (LED 365): in the range of carbonyl absorption (left); in the range of the absorption of unsaturated groups (right).

Fig. 16 .

 16 Fig. 16. Deconvoluted IR spectrum of a PE film after exposure in the SEPAP device (left) or in the LED 365 unit (right)

Fig. 17 .

 17 Fig. 17. Infrared spectra in the absorption range of carbonyl (left) and unsaturation (right) absorption of a PE film irradiated for 2270 h in the LED 365 device and then irradiated in the SEPAP unit.

Fig. 18 . 17 .

 1817 Fig. 18. UV-visible spectra of a PE A film during photooxidation in the SEPAP unit (left) and in the LED 365 unit (right)One can observe an absorption maximum at 275 nm that develops during exposure in the LED 365 device (the maximum at 215 nm is not considered, since the response of the detector cannot be considered relevant below 250 nm). The maximum at 275 nm indicates the formation of ketones.As recalled above, ketones are not stable under UV-light irradiation, and we have shown that a short irradiation time in the SEPAP unit (1-20 h) made ketones disappear from a film that was first photoxidized in the LED 365 unit for 2270 h. Recording the UV absorption spectra confirms the

Fig. 19 .

 19 Fig. 19. UV-visible spectra during exposure in the SEPAP setup of a PE film pre-irradiated for 1270 h in the LED 365 device.

Scheme 4 .

 4 Scheme 4. Simplified scheme of polyethylene photooxidation under polychromatic light or under "long" wavelength irradiation

  to natural weathering. The two selected polymers photodegraded with wavelength-dependent mechanisms.In the case of poly(N-vinylcarbazole (PVK) exposed to polychromatic irradiation (SEPAP), direct excitation of PVK units provokes scissions of the C-N bonds, a decrease in local mobility due to crosslinking, and the fluorescence attributed to the excimer rapidly decreased. In parallel, photooxidation occurs and provokes a yellowing of the material. Photooxidation involves the abstraction of a hydrogen atom that preferentially occurs at the tertiary carbon of the structure and leads to the formation of macro radicals that are likely to initiate the oxidation of the polymer, which propagates following a classical chain oxidation mechanism. The chain oxidation mechanism can also be initiated by light absorption due to chromophoric defects, but this does not provoke direct scissions of the C-N bonds. In the case of irradiation with LEDs with a peak wavelength of 365 nm and an FWHM of approximately 10 nm, only a minor part of the incident light is directly absorbed by PVK, which means that a minor importance is given to the direct scissions of the C-N bonds, and then the excimer fluorescence slowly decreases. The chain oxidation mechanism can be initiated by light absorption due to chromophoric defects, provoking the formation of oxidation products and yellowing. The formation of oxidation products and the yellowing follow the same routes, but the decrease of the fluorescence follows a different mechanism, which involves direct light absorption by PVK. Irradiations performed in the LED 365 setup cannot be claimed to be representative of conditions relevant to natural weathering.

Figures captions Scheme 1 .Scheme 2 .Scheme 3 .Scheme 4 .Table 1 .Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .

 123411234 Figures captions

Fig. 5 .Fig. 6 . 2 )

 562 Fig. 5. Emission spectrum of PVK after exposure in the SEPAP device (left) or in the LED 365 unit (right) Fig. 6. Absorbance at 1730 cm -1 as a function of exposure in the SEPAP (irradiance 90 W m -2) and in the LED 365 setup (irradiance 82 W m -2).

Fig. 7 . 5 Fig. 8 . 2 )

 7582 Fig. 7. Data for photooxidation (carbonyl formation) in the LED 365 setup superposed onto SEPAP data using a shift factor 3.5 Fig. 8. Absorbance at 400 nm as a function of exposurein the SEPAP (irradiance 90 W m -2 ) and in the LED 365 setup (irradiance 82 W m -2).

Fig. 9 . 5 Fig. 10 .

 9510 Fig. 9. Data for photooxidation ("yellowing") in the LED 365 setup SEPAP superposed onto SEPAP data using a shift factor 3.5 Fig. 10. Increase in absorbance at 400 nm vs. increase in absorbance at 1730 cm -1 in the SEPAP and LED 365 units.

Fig. 11 . 2 )

 112 Fig. 11. Emission intensity at 420 nm as a function of exposure in the SEPAP (irradiance 90 W m -2 ) and in the LED 365 setup (irradiance 82 W m -2).

Fig. 12 . 1 (

 121 Fig. 12. Decrease of the emission intensity at 420 nm as a function of the increase in absorbance at 1730 cm -1

Fig. 13 . 5 Fig. 14 .

 13514 Fig. 13. Data for photooxidation ("Emission intensity at 420 nm") in the LED 365 setup SEPAP superposed onto SEPAP data using a shift factor 3.5 Fig. 14. Subtracted infrared spectra of a PE film during photooxidation (SEPAP 12.24) in the absorption range of carbonyl absorption (left) and in the absorption range of unsaturations (right) (thickness 150 microns).

Fig. 15 .

 15 Fig. 15. Infrared subtracted spectra of a PE film during photooxidation (LED 365): in the range of carbonyl absorption (left); in the range of the absorption of unsaturated groups (right).

Fig. 16 .Fig. 17 .

 1617 Fig. 16. Deconvoluted IR spectrum of a PE film after exposure in the SEPAP device (left) or in the LED 365 unit (right) Fig. 17. Infrared spectra in the absorption range of carbonyl (left) and unsaturation (right) absorption of a PE film irradiated for 2270 h in the LED 365 device and then irradiated in the SEPAP unit.

Fig. 18 .Fig. 19 .

 1819 Fig. 18. UV-visible spectra of a PE A film during photooxidation in the SEPAP unit (left) and in the LED 365 unit (right)

Table 1 .

