Hélène Méheust

Jean-François Le Meins

Etienne Grau
email: etienne.grau@enscbp.fr

Henri Cramail
email: henri.cramail@enscbp.fr

Bio-based polyricinoleate and polyhydroxystearate: properties and evaluation as viscosity modifiers for lubricants

Keywords: polyricinoleate, polyhydroxystearate, lubricant, viscosity modifiers, thickeners, Viscosity Index

This paper aims to design bio-based polyester as viscosity modifiers for lubricant properties.

Bio-based polyricinoleate (PRic) and its saturated homologous polyhydroxystearate (PHS) have been synthesized from fatty acid methyl esters. The polycondensation performed in bulk in onestep reaction without any purification leads to two series of polyesters within a large range of molecular weights, with Mw between 3 and 130 kg.mol -1 . Their thermal properties were investigated. Good thermal stability was observed with degradation temperatures above 300 °C.

As expected, PRic appeared to be amorphous with a particularly low glass transition temperature while PHS is semi-crystalline. A rheological study determined that polyricinoleate entangled when its molecular weight is above 25 kg.mol -1 . These two bio-based and biodegradable polymers were then evaluated as viscosity modifiers in both organic and mineral oils. PHS with high molecular

Introduction

The global concern over environmental pollution has led to a growing interest in the use of renewable resources in the fields of polymers and lubricants. The abundant availability and relatively low cost of vegetable oils make them one of the most essential sustainable resources for the chemical industries. [START_REF] Gandini | The irruption of polymers from renewable resources on the scene of macromolecular science and technology[END_REF][START_REF] Maisonneuve | Structure-properties relationship of fatty acid-based thermoplastics as synthetic polymer mimics[END_REF][START_REF] Gandini | Polymers from Plant Oils[END_REF] Castor oil, in particular, represents a high interest for industrial applications; especially, ricinoleic acid can be recovered from castor oil triglycerides to its acidic form by saponification or to methyl ricinoleate by methanolysis. [START_REF] Mubofu | Castor oil as a potential renewable resource for the production of functional materials[END_REF][START_REF] Mutlu | Castor oil as a renewable resource for the chemical industry[END_REF] The natural presence of one OH group and a carboxylic or ester terminal function of this mono-unsaturated fatty acid/ester (C18:1, OH) enables its self-condensation to produce polyricinoleate which generally exhibit low molecular weights, i.e. 3-11 kg.mol -1 . [START_REF] Gandini | Progress of Polymers from Renewable Resources: Furans, Vegetable Oils, and Polysaccharides[END_REF][START_REF] Mutlu | Castor oil as a renewable resource for the chemical industry[END_REF][START_REF] Kunduru | Castor Oil-Based Biodegradable Polyesters[END_REF][START_REF] Vilela | The quest for sustainable polyesters -insights into the future[END_REF][START_REF] Teomim | Ricinoleic acid-based biopolymers[END_REF][10][START_REF] Slivniak | Lactic Acid and Ricinoleic Acid Based Copolyesters[END_REF][START_REF] Lebarbé | Fully bio-based poly(llactide)-b-poly(ricinoleic acid)-b-poly(l-lactide) triblock copolyesters: investigation of solid-state morphology and thermo-mechanical properties[END_REF] Only Matsumura and coll. [START_REF] Ebata | Lipase-catalyzed synthesis and curing of highmolecular-weight polyricinoleate[END_REF][START_REF] Ebata | Poly (Ricinoleic Acid) Based Novel Thermosetting Elastomer[END_REF] synthesized amorphous polyricinoleate with Mw up to 100 kg.mol -1 by mean of enzymatic catalysis. However, these systems require a large quantity of enzyme, 50 wt.% with respect to the monomer, very long reaction times and the use of solvents. More recently, our group reported the polymerization of methyl ricinoleate and its copolymerization with 12-hydroxystearate using Ti(OiPr)4 as a catalyst leading to the formation of polyricinoleate with Mw up to 60 kg.mol -1 . [START_REF] Dworakowska | Cross-Linking of Polyesters Based on Fatty Acids[END_REF] This amorphous bio-based polyester appeared to be soluble in non-polar solvent and oils with thickening ability. 10 Its high miscibility with apolar systems, its biodegradability feature and stability against temperature make polyricinoleate a promising environmental-friendly viscosity modifier for lubricants. [START_REF] Kunduru | Castor Oil-Based Biodegradable Polyesters[END_REF]10,[START_REF] Ebata | Lipase-catalyzed synthesis and curing of highmolecular-weight polyricinoleate[END_REF][START_REF] Ghosh | Castor oil as potential multifunctional additive in the formulation of eco-friendly lubricant[END_REF] The role of a viscosity modifier is to thicken a lubricant oil and to reduce its viscosity loss at high temperature which is usually determined by the Viscosity Index (VI). Thanks to the addition of a viscosity modifier, a lubricant can be used over a large range of temperatures. [START_REF] Mortier | Chemistry and Technology of Lubricants[END_REF][START_REF] Martini | Review of Viscosity Modifier Lubricant Additives[END_REF] Currently, mostly petroleum-based polymers such as polyalkylmethacrylates and polyolefins are used as viscosity modifiers. [START_REF] Rudnick | Lubricant Additives: Chemistry and Applications[END_REF][START_REF] Rizvi | A Comprehensive Review of Lubricant Chemistry, Technology, Selection and Design[END_REF][START_REF] Pirro | Lubrication Fundamentals[END_REF] While the research is active on bio-compatible lubricants [START_REF] Shylesh | Novel Strategies for the Production of Fuels, Lubricants, and Chemicals from Biomass[END_REF][START_REF] Mobarak | The prospects of biolubricants as alternatives in automotive applications[END_REF][START_REF] Panchal | A methodological review on bio-lubricants from vegetable oil based resources[END_REF] , only a few solutions have been described to replace viscosity modifier additives with bio-based polymers in accordance to new environmental concerns. [START_REF] Biresaw | Environmentally friendly and biobased lubricants[END_REF][START_REF] Davim | 29 ASTMInternational D2270-10[END_REF] Herein, polyricinoleate (PRic) was developed as well as its saturated homologous poly(12hydroxystrearate) (PHS) within a large range of molecular weights in order to evaluate these biobased polyesters as potential viscosity modifiers. The molecular weights were controlled as a function of the reaction time. Both polyesters were synthesized using one-step bulk polycondensation, without further purification, and their thermal and rheological properties, in the bulk state, analyzed as a function of their molecular weight. Finally, the potential of PRic and PHS as viscosity modifiers in mineral and organic lubricant oils were evaluated.

Material and methods

Materials

Bio-based methyl ricinoleate (Nu-chek-prep, >99%) and methyl hydroxystearate (Nu-checkprep, >99%) were used without further purification for polyester synthesis. Titanium isopropoxyde (Ti(OiPr)4, 99.99%, Acros Organics) was used as catalyst as received. Dichloromethane (DCM) was supplied from ABCR and used as received. Deuterated solvents were purchased from Eurisotop and used as received. Commercial mineral paraffinic oil, the Yubase 4+ (MO) and organic triglyceride oil, Radialube 7386 (OTO) were kindly supplied by TOTAL and Oleon, respectively. Their properties are given in Flash point (°C) [235] η at 40°C (mm².s -1 ) [START_REF] Gandini | The irruption of polymers from renewable resources on the scene of macromolecular science and technology[END_REF] 20.4

η at 100°C (mm².s -1 ) [START_REF] Gandini | The irruption of polymers from renewable resources on the scene of macromolecular science and technology[END_REF] 4.6 [4.5] Viscosity Index VI 152 1-η= dynamic viscosity, 1 mm 2 .s -1 = 1 cSt; Obtained using a densimeter-viscosimeter at 40°C.

2-Obtained by SEC in THF, PS calibration, Đ = Mw/Mn, the dispersity. PRic and PHS were prepared from methyl ester ricinoleate (1.5 g, 4.8 mmol) and methyl-12hydroxystearate (1.5 g, 4.8 mmol), respectively (see Figure 1), dried overnight under vacuum at 70 °C under mechanical stirring in 50 mL Schlenk flask at 200 rpm. The mixture was cooled at room temperature under static vacuum and a 5 wt.% solution of Ti(OiPr)4 in DCM (0.015 g of catalyst, 0.053 mmol, 1 wt.%) was added under nitrogen flow. The mixture was stirred at room temperature for 30 min under static nitrogen then put under vacuum and heated at 70 °C for 30 min. Then the mixture was heated at 120 °C for one hour, 140 °C for another hour and 180 °C for 45 hours still under dynamic vacuum to remove the methanol (MeOH) sub-product and mechanical stirring at 200 rpm. After 48 hours reaction, stirring was stopped, the highly viscous mixture was cooled to room temperature and the flask was opened to air in order to stop the reaction. No purification was performed on the final product.

Polyester synthesis

Methyl ricinoleate: δ (ppm): 0.82 (C18, -CH3, 3H, t); 1.24 (C4-C7, C14-C17, CH2, 16H, m); All the 1 H and 1D [START_REF] Ebata | Lipase-catalyzed synthesis and curing of highmolecular-weight polyricinoleate[END_REF] C-NMR (DEPT) spectra were recorded on Bruker Avance 400 spectrometer (400 MHz and 100.63 MHz for 1 H and 13 C, respectively) by using CDCl3 as a solvent at room temperature. [START_REF] Gandini | The irruption of polymers from renewable resources on the scene of macromolecular science and technology[END_REF] H NMR analyses were performed with 16 scans. Multiplicity dependent 1D [START_REF] Ebata | Lipase-catalyzed synthesis and curing of highmolecular-weight polyricinoleate[END_REF] C-NMR experiment (DEPT) was performed with deptsp135 pulse program (256 scans) Twodimensional analysis such as 1 H-1 H COSY (COrrelation SpectroscopY) was also performed on the same spectrometer.

Size Exclusion Chromatography in THF (SEC)

Polymer molecular weights were determined by Size Exclusion Chromatography (SEC) using tetrahydrofuran (THF) as the eluent. Measurements in THF were performed on an Ultimate 3000 system from Thermoscientific equipped with diode array detector DAD. The system also includes a multi-angle light scattering detector MALS and differential refractive index detector dRI from Wyatt technology. Polymers were separated on three G2000, G3000 and G4000 TOSOH HXL gel columns (300 x 7.8 mm) (exclusion limits from 1000 Da to 400 000 Da) at a flowrate of 1 mL.min - 1 . Columns temperature was held at 40°C. Polystyrene was used as the standard.

Differential Scanning Calorimetry (DSC)

Differential Scanning Calorimetry (DSC) measurements were performed on DSC Q100 (TA Instruments). The sample was heated from -130 °C to 150 °C at a rate of 10 °C.min -1 . Consecutive cooling and second heating run were also performed at 10 °C.min -1 . The glass transition temperatures (Tg) and melting temperatures (Tmelt) were calculated from the second heating run.

Crystallization temperatures (TCrys) were calculated from the cooling run.

Thermogravimetric analysis (TGA) Thermogravimetric analyses were performed on TGA-Q500 system from TA instruments at a heating rate of 10 °C.min -1 under nitrogen atmosphere from room temperature to 600°C.

Rheological measurements

The complete methodology is described in supporting information. Rheological measurements were monitored using an Anton Paar Physica MCR302 operating in the parallel plates geometry (diameter 8mm). The measurements were performed under nitrogen flow in the environmental chamber to avoid potential moisture effects. The temperature was controlled by Peltier device and the gap between plates was fixed at 1 mm. Samples were loaded at room temperature. The sample was stabilized at the desired temperature for 5 min before the measurement started.

Preparation of oil blended with viscosity modifiers (additives)

Viscosity modifiers were dissolved in the mineral or organic base oils at the concentration of 3 wt.%. The mixture was heated at 100 °C overnight under magnetic stirring to promote the solubilization and then cooled down without stirring at room temperature for 24 hours. The solubility of the additive in the oil was evaluated macroscopically. Samples were degassed under vacuum and magnetic stirring for 30 minutes right before viscosity measurement using a by LOVIS 2000 densimeter-viscometer.

Viscosity measurements

The viscosimetric tests were performed on a LOVIS 2000 apparatus from Anton Paar at several temperatures: 20 °C, 40 °C, 60 °C, 80 °C and 100 °C. Around 3 mL of solution were added in the densimeter cell and the capillary tube (Ø 1.8 mm for oils and Ø 1.59 mm for dodecane) containing a steel ball (Ø1.5mm, d=7.68 g.cm -3 ). The density, d, apparent viscosity, 𝜂𝜂 (mPa.s) and the kinematic viscosity, 𝜈𝜈 (mm 2 .s -1 ), with 𝜈𝜈 = 𝜂𝜂 𝑑𝑑 ⁄ , are determined directly from the apparatus. The relative viscosity, 𝜂𝜂 𝑟𝑟 , was then calculated following equation 1.