 1 Infrared characteristics of some of the oxidation products in PE

	Product	Conjugated ketone	Carboxylic acid	Ketone	Ester	Peracid	Lactone


Y El Bitouri

L Buffo-Lacarrière

A Sellier

X Bourbon²

Modelling of chemical evolution of low pH cements at long term

Keywords: Low pH cement, chemical evolution, modeling

In the context of the underground radioactive waste repository, low-pH cements were developed to reduce interactions between concrete and clay barrier. These cements contain high proportions of mineral additions like silica fume, fly ash or blast furnace slag for example. The high ratio of cement replacement by pozzolanic additions allows to reduce the pH by a global reduction of Ca/Si ratio of the hydrates (according to the one observed on CEM I pastes). In order to predict the short term development of the hydration for each component of this cement, a multiphasic hydration model, previously developed, is used. The model predicts the evolution of hydration degree of each anhydrous phase and consequently the quantity of each hydrate in paste (CH, aluminates, CSH with different Ca/Si ratios). However, this model is not suitable to determine the long term mineralogical and chemical evolution of the material, due to the internal change induced by chemical imbalance between initial hydrates. In order to evaluate the chemical characteristics of low pH cement based materials, and thus assess its chemical stability in the context of radioactive waste storage, a complementary model of chemical evolution at long term is proposed. This original model is based on "solid-solution" principles. It assumes that the microdiffusion of calcium plays a major role to explain how the different Ca/Si ratio of initial C-S-H tends together toward a medium stabilized value. The main mechanisms and full development of the model equations are presented first. Next, a comparison of the model with experimental data issue from EDS analysis on low pH cement allows to test the model.

Introduction

One of the main concerns in the context of geological repository for radioactive waste is the chemical and physical degradation of the clay barrier (bentonite and host-rock) due to the high pH of the pore solution of a conventional cementitious material (Portland type), and the high increase in temperature caused by the hydration of cement within very massive elements. Research has therefore been carried out to develop "low-pH cements" compatible with this application. The principle of formulation of low pH cement is that a high amount of Portland cement is replaced by high amount of silica materials such as silica fume, blast furnace slag, fly ash. The main hydrates that form in hydrated Portland cement are "jennite-like" C-S-H (with a high C/S), portlandite, ettringite, AFm and AFt [START_REF] Adenot | Durabilité du béton : caractérisation et modélisation des processus physiques et chimiques de dégradation du ciment[END_REF]. The addition of high amount of silica fume leads to the consumption of portlandite to form "tobermorite-like" C-S-H (with lower C/S). However, a large amount of residual silica remains unhydrated. At long term, the surplus of silica reacts with the high calcium C-S-H to form progressively more low calcium C-S-H [START_REF] Lothenbach | Supplementary cementitious materials[END_REF].

To assess the behavior of these materials at the long term, it is necessary to predict their chemical evolution. A multiphasic hydration model [START_REF] Buffo-Lacarrière | Multiphasic finite element modeling of concrete hydration[END_REF] is used to predict the short-term development of the hydration for each component of the binder. The model predicts the evolution of hydration degree of each anhydrous phase and consequently the quantity of each hydrate in paste (CH, aluminates, CSH with different Ca/Si ratios). As it was developed for early age applications, the model is based on a fixed stoichiometry of each hydrate produced by the different anhydrous (CSH from clinker, CSH form pozzolanic additions, CH, aluminates). For binders with high content of silica, this model reveals not suitable to determine the long term mineralogical and chemical composition of the material, due to the internal change induced by chemical imbalance between hydrates. In order to evaluate the chemical characteristics of low pH cement based materials, and thus assess its chemical stability in the context of radioactive waste storage, a complementary model of chemical evolution based on a variable stoichiometry is proposed. The results given by hydration model constitute the initial conditions in terms of chemical data for modelling the chemical evolution at long-term.

The main mechanisms and full development of the model equations are presented first. Then, an application for a binary low-pH cement (clinker and silica fume) is presented. We will show, in particular, how the model can do evolve the initial C/S ratios of CSH toward a medium stabilized value.

Model of chemical evolution of low pH cement

Chemical attacks of cementitious materials correlate strongly with the cement hydration processes. In the latter case, anhydrous grains gradually hydrate by following phenomena under/over saturation causing their dissolution and precipitation of hydrates. Then, these reactions (dissolution/precipitation) are kinetically limited by diffusion phenomena through porosity of material. Furthermore, dissolution and/or precipitation of solid phases occur when the material is exposed to an aggressive environment. The kinetic of these changes is also governed by the diffusion of species through the porosity.

The chemical stability of the solid phases in cement paste can be evaluated from a thermodynamic and kinetic approach. The thermodynamic approach uses the analysis of the solubility of the solid phases and allows knowing the equilibrium states. This is based on the assumption of local chemical equilibrium which considers equilibrium between solid and the solution in contact. Any variation in the composition of this solution would lead to a transformation in the solid phase [START_REF] Adenot | Durabilité du béton : caractérisation et modélisation des processus physiques et chimiques de dégradation du ciment[END_REF].The kinetic aspect is mainly based on an approach of reactive transport.

Main mechanisms

The cement notation is adopted to write the formula of oxides. Table 1 presents the notation system adopted for the modelling. The chemical evolution model assumes that the single evolution of calcium describes the chemical evolution of cement-based materials [START_REF] Gérard | Coupled diffusion-damage modelling and the implications on failure due to strain localisation[END_REF] (only the calcium in solution is assumed to diffuse) (Fig. 1). Therefore, the model is based on the resolution of the mass balance equation (eq.1) for calcium only:

(1) And:

(2

) i Clinker Silica Fume … k j anh hyd anh hyd anh hyd C C CH - - S S C1,7 SH S C1,15 SH A+F - C3AH6 AFm, Aft… - - Ca Ca S ) ( div t ) Ca w ( + - = ∂ ∂ φ ∑ ∂ ∂ - = k , ij ij k Ca t Ca S
Where: Where t is the time, is the calcium concentration in pore solution (mol/m 3 in solution), is the solid calcium (mol/m 3 of material), w is the water content. The source term describes the intake of calcium in the liquid phase by dissolving solid phases, and calcium intake in the solid phase by precipitation of liquid calcium (eq.2).

Moreover, the dissolution and precipitation of calcium solid phases obey the chemical equilibrium [START_REF] Adenot | Durabilité du béton : caractérisation et modélisation des processus physiques et chimiques de dégradation du ciment[END_REF]) (Fig. 2). The dissolution of solid calcium occurs when the global concentration of calcium (

) is lower than the concentration in equilibrium with the solid ( ) which depends only on . When the calcium concentration is greater than the local concentration, the solid calcium precipitates:

(3)

The equilibrium concentrations are determined thanks to the solid/liquid thermodynamic equilibrium which is summarized into a global equilibrium curve presented in Fig. 2. This curve presents C/S molar ratio of solid phases as function of liquid calcium concentration (at equilibrium). When the concentration varies from 0 to 2 mmol/l, the ratio C/S roughly increases. This abrupt change in the solid without significant change in the liquid characterizes an invariant point where coexist silica gel and C-S-H with low C/S. Between 2 and 19 mmol/l, the C/S ratio increases slowly which describes a partial calcification of C-S-H. Between 19 and 22mmol/l, the C/S ratio roughly increases. This invariant point characterizes the existence of C-S-H with high C/S ratio (1,7-1,8) and portlandite. For calcium aluminates, the stability domain is located in the second zone, ie, between 2 and 19 mmol/l [START_REF] Adenot | Durabilité du béton : caractérisation et modélisation des processus physiques et chimiques de dégradation du ciment[END_REF]. In this modeling, it is assumed that the dissolution/precipitation equilibrium of anhydrous calcium corresponds to the last zone (from 19 to 22mmol/l).

Ca ij k Ca Ca S Ca eq ij k Ca ij k Ca ! " # $ % & - = ∂ ∂ Ca Ca 1 t Ca eq ij k ij k ij k τ eq ij k Ca Fig. 2. Equilibrium solid calcium / liquid calcium
It should be noted that, reactions of dissolution/precipitation depend, not only of the equilibrium, but also of the micro-diffusion of calcium from the most concentrated site to the least concentrated site [START_REF] Gawin | Modeling of cementitious materials exposed to isothermal calcium leaching considering process kinetics and advective water flow, Part1: Theoretical model[END_REF]. So, to take this into account, a characteristic time which describes the delay of reactions (dissolution/precipitation) due to the micro-diffusion of calcium is defined:

(4)

Where:

-: reference characteristic time, -: accessibility of solid calcium -: influence of water content, -: influence of temperature

The function f in equation (II-4) models the effect of the hydrates layer, surrounding the anhydrous compounds, on the diffusion of calcium. For hydrates, as their surface is directly accessible, the function is equal to 1 (no reduction of the accessibility). For anhydrous phases able to retain or release calcium, the function is lower than 1 because their accessibility is reduced by the layer of hydrates created at their surface during hydration. As the decalcification of this layer enhances micro-diffusion of calcium, the function f is increasing with the decrease of calcium content. As this accessibility is managed by diffusion an exponential function is chosen (Table .2).

( ) ( ) ( )

T h w g Ca f 1 ij k ref ij k ⋅ ⋅ ⋅ = - τ τ ref τ ) f(Ca ij k ) w ( g (T) h Table 2. Values of f (Ca)
The function g in equation (II-4) models the effect of water content:

(5)

The function h in equation (II-4) models the thermal activation of the phenomenon of micro-diffusion. This data is described by a thermal activation law as it was proposed and experimentally validated by [START_REF] Peycelon | Long-term behaviour of concrete : Influence of temperature and cement binders on the degradation (decalcification/hydrolysis) in saturated conditions[END_REF], with an activation energy of 44 kJ/mol : (6)

k j anhydrous hydrates C 1 S 1 A+F untreated 1 ! ! " # $ $ % & ∂ ∂ -∫ dt t Ca exp ihyd S ( ) ij k Ca f ! ! " # $ $ % & ∂ ∂ -∫ dt t Ca exp ihyd S ( ) w 1 w g = D a E ! ! " # $ $ % & ! ! " # $ $ % & - = ref D a T 1 T 1 R E exp ) T ( h

Chemical evolution binder B40

Input data and model parameter

The low-pH cement modelled (named B40) is that used in the experiments described by [START_REF] Bach | Influence of temperature on the hydration products of low pH cements[END_REF]. This cement contains 60% of Portland cement and 40% of silica fume. It has a pore solution pH in the range 11-11,5. So as to predict the short term development of the hydration for each component of this cement, the multiphasic hydration model is used (for a complete explanation of the hydration model, see [START_REF] Buffo-Lacarrière | Multiphasic finite element modeling of concrete hydration[END_REF]. The model predicts the evolution of hydration degree of each anhydrous phase, and thus, the quantity of each solid phase in paste as presented in Table 3. This mineralogical composition is predicted at 28 days. The latter is chosen as moment of transition from the hydration model to the equilibrium model. The water content of paste is of about 0,41 m 3 /m 3 . Table 3.Quantity of each solid phase in paste predicted by the hydration model at 28 days These concentrations are the input data of the equilibrium model. Table 4 presents these concentrations is the system of notations used for the model. We can note that the main part of the silica is content in the residual anhydrous of silica fume which will mainly "attract" calcium of other solid phases. The only model parameter is the reference characteristic time managing the microdiffusion of calcium in the neighborhood on the silica phase (eqs 3 and 4). This parameter must be fitted on experimental results. In this study, it was calibrated on the measurements of liquid calcium concentrations performed by (bach et al., 2012).

Calcium equilibrium relation applied to the binary paste

As the calcium in solution is used to characterize the chemical equilibrium, the equilibrium calcium concentrations for each compound are calculated using the equilibrium curve by linear interpolation of the characteristic points (Fig. 3, Fig. 4). The average of these concentrations is the initial calcium concentration. According to equilibrium diagram, there exist local concentration gradients due to the chemical imbalance between initial compounds (given by hydration model), which induces microdiffusion of calcium (Fig. 5). An internal re-equilibrium of calcium occurs, and the system evolves toward a chemical equilibrium state.

Calibration of model parameter

As previously seen, the model parameter used in Eqs 3 and 4 must be calibrated on experimental results. The measurements of liquid calcium concentration were performed by [START_REF] Bach | Influence of temperature on the hydration products of low pH cements[END_REF]. The evolution of these concentrations allows estimating the reference characteristic time. Fig. 6 compares measured and predicted liquid calcium concentrations for a characteristic time equal to 1,6.10 4 s. For comparison, the characteristic times of micro-diffusion given by [START_REF] Gawin | Modeling of cementitious materials exposed to isothermal calcium leaching considering process kinetics and advective water flow, Part1: Theoretical model[END_REF] have values ranging from about 5,8.10 2 s for the ettringite to1,17.10 4 s for the portlandite. As can be seen in Fig. 6, the numerical results reproduce the progressive decrease in calcium concentration. Furthermore, measured values are not significantly different than the calculated values. The liquid calcium concentration at equilibrium is of about 2 mmol/l. Fig. 6. Evolution of liquid calcium concentration [START_REF] Bach | Influence of temperature on the hydration products of low pH cements[END_REF] 2.2.4. Illustration of calcium re-equilibrium on the binary binder Fig. 7 shows the evolution of solid calcium of each compound over time. Dissolution of portlandite and anhydrous calcium (hyd and anh_C) occurs rapidly, when calcium concentration is lower than 22 mmo/l, followed by a progressive dissolution of calcium aluminates (hyd_A+F). Calcium released participates in the calcium rebalancing of silica compounds. The calcification/decalcification of silica compound (anh_S) (hyd_S) occurs progressively, and leads to system at chemical equilibrium. The evolution of the C/S molar ratio allows visualizing the calcification/ decalcification of silica compounds (Fig. 8). For the clinker anhydrous silica (clinker_anh_S), the C/S molar ratio increases very rapidly to a maximum value and then gradually decreases. The rapid increase is due to the amount of clinker anhydrous silica which represents only 3,4% of the total silica. The molar ratio of hydrated silica (SF_hyd_S), initially at 1,15, increases slightly and then gradually decreases, while the anhydrous silica of SF (SF_anh_S) and clinker hydrated silica (clinker_hyd_S) follow the same trend, on the rise for the first or down for the second. The slope changes (at 2 and 20 month) are due to the presence of calcium sources (anhydrous calcium and aluminates), and the different characteristic times used.