𝜂𝜂 𝑟𝑟 = 𝜂𝜂 𝜂𝜂 0
Eq. 1

The relative viscosity, i.e. the viscosity of a system "additive in oil" (η) divided by the viscosity of the oil alone (η0), is used to evaluate the contribution of an additive to the viscosity of a solution.

It allows to estimate the thickening efficiency of this additive.

The kinematic viscosities at 40 °C, 𝜈𝜈 40°𝐶𝐶 , and 100 °C, 𝜈𝜈 100°𝐶𝐶 , were used to calculate the Viscosity Index (VI) according to Eq. 2 ASTM D 2270-10. 29

VI= 𝑣𝑣 100°𝐶𝐶 𝑣𝑣 40°𝐶𝐶
Eq. 2

The Q factor, defined according to equation 3, were calculated from specific viscosities 𝜂𝜂 𝑠𝑠𝑠𝑠 , at 40 °C and 100 °C, obtained according to equation 4.

𝑄𝑄 =

𝜂𝜂 𝑠𝑠𝑠𝑠 100 °𝐶𝐶 𝜂𝜂 𝑠𝑠𝑠𝑠 40 °𝐶𝐶

Eq.3 with

𝜂𝜂 𝑠𝑠𝑠𝑠 = 𝜂𝜂-𝜂𝜂 0 𝜂𝜂 0 Eq.4
The Q value is the ratio between the specific viscosities at 40°C (𝜂𝜂 𝑠𝑠𝑠𝑠 40 °𝐶𝐶) and at 100°C

(𝜂𝜂 𝑠𝑠𝑠𝑠 100 °𝐶𝐶 ). Specifically, 0<Q<1 indicates that the thickening power of the additive is less significant at 100°C than at 40°C. Conversely, Q values > 1 indicate the thickening power is more prominent at high temperature. The highest the Q value, the highest the additive capability to reduce the oil viscosity loss at high temperature.

Results and discussion

Syntheses of polyricinoleate and polyhydroxystearate within a broad range of molecular weights

Polyricinoleate and polyhydroxystearate were synthesized by polycondensation of methyl ricinoleate and methyl-12-hydroxystearate, respectively. Different molecular weights were targeted. Consequently, the choice of precursors, as well as the reaction conditions, were investigated to obtain high molecular weight polyester. Both A-B monomers were selected with a grade of purity above 99% in order to limit secondary reaction and polymerization termination due to the presence of impurities.

According to the literature, in the case of transesterification with hydroxyl-ester interchange reaction, Ti(OiPr)4 is largely described as a very efficient catalyst leading to high molecular weight polyesters [START_REF] Rogers | Synthetic Methods in Step-Growth Synthetic Methods in Step-Growth[END_REF][START_REF] Testud | Hyperbranched polyesters by polycondensation of fatty acid-based ABn-type monomers[END_REF][START_REF] Kasmi | Solid-State Polymerization of Poly(ethylene furanoate) Biobased Polyester, I: Effect of Catalyst Type on Molecular Weight Increase[END_REF] and notably for the synthesis of poly(ethylene naphtalate) [START_REF] Park | Kinetics for the catalyzed formation of poly(ethylene 2,6naphthalate) (PEN) by various metal compounds[END_REF] , poly(ethylene terephthalate) [START_REF] Rogers | Synthetic Methods in Step-Growth Synthetic Methods in Step-Growth[END_REF][START_REF] Otera | Transesterification[END_REF] and, more recently, linear bio-based polyesters [START_REF] Kasmi | Solid-State Polymerization of Poly(ethylene furanoate) Biobased Polyester, I: Effect of Catalyst Type on Molecular Weight Increase[END_REF][START_REF] Liu | Polymers from Fatty Acids: Poly(ω-hydroxyl tetradecanoic acid) Synthesis and Physico-Mechanical Studies[END_REF][START_REF] Lebarbé | Synthesis of Fatty Acid-Based Polyesters and Their Blends with Poly(l-lactide) as a Way To Tailor PLLA Toughness[END_REF] Consequently, this organometallic catalyst was selected. A temperature of 180 °C was chosen as a good compromise between high catalytic activity and the limitation of transfer reactions and terminations (especially due to the carbon-carbon double bond in the case of methyl ricinoleate). Finally, polymerization was performed in bulk, thus avoiding further treatment to remove the solvent. However, the high viscosity of the polymerization medium tends to slow down the polymerization process and limit the reaction extent. In order to overcome this issue, a mechanical stirring was used during polymerization process when high molecular weights PRic or PHS were targeted. Polyesters were then analyzed without further purification.

The structures of the polyesters were confirmed by [START_REF] Gandini | The irruption of polymers from renewable resources on the scene of macromolecular science and technology[END_REF] H NMR in agreement with previous publication [START_REF] Dworakowska | Cross-Linking of Polyesters Based on Fatty Acids[END_REF] (see Figure 2 for PRic and Figure SI-1-3 in Supporting Information for PHS).

Figure2: 1 H NMR spectra of (1) methyl ricinoleate monomer and (2) polyricinoleate in CDCl3

In both cases, the peak at 0.82 ppm, representative of the terminal CH3 protons of the fatty methyl esters, is used as a reference. The polycondensation is confirmed by the drastic decrease of the characteristic methoxy peak at 3.59 ppm and the shift of the peak corresponding to the proton in α position of the OH group from 3.5 to 4.88 ppm. The protons in α and β positions of the ester group are assigned at 2.26 ppm and 1.6 ppm, respectively. In the case of polyricinoleate, there is also a small shift of the protons in β position of the OH group, from 1.40 ppm to 1.55 ppm and 2.15 ppm to 2.26 ppm. Information) shows the standard step-growth polymerization profiles with a molecular weight distribution shifting to the higher molecular weights with time. Mn values obtained by SEC analysis using triple detection are in agreement with the ones determined by 1 H NMR using chainend analysis. PHS-3 is the only exception where Mn predicted by Carothers equation is twice the one obtained by SEC. This may be due to secondary reactions, such as cyclization, that decrease the concentration of terminal methyl esters. In the case of PRic, a broad range of molecular weights was obtained from Mw= 6 kg.mol -1 to Mw= 131 kg.mol -1 (17 and 78 kg.mol -1 for PHS) which is the highest molecular weight reported in literature to the best of our knowledge. [START_REF] Ebata | Lipase-catalyzed synthesis and curing of highmolecular-weight polyricinoleate[END_REF][START_REF] Ebata | Poly (Ricinoleic Acid) Based Novel Thermosetting Elastomer[END_REF][START_REF] Dworakowska | Cross-Linking of Polyesters Based on Fatty Acids[END_REF] While all polyesters exhibit a dispersity close to 2 as it is expected, the dispersity around 4.6 for PRic-5 suggests the occurrence of side reactions. Indeed, while a small fraction of oligomers can be detected whatever the final molecular weight distribution, in the case of PRic-5, this fraction is more intense leading to higher dispersity. This peak may be due to a backbiting reaction leading to the formation of ricinoleate lactone. Since there is no apparent broadening of the polymer peak (see Figure SI-4) the presence of this oligomeric fraction explains the dispersity value obtained.