The C/S molar ratio in the B40 paste hydrates (cured at 20°C) was estimated by EDS analysis on polished cross sections prepared from 6-month old samples [START_REF] Bach | Influence of temperature on the hydration products of low pH cements[END_REF]. The distribution mode is 0,85 ±0.05. Bach indicates that the system tends towards this value at long term, which is in good agreement with the calculated value (Fig. 8.).

Conclusion

To predict the long-term evolution of concrete used for the radioactive waste repository, a modelling of the chemical evolution has been presented. This modelling is based on "solid-solution" principles. Its resolution with a numerical method requires the knowledge of the equilibrium relation between the solid and the liquid phase, the quantity of each compound in paste, the variation of the water content and the calibration of kinetic parameter.

The model allows treating calcification/decalcification of C-S-H and thus knowing the equilibrium state towards which evolves a binder highly substituted. An experimental campaign based on EDS analysis is underway. It consists to determine the evolution of the distribution of C/S molar ratio over the time, in order to test the model. Additional databases will be added to this model, considering the effects of other factors, such as temperature and water content. The coupling of the model with a mechanical model in order to predict the long-term behavior of concrete will be performed.

Fig. 3 .

 3 Fig. 3. Equilibrium curve of anhydrous calcium, portlandite (clinker_hyd_C and clinker_anh_C) and calcium aluminates (clinker_hyd_A+F)

Fig

  Fig. 7. Evolution of solid calcium

Fig. 8 .

 8 Fig. 8. Evolution of C/S molar ratio of each silica compound

Table 1 .

 1 Nomenclature Fig. 1. Main mechanisms

Table 4 .

 4 Mineralogical composition at 28 days (mol/m 3 of paste)

	Solid phase	Anhydro us clinker	CSH (C/ S=1,7)	CH	Aluminates	Anhydrous silica fume	CSH (C/ S=1,15)
	Quantity (mol/m 3 of paste)	1101 (C) 338 (S)	2207	22	274	5176	2112

Acknowledgments. The present investigation was carried out with financial support from the ANDRA (Agence Nationale pour la Gestion des Déchets Radiacatifs)


Hugo Clémot
email: hugoclemot@gmail.com.

Keywords: Philosophie du cinéma, Films d'horreur, Monstre, Noël Carroll, Alien Philosophy of Film, Horror movies, Monster, Noël Carroll, Alien Zone géographique : États-Unis d'Amérique

Résumés :

Le monstre joue un rôle essentiel dans The Philosophy of Horror de Noël Carroll, l'ouvrage de référence pour la philosophie anglo-saxonne du cinéma d'horreur. Il n'est donc pas étonnant que ce livre ait suscité une réflexion sur l'essence du monstre, qui mobilise autant les ressources de la philosophie la plus traditionnelle, que l'expérience des films d'horreur les plus contemporains. Cet article vise à présenter cette réflexion et à défendre la nécessité d'un « changement focal » conceptuel qui accompagne les mutations cinématographiques du monstre.

Le monstre dans la philosophie contemporaine de l'horreur cinématographique L'ouvrage récemment traduit La philosophie de l'horreur1 , mais dont la sortie vient d'être repoussée, de Noël Carroll domine la réflexion philosophique anglo-saxonne sur le cinéma d'horreur. Or, le monstre joue un rôle essentiel dans la définition que le philosophe américain propose du genre cinématographique puisqu'il offre la solution du paradoxe de l'horreur, c'est-à-dire de l'apparente contradiction qu'il y a à prendre du plaisir à ce qui nous fait horreur. Sa solution consiste à dire que le plaisir pris aux films d'horreur est en fait pris à suivre la structure narrative d'un récit de découverte d'un monstre, dont l'identité dépasserait, par définition, nos catégories culturelles.

Cette puissante théorie de l'horreur a été souvent attaquée et a suscité une réflexion sur l'essence du monstre, qui puise autant dans les ressources de la philosophie la plus traditionnelle, que dans l'expérience des films d'horreur les plus contemporains. Ce texte vise à présenter cette réflexion et à défendre la nécessité d'un « changement focal » conceptuel qui accompagne les mutations cinématographiques contemporaines du monstre.