Thermal properties

The thermal stabilities of the PRic and PHS were investigated by thermogravimetric analyses (TGA), under a nitrogen stream at a heating rate of 10 °C.min -1 . The polymer degradation temperatures at 5 wt.% are reported in Table 3. Compared to both monomers which begin to degrade at 160 °C, the thermal stability of the polymer is higher with a degradation above 300 °C for all the polyesters. PHS possesses slightly better thermal stability compared to PRic which can be explained by the presence of unsaturation in the backbone. No influence of the polyester molecular weights on the temperature of degradation can be noticed.

PRic and PHS were also analyzed by differential scanning calorimetry analysis, traces of which are displayed in Figure 3. The glass transition temperature, Tg, the crystallization temperature, Tcris, the melting temperature, Tmelt and corresponding enthalpies were recorded after the second heating scan at a rate of 10°C.min -1 . All the results are reported in Table 3. with, Tg,∞ is the maximum glass transition temperature that can be reached at a theoretical infinite molecular weight and K a parameter related to the contribution of the chain-end to the free volume.

For PRic, experimental Tg fits with the following values: Tg,∞ = -66 °C and K = 4.1.10 4 g.mol -1 .

In the case of PHS, no effect of the molecular weight on the Tg was observed since the glass transition is controlled by the crystal phase.

Impact of PRic molar masses on its melt rheological behavior

As expected, PRic viscosity depends on its molecular weight. Indeed, at room temperature, PRic-1 (Mw = 6 100 g.mol -1 ) behaves as a viscous liquid while PRic-5 (Mw = 131 000 g.mol -1 ) does not flow at short time scale and appears as a viscoelastic solid. This observation suggests a strong effect of the molecular weight on the rheological properties of polyricinoleate. This effect can be quantified through the measurement of η0, the Newtonian viscosity.

As it was established by Fox and Flory [START_REF] Fox | Further Studies on the Melt Viscosity of Polyisobutylene[END_REF] , the viscosity of a polymer is strongly related to its molecular weight. This relationship varies whether the polymer is entangled or not, according to equation 5 and equation 6.

log 𝜂𝜂 0 = log 𝑀𝑀𝑀𝑀 + 𝐴𝐴 𝑓𝑓𝑓𝑓𝑓𝑓 𝑀𝑀 < 𝑀𝑀 𝑐𝑐 Eq.5

log 𝜂𝜂 0 = 3.4 log 𝑀𝑀𝑀𝑀 + 𝐵𝐵 𝑓𝑓𝑓𝑓𝑓𝑓 𝑀𝑀 > 𝑀𝑀 𝑐𝑐 Eq. 6

where 𝜂𝜂 0 is the Newtonian viscosity and 𝑀𝑀 𝑐𝑐 the critical molecular weight of entanglement. A and B are empirical constants dependent on the nature of the polymer and the temperature.

By rheometry analysis (see Supporting Information), Newtonian viscosities at 20°C was determined for a new PRic series with Mw ranging from 5 000 to 130 000 g.mol -1 , and plotted as a function of the PRic molecular weight (see Figure 4, and Table 4). corresponding to molar weight around Mw = 25 000 g.mol -1 . For Mw < 25 000 g.mol -1 , a slope of 1 is obtained suggesting that the chains are disentangled (PRic-6 and PRic-7) and probably present Rouse relaxation mode. For Mw > 25 000 g.mol -1 , a slope around 4.9 is obtained. This is superior to the theoretical value for entangled polymer chains, i.e. 3.4. whose dynamic is governed by reptation. The large dispersity of PRic-9 (Đ = 6.1) and PRic-10 (Đ = 4.6) could explain the discrepancy between the experimental and the theoretical value of 3.4. Indeed, it is reported that dispersity has an impact on the rheological behavior of the polymer chains and, consequently, on the sample viscosity. [START_REF] Struglinski | Effects of polydispersity on the linear viscoelastic properties of entangled polymers. 1. Experimental observations for binary mixtures of linear polybutadiene[END_REF][START_REF] Wood-Adams | Effect of Molecular Structure on the Linear Viscoelastic Behavior of Polyethylene[END_REF] However, as reported in the literature, this effect implies variation from 3.3 to 3.7. [START_REF] Cross | Viscosity, molecular weight and chain entanglement[END_REF][START_REF] Colby | The melt viscosity-molecular weight relationship for linear polymers[END_REF][START_REF] Bueche | Viscosity, Self-Diffusion, and Allied Effects in Solid Polymers[END_REF] There is also probably an impact of the pendant alkyl segments along the polymer backbone (comb-like structure). [START_REF] Wood-Adams | Effect of Molecular Structure on the Linear Viscoelastic Behavior of Polyethylene[END_REF][START_REF] Larson | Combinatorial Rheology of Branched Polymer Melts[END_REF]

Towards promising viscosity modifiers

All the so-formed PRic and PHS were then tested as additives in a mineral oil (MO) and an organic triglyceride oil (OTO) to be evaluated as viscosity modifiers for lubricants. A concentration of 3 wt.% was fixed. As reported in Table 2, the PRic with the highest molecular weights are not soluble in the oils: PRic-3 to 5 for MO, PRic-4 and 5 for OTO. Surprisingly, polyhydroxystearate is perfectly soluble in both oils, whatever the molecular weights. Only the oils containing soluble PRics of PHS as additives were then analyzed by viscosimetry. The kinematic viscosity of the mixtures was measured from 20 °C to 100 °C allowing determining the relative viscosity and the Viscosity Indexes. The relative viscosity versus the temperature is displayed in Figure 5 and the kinematic viscosities, the VI as well as the Q values are reported in Table 5. Their values were compared to two commercial additives, Ref-O, specific for the organic oil and Ref-M, specific for the mineral one. The most significant impact on the relative viscosity is related to the polymer molecular weights.

The highest the molecular weight, the highest the relative viscosity. The PHS-3 with a Mw = 80 kg.mol -1 shows the best thickening properties with an increase of the kinematic viscosity from 20 mm².s -1 to 45 mm².s -1 in OTO and from 19 mm².s -1 to 37 mm².s -1 in MO at 40 °C for 3 wt.% blend.

These results point out that high molecular weight PHS is a promising thickener in both oils tested.

The addition of a polymer additive in OTO induced a decrease of the relative viscosity with the temperature. This phenomenon is observed for all the polyesters tested, independently of their chemical composition and molecular weight leading to value of Q below 1 testifying that thickening power of the additive is less significant at 100°C than at 40°C. In the case of PHS, a slight increase of Q was observed with the molecular weight, while the Q values tend to decrease with PRic molecular weights. However, the Viscosity Index is significantly increased by the addition of a polymer additive in the oil. Even the blend with the lowest molecular weight PRic led to a significant VI increase from 152 to 163. In these conditions, whatever PHS molecular weight, the Viscosity Index is better than with the commercial additive tested. A maximum of VI = 204 is obtained for the oil blended with PHS-3 corresponding to a VI increase of +52. All these results demonstrate that PHS-3 could also be used as a Viscosity Index improver of OTO.

For MO, the Q values appears to increase with the molecular weights with values close to 1 for PRic-2 (Q=0.99) and PHS-3 (Q=0.94). These indicate a more stable viscosity with temperature which leads to better VI with less increase in the kinematic viscosity. For example, in the case of PRic-2, same VI were obtained for OTO and MO but in the first case kinematic viscosity at 40°C is increased by 33% compared to only 19% for MO. a Table 5 Rheometry analysis:

Methodology

The objective was to establish the evolution profile of the newtonian viscosity versus molecular weight of the different system at a fixed, reference temperature. Viscosity was estimated through the evaluation of complex viscosity η* measured at different temperature, and the establishment of master curves through the use of the Time Temperature Superposition (TTS).

The complex viscosity was calculated with the data obtained from the dynamic shear measurements according to equation 1. 1

|𝜂𝜂 * | = |𝐺𝐺 * | 𝜔𝜔 = �(𝐺𝐺 ′ )²+(𝐺𝐺 ′′ )² 𝜔𝜔 Eq.1
where the elastic modulus G' and the loss modulus G'' are given as a function of the angular frequency ω.

According to Cox-Merz Rule, 1 the dependence of the steady shear viscosity on the shear rate is equal to the dependence of the complex viscosity as a function of frequency. Therefore a plateau of complex viscosity at low angular frequencies reflects the Newtonian viscosity. In some cases, when the plateau value of complex viscosity could not be obtained with the master curves, creep experiments have then been performed to measure the viscosity.

The shift factor aT/Tref used to establish master curves follows an Andrade law [START_REF] Gandini | The irruption of polymers from renewable resources on the scene of macromolecular science and technology[END_REF] where 𝐸𝐸 𝑎𝑎 is the activation energy and R the universal gas constant. By using Andrade law, it is possible to determine the viscosity of the material at another temperature, as, the translation factor 𝑎𝑎 𝑇𝑇 is correlated to the melt polymer viscosity. [START_REF] Maisonneuve | Structure-properties relationship of fatty acid-based thermoplastics as synthetic polymer mimics[END_REF] and can be considered as the ratio of viscosity at two different temperature (eq 3).

𝑎𝑎 𝑇𝑇 = 𝜂𝜂 𝑇𝑇 𝜂𝜂 𝑇𝑇 𝑅𝑅𝑅𝑅𝑅𝑅 Eq.3

Then, the Newtonianviscosities could be estimated at 20 °C for all the polymers.. A shear strain of γ=1% was fixed for the frequency sweep experiments.

Figure 1 :

 1 Figure 1: Synthesis of PRic and PHS

- 34 1 1 Figure 3 :

 3413 Figure 3: DSC traces of (1) PRic and (2) PHS with both several molar masses. Second heating cycle rate of 10 °C.min -1

Figure 4 :

 4 Figure 4: Log-log plot of the Newtonian viscosity versus molar mass for PRic samples at 20 °C

Figure 5 :

 5 Figure 5: Relative viscosities of several PRic, PHS and commercial additives blended at 3 wt.% in

Figure SI - 1 : 1 H

 11 Figure SI -1: 1 H NMR spectra of (1) methyl-12-hydroxystearate monomer and (2)polyhydroxystearate in CDCl3 Figure SI -2: 1 H NMR spectra polyricinoleate in CDCl3 Figure SI -3: 1 H NMR spectra of polyhydroxystearate in CDCl3 Figure SI -4: SEC traces of (1)Polyricinoleate and (2) Polyhydroxystearate. Measurement performed in THF.

Figure SI - 5 :Figure SI - 6 :Figure SI - 7 : 1 Figure SI - 8 :Figure SI - 9 :Figure SI- 11 :S3Figure SI - 2 : 1 H

 5671891121 Figure SI -5: PRic glass transition temperature as a function of (1) PRic molar mass (Mn) and (2) 1/Mn Figure SI -6: Translation factor as a function of 1/T according to Andrade law Figure SI -7: Complex viscosity as a function of shear strain for a series of PRic with various Mw. Performed at 20°C with an angular frequency of 10 rad.s -1 Figure SI -8: Master curves at -20 °C of PRic samples. Reduced storage and loss modulus are expressed versus the reduced angular frequency Figure SI -9: Polyricinoleate reduced complex viscosity versus the reduced angular frequency obtained from TTS at -20 °C as reference temperature, 1% shear strain Figure SI -10: Viscosity versus shear rate obtained by creep measurements. (1) PRic-7 performed at 20 °C, (2) PRic-9 performed at 200 °C and (3) PRic-10 performed at 150 °C

Figure SI - 5 :

 5 Figure SI -5: PRic glass transition temperature as a function of (1) PRic molecular weight (Mn) and (2) 1/Mn

according to Equation 2 ,

 2 as illustrated in the Figure SI 6 ln(𝑎𝑎 𝑇𝑇 ) =

S7Figure SI - 6 :

 6 Figure SI -6: Translation factor as a function of 1/T fitted with Andrade law

Figure SI - 7 : 1 S8 8 S9Figure SI - 8 :

 7188 Figure SI -7: Complex viscosity as a function of shear strain for a series of PRic with various Mw. Performed at 20°C with an angular frequency of 10 rad.s -1

Table

Table 1 :