1 Le monstre dans la théorie de l'horreur de Noël Carroll

Le paradoxe de l'horreur

Le livre La philosophie de l'horreur de Noël Carroll est un classique de la philosophie analytique du cinéma en ce qu'il est l'un des premiers à proposer une théorie systématique du genre de l'horreur cinématographique, qui soit en même temps une explication nonpsychanalytique de l'émotion qui donne son nom et sa fonction au genre. La popularité des films d'horreur pose en effet la question de savoir comment on peut éprouver du plaisir à voir non seulement des hommes souffrir et mourir sous les coups des monstres qui peuplent ces films, mais aussi à souffrir soi-même d'une émotion aussi pénible que celle de l'horreur. À la suite de Noël Carroll, les philosophes analytiques du cinéma parlent du « paradoxe de l'horreur » 2 pour désigner la difficulté générale suivante : il semble contradictoire d'éprouver du plaisir à regarder ce qui provoque de l'effroi et du dégoût. Le paradoxe de l'horreur est donc soulevé par la question « comment les gens peuvent-ils être attirés par ce qui est repoussant ? » 1.2 La solution carrollienne du paradoxe de l'horreur : la théorie « coexistentialiste » du plaisir et de l'horreur Le paradoxe de l'horreur est en réalité une forme particulière du paradoxe de la tragédie, le problème plus général et connu depuis l'Antiquité de savoir comment on peut prendre plaisir à suivre des histoires tragiques. Pour surmonter le paradoxe de l'horreur, Noël Carroll s'inspire de la solution donnée par David Hume au paradoxe de la tragédie, selon qui le triste sort des personnages ne provoquerait en lui-même aucun plaisir, mais stimulerait émotionnellement le spectateur alors mieux capable d'apprécier les qualités formelles du récit 3 . Il soutient donc que l'horreur éprouvée devant les films ne provoquerait en elle-même aucun plaisir, mais coexisterait chez le spectateur avec le plaisir de suivre une structure narrative 4 de découverte, c'est-à-dire un récit dont le but serait la découverte et la confirmation de l'existence et des propriétés de ce qui est le mieux capable de susciter une soif de découverte, à savoir l'inconnu au sens le plus fort du terme : l'inconnaissable, ce qui dépasse nos catégories culturelles en tant qu'il s'agit d'un « être qui n'existe pas maintenant selon la science contemporaine. » 5 Mais comme ce qui dépasse nos catégories culturelles est jugé monstrueux et provoque, si l'on en croit l'anthropologue Mary Douglas, le dégoût 6 , alors les récits les mieux capables de nous procurer ce plaisir de la découverte seront structurés autour de la figure d'un monstre qui nous dégoûte au point de provoquer l'horreur. L'horreur « est le prix à payer pour que nous soit révélé ce qui est impossible et inconnu, ce qui viole notre schème conceptuel. » 7Carroll qualifie sa théorie de « coexistentialiste » au sens où l'émotion d'horreur « coexiste » avec le sentiment de plaisir sans le provoquer, ce qui permet de surmonter le paradoxe initial. Lorsque nous sommes confrontés à l'image d'un monstre qui nous effraie et nous répugne, comme un extra-terrestre, un vampire, un zombie, etc., « [c]e n'est pas que nous désirions le dégoût, mais ce dégoût est le concomitant prévisible de la découverte de l'inconnu. »8

On remarque que cette théorie ne résout le paradoxe que si le monstre est un être dont l'impureté surnaturelle échappe aux limites du scientifiquement possible. Il n'est donc pas étonnant que les critiques de la philosophie de l'horreur de Noël Carroll aient souvent interrogé cette conception du monstre.

2 Le monstre, possible ou impossible ? L'une des premières difficultés que l'on ait soulevées à l'encontre de la définition carrollienne du monstrueux est qu'elle présuppose que les monstres des films d'horreur ne peuvent pas exister. Or, cela conduit à exclure des films très populaires et décisifs pour l'histoire du genre comme Psychose d'Alfred Hitchcock (1960)9 et le sous-genre cinématographique du « slasher film » qui s'en est inspiré10 , dont les films fondateurs comme Massacre à la tronçonneuse (Hooper, The Texas Chainsaw, 1974), La Colline a des yeux (Craven, The Hills Have Eyes, 1977), Halloween : La Nuit des masques ou encore Vendredi 13 (Cunningham, 1980) mettent tous en scène des tueurs dont la science contemporaine ne nie malheureusement pas l'existence 11 .

La réponse de Carroll est que des tueurs comme Freddy Kruger dans Freddy, les griffes de la nuit (Craven, A Nightmare on Elm Street, 1984) ou Michael Myers dans Halloween (J.

Carpenter, 1978) 12 ont une invincibilité surnaturelle. Que ces personnages ne nous inspirent de l'horreur que parce qu'ils sont impossibles est pourtant discutable ; qu'on songe, par exemple, qu'avant d'être assassiné et de réapparaître dans les rêves des enfants de ses bourreaux et d'ainsi échapper aux lois de la nature telle que la science la conçoit 13 , Freddy Kruger était un psychopathe pédophile, un type d'hommes dont la science ne nie pas l'existence.

Pour intégrer ces contre-exemples à sa théorie, Carroll soutient que, puisqu'ils ne rentrent pas dans les classifications psychiatriques officielles 14 , il faut les considérer comme appartenant à la science-fiction et distinguer les personnages, dérivés de Norman Bates, qui relèvent de la « science-fiction psychologique » (science fiction of the mind), de ceux qui relèveraient, comme les monstres des séries Alien et Predator (J. McTiernan, 1987), de la « science-fiction du corps » (science fiction of the body).

Mais quand bien même cette distinction conceptuelle serait pertinente, il faudrait encore que la théorie de Carroll puisse rendre compte du sous-genre de « l'horreur réaliste » qui raconte les méfaits de tueurs en série ayant réellement existé 15 schèmes conceptuels actuels » (Carroll,The Philosophy of Horror,op. cit.,p. 184), on pourrait nier l'idée que ce qui se situe « en dehors de nos schèmes conceptuels actuels » (Carroll,ibid.,p. 184) Blackwell, 2007, p. 191-192.

Le monstre comme menace pour l'épanouissement humain

On a reproché19 à cette conception du monstre comme erreur de la nature de ne pas rendre compte du monstre qui donne son titre à l'un des plus célèbres films d'horreur : l'Alien de Ridley Scott (1979). L'alien n'est en effet pas monstrueux parce qu'il n'aurait pas réussi à atteindre la forme normale de son espèce, mais parce qu'il est, au contraire, comme le dit l'officier scientifique du Nostromo, Ash, un « organisme parfait » dont la « perfection L'exemple de l'alien ou des virus nous fait comprendre que ces deux conditions ne sont pas conjointement nécessaires et que la secondece qui constitue une menace pour une téléologie anthropocentrée -, est supérieure à la première dans les films d'horreur.

On a reproché à notre tentative pour sauver une définition du genre de l'horreur par le monstre de n'être pas assez restrictive. En effet, si tout ce qui constitue une menace pour l'épanouissement naturel de l'homme est un monstre, alors un tsunami devrait être considéré comme un monstre. Or, il ne semble pas que ce type d'appellation convienne pour ce que nous appelons des catastrophes naturelles. S'il semble que nous puissions pourtant parler de phénomènes monstrueux dans ce genre de cas, cette objection appelle au moins une autre réponse qui conduit à concevoir un autre sens du terme « monstre ».