 1 . Two commercial viscosity modifiers were kindly provided from Croda (Ref-O, specifically used in organic oil OTO) and from Chevron (Ref-M, specifically used in mineral oil). Oil characteristics, determined experimentally or from producer data sheet [in brackets]

	Lubricant oils	MO	OTO
	Density 1	0.8226 [0.825]	0.941 [0.945]
	Mn (g.mol -1 ) 2	600	750 [512.8]
	Ɖ²	1	1
		[220]
		18.6
		4.3 [4.1]
		128

Table 2 :

 2 Reaction extent (p), degree of polymerization (DPn), molecular weights and solubility in mineral oil (MO) or organic triglyceride oil (OTO) of a series of PRic and PHS

	Entry	Time	p 1	DPn 1	M n 1	M n 2	M w 2	Đ 2	Sol.	Sol.
		(h)			(g.mol -1 )	(g.mol -1 )	(g.mol -1 )		in MO 3	in OTO 3
	PRic-1 a	6	0.894	9.4	3000	4000	6100	1.5	Yes	Yes
	PRic-2 a	8	0.902	10.2	4200	7200	10600	1.5	Yes	Yes
	PRic-3 a	24	0.977	45	12400	18200	32200	1.7	Yes	No
	PRic-4 a	48	0.984	63	19800	21700	47100	2.2	No	No
	PRic-5 b	48	0.991	110	34000	28100	131500 4.6	No	No
	PHS-1 a	8	0.960	25	7700	8100	17500	2.1	Yes	Yes
	PHS-2 a	48	0.990	100	30200	24000	68100	2.4	Yes	Yes
	PHS-3 b	48	0.996	225	60000	28500	78400	2.5	Yes	Yes
	Reaction conditions: 180°C, 1wt.% of Ti(OiPr)4 in the melt under vacuum, 200 rpm
	a: Magnetic stirring and b: mechanical stirring
	1 Obtained by 1 H NMR using OCH3 peak at 3.6 ppm for calculation
	2 Đ = Mw/Mn, dispersity. Obtained by SEC in THF -triple detection, dn/dc values used for
	calculation
	3 Polymer solubility at 3wt% in oil after one night heated at 100°C under stirring and 24 hours
	at 20°C
	As indicated in

Table 2 ,

 2 molecular weights of PRic and PHS were impacted by the polymerization duration and mode of stirring. SEC traces (Figure SI-4, see Supporting

Table 3 :

 3 Thermal behavior of PRic and PHS determined by TGA and DSC

	Entry	M n 1	M w 1	Đ 1 Td 5% 2	T g 3	T melt 3	ΔH m 3	T cris 3	ΔH c 3
		(g.mol -1 )	(g.mol -1 )		(°C)	(°C)	(°C)	(J/g)	(°C)	(J/g)
	MRic	-	-	-	160	-	-7	79	-41
	PRic-1	4000	6100	1.5	296	-77	-	-	-	-
	PRic-2	7200	10600	1.5		-71	-	-	-	-
	PRic-3	18200	32200	1.7	303	-69	-	-	-	-
	PRic-4	21700	47100	2.2		-68	-	-	-	-
	PRic-5	28100	131500 4.6	300	-68	-	-	-	-
	MHS	-	-	-	160	-	54	235	47	201
	PHS-1	8100	17500	2.1	307	-37	-20	30	-31
	PHS-2	24000	68100	2.4	309	-44	-22	22	-33
	PHS-3	28500	78400	2.5	314	-41	-22	27

Table 4 :

 4 Molecular weights and melt Newtonian viscosity at 20°C

	Entry	M n 1 (g.mol -1 ) M w 1 (g.mol -1 )	Đ 1	η 0 20°C (Pa.s) 2
	PRic-6	3 000	5 000	1.7	6.9 ± 0.5
	PRic-7	8 000	18 000	2.2	28.81 ± 0.028
	PRic-8	11 000	31 000	2.8	872 ± 3.7
	PRic-9	15 000	92 000	6.1	2.60 10 5 ± 6.4 10 3
	PRic-10	28 000	131 500	4.6	8.53 10 5 ± 8.2 10 4
	1 Obtained by SEC in THF -triple detection, dn/dc values used for
	calculation
	2 See Supporting Information for more information about the determination
	of η 0

  : Kinematic viscosity, KV, at 40 and 100 °C VI and Q values of OTO and MO blended with 3 wt.% of commercial additives, PRic and PHS polymers. molecular weights, from Mw = 3 kg.mol -1 up to Mw= 130 kg.mol -1 in the case of PRic. The obtained PHS appeared to be semi-crystalline with a melting point around -20 °C while PRic was amorphous with a glass transition temperature around -70 °C due to the presence of an internal unsaturation in its backbone. The PRic rheological behavior was evaluated as a function of its molecular weight. It appears that, for low Mw, PRic behaves as a viscous material. Above Mw = 25 kg.mol -1 , its melt viscosity increases drastically due to the formation of entanglements.Finally, PRic and PHS have been tested as viscosity modifiers. Contrary to PHS, due to a lack of solubility for the highest molecular weights, only PRic with Mw ≤ 10 kg.mol -1 and Mw ≤ 32 kg.mol -1 could be tested in mineral and organic oil, respectively. Both PRic and PHS have a financial support from the CPER CAMPUSB project funded by the French state and the Région Nouvelle Aquitaine is gratefully acknowledged.For Table of Contents Use OnlyPolyester obtained by self polyesterification of ricinoleate derivatives were synthesized. Their properties in melt and oil solution were investigated in regards to their molecular weights.

	Supporting information
	At 3wt% in OTO Bio-based polyricinoleate and At 3wt% in MO
	KV 40°C polyhydroxystearate: properties and KV 100°C VI Q KV 40°C KV VI 100°C None 20.55 4.67 152 -18.71 4.34 145 evaluation as viscosity modifiers for	Q -
	Ref	27.19 5.98	175 lubricants 0.87 22.55	5.08	163	0.84
	PRic-1	22.73 5.12	163	0.90 20.45	4.61	147	0.69
	PRic-2 Hélène Méheust, Jean-François Le Meins, Etienne Grau*, Henri Cramail* 27.29 5.94 172 0.83 22.23 5.15 172 0.99
	PRic-3	30.57 6.52 Henri.Cramail@enscbp.fr 175 0.81 -	-	-	-
	PHS-1	28.82 6.25	176 egrau@enscbp.fr 0.84 24.56	5.49	171	0.85
	40.24 8.47 45.05 9.56 Number of pages: 13 PHS-2 PHS-3	195 204	0.85 0.88 36.62 33.1	7.51 8.22	205 209	0.93 0.94
	Number of Figures: 11
	Conclusion Number of Tables: 2
	Polyricinoleate and polyhydroxystearate were synthesized using Ti(OiPr)4 as a catalyst within a
	large range of S1

Author manuscript of article published in ACS Applied Polymer Materials 2021, https://doi.org/10.1021/acsapm.0c01153

ACKNOWLEDGMENT

This work was performed, in partnership with the SAS PIVERT, within the frame of the French Institute for the Energy Transition (Institut pour la Transition Energétique (ITE) P.I.V.E.R.T.