L'inhumain foyer du monstrueux

Relier le monstre à la notion de téléologie, naturelle ou anthropocentrée, semble permettre de définir le genre de l'horreur en référence à la monstruosité, tout en intégrant les contre-exemples énoncés à l'encontre de la théorie de Carroll. Cependant, cela présuppose que la Mais reconnaître que le foyer du monstrueux est l'humain lui-même conduit à déplacer le curseur conceptuel du monstrueux, de l'extracatégorialité du surnaturel à l'intrahumain, au sens du proprement « in-humain », en passant par le statut d'erreur de la nature. Autrement dit, notre plus grande peur, au point de mériter plutôt d'être appelée « horreur », serait celle qui naît lorsque nous comprenons qu'il est impossible de fonder rationnellement la confiance que nous avons dans le fait de ne pas pouvoir perdre nos caractéristiques essentielles en tant qu'êtres humains, celles auxquelles nous tenons. De ce point de vue, on pourrait dire que la possibilité de devenir monstre est essentielle à l'être humain. Cela semble justifier que le philosophe américain Stanley Cavell ait pu écrire jadis : L'horreur scelle ma perception de la précarité de l'identité humaine, du risque qu'elle encourt d'être perdue, ou violée (invaded), mon sentiment qu'il se peut que nous soyons déjà, ou qu'il se peut que nous devenions, quelque chose d'autre que ce que nous sommes, ou croyons être21 .

Des films récents comme Carriers, Funny Games (M. Haneke, 1997), Saw (J. Wan, 2004) et Hostel (E. Roth, 2006)22 ou encore les derniers épisodes d'une série télévisée comme The Walking Dead (Darabont, 2010-), nous révéleraient ainsi que l'horreur naît moins d'une peur d'une altérité radicale, que d'une prise de conscience de la précarité et de l'indétermination23 de l'identité humaine et de la possibilité que des circonstances conduisent tous les hommes à adopter des comportements trop contraires à nos attitudes et valeurs caractéristiques pour que nous puissions y reconnaître l'humanité, ou plutôt d'une prise de conscience de ce que l'altérité la plus radicale est celle que je contiens, que la pire menace est celle que constitue le monstre que je peux devenir : je peux être un monstre, un alien.

À propos d'Alien : je suis un monstre

« La science-fiction va chercher en nous nos peurs et nos espoirs les plus profonds puis nous les montre grossièrement déguisés : le monstre et la fusée. » 24 Pourra-t-on aller jusqu'à dire qu'un palier supplémentaire de l'horreur est franchi quand l'individu est amené à reconnaître qu'il est possible que la phrase « je suis un monstre » soit toujours déjà vraie de lui ? C'est en tout cas ce que semblent indiquer les interprétations les plus convaincantes du film Alien, le huitième passager (1979) de Ridley Scott. En rapportant le film au genre de l'horreur, Stephen Mulhall a ainsi fait de l'alien un déguisement de nos peurs relatives aux phénomènes de la nature, de la sexualité, de la grossesse et de la naissance 25 Mais la difficulté à s'exprimer, à faire entendre sa voix n'est pas moins grande pour les autres personnages que pour Ripley, d'autant que le mode normal des échanges verbaux est l'ironie, ce qui est le signe d'une incapacité à se faire confiance les uns aux autres, au point que l'amitié semble impossible : au contraire, à ne communiquer que sur un mode ironique, de peur de s'exposer, on finit par s'aliéner ses amis. En réalité, le scepticisme est si profondément ancré dans l'esprit des membres de l'équipage, qu'il en devient source d'agressivité et de violence. Scott parle ainsi d'une disparition de la camaraderie, de l'isolement ainsi produit, qui consiste en ce que chacun se retrouve seul avec ses pensées.

Si l'on accepte de considérer que Ripley fait le lien entre le processus de torture mentale ainsi mené par l'équipage et la torture physique exercée par l'alien, alors on pourra accepter de dire que c'est comme si le processus de pénétration, de fécondation et de parturition mené par l'alien n'était qu'un « déguisement grossier » du processus par lequel on peut insinuer en quelqu'un des doutes si forts qu'il en perde confiance en lui-même. Plutôt que d'identifier l'alien à la seule domination masculine, il serait donc préférable de l'identifier aux procédés violents qui naissent de la méfiance et de l'incapacité à coopérer les uns avec les autres.

L'alien rejoindrait alors une figure de l'extraterrestre présente dans un film comme Planète interdite (Fred M. Wilcox, Forbidden Planet, 1956) où le monstre, qui a réussi à exterminer une civilisation bien plus avancée que la nôtre, est une création de l'inconscient de ses victimes. Autrement dit, comme dans toute aliénation authentique, les artisans principaux de la servitude en sont aussi les victimes dans la mesure où la méfiance qui règle les rapports des uns avec les autres commence d'abord envers soi. De sorte que la menace que représente l'alien, c'est celle du comportement humain qui naît d'un manque de confiance en soi, du scepticisme dirigé vers soi et ses propres pensées.

Si cette interprétation a quelque valeur, alors on pourrait conclure que le film est un appel à prendre conscience de ce que je suis le monstre tant que je ne suis pas celui que je pourrais être si les autres et surtout moi-même ne m'en empêchions. La menace que symbolise l'alien, c'est bien celle d'une perte de confiance en soi, d'un scepticisme paralysant qui empêche l'individu de s'accomplir avec les autres et au milieu d'eux, et le condamne à ne jamais être celui qu'il devrait être, à toujours échouer à réaliser une téléologie intentionnelle, à être, en ce sens, le monstre le plus dangereux qui soit pour lui-même, un monstre qu'il devra apprendre à reconnaître et à contenir pour devenir celui qu'il est appelé à être. . Ormsby, 1974) Elephant Man (D. Lynch, 1980) Freaks (Tod Browning, 1932) Freddy, les griffes de la nuit (W. Craven, A Nightmare on Elm Street, 1984) Funny Games (M. Haneke, 1997) Halloween : La Nuit des masques (J. Carpenter, 1978) Henry: Portrait of a Serial Killer (J. MacNaughton, 1986)