(www.institut-pivert.com) selected as an Investment for the Future ("Investissements d'Avenir"). This work was supported, as part of the Investments for the Future, by the French Government under the reference ANR-001-01. The authors thank Equipex Xyloforest ANR-10-EQPX-16. The

thickening effect in oil, but PHS with Mw= 80 kg.mol -1 showed particularly good thickening efficiency by doubling the viscosity of both OTO and MO and by increasing the Viscosity index about + 52 and +64, respectively. As a result, the bio-based PHS with high molecular weights could be considered as promising viscosity modifiers for more environmentally friendly lubricant applications.

Supporting Information.

The following files are available free of charge: NMR of PHS, SEC traces of PRic and PHS, rheology methodology and results..

Corresponding Author

* henri.cramail@enscbp.fr etienne.grau@enscbp.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. HM performed the experiments, JFLM performed the rheology analysis.


N Berman

M Couttenier

A Leblois

R Soubeyran

Motivation Visual Data Method Results Discussion Références Is Worldwide Deforestation Associated with Agricultural Commodities Price Fluctuations?

al., 2019) & correlated with international agricultural export value per land unit (Leblois et al., 2017). Link already unveiled for some crops & regions (Rubber in Cambodia: Grogan, 2019; Soybean in Bolivia: Fehlenberg et al., 2017 in cross section) or in meta-analysis (Busch et al., 2017) Curtis et al. (2018) spatially attribute deforestation among a classification of drivers, ⇒ agricultural as the major driver of global forest loss (either commodity driven deforestation or shifting to agriculture) specifically in the Southern hemisphere.

Literature

• Expanding cropland, pastures and forest plantations responsible of:

• 70% of total tropical forest loss (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) in Lawson (2014)

• 80% in Hosonuma et al. (2012).

• 60% in Pendrill et al. (2019a) • Recent focus on imported deforestation around the world:

European commission roadmap for reducing deforestation impacts of products sold in the EU.

France: reflexion about the national strategic scheme to fight imported deforestation has been launched. US: carbon tax at the borders included in the green new deal.

Motivation

• Land use changes are known to account for more than 20% of human greenhouse gas emissions • Forest additionally provides numerous ecosystemic services • Prices provide incentives to orient agent decisions

Research questions:

To what extent locally identified agricultural expansion reacts to global international demand for commodities?

Global approach: = between temperate, tropical and boreal forests ? Future impacts considering price forecasts ?

• Pushes forward socio-economically focused models of deforestation & improves the predictive capacity of modeling spatial and temporal evolution of global tree cover losses.

What is new in our approach:

-We provide, to our knowledge, the 1 st worldwide robust statistical analysis of price shocks impact on forest disturbance -Quantification of global deforestation shocks, using recent high resolution data, complementary to existing studies of other disciplines Pendrill et al. (2019b) associate historical trade flows to land use change and compute carbon balance of trade flows. [START_REF] Barona | The role of pasture and soybean in deforestation of the Brazilian Amazon[END_REF] look at the specific role of pastures and soybean in Latin America. [START_REF] Abman | Does Free Trade Increase Deforestation? The Effects of Regional Trade Agreements[END_REF] show that, following the enactment of a regional trade agreement, signatory countries are strongly affected by deforestation. • Baseline variable: count of deforested pixels (30m) by cell (0.5 • : ≈55km).

Prices variations

Commodity price shocks

Cell-specific (c) time-varying (t) proxy for local agricultural output prices:

P ct = 15 crop i =1 α i c .P i t Visual Data Method Results
Discussion Références

Commodity price shocks

Cell-specific (c) time-varying (t) proxy for local agricultural output prices:

P ct = 15 crop i =1 α i c .P i t
• Annual world prices of commodities: World Bank (P t : index base 100 in 2000)

• Crop (N=42) specialization (α i c ): FAO-GAEZ suitabiliy index under current technology in 2000. • Significant commodity driven tree cover losses (68%) (column 1) in tropical, temperate & boreal forests (column 2)

• Souza-Rodrigues ( 2018) that shows that transport costs play an important role in deforestation decisions. → We find that the effect of agricultural commodities price variations becomes (slightly) weaker as remoteness increases (measured as the distance to the closest harbor) but it remains positive even for the most remote locations (column 3)

• While a drought does not seem to significantly increase deforestation, it may increase the effect of commodities (uncontrolled fires? Burgess et al., 2019) (columns 4-5). Plotted values are based on the estimates obtained using a panel poisson regression, projecting prices by using World Bank price predictions.

Preliminary results

-Role of agricultural prices -Boreal and temperate forest biomes seem to be subject to positive (avg.) agr. commodity related deforestation (median impact: negative).

-3 periods, deconnexion of the northern & the southern hemisphere in the 2000's?

-Large future (2030) impacts, whatever the underlying hypothesis (current trend or WB projections).

Figure :

 : Figure: Fao food price index

Figure :

 : Figure: Tropical Deforestation 2000-2018

Figure :

 : Figure: Cumulative deforestation (2001-2018, share of 0.5 • cells) Source: Hansen (2013)

Figure : Figure : Figure :

 ::: Figure: Avg. contribution of agr. commodity price var. to deforestation (2001-18). ⇒ Plotted values are based on the estimates obtained using a panel poisson regression, specification #1, effet (percent points) exp(α * (log (P) -log (avg .cellP)) -1) * 100

Figure : Figure :

 :: Figure: Contribution of agricultural commodity price variations to deforestation (2001-2018), by year and tropical (orange) vs. temperate countries (blue) vs. Bresil (green) Source: authors calculation of pixel specific annual deforestation shocs driven by agr. commodity price shocks, with country × year & cell fixed effects.

  Unified Framework for Estimation and Policy Analysis," Review of EconomicStudies, 86, 2713Studies, 86, -2744. .

	Visual Visual Visual Visual Variables / controls Data Thank you for your attention ! Method Results Data Method Results Data Method Results Data Method Results → Annual deflated commodity prices (World Bank, in log) Discussion Discussion Discussion Discussion → GAEZ (FAO) crop specific suitability for growing (spatial variations) Références Références Références Références → Rainfall Standardized Precipitation-Evapotranspiration Index (spei) → Distance to ports (km) → Tropics → Volatility / lags ? Visual Data Method Results Discussion Références Tableau: Drivers of deforestation (forest disturbances), in pixels with 50 % of forests (1) (2) Defor Defor log commodity price 1.282 * * * 1.279 * * (0.0950) (0.643) Drought spei 0.0477 -1.180 * * (0.0347) (0.503) DRspei × log commodity price g 0.287 * * (0.115) Constant 5.065 * * * 5.078 * * (0.369) (2.498) Observations 571,602 571,602 Cell & year FE Yes Yes Country × year FE Yes Yes Standard errors in parentheses * p < .1, * * p < .05, * * * p < .01 Visual Data Method Results Discussion Références Tableau: Drivers of tree loss: by geozones, panel (pseudo) poisson regression, in pixels with 50 % of forests (1) (2) (3) Defor 25 Defor 50 Defor 75 Price × Africa 1.343 * * * 1.219 * * * 0.963 * * * (0.0481) (0.0488) (0.0518) Price × Asia 1.332 * * * 1.280 * * * 1.172 * * * (0.0501) (0.0489) (0.0491) Price × Pacific Ocean 1.423 * * * 1.407 * * * 1.386 * * * (0.215) (0.216) (0.221) Price × Indian Ocean 1.886 * * 1.280 0.399 (0.739) (0.786) (0.740) Price × Europe 1.071 * * * 0.988 * * * 0.873 * * * (0.0629) (0.0627) (0.0649) Price × North America 0.518 * * * 0.373 * * * 0.275 * * * (0.0665) (0.0620) (0.0580) Price × Central America 0.790 * * * 0.798 * * * 0.858 * * * (0.116) (0.116) (0.117) Price × West Indies 0.828 * * * 0.849 * * * 0.900 * * * (0.280) (0.289) (0.314) Price × South America 0.227 * * * 0.107 * * -0.0649 (0.0505) (0.0497) (0.0507) Price × Atlantic Ocean -0.837 -0.883 -1.454 (1.161) (1.409) (1.441) Price × Australasia 0.225 0.633 * * * 0.495 * * * (0.212) (0.131) (0.125) Constant 6.970 * * * 7.297 * * * 7.812 * * * (0.179) (0.176) (0.179) Observations 587142 567,558 543,510 Cell & year FE Yes Yes Yes Country × year FE No No No Standard errors in parentheses * p < .1, * * p < .05, * * * p < .01 Visual Data Method Results Discussion Références Tableau: Drivers of tree loss: by continents, panel (pseudo) poisson regression, in pixels with 50 % of forests (1) (2) (3) Def 25 Def 50 Def 75 Price × Africa 1.344 * * * 1.220 * * * 0.962 * * * (0.0480) (0.0487) (0.0518) Price × Americas 0.383 * * * 0.256 * * * 0.125 * * * (0.0508) (0.0490) (0.0483) Price × Asia 1.378 * * * 1.304 * * * 1.164 * * * (0.0565) (0.0560) (0.0578) Price × Europe 0.509 * * * 0.465 * * * 0.455 * * * (0.0415) (0.0404) (0.0409) Price × Oceania 0.465 * * * 0.831 * * * 0.723 * * * (0.166) (0.0995) (0.0939) Constant 6.918 * * * 7.249 * * * 7.795 * * * (0.177) (0.175) (0.177) Observations 592,290 572,382 548,154 Cell & year FE Yes Yes Yes Country × year FE No No No Standard errors in parentheses * p < .1, * * p < .05, * * * p < .01 Visual Data Method Results Discussion Références -2 0 2 4 6 Country (2001-2018), by country. Visual Data Method Results Discussion Références Sierra Leone Equato rial Guinea Laos Liberia Vietna m Solom on Islands Cambo dia Sri Lanka Myanm ar (Burma ) Luxem bourg Bhutan iso not matche d Brunei Chile Czech Repub lic Hondu ras Zaire (Dem Rep of Congo ) Madag ascar Peru Korea, South Bolivia Paragu ay Russia Comor os Germa ny Guinea -Bissa u Malays ia Indone sia Belgium Thailan d Papua New Guinea Belize Argent ina Urugua y Camer oon China Afghan istan Congo , Repub lic of the Surina me Swede n Guyan a New Zealan d Mongo lia United Kingdo m Angola Mozam bique Albania Ugand a Fiji Ecuad or Guinea France iso not matche d Maced onia Slovak ia Haiti Bosnia and Herzeg ovina Reunio n Mexico Philipp ines Poland Iraq Centra l African Repub lic Japan Guatem ala Austria Morocc o Domin ican Repub lic Norwa y Algeria Italy Belaru s Ukrain e Tunisia -2 0 2 4 6 Country specific deforestation (km2/cell) +1sd in ag. commodity price (Hansen: 50 threshold) Visual Data Method Results Discussion Références Tableau: Drivers of deforestation: panel (pseudo) poisson regression, in pixels with 50 % of forests (1) (2) (3) (4) Defor 50 Defor 50 Defor 50 Defor 50 Log price index 1.256 * * * 1.500 * * * 1.199 * * * (0.0998) (0.106) (0.114) Monthly volatility (price) 0.0234 (0.0149) Lag (Log price index) 0.477 * * * (0.105) Lag(Monthly volatility (price)) 0.151 * * * (0.0156) av. Volatility (2 last y) 0.316 * * * (0.0233) av. Volatility (5 last y) 0.296 * * * (0.0652) Constant 5.130 * * * 7.978 * * * 3.697 * * * 4.853 * * * (0.379) (0.397) (0.424) (0.488) Observations 571,602 537,723 504,477 406,282 Cell & year FE Yes Yes Yes Yes Country × year FE Yes Yes Yes Yes Country specific deforestation (km2/cell) +1sd in ag. commodity price (Hansen: 50 thr Standard errors in parentheses Figure: Contribution of agr. commodity price variations to deforestation * p < .1, * * p < .05, * * * p < .01

While a drought does not seem to significantly increase deforestation, it may increase the effect of commodities (uncontrolled fires? Burgess et al., 2019). Countries Figure: Contribution of agricultural commodity price variations to deforestation (2001-2018), by country (75 largest impacts).

Source: Hansen (2013)

Visual