  et des films d'horreur épidémique puisque ce qui nous fait horreur, la contagion, ne se situe pas au-delà de nos catégories culturelles, mais est bien un phénomène naturel, malheureusement possible. Que le virus menace directement la vie des individus ou bien indirectement en produisant chez les contaminés des comportements monstrueux n'y change rien en effet : ce sont des phénomènes possibles et qui inspirent le dégoût sans « violer notre schème conceptuel » 16 . On sait, par exemple, que sous sa forme « furieuse ou psychiatrique », la rage humaine peut produire un comportement agressif chez le malade, comme dans 28 jours plus tard (D. Boyle, 2002), où les hommes sont littéralement enragés. Si la définition du genre de l'horreur devait nécessairement passer par une référence au monstre, le contre-exemple des films d'épidémie devrait nous inciter à rejeter la définition du monstre comme être horrible parce qu'impossible, au profit d'une conception capable d'intégrer à la fois les monstres impossibles, les tueurs en série et les épidémies. 3 Deux sortes de monstres possibles 3.1 Le monstre comme échec de la téléologie naturelle Pour faire droit à l'usage ordinaire du terme « monstres » pour désigner des êtres possibles, Robert Yanal a proposé de revenir à la définition aristotélicienne du monstre comme un être qui résulte d'un échec de la téléologie naturelle en général, c'est-à-dire qui est incapable d'atteindre la forme normale de l'espèce 17 . On pense à Freaks (Tod Browning, 1932) ou à Elephant Man (David Lynch, 1980). Parler de téléologie naturelle ici n'engage en rien à adopter un quelconque « finalisme » au sens d'une position selon laquelle les fins seraient des causes efficientes. Il s'agit seulement de reconnaître l'utilité et même la nécessaire complémentarité des explications téléologiques (ou fonctionnelles) et mécaniques en sciences de la nature. Autrement dit, parler d'échec de la téléologie naturelle pour désigner un membre d'une espèce qui ne possède pas les traits qui caractérisent d'ordinaire la forme normale de l'espèce, ce n'est pas expliquer que la nature a fait une erreur, mais c'est décrire le résultat d'un mécanisme qui reste à découvrir 18 .

  structurale n'a d'égale que [l']hostilité. » Cependant, la monstruosité peut aussi être définie en fonction d'une téléologie anthropocentrée, autrement dit un monstre est aussi ce qui constitue une menace pour l'épanouissement de l'homme, pris individuellement ou collectivement, et qui provoque souvent pour cela de l'horreur. Raymond Fernandez et Martha Beck, Ed Gein, mais aussi Henry Lee Lucas 20 sont des monstres en ce double sens qu'ils n'ont pas atteint le statut d'animal rationnel autonome et qu'ils menacent l'épanouissement d'êtres humains.

  présence d'un monstre est une condition nécessaire du film d'horreur. Or, s'il existe des films d'épidémie qui relèvent davantage du film catastrophe ou du thriller que de l'horreur, comme Alerte ! (W. Petersen, Outbreak, 1995) ou Contagion (S. Soderbergh, 2011), il ne semble pas impossible qu'un film s'insère de plein droit dans le genre horrifique sans que l'épidémie ne soit provoquée par des êtres monstrueux ou que des êtres monstrueux ne menacent à cause d'elle l'épanouissement de l'homme. Dans le film Infectés (D. et A. Pastor, Carriers, 2010), par exemple, le virus mortel se transmet par le moindre contact physique et même par l'air que l'on respire, mais on n'en connaît pas la cause et il ne transforme pas les gens en zombies. Les deux frères qui fuient le virus se sont fixé un certain nombre de règles pour survivre, qui les conduisent à adopter un comportement immoral, en abandonnant leurs parents, un père et sa fille sans ressources, la petite amie de l'un d'eux, pour s'offrir le plaisir égoïste de faire du surf sur la plage de leur enfance. Non seulement l'horreur ne naît pas ici du comportement des hommes contaminés, mais elle ne naît pas non plus seulement des comportements des hommes sains tant qu'ils demeurent fidèles à ces règles qui, malgré leur immoralité, semblent au moins devoir tirer une certaine légitimité de leur efficacité. L'horreur naît à partir du moment où les deux frères ne sont même plus capables d'être fidèles à leurs principes, ces « règles », à leurs buts et leurs valeurs. S'il y a des survivants à la fin du film, ils ne savent plus trop eux-mêmes qui ils sont et doivent reconnaître que la solitude à laquelle le sort les a condamnés, n'est pas seulement une affaire d'isolement géographique, mais a surtout à voir avec leur incapacité à reconnaître et à être reconnu par l'autre, faute d'avoir encore quelque chose à reconnaître. Dans la mesure où le film montre bien que la contamination induite par le virus n'est pas seulement la transformation directe, physique du corps, mais surtout la modification indirecte, morale des caractéristiques des survivants, ce film d'horreur sans monstre nous montre néanmoins la fabrique du monstrueux.

  . Mais l'alien contient aussi quelque chose de notre sens du lointain et relève ainsi d'une réflexion typique de la science-fiction en tant qu'il s'agit bien d'un récit qui vient préciser la conception que nous nous en faisons, en s'appuyant sur une possibilité technique pour l'instant hors d'atteinte, celle de voyager à plusieurs milliers d'années-lumière. Relève également de la science-fiction, ce qui intéressait spécialement Ridley Scott selon David Thomson, à savoir l'étude de « la façon dont les gens [contraints de vivre les uns avec les autres pendant une longue période] peuvent être affectés par la claustrophobie, la mélancolie et le fait de ne pas pouvoir échapper à la compagnie de compagnons que l'on n'a pas choisis. » 26 L'alien, c'est donc à la fois le lointain, avec la menace qu'il peut représenter, et l'insociabilité humaine. Cependant, quand on remarque que l'alien est d'abord un extraterrestre dangereux, un monstre semblable au requin géant des Dents de la mer (Spielberg, Jaws, 1975) et aux tueurs des slashers, on n'est pas loin d'y voir l'homme masculin prédateur pour qui la femme est une proie qui le nourrit en même temps que le moyen de sa reproduction 27 . Cette interprétation, qui vient identifier l'alien et la domination masculine, semble confortée par le fait que l'équipage semble ligué contre le lieutenant Ripley. Dans le Making of du DVD, Scott dit d'ailleurs qu'il voulait montrer que le « chauvinisme masculin » pouvait très bien traverser les siècles.

Filmographie

  28 jours plus tard (D. Boyle, 28 Days Later, 2002) Alerte ! (W. Petersen, Outbreak, 1995) Alien, le huitième passager (R. Scott, 1979) La Colline a des yeux (W. Craven, The Hills Have Eyes, 1977) Contagion (S. Soderbergh, 2011) Deranged (J. Gillen et A

  provoque nécessairement le dégoût puisque ni Dieu, ni Superman, ni le Saint Graal ne semblent devoir susciter une telle aversion ; voir A. Neill, « On a Paradox of the Heart », Philosophical Studies, vol. 65, n° 1-2, 1991, p. 55-56. 17 Yanal, art. cit. 18 Sur la réhabilitation contemporaine de la notion de téléologie naturelle, voir V. Descombes, La Denrée mentale, Paris, Minuit, 1995, p. 64-69, B. Gnassounou et M. Kistler, Causes, pouvoirs et dispositions en philosophie, Paris, PUF, 2005 et P.M.S. Hacker, Human Nature. The Categorial Framework, Londres,

Noël Carroll, The Philosophy of Horror or Paradoxes of the Heart, New York, Routledge, 1990 ; trad. fr. La philosophie de l'horreur, Paris, Aux Forges de Vulcain,

2014, à paraître ; nos traductions.

Carroll, ibid., p. 10.

Carroll ne reprend qu'une partie de la subtile théorie de Hume qui est plus complexe que ce qu'en dit la phrase ci-dessus. Voir Hume, « De la tragédie » (1757), Essais et traités sur plusieurs sujets. Essais moraux, politiques et littéraires, Première partie, trad. fr. MichelMalherbe, Paris, Vrin, 1999, p. 257-264 et Carroll, The Philosophy of Horror, op. cit., p. 179-181.

Carroll, ibid., p. 181.

Carroll, ibid., p. 27. Aaron Smuts remarque qu'il est préférable de concevoir l'expression de « science contemporaine » comme désignant la science contemporaine de l'univers diégétique pour éviter d'avoir à exclure un film du genre de l'horreur suite à des découvertes scientifiques réelles.Voir Smuts, « Horror », in Paisley Livingston et Carl Plantinga éd., Routledge Companion to Philosophy and Film, New York, Routledge, 2009, p. 19.

Carroll fait référence à Mary Douglas, De la Souillure. Essais sur les notions de pollution et de tabou(1967), Paris, Éditions La découverte, 1992. Il attribue à l'auteur l'idée selon laquelle ce qui provoque le dégoût est toujours, pour l'homme primitif comme pour l'homme moderne, une rupture de l'ordre symbolique et social.Voir Carroll, The Philosophy of Horror, op. cit., p. 31.

Carroll, ibid., p. 186.

Carroll, ibid., p. 85.

 : si l'on a tendance à ranger à tort Psychose dans la catégorie de l'horreur, c'est justement parce que Norman Bates est un monstre psychologique, plutôt que biologique : « He is Nor-man, neither man nor woman but both. He is son and mother. He is of the living and the dead. He is both victim and victimizer. He is two persons in one. He is abnormal, that is, because he is interstitial. » Plutôt que de constituer un contre-exemple à sa théorie, le film d'Hitchcock en illustrerait la puissance explicative pour rendre compte de la logique sous-jacente et souvent ignorée de nos tendances classificatrices. Le problème est que des individus comme Norman existent. S'il est un monstre, alors il faut redéfinir la catégorie du monstre de façon à ce qu'elle ne coïncide pas avec l'impossible. Si Psychose n'est pas un film d'horreur, mais simplement un conte de terreur (« tale of terror »), alors le paradoxe de l'horreur ne fait qu'être déplacé sur cet autre « genre » par la décision de Carroll. Voir Berys Gaut, « The Paradox of Horror », Arguing about Art,Alex Neill et Aaron Ridley éd., 2nd. éd., Routledge, 2003, p. 296.

C. J.Clover, « Her Body, Himself: Gender in the Slasher Film » (1987), in Barry Keith Grant éd., The Dread of Difference. Gender and the Horror Film, Austin, University ofTexas, 1996, p. 66-113.

Smuts, « Horror », art. cit., p. 506.

Les tueurs en série ayant réellement existé dont on suit la dérive dans les films The Honeymoon Killers, Deranged et Henry : Portrait of a Serial Killer.

Stanley Cavell, Les voix de la raison. Wittgenstein, le scepticisme, la moralité et la tragédie, Paris, Le Seuil, 1996[START_REF] Cavell | Les voix de la raison. Wittgenstein, le scepticisme, la moralité et la tragédie[END_REF], p. 600.

Voir Olivia Chevalier-Chandeigne, La philosophie du cinéma d'horreur, Paris, ellipses, « Culture pop », 2014, p. 65.

Voir la fin du livre d'Éric Dufour, Les monstres au cinéma (Paris, Armand Colin, 2009), à propos du cinéma italien des années 1960-1970 qui s'attachaient à montrer la monstruosité des comportements humains comme dans Les monstres (1963) de Dino Risi : « le monstre n'est plus un monstre physique qui vient d'ailleurs, mais un monstre psychologique engendré par la société. »

« Science fiction plucks from within us our deepest fears and hopes then shows them to us in rough disguise: the monster and the rocket. » (Wystan Hugh Auden) C'est l'une des deux citations sur lesquelles s'ouvre le script d'Alien de juin 1978, écrit par Walter Hill et David Giler, inspiré du scénario de Dan O'Bannon et d'une histoire de Dan O'Bannon et de Ronald Shusett.

Stephen Mulhall, On Film, 2e édition, New York, Routledge, 2008.

David Thomson, The Alien Quartet: A Bloomsbury Movie Guide, Londres, Bloomsbury Publishing, 1999, p. 10.

Voir Carol J. Clover, « Her Body, Himself: Gender in the Slasher Film », art. cit.

Hostel (E. Roth, 2006) Infectés (D. et A. Pastor, Carriers, 2010) Les dents de la mer (S. Spielberg, Jaws, 1975) Les monstres (Dino Risi, 1963) Massacre à la tronçonneuse (T. Hooper, The Texas Chainsaw, 1974) Planète interdite (Fred M. Wilcox, Forbidden Planet, 1956) Peeping Tom (M. Powell, 1960) Predator (J. McTiernan, 1987) Psychose (A. Hitchcock, Psycho, 1960) Répulsion (R. Polanski, 1965) Saw (J. Wan, 2004) Sisters (B. de Palma, 1973) The Walking Dead (série TV, F. Darabont, 2010-)

The Honeymoon Killers (L. Kastle, 1969) Vendredi 13 (S. Cunningham, 1980)

Bibliographie

Carroll, Noël, The Philosophy of Horror or Paradoxes of the Heart, New York, Routledge, 1990 ; trad. fr. La